# **Silicon Based Thin Film Solar Cells**

# **Edited By**

# **Roberto Murri**

*University of Camerino School of Science and Technology Physics Division Italy* 

© 201 by the Editor / Authors. Chapters in this eBook are Open Access and distributed under the Creative Commons Attribution (CC BY 4.0) license, which allows users to download, copy and build upon published chapters, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book taken as a whole is © 201 Bentham Science Publishers under the terms and conditions of

the Creative Commons license CC BY-NC-ND.

## **CONTENTS**


## **CHAPTERS**

### **SECTION I - THIN FILM SOLAR CELLS: GENERAL ASPECTS AND DEPOSITION TECHNIQUES**


*Mangiapane, Giampiero de Cesare and Domenico Caputo* 


## **FOREWORD**

For eons, Earth's water was allowed to fall naturally from mountains to seas, converting vast stores of potential energy primarily and wastefully into heat. The discovery of methods to put water power to use in mills of various sorts led eventually to its industrial exploitation on a grand scale in the eighteenth and nineteenth centuries. With the discovery of electricity, the power of falling water led to hydroelectric generation in the nineteenth and twentieth centuries, culminating in today's huge enterprises at Itaipu in Brasil (14 GW) and Three Gorges in China (22.5 GW).

Similarly, today we allow much of the Sun's solar insolation (800 watts per square meter, peak), mostly in the form of infrared radiation, to fall unproductively onto Earth as heat, adding to the already worrisome heat burden of the Planet. Thus, analogous to earlier experience with falling water, it behooves one to utilize at least part of this infrared radiation productively, to create the useful artifacts of civilization, before depositing a lesser amount of it on the Planet as heat.

Solar photovoltaic energy conversion addresses precisely this goal, in the form of photovoltaic cells made of various semiconductor materials, of which silicon is predominant. Thin films of silicon used for the construction of solar photovoltaic cells comprise the focus of the present volume.

One might do well to take a "top-down" view of one of the semiconductor materials challenges of solar photovoltaic energy conversion on a massive scale, to gather an overall sense of the magnitude of the endeavor. For this purpose, we may posit a few simple estimates, which leads to the scope of the issue at hand. To wit, there are 7 billion human inhabitants on Earth. Insofar as there is a general and historical movement toward improved standards of living, including electrical energy usage at a fully loaded, annual average level of about one kilowatt per person, and about 1% per year of the population experiences this relative advancement, there is an estimated need for 60 GW of additional electrical energy generating capacity worldwide each year.

It would be a pleasant environmental happenstance to have a significant fraction of this 60 GW arise from solar photovoltaic energy conversion, say 10 GW. However, due to diurnal effects, cloud cover, solar cell conversion efficiency, and so on, a useful estimate is that one square meter of solar cells (unconcentrated) provides an average of 25W of electrical power as an annual average. Therefore, 10 GW implies 400 million square meters annual production of solar cell materials. Due to the relatively small infrared absorption coefficient of silicon, the thickness of the silicon thin film must be at least about 40 microns.

Combining the above numbers, 4x10<sup>8</sup> m2 and 4x10-5 m, one finds that the annual production rate of photovoltaic silicon must be around 37,000 tonnes. While this may seem a daunting figure for a nascent enterprise, it does not greatly exceed current world-wide production of single-crystal silicon for electronics applications, generally.

Thus, one is led to conclude that impressive levels of production of thin-film photovoltaic silicon will be necessary if the enterprise is to succeed, giving cause to pay special attention to such largearea deposition methods as chemical vapor deposition (CVD) and its plasma variants, as well as the proven large-area method of choice, physical vapor deposition (PVD, or sputtering), which among others are well treated in the present volume.

Stepping back from the above grand overview, and observing a related technology, one cannot help but be impressed by the magnificent improvements wrought by the use of compositional heterostructure technology for photovoltaic cells in the case of the rather expensive compound semiconductors, which is their drawback. Alternatively, structural (as opposed to *compositional*) heterostructure technology is well-established in high-frequency low-noise compound semiconductor transistor technology. Unfortunately, Mother Nature's periodic table of the elements leaves silicon with a relatively paltry offering consisting primarily of carbon and germanium for compositional heterostructure technology. However, as is discussed in this volume, silicon does allow a myriad of possibilities for *structural* heterostructure technology, with silicon in its microcrystalline and amorphous states.

The microcrystalline forms of silicon exhibit increased energy gaps so that band-gap engineering may be usefully possible, *i.e.* heterostructure technology. Solid-state theorists are rather far behind the front lines of this initiative and their assistance might be helpful. Perhaps a hint could be offered? Pauling showed long ago ("The Nature of the Chemical Bond") that dangling bonds, such as are widespread in microcrystalline silicon, cause strengthening of back-bonds and contraction of interatomic bond lengths. This type of behavior has also been observed for the near-surface atomic layers of semiconductors. However, reduced interatomic bond length in semiconductor structures causes increased energy band gap. Therefore, there may be an essential interplay between the grain size of microcrystalline silicon (for grain sizes comparable to the de Broglie wavelength) and energy band gaps, notwithstanding Tamm states and deep-trap recombination.

There is ample opportunity here to do good for humanity and the environment, as well as to advance the solid-state and materials sciences. Further great work needs to be accomplished on a grand scale, comprising the microscopic nature of thin-film silicon and its myriad device possibilities, its commercial production on an impressive scale, and its insertion into the marketplace.

One can clearly see that there is an ongoing need for educational materials to advance the state of the art, and editor Professor Murri and his colleagues who have written this volume provide us with an important and generous contribution in this regard, for which we are grateful.

> *Daniel L. Rode* Shangri-La, Paraná-Brazil & Washington University in St. Louis USA

*ii* 

## **PREFACE**

Thin film silicon solar cells present all the basic physical pre-conditions for a successful development of the next generation of low cost, high efficiency photovoltaic devices, capable to fulfill the needs of a future Green Energy Society.

Their industrial development still presents, however, a number of problems associated to the diverse nature of these devices, with respect to the today generation of solar cells based on the use of crystalline silicon. In fact, here a multidisciplinary micro- and nano-technological approach is requested, applied to thin film modellization, large scale deposition, material characterization and solar cells fabrication, paying attention, as well, to quanto-mechanical issues, whose full application will only allow to go above the classical Shockley and Queissser limit of photovoltaic efficiency.

While the physics and engineering of crystalline silicon solar cells is covered by the content of a relevant number of Handbooks and Textbooks, the same does not apply to thin film solar cells, and this is the main reason why the publication of this eBook seems appropriate to supply, on time, to the absence. It is intended for non-specialists, i.e. for graduate and PhD students with a sufficient background in solid-state physics as well as for professional physicist and engineers who are not fully familiar with all the aspects of thin film technology, but who might be potential contributors to the development and industrialization of this opportunity. This eBook critically covers, in fact, in its three Sections all the main aspects of thin film solar cells physics and engineering and is coauthored by recognized experts in the field, whose view is not at all a personal view, but reflects the state of the art of the field and the opinion of the international thin film community.

Section I contains four Chapters describing, respectively, the basic elements of thin film solar cells (Ch.1) and deposition of thin films by: Ch.2, plasma enhanced chemical vapor deposition (PECVD), sputtering (Ch.3) and, finally, Ch.4, molecular beam epitaxy (MBE).

Experimental techniques to measure film and device parameters are discussed in the four Chapters of Section II. In details, Infrared and Raman spectroscopies (Ch. 5), Morphological and structural properties (Ch.6), while Ch.7 and Ch. 8 present how to measure optical and electrical parameters, respectively.

The last three Chapters of Section III discuss the physics of two classes of devices, Heterojunctions for silicon photovoltaics (Ch. 9) and Micromorph cells (Ch.10), widely studied as structures able to improve the conversion efficiency of a solar cell. Finally, Ch.11 underlines the role of light trapping increasing the capture of solar radiation and then, again, the conversion efficiency.

I would like to thank all Authors, Prof. Daniel Rode for writing the Foreword, Prof. Sergio Pizzini for his Introduction discussing the general aspects of the subject of the eBook, Mrs. Lisa Kramer Taruschio for language revision of Chapters 1,4,7 and 8 and Bentham Science Publishers, in particular Mrs. Salma Sarfaraz for her support, efforts and patience. The University of Camerino - School of Science and Technology, togheter with Elena Tresso -DISAT, Department of Applied Science and Technology, Politecnico di Torino, and Maurizio Acciarri - Department of Materials Science and Solar Energy Research Center (MIBSOLAR) Università degli Studi Milano Bicocca, partially supported the publication costs of the eBook for its open access.

### *Roberto Murri*

University of Camerino School of Science and Technology Physics Division Italy

*iv* 

## **List of Contributors**

*v* 

**Angelica M. Chiodoni** Center for Space Human Robotics (CSHR@POLITO), Italian Institute of Technology, Corso Trento 21, Torino, IT-10129, Italy.

**Armando M. Estrada** Energy Area, ITMA Materials Technology, Parque Empresarial P.E.P.A., c/Calafates 11, Parcela L.3.4, 33417, Avilés (Asturias) Spain.

**David Gómez** Energy Area, ITMA Materials Technology, Parque Empresarial P.E.P.A., c/Calafates 11, Parcela L.3.4, 33417, Avilés (Asturias) Spain.

**Dipak K. Basa** Department of Physics, Utkal University, Bhubaneswar-751004, India.

**Domenico Caputo** DIET Department of Information, Electronics and Telecommunication Engineering, University of Rome "Sapienza, Via Eudossiana 18, 00184 Rome, Italy.

**Elena Tresso** DISAT, Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, and Center for Space Human Robotics (CSHR@POLITO), Italian Institute of Technology, Torino Italy.

**Enrico Salza** ENEA, Research Center Casaccia, Via Anguillarese 301, 00123 Roma Italy.

**Giampiero de Cesare** DIET Department of Information, Electronics and Telecommunication Engineering, University of Rome "Sapienza, Via Eudossiana 18, 00184 Rome, Italy.

**Giuseppina Ambrosone** Department of Physical Sciences, University of Naples "Federico II", Complesso Universitario MSA, Via Cintia, 80126 Napoli, Italy and CNR-SPIN, Complesso Universitario MSA, Via Cintia, 80126 Napoli, Italy.

**Lorenzo Morresi** School of Science and Technology, Physics Division, University of Camerino, Via Madonna delle Carceri, 9-62032 CAMERINO (MC) Italy.

**Luca Serenelli** ENEA, Research Center Casaccia, Via Anguillarese 301, 00123 Roma Italy.

**Marco Ficcadenti** School of Science and Technology, Physics Division, University of Camerino, Via Madonna delle Carceri, 9-62032 Camerino (MC) Italy, now at CESI Spa,Via Rubattino 54, 20134 Milan, Italy.

**Marian Nowak** Institute of Physics, Silesian University of Technology, 8 Krasińskiego, Katowice, PL-40019, Poland.

**Mario Tucci** ENEA, Research Center Casaccia, Via Anguillarese 301, 00123 Roma Italy.

**Massimo Izzi** ENEA, Research Center Casaccia, Via Anguillarese 301, 00123 Roma Italy.

**Maurizio Acciarri** Department of Materials Science and Solar Energy Research Center (MIB-SOLAR,)Università degli Studi Milano Bicocca, Via Cozzi, 53-20125 Milan, Italy.

**Nicola Pinto** School of Science and Technology, Physics Division, University of Camerino, Via Madonna delle Carceri,9-62032 Camerino (MC) Italy.

**Pascal Sánchez** Energy Area, ITMA Materials Technology, Parque Empresarial P.E.P.A., c/Calafates 11, Parcela L.3.4, 33417, Avilés (Asturias) Spain.

**Pietro Mangiapane** ENEA, Research Center Casaccia, Via Anguillarese 301, 00123 Roma Italy.

**Roberto Murri** University of Camerino, School of Science and Technology, Physics Division, Via Madonna delle Carceri 9, 62032 Camerino (MC) Italy.

**Paolo Rava** Elettrorava SpA, Via Don Sapino 176, 10078 Venaria, Torino, Italy.

**Sergio Pizzini** Department of Materials Science, Università degli Studi Milano Bicocca, Via Cozzi, 53-20125 Milan, Italy.

**Simona de Iuliis** ENEA, Research Center Casaccia, Via Anguillarese 301, 00123 Roma Italy.

**Ubaldo Coscia** CNISM Naples Unit, Complesso Universitario MSA, Via Cintia, 80126, Napoli, Italy and Department of Physical Sciences, University of Naples "Federico II", Complesso Universitario MSA, Via Cintia, 80126 Napoli, Italy.

*vi* 

## **INTRODUCTION**

### **Sergio Pizzini\***

*University of Milano-Bicocca, Department of Materials Science, Via Cozzi, 53-20125, Milano, Italy* 

**Abstract:** This short introduction presents the general situation of photovoltaic conversion, with emphasis on possible use of thin film solar cells.

This work is intended as a textbook which deals with thin films technologies and device structures for silicon based photovoltaic applications. Therefore, the focus of the eBook is to present an overview of the deposition and characterization methods of thin film silicon solar cells. These kinds of cells can make photovoltaic power production more economically viable than to crystalline silicon cells, contributing to a major expansion of the related market. In fact, nowadays about 90% of solar cells are manufactured from crystalline Si substrates with a typical thickness of about 0.2 mm but which are still expensive to produce, although extremely efficient. To reduce these costs, a transition from bulk crystalline Si solar cells to thin-film technologies, with both reduced usage of active material in the device and the introduction of new technological concepts such as nanotechnologies, might be the ultimate solution. Despite their importance, the scientific development and understanding of new solar cell concepts are not very advanced, and the education of specialized engineers and scientists has not even started. The primary reason for this is the multidisciplinary nature of thin film growth technology. Other reasons for the lack of development and recognition are the complexity of the multi-parameter growth processes, the complex phase transformation from the precursor's liquid or gaseous phase toward a solid one, and the scaling problem with the required growth-interface control on the nanomicrometer scale within growth systems of micrometer scale.

**Figure 1:** Summary of the efficiency values for different types of solar cells classed by generation. Data are taken from: Solar cell efficiency Tables (Version 38), M. A. Green, K. Emery, Y. Hishikawa, W. Warta and E. D. Dunlop, Prog. Photovolt: Res. Appl. 2011; 19:565–572. Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/pip.1150

**<sup>\*</sup>Address correspondence to Sergio Pizzini:** Department of Materials Science, Università degli Studi Milano Bicocca, Via Cozzi, 53-20125 Milan, Italy; Email: sergio.pizzini@mpvresearch.eu

Therefore, the text is designed to provide much needed information on the fundamental scientific aspects of thin films growth technologies, as well as a clear understanding of the properties of the material and how it is employed in new generation photovoltaic solar cells.

The following Table **1** (M.Tao, The Electrochemical Society Interface, vol. 17, no. 4, pp. 30-5 (2008)) summarizes all the main properties and requirements of materials suitable for terrestrial photovoltaic conversion.


**Table 1:** Material requirements for terrestrial solar cells (reproduced by permission of ECS-The Electrochemical Society)

As one can see in the Table, there is not one "winning" material, but a plurality of materials, all suitable for photovoltaic (PV) devices, even if with differing fields of applicability.

While early in the PV age solar cells built on silicon wafer controlled the market, its today's market sharing is presented in Fig. **2**, where it is shown that thin film materials already play a significant role into the market, which is forecast to overcome that of silicon in the next decade.

Among materials suitable for thin film applications, the III-V compound semiconductors (GaAs, InP, and their alloys or compounds), even if nearly ideal due to their direct bandgap, remain too expensive for large scale terrestrial applications and are mainly used for concentration applications. Their high costs are determined by the chemical precursors required for deposition and by the sophisticated deposition techniques (Molecular Beam Epitaxy, MBE or Metalorganic Chemical Vapour Deposition, MOCVD).

II-VI compound semiconductors (Cadmium Telluride, CdTe or Copper Indium Diselenide, CuInSe2 or similar), which share a consistent fraction of the thin film market, allow for tailoring the bandgap, the optimization of the optical absorption and the design of multijunction solar cells. Thin films of these materials can be easily deposited with passivated grain boundaries and then with low recombination rates for excess carriers.

The content of this eBook is limited to solar cells based on silicon thin film, the main reason for this choice being the environmental friendship of silicon and the almost unlimited source of silicon

*viii* 

precursors in the earth crust. It should be noted that thin films of crystalline silicon need to improve their optical absorption properties by using nanotechnologies to insert into the structure of the PV device optical active layers with modified physical properties. This point will be a prominent part of the future research in the field of thin film crystalline Si.

The general intent of the eBook is to provide the basic elements and the reasons for this choice, discussing the fundamental aspects of silicon thin films suitable for solar radiation conversion.

**Figure 2:** Sharing of the PV market among different technologies of PV cells. All values refer to 2008. \* percentage share of 2008 market. Reproduced from IEA International Energy Agency-Technology Roadmap-Solar photovoltaic energy (2010), www.iea-pvps.org

All this to give the core subjects to deposit and to characterize thin films suitable to design and to produce structures able to improve the conversion efficiency of the solar radiation.

This last is the main objective, to be achieved by the study and selection of a multiplicity of possible solutions based on inorganic and/or organic materials. While it is likely that many of these solutions could lead to efficient devices, the differences among them will be generated by the technologies employed and by how these can be transferred to an industrial production process, if we like to use extensively photovoltaic conversion for mass energy production.

In this context, the "third generation" photovoltaics will utilise new concepts to design and new technologies to produce high efficiency devices. It is reasonable to expect that within the next 10- 15 years, photovoltaics will move to third generation devices with a significant cost reduction. It is difficult to define values for competitive solar energy, which depends on the scenario proposed for the future of fossil fuels. However, if we correctly assume that this cannot be the only parameter for the evaluation and decision-making regarding the use of the PV energy, the PV costs must be considered together with the efficiency in a larger technical, environmental and political picture.

Very good reviews discussing the physics and the problems of photovoltaics cells can be found in:

Nelson, J. The physics of solar cells. London: Imperial College Press 2003; Aberle AG. Thin-film solar cells. Thin Solid Films 2009; 517: 4706–10; Markvart T. Castañer L. (Eds). Practical Handbook of Photovoltaics: Fundamentals and Applications. Oxford: Elsevier 2006; Boreland MB, Bagnall DM. Current and future photovoltaics. Foresight 2006; 1-21. Available at: http://eprints.ecs.soton.ac.uk/14403/; Shah A. (Ed). Thin-Film Silicon Solar Cells. Lausanne: EPFL Press 2010; and Poortmans J. Arkhipov V. (Eds). Thin Film Solar Cells: Fabrication, Characterization and Applications. Chichester, UK. John Wiley and Sons, Ltd 2006.

*x* 

# **SECTION I - THIN FILM SOLAR CELLS: GENERAL ASPECTS AND DEPOSITION TECHNIQUES**

*Silicon Based Thin Film Solar Cells,* **2013***,* **3-28 3**

# **CHAPTER 1**

## **Basics of Thin Film Solar Cells**

## **Marco Ficcadenti\*,+ and Roberto Murri**

*University of Camerino, School of Science and Technology, Physics Division, Via Madonna delle Carceri 9, Camerino, 62032, Italy* 

**Abstract:** The chapter presents a short review of the general principles of photovoltaic conversion and different types of thin films solar cells. The aim is to present how a device can evolve from the classical Si *p-n* junction, with its physical constraints limiting the conversion efficiency, to devices where higher absorption of the light and improved structural design result in higher conversion efficiency. It is now well recognized that these devices have to be based on thin film structures. As a consequence, we have to be able to design the whole stacked thin film structure, and within this, each film must be deposited with well-defined properties. Several deposition techniques can be used, and we will shortly discuss the so-called Plasma Enhanced Chemical Vapour Deposition (PECVD), considering the evolution of the film structure.

**Keywords:** Solar cells, thin films, silicon, microcrystalline, protocrystalline, amorphous, cadmium telluride, copper indium diselenide, PECVD, CVD, sputtering, p-n junction solar cells, solar energy conversion, conversion efficiency, electron-hole pair, antireflection coating, light absorption, energy gap, photon energy, parasitic resistance, stacked cell, graduated band gap, thin film structure, protocrystalline film, density of states (DOS), deposition parameters, dilution ratio, crystal nucleation, growth mechanisms, thin film hydrogenation, light soaking.

### **1. INTRODUCTION**

The production of solar cells was and is still based mainly on crystalline silicon wafers holding about 81% of the photovoltaic world market [1]. Despite that, the wafer based technology is seen as a limiting factor for the growth of the market.

The development and the time duration of a diffused photovoltaic market requires that solar cells have higher conversion efficiencies and lower costs than actual devices (cells and modules). Much research and many technological efforts have been carried out to attempt to reduce the thickness of the silicon wafers. Sanyo has been able to produce HIT (heterojunction with intrinsic thin layer) cells on about 70 μm thick wafer, compared with about 180 μm of normal production p-n junction cells [2].

Other attempts have been made using the so-called transfer [3] and silicon ribbon technologies [4]. In the former instance, the complexity of the technology can be a deterrent for the mass production of solar cells, even if relatively high conversion efficiencies are present [5]. In principle, silicon ribbon can be used to develop on-line production, with a strong reduction of costs [3, 4, 6].

In this chapter and in the eBook as well, we will focus mainly on a discussion of thin film silicon (Si) technology. However, other materials are now being used for low cost photovoltaic. In particular, Cadmium Telluride, CdTe) [7] and Copper Indium (Gallium) Selenide, CuIn(Ga)Se2 (CI(G)S), seem to

**Address correspondence to Marco Ficcadenti:** CESI SpA,Via Rubattino 54, 20134 Milan, Italy; Tel: +39 221255183; E-mail: marco.ficcadenti@cesi.it

<sup>+</sup> Now at CESI SpA, Via Rubattino 54, 20134 Milan, Italy

be very promising, thanks in part to the considerable research carried out and technology investments made over many years. For the most part, First Solar is pushing for CdTe realm [8]. Different structures are involved in CI(G)S solar cell research and technology development [9, 10].

Starting from the broad experience of research on amorphous silicon, many ideas are being tested, the common goal being high conversion efficiency and low cost per Wp. The base material is nano-crystallized silicon (nc-Si), while the cell device combines nc-Si with amorphous silicon (*a*-Si) in different junction structures (tandem, micro-morph, and multiple junctions).The focal point is the ability to control the physical properties of the deposited silicon thin films. In fact their features must be suitable for the role that each functional layer carries out in the whole solar structure. This means that we have to modulate deposition parameters in order to obtain given structural and physical properties of each layer. In particular, the "crystallinity" of the film must span a wide range reaching from amorphous to micro-crystalline material. Ample work has been done on the evolution of crystallinity [11-15]. Werner and Bergman operatively defined three possible categories of thin silicon solar cells [16]:


In this chapter we will discuss some physical properties of silicon thin films deposited by PECVD, with the film structure as the leading parameter [17].

We begin with a consideration of amorphous structures and progress by increasing the crystallinity of the film, to end with polycrystalline films. We will try to demonstrate how to obtain the desired properties of the material through precise control.

### **2.** *p-n* **JUNCTION SOLAR CELLS**

We will shortly review the basic concepts of solar energy conversion using a silicon *p-n* junction solar cell [18-20].

A solar cell is an electronic device which directly converts sunlight into electricity. Light shining on the solar cell produces both a current and a voltage to generate electric power. This process requires first, a material in which the absorption of light raises an electron to a higher energy state, and second, the movement of this higher energy electron from the solar cell into an external circuit. The electron then dissipates its energy in the external circuit and returns to the solar cell.

In principle, a variety of technologies using different materials and processes can satisfy the requirements for photovoltaic conversion. In practice nearly all photovoltaic devices need an internal electric field leading to the separation of the photogenerated charge carriers (electrons and holes).

At the present time, the conversion devices use, for the most part, semiconductor materials in the form of a p-n junction.

The general design pattern scheme of a crystalline silicon solar cell based on a p-n junction is shown in Fig. **1**. To date, this structure has been commonly built using mono or poly crystalline silicon wafers, 200-300 micron thick [20, 21].

The electrical contact layer on the front of the cell where light enters is a metallic grid pattern designed to minimize the covering of the surface of the cell but to maximize the photogenerated carrier collection.

**Figure 1:** Structure of a standard p-n junction solar cell.

Specialized simulation software allows for striking a balance between two opposite needs. The grid pattern must be widely spaced to allow light to enter the solar cell, but not to the extent that fingers have difficulties collecting the current produced by the cell. These restrictions do not apply to the rear metallic contact layer, which need function only as an electrical contact and thus cover the entire back surface of the cell. To improve the conversion efficiency of a solar cell, the amount of reflected light (about 30 %), must be minimized [19, 20]. To increase the amount of light absorbed by the cell, an antireflection coating (ARC) is typically applied on the front surface [22].

Today silicon nitride is commonly used as ARC due to its functional optical properties and, in addition, to its excellent surface passivation properties which prevent carrier recombination at the surface of the solar cell [23-25]. Silicon nitride is typically deposited in the shape of a thin layer (about 70 nanometres) using PECVD [22, 25-27].

The photons of the radiation incident on the surface of a semiconductor can be either reflected from the top surface or absorbed into the material. Failing these two processes, they are transmitted through the material. If the photon is absorbed, it will raise an electron from the valence band to the conduction band. For photovoltaic devices, reflection and transmission are typically considered loss mechanisms because photons that are not absorbed do not generate free carriers.

The key factor in determining if a photon is absorbed or transmitted is its energy, Eph, and its relationship with the energy gap, Eg, of the semiconductor material.

The three possibilities are shown in Fig. **2**:


**Figure 2:** Energy diagram of a *p-n* junction under illumination.

The electrical equivalent circuit of a solar cell is a current generator in parallel with an asymmetric, nonlinear resistive element, *i.e.* a diode (see Fig. **3**).

**Figure 3:** Equivalent circuit of an ideal solar cell.

The current voltage relationship of a p-n junction diode in the dark is given by [18-20]:

$$I\_{duk} = I\_o \left( \mathbf{e}^{qV/kdT} \text{ -I} \right),\tag{1}$$

while under illumination the ideal current-voltage characteristic is given by:

$$I = I\_o \left( \mathbf{e}^{\circ \theta^\prime / \sin \Gamma} \text{ -I} \right) \cdot I\_L \tag{2}$$

where IL is the light generated current, I0 is the dark saturation current of the diode, n is the ideality factor (typically in the range 1 to 2), *q* is the electronic charge, *k* the Boltzmann's constant and *T* is the temperature in degrees Kelvin.

Fig. **4** plots the current-voltage (*I-V*) characteristic for a solar cell in dark conditions (see the curve a).

**Figure 4:** Current-voltage characteristic of ideal solar cell in the light and the dark.

Curve b) in Fig. **4** shows the *I-V* characteristic of the illuminated device, shifted in the fourth quadrant, where the device can generate electrical power.

Usually this curve is presented reflected around the voltage axis as shown in Fig. **5**. Ideally the short circuit current *Isc* is equal to the light generated current *IL*.

**Figure 5:** Output characteristic of a solar cell as normally plotted.

Setting *I* to zero in Eq. **2**, gives the open circuit voltage Voc:

$$V\_{oc} = \frac{nkT}{q} \ln\left(\frac{I\_L}{I\_0} + 1\right) \tag{3}$$

The voltage operating regime of the solar cell is the range from 0 to Voc, in which the cell can supply power to an external load. The output power is given by:

$$P = V \times I \tag{4}$$

*P* reaches a maximum at the cell's operating point or maximum power point. This occurs at a welldefined point with coordinates *Vm-Im* (Figs. **4** and **5**), defining the optimum resistive load as *Vm/Im.*

A working parameter for solar cells is the Fill Factor, *FF*, defined as:

$$FF = \frac{I\_m V\_m}{I\_{sc} V\_{oc}} \tag{5}$$

It measures how *Pm* covers the ideal power given by *IscVoc*. In practice, it is a measure of how "square" the output characteristics are. The conversion efficiency of a solar cell is the power delivered to the operating point as a fraction of the incident light power *Pin*,:

$$
\eta = \frac{I\_m V\_m}{P\_m} \tag{6}
$$

Conversion efficiency relates to Isc and Voc using FF,

$$
\eta = \frac{I\_{sc} V\_{oc} FF}{P\_{in}} \tag{7}
$$

The four quantities *Isc, Voc, FF*, and are the key parameters for defining energy conversion performances of a solar cell, and should be given for well-defined illumination conditions. The Standard Test Condition (STC) for solar cells is the Air Mass 1.5 spectrum, an incident power density of 1000 W/m2 and temperature of 25 °C [28, 29].

### **2.1. Effect of Parasitic Resistances**

Resistive effects in real solar cells reduce efficiency by dissipating power in the resistances. The most common parasitic resistances are series resistance (*Rs*) and shunt resistance (*Rsh*).

The inclusion of the series and shunt resistance on the solar cell equivalent circuit is shown in Fig. **6**.

Series resistance derives from three causes: i) the movement of carriers through the emitter (*n* type zone) and base (*p* type zone) of the solar cell; ii) the interface between metallic contact and silicon; and iii) the resistance of the metallic films used for both top grid and rear contacts.

The main impact of series resistance is to reduce the fill factor; excessively high values may also reduce the short-circuit current. Significant power losses caused by the presence of shunt resistance are typically due to manufacturing defects, rather than poor solar cell design. Low shunt

resistance causes power losses in solar cells because it provides an alternative current path for the light-generated current. Such a diversion reduces the amount of current flowing through the solar cell junction and reduces the voltage of the solar cell. The looping effect of shunt resistance is particularly severe at low light levels. The light-generated current diminishes and the loss of this current to the shunt therefore has greater impact. In addition, at lower voltages where the effective resistance of the solar cell is high, the impact of parallel resistance is relatively larger.

**Figure 6:** Equivalent circuit including series and shunt resistance.

Including the parasitic resistances the current voltage equation is given by [19, 20]:

$$I = I\_L - I\_0 \left\{ e^{\left[\frac{q\left(V + R\_i I\right)}{\kappa hT}\right]} - 1 \right\} - \frac{V + R\_i I}{R\_{sh}} \,. \tag{8}$$

#### **3. FROM VOLUME TO THIN FILM SOLAR CELL**

Recent research and technological developments tend to broaden the realm of photovoltaic devices, adding to the classical silicon wafer technology and to other amorphous silicon *p-i-n* devices, perhaps more complex but of higher conversion efficiency and at lower cost. Polycrystalline silicon thin film converters on glass and tandem solar cells built by stacking microcrystalline and amorphous silicon films in a due sequence are about to enter the market. However, studies continue to improve the properties of amorphous silicon devices that can stabilize the physical properties of the basic material.

The high growth rate of the photovoltaic market all over the world requires production levels of hundreds of GW/year to contribute significantly to the generation of electricity worldwide. This mass production must be based on reliable and safe technologies and reasonable cost, even when the internal and external costs of the price per Wp are included [30].

The reliable crystalline silicon wafers technology dominates the market [1], but the high cost of silicon wafers and the demands energy makes on silicon ingots production preclude cost reduction. The wafer accounts for more than 50 % of the cost at the module level. This problem forced production of Si substrates of so called solar grade Si [31] which have more lax specifications in terms of impurities as compared with electronic grade material.

#### **10** *Silicon Based Thin Film Solar Cells Ficcadenti and Murri*

Thinner wafers, an increased efficiency in Si production and an increase of the module efficiency to about 18-20 % will have to contribute to cost reduction in the next ten years.

In any case, if we think of other ways involving i) reduced semiconductor material consumption, ii) lowered energy needs, iii) technologies to fabricate solar cells on inexpensive large area substrates and (iv) integration technologies to electrically connect the fabricated solar cells, we find that thin-film PV has the potential of achieving module costs less than €1 per Wp [32].

A critical point when comparing different PV technologies is the energy pay-back time (EPBT), *i.e.* the time in which the energy input during the PV system life-cycle is compensated by electricity generated by the PV system [33].

The thin film technologies have an EPBT of about 1 year, (depending on the technology) compared with multicrystalline Si modules EPBT of about 1.5-2 years in southern regions as reported by M. de Wild Scholten in [33]. An accurate comparison of the payback times must take into account all the components of the photovoltaic system.

A well accepted working definition of thin film was given by Chopra *et al.* [34] as a material created *ab initio* by the random nucleation and growth processes of individually condensing/reacting atomic/ionic/molecular species on a substrate. The structural, chemical, metallurgical and physical properties of such a material are strongly dependent on a large number of deposition parameters and may also be thickness dependent. Thin films may encompass a considerable thickness range, varying from a few nanometers to tens of micrometers and thus are best defined in terms of the production processes rather than by thickness".

Plasma deposition, sputtering, evaporation, deposition from the liquid phase, *etc.* all meet the previous definition of thin film and in addition allow for tailoring of its electrical and morphological properties (crystalline, amorphous and intermediary forms).

We will discuss in some detail inorganic non-crystalline Si deposition which allows for the formation of charge-carrier separating junctions: homojunction (*p-n* in Si) or heterojunction with other materials to collect the excess carriers created by the light exposition. Ideally, the absorber material of an efficient terrestrial solar cell should be a semiconductor with a band gap of 1–1.5 eV, with a high solar optical absorption (104 105 cm<sup>−</sup><sup>1</sup> ) in the wavelength region of 350 nm 1000 nm, a high quantum yield for the excited carriers, a long diffusion length and low recombination velocity.

For historical reasons (development of electronic devices), Si and its wafers dominate the market, even if its 1.1 eV band gap, with indirect character for photons with energy lower than 3.4 eV, make it less than ideal for thin-film solar cells. Nevertheless, many efforts have gone into developing thin-film solar cells based on amorphous-microcrystalline-crystalline Si. The prospect of borrowing technologies from microelectronic production supports these research efforts.

Due to its low absorption coefficient, Si layers have to be at least 30 μm thick to absorb enough light, but optical light trapping or confinement improve the effective absorption.

Si can also be deposited in its amorphous form. Amorphous hydrogenated silicon (*a*-Si:H) has a number of properties which make it attractive as an absorber layer for thin-film solar cells. The band gap, the density of states distribution and the ratio between crystalline and amorphous phases (crystallinity) of the deposited material can be modulated by the method and conditions of deposition, achieving efficient doping and suitable high optical absorption coefficient. Recent results [11, 13] show how to reduce instability problems. Furthermore, developments around multijunction structures and micro/nanocrystalline Si extensions provide space for solar cells using "amorphous" silicon.

To summarize, we can have different kinds of silicon thin film solar cells.

### **a) Crystalline Silicon Thin Film Solar Cells**

The *p-n* homojunction structure is built by depositing, by epitaxial growth, a thin crystalline Si film on a low cost Si substrate or non-Si substrate which is, however, prepared to accept the Si films.

#### **b) Amorphous and Microcrystalline Silicon Thin Film Solar Cells**

Typically, amorphous silicon thin-film cells use *p-i-n* structure, see Fig. **7**.

**Figure 7:** Schematic of a *p-i-n* solar cell on a glass substrate.

The top layer is *p*-type *a*-Si, the middle layer is intrinsic silicon, and the bottom layer is *n*-type *a-*Si. The *p-i-n* structure is sandwiched between a transparent conductor (*i.e.* tin oxide or zinc oxide) and the back metallization. The transparent conductive oxide (TCO) layer is made thin enough and relatively transparent to allow light to pass right through it, generating free electrons in the intrinsic layer. The structure can be deposited on glass or other substrate. This geometry sets up an electric field, between the *p*-type and *n*-type regions, that stretches across the middle intrinsic resistive region and separates the photogenerated free carriers.

It is possible to absorb the solar spectrum more efficiently and to improve cell stability by using stacked *p-i-n* structures and different band gaps to produce 'double junction' or 'triple junction', see Fig. **8**.

#### **12** *Silicon Based Thin Film Solar Cells Ficcadenti and Murri*

**Figure 8:** Schematic of a triple junction amorphous Si solar cell.

Another possible structure is the micromorph cell (see chapter 5). In addition to the *a*-Si cell, the micromorph cell has a tandem structure with an additional microcrystalline absorber, see Fig. **9**. This layer allows for conversion of the energy of the red and near infrared spectrum, providing increased efficiency.

**Figure 9:** Schematic structure of micromorph tandem cell.

We will focus our work on b) class of solar cells.

Good reviews of problems linked to various kinds of Si solar cells are given in [5, 35, 36] with different approaches.

### **4. THIN FILMS DEPOSITION**

A thin film is a structure with low dimensionality (2D) grown step-by-step according to a welldefined deposition sequence [37].

The energetic atomic, molecular or ionic species impact the substrate and, losing part of their energy, are adsorbed on the substrate surface (physi-adsorption), see Fig. **10**.

**Figure 10:** Adsorption processes. A red vertical connecting bar denotes a chemical bond.

The temperature differences among impinging particles and substrates stimulate lateral movements of the particles on the surface.

The interaction of moving particles allows clusters to form. These structures, thermodynamically unstable, tend to be desorbed from the substrate unless other interactions create appropriate energy conditions to start a so-called nucleation stage of minimal critical size. This nucleation process takes place in many substrate points, randomly distributed.

Going through complicated chemical-physical processes (species and energies of the impinging particles, impinging rates, adsorption-desorption rates, thermal diffusion, substrate and its surface properties, *etc.*), the rate of lateral growth is higher than the perpendicular growth, originating the so-called islands.

A continuous film originates from a coalescence process, where islands agglomerate, favoured by high surface mobility. The film assumes a continuous structure when the coalescence of the islands fills all the open channels. As a result, the outer surface presents a coarse, textured structure.

The very complex processes leading to the growth of a thin film are statistical processes of particle-particle and particle-substrate interaction.

Depending on the thermodynamics of the process and on the substrate surface, the initial stages of thin film growth on a solid substrate correspond to three possible situations: i) fragmented island structure (Volmer-Weber model); ii) uniform film (Frank-van der Merwe model), and iii) a mixed, fragmented island structure on uniform film (Stranski-Krastanov type).

#### **14** *Silicon Based Thin Film Solar Cells Ficcadenti and Murri*

The thickness of a thin film ranges from several nanometres to several tens of micrometres; over this generic limit, the film behaves like a thick structure, low dimensional too, but with a "volume" (3D) response.

The properties of the thin film material are determined by the deposition conditions not only at macroscopic level (substrate temperature and chemistry, pressure, power, *etc.*), but also at nucleation stage; however, this must not be interpreted negatively but rather as a powerful key for achieving fine tuning of the material properties.

Thin film deposition allows for the construction of artificial nano-materials, structures with one or more dimensions of nanometre size (1 nm = 10-7 cm = 10Å).

Examples of nanostructure are a quantum dot (0 D); a quantum wire (1 D) and a superlattice or, in general, a thin film (2 D).

The ratio among the nanodimensions and the value of other physical parameters sets the size depending upon the behaviour of the physical properties of the artificial structure. Physical parameters to be considered are, for example: conditions of quantum confinement (≤ 100 atoms); mean free path of conduction carriers (< 10 nm); mean free path of hot electron (< 1nm); de Broglie wavelength (< 1 nm) and Bohr excitation diameter (Si = 8,5 nm; GaAs = 196 nm; CdS = 6 nm) [38].

In general it can be said that the deposition method controls the properties of each thin film, see Fig. **11**.

**Figure 11:** Correlations between growth conditions and the properties of the resultant thin films.

Among these methods, Chemical Vapour Deposition, CVD, implies a decomposition of source material, while Sputtering (SP) uses energetic species (1-10 eV) irradiated from a solid source. In CVD deposition, and in thermal evaporation as well, material grows in thermodynamic equilibrium; films deposited by SP are far from equilibrium because species impinging on the substrate lose their energy very rapidly. As a general result, the density of lattice defects is greater than in the same bulk material.

A variety of experimental techniques are employed to characterize thin films (see Table **2.9** and Table **2.10** in [38]).

### **5. SILICON THIN FILMS**

We begin with a consideration of today's most common procedure for depositing silicon thin films: PECVD of silicon based gas compound and mixture of other gases such as methane, ammonia, *etc.*

Work on thin films deposition using PECVD started in the sixties with a strong emphasis on amorphous silicon, its hydrogenation (*a*-Si:H) and doping. The studies were focused on the properties of *a*-Si alloys materials and their applications [39-41].

The properties of films deposited by PECVD are defined and controlled by many parameters, all more or less critical. This strong dependence is negative in some aspects, requiring a fine control of the deposition process, but on the other hand it allows for wide variability of the material properties. PECVD allows controlled changes in structure and chemical composition of the films through very fine tuning of the values of the parameters during growth.

Another interesting and powerful aspect of PECVD is that the deposition process can take place at low temperatures, thus enabling large area deposition and uniformly high thickness on a great variety of substrates.

As one can see in Fig. **12**, the structure of the deposited films changes according to the deposition parameters, in this case hydrogen dilution, allowing for modulation of the properties of each film in a multilayered structure. In particular both microstructure evolution and network reconstruction, during the growth process, are strongly dependent on hydrogen dilution.

**Figure 12:** Scheme of the phase evolution in the protocrystalline growth regime as a function of the hydrogen dilution ratio, [12].

The presence of hydrogen plays a specific and crucial role in the nucleation and the coalescence of film (Fig. **12**) as well as in the grown bulk and the growing surface [42-45]. Phase diagrams of growing structure can be obtained by using *in situ* real time spectroscopic ellipsometry [46]. Measuring the increasing thickness of the film, one follows the transition from initial amorphous film (*a*-Si:H) to microcrystalline film (*μc*-Si:H) passing through a mixed amorphousmicrocrystalline phase. It is interesting to note that the evolutionary structure of thin film influences the way in which hydrogen links to the structure and *vice versa,* looping a feedback circuit*.* This feedback controls the transition from an amorphous to a microcrystalline network, and then the band gap, *Eg*.

#### **16** *Silicon Based Thin Film Solar Cells Ficcadenti and Murri*

Wronsky and Collins [11, 40, 42] introduced the concept of protocrystalline state, for *a*-Si:H growth regime, as an evolutionary state but able, under specific growth conditions, to produce well defined physical properties (band gap, doping, *etc.*) and, most importantly, reproducible.

A strong argument for using amorphous silicon is its very high absorption coefficient. This originates from the continuous distribution of electronic localised states in the material band gap, *Eg*. Optical transitions can be done without preserving momentum: as a consequence *a*-Si behaves like a direct band gap semiconductor. In the visible range, the optical absorption coefficient *α*, of *a*-Si, is much higher than that of crystalline phase, see Fig. **13**.

The two properties (strong optical absorption and band gap, modulated varying deposition parameters) are key in preparing amorphous silicon suitable for use in efficient solar cells.

Thin film also means less material than in crystalline wafer cell. Incorporating hydrogen, germanium and carbon in the *a*-Si network, to form *a*-Si:H, *a*-SiGe:H and *a*-SiC:H, respectively, removes defects, thus lowering the density of their states in the gap, and affects the band gap *Eg*, increasing its value. Diluting silane with hydrogen (H), the band gap can move from about 1.4 eV of unhydrogenated material to about 2.0 eV when H ≈ 10 at. % is included in the film. High content of H in the film network tends to cause the electronic properties of the material to deteriorate and to coerce the film structure to evolve from proto to microcrystalline in a very thin layer [48-51].

Use of PECVD allows for the deposit of *a*-Si-H material with a density of dangling bond defects lower than 1016 cm-3 hydrogen content is about 10 at. %.

The creation of free carriers needed for an efficient solar converter requires an absorption coefficient higher than ≈ 103 cm-1. In this situation, energy of photons is greater than the band gap of the material. The different alloying of amorphous silicon means that *Eg* can be spanned in the range from ≈ 1.9 eV (*a*-Si:H) to ≈ 1.3 eV (*a*-SiGe:H), which is useful for building efficient solar cells in different junction configurations.

A fundamental point in the design of a solar cell based on silicon films is the knowledge of the density of states (DOS) and their energy distribution into the band gap of the material. The DOS general structure is now well recognized as represented by two tails entering the band gap from the valence and conduction band and a complicated in gap structure, strongly dependent on the deposition conditions (temperature, silane dilution, radio frequency power, *etc.*). The design of efficient solar cells requires a deep knowledge of the DOS.

Experimental measurements of the DOS distribution can be taken by different methods, given that it is a very complicated measurement subject to a high degree of uncertainty. Suitable techniques are: Deep level transient spectroscopy (DLTS), Photoconductivity (PC) and photoconductivity decay (PCD), Capacitance-Voltage curves (CV), Field Effect (FE), *etc.* [52-54].

The structure of the defects distribution in the centre of the gap (deep states) presents a multipeaked profile. In general, the profile presents three dangling-bonds (*D*) peaks: *D0* , (neutral states) in the centre of the band gap, *D-* , (negatively charged states) below the centre of the gap and *D<sup>+</sup>*, (positively charged states) above the centre of the gap.

**Figure 13:** The absorption coefficient, α, in a variety of semiconductor materials at 300K as a function of the vacuum wavelength of light (http://pvcdrom.pveducation.org/index.html).

Intrinsic materials (*i.e.* nominally undoped) have Fermi level *EF* near the centre of the band gap. The conduction process is *via* extended states for free carriers, even if with very low mobility μ. In *a*-Si:H, μ is about 10 15 cm2 V-1 s -1 for electrons and about 1 cm2 V-1 s -1 for holes.

Deep lying states with their distribution inside the mobility gap control the collection of photogenerated carriers, acting as traps or recombination centres, and values of the order 1015 1016 cm-3, typical for good deposited *a*-Si:H, are focal points for an efficient solar cell conversion. With those values, lifetimes are in the range 10-8 10-6 s and the depletion region extends over the entire thickness of the solar cell.

Doping of amorphous materials can be made when the density of states at midgap is low, *i.e.* when the Fermi level is at or near the middle of the gap. Typically, *a*-Si:H based materials meet this condition and, as a consequence, they can be doped: the Fermi level moves towards the conduction or valence band, according to the donor or acceptor doping type. Doping can be done using the same elements as in the case of crystalline silicon: phosphorous for *n*-type and boron for *p*-type, respectively. The consequent increase of defect states near midgap limits both doping efficiency and free carrier lifetimes [55], thus precluding the use of amorphous doped silicon as an active absorbing layer in solar cells. However, doped materials can be used as contact layers. For example, by incorporating *n*-type *a*-Si:H (Fermi level about 0.2 eV from conduction band edge) or *n*-type *c*-Si:H (*EF* about 0.05 eV from *EC*) into a *p-i-n* or a *n-i-p* structure, the ohmic behaviour of the contacts allows for built-in voltages of higher than one volt [56].

In a specular sense, *p*-type *a*-SiC:H (*EF* about 0.4 eV from *EV*) and *p*-type protocrystalline-Si:H (*EF* about 0.05 eV from *EV*) layers act efficiently as window contacts [56].

The possibility of graduating band gap and density of deep lying gap states of the intrinsic layer in a wide range, in combination with doped *p*-type and *n*-type layers of well controlled characteristics, is the main argument for use of this kind of material.

A weakness in the case for the use of amorphous materials is the need for hydrogenation to reduce the density of states, passivating dangling bonds. It is well known that hydrogen plays an important role in the so-called Stabler-Wronski effect [57].

In essence, the effect concerns the creation of defects under illumination, lowering both photoconductivity and dark conductivity. These quantities evidence reversible behaviours, returning to as-deposited values with an annealing at a relatively high temperature (~ 150 °C) [57].

The mechanism of the Stabler-Wronski effect is not yet completely understood, although there is clear relationship with the microstructure of the deposited film. For example, solar cells made with protocrystalline *a*-Si:H material show an improvement in fill factor under prolonged sun illumination [58, 59], see Fig. **14**.

**Figure 14:** Degradation of the fill factor of a *a*-Si:H *p-i-n* cells with undiluted (R=0= and protocrystalline (R=10) intrinsic layers under 1 sun illumination at 25 °C [59].

To attain a broader use of silicon thin films deposited by PECVD technique, a greater understanding of the microscopic mechanisms of the effect of hydrogen incorporation is needed. The main objective is to achieve a thorough description of the growth process. Thus the interaction of the incipient film with the substrate and its evolution during growth must be described. Considerable work has been done on these points [11, 14, 60].

In particular, van Elzakker [60] recently presented his PhD thesis stating an improvement of the conversion efficiency of amorphous solar cells from 7 to 9% [61].

The hydrogen-silane dilution ratio, *R = H2/SiH4,* can be used as an efficient parameter to represent the structural evolution of Si films deposited by PECVD. We can focus on *R* because the other parameters (pressure, power, *etc.*) must be set to obtain, at least in principle, the highest decomposition ratio of the reactor filing mixture.

As show in Fig. **12**, we can picture the evolution of the film structure evolution as a function of R. Wronsky *et al.* [11] proved that the growth of the film evolves through three phases. In the range where the dilution ratio is lower than 10, the film structure is truly amorphous. Structure changes can be induced, and more importantly, controlled, moving *R* towards higher values than 10: in a wide range of *R*, the structure is mixed (amorphous + microcrystalline), attaining microcrystallinity at very high *R* values.

The great advantage of the protocrystalline silicon is its high insensitivity to light action, avoiding light soaking. This fundamental property must be compared to the situation of *a*-Si:H films deposited with low hydrogen content. These last typically show Staebler-Wronsky effects, attributed to structural instabilities.

In the last decade, extensive work has been done toward greater understanding of how deposition conditions influence the growth of the thin films and their physical properties.

Collins and Ferlauto obtained a detailed deposition phase diagram [47].

Using this phase diagram, the deposition region suitable for the application of the PECVD deposited films can be chosen. A device structure can be built with each layer deposited according to well-defined conditions. In particular, protocrystalline films have been incorporated in solar cells structures [47].

In-depth knowledge of the amorphous-microcrystalline transition is also essential to the design of the micromorph solar cell. This last structure is recognized as a possible solution to increase the conversion efficiency.

Van Elzakker *et al.* [60] performed a series of experiments to trace the transition from amorphous to microcrystalline structure of PECVD silane films. The evolution of structural properties was followed using cross sectional TEM micrographies.

Van Elzakker's results are presented in Fig. **15**. The varying deposition parameter is the dilution ratio *R*.

Results of the van Elzakker study show that crystal grains start to nucleate when *R* is greater than 25 and thickness is around 100 nm from the substrate: nuclei are dispersed in the top layer of the film. This first result shows the influence of both *R* and film thickness on nucleation.

By increasing *R*, nucleation of crystals starts almost immediately and the transition between mixed and microcrystalline phases appears at a thickness of about 500 nm, even if an amorphous layer is still present in contact with the substrate. At *R*=40, nucleation starts immediately with a dense population of nuclei.

The mixed nucleation layer is very thin: about 50 nm. The evolution of the crystalline phase inside the deposited layer is also shown by the diffraction pattern. These results allow for control of the structural properties of Si:H, going from a fully amorphous layer for thicknesses lower than about 1 μm and *R* ≤ 20 to an evolutionary situation when *R* ≥ 25. In this case, the mixed phase tends to

#### **20** *Silicon Based Thin Film Solar Cells Ficcadenti and Murri*

be diffused and slowly evolving for films with lower dilution. Van Elzakker *et al.* found a clear correspondence between these results and optical measurements taken on the same samples.

**Figure 15:** Bright field electron micrographs of Si:H layers deposited on glass with dilution ratios R as indicated. The inserted diffraction patterns were taken from each layer with a selective aperture of 1 m diameter. The scale bar applies to all images [61].

Absorption spectra can estimate the density of defect states at low photon energy, using suitable calibration factors [62]. The density of defects evolves from about 9 x 1015 cm-3 (*R* = 0) to about 1.7 x 1017 cm-3 for *R* = 40.

Increasing hydrogen dilution creates material with both increasing real defect density and Urbach characteristic energy.

The density of states and their energy distribution in the layer, used as light absorber, is one of the most important parameters both in solar cell simulation and hence in real cells.

Techniques to measure density of states are for example Photothermal Deflection Spectroscopy (PDS) and Dual Beam Photoconductivity (DBP) [63, 64].

*a*-Si:H light conversion devices made by using specific dilutions of silane with hydrogen are promising for solar conversion because they show better performance after light exposure. In particular, the enhancement of performance could be related to three possible different phases of thin film growth: i) amorphous, ii) protocrystalline, (*i.e.* amorphous with various crystalline content) and iii) microcrystalline.

Values and ranges of deposition parameters define the protocrystalline regime. Given that protocrystallinity requires hydrogen dilution, silicon deposited under these conditions presents improved stability against light soaking. However, even if hydrogen dilution is beneficial, it tends to speed up the structural transition of the film to microcrystallinity. Unfortunately, the best absorption coefficient is presented by amorphous silicon and the problem now becomes how to

obtain high quality amorphous layers at high dilutions. Possible approaches are: a) dilution profile: *R* is decreased during growth to avoid transition to microcrystallinity; and b) layer-by-layer technique, to avoid phase transition.

An amorphous silicon layer is deposited by diluted silane, followed by a very thin layer of pure silane (interlayer). The role of this last layer should be to create an amorphous interface to support the growth of another silicon film deposited with increased dilution [65, 66].

Van Elzakker *et al.* used Raman spectroscopy to evaluate the crystalline fraction according to standard methods [13].

Depending on the thickness of the inter-layers, the crystallinity of the whole stacked structure is changing. It looks like a mixed phase when interlayers are 5 nm thick, with a decreasing crystalline fraction for increasing interlayer thickness.

As clearly presented in the following Fig. **16**, the optical absorption, α, is close to values and behavior of *a*-Si, in samples with an interlayer 15 nm thick.

The α difference between amorphous reference and 15 nm thick layer can be partially attributed to the absorption of microcrystalline phase.

Detailed studies of the growth mechanisms, done using real time spectroscopic ellipsometry [11, 34, 38], provided an understanding of the properties of undoped and doped thin films and their behaviour when used in solar cell structures. For example, one can define the optimal *R* range to deposit *p*-layers for *Voc* maximization, according to the required crystalline structure of the layers. The general problem is to obtain the lowest recombination at *p/i* interface. Studies by Wronky *et al.* clearly show that the deposited material must be in its protocrystalline *a*-Si:H phase [67]. The low recombination at *p/i* interface is attributed to the modification of the sub-interface volume inside the intrinsic layer during the growth of the *p* doped contact film. High hydrogen content and protocrystalline phase during *p*-Si:H film growth seem to be the keys for the beneficial effect on lowering of carrier recombination.

An interesting point concerns the relationship between PECVD frequency and hydrogen dilution. Wronsky *et al.* [68] found that a frequency (f) of 60 MHz improves the properties of silicon films at high deposition rates when compared to f = 13.56 Mhz. However, if the deposition is made with parameter values near the phase border between amorphous and mixed (amorphous + microcrystalline material), high deposition rates lead to good material regardless of the choice of frequency.

### **6. OTHER KINDS OF Si THIN FILM**

Till now we have discussed deposition of Si thin films by radio frequency (RF) PECVD, considering crystalline structure evolution with its phase diagram, suitable for obtaining thin layers with defined and controlled properties.

However, many different techniques and deposition methods have been presented, and many of these are possible candidates for photovoltaic devices with high conversion efficiency.

**Figure 16:** Absorption coefficient spectra of samples with different interlayer thicknesses in the as-deposited state compared to crystalline and amorphous reference curves [61].

Extensive reviews can be found in Bergmann [5, 15].

Moreover, updated numerical values of photovoltaic parameters in experimental devices can be found with references in the Solar Cells Efficiency Tables presented by M.A Green *et al.* [69]. The references quoted in [69] allow the reader to go as far as the description of the device details.

We will try to give a short non-exhaustive survey of the possible methods.

The development of silicon thin film solar cells rather than wafer cells means lower costs. The actual wafer thickness is about 180 200 μm. Further reduction is possible but it seems unlikely that a value of 50 μm, well recognized as effective thickness (= ratio of cell volume to cell area) with wafer structures, can be attained.

It is difficult to give a short and overall breakdown of the technologies due to the large quantity of variables to be controlled: designs of the cell and sequence of layer deposition, substrates, and different deposition techniques, each with its own parameters. All these variables must be defined according to cell or module production, cost savings, and large scale production.

We decided to follow the working scheme presented by Brendel [5], using substrate as the guide to classify photovoltaic structures. The substrate is necessary to mechanically support the structure, but the physico-chemical properties of the substrate surface and of the growing interface define the properties of the Si layers. Following Brendel's scheme, we have:


In detail, we have:

**1)** High temperature deposition (1000-1200 °C) is made using CVD or PECVD and silane or chlorosilane. The high deposition rate (several μm min-1) limits the Si grain dimensions in the range 1-5 μm as an acceptable compromise to shortening deposition time. An annealing process performed with light or laser allows a recrystallization of the Si layer, increasing grain dimensions up to several millimetres. The reduction of the density of grain boundaries is required to control the recombination effects, which limit the conversion efficiency.

It is important to note that the deposition and annealing steps are energy intensive, thus increasing the costs of the cell, even if the cell is a high efficiency structure.

Mullite, a mixture of Al2O3 : SiO2 seems to be the most promising substrate given its high reflectance of light, which generates a light trapping mechanism.

However, graphite, glass, mono-and polycrystalline silicon or silicon charged with other materials, metals and ceramics of different kinds have can be used to deposit the silicon film [70, 71].

Published results for cells built using high temperature deposition of silicon lead to conversion values in the range of 8-11 % [72, 73].

**2)** The low temperature deposition range essentially fits the PECVD technique, where deposition is made in the temperature range of 150-500 °C. All these points have been already discussed, having used PECVD widely to deposit thin silicon films.

In addition to the parameters previously quoted, we can choose an excitation frequency of 13,56 MHz (High Frequency, HF) or higher than 50 MHz (Very High Frequency, VHF), for the plasma process.

According to the film growth mechanism, using VHF leads to a less damaged structure due to the reduced energy of the ions impinging on the growing surface [67, 68]. This fact adds another degree of freedom in the growing parameters-material properties matrix, so that in principle the characteristics of the material can be tailored to the application.

Updated conversion efficiencies of devices made using PECVD films under different conditions can found in "Solar cell efficiency tables" by Green *et al.* [69]

**3)** The third point to consider is the layer transfer process method. In this case, silicon layer(s) are deposited, according to a given structure on an expressly prepared substrate permitting transfer of the device layered structure from the high cost reusable substrate to a low cost one. The substrate growing surface can be prepared in different ways. Today several layer transfer processes are being studied. Presently, the best efficiency for devices built with this technique attains 16,7% on an area of about 4 cm2 [69].

### **7. BASIC PRINCIPLE OF LIGHT TRAPPING**

The problem of the relatively weak absorption of near-band gap energy photons in thin silicon solar cells can be overcome by attempting to augment the optical path of the light inside the solar cell. One solution might be to implement mechanisms of light trapping, *i.e.* multiple reflections of light between the two outer surfaces of cell structure. The back side of the cell can be roughened (by blazing, texturing, grooving, *etc.*) but must be back-reflective, coated with a metal or by achieving a discontinuity in refractive index. The inner wafer surface acts as a reflective mirror when the thin cell structure is deposited on this substrate.

The multiple reflections of light increase the length of the optical path several times. In this way, the effective thickness of the cell is several times its actual thickness, greatly increasing the light absorption and carrier generation. Several constraints should be met to improve the light absorption. For example, the two outer surfaces of the cell must be non-parallel, and the antireflective optical coating on the front surface of the cell must be accounted for to maximise transmission. The symmetry of light transmission reduces the internal reflection upon the front surface. Moreover, if the incidence angle of the rays coming from inside on the top surface is greater than about 16 degrees, the light is completely reflected internally.

Barnett *et al.* [74] studied the behaviour of cell parameters open circuit voltage, VOC, and short circuit current, *Isc* from Z, ratio of effective optical thickness to actual thickness under weakly light absorption conditions.

A detailed discussion of light trapping principles will be given in Chapter 11.

#### **ACKNOWLEDGEMENT**

Declared none.

#### **CONFLICT OF INTEREST**

The author(s) confirm that this chapter content has no conflict of interest.

#### **REFERENCES**



#### **26** *Silicon Based Thin Film Solar Cells Ficcadenti and Murri*


#### *Basics of Thin Film Solar Cells Silicon Based Thin Film Solar Cells* **27**


#### **28** *Silicon Based Thin Film Solar Cells Ficcadenti and Murri*


© 2013 The Author(s). Published by Bentham Science Publisher. This is an open access chapter published under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/legalcode

## **Deposition of Thin Films: PECVD Process**

#### **Armando Menéndez\* , Pascal Sánchez and David Gómez**

*Energy Area, ITMA Materials Technology, Parque Empresarial P.E.P.A., c/Calafates 11, Parcela L.3.4, 33417, Avilés (Asturias) Spain*

**Abstract:** Plasma enhanced chemical vapor deposition technique plays a key role in the development of solar cells based on amorphous and microcrystalline silicon thin films. The deposition process depends strongly on physical and chemical interactions in the plasma. Subsequently, the film properties are dependent on different parameters such as power and frequency, the substrate temperature, the gas pressure and composition, the magnitude and the pattern of the gas flow, the electrode geometry, *etc.* The aim of this chapter is to discuss all effects of these parameters in detail.

**Keywords:** Plasma deposition, deposition rate, solar cell, PECVD system, flow rate, high frequency, amorphous silicon, microcrystalline silicon, large area, electrode, production system, roll-to-roll, photovoltaic, thin film, vapor deposition, substrate, microstructure, cluster configuration, in-line configuration, bandgap.

### **1. FUNDAMENTALS OF CVD PROCESS**

### **1.1. Definition**

Over the last years, Chemical Vapor Deposition (CVD) has emerged as one of the most interesting deposition techniques in industry. In spite of being a mature and well-known technology, recent developments (for example, new plasma sources or novel activation methods for low temperature deposition) have allowed CVD to be used successfully in different fields, such as microelectronics, optics, manufacturing or photovoltaics.

Chemical Vapor Deposition may be defined as a deposition technique in which a solid is obtained on a heated surface from a chemical reaction where the precursor or precursors are introduced in the vapor phase. The reaction mechanisms are usually considered as atomistic, that is, the deposition takes place atom by atom or molecule by molecule. As an example, Fig. **1** represents a CVD reaction where A and B are precursor gases and C is a solid product of this reaction acting as a coating on a given substrate.

CVD has many advantages when compared to other deposition techniques as (i) the process allows a high quality conformal deposition, even in complex three dimensional structures, with aspect ratios above 10:1 [1], (ii) the deposition rates are usually high, which leads to competitive industrial implementation and (iii) the CVD equipment is simple and flexible. In addition,

**Address correspondence to Armando Menéndez:** Energy Area, ITMA Materials Technology, Parque Empresarial P.E.P.A., c/Calafates 11, Parcela L.3.4, 33417, Avilés (Asturias) Spain; Tel: +34 985129120 (ext. 351); Fax: +34 985129008; E-mail: a.menendez@itma.es.

#### **30** *Silicon Based Thin Film Solar Cells Menéndez et al.*

although CVD is only considered as a deposition technique, its availability for the synthesis of nanomaterials in different shapes (nanotubes, foams, whiskers, fibers, *etc.*) has attracted a great deal of attention in the last years and CVD represents a commercial way of fabricating nanoparticles, carbon nanotubes [2], graphene [3], *etc.*

On the other hand, one of the main disadvantages of CVD is the need of heating the substrate to be coated up to very high temperatures, which disables the use of this technology for some applications. As will be explained later, the development of CVD techniques as new plasma activated methods or metal organic strategies have allowed the extention of the range of process application. Nowadays, some industrial CVD processes are carried out at temperatures below 200ºC. It is also important to remark in this section that some CVD processes still require inexpensive and toxic gas precursors. In other cases, this problem involves the gas by-products and special exhaust devices and cleaning procedures are required. A great effort has been made in the last decade for new processes to overcome these issues.

A thorough understanding of the CVD process specifies the analysis of different scientific and technological areas, such as thermodynamics, kinetic theory or fluid dynamics. From a chemical point of view, the proper selection of precursor gases leads to pyrolysis, oxidation, reduction, nitride and carbide formation, *etc.*, that allows the synthesis of a wide range of coatings. The way these reactions are activated (thermally, by plasma, by laser, *etc.*) split the CVD concepts into different CVD specific techniques such as Plasma Enhanced CVD, Hot Wire CVD, Metal-Organic CVD, as described in detail below.

### **1.2. The Physics of CVD**

Besides chemistry, CVD processes involve many other scientific and technological disciplines such as thermodynamics, plasma physics, fluid dynamics or growth mechanisms to be considered. In this section, a general overview of these aspects is given.

#### *a) Thermodynamics of CVD*

The satisfaction of thermodynamic laws is a necessary condition for any irreversible process. In this sense, thermodynamics is a general criterion that makes the hypothetical process be possible or impossible even though it does not state how long it will take for the possibility to be fulfilled. According to these laws, a desired CVD reaction will take place if the free energy changes the reaction, Gr, is negative. This analysis can be carried out starting from free energy values corresponding to the products and reactants, Gf (products) and Gf (reactants), respectively:

Gr = Gf (products)-Gf (reactants) < 0

Gr depends on the product's and reactant's nature, composition and dilution. The selection of initial products (gas precursors) on the basis of this analysis constitutes an important issue in order to achieve the optimal and favorable growth mechanism. It is also important to point out that some external factors such as pressure and temperature are also involved in estimating Gr. This determines the way that different CVD processes are activated.

The calculation of Gr is usually made by minimizing the Gibbs free energy, which delimits the thermodynamical equilibrium condition. When temperature, volume and pressure are considered as additional parameters this calculation becomes complicated and numerical methods are commonly used for this purpose (see, for example, [4]). These theoretical results are then compared with initial experimental processes.

#### *(i) Fluid Dynamics and Deposition Kinetics*

The knowledge of fluid dynamics and deposition kinetics represent a key issue in order to:


The analysis of a CVD process from a fluid-dynamical point of view clearly represents a complex problem as gas precursors are conducted through pipes and valves to a deposition chamber where a heterogeneous reaction takes place and gaseous by-products exhaust. This sequence is summarized in Fig. **2**.

**Figure 2:** Chemical Vapor Deposition sequence from a fluid dynamic perspective [1].

#### **32** *Silicon Based Thin Film Solar Cells Menéndez et al.*

In general, processes and reactor design are considered in order to obtain the laminar flow, that leads to null velocity in the substrate surface and creates a boundary layer where the reaction takes place. The thickness of this layer is proportional to R-0.5, where R represents the Reynolds number. In a similar way, a boundary layer is also created in the upper wall of the reactor and a velocity profile created (Fig. **3a**). Following a similar procedure for temperature, a temperature profile is generated (Fig. **3b**).

**Figure 3:** Velocity (a) and temperature (b) profiles along a tubular reactor geometry [1].

### *(ii) Growth Mechanism*

The deposition mechanisms governing CVD are still a focus of controversy and nowadays complex thermodynamic and atomistic nucleation theories coexist [1]. From a practical point of view, three important concepts have to be considered so as to understand the nature and properties of CVD coatings:

*Epitaxy:* Consists of the growth of a crystalline layer on a crystalline substrate of the same material (homoepitaxy) or different (heteroepitaxy). The growth of epitaxial layers leads to high quality materials and it is commonly desired in the semiconductor industry. In the case of heteroepitaxy, this is only possible when the lattice constants of the coating and substrate are similar. For lattice mismatches above 10%, the use of buffer (intermediate) layers has to be considered.

*Gas Phase Precipitation:* Under some experimental conditions, the CVD reaction can be carried out in the gas phase instead of the substrate, which leads to the subsequent precipitation of particles in the surface. Although this has been seen as a source of defects primarily affecting coating homogeneity, this is currently being applied to the manufacturing of powder and nanoparticles.

CVD processes are always related to thermal stresses, as the sample is heated and cooled in a predetermined sequence. Once the CVD coating is formed, this stress can lead to crack generation. In order to solve this difficulty, buffer layers are considered when low temperature processes such as plasma assisted or metal-organic CVD processes are not possible.

Basically, the structure of CVD materials is classified according to three different morphologies: columnar, faceted-columnar and equiaxed grains, as shown in Fig. **4**.

*Deposition of Thin Films: PECVD Process Silicon Based Thin Film Solar Cells* **33**

**Figure 4:** Different morphologies of CVD grown materials. (a) columnar, (b) faceted-columnar and (c) equiaxed grains [1].


The deposition parameters, such as temperature, pressure, saturation and selected reaction sequence.

### **2. CLASSIFICATION OF CVD TECHNIQUES**

As previously commented, CVD is a coating technique where gas precursors are introduced in a deposition chamber and react, giving as results a solid product (coating) and gaseous by-products. This definition represents a broad concept and comprises different specific CVD techniques grouped according to different criteria.

Depending on the **experimental conditions**, CVD can be classified as Atmospheric Pressure CVD, Low Pressure CVD and Ultrahigh Vacuum CVD. In a similar way, CVD processes have emerged considering the **activation mechanism** of the CVD reaction. This leads to thermally (Thermal CVD, Hot Wire CVD), optically (Photo CVD, Laser CVD) or plasma (Plasma Enhanced CVD, Microwave CVD, Remote Plasma Enhanced CVD) activated processes. Finally, it is important to remark on the CVD techniques based on the **nature of precursors**. Aerosol assisted CVD, Direct Liquid Injection CVD and Metal Organic CVD are some examples of these processes.

Although the description of all these techniques is not approached in this work, some of the most representative are briefly depicted. Those that are usually implemented in solar cell production have been selected.

*Low Pressure Chemical Vapor Deposition (LPCVD):* In the case of LPCVD, the coating is deposited at a low pressure in a heated CVD reaction chamber. Basically, the LPCVD configuration is similar to a conventional CVD chamber (heaters, temperature control, gas inlet and exhaust, *etc.*), adding a vacuum system (pumps, valves and sensors).

#### **34** *Silicon Based Thin Film Solar Cells Menéndez et al.*

LPCVD processes lead to highly reproducible, uniform and throughput coatings and are commonly used in the semiconductor industry for the development of thin film dielectrics (SiO2, Si3N4, Al2O3), thin film conductors and semiconductors (polysilicon, molybdenum, TiSi) and hard coatings (TiN, SiC, WC).

LPCVD is used in the photovoltaic sector for the development of transparent conductive oxides. In particular aluminum and boron doped zinc oxide materials are commonly obtained by means of this technique [7]. The process allows a precise control of the roughness surface. This fact represents an important issue for this application, since texturing favors light trapping mechanisms and subsequent increase in solar cell efficiency [8].

*Plasma Enhanced Chemical Vapor Deposition (PECVD).* The PECVD process uses electrical energy to create a glow discharge, plasma, and the energy is transferred into a gas mixture. Plasma is achieved by having a radio frequency in between two electrodes and energy is used to ionize and transform the precursor gases into reactive radicals, ions, neutral atoms, and molecules. Since the formation of the reactive and energetic species occurs in the gas phase by collision, thermal activation is minimized and the substrate can be maintained at low temperatures. This constitutes one of the most interesting advantages of PECVD, decreasing operating temperatures to below 200ºC in many cases. This permits the use of polymeric materials such as substrate. In a similar way, PECVD allows the fabrication of thin film coatings with excellent mechanical properties, as stress can easily be controlled and deformation and cracking are avoided.

The PECVD process has been widely used in microelectronic and optoelectronic applications for the deposition of semiconductor and dielectric materials. In photovoltaic, this technique has allowed the development of silicon based thin film solar cells as an interesting alternative to conventional crystalline and polycrystalline technologies.

*Hot Wire Chemical Vapor Deposition (HWCVD).* Hot Wire CVD (also called Catalytic CVD) is a low pressure CVD process based on the decomposition of precursor sources on a hot filament (1200ºC– 2000ºC) [9]. The solid product is then deposited on the substrate, heated by an external source or by the filament itself. A schematic view of a typical HWCVD reactor is presented in Fig. **5**.

**Figure 5:** Schematic view of a HWCVD reactor [10].

#### *Deposition of Thin Films: PECVD Process Silicon Based Thin Film Solar Cells* **35**

The main advantages of HWCVD when compared to other CVD techniques are:


*Metal-Organic Chemical Vapor Deposition (MOCVD).* MOCVD is a technique that was initially developed in the 60s for the deposition of high quality semiconductors, in particular indium phosphide and indium antimonide. Metallo-organic compounds are usually referred to as molecules formed by a metallic (or semiconductor) atom bound to one or more atoms of an organic hydrocarbon group. Under appropriate experimental conditions, a pirolytic CVD reaction occurs and metallic (or semiconductor) coatings can be obtained with good quality, thickness control and epitaxy. In addition, this technology represents the only way to obtain some materials such as coatings in the nanometric range.

Although MOCVD has been widely used for microelectronic and optoelectronic applications due to the high requirements in these sectors, the process has also been extensively used as a deposition technique for the fabrication of solar cells. Initial studies were made in the use of MOCVD for the development of gallium based materials (GaAs, GaInP, AlGaAs, GaInAs) [14, 15]. In a similar way, MOCVD is currently used in the development of buffer layers for CIGS cells [16] and CdTe compounds [17] and novel transparent conductive oxides with enhanced properties [18].

#### **3. PLASMA ENHANCED CHEMICAL PLASMA DEPOSITION**

Today, silicon-based thin-film solar cell is a well-established technology and must be taken into account in the race to achieve the important goal of cost reduction of photovoltaic devices. First hydrogenated amorphous silicon (a-Si (-H)) devices were carried out by Sterling and Swann [19] and by Spear and Lecomber [20] using a reactor with a silane (SiH4) glow discharge induced by radio frequency (RF) voltages. This was the base of the nowadays plasma enhanced chemical vapor deposition (PECVD). An important advantage of PECVD deposition is that the deposition temperature of a-Si (-H) is usually quite low, between 150ºC and 350ºC which allows the use of a variety of low cost materials such as a substrate, glass, stainless steel and flexible plastic foils. Since the pioneer experiments, a wide range of different deposition techniques have been investigated with the intention of achieving higher material quality and increasing the deposition rates. RF-PECVD [21, 22], "high power high pressure" regime RF-PECVD [23, 24], very high frequency (VHF) PECVD [25, 26] and microwave (MW) assisted CVD [27, 28] are some of the main techniques being extensively explored. However, although its main drawback is its low deposition rate (1Å/s–2Å/s), the RF-PECVD using an excitation frequency of 13.56MHz is still the most widely used technique today both in laboratory and industrial scales to manufacture silicon-based thin film solar cells.

In this chapter, an overview is proposed of the deposition of a-Si (-H) and microcrystalline silicon (µc-Si) based thin films by using these different techniques. Deposition conditions, mechanisms of layers growing, advantages and drawbacks of the different methods are extensively described.

#### **3.1. Amorphous Silicon Deposition by PECVD**

#### *3.1.1. RF-PECVD Technique*

Although different ways of depositing amorphous silicon have been investigated, the RF-PECVD, considering an excitation frequency of 13.56MHz, is still the most widely used deposition technique. RF-PECVD systems may be designed with different geometries, generally with substrate and electrodes placed horizontally for research devices and vertically for industrial processes.

#### *PECVD System*

Basically, a PECVD deposition system is composed of the following parts:


In cluster configuration systems, (Fig. **6**), a transfer system is employed to move the sample inside the vacuum system between various deposition chambers. Gate valves are used to separate the different chambers.

*Deposition of Thin Films: PECVD Process Silicon Based Thin Film Solar Cells* **37**

**Figure 6:** RF-PECVD multi-chamber (Elettrorava-ITALY) for silicon based thin film depositions installed at ITMA Materials Technology, Energy Area (Avilés, Spain).

### *Film Growth: Basic Chemical Approach*

When a process is working, SiH4 molecules will be dissociated inside the plasma by collisions with electrons, creating active particles called radicals. The growth of a-Si (-H) film is accomplished by attaching these reactive particles to the surface of the growing film. a-Si (-H) film growth from SiH4 plasma in a PECVD system is a complex phenomenon and several spectroscopic techniques, such as optical emission spectroscopy, optical absorption spectroscopy and residual gas mass analyzer, have often been used to study the plasma and to determine the concentration of different species inside the reactor. From the results obtained, it seems that the SiH3 radical is the main responsible molecule for the growth of high-quality a-Si (-H) films [29]. SiH3 radical does not readily bond to the growing film but diffuses over the surface until it finds a dangling bond due to the fact that most of the growing substrate is ended by H2 [30]. Bonding of the SiH3 to the growing surface requires available dangling bonds, which are created when H2 is removed from the surface by thermal excitation or by abstraction by a SiH3 radical (in that case a dangling bond and a SiH4 molecule are formed).

Other possible radical forms involved in the plasma during the process, such as SiH2 and higher SiH4 radicals contribute much less to the growth but they play an important role in determining the properties of the film. The SiH2 and higher SiH4 radicals have higher sticking coefficients than SiH3 and can be incorporated directly in the H2 terminated surface [31]. The presence of these radicals in the plasma should be avoided because their contribution to the growth results in poor quality films.

### *Process Conditions*

Typical deposition parameters to obtain uniform films of device quality a-Si (-H) in a laboratory RF-PECVD deposition system are the pressure, the substrate temperature, the electrode spacing, gas flows and RF power density.

*Pressure*: the pressure range is usually set between 500mTorr and 800mTorr. Low pressure generally allows uniform deposition whereas high pressure is used for microcrystalline silicon films preparations.

*Substrate temperature*: is usually fixed between 150ºC and 350ºC. Low substrate temperature allows the incorporation of more H2 in the layer and a slight increase of the bandgap of a-Si (-H) is reached. However, it is important to notify that a lower substrate temperature than 150ºC would induce the formation of silicon polyhydride powder.

*RF power density*: one of the main parameters leading the deposition rate is the power absorbed by the plasma. In fact, by applying a high power, a high electron density and electron temperature in the plasma is achieved. As a consequence, more SiH4 molecules are dissociated in SiH3 and other radicals which contribute to a higher deposition rate. The RF power density should be set between 20mW/cm2 and 50mW/cm2 for a capacitively coupled reactor. Below 10mW/cm2 it is difficult to maintain the plasma. Higher power is desirable but, above 100mW/cm2 , silicon polyhydride powder can appear due to rapid reactions in the gas.

*Electrode spacing*: in an RF a glow discharge reactor is usually set between 1cm and 5cm for a-Si (-H) deposition. Narrow spacing is more desirable for a uniform deposition, whereas a large one offers an easier condition to maintain the plasma.

*Flow rates*: the flow rate required depends on the area of the reactor plates and the deposition rate. Some of the silicon atoms in the gases directed into the chamber are deposited onto the substrates or the chamber walls; the remainder gets pumped to the exhaust. For a research system with a 200cm2 electrode area and for the deposition of a-Si (-H) at the rate of 1Å/s-2Å/s, only around 20sccm of SiH4 flow is necessary. For the deposition of high-quality, stable a-Si (-H) material, a H2 dilution at an appropriate level is also used. Depositing a 350nm thick a-Si (-H) intrinsic layer (i-layer) takes from 30 to 60 minutes which is an important drawback for industrial production. Therefore there is a lot of investigation focused on increasing the deposition rate with the aim of reaching 10Å/s–20Å/s.

Another important aspect of the growth of high-quality a-Si (-H) films is the presence of contaminants, such as oxygen, carbon, nitrogen, or metal elements. Concentration levels of O, C, and N higher than 1*.*3×1019, 2*.*2×1018, and 1*.*7×1017at/cm3 , respectively, in the i-layer show poorer solar cell performance mainly due to the difficulty of photogenerated carriers diffusion. To avoid the presence of contaminants, a high vacuum level (<1x10-7mTorr) is desirable prior to the introduction of the bearing gas. On the other hand, H2 dilution of the SiH4 gas mixture during a-Si (-H) deposition (both for intrinsic and doped layers) has been found to reduce the density of defect states, to improve the stability of the material against light-soaking effects and to show better solar cells performance. However, as the H2 increases, the deposition rate declines.

### *3.1.2. VHF-PECVD Technique*

The main drawback of the a-Si (-H) achieved by RF-PECVD is its low deposition rate (1Å/s– 2Å/s). As mentioned in the previous section, high RF power allows the increase of the growth rate but silicon polyhydride powder may also appear. The VHF-PECVD, with an excitation frequency between 30MHz and 300MHz, is a solution as it presents the advantage of high plasma densities and low ion bombardment. Therefore, it has been widely used to deposit silicon thin films.

The Institute of Microtechnology of the University of Neuchâtel (IMT) was pioneered as a very high frequency glow discharge (VHF-GD) deposition technique and showed how it was possible

#### *Deposition of Thin Films: PECVD Process Silicon Based Thin Film Solar Cells* **39**

to considerably increase a-Si (-H) deposition rates. Since then, it has been demonstrated [32] that, at constant power, the increase of the frequency shows a linear increase of the deposition film. Several research groups have found higher deposition rates, up to ten times, maintaining good quality a-Si (-H) films. Applying higher excitation frequencies allows the modification of the electron energy distribution function in plasma. As a consequence, faster dissociation rates of source gases and higher deposition rates can be observed. Moreover, the VHF deposition technique allows the application of higher power densities in plasma at the same time as a powder free operational regime is established [33] due to fundamental physical changes in the capacitively coupled glow discharge plasma. As a consequence of these physical modifications (in the plasma impedance and with a reduction of the sheath thickness), a much better coupling of the RF power into the bulk plasma rather than into the sheath can be obtained at higher excitation frequencies. Thus, higher electron densities and better SiH4 dissociation in the bulk plasma, as well as increased radical and ion flux onto the growing surface, can be achieved resulting in an increase in the deposition rate.

Although the advantages of using VHF deposition for high-rate growth have been clearly demonstrated, the main challenges to apply VHF-PECVD on an industrial scale are:


#### *3.1.3. Alternatives Deposition Techniques*

*High pressure RF-PECVD mode*: in this mode, higher gas pressures between 4 to 10Torr instead of about 500mTorr (conventional deposition mode) are employed. The main objective of this high pressure mode is to increase the ions collisions in the plasma in order to reduce their energy and offer a softer impact of the substrate surface. As a consequence, it is possible to highly increase the power fed to the plasma and also the deposition rate. Thin film solar cells based on amorphous silicon have been produced with a deposition rate of 12Å/s with a stabilized efficiency of 6.5% [23]. The depositions were carried out under high pressure (4Torr-7.5Torr) and high RF-power density (270mWcm<sup>−</sup><sup>2</sup> –530mWcm<sup>−</sup><sup>2</sup> ) at 190ºC using a gas mixture of SiH4 and H2. It is shown that the increase of SiH4 flow rate in the gas mixture as well as of the RF power can lead to higher concentration of reactive species and, therefore, can stimulate secondary reactions in the gas phase which lead to the growth of microcrystalline silicon. An increase has been observed in the bandgap and the open circuit voltage (Voc) for high rate a-Si (-H) cells compared to standard a-Si (-H) prepared at a low H2 dilution and at a low rate (1.5Å/s). Therefore, the results obtained make a-Si (-H) into interesting candidate for top cells in a-Si (-H)/a-Si (-H) stacked solar cells.

*Microwave frequency (MW)*: glow discharge deposition at a microwave frequency of 2.45GHz also allows very high deposition rates to be reached. Two chamber configurations have been studied; direct contact and remote mode between the MW plasma and the substrate. The first case has the advantage of high deposition rates (>100Å/s) but the deposited layers show poor optoelectronic properties. In contrast, the remote MW-PECVD method shows high-quality films.

#### **40** *Silicon Based Thin Film Solar Cells Menéndez et al.*

In this case, the plasma is generated, by MW excitation in a remote chamber, in a carrier gas such as He, H2 or Ar that passes through the MW zone toward the substrate which is located outside the plasma region. The excited carrier gas then excites SiH4 which is introduced into the chamber close to the substrate. The plasma is characterized by a high density of high energy electrons, which leads to a high dissociation rate. Another advantage is that the plasma can be maintained at low pressures (1mTorr). Furthermore, the concentration of SiH3 radicals can be sustained, while the concentrations of other radicals (SiH2, SiH, *etc.*) are minimized. Generally, the structural and optoelectronic properties of a-Si (-H) layers carried out by MW technique are worse than RFdeposited films. However, if only the very high deposition rate (for example 50Å/s) is considered, the MW-deposited films quality will be better than layers carried out by using RF and VHF techniques.

### *3.1.4. Amorphous Silicon Doped Layers*

The main aim of doping is to modify the electrical conductivity and its magnitude of layers that encompass the photosensitive one in order to establish an electrical field necessary for a correct extraction of the electrons generated in the intrinsic film. It is important to point out that a-Si (-H) solar cell cannot work successfully as a p-n junction because the diffusion length of charge carriers in doped a-Si (-H) is very small compared to single crystal silicon. For this reason, a relatively defect free intrinsic layer has to be inserted between the p type and n type layers for the generation of the charge carriers and the role of the doped films is to set up the electrical field.

The doping process is carried out by adding a controlled amount of special impurity so as to get defect density two or three orders of magnitude larger than intrinsic a-Si (-H). Pioneer works carried out by Spear and LeComber in 1975 [20] showed that a-Si (-H) could be doped by addition of boron and phosphorus.

The performance of solar cells strongly depends on the properties of the p-layer, generally called the "window layer" that should meet the requirements of high conductivity and low absorption. Unfortunately, boron tends to alloy with a-Si (-H) instead of doping it which leads to a strong reduction in the bandgap. This drawback can be solved by adding carbon (CH4) to the lattice. Moreover, boron originated from B2H6 tends to cluster within the network which also degrades the transmission of the layer. Other dopant gases can be used such as B(CH3)3, BF3, and B(C2H5)3, having claimed to lead superior p properties. On the other hand, boron from the p type layer may diffuse into the intrinsic one and lead to a back diffusion of the photogenerated electrons from the intrinsic into the p type layer. A possible solution is to incorporate a thin buffer layer at the p/i interface made of a-SiC (-H) with a low defect density.

#### *Physical Properties*

Typical criteria for intrinsic and doped a-Si (-H) layers for application in p-i-n or n-i-p type solar cells are listed in Table **1**.

#### **3.2. Microcrystalline Silicon Deposition by PECVD**

The term microcrystalline silicon (c-Si) designates a material containing amorphous tissues and crystalline grains (typically 20nm–30nm). The depositions are carried out at low temperatures

#### *Deposition of Thin Films: PECVD Process Silicon Based Thin Film Solar Cells* **41**

(<400ºC) by PECVD technique, commonly from a mixture of SiH4 and H2. Low temperature process allows the reduction of contaminations as well as to offer a better incorporation of H2 in order to passivate the electronic defects and grain boundaries. Fig. **7** shows an electronic microscope image obtained from n-type µc-Si layer.

**Table 1:** Physical properties of intrinsic and doped a-Si (-H). σd, dark conductivity; σph, photoconductivity; Eg, energy gap; Ea, activation energy; α, absorption coefficient; [H], hydrogen concentration.


Pioneer works were reported by Veprek and Marecek [34] in 1968 by using a chemical vapor transport technique with deposition precursors based on SiH4 related radicals and atomic H2 which plays a crucial role in layer growth. In 1979, Usui and Kikuchi [35] observed that it was easy to dope c-Si comparing with a-Si (-H). But the first c-Si layers, mainly due to their high defect density, own a poor quality level and it was concluded that it would be very difficult to manufacture solar cells based on c-Si intrinsic layer.

The use of c-Si as the active layer within a thin-film solar cell was not easy, for the following reasons:


Such as in a-Si (-H), one still always uses the p-i-n type configuration for manufacturing c-Si cells (instead of p-n junction) because the diffusion lengths are far too low, even though doping is far easier in c-Si than in a-Si (-H), and even though doped c-Si layers do not have additional defects introduced by the doping process. Consequently, in a first step, only p-type c-Si layers were used for incorporation within p-i-n type thin-film silicon solar cells, where the active intrinsic layer consists of a-Si (-H) [36], due to its high conductivity and low absorption coefficient in the visible range.

Another useful application is also for the tunnel/recombination junctions that form the connection between individual cells, in a double-junction (tandem) or triple-junction a-Si (-H) solar cell. In 1996, J. Meier and *et al.* [37] reported on a p-i-n type fully microcrystalline thin film silicon solar

#### **42** *Silicon Based Thin Film Solar Cells Menéndez et al.*

cells with an efficiency value of 7.7%. The intrinsic microcrystalline layer was carried out by using a gas purifier with low oxygen content and consequently it was observed that this c-Si solar cell was not suffering from a pronounced Staebler–Wronski effect.

**Figure 7:** Emission field secondary electron microscope image corresponding to n-type µc-Si layer.

Nowadays the best way to advantageously employ a fully c-Si solar cell is to combine it with an a-Si (-H) solar cell in a tandem system called the ''micromorph'' or ''hybrid'' concept and up till now, efficiencies up to 14.7% have been reached on laboratory scale.

High density of atomic hydrogen is a crucial condition for µc-Si [38] and it can be reached in different ways. The easiest one consists of increasing the hydrogen flow to the plasma. Higher plasma excitation frequency or plasma power are also valid solutions. One of the main drawbacks of µc-Si is its low absorption coefficient compared with a-Si (-H). Therefore, intrinsic layer with thickness of between 1µm-2µm is necessary. Consequently, important research lines are focused on high rate deposition regime (>5Å/s).

### *3.2.1. Effect of H2 Dilution on Layer Crystallinity and Microstructure*

In the usual type of PECVD reactor where the resulting layers are amorphous, pure SiH4 plasma is used for the deposition. If H2 is now added to the plasma, the layer quality is slowly altered and if the concentration of H2 is further increased, crystallites begin to deposit. Then the crystalline volume fraction rapidly increases until layers will be essentially microcrystalline. By increasing the H2 dilution of the plasma even more, the microstructure of the layers is varied and at high values of H2 dilution, high columns separated by cracks appear. The three following points can explain the effects of H2 dilution during the c-Si growth:

#### *Deposition of Thin Films: PECVD Process Silicon Based Thin Film Solar Cells* **43**


For the same reasons, sufficiently large H2 dilution induces the formation of microcrystalline Si and the best microcrystalline solar cells quality is deposited near the threshold concentration. For very high values of H2 dilution, cracks that can provoke shunts in the solar cells and also act as channels by which contamination (*e.g.* oxygen) can enter into the layer appear and are responsible for a non usability of this material for solar cells. The amorphous phase is the first phase deposited. A minimum thickness called the incubation phase is generally needed before a localized phase transformation takes place, which is called nucleation. Finally from the nucleation centers the crystals start their growth. Other deposition conditions than the H2 dilution level influence in the transition from amorphous to microcrystalline. High substrate temperatures (above 300ºC) and low substrate temperatures (below 250ºC) require higher H2 dilution in order to reach the amorphous/microcrystalline transition. This is respectively due to the low sticking coefficient of H2 and to the low surface diffusivity of H2 during growth.

### *Physical Properties*

Typical criteria for intrinsic and doped c-Si layers for application in p-i-n or n-i-p type solar cells are listed in Table **2**.


**Table 2:** Intrinsic and doped c-Si physical properties. σd, dark conductivity; σph, photoconductivity; Eg, energy gap; Ea, activation energy.

#### *3.2.2. High Pressure Depletion (HDP) RF-PECVD*

The use of HPD allows that a great amount of atomic H2 generated in the plasma, owing to the depletion of SiH4, promotes crystallization without increasing ion bombardment under a high deposition pressure condition [39]. The HPD method has the advantage that good crystalline c-Si film can easily be obtained in a large area by optimizing the deposition condition without modifying the deposition system. However, it is also necessary to have plasma conditions where SiH4 is depleted and relatively more H2 is present in the plasma in order to obtain μc-Si rather than a-Si (-H) growth. Non uniform layers, high H2 consumption and powder formation are some of the problems that have to be faced when optimizing HPD deposition. Moreover, film quality parameters such as defect density and crystallinity deteriorates gradually with an increasing growth rate of over 50Å/s.

Researchers from Juelich Institute (Germany) reported μc-Si solar cells with deposition rates of 5Å/s by using 13.56MHz [40]. Higher values (11Å/s) were achieved at a frequency of 95MHz [41] and an excellent efficiency of 9.8% was obtained. On the other hand, Suzuki [42] has improved the film qualities such as crystallinity and defect density of c-Si films (2.6x1016cm-3) at a growth rate of 58Å/s by using a triode technique and a shower-head cathode combined with the HPD deposition conditions. High input powers are also an effective method for increasing the growth rate by keeping the low defect density because the high electron density and the low electron temperature can be simultaneously obtained [43]. It was reported [44] that, employing high pressures of up to 24Torr, very high growth rates of c-Si photovoltaic layers can be reached. Future investigation is now focused on designing a production type large area reactor based on a combination of HPD and VHF principles [45].

#### *3.2.3. Deposition of µc-Si by VHF-PECVD*

A high deposition rate with uniform layer properties is necessary due to the requirement of a relatively large thickness of the microcrystalline absorber (1μm–2μm) in order to be competitive for industrial production. Up to now, VHF-PECVD [46] and RF-PECVD [47] in the high power, high pressure depletion regime allow the best solar cell results to be reached. VHF plasmas allow high deposition rates due to changes in the plasma leading to an enhanced dissociation of the SiH4 in the plasma. Moreover, due to a reduction of the energies of the ions impinging on the growing surface observed at higher frequencies, a "softer" plasma is led that induces a reduction of the defect creation in crystallites. These results might explain why VHF plasmas allow a better growth of c-Si as compared to conventional plasma deposition at 13.56MHz. These phenomenon, prevalent in VHF plasmas, are also propitious to the growth of high-quality c-Si layers at high rates. Some authors [48] have investigated that crystallite size increases, as excitation frequency (fexc) is increased. Because the deposition rate is one of the main existing bottlenecks when one wants to reduce the production cost of c-Si solar cells and modules, this increase is a significant advantage for an industrial plant. Finally, one also has to take into account the powder limit factor which can be defined as the maximum power level or maximum deposition rate above which a significant amount of powder is formed in the reactor.

High deposition rates from 4.5Å/s to 45Å/s at 60MHz were achieved by Gordjin *et al.* [49] and microcrystalline single junction solar cells efficiencies of 10% and 6.4% were reached, respectively. This increase by a factor of ten of the deposition rate involved a higher defect density (growing in the same proportion) was also found.

It is important to notify that the curves of the deposition rate *vs.* excitation frequency possess, in general, a maximum at a certain "optimal" frequency and show, thereafter, a decrease of the deposition rate for yet higher frequencies. This decrease can be attributed to engineering aspects such as reactor design. On the other hand, fundamental physical changes in the capacitivelycoupled glow discharge plasma can explain the general trend of an increase in deposition rate with increasing excitation frequency. As the excitation frequency is increased, the sheath thickness decreases and the plasma impedance significantly changes.

Using the VHF-PECVD technique, researchers at the University of Neuchâtel in the 1990s succeeded in manufacturing the first hydrogenated microcrystalline silicon (μc-Si) cells at 200°C with reasonable efficiencies [50]. Importantly, the efficiencies of up to 4.6% of these cells were stable under light soaking conditions, giving hope to significantly elevate the stable module efficiency more for a-Si (-H) modules. Y. Nakano *et al.* [51] found that the distance between the substrate and the electrode has a substantial influence in order to satisfy both high rate and highquality deposition of c-Si. Gap length of 10mm or less allows a cell efficiency of 8.5% at a deposition rate of 3.1nm/s in c-Si single junction p-i-n solar cells to be obtained. Finally, new research shows that the microstructure evolution in c-Si films can be controlled by VHF power profiling [52]. The profiling parameters such as the amount and the rate of change in VHF power allows a control of the microstructure evolution and a reduction of ion bombardments on the growth surface. Using this method, a significant improvement in the solar cell performance is achieved. A high conversion efficiency of 9.36% was obtained for a single-junction c-Si p-i-n solar cell at a deposition rate of 12Å/s.

### *3.2.4. Microwave (MW) CVD*

In MW plasmas, high deposition rates are achieved for μc-Si due to the reduction of the ion bombardment compared with the standard 13.56MHz plasma deposition process. The use of MW allows high SiH4 decomposition rates and a large amount of H2 etching of the film growth surface, as required for microcrystalline film formation. Research on the application of MW technique for the deposition of c-Si has started recently, demonstrating the potential of high deposition rates [53, 54].

The effect of Ar dilution on the deposition process of μc-Si by MW-PECVD has also been investigated [28]. Ar helps to stabilize the MW plasma, in particular at high H2/SiH4 ratios and at low power conditions, but it has a detrimental effect on the density of the layers. No significant effect of Ar on the growth rate of the layers was observed. The structure of the layers becomes more amorphous and the layers contain more defects when H2 is partially replaced by Ar as a process gas. The main effect of Ar dilution to the growth of silicon layers in MW-PECVD is probably due to a change in plasma chemistry, where Ar metastable forms favor the formation of (unwanted) SiH2 species at the expense of SiH3 formation.

On the other hand, research has demonstrated the fast deposition of hydrogenated chlorinated microcrystalline Si (c-Si:Cl) films (27Å/s) with less volume fraction of void using a high-density MW plasma source of a SiH2Cl2–H2 mixture rather than those from SiH4 [55]. The role of chlorine in the growth of c-Si:Cl films is the effective termination of dangling bonds and the suppression of the excess film crystallization on the growing surface. Other authors report high-density MW plasma [56] obtained using a spokewise antenna in order to produce microcrystalline films from SiH4 (without H2 dilution and applying SiH4 depletion and low pressure) at a growth rate of 4.7nm/s and a low substrate temperature of 250ºC.

#### **46** *Silicon Based Thin Film Solar Cells Menéndez et al.*

#### *3.2.5. Light-Induced Degradation*

The Staebler–Wronski effect or light-induced degradation effect is a generalized defect of all kinds of a-Si (-H) layers and solar cells produced up till now. Not having, in general, any light-induced degradation seems quite surprising for c-Si solar cells [57]. But it is important to notify that, by the term c-Si, several different materials, showing appreciable differences such as crystallite orientation and form, microstructure and crystalline/amorphous volume fraction, can be considered. Therefore, it must be pointed out that certain types of c-Si layers may suffer from light-induced degradation [58].

### *3.2.6. Post-Oxidation*

Oxygen contained in the air will contaminate microcrystalline silicon layers when exposed to air over a period of weeks or longer. This phenomenon called "post-oxidation" induces a change in the Fermi level which is pushed towards the conduction band edge. Due to this, characterization measurement such as electrical conductivity and long-term electrical transport on c-Si layers are delicate. Microcrystalline silicon layers produced by high plasma power and strong H2 dilution, due to the possible cracks induced, are more susceptible to present post-oxidation than the more compact c-Si layers produced near the amorphous/microcrystalline transition [59]. Although post-oxidation is a severe problem for c-Si layer measurements, c-Si solar cells have shown to be unaffected by this problem. This may be mainly due to the sealing effects provided by the relatively thick TCO (transparent conductive oxide) and metallic contact layers, on both sides of the cell.

### **4. LARGE AREA DEPOSITION**

The solar cell production scale is very important for economic reasons. In order to accelerate the spread of solar cells and further expansion of the photovoltaic (PV) market, it is crucial to develop application systems that utilize building integration (*i.e.* walls of industrial factories, public buildings or architectural structures) as the final objective. These systems must be made up of large area photovoltaic devices. a-Si (-H) thin film has been the most promising material in the PV application, especially for low cost and large area solar cells. Therefore, a-Si (-H) thin film solar cells technology is suitable to achieve this purpose. Moreover, in the last few years, the development of tandem solar cells consisting of a-Si (-H) top cells and microcrystalline silicon (µc-Si) bottom cells are promising for the achievement of high conversion efficiency.

For the cost-effective mass production of thin film silicon solar cells, the industry requires higher deposition rates and uniform film thickness over large areas, while maintaining a high quality. Consequently, it is necessary to have suitable deposition techniques capable to satisfy these requirements, especially in the case of µc-Si solar cell, where intrinsic layer thickness of around 1.5µm is used due to the low absorption coefficient. PECVD deposition technique is particularly suitable for producing thin films for large areas, although some design modifications are necessary when going from small to large areas in order to maintain the material quality and the film's uniformity.

The ultra high vacuum (UHV) used in laboratory scale deposition equipment is required to reduce contaminant incorporation. However, the UHV is very difficult to maintain in sufficiently large

#### *Deposition of Thin Films: PECVD Process Silicon Based Thin Film Solar Cells* **47**

size reactors and cannot be applied to large area equipment due to excessive costs. An approach used to simulate UHV conditions in large area reactors is the double shell geometry or plasma box configuration [60], and it is widely used in production systems. In this configuration, the plasma box forms an enclosed, separately pumped volume within the deposition chamber as a double shell, in which plasma is confined between the electrodes and the substrate, the temperature is uniform and the deposition volume is protected from impurities. The outer shell is pumped to a low pressure while the plasma box, containing the substrate, is pumped *via* a throttle valve to the process pressure. In systems without a plasma box configuration, similar low contamination levels can be obtained by using a continuous flow arrangement using high purity gases.

VHF-PECVD is a particularly suitable technique for large scale thin films deposition, because it provides high deposition rate plasma reactors and a good uniformity of the film thickness at high power. The field of VHF-PECVD in terms of high rate and high quality deposition has been active since the late 1980s, when various researchers reported deposition rates improvements on a-Si (-H) thin films [61, 62]. Subsequently, a study on a-Si (-H)/µc-Si tandem solar cells using the same deposition technique was reported from Neuchatel University (Switzerland) in the mid-1990s [37, 50]. However, the high frequencies studies were performed in small reactors and they needed to be upscaled in order to meet the large area requirements for industrial applications.

Results have been reported by using 13.56MHz PECVD in order to avoid the non-uniform voltage distribution across the electrode and, therefore, to facilitate a-Si (-H) and µc-Si thin films depositions on larger substrates. It was found that a high deposition pressure ("high pressure deposition regime") is one of the key factors necessary to obtain high deposition rates and still maintain a good thin film quality [26, 63].

As was mentioned before, VHF plasma is more suitable for high rate and high quality deposition thin films than conventional RF (13.56MHz) plasma by using the most common electrode design of two conventional plane parallel plates. However, in the field of large areas, a lot of electrical problems were reported when the frequency of the RF power source was increased [64-66]. These electrical problems occur when the electrode's dimension become comparable to a quarter of the free-space wavelength associated with the excitation frequency (5.53m at 13.56MHz but only 0.75m at 100MHz), and generates non-uniform voltage distribution across the electrode area. For example, at 80MHz power frequency, the limit in the size of parallel plate type electrodes to obtain uniform deposition is reported to be 40cmx40cm [67]. Consequently, results in inhomogeneous thin film RF plasma deposition in large-area reactors were obtained. The problem of voltage distribution across the electrode surface becomes important if the RF frequency is increased for a fixed reactor size, or at the standard 13.56MHz frequency for larger reactors.

Many attempts have been made by researchers to overcome the problem mentioned above to realize low cost and large area uniform VHF-PECVD systems for the deposition of a-Si (-H) thin films on square substrates higher than 1m2 . The aim of these attempts was to take special care in the power feeding system in order to introduce VHF power efficiently and uniformly to the plasma source. Three different electrode concepts are promising to overcome the non-uniform voltage distribution: ladder-shaped electrode, linear source and U-shapped array antenna. These designs are detailed below.

Murata *et al.* and Takeuchi *et al.* developed a novel CVD technique using an electrode of a laddershaped antenna, first at the conventional frequency of 13.56MHz [68-70] and later at VHF [26, 45, 71, 72]. A schematic diagram of the ladder-shaped electrode is shown in Fig. **8**. As can be seen, the RF power goes through a power divider and is applied to eight loading points on the laddershaped antenna.

**Figure 8:** A schematic of the ladder shaped antenna [71].

These studies resulted in a high quality and high deposition rate (15Å/s) thin films a-Si (-H) over large area glass substrates, up to 1.1mx1.4m [73], with distribution ±10% in both of them, and therefore, the subsequent development of a VHF-PECVD technique based on a ladder-shaped electrode suitable for the production of a large area and high quality a-Si (-H) thin film deposition.

On the other hand, Applied Films (Germany) developed the linear plasma source designed to decrease the active electrode area in one spatial dimension [74-76]. Through this configuration, uniform plasma with high density is obtained in the longitudinal direction by feeding power by multiple points. In this way, deposition of a-Si (-H) and µc-Si thin films on large area substrates (30cmx30cm) is achieved by moving the substrate in the direction perpendicular to the longitudinal dimension of the electrode (continuous deposition process). Using this continuous deposition method, which is also well suited for roll-to-roll processes, a high productivity can be achieved. Deposition rates up to 11Å/s and film homogeneity better than ±5% were obtained. Fig. **9** shows a sketch of the source module developed (LQ500 or LQ type plasma source) which is implemented as complete electrical units on rectangle flanges. The excitation frequency used was 81.36MHz, which represents a compromise between a high deposition rate and minimum rate film homogeneity over the source width. The number of power feed-ins is generally determined by the source width and the excitation frequency.

**Figure 9:** A schematic of the linear source (one dimensional electrode) [75].

The U-shaped array antenna consists of plural U-shaped loop antenna type electrodes where uniform deposition is realized by controling the power and the phase VHF power introduced to the electrodes [77-79]. This electrode was designed to generate and maintain plasma at a specific power frequency. Fig. **10** shows a schematic diagram of U-shaped electrode, where one end is connected to the chamber wall (grounded point) and the other end to the power-feeding point.

**Figure 10:** Schematic diagram of a U-shaped electrode [77].

In a VHF-PECVD system, a group of U-shaped electrodes are arranged to form one array of antenna, as can be seen in Fig. **11**. A pair of glass substrates is placed on both sides of array antenna, facing each other. Homogeneous deposition a-Si (-H) and µc-Si thin films on square glass substrates higher than 1m2 at 85MHz were obtained by using this configuration.

Since high plasma densities and low ion energies are key issues for efficient PECVD processes, microwave energy appears to be the best choice for high rates. However, the main problem is again how to sustain a uniform and steady plasma discharge over areas much larger than the wavelength of the applied wavelength power. To overcome this problem, the coaxial line plasma source appears to be the only industrially viable way of microwave PECVD (MWCVD) for large area depositions, in the area range higher than 1m2 [80].

### **5. PRODUCTION SYSTEMS**

Taking into account the configurations of the thin film solar cells, there are several possibilities for processing the different layers on large areas (m2 -size). In general, it is possible to distinguish different production schemes, such as single panel, batch (where several substrates are processed at the same time) and roll-to-roll processes. The final design of the PECVD equipment is determined by these possibilities.

**Figure 11:** Schematic side view of VHF-PECVD system with an array antenna [77].

In single panel and in batch processing, the deposition of all layers can be carried out either in a single chamber system or each individual layer is deposited in an independent chamber. Next, both possibilities will be compared.

#### **5.1. Single Chamber System**

This system has the advantage that p-i-n layer deposition takes place in a static deposition mode without movement of the substrates during the deposition process under vacuum conditions. Therefore, the capital investment is low compared to other configurations. However, precautions need to be taken in order to avoid cross contamination between the doped and the intrinsic layers depositions, particularly boron tailing from the p layer into the intrinsic layer. Consequently, several purge and pump-down steps are required to obtain a good quality and uniform layer.

As an example, a successful and proven single chamber PECVD system has been developed by Oerlikon Solar and is so-called "KAI" (concept of UNAXIS) [81]. This system is based on the plasma box concept and large area deposition up to 5m2 has already been demonstrated. In KAI 1200 system, 20 reactors operate in parallel and, therefore, 20 sheets of glass, with a size of 1.4m2 , can be processed simultaneously.

#### **5.2. Multichamber System**

The multichamber system configuration has the advantage that the deposition parameters such as temperature, internal geometry or even the discharge frequency can be optimized for each

#### *Deposition of Thin Films: PECVD Process Silicon Based Thin Film Solar Cells* **51**

individual layer. However, the investment cost is quite large compared with the single chamber configuration. Besides, the size of the panels may be limited. Two types of multichamber configurations can be distinguished, depending on the movement of the substrate during the deposition process.

### *5.2.1. In-line Configuration*

An important challenge for the cost effective mass production of silicon thin film solar cells is the development of highly productive dynamic in-line deposition systems, although it must be noted that the equipment cost is very high, because special isolation chambers and vacuum valves are needed between the deposition chambers.

Some industrial lines for the dymanic in-line deposition of a-Si (-H) and µc-Si have been developed to demonstrate the feasibility of this configuration, based on MWCVD [27, 28], Ushaped electrode [79] or linear plasma source [76], all of them in combination with moving substrates. In Fig. **12** a schematic view of an example of in-line deposition system consisted of three deposition chambers (p-i-n layers) and a load lock to charge the carrier is shown. Note that the substrate is located on the grounded carrier and moves horizontally inside the tunnel.

**Figure 12:** Schematic view of an entire in-line deposition system [76].

#### *5.2.2. Cluster Configuration*

This configuration has all the advantages of the multichamber system, *i.e.* control of the deposition parameters in each individual layer, complete control of the level of dopants and other contaminants, lower investment than in-line configuration due to the fact that transport and isolation chambers can be shared by many deposition chambers, *etc.* In addition, this configuration

#### **52** *Silicon Based Thin Film Solar Cells Menéndez et al.*

makes it possible that the transfer from the laboratory to the production scale represents only a small step. Applied Materials has developed a standard PECVD production equipment based on cluster configuration (model AKT) to deposit silicon thin films on large areas [82]. This equipment is basically the same design as in a small area laboratory multichamber system [83]. In Fig. **13** a scheme of a cluster PECVD configuration is represented.

**Figure 13:** Schematic of the cluster PECVD configuration [83].

**Figure 14:** Schematic diagram of a roll-to-roll a-Si (-H) alloy triple-junction solar cell processor [85, 86].

### *5.2.3. Roll-to-Roll Configuration*

Another important PECVD configuration for the development of low-cost photovoltaic modules based on a-Si (-H) solar cells on flexible substrates in a large scale production is a dynamic roll-toroll method. Various research and industrial groups have developed their own device structures and processes, such as United Solar [84-87], Helianthos project [88], VHF-Technologies [89] and Fuji Electric [90], which uses the "stepping" roll-to-roll (non continuous motion). In all of these processes, the transport mechanism can be cheaper than in most in line systems described before. As an example, Fig. **14** illustrates the roll-to-roll triple-junction deposition scheme followed by United Solar, where a roll of 127µm thick stainless steel (SS) substrate goes through four consecutive roll-to-roll machines first to wash, and then to deposit the back reflector, triplejunction structure, and top conductive layer. The width of the SS rolls used is 356mm, and the length is 2.59km.

One of the most important problems is to prevent cross contamination due to the fact that all deposition zones are connected to each other. This problem was solved by Energy Conversion Devices by using a laminar gas flow through a constant geometrical cross section opposite to the diffusion gradient of the dopant gasses.

#### **ACKNOWLEDGEMENT**

Declared none.

### **CONFLICT OF INTEREST**

The author(s) confirm that this chapter content has no conflict of interest.

#### **REFERENCES**


#### **54** *Silicon Based Thin Film Solar Cells Menéndez et al.*


#### *Deposition of Thin Films: PECVD Process Silicon Based Thin Film Solar Cells* **55**


#### **56** *Silicon Based Thin Film Solar Cells Menéndez et al.*


#### *Deposition of Thin Films: PECVD Process Silicon Based Thin Film Solar Cells* **57**


© 2013 The Author(s). Published by Bentham Science Publisher. This is an open access chapter published under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/legalcode

**58** *Silicon Based Thin Film Solar Cells,* **2013***,* **58-80**  *Send Orders of Reprints at reprints@benthamscience.net*

# **CHAPTER 3**

## **Sputtering of Thin Films**

## **Paolo Rava\***

*Elettrorava SpA, Via Don Sapino 176, 10078 Venaria, Torino, Italy* 

**Abstract:** Sputtering is one of the most widely used techniques for deposition of thin films. This chapter reviews the physical foundations of sputtering in a plasma and its application to the deposition of thin films. Different sputtering techniques are described and their advantages and disadvantages are highlighted.

**Keywords:** Sputtering, plasma, glow discharge, thin films, magnetron cathode, ion beam, deposition, targets, ionization, gases.

### **1. INTRODUCTION**

Sputtering is a process whereby atoms are ejected from a solid target material due to the bombardment of the target by energetic particles [1]. It is commonly used for thin-film deposition, etching and analytical techniques.

### **2. PHYSICS OF SPUTTERING**

Physical sputtering is driven by momentum exchange between the ions in an ionized gas (plasma) and the atoms in the solid material, as a result of collisions [1-3]. The primary particles for the sputtering process are supplied in general by either a plasma generated by a cathode or by an ion source (Fig. **1**).

The figure illustrates the effect of an incident gas atom from the initial impact collision onto a target surface. This generates primary, secondary, tertiary and quaternary recoils of the target atoms. Two of the atoms are shown being ejected from the sample, *i.e.* sputtered.

The incident ions set off collision cascades in the target. When such cascades recoil and reach the target surface with an energy above the surface binding energy, an atom can be ejected. The average number of atoms ejected from the target per incident ion is called the sputter yield and depends on the ion incident angle, the energy of the ion, the masses of the ion and target atoms, and the surface binding energy of atoms in the target. For a crystalline target, the orientation of the crystal axes with respect to the target surface is also relevant.

Physical sputtering has a well-defined minimum energy threshold which is equal to or larger than the ion energy at which the maximum energy transfer of the ion to a sample atom equals the binding energy of a surface atom. This threshold is typically in the range 10–100 eV.

**<sup>\*</sup>Address correspondence to Paolo Rava:** Elettrorava SpA, Via Don Sapino 176, 10078 Venaria, Torino, Italy; Tel: 0039- 011-4240237; E-mail: paolo.rava@elettrorava.com

**Figure 1:** Sputtering from a linear collision cascade (courtesy of Materials Research Corporation Inc.).

#### **3. FILM SPUTTERING DEPOSITION**

Sputter deposition is a physical vapor deposition (PVD) method of depositing thin films which involves the ejection of material from a target, that is then deposited onto a substrate.

In this thin film deposition technique, the source material (target) is placed in the form of a plate as the cathode in a vacuum chamber and ionization of a gas is generated by a high voltage discharge (Fig. **2**). Positive ions are accelerated against the cathode causing removal of atoms from the target as a direct result of mechanical collisions. Sputtered atoms ejected from the target have a wide energy distribution, typically up to tens of eV (100000°K). A small fraction of the ejected particles are ionized (typically around 1%). These ions travel from the target in straight lines and impact energetically on the substrates or vacuum chamber walls causing resputtering (re-emission of the deposited material during the deposition process by ion or atom bombardment).

**Figure 2:** Schematics of sputtering [4].

#### **60** *Silicon Based Thin Film Solar Cells Paolo Rava*

Alternatively, at higher gas pressures, the ions collide with the gas atoms that act as a moderator and move diffusively, reaching the substrates or vacuum chamber walls and condensing there after undergoing a random walk. A wide range of different energy collisions from high-energy ballistic impact to low-energy thermalized motion can be obtained by varying the background gas pressure. Sputtered atoms ejected into the gas phase are not in their thermodynamic equilibrium state, and tend to deposit on all surfaces in the vacuum chamber: in particular they deposit on the substrates to be coated which act as an anode, where they condense to form the desired film.

The sputtering process begins when a negative voltage is applied to the target: the positive gas ions move towards the target, and, on impact, some atoms from the surface are displaced.

For efficient momentum transfer, the atomic weight of the sputtering gas should be close to the atomic weight of the target, so for sputtering light elements neon is preferable, whilst for heavy elements krypton or xenon can be used. In practice a gas with an intermediate weight such as Ar is commonly used as it is easily available. Reactive gases can also be used to sputter compounds. The compound can be formed on the target surface, in-flight or on the substrate depending on the process parameters.

Sputtering deposition can overcome problems related to weak binding forces between atoms during the deposition of a thin film.

The process of sputtering uses as a source of ions a glow discharge generated by the application of a potential between two electrodes immersed in a gas. A series of ionization processes occur (formation of electrons and positive ions) leading to the creation of plasma.

The availability of many parameters that control sputter deposition makes it a complex process, but also allow experts a large degree of control over the growth and microstructure of the film that is deposited.

The figure illustrates the effect of an incident gas atom from the initial impact collision onto a target surface. This generates primary, secondary, tertiary and quaternary recoils of the target atoms. Two of the atoms are shown being ejected from the sample, *i.e.* sputtered.

The incident ions set off collision cascades in the target. When such cascades recoil and reach the target surface with an energy above the surface binding energy, an atom can be ejected. The average number of atoms ejected from the target per incident ion is called the sputter yield and depends on the ion incident angle, the energy of the ion, the masses of the ion and target atoms, and the surface binding energy of atoms in the target. For a crystalline target, the orientation of the crystal axes with respect to the target surface is also relevant.

Physical sputtering has a well-defined minimum energy threshold which is equal to or larger than the ion energy at which the maximum energy transfer of the ion to a sample atom equals the binding energy of a surface atom. This threshold is typically in the range 10–100 eV.

### **4. PLASMA**

Plasma can be defined as a gas containing electrically charged species and electrically neutral species [5]. Therefore it contains electrons, positive ions, negative ions, atoms and molecules. In

overall terms a plasma is electrically neutral and any charge imbalance is compensated for by the existing electric field moving the charged particles in order to maintain neutrality. The first important consideration that emerges is that in a plasma the sum of the density of electrons and of negative ions present is equal to the density of positively charged ions.

Usually, plasma characteristics vary greatly depending on the type of atoms or molecules that constitute the gas, and on their density and energy levels. However, there is a common factor in all types of plasma: free charges present in the gas respond to the effects of an electric field in the same way, *i.e.* trying to minimize the effects of this field. In particular, electrons are lighter and more mobile so that they respond more quickly to the effect of an electric field whereas ions are strongly influenced by their mass and show a large inertia to field variations.

As stated previously, plasma is characterized by a balance between ionic and electronic density, in which the various recombination processes are immediately offset by ionization processes. The existence of this dynamic balance condition is subject to a constant energy input from outside, which can create, through the formation of an electric field, the appropriate environment for the plasma regime.

Although plasma is a neutral gas in terms of total charge, it is characterized by a strong interaction between atoms and electrons with collisions and local energy transfer. Atoms are effectively stationary with respect to electrons because of their mass and can be considered to represent the "targets" of electrons. The main phenomena deriving from inelastic collisions of electrons and atoms are:


In a normal plasma regime the temperature of the gas ions is close to room temperature; however the electron gas dramatically raises the plasma temperature to thousands of degrees Kelvin. To produce the ions necessary to sustain the plasma, in the case of sputtering, DC (direct current) or RF (radio frequency) glow discharges are used.

### **5. COLLISION PROCESSES IN PLASMA**

As previously noted, plasma is characterized by interaction between atoms and electrons which collide and create local energy transfers.

The target particles may be considered spherical, with a cross section for electron impact equal to the area of their midsection. A sphere of radius r has a section σ = πr 2 , where σ is the cross-section, which is proportional to the probability that a given collision can occur.

Considering n molecules enclosed in a volume of section A and thickness Δx, the probability that an electron collides into one of these molecules is:

$$\mathbf{P} = (\mathbf{n} \, \mathbf{A} \, \mathbf{\sigma}) \Delta \mathbf{x} / \mathbf{A} = \mathbf{n} \, \mathbf{\sigma} \, \Delta \mathbf{x} \tag{1}$$

The average distance that an electron can travel within the volume between collisions is the mean free path (MFP) and is denoted by λ:

$$
\lambda = 1/\mathfrak{n} \cdot \mathfrak{a} \tag{2}
$$

Collision processes require a preliminary distinction: they can be:


If during an elastic collision a particle of mass mi and speed vi hits a stationary particle of mass mt,, the transfer function of kinetic energy;

$$\mathbf{E}\_l \mathbf{E}\_i = 4 \mathbf{m}\_l \mathbf{m}\_l \cos^2 \theta (\mathbf{m}\_i + \mathbf{m}\_l)^2 \tag{3}$$

indicates that an efficient energy transfer occurs between atoms of the same gas and from atoms to electrons whereas if an electron strikes an atom or molecule a very small amount of energy is transferred.

When the collision between a particle of mass mi and speed vi against a stationary particle of mass mt is inelastic, the particle of mass mt increases its potential energy by a value of ΔU and the transfer function;

$$
\Delta \mathbf{U} / \mathbf{E}\_i = \mathbf{m}\_i \cos^2 \theta (\mathbf{m}\_i + \mathbf{m}\_i) \tag{4}
$$

indicates that the electron kinetic energy is efficiently transferred into potential energy of the atom. The pure transfer of kinetic energy from an electron to an atom in the case of an inelastic collision is negligible. Inelastic collisions are of great importance when analyzing the phenomena that occur within a plasma.

#### **6. BREAKDOWN**

The phenomenon of breakdown is the process immediately preceding the formation of a glow discharge. The simplest system capable of creating and sustaining a glow discharge consists of two electrodes connected to an external generator (DC or RF) which are placed at a distance d, and enclosed in a volume V into which an inert gas (Ar) is introduced.

If a DC generator is used to create a potential difference Vp between the electrodes, the electric field accelerates the few electrons present in the gas from the cathode to the anode, providing them with the necessary energy to ionize neutral particles along their path. This will lead to a rapid

increase in the number of electrons in the gas. The electric field accelerates the ions in the opposite direction. When the ions strike the cathode, they cause the emission of secondary electrons. The process repeats again and again, thus generating more and more ions and electrons. The "avalanche" generation of electrons and ions leads to a marked increase in the value of the anode current and to a potential drop across the electrodes: the system is now in the state of dc breakdown.

If the electric field created is oscillating as in the case of radio frequency (RF), the phenomenon shows some differences with respect to DC excitation. In fact, the electrons gain energy by simply following the oscillations induced by the electric field. The alternating electric field can then provide enough energy to electrons so that they can sustain ionization processes. In this case the contribution of secondary electrons is not required.

Before breakdown, a constant electric field and therefore a voltage drop across the electrodes is applied. Following breakdown, a glow discharge is formed with an intensity that increases with the applied voltage to the electrodes. The increase in current leads to the avalanche formation of ions and electrons so that the discharge enters the full state of breakdown.

### **7. DC GLOW DISCHARGE**

The glow discharge formed as a result of breakdown, is composed of several regions with different characteristics, arranged so as to balance the energy input from the outside with processes involving particles in the gas (Fig. **3**).

Although the DC glow discharge is composed of several regions that merge into each other, for an effective description it is convenient to separate and analyze these regions separately.

The most extended zone is the negative glow which forms the plasma discharge in most deposition systems. It is a luminous plasma region, in which electronic and ionic densities are nearly equal.

Because of the lighter and faster electrons, the random ionic current density (*i.e.* without applied electric field);

$$\mathbf{J}\_i = \mathbf{n}\_c \mathbf{c}\_i / 4 \tag{5}$$

is much smaller than the random electronic current density;

$$\mathbf{J}\_{\mathbf{e}} = \mathbf{n}\_{\mathbf{e}} \mathbf{c}\_{\mathbf{e}} / 4 \tag{6}$$

Therefore, in order to maintain the same current densities in the negative glow region, a certain number of electrons must move away from it. The lack of electrons in that region brings it to a positive potential higher than all the other regions that make up the glow discharge; the equality of electronic and ionic density make this region equipotential and therefore this region has a very low electric field.

The sources for energy input to the negative glow include secondary electrons emitted from the cathode and accelerated through the sheaths, and electrons accelerated into the glow region. Their

#### **64** *Silicon Based Thin Film Solar Cells Paolo Rava*

acceleration is given by the presence of a strong electric field adjacent to the glow region. The electric field automatically changes its intensity so that the discharge glow in this region can be sustained.

**Figure 3:** Glow discharge zones [5].

The ions generated in the negative glow are instead accelerated toward the cathode, contributing to the generation of secondary electrons.

The negative glow region is surrounded by sheaths: the cathode sheath separates it from the cathode, on the opposite side are the Faraday dark space sheaths.

Sheaths are regions with varying potential, where electric fields are formed and can influence the motion of electrons and ions.

The sheaths have a strong influence on the electrons, whereas ions are not strongly influenced due to their relatively high mass.

Variations in potential due to the sheaths are observed near the electrodes, and they balance the current supplied to the system from outside with the current flowing to the electrodes. The electric field formed near the cathode (cathode dark space sheath) has sign and value such as to attract the ions and repel the electrons and has a positive space charge.

The cathode sheath plays an important role in accelerating and transferring charged particles to the plasma. The ions accelerated by the sheath collide with electrically neutral species, and exchange charge (Fig.**4**).

The cathode sheath plays a fundamental role also with regard to the ionization of particles: ionization occurs not only in the cathode sheath but also at its interface with the negative glow region. In addition, plasma is sustained partly from the generation of secondary electrons as previously described.

Sheaths are also present on an insulating substrate immersed in a plasma. In fact, by placing an insulating substrate in the plasma, it is negatively charged due to the higher electron current than ionic current. In order to restore the balance between the densities on the surface of the substrate, the incident electron current decreases down to the value of ion current. This creates a positive space charge sheath on the substrate, at a potential lower than the plasma potential, which can repel the electrons.

On the anode there is another positive dark space charge sheath (anode sheath) with an electric field that is of value and sign to decrease the density of electron current to the electrode. The most common systems on the market use different elements as the anode. Dependent on the geometric characteristics of the plasma, the walls of the deposition reactor, the substrate or both can function as an anode. In order for the electrical circuit formed between the anode and cathode through the discharge to have continuity, the ionic current at the cathode must be equal to the electron current present on the anode. If the geometric dimensions of the anode are not sufficient to carry the required electron current, an electric field is generated of value and sign such as to increase the electronic current to the required value.

Far away from the negative glow region, towards the anode, are located the Faraday dark space sheath and the positive column. The Faraday dark space sheath is located adjacent to the negative glow. The border between the two regions is the point up to which the electrons of the negative glow can travel (Fig. **4**).

**Figure 4:** Processes and zones in a DC Diode Discharge (courtesy of Materials Research Corporation Inc.).

#### **66** *Silicon Based Thin Film Solar Cells Paolo Rava*

The positive column consists of a relatively large bright area, with characteristics that approach those of an ideal plasma. In this region the electrons are in equilibrium with the electric field present: they gain energy as a result of their acceleration which is induced by the field, and they lose energy through recombination, emission and diffusion towards the walls of the chamber. The regions between the negative glow and the anode are not significant in plasma applications for sputter deposition.

#### **8. RF GLOW DISCHARGE**

DC glow discharges have limitations that confine their use only to special cases: the vast majority of the input power is used for the transport of ions to the cathode across the sheaths. This means that only a small fraction of the energy supplied from outside is available to accelerate the secondary electrons, which are the main source of the plasma, generated by ionic impact on the cathode. In addition, DC glow discharges require flow of electrical current to sustain the discharge. The presence of insulating parts in the system can make it difficult to control or even to establish the plasma process. AC discharges provide a solution to these problems (Fig. **5**). If the system under consideration involves the use of fields (and current) at low frequency and the presence of only conducting elements, the discharge shows a behavior very similar to a DC glow discharge. If an insulating electrode is placed in the system, the following phenomena occurs: its surface becomes electrically charged within a certain period of time, quenching the discharge in the first half of the cycle, and then igniting it again in the opposite direction, during the second half of the cycle. The system is fully comparable to a capacitor, being charged by plasma in alternating directions during each cycle. By increasing the frequency of the field up to 100 kHz, the ratio between the insulating substrate charging and discharging time and the cycle time can be increased. The effect is a continuous flow of current inside the plasma, despite the presence of the insulating substrate. If radio frequency excitation is used, ions show a large inertia in responding to changes in the field, whereas the lighter electrons do not present any difficulty in oscillating with the field.

**Figure 5:** Schematic of a Conventional Diode Sputtering System (courtesy of Materials Research Corporation Inc.).

#### *Sputtering of Thin Films Silicon Based Thin Film Solar Cells* **67**

In properly configured systems, the phenomenon described above causes deviations in the curve of the applied potential. The characteristic current response of a plasma with respect to an applied voltage is in fact asymmetric, and qualitatively similar to that of a diode (Fig. **5**). There is in fact a large electron discharge current at a positive potential and a small ion current at a negative potential. To satisfy the condition of the balance at the electrodes between the ionic and the electronic current, the potential curve for the discharge generated is shifted so as to increase the ionic component and to decrease the electronic component. The points of the maxima and minima on the graph progressively move to lower values to achieve that balance. This is possible only by means of an appropriate configuration: capacitive coupling between the RF power generator and the plasma and proper sizing of the electrodes. The capacitor accumulates and redistributes the current generated in the plasma at a rate dependent on the resistance encountered by the charges: the electron current will be discharged faster than the ionic current because of the higher electron mobility. The electrode connected to the capacitor must be smaller than the other (grounded) electrode. The asymmetry of the system and the presence of the capacitor make the plasma potential on average greater than zero. The self-bias, which is the phenomenon of deviation of the potential in the plasma, appears on the smaller electrode. As a result, the plasma potential, even though it is subject to an oscillating field, remains constant at a value greater than zero.

**Figure 6:** Sputtering cathode with plasma.

**Figure 7:** Typical ring-geometry sputter target (gold) showing the cathode made of the material to be deposited, the anode counter-electrode and an outer ring designed to prevent sputtering of the hearth that holds the target [4].

#### **9. USES OF SPUTTERING**

Sputtering (Figs. **6-8**) is used extensively in the semiconductor industry to deposit thin films of various materials in integrated circuit processing and in the optical industry to deposit thin antireflection coatings or multilayer filters on glass for optical applications. Because of the low substrate temperatures used, sputtering is an ideal method to deposit contact metals for thin-film transistors. Perhaps the most familiar products of sputtering are low-emissivity coatings on glass, used in double-pane window assemblies. The coating is a multilayer containing silver and metal oxides such as zinc oxide, tin oxide, or titanium dioxide. Sputtering is also used to metalize flexible plastics. A large industry has developed around tool bit coating using sputtered nitrides, such as titanium nitride, creating the familiar gold colored hard coat. Sputtering is also used as the process to deposit the metal (*e.g.* aluminum) layer during the fabrication of CD and DVD discs. Hard disk surfaces use sputtered CrOx and other sputtered materials. Sputtering is one of the main processes of manufacturing optical waveguides and is another way for making efficient photovoltaic solar cells.

**Figure 8:** A commercial sputtering system for thin film deposition.

#### **10. COMPARISON WITH OTHER DEPOSITION METHODS**

An important advantage of sputter deposition is that even materials with very high melting points are easily sputtered while evaporation of these materials in a resistance evaporator or Knudsen cell is problematic or sometimes impossible. Sputter deposited films have a composition close to that of the source material. The variance is due to different elements spreading differently as a consequence of their different mass (light elements are deflected more easily by the gas) but this difference is constant. Sputtered films typically have a better adhesion on the substrate than evaporated films. A target contains a large amount of material and is maintenance free which means that the technique is well suited for ultrahigh vacuum applications. Sputtering sources contain no hot parts (to avoid heating they are typically water cooled) and they are also compatible with reactive gases such as oxygen. Sputtering can be performed either bottom-up or top-down whilst evaporation must be performed bottom-up. Advanced processes such as epitaxial growth

are possible. One disadvantage of the sputtering process is that the process is more difficult to combine with a lift-off process for structuring the film. This is a consequence of the diffuse transport characteristic of sputtering, which makes a perfect shadow impossible. Thus, one cannot fully restrict where the atoms go, which can lead to contamination problems. Also, active control for layer-by-layer growth is difficult in the sputtering process compared to pulsed laser deposition and inert sputtering gases can become incorporated into the growing film as impurities.

### **11. SPUTTERING PROCESSES**

Sputtering processes can be divided into 4 subcategories:


Different combinations or variants can be deposited using these four main types of sputtering.

### **11.1. DC Sputtering**

This system uses a direct current to generate the discharge. The deposition rate of thin films depends on the sputtering pressure as well as on the applied current and voltage. The pressure in particular is a variable that should be treated with some care to achieve an efficient process. At low pressures (about 20 mTorr) the cathode sheath is extended, so the ions have difficulty in reaching the target, which implies a low ionization efficiency. If the pressure is increased, whilst maintaining a constant voltage to the electrodes, the mean free path of electrons decreases: this leads to an increase of the ionization efficiency and hence to an increased current flow. If the pressure increases further, then the electronic scattering also increases, with resulting decrease in sputtering rate.

### **11.2. RF Sputtering**

Charge build-up on insulating targets can be avoided by the use of RF sputtering (Fig. **9**), where the sign of the anode-cathode bias is varied at a high rate. RF sputtering works well to produce highly insulating oxide films but this is only possible with the addition of RF power supplies and impedance matching networks. The principle of the discharge by applying a radio frequency voltage was already discussed above. Now the system as a whole is analyzed. Forward and Reflected power are shown separately on the generator; a matching network is placed between the generator and the load with the function to increase the power dissipation in the discharge. A matching network is composed of an inductor connected in series with a variable capacitor and in parallel with another variable capacitor.

RF sputtering works thanks to the ability of the target to charge to a negative potential and then behave like a classic target in a DC sputtering configuration. Due to the different mobility of ions

#### **70** *Silicon Based Thin Film Solar Cells Paolo Rava*

and electrons and to the positioning of a series capacitor close to the target, the net current is still zero but the large flow of electrons keeps the target at a negative voltage.

**Figure 9:** RF Diode schematics (courtesy of Materials Research Corporation Inc.).

The target surface area must be less than that of any other electrode in the sputtering chamber. In practice the area of the target placed on the cathode must be less than the area of the anode. The anode typically consists of the chamber walls, the substrate support, and the system ground connection.

RF sputtering is used in almost all cases, except in systems that use another method for plasma enhancement.(*e.g.* magnetrons).

#### **11.3. Sputtering Systems with Magnetic Intensification**

Sputtering sources are usually magnetrons that utilize strong electric and magnetic fields to trap electrons close to the surface of the magnetron, where the material target is placed. The electrons follow helical paths around the magnetic field lines and undergo more ionizing collisions with gaseous neutrals near the target surface than they would otherwise encounter (Fig. **10**). The extra argon ions created as a result of these collisions result in a higher deposition rate being achieved. It also means that the plasma can be sustained at a lower pressure. The sputtered atoms are neutrally charged and so are unaffected by the magnetic trap. In these systems a magnetic field B is applied in order to increase the plasma ionization by electrons. The magnetic field can be applied parallel or perpendicular to the electric field ξ. In the former case the magnetic fields, in opposition to applied electric fields, are called axial. The law that relates the electric field ξ with the magnetic field B is given by:

$$\mathbf{F} = \mathbf{[m} \ \mathbf{dv} \ ] \text{/dt} = \mathbf{-e} (\mathbf{\tilde{\xi}} + \mathbf{v} \mathbf{B}) \tag{7}$$

When electrons are emitted normal to the target, the term vB disappears and they are only influenced by the electric field that accelerates them linearly towards the anode. If the electric field is negligible, the magnetic field moves the electrons towards the anode in a spiral motion. If both fields are applied, the motion of electrons will be spiral but the pitch will increase with time. The magnetic fields extend the residence time of the electrons in the plasma, so increasing the probability of ionic collisions and therefore the discharge current and the deposition rate. The increase in the percentage of ionization is caused by the corresponding increase in the mean free path of electrons that enhances the number of collisions. This effectively reduces their speed to zero on the walls and so reduces the possibility for them to recombine to form neutral atoms. Similar DC discharges require the application of larger currents and pressures.

**Figure 10:** Magnetron source schematics (courtesy of Materials Research Corporation Inc.).

A second type of magnetic sputtering system uses intensification transverse magnetic fields (magnetron).

Historically magnetrons originated as thermoelectric power microwave tubes capable of amplifying signals at high frequency up to 5 MW power with an efficiency range of between 40% and 70%. By using a magnetic field parallel to the target and perpendicular to the electric field, the electrons cannot reach the anode and remain in the vicinity of the target, so increasing the ionization efficiency. The electrons initially emitted from the cathode are accelerated towards the anode, moving in a spiral motion, (Fig. **11**) the parallel magnetic field then sends them back towards the target. This path results in a reduction of the recombination losses both at the anode and at the chamber walls.

In this system the electron follows cycloid orbits with electron cyclotron frequency;

$$\boldsymbol{\alpha}^2 = \mathbf{e} \cdot \boldsymbol{\xi}\_0 \prime \mathbf{m}\_\mathbf{e} \mathbf{L} + \left(\mathbf{e} \mathbf{B} \prime \mathbf{m}\_\mathbf{e}\right)^2$$

<sup>2</sup> **(8)** 

#### **72** *Silicon Based Thin Film Solar Cells Paolo Rava*

where ξ 0 is the electric field at the target, L is the width of the dark space, B is the applied magnetic field, me is the electron mass, e is the elementary charge.

**Figure 11:** Electronic paths in a magnetron (courtesy of Materials Research Corporation Inc.).

Currently this technique is widely used for most sputtering systems due to its ability to deliver deposition rates up to ten times higher than the other techniques. On the other hand, its main limitation is the difficulty this sputtering technique can have in achieving uniform deposition thickness: this derives from the impossibility of creating uniform magnetic fields. The magnetron sputtering configurations that are commonly used include the use of planar, toroidal and conicaltoroidal targets (Figs. **12** and **13**).

**Figure 12:** A magnetron sputter source showing the target-mounting surface, the vacuum feedthrough, the power connector and the water lines. This design uses a disc target as opposed to the ring geometry illustrated above [4].

*Sputtering of Thin Films Silicon Based Thin Film Solar Cells* **73**

**Figure 13:** Magnetron sputter sources configurations [4].

The common point between the three devices shown is the formation of an intense ring-shaped plasma. Free electrons in the plasma perform cycloid motion along the magnetic field lines and the electron cloud moves around the ring, generating a strong current. It is to be noted that the impedance of the system varies whilst the target is subject to erosion.

In contrast to other sputtering systems, the current density within a magnetron discharge is highly uneven, but of very high value. This leads to a high but non uniform deposition rate and also to non-uniform heating of the target surface. Fortunately, sputtering yields are rather insensitive to slight variations in temperature. Whilst the target is being eroded by the sputtering process, the geometry and position of the discharge changes, moving to regions with higher magnetic field. A variation of the field affects the motion of electrons and even the voltage, current and power curves can change drastically. Too low a pressure may also increase the volume of the discharge until it becomes too large compared to the target, thus extinguishing the discharge.

Stray magnetic fields leaking from ferromagnetic targets can disturb the sputtering process. Specially designed sputter sources with unusually strong permanent magnets must often be used to compensate for this (Fig. **14**).

**74** *Silicon Based Thin Film Solar Cells Paolo Rava* 

**Figure 14:** Two used targets: on the left is a target used on a normal magnetron, on the right is one used on a special magnetron with magnetic field developed for high target utilization [4].

### **11.4. Reactive Sputtering**

In this technique, thin film layers are deposited by sputtering from metal targets in the presence of a reactive gas (*e.g.* O2, N2), usually mixed with the usual inert gas (Ar). Sputtering is mostly accomplished by the inert gas, whereas the reactive gas combines with the sputtered atoms to form the compound. The most common compounds that can be deposited by this technique include oxides (Al2O3, SiO2), nitrides (TiN), sulfides (CdS, ZnS, CuS), carbides (TiC, WC).

**Figure 15:** Hysteresis Curve for Reactive Sputtering (courtesy of Materials Research Corporation Inc.).

During reactive sputtering the exact composition of the resulting film, formed by one of the target components mixed with the reactive gas, can be largely controlled by varying the relative pressures of the inert and reactive gases; however the exact composition will depend also on several other process parameters, such as the total pressure and the sputtering power. The

sputtering of a compound can be managed by controling the total pressure of the system as a function of flow rate of reactive gas. The total pressure of the system should increase when a partial pressure of reactive gas is injected into the chamber. However, as the reactive gas combines with an element of the target to form a solid compound, the amount of reactive gas used is no longer seen in the gas phase and therefore it cannot make a contribution to the increase in system pressure. When reactive sputtering from a metal target, changes in target composition can occur as a direct consequence of varying the reactive gas flow and over time the target surface can become "poisoned" with the reactive gas changing some sputtering parameters and causing a hysteresis effect (Figs. **15** and **16**).

**Figure 16:** Voltage Hysteresis Curve (courtesy of Materials Research Corporation Inc.).

Film stoichiometry is an important parameter for optimizing functional properties like the stress in SiNx and the index of refraction of SiOx. The transparent indium tin oxide and zinc oxide conductors that are used in optoelectronics and solar cells are deposited by reactive sputtering.

#### **12. COMPARISON OF DIFFERENT SPUTTERING TECHNIQUES**

Figs. **17** and **18** show the working regions for the different sputtering systems previously presented. In summary:


**76** *Silicon Based Thin Film Solar Cells Paolo Rava* 

**Figure 17:** Comparison of 3 sputtering techniques (courtesy of Materials Research Corporation Inc.).


**Figure 18:** Typical Operating Parameters (courtesy of Materials Research Corporation Inc.).

### **13. BIAS SPUTTERING**

This technique resorts to the modification of electric fields by the application of a separate and additional externally generated voltage onto the substrate to vary the flow and energy of the incident charged species to the substrate. It has been applied in the industrial field in all its possible configurations (DC, RF, magnetron, reactive). The main characteristic of bias sputtering is to achieve significant changes in the properties of deposited films. The most reliable theories claim that the bias voltage can control parameters such as gas content and stress in the deposited thin film. Also the effect of resputtering from the substrate can be controlled by the application of bias to help control the deposited thickness on non-conformal surfaces: the so called step coverage.

In conclusion, bias voltage applied to the substrate determines the conditions of film growth on the substrate; the amount of weak and strong bonds during the film growth can be controlled with ensuing effects on the resistivity, hardness, dielectric properties, optical properties, density and adhesion.

#### **14. SPUTTERING OF ALLOYS**

Preferential sputtering can occur at the start of the sputtering process when a multicomponent solid target is bombarded and there is no solid state diffusion. If the energy transfer is more efficient

with one of the target components compared to another, and/or it is less strongly bound to the solid, it will sputter more efficiently and its sputtering yield S will be higher. If in an AB alloy the component A is sputtered preferentially, during the first stages of the process the surface layer of the target is depleted of the target compound of higher sputtering yield S. Then the surface of the solid will, during prolonged bombardment, become depleted in the A component and enriched in the B component thereby increasing the probability that B is sputtered such that the composition of the sputtered material will be AB.

Only after the stoichiometry of the target surface has reached a dynamic equilibrium, should the deposition process be started by opening a shutter that allows the sputtered material to reach the substrate. To be able to deposit a film of a given composition it is necessary to know that the surface composition of the target is different from the composition of the inner areas not affected by the sputtering process.

### **15. ION BEAM SPUTTERING**

Ion-beam sputtering (IBS) is a method in which the target is external to the ion source. A source can work without any magnetic field, as in a hot filament ionization gauge. In a Kaufman source, ions are generated by collisions with electrons that are confined by a magnetic field as in a magnetron. They are then accelerated by the electric field emanating from a grid towards a target. As the ions leave the source they are neutralized by electrons from a second external filament. IBS has an advantage in that the energy and flux of ions can be controlled independently. Since the flux that strikes the target is composed of neutral atoms, either insulating or conducting targets can be sputtered. IBS has found application in the manufacture of thin-film heads for disk drives. A pressure gradient between the ion source and the sample chamber is generated by placing the gas inlet at the source and shooting through a tube into the sample chamber. This minimizes gas usage and reduces contamination in UHV applications.

### **15.1 Ion-Assisted Deposition**

In ion-assisted deposition (IAD), the film growing on the substrate originating from a primary deposition source (thermal or electron beam evaporation, sputtering) is exposed to a secondary ion beam operating at a lower power than the sputter gun. Usually a Kaufman source similar to that used in IBS supplies the secondary beam. IAD can be used to deposit carbon in diamond-like form onto a substrate. Any carbon atoms landing on the substrate which fail to bond properly in the diamond crystal lattice will be knocked off by the secondary beam. NASA used this technique to experiment with depositing diamond films on turbine blades in the 1980's. IAD is used in other important industrial applications such as those for creating tetrahedral amorphous carbon surface coatings on hard disk platters, hard transition metal nitride coatings on medical implants and hard coatings for optical devices.

A Dual Ion Beam Source Sputter Deposition (DIBSD) System uses an Ion Beam Source to sputter materials from a multiple target carousel and a second Ion Beam Source to bombard the film growing on the substrate (Fig. **19**). The primary sputtering IBS typically operates at voltages around 1000 V to provide the ions with the energy required for effective sputtering. The second (so called assist) IBS operates at voltages around 100-250 V to provide the ions with the energy required for film densification by removing weak bonds. A DIBSD system with appropriate layout of components can be used to deposit films with extremely high uniformity and excellent materials properties and represents the state of the art in sputtering technology.

## 3+

**Figure 19:** Dual Ion Beam Sputtering System (courtesy of Kaufman & Robinson Inc.).

### **16. GAS FLOW SPUTTERING**

Gas flow sputtering makes use of the hollow cathode effect, the same effect by which hollow cathode lamps operate. In gas flow sputtering a working gas like argon is led through an opening in a metal subjected to a negative electrical potential [6, 7]. Enhanced plasma densities occur in the hollow cathode, if the pressure in the chamber p and a characteristic dimension L of the hollow cathode obey the Paschen relation 0.5 Pa·m < p·L < 5 Pa·m.This causes a high flux of ions on the surrounding surfaces and a large sputter effect. The hollow-cathode based gas flow sputtering may thus be associated with large deposition rates up to values of a few µm/min [8]. Hollow cathode devices are also used as electron sources to neutralize an ion beam emitted from a Kaufman source.

### **17. STRUCTURE AND MORPHOLOGY**

In 1974 J. A. Thornton applied the structure zone model for the description of thin film morphologies to sputter deposition. In a study on metallic layers prepared by DC sputtering [9], he extended the structure zone concept initially introduced by Movchan and Demchishin for evaporated films [10]. Thornton introduced a further structure zone, which was observed at low argon pressures and characterized by densely packed fibrous grains. The most important point of this extension was to emphasize the pressure p as a decisive process parameter. In particular, if hyper thermal techniques like sputtering *etc.* are used for the sublimation of source atoms, the pressure governs (*via* the mean free path), the energy distribution with which they impinge on the

surface of the growing film. Next to the deposition temperature Td the chamber pressure or mean free path should thus always be specified when considering a deposition process.

Since sputter deposition belongs to the group of plasma-assisted processes, both neutral atoms and charged species (like argon ions) can also strike the surface of the growing film, and this component may exert a large effect. Denoting the fluxes of the arriving ions and atoms by Fi and Fa, it turned out that the magnitude of the Fi/Fa ratio plays a decisive role on the microstructure and morphology obtained in the film [9]. The effect of ion bombardment may quantitatively be derived from looking at structural parameters like the preferred orientation of crystallites or texture and from the state of residual film stress.

# 2!2+

**Figure 20:** The structure of PVD deposited films (courtesy of Materials Research Corporation Inc.).

### **18. SPUTTER ETCHING AND CHEMICAL SPUTTERING**

The sputtering technique can also be applied by configuring the elements so that they reverse their function: the substrate is placed on the cathode and its surface layers are removed by ionic bombardment: this layer removal technique is called sputter etching. It is the reverse process compared to sputter deposition and is often used for substrate surface cleaning before sputter deposition is started. Removing atoms by sputtering with an inert gas is called `ion miling' or 'ion etching'. The main parameter of interest is the "etching rate", *i.e.* the rate at which the surface of the substrate is etched.

Sputtering can also play a role in reactive ion etching (RIE), a plasma process carried out with chemically active ions and radicals, for which the sputtering yield may be enhanced significantly compared to pure physical sputtering. Reactive ions are frequently used in Secondary Ion Mass Spectrometry (SIMS) equipment to enhance the sputter rates. The mechanisms causing the sputtering enhancement are not always well understood, but for instance the case of fluorine etching of Si has been modeled well theoretically.

#### **ACKNOWLEDGEMENTS**

The author wishes to acknowledge Thin Film Equipment srl and Kaufman & Robinson Inc. for providing some of the figures used in the article.

### **CONFLICT OF INTEREST**

The author(s) confirm that this chapter content has no conflict of interest.

### **REFERENCES**


© 2013 The Author(s). Published by Bentham Science Publisher. This is an open access chapter published under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/legalcode

## **Molecular Beam Epitaxy (MBE)**

## **Lorenzo Morresi\***

*University of Camerino-School of Science and Technology-Physics Division, Via Madonna delle Carceri, 9-62032 CAMERINO (MC), Italy* 

**Abstract:** Molecular Beam Epitaxy (MBE) represents a widely used growth technique to approach the basic research applied to the growth of semiconductor films and multilayer structures. The main features that distinguish the MBE from other growth techniques are the precise reproducibility of all parameters involved during the epitaxial process, the growth conditions far from thermodynamic equilibrium, and the possibility of controling the kinetic evolution of the outermost layers of the epitaxial film. Nowadays, MBE is also used to grow and investigate nanosized semiconducting materials, which are profoundly interesting for photovoltaic future applications as well.

**Keywords:** Molecular beam epitaxy, semiconductor thin films, nucleation in film growth, nanocrystalline materials, electron beam deposition, doping thin films, impurities in crystals, quantum dots, RHEED, surface reconstruction, dislocations.

### **1. INTRODUCTION**

Molecular Beam Epitaxy (MBE) is a technology used for the deposition of thin film compound semiconductors, metals or insulators that allows a precise control of compositional profiles by using a process far from the thermodynamic equilibrium. The term epitaxy originates from the Greek roots "epi" and "taxis" which mean to arrange upon. In other words, the epitaxy is the arrangement of one or more thermal particles atop a heated and ordered crystalline substrate to form a thin layer whose crystallinity matches that of the substrate even though the composition of the materials may differ (*e.g.* SiGe/Si, GaAlAs/GaAs, CdTe/GaAs,…). Again, the term beam means that evaporated elements (atoms and/or molecules) do not interact with each other or with vacuum chamber gases until they impinge the substrate because of their long mean free paths which are involved in the deposition process.

This unique growth technique is widely used to produce superlattice structures consisting of many alternate thin layers with single thickness as low as 10 Å. Furthermore, impurities are evaporated onto the growing film through separate sources. In this way the doping profile, orthogonal to the surface, may be varied and controlled with a spatial resolution not easily achieved by more conventional techniques.

MBE was developed by Alfred Cho and John Arthur at Bell Telephone Labs in the early 1970s, in

**<sup>\*</sup>Address correspondence to Lorenzo Morresi:** University of Camerino, School of Science and Technology, Physics Division, Via Madonna delle Carceri 9, Camerino, 62032, Italy; Tel: +39 333 9961198/+39 737 402528; Fax: +39 737402853; E-mail: lorenzo.morresi@unicam.it

#### **82** *Silicon Based Thin Film Solar Cells Lorenzo Morresi*

an attempt to develop a new variety of high-frequency and high-temperature devices such as injection lasers, electro-optic phase modulators, photocathodes and oscillators [1], as well as IMPATT diodes [2], mixer diodes [3] and optical waveguides [4] all based on the same requirement: the development of thin layer structures. Their pioneering work was focused mainly on preparing AIIIBV compound films (like GaAs) overlapping compliance due to the large difference in vapor pressures between the group III and group V elements. Their efforts bring to the formation of stoichiometric III-V films by the molecular beam epitaxy method, and demonstrated by optical and electron diffraction measurements [5, 6].

Adding the Auger spectroscopy for the surface chemical analysis to the vacuum system, and the reflection electron diffraction for *in situ* structural analysis, they were able to resolve the original uncertainties over film stoichiometry and substrate cleanliness. Improving the characterization of both the epitaxial layer and the substrate by incorporating these surface diagnostic techniques into the chamber process, the progress in MBE was very rapid.

The strength of this particular growth process is due to the very low deposition rates (generally few Å per second) generated by the sublimation of extremely pure solid elements heated in separate effusion cells (mostly based on Knudsen concept). In fact, the source material is transformed into its gaseous state by raising its vapor pressure through an increase in temperature. The gaseous particles expand into the evacuated space between the orifice's source and the substrate, where the condensation process takes place. The condensate reacts with the surface until the epitaxial arrangement takes place and the crystalline structure grows with a comparable growth rate. To reduce the impurity levels in the growing layers to an as low as possible value, the epitaxial growth occurs in Ultra-High-Vacuum (UHV) conditions, with a total pressure within the deposition chamber lower than 10-10 Torr.

Intricate structures of few monolayers (MLs) composed by different materials may be fabricated by controling the movements of shutters placed in front of each evaporator source. Such control has allowed the development of structures with abrupt and sharp interfaces where the charge carriers can be bi-dimensionally confined in space, due to quantum wells [7-10], or even onedimensionally confined, due to quantum dots [11-13]. Such layers are nowadays a critical part of many modern semiconductor devices (Fig. **1**), including semiconductor lasers [14-16], lightemitting diodes [17], photodetectors [18, 19] and solar cells [20-23].

The UHV conditions in the environment and control of the quality of the source materials allow much higher film purity, compared to other growth techniques.

Moreover, the vacuum condition allows for the use of electron diffraction probes, which provide fundamental information on the growth mechanisms. On the other hand, MBE suffers of lower yield compared to other techniques such as Liquid Phase Epitaxy (LPE), Metal-Organic Vapor Phase Deposition (MOCVD), Sputtering and Plasma Enhanced Chemical Vapor Deposition (PECVD) due to a lower speed process and dimension wafer capability.

### **2. MBE SYSTEM**

A molecular beam epitaxy system is basically a vacuum evaporation apparatus. What may be considered a standard MBE system is shown schematically in Fig. **2**.

*Molecular Beam Epitaxy (MBE) Silicon Based Thin Film Solar Cells* **83**

**Figure 1:** (a) Structure of the 50 stacked quantum dot solar cell grown by MBE. Each GaP layer has a nominal thickness of 1 ML = 0.273 nm. (b) Cross-sectional TEM image of the 50 stacked quantum dot layers. The arrows indicate the defects observable in the image (AIP license n. 2546451267415).

The system consists of a stainless-steel growth chamber connected to other chambers by gate valves. These latter are needed to avoid contamination of components and materials sources by both external and process gases, and to maintain pressure into the growth chamber as low as possible. Modern systems are provided with a proper treatment chamber, and a load lock module represents the only way to transfer the sample to and from the air.

The pumping system, a combination of ion pump, titanium sublimation pump and liquid N2 cryopanels, can reduce the residual impurity density to a minimum. The two parameters that characterize the vacuum into the growth chamber are: the mean free path, *L*, (average distance traversed by reactant gas molecules between successive collisions), and the partial pressure of the residual gas molecules, *pr*. The highest admissible *pr* value depends on *L* being larger than the distance from the outlet orifice of the beam source to the substrate surface (*L* > 0.2 m).

Using the ordinary assumptions of the kinetic theory of an ideal gas and, for example, the typical numerical data for conventional MBE growth of Si, the maximum value of the residual gas pressure is 10-5 Torr [24], well behind the UHV conditions present in the chamber. Again, one can assume that the time required for the deposition of 1 mono- layer (ML) of residual contaminants is 105 times those necessary for the deposition of 1 ML of film from the molecular beams. Consequently, it can be demonstrated that very low deposition rates (*i.e.* 1 ML s-1) should be employed in an UHV environment [24]. However, it should be noted that *pr* increases during

#### **84** *Silicon Based Thin Film Solar Cells Lorenzo Morresi*

deposition due to the increased heat load from the effusion cells and the substrate. In the event that this occurs, a titanium filament sublimation pumping can reduce the residual gas pressure down to the minimum values. The entire vacuum system is bake able up to 250 °C for extended periods of time, to minimize outgassing from the internal walls during the deposition process. After a complete bake out cycle, the system with all the components installed reaches ~ 2 10-10 Torr, using only the main ion pump. Moreover, both CO2 and H2O gas pressure is drastically reduced by cooling the cryopanels with liquid nitrogen. Cryogenic temperatures act as an entangled for impurities, so vacuum levels of the orders of 10-11 Torr can be obtained. The substrate older is located a few centimeters away from the openings of the effusion cells, along the centerline of the system. The temperature of the substrate can be set during the deposition (from room temperature up to about 1400 °C), at a suitable temperature depending on the epitaxial process. It can also be heated before deposition primarily for cleaning and\or surface reconstruction, and afterwards for various heat treatments. As shown in Fig. **2**, the chamber is provided with a spectral mass analyzer to detect the residual atoms or molecules and thus to monitor the environment under which the film is grown.

**Figure 2:** Schematic representation of a molecular beam epitaxy growth chamber. The main experimental features component the system are shown.

#### **2.1. Effusion Cells**

Fig. **2** shows three effusion cells, although as many as ten can be found in modern apparatus. A schematic illustration of a standard effusion cell is shown in Fig. **3 (a)**. In the growth of compound semiconductors the materials contained in the crucible could be the compounds themselves, their components, or different elements to be used as doping impurities. The crucible is usually made of pirolytic boron nitride (PBN), which can stand temperatures up to 1400 °C without harmful material dissociation on the grown layers. Standard effusion cells are limited to operate at a temperature lower than 1200 °C, which is only just within the range of that required for Si, Ge, Al, Ga evaporation. The shape can be either cylindrical or conical, with different tapering angles, depending on the material to be evaporated as well as its diameter.

The total effusion rate can be approximately described by the Knudsen effusion equation [24]:

$$R = 8.33 \times 10^{22} \left[ \frac{p \cdot A\_e}{\sqrt{M \cdot T}} \right] \text{molecules } \text{s}^{-1} \text{ }\tag{1}$$

where *p* is the pressure in the effusion cell, *Ae* is the surface area from which molecules evaporate, *M* is the molecular weight of the evaporating species and *T* is the temperature of the melt. Combining the Knudsen equation with the cosine law (given that the ideal Knudsen cell exhibits an angular distribution of the evaporated particles) [24], the impingement rate (also called flux) at the central point of the substrate axially aligned with the orifice can be written in the form:

$$I = 2.653 \times 10^{22} \frac{p \cdot A\_e}{r^2 \sqrt{M \cdot T}} \left[ mol \text{ } m^{-2} \text{ s}^{-1} \right] \tag{2}$$

where *r* is the distance between the orifice and impingement point. The rate at the edge point of the substrate, forming an angle with respect to central point can be easily calculated by multiplying the previous relation by cos4. A standard effusive cell can assure flux stability greater than 1% during the deposition process, with a daily variation lower than 5% [25]. A Ta filament (or foils in other models) provides heating, while multiple Ta foils provide heat shielding to improve both the temperature stability and the thermal efficiency. Generally, a W-Re (5% and 26% Re) thermocouple is properly attached to both measure the material temperature and assure chemical stability. These refractory materials are thermally inert and suitable for operating at elevated temperatures.

**Figure 3:** Schematic illustration of two present-day effusion cells used in MBE systems: (a) Standard Knudsen cell; (b) Two stage Cracking effusion cell (Courtesy of Prof. Klaus H. Ploog).

#### **86** *Silicon Based Thin Film Solar Cells Lorenzo Morresi*

PID regulators provide high precision temperature regulation of 1 °C up to the maximum operating temperatures. Mechanical or pneumatic shutters, usually made of Ta or Mo, are placed in front of the orifices to trigger the fluxes (see Fig. **2**). The shutters operate faster than the growth rate (typically 0.1 s), and should be computer controlled to provide reproducible growth structures.

An important variation to the standard designs is provided by the so-called cracking cells. They are mainly employed for evaporation of group-V and VI elements (see Fig. **3 (b)**). In this cell, the material is first thermally evaporated (in form of tetramers) from the crucible; subsequently it passes through a hotter cracking zone where molecules are dimerized.

#### **2.2. Electron Beam Evaporator**

Molecular beams for MBE may also be generated by electron bombardment of suitable sources, by concentrating the heating energy onto just the evaporating load. The main property of this evaporation technique is the fast response process time, which permits high growth rates for low vapor pressure materials, especially when high purity of the evaporant is desired [26].

**Figure 4:** (a) Schematic overview of an electron-beam gun, with a horizontal source assembly (Courtesy of MDC Vacuum Limited). (b) Silicon electron bent-beam heated MBE source; electrons are forced into a curved path through a transverse magnetic field that permits focusing of the electron beam.

A proper filament emits electrons, and the stream is accelerated through a field of typically 4-10 kV. The electron gun is designed to eliminate nearly all ion bombardment effects on the filament thanks to the 270° electron beam deflection and the very sharply bent electron beam path near the exit of the aperture. Fig. **4 (a)** shows the inside of an electron gun mounted in a MBE chamber through 10" CF Flange. The figure shows the main assembly features including rotary, linear and electrical feedthroughs, clamps, linkages, water flow switch and water connections. In principle, due to the electrons impinging on the source, almost all the kinetic energy is converted into heat, and temperature exceeding 1500 °C may be obtained. During the film growth, the electron beam impinges on the center of the truncated cone of shaped source (Fig. **4 (b)**) [24]. For an electron beam current of 150 mA, the molten area can be lower than 10 mm in diameter. Electron beam evaporators are frequently used for evaporation of refractory metals, *e.g.* Mo, Nb, Ta, W, Zr, and are well suited for high-rate evaporation of Al, and of course for semiconductors like Si and Ge. Finally, a typical application is SiGe MBE for the generation of the main lattice element.

#### **2.3. RHEED**

For *in situ* monitoring of the thin films epitaxial growth, the system further incorporates a scanning high-energy electron diffraction apparatus, employing the small glancing angle reflection mode of operation (RHEED in Fig. **2**).

The feature of glancing incidence makes RHEED sensitive to the very uppermost layers, rather than the bulk structure. This tool reveals in real time changes either in the growing surface or in the surface structure (crystallographic orientation and morphology) of a thin film, without any interference with the growth process [27]. In RHEED, an incident electron beam strikes the sample's surface at near-grazing incidence (typically making an angle of incidence of lower than 3°) and is reflected onto a phosphorescent screen, as shown in Fig. **5**.

**Figure 5:** Schematic diagram of RHEED geometry showing the incident beam at an angle to the surface plane; is the azimuthal angle. *W* indicates the spacing among spot features; *L* is the distance between the point of incidence and the screen.

**88** *Silicon Based Thin Film Solar Cells Lorenzo Morresi* 

**Figure 6:** Intersection between the Ewald sphere and a particular reciprocal lattice rod. The corresponding electrons (having *k'* wave vectors) that satisfy this particular Laue condition form a diffraction spot on the screen.

**Figure 7:** Schematic representation of the relation between the intrarow spacing *a\** of the reciprocal lattice rods and the spacing W of the observed streaks.

In the framework of the Laue diffraction, the maximum intensity of the diffracted beams originates when the difference between the wave vectors of the incident and diffracted beams (*k* and *k*' respectively) intercept the reciprocal lattice rods. In this way it can be defined an Ewald sphere of radius *k* (Fig. **6**). The intersection of the Ewald sphere with the reciprocal lattice rods selects the electrons with wave vectors *k'*, forming some spots on the screen. If the surface is not flat, many electrons will be transmitted through surface asperities and scattered in different directions, resulting in a RHEED pattern constituted by many spotty features. However, thermal vibrations and lattice imperfections can cause the reciprocal lattice rods to have a finite thickness, while the

Ewald sphere itself has some finite thickness, due to divergence and dispersion of the electron beam [28].

Therefore, diffraction from a perfectly flat surface results in a diffraction pattern consisting of a series of streaks with modulated intensity (rather than points) superimposed on a fairly uniform background, due to inelastically scattered electrons. Therefore, RHEED analysis provides important information concerning the flatness of the growing film surface. Furthermore, it is evident that diffraction from an amorphous surface (such as an oxide on top of the substrate) gives no diffraction pattern at all. In this case only a diffuse background will result. The distance between the streaks of static RHEED pattern is an indication of the surface lattice unit cell size.

Fig. **7** shows a single row of rods that has a lateral spacing of *a\** and indicate the Miller (hk) indices of several points of the reciprocal net; these same indices are given to their rods, and to the spots or streaks they create in the RHEED pattern. The observed streak spacing is *W*; the distance to the screen from the point of incidence is *L*. We may utilize the principle of similar triangles to show that *W*/*L* ~ *a\**/(2/). Thus, the observed streak spacing indicates a rod spacing of:

$$a^\* = \frac{2\pi \cdot W}{\lambda \cdot L} \tag{3}$$

where the wavelength = 12.3/[*V* (1+1.95 10-6 *V*)]1/2 Å, is expressed as function of the accelerating potential, *V* [28]. Potentialities of this method are expanded to oscillations of the electron beam reflected from a growing film surface in the process of MBE (RHEED oscillations) [29].

For a 2D growth, one oscillation period of a specular electron beam corresponds exactly to a monolayer of the film grown during this period. The oscillation period depends on the material flux to the surface, the substrate temperature and the growth mechanisms.

As an example, Fig. **8** compares different evolution of either RHEED intensity oscillation (left side) and RHEED patterns (right side) taken during and after, respectively, the growth of 5.5 ML (monolayers) of strained Ge on Si (100) at 400 °C, followed by heteroepitaxial Si growth at deposition rates with **(a)** and without **(b)** H supplies. The pattern **(c)** corresponds to case **(a)** followed, however, by a quick (1 min) after growth desorption annealing at 600 °C.

The top figures show the oscillation vanishing after 5 ML relative to the Ge cluster installation and the corresponding RHEED pattern signature. One oscillation period corresponds to the growth of one atomic ML [30].

#### **3. SURFACE RECONSTRUCTION**

A clean substrate is an important prerequisite for epitaxial growth, since its oxidation due to atmospheric exposure causes crystal defects that degrade both the optical and electrical features of the epitaxial layer. Nowadays, vendors supply 'epi-ready' wafers pre-cleaned and oxidized in a controlled environment, in order to form an oxide protective layer that can be removed inside the growth chamber.

**90** *Silicon Based Thin Film Solar Cells Lorenzo Morresi* 

**Figure 8:** The top figure provides the corresponding signatures of an uninterrupted Ge growth. Si capping growth modes with (a) or without (b) hydrogen onto strained Ge. (c) Surface restoration and growth reorganization of the rough homogeneous Si covering into a smooth one (Elsevier license n. 2558160456690).

The use of such 'epi-ready' wafers has led to consistent results without the need for elaborate wafer cleaning procedures, such as Shiraki for the Si (100) and Si (111) [31], or Hakane for the Ge (100) [32]. However, even using 'epi-ready' substrates, proper thermal treatments must be used to obtain well-ordered surfaces after the oxide removal. In fact, in order to minimize the under coordinated surface, which presents one or more highly energetic dangling bonds, the system tries to arrange the surface atoms in different configurations, which differ from the bulk-like positions.

These new arrangements, involving the elimination of some atoms or their movement to non-epitaxial sites as well, are called surface reconstructions and deeply affect the further epitaxial processes.

The (001) is one of the most popular and widely studied surfaces for silicon and germanium.

It presents a very simple structure characterized, for the as-cut configuration, by square symmetry (see Fig. **9 (a)**, where the 11 surface unit cell is indicated). The surface lattice parameter is *as* = *a*2/2 = 3.84 Å for Si and *as* = 4.0 Å for Ge, where *a* is the equilibrium bulk lattice constant. In the as cut geometry, each surface atom has two dangling bonds, making this a highly unstable configuration.

To reduce the dangling bonds density, neighboring Si atoms pair to form parallel dimmers, which represent the fundamental unit characteristic of the Si (001) (Fig. **9 (b)**). The dimerization has the direct effect of modifying the surface periodicity along the direction of the dimer bond, leaving the perpendicular direction unchanged. Therefore, the reconstruction is defined as (2×1) Si (001). The dimerization process allows the system to reduce the number of unsatured bonds through the formation of a covalent directional bond connecting the two surface atoms. Moreover, the system can reduce its total energy by some hybridization processes, and reconstruction like *p*(21) and *c*(42) can be obtained (see Fig. **9 (c)** and **(d)** respectively).

**Figure 9:** The topmost layer is painted in dark gray. (a) Top view of Si (001) in the as cut geometry, showing a surface unitary (1×1) cell. (b) (2×1) dimerized Si (001). (c) Dimerized Si (001) with all the dimers tilted along the same direction, forming a (2×1) periodicity. (d) Si (001) whose (2×2) dimers are tilted alternately along the dimmers row.

In the case of Si (111), the system presents the lowest dangling bond density over the surface area (*dH* = 0.07 Å). Fig. **10 (a)** shows the top view of non-reconstructed Si (111).

Having such a low dangling bond density, the Si (111) is the cleavage surface obtained when an external strain is applied to split a Si crystal, but it is also one of the most frequently exposed surfaces when microcrystalline structures nucleate into amorphous matrix. The (111) surface assumes different reconstructions, like the chain geometry (Fig. **10** (**b**)).

**Figure 10:** The topmost layer is painted in dark gray. (a) Top view of Si (111) in the as-cut geometry. (b) Top view of Si (111) -chain.

### **4. DEPOSITION PROCESSES**

The main substrate surface processes are schematically illustrated in Fig. **11**.

**Figure 11:** Schematic illustration of the surface processes occurring during MBE growth.

These processes involved during the epitaxial growth can be summarized as: a) adsorption of the evaporated atoms or molecules impinging on the surface; b) surface diffusion and dissociation of the absorbed atoms; c) atoms arrangement into the crystal lattice; d) thermal desorption of the species not arranged into the lattice [24]. The adsorbed molecules (or atoms) first combine to reach a critical size, **i**, and then become stable nuclei (or clusters) on the substrate. The main factors affecting **i** are the substrate temperature, the arrival rates and the affinity with the substrate. Subsequent molecules (or atoms) may condense directly onto these nuclei, decreasing the rate of formation of new nuclei and increasing the size of existing ones to form islands that may coalesce upon surface contact.

However, a distinction must be made in the initial growth process between the heteroepitaxial and homoepitaxial. Fig. **12** shows the behavior of the deposition rate as a function of arrival rate (the flux described by eq. 2), at a given substrate temperature. For the MBE growth of compound semiconductors, the required fluxes are typically between 1018-1020 *atoms m-2 s -1*.

Fig. **12 (a)** represents the case of a single component A. The dashed line indicates the asymptotic deposition rate applicable to both homoepitaxial growth at all stages and heteroepitaxial growth after nucleation. In order to initiate the nucleation process for heteroepitaxial growth at the given substrate temperature, the super saturation rate must be greater than the reevaporation rate: *RS A* > *RE <sup>A</sup>*. The solid line indicates the case where other low-energy sites (*i.e.* surface impurities) are available to initiate the nucleation.

For a process involving an *AB* compound (see Fig. **12 (b)**) with a fixed evaporation rate of B, *RB*, nucleation initiate when the evaporation rate of A exceeds the super saturation rate of the compound: *RA* > *RS AB*. After nucleation, the deposition rate is proportional to *RA* and becomes a constant, and *RB* limits it. In the case of *RA* > *RS <sup>A</sup>* the deposition rate increases, and the growing film becomes A-rich [33].

**Figure 12:** Schematic illustration of deposition rate *vs.* arrival rate of component A for (a) one component system; (b) two component system A and B, with a fixed arrival rate of component B. Superscripts E and S indicate reevaporation and super saturation, respectively.

The whole growth process can generally be described by few parameters, such as the sticking coefficient, *s*, the thermal accommodation coefficient, *ac*, the condensation coefficient, *c*, the diffusion coefficient, *D*, and the mean stay time, *a*:

$$s = \frac{N\_{adh}}{N\_{air}}\tag{4}$$

the sticking coefficient is the ratio of the number of atoms (or molecules) adhering to the surface to the number of atoms (or molecules) arriving there. Depending on the growth regime, *s* could be less than unity when the adsorption energy of atoms is low, or the surface temperature is high;

$$a\_c = \frac{T\_i - T\_o}{T\_i - T\_s} \tag{5}$$

the thermal accommodation coefficient defines the atoms (or molecules) fraction that is in thermodynamic equilibrium with the substrate. *Ti* is the effusion cell temperature; *Te* is the energy corresponding temperature of atoms that immediately re-evaporate; *Ts* is the substrate temperature;

**94** *Silicon Based Thin Film Solar Cells Lorenzo Morresi* 

$$\mathbf{c} = \frac{N\_{\text{adh}}'}{N\_{\text{bar}}} \tag{6}$$

the condensation coefficient, differently by *s*, describes the fraction of atoms (or molecules) that immediately adhere to the surface. In this case atoms (or molecules) are desorbed before their chemical-physical reaction to the surface;

$$D = \left(\frac{a \cdot \upsilon}{N\_0}\right) \exp\left(-\beta E\_d\right) \left[cm^2 \text{ s}^{-1}\right] \tag{7}$$

the diffusion coefficient is defined as the product of the atom surface diffusion length before lattice incorporation and its surface mean speed. In this case depends on the lattice parameter, is the atomic vibration frequency, *N0* (cm-2) is the substrate sites number of equal adsorption energy *Ea* of isolated adatoms on the substrate, is written for (*kTs*) -1, *k* is the Boltzmann's constant and *Ts* is the surface temperature;

$$\tau\_a^{-1} = \upsilon \cdot \exp\left(-\beta E\_a\right) \left[\mathbf{s}^{-l}\right] \tag{8}$$

finally, *<sup>a</sup>* is the atomic mean stay time on the substrate surface before their reevaporation [33, 24].

#### **4.1. Processes of Nucleation and Growth**

The formation of a large cluster is an example of a chain reaction that starts with the formation of a small stable nucleus. In fact, above the critical size (n > **i**), growth is more probable than decay, and all large clusters may be considered stable, even if some atoms leave them during the growth process. The single atoms can diffuse across the substrate to join a stable cluster, or they can impinge directly on the growing clusters and be incorporated by them, as illustrated in Fig. **11**. The binding energy *Ej* of a *j*-cluster (with size *j* **i**) can be related to the energy *E2* of a pair of atoms on the substrate, by considering nearest-neighbor bonds [34].

**Figure 13:** Binding energies of atoms and clusters that nucleate and growth on a square lattice. Single atoms: (a) *Ea*; (b) *Ea* + 2*E2*; (c) *E' a*=4*E2*; (d) *E' <sup>a</sup>*+2*E2*=6*E2*; (e) *Ea*-*Ed*; clusters; (f) 4*Ea*+4*E2*; (g) 4*Ea*+8*E2*. *Ed* is the diffusion energy; *E' <sup>a</sup>* is the adsorption energy of an atom on a monolayer of the condensate; E' d is the diffusion energy of an isolated atom on top of a monolayer; (f) and (g) refer to the 2D and 3D surface nucleation of clusters respectively.

**Figure 14:** Regimes of nucleation and growth of clusters.

The processes are illustrated schematically in Fig. **13**, for an epitaxial growth in an orientation with four-fold symmetry. The three most important activation energies *Ea*, *E2* and *Ed*, with the experimental variables *R* and *Ts*, determine the nucleation regime observed (see Fig. **14**), which can be described using the parameter *R/N0 <sup>2</sup> D*. The growth process at the lowest temperature *Ts* and higher arrival rate *R* is described in Fig. **14 a)**. In this case *R/N0 <sup>2</sup> D*  1 and the atoms stay exactly where they have arrived. An irregular layer is built up, and if atoms have directional bonds the layer will tend to be amorphous. The second regime, illustrated in Fig. **14 b)**, is the case of "layerby-layer" growth. It is characterized by *R/N0 <sup>2</sup> D* << 1, *Ea E' <sup>a</sup>*, and *Ts* must be low enough so that 2D crystal layers can grow, even though single atoms may reevaporate. The regime illustrated in Fig. **14 c)** corresponds to the equilibrium adsorption, where the same conditions as case **b)** apply, but the surface temperature is higher or the arrival rate lower. Furthermore, atoms, at least from the highest layers, are quickly desorbed parallel to the surface, and the film growth only proceeds to a certain thickness whilst bulk crystals do not grow. In this case, there is no stable microstructure of the film in the long term, and adsorption is usually described only in thermodynamic terms.

In the regimes illustrated in Fig. **14 d)** and **e)** the film initially forms a three dimensional cluster on the substrate, the condition 4*E2 Ea* applies and the surface temperature is lower for case **d)** and higher for the case **e)**. If *E2 > Ea*, the cluster will have a 3D shape from the beginning of growth. For the regime illustrated by case **d)**, all atoms condense, since the rate of formation of new clusters is faster compared to the rate of reevaporation, whilst for case **e)** the condensation is incomplete. Finally, in the regime illustrated in Fig. **14 f)**, if either *E2*/*kT* or *Ea*/*kT* is small, the nucleation will be impossible on a perfect substrate, due to the effect of defects sites on the surface. An intermediate regime occurs when *E' <sup>a</sup>* is lower than the value for an infinite crystal after some finite layers have been deposited. In this case growth starts in the "layer-by-layer" mode and then 3D crystals nucleate on the top. The term to describe this regime is the "Stranski-Krastanov" growth mode [34]. The three growth modes previously described are schematically illustrated in Fig. **15**.

**Figure 15:** Schematic illustration of the three main growth modes: "layer-by-layer"-Frank-Van der Merwe; "island"-Volmer-Weber; "layer plus island"-Stranski-Krastanov.

These modes can also be classified by the behavior of the surface free energy during the epitaxial process, since it strongly determines the equilibrium morphology. In fact, considering a latticematched growth mode, in Frank-Van der Merwe, the sum of the free energy associated with the free surface of the epitaxial film, e/v, and with the interface between the substrate and the epitaxial surface, s/e, is less than or equal to that associated with the original substrate surface, s/v. Then, the overall free energy decreases faster over the first layer (or two), before settling down to a steady state slope for thicker films. Therefore, the system is thermodynamically stabilized against breakup into inhomogeneous regions, some thicker and some thinner. In Volmer-Weber, the sum e/v and s/e is greater than s/v. The overall free energy then increases over the first layer (or two), before reversing and decreasing as next layers are deposited. Therefore, the system of uniform thickness is thermodynamically unstable for breakup into inhomogeneous regions, some very thick and some completely uncovered. In Stranski-Krastanov, the sum e/v and s/e is less than s/v. Therefore, the surface free energy decreases rapidly as the first layer (or two) is deposited, before decreasing, less steeply than the "layer-by-layer" growth mode, for thicker films. Therefore, films thicker than a few monolayers are unstable and can breakup into inhomogeneous regions, some very thick and some having only one layer (or two) [35]. For a strained epilayer there is the additional possibility that island formation may allow the system to introduce misfit dislocations underneath the islands to relax strain energy. For a system with small interface free energy but large lattice mismatch, initial growth is "layer-by-layer", but a thicker layer has greater strain energy and can lower its total energy by forming isolated thick islands in which the strain is relaxed by interfacial misfit dislocations [36].

#### **5. MISFIT DISLOCATIONS AND DEFECTS**

Generally, a heteroepitaxy process is related to lattice mismatch since a layer with atomic spacing or lattice symmetry different from those of the substrate is epitaxial grown. This disregistry can accommodate by strain connected to a relevant interfacial energy or by structural defects in the layer. In fact, when both the epilayer thickness and the mismatch between the stress-free lattice parameters of the two crystals are small, the separation of the dislocation becomes infinite and all mismatch is accommodated by elastic strain [37]. In order to introduce an easy explanation of the misfit concept, some important parameters will be considered, and the simplest situation where both layers have rectangular symmetry (*i* = x, y) at the interface plane is used. If the thickness of the epitaxial layer is thinner than that of the substrate, the mismatch parameter can be defined by:

$$f\_i = \frac{a\_{al} - a\_{al}}{a\_{al}} \tag{9}$$

where *a* is the lattice parameter and *s* and *e* indicate the substrate and the epitaxial layer, respectively. A positive value of *f* implies that the strain is tensile. Moreover, the misfit strain is defined as:

$$\mathbf{e}\_{l} = \frac{\mathbf{a}\_{al}^{s} - \mathbf{a}\_{al}}{\mathbf{a}\_{al}} \tag{10}$$

where *a<sup>s</sup> <sup>e</sup>* indicates the lateral atomic spacing in the strained epilayer. However, when the coherence between the strained layer and the substrate is lost, the misfit strain is shared between a plastic strain component, *d*, due to the misfit dislocations and a residual elastic strain component:

$$f\_i = \mathbf{e}\_i + d\_i \tag{11}$$

The value of *d* can be estimated from the misfit dislocation spacing, *S*: *d = bn/S*, where *bn* is the interface-plane component of the Burgers vector in the direction of the misfit dislocation spacing. It is well known that under adequate conditions, overgrow layers can be deposited epitaxially on the substrate with different lattice parameters up to a critical thickness *hcrit* [38, 34]. Epilayers thinner than *hcrit* adapt the lattice parameter of the substrate, a condition known as "pseudomorphic" growth [39, 40].

The misfit between the substrate and the overgrown layer is sufficiently small, and the first deposited layers are strained to match the substrate and a coherent (perfect matched) epilayer is formed. The situation is depicted in Fig. **16**. If the lattice parameter of the epilayer is greater than that of the substrate, the film grown undergoes a compressive strain on the interface plane. *Vice versa*, the strain will be tensile. Moreover, since the total volume of the unit cell must remain unchanged, the cell is also distorted perpendicularly to the plane interface. As the epilayer thickness increases, overlapping *hcrit*, the homogeneous strain energy becomes favorable for the introduction of misfit dislocations (see Fig. **16**) [40]. Fig. **17** reports an example of the result of the Matthews-Blakeslee theory for 60° a/2 <101> misfit dislocation in the Si1-xGex/Si (100) system and experimental measurement of critical thickness *hcrit* for different growth\annealing temperatures [40]. It is also possible to change the value of *hcrit* by growing one or more

#### **98** *Silicon Based Thin Film Solar Cells Lorenzo Morresi*

subsequent epilayers. In fact, if an epilayer B is deposited on a substrate A, and the layer thickness exceeds the critical value, it might be possible to restore coherency by the deposition of a layer of the same material of A.

**Figure 16:** Growth of a layer on a substrate with different lattice parameters; the pseudomorphic (coherent mode) and the unstrained growth cases are illustrated. The red arrows indicate the presence of misfit dislocations at the interface, due to a non-coherent growth.

**Figure 17:** Measurement of critical thickness in the Si1−xGex/Si (001) system for different growth temperatures *vs.* the prediction of the Matthews–Blakeslee model [40].

However, there is a second critical thickness of the epilayer B, above which it is not possible to restore coherency. Depending on the crystalline structure of the growing material and on the quality of both the epitaxial process and the surface of deposition, a wide variety of dislocations and effects can originate in the epilayers. Even though the presence of most of these crystalline defects is undesirable, certain types are essential in semiconductor manufacturing. In the following sections the most common will be described briefly.

### **5.1. Dislocations**

Considering a single epilayer in which the perfect coherent registry with the substrate is broken, the simplest consequence might consist of a half plane missing from the epitaxial film. In this case, the most useful definition to introduce is that related to the Burgers circuit. It is the atom-to-atom path that forms a closed loop in a crystal with dislocations. If the same atom-to-atom sequence is formed in a dislocation free crystal, and the circuit does not close, then the original loop must enclose one or more dislocations. The vector required to fill the gap in the circuit is called the Burgers vector (the red arrows illustrated in Fig. **18**).

**Figure 18:** Pure edge and pure screw dislocations arising from the missing half of the epitaxial plane. The blue arrows indicate the Burgers vectors circuit. The red arrows indicate the Burgers vector *b* .

In particular an edge dislocation has *b* perpendicular to the dislocation line. It marks the edge of a missing (or extra) half-plane of atoms. On the other hand, in a screw dislocation atoms are connected in a spiral around the screw dislocation. It has *b* parallel to the dislocation line. Generally, in most cases, the dislocation line lies at an arbitrary angle to its Burgers vector and the dislocation line has a mixed edge and screw character [41].

#### **5.2. Stacking Faults**

A stacking fault is a planar defect due to the interruption of the regular sequence layers within the crystal in a local region. This type of defect destroys the perfection of the host crystal, and the associated energy per unit area of fault is known as the "stacking fault energy". Two types of stacking faults referred as to intrinsic and extrinsic are expected in a face centered cubic lattice. These are best described by considering the change in sequence resulting from the removal or introduction of an extra layer (see Fig. **19**).

**100** *Silicon Based Thin Film Solar Cells Lorenzo Morresi* 

**Figure 19:** Stacking faults in the face-centered cubic structure.

In the intrinsic stacking fault, part of a layer has been removed which results in a break in the stacking sequence. Clearly, the stacking sequence above and below the fault plane are continuous right up to the fault itself. In the extrinsic stacking fault, an extra layer has been introduced. There are two breaks in the stacking sequence, and the extra layer does not belong to the continuing patterns of the lattice either below and or above the fault.

#### **5.3. Grain Boundaries**

A crystalline solid can also consist of a large number of randomly oriented grains (single crystals) separated by grains boundaries (defects). When the misorientation between the grains is too great, the atomic arrangements at the boundaries are very complex and vary significantly with the angles of misorientation (see Fig. **20**).

**Figure 20:** (a) Schematic illustration of differently oriented crystal grains in a polycrystalline material. (b) Representation of a grain boundary separating two crystallites.

A notable feature of the boundary structure is that the region of disorder is very narrow, limited to one or two atoms on each side of the boundary.

#### **5.4. Twinning**

Formation of twin boundaries is a process in which a region of a crystal undergoes a homogeneous shear that produces the original crystal structure in a new orientation. Deformation twinning can be induced by plastic deformation and is particularly important in body-centered and close packed hexagonal crystals. For example, in a face-centered cubic crystal the "ABC" notation adopted in

section **5.2** can be used to represent the relative atom positions in matrix and twin. Fig. **21** shows the stacking sequence of a (111) twin. The planes I-II and III-IV indicate the "coherent" twin planes; nearest-neighbor atom distances are unchanged across these planes. The plane II-III is called an "incoherent" twin plane; the two lattices do not fit exactly on them, and consequently there is considerable atomic misfit.

### **5.5. Point Defects**

The 1D defect is called a point defect, since it involves only one atom surrounded by a perfect lattice. However, the presence of a point defect may affect the properties of its nearest neighbors, and by elastic interactions, a sizable spherical region of the lattice surround itself. Fig. **22** shows some forms of crystal point defects. A defect where an atom is missing from a lattice site is known as a vacancy defect. Vacancies are expected at high growth temperatures because the surface atoms mobility (*i.e.* the diffusion coefficient in eq. 7) in these cases must be quite high for them to change their positions leaving behind empty lattice sites.

If an atom is located in a non-lattice site within the crystal, it is said to be an interstitial defect. When the interstitial defect involves an extra atom, it is referred to as a self-interstitial defect. Vacancies and self-interstitial defects are classified as intrinsic point defects. A substitutional defect refers to an atom of a different type than the lattice composition, which has replaced one of the bulk atoms in the lattice. Substitutional and interstitial defects are classified as extrinsic point defects because foreign atoms are involved. If an atom leaves its site in the lattice, creating a vacancy, and then moves toward the surface of the crystal, it becomes a Schottky defect. On the other hand, an atom that vacates its position and transfers to an interstitial position in the crystal is known as a Frenkel defect. However, the management of defects during the epitaxial growth is an indispensable factor for obtaining materials with engineered performances (both electrical and optoelectronic). In fact, defects can be classified as undesired or desired impurities: the former generally refer to the contaminants into the lattice, the latter to the dopants.

**102** *Silicon Based Thin Film Solar Cells Lorenzo Morresi* 

**Figure 22:** Schematic representation of the most common point defects in crystals.

#### **6. DOPING**

The main problem with the application of MBE for the fabrication of semiconductor devices is dopant incorporation. From a grower point of view, this topic should be divided into two parts: unintentional (and generally undesired) doping, which is caused by the presence of residual gases in the deposition chamber, and intentional (desired) doping, achieved for example by a thermal beam co-deposition process. As to the contribution of residual gas species, it should be noted that the value of the residual gas pressure achieved during the epitaxial deposition is lower than 5 10-11 Torr. At this low pressure the residual gas contains mainly H2, H2O, N2 and COx molecules. In order to reduce to a minimum the incorporation of these contaminants it is a good practice turn off all hot filaments (such as the ionization gauges in Fig. **2**) not necessary during the epitaxial process. Moreover, it is important to restrict temporal and spatial variations in the temperature of LN2 cryopanel surfaces during growth, as these spatial and temporal variations can result in variations in desorption and adsorption of trapped gas molecules. During the intentional doping of a semiconducting compound *Ai Bj* (*A* and *B* are the elements, while *i* and *j* are the numbers denoting columns in the Mendeleeev's table), different chemical reactions can take place [24]. If a cation element (*A*) is replaced by an element atom (*C*) of the group (*i-*1), a *p*-type doping is achieved:

$$C\_{\ell}^{(\iota-1)} + V\_{\iota\iota} \leftrightarrow C\_{\iota\iota}^{(\iota-1)(-\iota)} + h \tag{12}$$

where *VAi* is a vacant *A* site in the *Ai Bj* compound, *CAi (i-1)(-)* is the ionized *C* acceptor, *h* is a free hole in the valence band of *Ai Bj* , and (*g*) denotes the gas phase of the element. If an anion atom (B) is replaced by an element atom (*D*) of the group (*j* + 1), an *n*-type doping is achieved:

$$\frac{1}{2} \frac{1}{2} D\_{2(g)}^{(\cdot \vee \cdot \mathbb{I})} + V\_{\mathbb{N}} \leftrightarrow D\_{\mathbb{N}}^{(\cdot \vee \cdot \mathbb{I})(\ast)} + e$$

where *e* is a free electron in the conduction band of *Ai Bj* , *DBj (j-1)(+)* is an ionised donor. Replacement of a cation atom by doping atom (*D*) of the group (*i+j*)/2 of the periodic table gives *n*-type doping:

$$D\_{(g)}^{(i+j)\dagger^2} + V\_{Al} \leftrightarrow D\_{Al}^{(i+j)\dagger^2(i)} + \left(\stackrel{j-i}{\prime}\stackrel{j}{\prime}\right) \mathbf{e} \tag{14}$$

Replacement of the anion atoms by doping elements (*C*) of the group (*i+j*)/2 gives *p*-type doping:

$$C\_{(\mathfrak{g})}^{(\iota+j)\natural^2} + V\_{\mathfrak{g}\mathfrak{g}} \leftrightarrow C\_{\mathfrak{g}\mathfrak{g}}^{(\iota+j)\natural^2(-)} + \left(\stackrel{j}{\smile}\stackrel{i}{\smile}\right)\hbar\tag{15}$$

However, the analysis of the previously illustrated reactions requires knowledge of quantities such as the enthalpy and entropy of the system of defects involved in the doping. A good approach to understanding the principles of this problem is that proposed by Heckingbottom [42], where thermodynamic considerations can determine whether a doping process is possible or not during the epitaxial deposition. This model is useful in the selection of dopants that are more suitable. In a more detailed study of a particular reaction, the comparison of the thermodynamic framework with experimental data provides identification of any kinetic barriers and hence leads to a clearer understanding of the reaction mechanism [43].

#### **7. IV-GROUP MBE**

The "Stranski-Krastanov" growth mode illustrated in sec. **4.1** is a powerful technique applied for fabrication of a large number of high-quality nanosized atomic clusters (quantum dots-QDs). These dots have unique properties which can be tuned by the grower by varying the epitaxial growth parameters. Due to the importance of Si in opto-electronic device applications and energetic device productions, nano-sized materials based on silicides are under continuous investigation to optimize their performance and to scale down dimensions. Arrays of Ge, Si and SiGe nano-islands, so called "pyramid" and "dome" clusters, grown on Si(001) are typical examples of such systems (see Fig. **23**). However, as previously illustrated, different growth conditions play crucial roles for the appearance of these islands grown on Si (001).

**Figure 23:** (a) Scanning Tunneling Microscopy (STM) image (108 108 nm2 ) of a faceted island obtained by depositioning Si0.6Ge0.4 on Si (001) [44]. (b) Cross-sectional TEM image of a Ge/Si multilayer structure consisting of five individual Ge layers. (c) Dark field image exhibiting Ge islands buried in the Si layers (AIP license n. 2571411082174) [45].

#### **104** *Silicon Based Thin Film Solar Cells Lorenzo Morresi*

Table **1** shows the results obtained by A. Malachias *et al.* [46], demonstrating how strong changes in interdiffusion and resulting atomic ordering arise from the different growth parameters used during the MBE deposition of Ge domes on Si(001). Another intriguing possibility is related to the formation of a patterned substrate, above which nanocrystals are subsequently self-assembled by solid phase epitaxy [47-49].

**Table 1:** Growth parameters used during MBE deposition of Ge:Si(001) films. Domes with different width/height ratio can be obtained.


**Legend**. The monolayer (ML) thickness is considered as 0.1413 nm for Ge, and 0.1385 nm for Si0,5Ge0,5.

In this model highly dense two-dimensional periodic arrays of ordered QDs can be nucleated, with lateral dimensions depending on the holes' properties. The 2D array of holes with different size, depth and pitches can be fabricated by a focused ion beam (FIB), both on SiO2/Si(001) and Si(001) substrates. After the MBE evaporation of few monolayers of Ge (at room temperature), the system is annealed at about 500-550 °C, in order to raise the surface mobility of the Ge atoms, and then fill the holes by Ge QDs (see Fig. **24**). However, several theoretical models include the utilization of intermediate band solar cells [50], up-conversion for the absorption of sub-band gap light [51], and control of the strain, shape, and local Ge fraction in multicrystalline SiGe for the absorption of the near-infrared light [52]. Furthermore, experiments were also performed to improve the performance of the solar cells by 1) absorbing the low-energy photons, 2) by using SiGe multicrystalline with microscopic compositional distribution to enhance the absorption performance [53, 54], and 3) by exploiting the advantage of quantum well solar cells to independently optimise the absorption edge and spectral characteristics [55]. Another way to absorb the low-energy photon might be the incorporation of doped Ge dots in the intrinsic region of Si-based solar cells [23, 56-61].

**Figure 24:** Atomic force microscopy (AFM) image of the organization of Ge dots on patterned areas by Ga+ source (FIB), at a growth temperature of 550 °C and Ge thickness of 14. The initial holes diameter was 40 nm with a pitch of (a) 200 nm, and (b) 75 nm (AIP license n. 2573690146603).

Even though the MBE cannot represent a valuable growth technology for large production of semiconducting devices, it does represent an excellent way to investigate the basic properties of the materials and solutions previously mentioned, in order to employ them in either opto-electronic or energetic device applications produced by other industrial growth technologies widely used in the field of device fabrication.

### **ACKNOWLEDGEMENT**

Declared none.

### **CONFLICT OF INTEREST**

The author(s) confirm that this chapter content has no conflict of interest.

#### **REFERENCES**


#### **106** *Silicon Based Thin Film Solar Cells Lorenzo Morresi*


#### *Molecular Beam Epitaxy (MBE) Silicon Based Thin Film Solar Cells* **107**


© 2013 The Author(s). Published by Bentham Science Publisher. This is an open access chapter published under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/legalcode

## **SECTION II - EXPERIMENTAL TECHNIQUES TO MEASURE FILM AND DEVICE PARAMETERS**

# **CHAPTER 5**

## **Infrared and Raman Spectroscopies**

**Ubaldo Coscia1,2,\*, Deepak K. Basa3 and Giuseppina Ambrosone2,4** 

*1 CNISM Naples Unit, Complesso Universitario MSA, via Cintia, 80126, Naples, Italy; 2 Department of Physical Sciences, University of Naples "Federico II", Complesso Universitario MSA, Via Cintia, 80126 Naples, Italy; <sup>3</sup> Department of Physics, Utkal University, Bhubaneswar-751004, India and <sup>4</sup> CNR-SPIN, Complesso Universitario MSA, via Cintia, 80126 Napoli, Italy* 

**Abstract**: The chapter is devoted to the Fourier transform infrared (FTIR) and Raman spectroscopy. The theory of both techniques has been briefly treated and the most widely used experimental apparatus have been described. The use of the FTIR and Raman spectroscopy for the characterization of silicon based films and the optimization of microcrystalline solar cell parameters, as examples of applications, have been reported. In particular, it has been shown that by means of FTIR it is possible to detect oxygen impurity in microcrystalline silicon, to individuate the device grade microcrystalline silicon for solar cells fabrication and to study the phase transition due to the thermal annealing of amorphous silicon carbon alloys (a-Si1-xCx:H) and a-Si1-xCx:H/SiC multilayers. Furthermore, it has been demonstrated that the Raman spectroscopy can be used for the optimization of J-V parameters of microcrystalline silicon solar cells, for the study of boron doping effect on the crystalline volume fraction in microcrystalline silicon carbon, for the investigation of crystallization process induced by thermal annealing in a-Si1-xCx:H/SiC multilayers, for determining the influence of the carbon alloying as well as the substrate on the crystalline volume fraction in nanostructured silicon carbon films and, finally, for the study on the medium range order in nanocrystalline silicon.

**Keywords:** Fourier transform infrared spectroscopy, raman scattering, vibrational modes, structural properties, silicon (hydrogenated) thin films, silicon carbon (hydrogenated) thin films, silicon nanocrystallites, solar cells parameters, thermal annealing, plasma enhanced chemical vapour deposition, average grain dimension, crystalline volume fraction, microstructure factor, oxygen impurities.

### **1. INTRODUCTION**

Silicon based thin films are widely used in photovoltaic (PV) applications. Hydrogenated amorphous silicon (a-Si:H) and related alloys have been employed in the production of single and multijunction solar cells [1-4]. However, a-Si:H solar cells undergo a loss of efficiency under light soaking conditions due to the Staebler-Wronski effect [5]. Hydrogenated micro/nano crystalline silicon films, because of their better transport properties, resistance to light-induced degradation and superior long wavelength response as compared to amorphous counterpart, have been used to replace or supplement amorphous Si in solar cells in order to improve their stability and efficiency [6-8]. Indeed, these materials have been incorporated in p-i-n and n-i-p structures [9-16] or in

**<sup>\*</sup>Address correspondence to Ubaldo Coscia:** Department of Physical Sciences, University of Naples "Federico II", Complesso Universitario MSA, Via Cintia, 80126 Naples, Italy; Tel: +39 081 67 6102; Fax: +39 081 67 6346; E-mail: coscia@na.infn.it

stacked tandem cells in micro morph configuration [17-20] as well as in triple junction solar cells [3, 21].

Recently, nanostructured films composed of silicon nanocrystals (SiNCs) embedded in amorphous dielectric matrix of different kinds (SiO2, Si3N4, SiC) have opened up alluring possibilities for the third generation "all Si" tandem solar cells [22-25]. Nanocrystals having size less than 7 nm dispersed in such matrices behave as quantum dots exhibiting quantum confinement effects of carriers [26, 27] which results in an enlargement of the band gap and efficient light emission in the visible range at room temperature [28-34]. It has been reported that SiNCs embedded in a near stoichiometric amorphous silicon carbide matrix can exhibit larger quantum confinement effects as compared to SiNC in SiO2 or Si3N4 matrix because of a significantly lower barrier height of SiC matrix [35-39]. In order to obtain highly efficient solar cells an optimization process of the optical, electrical and structural properties of the above-mentioned materials has become indispensable.

The structural characterizations are performed by using several techniques such as transmission electron microscopy (TEM), X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, Raman spectroscopy. In this chapter, we focus on FTIR and Raman spectroscopy that have the capacity to analyse samples in different phases such as crystalline, micro crystalline, nanocrystalline and amorphous both in bulk and thin film. These techniques are popular as structural probes because of their speed, accuracy, sensitivity and, above all, their being nondestructive.

Infrared and Raman techniques have common attributes. They are optical probes and are spectroscopic in nature implying that the intensity of signal is measured *versus* wavenumber (inverse of wavelength). Both Infrared and Raman spectroscopy require a light source, a means to set and/or measure the wavelength, a detector and a spectra recorder. However, the techniques are distinctly different because of the different processes they are based on (absorption for infrared and scattering for Raman) and the different intensity levels they handle. In Infrared spectroscopy, infrared energy covering a wide range of frequencies is directed onto the sample. Absorption occurs at certain resonant frequencies resulting in a series of vibrational peaks in the spectrum, which are used for the identification and quantification of the vibrational modes. In the Raman spectroscopy, on the other hand, a radiation of single frequency impinges on the sample and the scattered radiation, which is one vibrational unit of energy different from that of the incident beam, is detected. The study of the intensity distribution of inelastically scattered light provides valuable dynamical and structural information on the sample.

The FTIR spectroscopy is a very powerful tool to determine the bonding configurations as well as the hydrogen and oxygen contents, in hydrogenated amorphous, microcrystalline and nanocrystalline silicon based films. This technique is therefore extensively used in investigating the properties of these materials affected by hydrogen, oxygen and other impurities. Indeed, hydrogen plays an important role by passivating the dangling bonds in a-Si:H and its alloys as well as the grain boundaries in the micro/nano crystalline materials, thus improving their electrical and optical properties [40, 41]. Further, it is well-known that hydrogenated microcrystalline silicon (c-Si:H) layers show a pronounced n-type behaviour [19, 42] due to the unwanted oxygen impurities. Since p-i-n solar cells require intrinsic c-Si:H as absorber layers a reduction of the inherent oxygen impurities is necessary.

Raman spectroscopy, on the other hand, is sensitive to the structural changes and, in the case of Si based materials, gives information on the degree of disorder and provides a means for quantitative measurements of Si crystalline size and volume fraction useful for solar cell optimization.

In this chapter we will first treat briefly the background and the theory of FTIR and Raman spectroscopy, then we will describe their experimental apparatus. Furthermore, we will discuss the quantities and the properties obtained by means of these techniques taking a few examples from the literature concerning a-Si:H, hydrogenated amorphous silicon carbon alloys (a-Si1-xCx:H), micro/nano crystalline Si films and nanostructured materials composed of Si nanocrystals embedded in a-Si1-xCx:H matrices. Structural properties of micro crystalline and polycrystalline SiC as well as self-organized nanostructured films obtained by post thermal annealing of amorphous precursors were also dealt with.

### **2. FOURIER TRANSFORM INFRARED SPECTROSCOPY**

In the conventional dispersive method, which is a standard technique for the visible light spectroscopy, a dispersive grating (prism) spectrometer is used as the wavelength selector and the wavelength (energy) of the incident radiation on the sample is varied over the desired range to obtain the spectrum. IR spectroscopy in earlier time was based on this conventional technique. However, because the power available for the infrared sources is low (particularly at longer wavelength useful to study impurities, lattice modes and free carriers) and the grating technique does not make the most effective use of the limited infrared power, the Fourier transform infrared spectroscopy has been developed. FTIR spectroscopy allows the simultaneous analysis of many frequency components in a single operation as well as the efficient use of the low power IR sources.

In Fourier transform infrared spectroscopy, the dispersive grating is replaced by the Michelson interferometer and the sample is exposed to a single pulse of radiation consisting of many frequencies to obtain the interferogram, *i.e.* the Fourier transform of the desired spectrum. The spectrum (intensity *versus* wavenumber) is constructed from the interferograms using extensive computer manipulation.

### **2.1. Background**

Although the theory of Fourier transform, developed by J. B. Fourier in 1807, is at the heart of FTIR technique, the science and the technology of Fourier transform spectroscopy was initiated in 1880 with the invention of Michelson interferometer by Albert A Michelson. Michelson was also the first to demonstrate that the inverse Fourier transform of the interferogram coincides with the spectrum, but, even though he was well aware of the potential of the interferometer, he could not take advantage of his technique in the absence of computer and other associated algorithm [43, 44]. During the 1950s, Strong and his group [45] made a serious attempt to study the fundamental aspect of the technique and develop the applications of FTIR which generated interest in the interferometric spectroscopy.

Important developments were made possible by the work of Cooley and Tukey [46] in 1965 on the fast Fourier transform (FFT) algorithm, which allowed one to calculate easily the Fourier

transforms using electronic computers. Interestingly, by 1970 commercial Fourier transform spectro-meters were made available and were also widely accessible. There is a number of excellent books on FTIR spectroscopy. For an in-depth examination see the refs. [44, 47-50].

### **2.2. FTIR Spectroscopy Advantages**

The distinctive advantages of FTIR spectroscopy over the conventional dispersive spectroscopy stem from higher signal-to-noise ratio as well as from the higher accuracy in the frequency measurement of the spectra. Further merit is the high stray light rejection efficiency, because the sample is placed between the interferometer and the detector. Multiplex or Fellgett advantage [51] and throughput or Jacquinot advantage [52] make possible the increased signal-to-noise ratio of the FTIR technique, while Connes advantage [53] offers improvement in frequency accuracy. In the following, we will describe them briefly.

### *2.2.1. Multiplex or Fellgett Advantage*

Fellgett advantage states clearly that the signal-to-noise ratio of FTIR spectrometer is higher than that of a dispersive instrument for the same resolution and spectral range [51]. This is due to the different ways in which the various frequencies of radiation are handled. In Fourier spectroscopy many wavelengths are measured simultaneously while in a dispersive instrument a narrow band of frequencies is measured for unit time. This advantage emphasizes that Fourier spectroscopy takes less time than dispersive spectroscopy to measure the entire spectrum.

If a broad spectrum between wavenumber f1 and f2 is scanned in time T with a resolution of f, the number of spectral elements in the band, M, is given by:

$$M = \frac{f\frac{1}{2} - f\frac{1}{2}}{\Delta f} \tag{1}$$

In the dispersive spectroscopy using grating (or prism), each small band f can be observed for a time (T/M), therefore, the signal in f is proportional to (T/M). The noise is proportional to (T/M)1/2 because it is random and independent of signal level. Hence, signal-to-noise ratio for the dispersive spectroscopy (S/N)G should be:

$$\left(\frac{S}{N}\right)\_G \propto \left(\frac{T}{M}\right)^{\frac{1}{2}}\tag{2}$$

In the Fourier spectroscopy, all the small bands of resolution f in the broad band (f2-f1) are detected simultaneously. Therefore, the signal in f is proportional to T. The noise is proportional to (T)1/2 for being random and independent of signal level. Therefore, the signal to noise ratio for the Fourier spectroscopy (S/N)F should be:

$$
\left(\frac{S}{N}\right)\_F \propto T^{\frac{1}{2}}\tag{3}
$$

Assuming the proportionality constant to be the same, the following ratio can be obtained:

$$\left(\frac{S}{N}\right)\_{\!F} : \left(\frac{S}{N}\right)\_{\!G} = M^{\frac{1}{2}}\tag{4}$$

Because M is normally very large (typically around 10<sup>4</sup> or more), the (S/N)F is at least 10<sup>2</sup> times more than (S/N)G. However, this improvement in (S/N)F is possible only if the noise of the spectrum is due to the detector noise which, in turn, is not proportional to the detector signal.

#### *2.2.2. Jacquinot or Throughput Advantage*

Jacquinot was the first to demonstrate [52] the increase in throughput of FTIR spectroscopy (Jacquinot advantage). This advantage essentially means that high resolution can be obtained in FTIR spectroscopy without using narrow slits, while in the dispersive spectroscopy there is always a trade-off between the resolution and the amount of light reaching the sample.

In the dispersive spectroscopy, the gratings (or prisms) allow the observation of the desired nearly monochromatic frequency domain and the spectra are recorded by scanning them at successive resolution intervals. Better resolution requires the presence of narrower entrance and exit slits which, in turn, decrease the energy entering the monochromators. Accordingly, only a small portion of the energy emitted by the source can be utilized by the detector, requiring the increase in the time of measurement thus decreasing the scanning rate. Clearly, the requirement for good resolution results in throwing away most of the valuable energy. In the Fourier transform spectroscopy, the wide circular apertures as well as the use of the collimator (to focalize the radiation) ensure that more energy reaches the sample and detector thus increasing the signal-tonoise ratio.

The throughput U is defined as the product of the cross-sectional area A and solid angle of the beam at any focus of the optical beam. The product also determines the total radiant power accepted by the optical system for a source of given brightness. Therefore, it is essential to maximize the throughput and, accordingly, the energy reaching the detector, in order to maximize the signal-to-noise ratio [44].

In the Fourier transform spectroscopy, the resolving power of the Michelson interferometer RF is given by [49]:

$$R\_F = \frac{\text{g}F}{d}^2\tag{5}$$

where d is the diameter of the circular infrared source and F is the focal length of the collimating mirror. The solid angle subtended by the source at the collimating mirror, taking into account the eq. (5), results as:

$$
\Delta\Omega\_F = \frac{\pi d^2}{4F^2} = \frac{2\pi}{R\_F} \tag{6}
$$

Assuming the area of the collimating mirror to be AF, the throughput of the Fourier transform spectroscopy UF is given as:

$$\Delta U\_F = A\_F \Omega\_F = \frac{2\pi\_{AF}}{R\_F} \tag{7}$$

In the dispersive (grating) spectroscopy, the area of the slit is essentially the effective area of the source. If AG is the area of the grating, d is the dimension of the slit, F is the focal length of the collimating mirror and RG is the resolving power of the grating, the energy throughput of the grating spectrometer UG is given by [44]:

$$U\_{\mathcal{O}} = \frac{d\_{AG}}{F\_{\mathcal{R}\mathcal{G}}} \tag{8}$$

Assuming the resolving power, the area and the focal length of the collimating mirror to be the same for Fourier transform and dispersive spectrometer, the ratio of the throughputs of the Fourier transform and dispersive spectrometer is given by:

$$\frac{U\_F}{U\_G} = 2\pi \left(\frac{F}{d}\right) \tag{9}$$

For the good quality spectrometers (F/d) values are typically around 30, indicating that UF is about 200 times more than UG. Clearly, about 200 times more power can be put through the Fourier transform spectrometer as compared to the dispersive spectrometer. This throughput advantage is of considerable importance since IR sources are inherently weak.

#### *2.2.3. Laser Reference or Connes Advantage*

In the dispersive spectroscopy, the ability of the electro-mechanical mechanism to move the gratings and slits uniformly as well as the precise calibration with an external standard determine the accuracy and precision in the frequency measurements. In the FTIR spectrometer, the frequency is measured by direct comparison with a visible laser output (usually He-Ne laser), thus making redundant the calibration using an external standard. Furthermore, since the laser wavelength is known very accurately and is also very stable, the FTIR spectroscopy allows a considerable improvement in frequency accuracy as determined by Connes [53] for the first time (Connes advantage). This advantage offers the accurate alignment of the spectra thus facilitating measurements of difference spectra.

### **2.3. Theory**

The cardinal principle of Fourier transform spectroscopy is the light wave interference. Although different FTIR apparatus use different interferometers such as Michelson, lamellar grating, and Fabry-Perot, Michelson interferometer is the most preferred one because of its easy construction and operation as well as high resolving power.

The schematic diagram of the Michelson interferometer is shown in Fig. (**1**). The radiation from the source reaches the beam splitter (BS). Part of the beam passes through the beam splitter and is reflected back from the fixed mirror while the part reflected from the BS is reflected back again from the moving mirror. The movement of mirror introduces path difference between the two light beams. The beams recombine producing an intensity variation which depends on , known as interferogram I() and is given by:

$$I(\Delta) = \bigcap\_{-n}^{n} S(f) \left[ 1 + \cos(2\pi f \Delta) \right] df = \frac{1}{2} I(0) + \int\_{-a}^{a} S(f) \cos(2\pi f \Delta) df \tag{10}$$

where S(f) is the intensity spectrum of the source as a function of wavenumber and I(0) is the intensity at zero path difference.

Clearly, the interferogram is the Fourier transform of the spectrum emitted by the source. Accordingly, one can express S(f) as the inverse Fourier transform of the interferogram I() by calculating the integral for every wavenumber f:

$$S(f) = \bigcap\_{-\epsilon}^{\alpha} \left[ I(\Delta) - \frac{1}{2} I(0) \right] \cos(2\pi f \Delta) d\Delta \equiv F^{-1}(I(\Delta)) \tag{11}$$

The equation (11) is of considerable importance since it enables the determination of the spectrum of the source for every wavenumber from the interferogram I(). To measure the sample transmission, rather than the source spectrum, the sample is to be placed between BS and detector. The eq. (11) then yields the measure of TR(f)S(f) where TR(f) is the wavenumber dependent transmission coefficient. If TR(f)S(f) is measured when the sample is present and the source spectrum S(f) is measured when the sample is removed, the ratio of the two quantities gives TR(f).

**Figure 1:** Schematic diagram of Michelson interferometer.

In order to compute the spectrum of the source from the interferogram, important mathematical procedures have to be used in FTIR spectroscopy. First, it is to be noted that the equations (10) and (11), which relate the source spectrum to the interferogram, have been derived on the assumption that the optical path difference between the two beams is known from- to +. On the other hand, the movable mirror of the interferometer has limited displacement from-L to +L which limits the acquired values of interferogram to the same interval. As a result, the interferogram has not only the central peak with finite width but also negative side lobes. These lobes introduce artefacts causing distortions, making the calculated spectrum different from the actual one. In order to match the calculated and actual spectra, these negative side lobes have to be eliminated by means of a procedure called apodization (from Greek word "apodos" meaning "without feet"), which consists of multiplying the interferogram by suitable mathematical functions (apodization functions) prior to Fourier transformation. Codding and Horlick [54] may be referred for details on various apodization functions.

Secondly, an interferogram ideally should be symmetric about the point of zero path difference, while in reality the interferogram is never symmetric since all the frequency components of the wave do not reach their maxima at exactly the same time thus requiring a phase correction. By using a linear function that relates the phase shift with frequency, a correction for this asymmetry is obtained [54, 55]. Finally, when the spectrum of the source consists of various absorption lines close to each other, it is quite likely that they will overlap due to the instrumental enlargement caused by the finite optical path displacement. Therefore, it is necessary to determine the criterion which ensures that two adjacent spectral lines are resolved. Rayleigh criterion of resolution is also used for the interferograms. In FTIR spectroscopy the resolution is found to depend only on the maximum displacement of the movable mirror. Fourier self deconvolution is currently becoming popular as a method for band sharpening as well as a means for peak finding in systems of overlapping infrared bands whose widths are considerably larger than the instrumental resolution [56, 57].

### **2.4. Experimental Apparatus**

The infrared radiation covers a wide range spanning from 10 to 5.5 × 104 cm-1 corresponding to far infrared (10-400 cm-1), mid infrared (400-4400 cm-1) and near infrared (4400-5.5 10<sup>4</sup> cm-1) regions. The Fourier transform infrared spectroscopy apparatus essentially consists of interferometer (involving light sources, beam splitter, mirrors), detectors and a dedicated computer. The computer controls the optical components, collects and stores data, carries out mathematical operations (apodization, phase correction and Fourier self deconvolution) before computing the spectrum from the interferogram.

Fig. (**2**) displays the schematic diagram of commercial Fourier transform infrared set up using the Michelson spectrometer. The infrared source corresponding to the desired spectral range is selected and a mirror collimates the source radiation. The resulting parallel beam is sent to the beam splitter of the Michelson interferometer. The thickness and the coating of the beam splitter have to be proper and right in order to ensure that short wavelengths are not retarded or advanced with respect to the long wavelengths, avoiding the frequency-dependent delay in phase. The beam is divided by the beam splitter and one part of the beam goes to the fixed mirror while the other part to the moving mirror. A frictionless bearing with an electromagnetic drive is used to ensure smooth travel of the moving mirror. The returned beams from the mirrors recombine again at the beam splitter and pass through the sample and are focused onto the detector. The motion of the mirror introduces path difference between two interfering beams and the detected signal as a function of the optical path difference, *i.e.* the interferogram, is recorded. Each wavelength will produce its own characteristic intensity pattern of particular magnitude. Clearly, for a source of many frequencies, the interferogram will be the sum of variation of intensity of each wavelength pattern at the detector.

**Figure 2:** Schematic diagram of typical FTIR set up using the Michelson interferometer.

The sample is always put between the interferometer and the detector to have high stray light rejection since this arrangement allows the modulation of infrared light by the interferometer, while the emission from the sample would not be modulated and accordingly will not contribute to the spectrum. The position of the moving mirror and hence the path difference is measured by the He-Ne laser (reference laser in Fig. **2**). Because the wavelength of the laser is known very precisely the mirror position can be determined very accurately by counting the number of fringes in a highly defined laser pattern. The point of zero path length difference is obtained by using white light in place of He-Ne laser and finding the position of the highest amplitude intensity.

Since the IR radiation covers a wide range, different kinds of sources and beam splitters are used. Fast response time detectors (pyroelectric or semiconductors detectors) are necessary because of the fast movement of the mirror. The standard configuration corresponding to the mid infrared range (400-4400 cm-1) uses globar source, a potassium bromide (KBr) beam splitter and a pyroelectric detector, comprising single crystal wafer of triglycerine sulphate (TGS). Germanium, mylar or quartz as beam splitters and mercury-cadmium-telluride (MCT) or indium antimonide (InSb) units operating at 77 K as semiconductor detectors are also used in the mid infrared region. In the near infrared region (4400 cm-1 to 5.5 ×104 cm-1), quartz halogen lamp source, calcium fluoride (CaF2) or quartz beam splitters and cooled InSb or lead selenide (PbSe) detectors are employed while the far infrared (10 to 400 cm-1) requires a mercury vapour arc lamp, mylar or metal mesh beam splitters and pyroelectric detectors.

#### **2.5. IR Spectra**

In the interaction of the IR radiation with matter some of the radiation is absorbed by the atoms of the sample and some is transmitted. The absorption peaks of the resulting spectrum correspond to the frequencies of vibrations between the bond of atoms forming the material. IR spectroscopy accordingly enables one to identify different atoms (qualitative analysis) and also to perform a quantitative analysis because the intensity of the peaks allows an evaluation of bond concentrations. The frequency of the fundamental modes depends on the masses of the oscillating atoms and the strength of the bond between the atoms.

The vibrational spectra of hydrogenated amorphous silicon and hydrogenated amorphous silicon carbon films with different carbon content *x* (*x* =[C]/([C]+[Si]) covering the mid infrared region (2.5-50 m/400-4000 cm-1) are shown in Fig. (**3**) as an example [58]. The spectrum of hydrogenated amorphous silicon film (*x* = 0) exhibits peaks near 2000 cm-1 and 640 cm-1 and feeble peaks near 800-900 cm-1 corresponding to Si-H stretching, Si-H rocking/wagging and SiH2 bending modes respectively [59-61]. It is noteworthy that vibrational modes due to the a-Si structures, *i.e.* Si-Si bonding are absent for being IR inactive.

The spectra of hydrogenated amorphous silicon carbon films, in addition to the above said peaks, display others in the 2800-3000 cm-1, near 1000 cm-1 and near 780 cm-1 regions, ascribed to C-H stretching, CHn wagging and Si-C stretching modes, respectively [62-64]. In a-Si1-xCx:H spectra, the peak of Si-H stretching modes moves toward the higher wavenumber due to the presence of the carbon back bonded to Si-H bond [64].

**Figure 3:** IR spectra of amorphous silicon and amorphous silicon carbon alloys with different carbon content *x*. In the inset the bond concentration N of Si-H, C-H, Si-C *vs. x*. (Reprinted with permission from Ambrosone *et al.* Ref [58], Copyright (2008), American Institute of Physics).

The IR spectra of hydrogenated microcrystalline silicon films exhibit similar modes to that of hydrogenated amorphous silicon. Interesting differences, observed in the Si-H stretching region, have been utilized to identify the device quality microcrystalline silicon films which will be discussed in the paragraph 4.

The FTIR spectroscopy is a powerful technique for the detection and for the quantitative evaluation of impurities. For example, the oxygen, if incorporated in amorphous or microcrystalline silicon and related alloys, can give rise to Si-O stretching mode in the 950-1200 cm-1 range and also can cause the shift of Si-H stretching mode to higher wavenumber.

The bond concentrations of Si-C, (NSi-C), Si-H (NSi-H), C-H (NC-H), Si-O (NSi-O) are given by:

$$\text{If } N\_{\text{XY}} = A\_{\text{XY}} \cdot \int \frac{a(f)}{f} df \text{ "XY = Si-C, Si-H, C-H, Si-O} \tag{12}$$

where f is the absorption coefficient. The integration is performed on the respective IR deconvoluted peaks after the subtraction of the baseline. In eq. (12) AXY is the appropriate inverse cross-section which assumes the following values:

$$\mathbf{A}\_{\text{Si-C}} = 2.13 \times 10^{19} \text{ cm}^{\cdot 2} \text{ [63]}$$

$$\mathbf{A}\_{\text{Si-H}} = 1.4 \times 10^{20} \text{ cm}^{\cdot 2} \text{ [65]}$$

$$\mathbf{A}\_{\text{C-H}} = 1.35 \times 10^{21} \text{ cm}^{\cdot 2} \text{ [63]}$$

$$\mathbf{A}\_{\text{Si-O}} = 1.5 \times 10^{19} \text{ cm}^{\cdot 2} \text{ [63]}$$

The characteristics of the spectra such as the position, the full width at half maximum (FWHM), the intensity and the line shape of the peaks are related to the physical properties of the materials, as discussed in paragraph 4.

### **3. RAMAN SCATTERING**

Raman scattering is the inelastic scattering of light by the matter. Since the energy of the incoming and scattered photons are different, the difference in energy must have to be provided or absorbed by the excitations of the material. The nature of these excitations can be vibrational (phonons), electronic, magnetic *etc.* and, accordingly, Raman scattering can yield structural and dynamical information on molecular levels. In the crystalline solids, the scattering by optical phonons is known as Raman scattering while the scattering by acoustic phonons is termed Brillouin scattering. The Raman scattering process involves a change in photon frequency. The scattered photons can lose energy by emitting a phonon (Stokes shift) or gain energy by absorbing a phonon (anti-Stokes shift) according to the energy and momentum conservation rules. It has been shown [66] that the conservation rules allow only the phonons with wave vector q ≈ 0 (the phonons near the centre of the Brillouin zone) to be effective in one-phonon process resulting in the narrow peaks in the Raman spectrum of the crystalline materials. In the amorphous materials there is no well-defined crystal momentum. As a result of which the q ≈ 0 selection rule does not exist. In principle, all vibrational states can take part in the scattering process and, therefore, the Raman spectrum is observed to have broad peaks.

The Raman scattering is always accompanied by the dominant elastic scattering of light (Rayleigh scattering). The Rayleigh scattering process tends to be very intense since most photons are scattered elastically, while in Raman scattering approximately one photon in 106 -10<sup>9</sup> is scattered inelastically. Furthermore, Raman peak is not only very weak but also very near in energy to the exciting signal because the energy of the scattered photon differs by one vibrational unit from that of the incident photon. In consequence, the feeble Raman peak must be measured against the background of a very close and intense Rayleigh peak.

The technological advancement in the fabrication of lasers, multi-channel detection systems, Rayleigh filters and detectors have made the non-destructive Raman scattering an indispensable technique for material characterization. There are a number of excellent books on Raman spectroscopy [50, 67-75] to refer just a few. In this paragraph, we will discuss briefly about the history and theory of Raman scattering, which will be followed by the details of experimental techniques.

### **3.1. Background**

The inelastic scattering of light postulated by A. Smekal in 1923 [76] was observed experimentally for the first time in 1928 by C.V. Raman [77, 78], who was awarded Noble prize in 1930. In the original experiment conducted in India by C.V. Raman, sun-light was focused onto purified liquid as well as onto dust-free vapour by a telescope and a second lens was placed near the sample to collect the scattered light. A system of optical filters was used to demonstrate the existence of the scattered light with different frequencies as compared with incident light which is the essence and characteristic of Raman effect. Because Raman scattering is inherently weak, the wide application of Raman spectroscopy had to wait until the development of lasers. The pulsed Ruby laser operating in near IR (694 nm) was used as the light source to obtain the first laser Raman measurements. Pulsed laser sources usually have significant pulse-to-pulse energy fluctuation which, in turn, results in low spectral signal-to-noise ratio implying the need for continuous wave (CW) lasers. Accordingly, the red 632.8 nm CW He-Ne laser was the first to be incorporated in the commercial Raman instruments and subsequently higher power lasers like CW Ar+ and Kr+ lasers have been employed [79, 80]. Many others, such as IR diode or diode pumped lasers [81], have been developed since then for the purpose.

### **3.2. Theory**

In the Raman effect, the inelastic scattering of light manifests itself by a frequency shift from the incident light. The vibrations (or other excitations) modulate the polarizability tensor and cause the induced dipole moments to radiate at frequencies different from that of the electric field vector of the incident light wave.

The precise treatment of Raman scattering requires the quantum mechanical theory. However, a simple classical theory is adequate to understand the basic process. The frequency shifted Raman bands can be described as the side bands at the phonon frequency due to the non-linear interaction between the incident light and the lattice. In classical theory [73] this nonlinear interaction depends on the change in polarizability of the lattice. If u is the co-ordinate describing the phonon normal modes, the dependence of the dielectric function on u where is the radiation frequency, can be expanded as Taylor series.

$$\varepsilon(\alpha, u) = \varepsilon(\alpha) + \left(\frac{d\varepsilon}{du}\right)u + \frac{1}{2}\left(\frac{d\varepsilon^\circ}{du}\right)u^\circ + \dots \tag{13}$$

Since *P E* , where *<sup>P</sup>* is the dipole moment induced by the electric field *E* of the incident light, this implies:

$$
\vec{P} = \mathcal{E}(\phi o)\vec{E} + \left(\frac{d\mathcal{E}}{du}\right)u\vec{E} + \frac{1}{2}\left(\frac{d\stackrel{\text{\*}}{}^{\text{e}}}{du}\right)u^{\frac{1}{2}}\vec{E} + \dots \tag{14}
$$

Since 0 *EE t* cos and u = u0cos St, where S is the phonon frequency, neglecting the higher order terms in (14) one obtains

$$\vec{P} = \mathcal{E}(\phi) \,\vec{E}\_0 \cos\alpha t + \left(\frac{d\varepsilon}{du}\right) \mu\_0 \,\vec{E}\_0 \cos\alpha t \cos\alpha\_S t$$

or

$$\vec{P} = \varepsilon(\alpha)\vec{E}\_0\cos\alpha t + \frac{1}{2} \left(\frac{d\varepsilon}{d\mu}\right) \mu\_0 \vec{E}\_0 \cos(\alpha + \alpha\_\circ)t + \frac{1}{2} \left(\frac{d\varepsilon}{d\mu}\right) \mu\_0 \vec{E}\_0 \cos(\alpha - \alpha\_\circ)t \tag{15}$$

Clearly, the first term of equation (15) describes Rayleigh scattering. The second and third terms represent the frequency-shifted inelastically scattered light, known as anti-Stokes and Stokes Raman scattering respectively.

A Hertzian dipole emits electromagnetic radiation whose intensity Y is proportional to the square of the absolute value of the second time derivative of the induced dipole moment.

$$Y \propto \left| \begin{matrix} \ddot{\vec{P}} \\ \ddot{\vec{P}} \end{matrix} \right| \tag{16}$$

The intensity of the Stokes and anti-Stokes lines for the single phonon term in equation (14) and (15), as reported by Cardona [73], is:

$$Y \ll \alpha^4 \left(\frac{d\varepsilon}{du}\right)^2 \left\langle u^2 \right\rangle \tag{17}$$

where the term in the angle bracket is the thermal average of the phonon displacement. The <sup>4</sup> dependence is the characteristic of the scattering process (for example, Rayleigh scattering). The square dependence of small polarization term (d/du) demonstrates the low intensity of Raman scattering even for single phonon and the higher order terms of equation (14) are still weaker making Raman scattering inherently a weak process.

The intensity ratio of the anti-Stoke to Stokes line is given by the Boltzmann factor exp(- S/kBT0) where is the Plank's constant divided by 2, kB is the Boltzmann constant and T0 is the absolute temperature. Accordingly, the Stokes lines are stronger and generally dominate in the measurements. Further, for the crystalline material it must be emphasized that since the scattering process involves the interaction of electric field vector and the polarization vector, the direction of electric field relative to the crystal geometry defines the strength of the Raman signal and the Raman intensity is further proportional to the square of the Raman tensor as given by the equation

$$Y \propto \left| \hat{\mathbf{e}}\_i \cdot \mathbf{R} \cdot \hat{\mathbf{e}}\_3 \right|^2 \tag{18}$$

where ˆ *<sup>i</sup> e* and ˆ*<sup>S</sup> e* are unit vectors in the direction of the incident and scattered electric field respectively, while R is the Raman tensor which embraces the geometric information about the crystal. The above equation determines which phonon modes are allowed and forbidden for different orientations.

### **3.3. Experimental Apparatus and Techniques**

The Raman scattering signal is inherently weak and very close to the intense Rayleigh signal (the relative intensity ratio is around 109 [79]) implying that a feeble Raman peak must be measured against an intense background. Accordingly, powerful laser as the exciting source is required, while the large disparity between the Rayleigh and Raman intensities makes the optical methods for Rayleigh rejection mandatory.

It is known [70, 82] that the fluorescence bands, which can be intrinsic or due to trace impurities, are excited by resonance with electronic states. These bands are broader and much stronger than the Raman peaks, which lead to significant reduction in the signal-to-noise ratio. Furthermore, the contribution of fluorescence to signal-to-noise degradation is maximum for the excitation wavelengths covering the range 300-600 nm. Clearly, a minimization of sample fluorescence is necessary.

High spectral signal-to-noise ratio is the most prominent requirement of Raman spectroscopy and it has been well established that Fourier transform technique can enhance the signal-to-noise ratio. All these considerations have to be taken into account in the design of the Raman spectroscopy apparatus.

At present, most laboratories of the world use either a dispersive or FT-Raman spectroscopy. The dispersive Raman spectroscopy apparatus uses a ultra-violet (UV) or visible laser for excitation, a dispersive spectrometer and detectors (photomultiplier tubes, PMT, or charged coupled device, CCD) and a single monochromator with Rayleigh rejection filter or double/triple monochromator (gratings) as the dispersive element. The FT Raman spectroscopy apparatus, on the other hand, employs a near IR laser for excitation, an interferometer as spectrometer and IR detectors such as CCD or photodiode.

A schematic setup for Raman spectroscopy using a single monochromator and filter for Rayleigh rejection is shown in Fig. (**4**). Raman scattering is excited either by Ar+ or Ti:Sapphire laser. The scattered light is collected through the notch filter for Rayleigh rejection and focused onto the monochromator which separates out the different energies of the Raman scattering and finally focused onto the CCD detector.

These Raman instruments are dominating the market because of their small size and efficiency. However, the filter based dispersive Raman systems have the disadvantage that the Raman signal, very close to the exciting laser line cannot be detected. Moreover, the change of laser wavelength is a costly affair because it requires also the change of filter of the corresponding wavelength.

**Figure 4:** Schematic diagram of Raman spectroscopy apparatus using a single grating spectrometer and filter for Rayleigh rejection.

Instead of single monochromator with rejection filter, a double or triple monochromator can be used to discriminate the weak Raman signal from the strong Rayleigh light and reduce considerably the intensity of stray back ground light. A typical schematic diagram of dispersive Raman spectroscopy using double monochromator is shown in Fig. (**5**). The exciting laser light is focused on the sample and the scattered light is reflected by the mirror and collected by the lens for transmission to the double monochromator that essentially consists of two ganged gratings which turn together and sequentially select the desired Raman signal. Triple monochromators are used for still better performance. In spite of the limitations such as loss in light throughput and their relatively large size, the Raman spectroscopy utilizing double or triple monochromators is still used extensively for its high resolution and because it can operate on a wide range of wavelengths. This kind of spectroscopy is also the preferred choice if the change of exciting wavelength or the use of techniques such as resonance Raman scattering or flexible sampling are required during the measurements.

**Figure 5:** A typical schematic diagram of dispersive Raman spectroscopy apparatus using double monochromator.

The near infrared lasers as the exciting sources are used to avoid the fluorescence prevalent in the visible region. However, the smaller Raman cross-section in the near IR gives poorer performance requiring the FT-Raman instruments based on the interferometric method.

The schematic diagram of a FT Raman set up using the Nd:YAG (Neodymium:Yttrium Aluminium Garnet) laser as the exciting source is shown in Fig. (**6**). The scattered radiation is focused on the entrance part of the conventional FTIR spectrometer which essentially replaces the internal IR light source. FT-Raman spectroscopy not only offers multiplex and throughput advantages, resulting in significant increase in signal-to-noise ratio but also provides the higher wavelength accuracy of the interferometric method.

**Figure 6:** The schematic diagram of a FT Raman set up using the Nd:YAG laser.

#### *3.3.1. Laser Sources*

Being a high intensity and single frequency light source, laser is ideally suited as an excitation source for the Raman spectroscopy. However, incident laser power must be kept low so as to ensure that focused laser power density is below the value that causes thermal and/or photochemical degradation as well as nonlinear optical processes. In Raman spectroscopy the continuous wave lasers are used instead of the pulsed lasers because the latter have low signal-tonoise ratio and increased peak power, facilitating nonlinear processes and degradation of the samples. Furthermore, equation (17) reveals that intensity of Raman scattering depends on the fourth power of the frequency implying that lasers of higher frequencies, like UV and visible used as excitation sources, improve Raman sensitivity. UV lasers, accordingly, are the most preferred choice for Raman spectroscopy and have also higher signal-to-noise ratio because there is no or less fluorescence as compared with visible lasers. However, UV laser sources suffer from the following limitations [83]: they are more complex, quite expensive, have inherent problems with safety, require specialized optics and finally, the UV high power can lead to sample degradation.

The visible lasers as exciting sources for Raman spectroscopy are largely used because they provide reasonably high intensity of Raman peaks and require less expensive optical components. CW Ar<sup>+</sup> and Kr+ lasers are the most popular in the visible region because of their reasonable power, flexibility and limited ability to excite resonance. Moreover, these lasers can be used to pump dye lasers for obtaining tunable lasers, necessary for resonant Raman scattering experiments. The only limitation of visible lasers is the presence of fluorescence in the visible region, which reduces the signal-to-noise ratio.

The near infrared laser as exciting source is also used in spite of the reduction in the Raman scattering intensity, and hence in the sensitivity, due to the low frequency (see equation 17). In order to compensate for the loss in sensitivity, the Fourier transform technique is incorporated in Raman apparatus. The advantage of this source is that fluorescence is less likely.

In recent years, near IR diode lasers operating ~780 nm [81] as well as diode pumped YAG lasers operating ~1064 nm have become popular as the exciting source for the new generation of inexpensive, small commercial Raman spectrometers because of their low cost, small size, low power consumption and reliability.

### *3.3.2. Rayleigh Rejection Filters and Detectors*

The most used Rayleigh rejection filters are holographic notch filters [84], crystalline colloidal array Bragg diffraction filters [85] and dielectric edge filters [86, 87]. These filters, particularly the notch filters, being small and efficient, have reduced the size of the Raman spectrometers and improved their efficiency.

The most widely used detectors are PMT or CCD. PMT are almost ideal detectors because of their broad spectral range. The cooled PMTs typically have higher sensitivity and linear dynamic range greater than 10<sup>6</sup> . CCD detectors have the following characteristics: a high dynamic range (about 10<sup>5</sup> ), high quantum efficiency (about 90%), wide spectral range, low readout noise (2-5 e/pixel) and relatively small size.

The PMT detectors are indispensable for very high resolution Raman measurements because of their limit of a few micron much less than ≈25 m limit associated with CCD detectors. However, multichannel CCD detectors [88] are far superior for relatively lower resolution studies (> 1 cm-1) because of their multiplex advantage resulting in the improved spectral signal-to-noise ratio.

### *3.3.3. Raman Microprobe*

Raman microprobe, which is essentially Raman spectroscopy with microscope, is becoming widespread for Raman characterization of the samples, because the use of high quality microscope in a 180° back scattering geometry eliminates the need to continuously adjust the laser and the sample and to focus the scattered light on the spectrometer.

The high numerical aperture of microscope objectives greatly increases the spatial resolution and the optical collection power of the Raman microprobe. In addition, the exciting visible light is coupled with the sample by means of a microscope whose objective lens focuses the laser beam to a small spot size (approximately 1 m) of the sample and the scattered light is transmitted through the beam splitter to the double monochromator (see Fig. **7**). Surely, the use of visible laser and associated visible optics is an inherent advantage of Raman microprobe.

**Figure 7:** Schematic diagram of a Raman microprobe apparatus.

The Raman microprobe has made possible the study of extremely small samples by means of a video camera that allows one to obtain the real time image of the sample surface area as small as beam size. Finally, this technique can also discriminate the weak signal against fluorescence because an extremely small region of the sample is irradiated with high power laser.

#### **3.4. Raman Spectra**

Raman spectroscopy allows one to characterize layers as well as bulk materials because a wide range of penetration depth is possible by changing the wavelength (from UV to NIR) of laser exciting source. A depth profile of samples can also be obtained from different kinds of laser radiation. All the Raman spectra parameters such as peak position, intensity, line shape and line width are useful for characterization of the materials. The line widths increase when a material is damaged or disordered. The broadening arises from increased phonon damping due to the decrease in the life time of phonons or relaxation of momentum conservation in the Raman scattering process.

The typical Raman spectra of amorphous and nanocrystalline silicon films [89] in the range 100- 600 cm-1 are shown as examples in Fig. **8(a)** and Fig. **8(b)** respectively. In the spectrum of a-Si:H film four peaks can be identified: the transverse acoustic (TA) located at ~150 cm-1, the longitudinal acoustic (LA) located at ~310 cm-1, the longitudinal optical (LO) located at ~380 cm-1 and the transverse optical (TO) located at ~475 cm-1. In the spectra of the nano/micro crystalline silicon films two additional peaks at 520 and ~510 cm-1 are observed due to crystalline and crystallinelike (nanocrystals and/or grain boundary) phases.

The width of the TO peak is a good measure of the local order [64] and is well correlated with disorder related parameters (for example, the Urbach energy). Moreover, the TA mode provides a description of the medium-range order and the TA/TO intensity ratio depends on bond angle distribution [89].

The determination of the crystalline volume fraction and the size of the crystallites for microcrystalline and nanostructured silicon films is commonly obtained by the analysis of TO mode of the Raman spectra. The crystalline volume fraction Ic RS of the films is determined using the empirical expression [90].

$$I\_{\mathbf{c}}^{RS} = (I\_{\mathbf{c}} + I\_{\mathbf{w}}) / (I\_{\mathbf{c}} + I\_{\mathbf{m}} + \mathbf{y}I\_{\mathbf{o}}) \tag{19}$$

where Ic, Im and Ia are the integrated intensity of peaks at ~520 cm-1, at ~510 cm-1 and ~475 cm-1 corresponding to the crystalline, crystalline like and amorphous Si phase respectively. The y represents the Raman emission cross-section ratio which depends upon the size of crystallites and also on the excitation wavelength used for the Raman experiment. Usually, the value of y is chosen to be 1 [91].

**Figure 8:** a) Raman spectra of amorphous and b) nanocrystalline silicon films. RH is the hydrogen dilution H2/(H2+SiH4). (Reprinted with permission from Zhang S *et al.* [89]. Copyright (2006) Elsevier Science B.V.).

The size of the crystallites G is obtained from the empirical formula [92]:

$$\mathbf{G} = \mathcal{Z}\pi(\mathbf{B}/\Lambda\alpha)^{l/2}$$

where B is a constant with the value of 2 cm-1 nm2 and is the difference between the TO peak frequency of monocrystalline Si and TO peak frequency of Si crystallites.

### **4. APPLICATIONS**

In this paragraph we will illustrate the applications of FTIR and Raman spectroscopy taking the examples concerning the microcrystalline and nanocrystalline silicon films used in solar cells as well as the nanostructured silicon carbon films that have emerged as the potential material for the new third generation solar cells [22-24]. However, the examples presented are not exhaustive but limited and fragmentary.

### **4.1. Applications of FTIR Spectroscopy**

We will discuss the use of FTIR spectroscopy as applied to following topics:


### *4.1.1. Detection of Oxygen Impurities*

The detection and quantification of oxygen is a major concern in the semiconductor industry. The unintentional oxygen incorporation during the growth leads to a pronounced n-type behaviour of the microcrystalline silicon layer in solar cells thus causing deterioration of their electrical properties. Torres *et al.* [93] have demonstrated that there is considerable increase in the spectral response of c-Si:H solar cells with decreasing oxygen impurity, obtained by means of a feed gas purifier during the growth (see Fig. **9**).

Furthermore, amorphous and microcrystalline silicon as well as related alloy films can easily incorporate oxygen from the atmosphere with time or when subjected to annealing [63].

The incorporation of oxygen with time results in the formation of Si-O bonds. Indeed, the outdiffusion of the loosely bonded hydrogen present in low-density region causes dangling bonds which are satisfied by the oxygen from the atmosphere. In the case of thermal annealing at high temperature, more dangling bonds are formed because of the breaking of the bonds by thermal agitation, and their satisfaction with oxygen also results in increased number of Si-O bonds [63].

The oxygen incorporated in the films is easily detected by the presence of the relatively strong absorbing Si-O stretching mode in the 950-1200 cm-1 region. The bond density of Si-O mode is determined from the integrated area of the peak using the inverse cross section value of 1.5 10<sup>19</sup>

cm-2 [63]. The incorporation of oxygen also results in the upshift of the Si-H stretching mode. Smets *et al.* [11] have reported that in c-Si:H films oxidation of crystalline grain boundaries results in OySiHx mode near 2250 cm-1.

**Figure 9:** Comparison of the spectral response of two entirely *c*-Si:H solar cells. One produced with and one without a feed gas purifier. (Reprinted with permission from Torres *et al.* Ref [93]. Copyright (1996), American Institute of Physics).

#### *4.1.2. Optimization of c-Si:H Films for Solar Cells*

Device quality a-Si:H films are optimized by the microstructure factor defined as A2100/(A2000+A2100), where A2000 and A2100 are the area under the deconvoluted Si-H stretching peaks at 2000 and 2100 cm-1 respectively [94]. However, it is difficult to quantify the device grade microcrystalline silicon films using the microstructure factor because of the presence of the grain boundaries in these films. The only reliable way to quantify the "device grade" material involves the time-consuming process of the integration of every intrinsic film in a solar cell. Smet *et al.* [11, 95] have demonstrated that the properties of microcrystalline silicon bulk for solar cells can be optimized by monitoring the presence of crystalline grain boundaries, that can easily be detected *via* the crystalline surface hydrides contribution to narrow high stretching mode (SM) using FTIR spectroscopy. Therefore, this technique can be used as a simple, fast and reliable optimization tool for assessing the "device grade" microcrystalline silicon material for solar cells.

Fig. (**10**) displays the FTIR spectrum of undoped microcrystalline silicon film representing all the silicon hydride (Si-H) stretching modes, identified by Smet *et al.* [11, 95]. In the following we will summarize their results. The low stretching mode (LSM) covering the range 1980-2010 cm-1 and the high stretching mode (HSM) spanning the range 2070-2100 cm-1 have their origin from the a-Si:H tissue in the bulk [96]. However, for the c-Si:H phase, the range of HSM is further extended due to the presence of two other additional modes located near 2120 and 2150 cm-1. In the FTIR spectrum of the c-Si:H, the presence of the crystalline surfaces (grain boundaries) in the bulk is revealed by the NHSMs at 2083, 2102 and 2137 cm-1 corresponding to mono, di and tri hydrides of crystalline grain boundaries [97]. In the region below LSM, three modes located near 1895,

1929 and 1950 cm-1 termed as extreme LSM (ELSM) are also present in the c-Si:H. ELSMs are unique to c-Si:H and have the maximum intensity only when NHSMs are absent.

**Figure 10:** A close-up of the hydride stretching modes (open circles) in the IR spectrum of a *c*-Si:H film. This example of a spectrum shows all possible modes observed for the *c*-Si:H phase. The lines correspond to the total fit and the 11 Gaussian shaped stretching modes. (Reprinted with permission from Smets *et al.*  Ref [11], Copyright (2008), American Institute of Physics).

The NHSMs are dominantly present in less dense c-Si:H with a high crystallinity. Furthermore, these modes exhibit post-deposition oxidation when exposed to the ambient atmosphere reflected through the presence of Si-O-Si modes in the range 950-1200 cm-1 as well as the O3-Si-H modes (near 2250 cm-1), whose intensity increases while the intensity of NHSMs decreases with longer exposure to atmosphere as shown in Fig. **11(a-d)**. The presence of crystalline grain boundaries, reflected through NHSMs and the associated post-deposition oxidation, is a clear signature of inferior material quality and inferior efficiency of 4.5% of the fabricated solar cells.

The FTIR spectra of the intrinsic c-Si:H film, shown in Fig. **11 (e)** and **(f)**, do not have NHSMs, while the ELSMs absorption is at its maximum and no post deposition oxidation is observed, reflecting device grade material. The p-i-n device, incorporating this material as intrinsic layer, reaches a conversion efficiency of 9.1 %.

#### *4.1.3. Characterization of Phase-Transition*

It has been demonstrated [36-39] that Si nanocrystals embedded in the SiC matrix can be formed by the high temperature post deposition thermal annealing of the single Si-rich a-Si1-xCx precursor layer as well as a-Si1-xCx/SiC multilayers which are subsequently used for the fabrication of Si nanocrystals/c-Si heterojunction photovoltaic devices. It is needless to state that these devices are an important step towards the realization of "all Si" tandem solar cell based on Si nanocrystal materials [22, 23]. Clearly, an understanding of the structural changes brought about by thermal annealing of hydrogenated amorphous silicon carbon films has become necessary.

Basa *et al.* [63, 98] have demonstrated that the evolution of structural changes from amorphous to microcrystalline and to polycrystalline phase, for amorphous silicon carbon film thermal annealed from 250 to 1200 °C, has been concluded using only FTIR spectroscopy by analysing line shape along with the peak position and peak width (FWHM) of IR modes. Basa *et al.* [63, 98] have reported that the intensity of hydrogen related mode, Si-H rocking/wagging (r/w) at ≈630 cm-1,

decreases while the intensities of non-hydrogenated modes, Si-C stretching (s) and Si-O(s) at ≈780 and ≈1100 cm-1, respectively, increase with the increase in the annealing temperature Ta (see Fig. **12**). The line shape of Si-C(s) as well as Si-O(s) are Gaussian up to 650 °C while for Ta in the range 800-1000 °C the line shape changes to Lorentzian. The sample annealed at 1200 °C exhibits only an asymmetric Si-C stretch peak without any Si-O stretch peak. The peak position and the FWHM as a function of Ta are shown in Fig. **13(a)** for Si-C(s) and in Fig. **13(b)** for Si-O(s).

**Figure 11:** (a) and (b) depict the measured Si–O–Si SMs and the hydride SMs for porous highly crystalline *c*-Si:H as deposited, 10 days and 10 months after deposition. (c) and (d) depict the Si–O–Si modes and the hydride SMs for *c*-Si:H films, when integrated into a *p*-*i*-*n* device, resulting in a conversion efficiency of 4.5%. (e) and (f) depict the Si–O–Si modes and the hydride SMs for c-Si:H films, when integrated into a *pi*-*n* device, resulting in an conversion efficiency of 9.1%.(Reprinted with permission from Smets *et al.* Ref [11], Copyright (2008), American Institute of Physics).

**Figure 12:** Absorbance of Si–C(s), Si–O(s) and Si–H(r, w) modes *vs.* wavenumber for a-Si1-xCx:H sample after thermal annealing at the indicated temperatures Ta. In the inset: (a) extinction coefficient k *vs.*  wavelength of a-Si1-xCx:H film annealed at 1200 °C and (b) extinction coefficient k *vs.* wavelength of crystalline SiC. (Reproduced with permission from Basa *et al.* Ref [98]. Copyright (2009) Elsevier Science B.V.).

The interesting features associated with Si-C(s) and Si-O(s) modes are as under. The blue shifts of peak position of Si-C and Si-O stretch occur up to 1000 °C while above that temperature Si-O(s) bonds disappear and Si-C(s) mode shifts to a lower wavenumber. The peak widths (FWHM) of both Si-C (s) and Si-O(s) increase up to Ta = 650 °C then suddenly drop to lower value for Ta = 800 °C and keep decreasing with further increase in Ta. The normalized area under Si-C(s) increases in all Ta range indicating that the increase in annealing temperature favours the formation of additional Si-C bonds.

The Gaussian line shape indicates a Gaussian distribution of bond lengths and bond angles typical of the amorphous phase. The Lorentzian line shape, on the other hand, reflects smaller bond angle distortion and narrow bond angle distribution, indicating a more uniform and ordered environment which is characteristic of crystalline phase [63]. The change in the line shape of Si-C(s) and Si-O(s) modes from Gaussian to Lorentzian together with the decrease in the FWHM for Ta = 800 °C, demonstrates clearly the transition from the amorphous to microcrystalline phase. With increase in Ta from 800-1000 °C the peak shifts to higher wavenumber along with the decrease of FWHM because of the increase in the crystallinity degree [99]. The extinction coefficient k of the film annealed at 1200 °C, inset (a) of Fig. (**12**), being very close to k of the hexagonal polycrystalline SiC, inset (b) of Fig. (**12**), demonstrates the further transition from microcrystalline to poly crystalline phase [100] with increasing Ta.

**Figure 13:** (a) Peak position and width of Si–C(s) *vs.* annealing temperature Ta and (b) peak position and width of Si–O(s) *vs.* annealing temperature Ta. (Reproduced with permission from Basa *et al.* Ref [98]. Copyright (2009) Elsevier Science B.V.).

The increase of Si-O bonds during the annealing from 250 to 1000 °C, as shown by the increased normalized area under Si-O(s) (see Fig. **12**), is due to the substitution of the effused hydrogen from the low-density regions of the film with the oxygen from atmosphere and the disappearance of Si-O bond at Ta = 1200 °C is attributed to the formation of Si-O (*via* the reaction Si + SiO2 = 2SiO) which being volatile at 1200 °C leaves the film [101].

Recently, Song *et al.* [36-39], in order to obtain self-organized Si nanocrystals embedded in dielectric SiC matrix, have annealed at high temperature multilayers of Si-rich a-Si1-xCx and nearstoichiometric a-SiC deposited by magnetron co-sputtering [36-37]. The FTIR spectra of these multilayers as a function of the annealing temperature Ta are displayed in Fig. (**14**) [39].

**Figure 14:** (a) FTIR absorption spectra obtained from Si0.96C0.04SiC multilayer films with annealing temperature as a parameter; (b) The peak position and FWHM of the Si–C absorption peak *vs.* annealing temperature. The dashed lines are guides for the eye. (Reprinted with permission from Song *et al.* Ref [39], Copyright (2008), American Institute of Physics).

The evolution of the Si-C stretching peak with Ta reveals that: i) the absorption band becomes more pronounced and the peak position is shifted to a higher wavenumber, ii) the FWHM decreases, and iii) the lineshape changes from Gaussian distribution to a mixture of Gaussian and Lorentzian distribution, implying the formation of nanocrystallites. These results along with other measurements (XRD and Raman) have demonstrated the transition from amorphous to nanocrystalline phase.

Finally, the Si-C bond concentration increases, confirming that the thermal annealing leads to the formation of additional Si-C bonds. The line shape analysis of IR modes supported by other measurements have also demonstrated [31] a transition from micro crystalline to nanocrystalline phase. Thus, establishing that FTIR spectroscopy can be a effective probe similar to XRD and Raman to investigate phase transitions. However, it turns out to be ineffective when the crystallization is confined to the thin top layer, as is the case with the excimer laser annealed silicon based films [98].

### **4.2. Applications of Raman Spectroscopy**

We will discuss the use of Raman spectroscopy as applied to the following topics:


#### *4.2.1. Crystalline Volume Fraction and c-Si Solar Cell Performances*

Crystallinity affects many parameters of Si thin films such as optical band gap, defect density, dark and photo conductivity [5-10, 102-104] as well as J-V parameters of solar cells such as efficiency , fill factor FF, open circuit voltage VOC, and short circuit current density JSC [17-20, 91, 105].

Many authors [91, 105-107] have characterized the c-Si solar cells by Raman scattering and related the crystalline volume fraction IC RS with the J-V parameters in order to optimize cell performances. In the following we report the data of Mai *et al.* [106, 107] concerning different c-Si solar cells. Three different c-Si solar cells series were prepared with plasma enhanced chemical vapour deposition (PECVD) i layers, hot wire (HW) CVD i layers and PECVD i layers with HWCVD p/i buffer layers on similar substrates with identical doped layers and similar total i layer thickness. Fig. **15** [106] shows the J-V parameters of c-Si solar cells as a function of the ilayer crystalline volume fraction.

An efficiency of 8% is obtained at intermediate IC RS for solar cells of HWCVD and PECVD series, demonstrating that both deposition techniques are able to provide high quality materials. VOC increases with decreasing i-layer crystallinity and the VOC values of HWCVD series are about 20 mV greater than VOC of PECVD series corresponding to IC RS in the range 10-60%. In particular, the efficiency of the PECVD series reaches the maximum at 540 mV, in agreement with others [12, 108], while the HWCVD solar cells series have VOC about 588 mV at maximum . In the region 10-60% of Ic RS the FF of the HWCVD series is also higher than those of the PECVD ones. Finally, the ISC of both series are similar and decrease with decreasing crystallinity in the range 60- 10% because with an increase in the amorphous phase the absorption coefficient of long wavelength light reaches low values.

### *4.2.2. Raman Scattering as a Probe of Structural Depth Profiles*

The structural development of c-Si:H solar cells was also investigated [107] by Raman scattering experiments with different excitation wavelengths (488 and 647 nm). The solar cells were prepared on texture-etched ZnO-coated glass substrates. c-Si:H p and i layers were prepared in VHF-PECVD system while a-Si:H n layers were deposited in rf-PECVD. Different series were deposited by varying the discharge power and total flux in high pressure-high power (hphP) conditions. In order to obtain i-layers with different crystallinity for each series the silane concentration was varied. A series deposited in low power and low pressure conditions (lplP) was also presented for comparison.

Crystalline volume fractions Ic RS obtained for different laser wavelength are compared in Fig. (**16**) [107] and it has been shown that the samples deposited at low pressure and low power have a very homogeneous structure along the growth direction while a structure composition difference between the top and bottom is present for cells deposited at high pressure and high power.

**Figure 15:** *J*-*V* characteristics, *V*OC, FF, and *J*SC, of c-Si:H solar cells with *i* layers deposited by PECVD (open squares) or HWCVD (solid stars), plotted as a function of crystalline volume fraction *IC* RS. A 100 nm thick HW *p*/*i* buffer layer in PECVD solar cells (open stars) nearly eliminates the differences between the PECVD and HWCVD solar cells. Lines are guides for the eye. (Reprinted with permission from Mai *et al.*  Ref [106], Copyright (2005), American Institute of Physics).

*Infrared and Raman Spectroscopies Silicon Based Thin Film Solar Cells* **135**

**Figure 16:** *IC* RS647 of the lplP and hphP solar cells plotted as a function of *IC* RS488. (Reprinted with permission from Mai *et al.* Ref [107], Copyright (2005), American Institute of Physics).

A better evaluation of the crystallinity at different stages of the i-layer growth is obtained by means of Raman measurements with 488 nm excitation carried out on craters with different depth, etched into solar cells by KOH. In Fig. (**17**), Ic RS is plotted as a function of the crater depth where 0 and 1000 along the growth direction correspond to the position of n and p layers, respectively. Clearly, the lplP solar cells have no structure evolution, while the hphP cells have differences of up to 20% between the top and the bottom of the i-layer.

**Figure 17:** The *IC* RS488 at different depths in the *i* layer show the structure development along the growth axis. Solar cells are optimum cells of three SC series deposited by lplP and hphP. For the 1 m thick solar cells, crater depth of 0 and 1000 nm correspond to the *n* and *p* layers position, respectively. (Reprinted with permission from Mai *et al.* Ref [107], Copyright (2005), American Institute of Physics).

### *4.2.3. Crystallinity Evolution in p-Type Microcrystalline Si1-xCx:H Films*

In order to understand the effect of boron doping on crystalline volume fraction the Raman spectroscopy was used by Miyajima *et al.* [109]. Fig. (**18**) [109] exhibits the Raman spectra of ptype microcrystalline Si1-xCx:H films prepared from silane and acetylene diluted in hydrogen with different doping ratio r = B2H2/(SiH4 + C2H2) using capacitively coupled PECVD system. The carbon content of the films is approximately 8 at%. It is reported that as doping ratio increases from 0 to 0.0714, the crystalline volume fraction decreases from 44.4% to 27.4%.

### *4.2.4. Crystallinity Evolution in Nanostructured Silicon Carbon Films*

The nanostructured films composed of silicon nanocrystallites embedded in the amorphous silicon carbon matrix have generated considerable interest in recent years [30, 31, 35, 39, 110] as materials for new generation solar cells. Indeed, the relatively lower bandgap (~2.5 eV) of SiC matrix as compared to ~9 eV for SiO2 and ~5.3 eV for Si3N4 is more favourable for the carrier transport.

**Figure 18:** Raman spectra of p-type c-Si1-xCx:H films deposited at different doping ratios. (Reproduced with permission from Miyajima *et al.* Ref. [109]). Copyright (2003) Elsevier Science B.V.).

In the following we will discuss the use of Raman spectroscopy to study the dependence of the crystalline degree of the nanostructured silicon carbon films on annealing temperature, carbon alloying and the kind of substrate.

In order to obtain self organized silicon nanocrystals embedded in dielectric SiC matrix, Song *et al.* [37-39] have performed the thermal annealing of multilayers of Si-rich a-Si1-xCx and near stoichiometric SiC, deposited by magnetron co-sputtering. The Raman spectra of two multilayers Si0.9C0.1/SiC and Si0.96C0.04/SiC are displayed for different annealing temperatures Ta in Fig. **19(a)** and **19(b)** [39] respectively. The spectra of the two as deposited multilayers are very similar showing only an asymmetric bump centred at 470 cm-1, due to TO mode of a-Si. After annealing at 800 °C the spectrum of Si0.9C0.1/SiC multilayer reveals the still amorphous structure while the spectrum of the Si0.96C0.04/SiC sample exhibits a small peak at 511 cm-1, which can be attributed to Si nanocrystals. For Ta ≥ 900 °C Si nanocrystals were formed in both samples as revealed by pronounced Raman peak at 511 cm-1. In addition, a feeble band at 940 cm-1, attributed mainly to SiC, is identified [111] implying the formation of SiC nanocrystals.

It is known that the increase in carbon content in silicon carbon hinders the formation of silicon crystallites [30, 112]. The evolution of crystallinity with carbon content in a-Si1-xCx:H can be monitored by Raman spectroscopy as reported by Cheng *et al.* [110]. Fig. **20(a)** displays the Raman spectra of Si nanocrystals embedded in an a-Si1-xCx:H matrix of different carbon content prepared by a low frequency (460 kHz), low pressure, thermally non equilibrium, high density inductively coupled plasma reactor using silane and methane without hydrogen dilution [110].

*Infrared and Raman Spectroscopies Silicon Based Thin Film Solar Cells* **137**

**Figure 19:** Raman spectra of (a) Si0.9C0.1SiC and (b) Si0.96C0.04SiC multilayer films with annealing temperature as a parameter. The films were deposited on quartz substrates. (Reprinted with permission from Song *et al.* Ref [39]. Copyright (2008), American Institute of Physics).

The Fig. **20(a)** reveals that only a broad peak near 480 cm-1 is present in the spectrum of sample with carbon content of 18.3 at%. When the carbon content decreases to 10.7 at% two peaks near 480 and 510 cm-1 appear in the spectrum. With further reduction of carbon content to 6.1at%, the crystalline silicon peak located near 515 cm-1 dominates the spectrum. Typical deconvolution of Raman spectrum using three Gaussian curves centred at ~480, ~510 and ~520 cm-1, shown in Fig. **20(b)**, allows one to calculate the crystalline volume fraction using the formula (19). The crystalline volume fraction displayed as a function of carbon content in Fig. **20(c)** is found to decrease with increase in carbon content.

The undoped nanocrystalline silicon carbon films are potentially suitable as active layer for multijunction solar cells, UV photodetectors and LEDs. To fabricate these devices, the active layer is usually grown after the deposition of p-layer on transparent conductive oxide like tin oxide (SnO2) substrate.

Accordingly, Coscia *et al.* [113] using Raman spectroscopy have compared the evolution of the growth of the silicon nanocrystals embedded in a-Si1-xCx:H matrix on p-layer/SnO2 and Corning glass by varying rf power in PECVD system using silane and methane mixture highly diluted in hydrogen.

**Figure 20:** (a) Raman spectra of the samples with different carbon contents XC (b) A typical deconvoluted Raman spectrum of the sample with the carbon content XC = 10.7 at.%. (c) Variation of the crystalline volume fraction as a function of Xc. (Reproduced with permission from Cheng *et al.* Ref. [110]. Copyright (2010) Elsevier Science B.V.).

From the Raman spectra of Figs. (**21**) and (**22**) [113] it can be seen that the samples deposited on p-layer/tin oxide have a more pronounced crystalline phase even at higher rf power implying that this kind of substrate favours the nucleation process.

The Si crystallite size and crystalline volume fraction, determined as described in 3.4, are plotted as a function of rf power in Fig. (**23**) for the films deposited on both substrates. These quantities decrease with increase in rf power for the films deposited on both substrates and are observed to

be higher for the films deposited on p-layer/tin oxide. The decrease in crystalline fraction and Si crystallite size results because an increase in rf power leads to an increase in carbon content [114] which, in turn, hinders the formation of crystallites.

**Figure 21:** The Raman spectra of samples deposited on Corning glass at different rf powers. (After Coscia *et al.* Ref [113]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission).

**Figure 22:** The Raman spectra of samples deposited on p/SnO2 at different rf powers. (After Coscia *et al.* Ref [113]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission).

**C**

**Figure 23:** The Si crystallite size and crystalline volume fraction IC RS of samples deposited on Corning glass and p/SnO2 *vs.* the rf powers. (After Coscia *et al.* Ref [113] Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission).

#### *4.2.5. Raman Spectroscopy as a Probe of Medium Range Order in Nanocrystalline Silicon*

It is well known that crystalline/microcrystalline materials are characterized by long range order (LRO) while the amorphous materials are identified by short range order (SRO). The medium range order, the next higher level of order with respect to SRO, is the characteristic of nanocrystalline materials. A signature of MRO has been reported by Williamson [115] using XRD analysis, by Voyles *et al.* [116] using the fluctuation electron microscopy and by Basa *et al.* [31] using FTIR and other measurements. On the other hand, Raman spectroscopy allows one to obtain information easily on MRO by evaluating the behaviour of TA and TO modes, centred at ~150 and ~475 cm-1, respectively. With this objective Zhang *et al.* [89] have compared the Raman spectra, displayed in Figs. **8(a)** and **8(b)**, of amorphous and nanocrystalline silicon films deposited with the hydrogen dilution RH = H2/(H2+SiH4) of 10 and 100 respectively, in PECVD system. From the observed decrease of the width of TA mode and TA/TO intensity ratio with increasing the hydrogen dilution, the authors have demonstrated the improvement of medium range order in nanocrystalline films.

#### **ACKNOWLEDGEMENT**

Declared none.

#### **CONFLICT OF INTEREST**

The author(s) confirm that this chapter content has no conflict of interest.

#### **REFERENCES**







© 2013 The Author(s). Published by Bentham Science Publisher. This is an open access chapter published under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/legalcode

# **CHAPTER 6**

## **Morphological and Structural Properties**

**Angelica M. Chiodoni1,\* and Elena Tresso1,2** 

*1 Center for Space Human Robotics (CSHR@POLITO), Italian Institute of Technology, Corso Trento 21, Torino 10129, Italy and <sup>2</sup> DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, IT-10129, Italy* 

**Abstract:** The chapter is devoted to the surface and structural characterisations of the materials used in photovoltaic applications for the determination of the topographic/morphological and structural properties.

In the first part of the chapter Scanning Electron Microscopy (SEM), Transmission Electron Microscopy (TEM), Atomic Force Microscopy (AFM) and X-ray Diffraction (XRD) are illustrated, with particular emphasis on the working principles. In the second part, some examples of application of these techniques to the silicon-based thin films solar cells are described. Recent and important experimental results obtained in these fields are examined and discussed, showing what kind of information they have provided.

**Keywords:** Atomic force microscopy (AFM), X-ray diffraction (XRD), transmission electron microscopy (TEM), scanning electron microscopy (SEM), surfaces, interfaces, morphology, structural properties, amorphous thin films, amorphous metals, microcrystalline thin films, crystalline fraction, growth processes, crystallization processes, nanostructures, semiconductors, defects, roughness, texture, crystal size.

### **1. INTRODUCTION**

In the recent past, silicon-based solar cells have witnessed a rapid commercial development, mainly due to both reduced costs through large-scale production, and quite good cell efficiency values, in comparison with other solar cells.

There is not doubt that surface and structural characterisations play an essential role in determining the topographic/morphological and structural properties of the materials used in solar cell applications. In fact, the control of the interfaces and of the roughness of the materials, of the eventual doping, of the quality of the material and the presence of macro-micro or nano-defects has to be considered one of the most important topic to be optimized while a solar cell is configured and produced. Since the first generation of solar cells, based on mono-crystalline, polycrystalline, micro-crystalline and amorphous Si, or a combination of some of them, it has always been necessary to control the structural and the morphological properties of these materials. This means that some techniques such as scanning and transmission electron microscopies (SEM,

**Address correspondence to Angelica M. Chiodoni:** Italian Institute of Technology, Corso Trento 21, 10129, Torino, Italy; Tel: +39 110903402 (ext.7385); Fax: +39 110903401; Italy; E-mail: angelica.chiodoni@iit.it

Scanning Electron Microscopy; TEM, Transmission Electron Microscopy), atomic force microscopy (AFM) and X-ray diffraction become strategically important. This chapter is devoted to illustrate how these techniques work and what kind of information they can provide. In Section 2 we will describe the working principles of SEM, TEM, AFM and XRD instrumentations, while in Section 3 we will focus on some applications of these techniques to the study of morphological and structural properties of silicon based thin films solar cells.

### **2. INSTRUMENTATION**

All of the described techniques are characterized by a probe and a detection system that is able to collect the signals coming from the specimen after the interaction with the probe itself. Each technique investigates, from a different point of view, the structural and/or morphological characteristic of the material constituting the specimen. In the following, a brief description of the instruments and the physical principles behind the techniques are reported.

### **2.1. Scanning Electron Microscopy (SEM)**

The first generation of scanning electron microscopes was introduced in the 1930's. In academic and industrial research institutes, it is one of the most diffused non-destructive large-area surface imaging techniques, because it provides relatively fast and high depth-of-field images of the surface of samples with a simple preparatory procedure. An SEM is an important and versatile tool to investigated large area (some centimetres) samples, powders, nanostructures, bulk materials, thin films, multilayers, and small devices. It can be used to characterise metals, ceramics, oxides, nitrides, semiconductors, soft materials, and with some dedicated instruments, also biological materials. Depending on the configuration of the microscope, it is possible to have an overview of centimetre-sized samples and at the same time to get information at the nanometer-scale. A simplified scheme of an SEM is depicted in Fig. **1**.

The working principle of the system can be described in a number of quite simple steps [1]. A highenergy electron beam (up to 30 KeV), produced by an electron source, is accelerated across the column and focalized with electromagnetic lenses along the optical axis. The electron beam strikes the sample by a raster scanning of the surface, producing a number of signals, mainly electrons but also photons, which provide information about topography (secondary electrons), compositional contrast (backscattered electrons) and composition (characteristic X-rays), as in Fig. **2**.

The sources of the electron beam are of two different types: the thermoionic sources and the field effect sources. The field effect sources exhibit superior performances with respect to the thermoionic ones. In the thermoionic sources, which are usually made up of a W filament or a LaB6 single crystal, the materials are heated to a certain temperature (some hundreds of Kelvin degrees) to overcome the work function and let the electrons escape from the material, thus producing the electron beam.

In the field effect sources, usually a cold cathode or a Schottky cathode, a high electric field is applied between a W nanowire ending with a sharp tip and an extractor electrode. In this case, it is mainly the electric field that lowers the work function and promotes the emission of the electrons.

**148** *Silicon Based Thin Film Solar Cells Chiodoni and Tresso* 

**Figure 1:** Scheme of a scanning electron microscope.

**Figure 2:** Signals produced by the electron-matter interaction. Reprinted with permission of Carl Zeiss NTS GmbH [2].

The electromagnetic lenses control the electron path along the column down to the end of the objective lens, as the glass lenses do in the optical microscope. At the end of the column the scanning coils can be found, which provide the rastering of the beam on the sample. In Fig. **3** a scheme of the lenses in an SEM is reported.

The signal produced by the rastering of the electron beam on the surface of the sample is collected by dedicated detectors, which reproduce a grey-scale image on a screen. The collection of secondary electrons (SE) is provided by the standard Everhart-Thornley (ET) detector or by the more efficient through-the-lens detector. In both, the electrons strike a scintillator that converts electrons into photons. Subsequently, the photons are collected by a light-pipe and sent into a

#### *Morphological and Structural Properties Silicon Based Thin Film Solar Cells* **149**

photomultiplier tube for amplification, at the end of which an electrical signal is provided. The collection of backscattered electrons (SE) is provided by the standard Everhart-Thornley (ET) detector or by the more efficient dedicated solid-state detectors, one placed at the end of the objective lens (AsB) and the other in the column (EsB). The dedicated BSE detector is usually a pn junction that, when hit by electrons, produces electron-hole pairs in a number proportional to the atomic number.

**Figure 3:** Scheme of the lenses in scanning electron microscope.

**Figure 4:** Schematic drawings related to the position of the main SEM detectors in the columns or in the chamber: upper SE (in-lens) detector, lateral ET detector, upper EsB detector and AsB detectors. Reprinted with permission of Itakura *et al*. [3], Copyright (2010), Oxford Journals.

The characteristic X-rays are collected by a dedicated detector (Energy Dispersive X-rays-EDX detector), usually cooled by liquid nitrogen. This is composed of a thin silicon crystal doped with lithium, so that the central intrinsic region is sandwiched between a thin p-type layer and a thin ntype layer. When an X-ray photon hits the detector, it produces electron-hole pairs in the Si(Li) region. The electrons are accelerated towards the positive side, and the holes towards the negative side. Thus, a pulse of current, which is proportional to the X-ray energy, is generated.

As an example, in Fig. **4** a scheme showing the position of the detectors in a microscope used to characterize SiGe whiskers and in an amorphous matrix is reported [3].

#### **2.2. Transmission Electron Microscopy (TEM)**

Transmission Electron Microscopy (TEM) is an important characterization technique to get local (few microns) and extremely detailed structural information about mainly crystalline but also amorphous materials. It is a powerful but destructive technique, because a small piece (1-2 mm) of specimen has to be cut from the sample of interest and thinned down to about 100-200 nm in order to be electron transparent and produce a transmitted electron beam to analyse. The TEM is the only technique able to provide at the same time information about structure, composition and defects at the atomic scale.

**Figure 5:** The two illumination systems in a TEM: (A) Parallel-beam mode; (B) Convergent-beam/probe mode.

The first Transmission Electron Microscope has been built by Ruska and Knoll, in Berlin in the early 1930s. In a transmission electron microscope [4], the illumination system is constituted by a high-energy electron beam that is focused on a very thin sample by means of electromagnetic lenses, and is transmitted to image and analyze the microstructure of materials with atomic scale resolution. The image is observed on a fluorescent screen, or recorded on film or digital camera. The electrons, produced by guns similar to those described in §2.1, are accelerated at several

#### *Morphological and Structural Properties Silicon Based Thin Film Solar Cells* **151**

hundreds of kV, corresponding to wavelengths much smaller than that of light. For example, electrons accelerated at 200kV have a wavelength of 0.0025 nm. Even if the wavelength is so small, the final resolution of the microscope is limited by the aberrations related to the electromagnetic lenses. As it is shown in Figs. **5** and **6**, several lenses have important roles in determining the illumination and the collection modes.

**Figure 6:** The two basic operations of the TEM imaging system: (A) diffraction mode, projecting the diffraction pattern onto the viewing screen; (B) image mode, projecting the image onto the screen.

The C1 and C2 lenses determine the illumination mode. Two main illumination modes are possible: the parallel beam and the convergent beam. The first is used for TEM imaging and for selected-area diffraction (SAD), while the second is used for scanning TEM (STEM) imaging, for convergent beam electron diffraction (CBED) and for spectroscopy (X-ray and electron energy loss spectroscopies).

The objective lens and the specimen holder/stage system is the heart of the TEM. Here the beamspecimen interactions take place and the creation of images and diffraction patterns occur. These images and patterns are subsequently magnified for viewing and recording. Several lenses (intermediate and diffraction lenses) are used to magnify the image or the diffraction pattern produced by the objective lens and to focus these on the viewing screen or computer display *via* a detector, CCD, or TV camera (projector lens).

Parallel-illumination TEM mode is chosen for diffraction-contrast imaging and SAD pattern formation. To see the diffraction pattern, the back focal plane of the objective lens has to be set as the object plane for the intermediate lens. Then the diffraction pattern is projected onto the viewing screen/CCD as shown in Fig. **6A**. Otherwise, to look at an image, the object plane of the intermediate lens has to be set as the image plane of the objective lens. The image is then projected onto the viewing screen/CCD, as shown in Fig. **6B**. When the SAD pattern is projected onto the viewing screen/CCD, it is possible to use the pattern to perform the two most basic imaging operations in the TEM. No matter what kind of specimen is, the SAD pattern will include a bright central spot that contains the direct-beam electrons and some scattered electrons. By selecting the direct beam, a Bright Field (BF) image is formed. By selecting only electrons that are not in the direct beam, a Dark Field (DF) image is formed.

The TEM images the crystal lattice of a material as an interference pattern between the transmitted and diffracted beams. Thus, TEM provide information about planar and line defects, grain boundaries, interfaces, *etc.* with an atomic scale resolution. The bright-field and dark-field imaging modes of the microscope, which provide morphological (bright-field) and Z-contrast (dark-filed) information, combined with electron diffraction, which provide crystallographic information, are invaluable tools to have a complete knowledge of the examined materials.

TEM microscope could also be optionally equipped with a STEM module, which provides the scanning of the electron beam on the sample and is essential for the Energy Dispersive X-ray Spectroscopy (EDS) and the Electron Energy Loss Spectroscopy (EELS). EDX and EELS are complementary techniques and are essential to get information about composition of the samples with a resolution close to the probe size. In Fig. **6**, the ray diagram for the different operating modes is reported.

#### **2.3. Scanning Probe Microscopy (SPM)**

Scanning Probe Microscopy (SPM) refers to a group of techniques that use the interaction of a microscopic probe, usually a sharp tip, with the surface of a sample to measure characteristics of the sample at localized points. This technique is not destructive and extremely surface-sensitive. The interaction between the probe and the sample provides topographical information. As the scanning range is reduced (hundreds of microns down to tenths of nanometres), it is not possible to map "big" surfaces in one single step. The basis of the scanning probe microscopy is depicted in Fig. **7**. The resolution obtainable with this technique can reach the atomic scale and with some cases it is also possible to map the position of single atoms.

**Figure 7:** Basis of the scanning probe microscopy. Reprinted with permission of Binning and Quate [5], Copyright (1986), American Physical Society.

#### **2.4. Atomic Force Microscopy (AFM)**

Among the SPM techniques, there is the Atomic Force Microscopy (AFM), invented by Binning, Quate and Gerber in 1985 [5]. It is related to the repulsive force between the probe and the surface of the sample. In AFM, imaging is produced by measuring the deflection of a cantilever hosting the tip (in an ideal case, a single atom), while raster scanning the sample surface (Fig. **8**). The deflection is due to the interaction force between the tip and the surface.

**Figure 8:** Sketch of the basis of the AFM technique. Reprinted with permission of Meyer [6], Copyright (1992), Elsevier.

AFM is essentially based on the collection of short-range repulsive interatomic forces, which are low repulsive forces (in the scale of nano-Newton or less). In addition to these short-range forces, also long-range forces such as Coulomb forces, dipole-dipole interaction, van der Waals dispersion forces, polarisation and capillary forces, which are attractive or repulsive, could also be encountered, but they can be minimized in order to improve the resolution and to reduce possible damage to the sample [6].

In Fig **9**, an example of a force-distance curve is reported [7], showing how the force changes when the tip approaches the sample.

The AFM can operate at a constant force or at a constant height. In the latter there is a risk that the tip may collide with the surface, thus causing damage. There are also two main operation modes: the static mode and the dynamic mode. In static mode, the cantilever is swept along the surface of the sample and therefore measures the surface topography directly by using the deflection of the cantilever. In the dynamic mode (also commonly referred to as tapping mode or non-contact mode), the cantilever is externally oscillated at or close to its fundamental resonance frequency or a harmonic. These changes in oscillation with respect to the external reference oscillation provide information about the sample's characteristics.

### **2.5. Conductive Atomic force Microscopy (C-AFM)**

Conductive atomic force microscopy (C-AFM) is a variation of atomic force microscopy. It uses an electrical current to construct the surface profile of the studied conducting specimen. This current flows through the metal-coated tip of the microscope and the sample. It is acquired simultaneously with the usual topographical mapping of the standard AFM. This enables to correlate a spatial feature on the sample with its conductivity. The C-AFM can be operated in the imaging mode and spectroscopic mode. The imaging mode is the same as described in § 2.4. In the spectroscopic mode, the tip is stationary, while the voltage is being swept. This allows recording conventional current–voltage characteristic from tiny areas of the sample. Thereby information on the local electronic properties, such as local density of states, can be extracted.

**Figure 9:** Force-distance curve, showing how the force changes when the tip approaches the sample. Reprinted with permission of Shahin *et al.* [7], Copyright (2005), The Company of Biologists Ltd.

#### **2.6. X-ray Diffraction (XRD)**

X-ray diffraction is one of the most powerful tools for investigating the crystalline structure of materials. In fact, the discovery in the early 1900s made by Laue of the ordered atomic arrangement of crystalline materials, opened new possibilities to go deeper into the structure of the matter. This technique is based on the elastic scattering of X-rays from the electron clouds of individual regularly arranged atoms that constitute the crystalline structure of materials.

X-ray diffraction is a versatile technique that is useful not only for obtaining information about the crystalline orientation but also on the texture and on the quality of the materials. Nowadays, new instrument technology development has provided modular systems, which in few minutes are able to vary measurement configuration. In addition, new detection systems are now able to collect spectra with a very good signal-to-noise ratio within a couple of hours. New tools also allow the warming or cooling of the samples to follow the phase transitions.

The basis of the technique is depicted in Fig. **10**. The X-ray plane waves incident on a crystal lattice at angle *θ*, are partially reflected by successive parallel crystal planes of spacing *d*. The

superimposed reflected waves interfere constructively if the Bragg condition 2*d*sin*θ* = *n*λ is satisfied [8].

**Figure 10:** Scheme showing plane waves interacting with a crystal lattice.

The source of the X-rays is a tube where an accelerated electron beam hits a specific target, usually Cu, but also Co and other transition metals. As described in § 2.1, the electron matter interaction produces a number of signals, and among them there are characteristic X-rays. For the Cu target, the X-ray wavelength is 0,154 nm. Different geometries can be selected for this technique, depending on the information needed. In order to check the phase identification, the crystalline quality and the orientation, the most widely employed geometry is the Bragg-Brentano geometry (Fig. **11**), usually chosen for randomly oriented powders, bulk materials and thin films. In this configuration, the X-rays are focused on the sample at an angle *θ* and the diffracted beam is collected at the same angle *θ*. The angle is scanned in a defined angular range selected on the basis of the material to be measured. The incidence angle is the same as the collecting angle. Several detection systems exist, such as proportional counters, scintillation counters, semiconductor counter, CCDs. One of the most widely used is the proportional counter, where the ionization of an inert gas contained in a small chamber by an X-ray photon in an electrical field produces an avalanche of electrons. Since the number of electrons collected is proportional to the number of Xrays collected at a certain angle *θ*, the detector is able to give a spectrum providing the X-ray intensity as a function of the scanned angle. For thin film analysis, the thin film geometry (Fig. **12**) is preferred in order to suppress the substrate signal and improve the surface sensitivity by increasing the length of X-ray's path through the film. In this configuration, the incident angle *ω* is fixed. The detector scans over an angular range, and collects the diffraction peaks. The penetration depth can be varied by changing the incidence angle *ω* of the X-ray beam to the sample surface. The drawback of this technique is that usually the resolution is worse when compared to Bragg-Brentano geometry. The analysis of the diffraction pattern can be very complex, especially when the material presents some preferred orientation of when it does not have a fixed stoichiometry. To assign an "identity" for each peak in the diffraction pattern, scientists usually refer to the JCPDS (Joint Committee on Powder Diffraction Standards) database, which contains thousands of diffraction patterns of inorganic materials.

By analyzing a diffraction pattern, it is also possible to evaluate the size of the coherent diffraction domains, which may be smaller or equal to the grain size. This analysis works if the crystallites are

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less than approximately 100 nm in size. In this case, an appreciable broadening in the X-ray diffraction lines occurs. A very simple way to evaluate the average crystallites size is to apply the Scherrer formula [9]:

**Figure 11:** Scheme of the Bragg-Brentano geometry.

**Figure 12:** Scheme of the thin film geometry.

$$D = \frac{K \text{ } \lambda}{\beta \text{ } \cos \theta}$$

where *K* is a dimensionless shape factor, usually fixed at 0.9, is the X-ray wavelength, is the line broadening at half the maximum intensity (FWHM) in radians, is the Bragg angle and *D* is the mean size of the ordered (crystalline) domains. This method is based on the assumption that the material is stress-free and the shape of the crystalline domains is spherical and can be considered reliable when the contribution of the instrument to the broadening of the peaks is properly taken into account. By using this method, the size can be estimated from a single diffraction peak.

When both the stress and the particle size are influencing the broadening of the diffraction peaks, a more comprehensive method must be used to separate the different contributions. The most common method of strain/size analysis is based on the assumption that the broadenings from the two different sources have different angular relationships. For instance, the size broadening, as described in the Scherrer method, has a 1/cos() relationship, while the strain follows a tan() function. The Williamson-Hall plot [10] can be used to compute the average particle size *D* and the strain *ε* simultaneously, by using the following equation:

$$\beta = \frac{\lambda}{D\cos\theta} + 4\,\text{g}\,\text{tg}\,\theta$$

Also in this case the instrument contribution to the peaks broadening must be taken into account and must "subtracted" to the total line broadening β at FWHM.

#### **3. APPLICATIONS TO THE ANALYSIS OF THIN FILMS AND DEVICES**

In Fig. **13**, the basic structure of an amorphous silicon solar cell is reported: starting from the top, it consists of a sequence of different layers (a "multilayer") on a glass substrate which is coated with a transparent conductive oxide which allows both the light to enter and the electrical current to be collected; the back contact is generally made in stainless steel. Since the first cells appeared, a lot of research efforts have been devoted to modifying this basic structure in order to enhance the performance, and different multilayer configurations have been proposed and produced, by introducing various modifications: wide-bandgap alloy, micro and nano-crystalline semiconducting layers, texturized front contact layers, highly reflective back contacts, tandem cells incorporating amorphous silicon based alloys, buffer layers, nanostructures such as quantumdots and nanocrystals.

The morphological and structural properties of each layer that constitute the multilayer, do affect the performance of the final device and for this reason they have to be carefully measured and correlated to electrical, optical and photovoltaic properties.

Up to now the previously described techniques (AFM, SEM, TEM and XRD) have been used to study and investigate the following:


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In the following section the recent and most important experimental results obtained in these fields will be examined and discussed.

**Figure 13:** Structure of a typical amorphous silicon solar cell.

### **3.1. Semiconducting Films Structure**

The material quality of the semiconducting films and the efficiency of the solar cells continue to improve, and a big research effort has focused on the structure of the semiconducting films. Recently, the use of hydrogenated nanocrystalline silicon (nc-Si:H) in the middle and/or bottom cells in hydrogenated amorphous silicon (a-Si:H)-based multi-junction solar cells has been studied in depth. These new complex film structures are generally obtained under deposition conditions close to the amorphous/nanocrystalline transition and include nanocrystallines, grain boundaries, and amorphous regions. Microscopy measurements provide valuable information for characterizing material properties. In particular the morphological study of the silicon-based films used in solar cell fabrication is often performed by means of SEM, which enables the identification of crystal grains and of the amorphous phase. In general, due to the small examined area and to the difficulty of evaluating crystal fractions, only a qualitative information is obtained from SEM or TEM images, but these images are invaluable for supporting the results obtained from structural analysis such as Raman or XRD. As an example in Fig. **14** the SEM images of hydrogenated silicon films deposited by Plasma Enhanced Chemical Vapor Deposition with crystalline phases ranging from 0 to 75% are reported: in (a) the typical amorphous morphology, corresponding to a low-roughness, homogeneous surface is shown; in (b) and (c) a uniform distribution of silicon grain aggregates separated by an amorphous phase is evidenced. In (b) smaller crystallites of silicon in the agglomerated form are distributed over the scanned area, and also a bigger cluster can be seen at the centre of the image; in (c) uniformly distributed dense crystalline structures confirm the presence of 75% of the crystalline phase, with an average crystallite size of 12 nm, obtained from Raman measurements [11].

**Figure 14:** SEM images obtained for PECVD films of amorphous (a) and nano-crystalline silicon films with crystalline fractions of 45% (b) and 75% (c). Reprinted with permission from Parashar *et al.* [11], Copyright (2010), Elsevier.

Another example is given in Fig. **15** where TEM images, taken from [12] are reported and related to amorphous hydrogenated silicon carbide thin films deposited from argon diluted silane, ethylene, and hydrogen mixture by PECVD. In (a), a typical low-magnification cross section is reported showing the contrast between the thin film and the crystalline silicon substrate; in (b), a typical cross section high resolution (HR) TEM image of an a-Si1-x Cx:H/c-Si (001) specimen is reported. The micrograph reveals an abrupt interface, with a maximum asperity of three atomic planes, attributed to the substrate pre-treatment (HF dip) or etching in the early stages of the film growth. In (c) a typical plane view HR-TEM image of an a-Si1-x Cx:H thin film is reported. HR-TEM observation reveals a homogeneous micro-structure without any nanocrystalline clusters in all the samples. This result is also confirmed by the Selected Area electron Diffraction (SAD) patterns, which show diffused rings that are characteristic of an amorphous material.

**Figure 15:** TEM images as described in text. Reprinted with permission from Wang *et al.* [12], Copyright (2002), Elsevier.

The SAD is indeed frequently used in TEM investigations of amorphous, micro or nano-crystalline silicon films in order to obtain important information such as the orientation of crystallites or the presence of defects. As an example [13] in Fig. **16** diffraction patterns are reported, taken on films of hydrogenated microcrystalline silicon–carbon deposited on c-Si substrate by PECVD at different power densities and with different crystalline microstructures (varying from columnar silicon crystals to crystallites uniformly dispersed in an amorphous matrix). In both images the diffraction spots coming from the silicon substrate in <110> orientation can be seen and the

#### **160** *Silicon Based Thin Film Solar Cells Chiodoni and Tresso*

corresponding cell is highlighted by the continuous lines. Only silicon crystals are present. The three main diffraction rings, shown in the Fig. **16(a)** and **16(b)**, are due to <111>, <220> and <311> planes of c-Si. The diffraction rings visible in Fig. **16(b)** indicate that the crystals are randomly oriented in this film and the diffused intensity among the rings is attributed to the presence of an amorphous phase. The sample of Fig. **16 (a)**, deposited at lower power, shows diffraction rings that are discontinuous in intensity because of a non-homogeneous distribution in the orientation of the crystallites. Moreover, the superposition of several diffraction patterns does not reveal a preferred crystal orientation.

The micro-structure of the micro-and nano-crystalline silicon-based films can be determined from the X-ray diffaction (XRD) patterns. As can be seen in Fig. **17,** the typical Si(111) peak is located at 2θ=28.5°, the Si(220) peak at 2θ=47,4° and the Si(311) peak at 2θ=56,2°. Moreover the average crystallite size can be estimated as a first approximation according to the Scherrer formula. In Ref.4 the evolution of the layer crystallinity of p-doped microcrystalline hydrogenated silicon thin films deposited under different substrate temperature is demonstrated with an XRD spectrum.

**Figure 16:** Selected Area Electron Diffraction patterns for micro-crystalline hydrogenated silicon carbide films at different power densities: (a) 5W, completely crystallized film, with generally columnar crystal shape; (b) 25 W, silicon crystallites uniformly dispersed in an amorphous matrix. Reprinted with permission from Ambrosone *et al.* [13], Copyright (2004), Elsevier.

**Figure 17:** XRD measurement of p-doped microcrystalline hydrogenated silicon films thin films (about 30– 40 nm thickness) deposited on glass under different substrate temperature. The inset shows the change of the average crystallite size deduced using the Scherrer formula. Reprinted with permission from Tao *et al.* [14], Copyright (2010), Elsevier.

#### *Morphological and Structural Properties Silicon Based Thin Film Solar Cells* **161**

From the XRD pattern reported in Fig. **17**, it can be seen that the X-ray diffraction signal becomes weaker as the substrate temperature decreases, and the diffraction peak Si (311) disappears to temperatures below 150°C. In fact, the amorphous films do not show peaks in diffraction analysis, but only a typical broad band at around 2θ=20°-30°. The decrease of the crystallite size with decreasing temperature was calculated from (111) peak and is reported in the inset.

Scanning probe microscopies such as AFM are used in studies of hydrogenated amorphous silicon-based films, even if the complex structure of the films, which has a markedly statistical character, can give an ambiguous interpretation of the results. The film surface is generally very smooth, with the root-mean-square (rms) surface roughness in the range 1-2 nm, and hence suitable for the integration of the film in a device structure. As an example, in Fig. **18** a typical three-dimensional AFM image of an as-deposited amorphous silicon carbide thin film is shown, taken from ref. [12].

**Figure 18:** Typical three-dimensional AFM image of PECVD as deposited amorphous silicon carbide thin film. Reprinted with permission from Wang *et al.* [12], Copyright (2002), Elsevier.

A number of structural elements of the amorphous film surfaces have been identified: denselypacked convex structures ("hills") covering the total surface area [15], with dimensions ranging from few to several tenths of nm [16]; atomically smooth areas of approximately 0.03 nm rms local roughness occurring predominantly at the top of the hills and extended regions covered by sub-nanometric structures [17]. Finally, it is interesting to note that particular techniques such as conductance AFM (C-AFM) are useful for studying the transport mechanism in the material and for correlating electrical conduction to morphological properties. C-AFM has been used for measuring the local current flow distribution in mixed-phase (amorphous and nanocrystalline) solar cells, in the area of no ITO coverage. The results have been interpreted with the assumption that the nanocrystallines embedded in the amorphous phase behave as microscopic diodes [18]. Moreover cone formation and tree-like nanocrystalline structures, correlated to the hydrogen dilution used during the deposition, have been demonstrated to have a strong effect on the light induced open circuit voltage value [19].

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### **3.2. Front Contact Layer Surface**

As reported in Fig. **19**, the front contact layer, which is generally made of transparent conductive oxides (TCO) such as tin oxide (SnO2) or indium tin oxide (ITO), has the role of permitting the electrical current collection. The structure and the morphology of the first layer, which is exposed to the solar radiation, are of fundamental importance.

Any roughening of the surface of the front TCO contributes to enhance the light absorption, since it reduces reflection by increasing the possibility that the reflected light bounces back to the surface rather than out to the surrounding air. TCO morphology depends on a wide variety of growth factors, such as deposition temperature, flow rate of the gases, gas precursor used and substrate material. The demand for these TCO films is rapidly increasing due to the extensive market growth in photovoltaic areas. A lot of different solutions are continuously being studied and proposed, in order to fulfil the requirements on low resistivity, high transmittance, large area deposition, low cost manufacturing.

Furthermore the ability for fine patterning, light scattering and precise alignment of the electronic structure to the surrounding semiconductors are frequently requested.

**Figure 19:** SEM images of SnO2:F deposited with different precursors: (a). TMT, (b). MBTC, (c). TTC, (d). Asahi U-type. Reprinted with permission from De Graaf *et al*, [21], Copyright (2010), Elsevier.

#### *Morphological and Structural Properties Silicon Based Thin Film Solar Cells* **163**

Fig. **19** shows SEM images of SnO2 layers produced with different tin precursors [20, 21]. From these images it becomes clear that the highest surface roughness is obtained by using tin tetrachloride (TTC). The morphology resembles that of the commercially available and largely used Asahi U-type, which is also deposited with TTC. In contrast, tetramethyltin (TMT) yields much smoother layers. The RMS surface roughness measured on an area of 5 × 5 μm2 is as follows: a. 7 nm, b. 22 nm, c. 39 nm, d. 40 nm.

In [22] the optimization procedures followed for enhancing the photovoltaic efficiency by an appropriate design of the indium–tin oxide (ITO) thin films are reported. In particular the deposition conditions of ITO film by electron-gun evaporation were optimized for hetero-junction microcrystalline silicon solar cells. Microstructure, surface morphology, electrical and optical properties of these films were characterized and analyzed. The substrate temperature and the ITO thickness were optimized, arriving at a solar cell conversion efficiency of 16.4%. In Fig. **20** the SEM and AFM images of the ITO film surfaces are reported.

**Figure 20:** (a) SEM and (b) AFM images of ITO films prepared by electron gun evaporation at a substrate temperature of 230 °C. Reprinted with permission from Lien SY, [22], Copyright (2010), Elsevier.

The fundamental solar cell parameters (the fill factor, FF, open circuit voltage, VOC, and also the short circuit current, Jsc) exhibit a strong dependence on the surface properties of the front contact layer [23, 24]. In ref [23], the plasma-induced chemical and morphological modifications of the boron doped zinc oxide front layer are shown to produce appreciable PV performance improvements for solar cells produced on these plasma treated substrates. By varying the etching time, different surface roughnesses were obtained and the evolution of the surface morphology was correlated with its scattering properties. The best device parameters have been reached through a compromise between an effective sharp edge rounding off (improved ZnO:B/p-layer interface) and a sufficiently high roughness (high Jsc value).

#### **3.3. Interface Properties**

Since the last century, major improvements in the performance of amorphous silicon solar cells have been obtained by changing the initial p-i-n configuration, using wide-bandgap alloys and microcrystalline p-layers, enhanced reflective back contacts, tandem cells incorporating a-Si/Ge:H alloys, and buffer layers [25]. For an appropriate design of the solar cell it is necessary to characterise and control the morphology of the interfaces, in particular the interface between the back contact and the bottom semiconducting film. As an example, in hetero-junction solar cells, the hetero-interfaces have been particularly studied, since they can affect the device performances.

The use of textured metal oxide back contacts instead of plain stainless steel ones can provide a significant current enhancement. The textured interface acts as a diffuse scattering mirror, which results in the lengthening of the optical path in the cell. Optimized back reflectors can lead to an enhancement of the photocurrent by as much as 50%. However, as reported in [26], the morphology of the surfaces needs to be controlled to avoid cavities and shunting paths. A further drawback of such rough metallic surfaces is the parasitic absorption due to surface particle plasmons. The surface properties of gallium doped zinc oxide (GZO) films, used as back contacts in amorphous silicon thin film solar cells, have significant influence in the final conversion efficiency. In Fig. **21**, taken from [27], a comparison of the GZO films with and without texturing obtained by plasma etching is shown: (a) as-grown GZO film (3.2 wt% Ga2 O3 ) on a-Si cell and (b) the same GZO film after 30 min roughening. The treatment increases the optical scattering reflectance and reflection haze, and consequently, the relative increase in the solar cell efficiency is 4.6%.

Also in the fabrication of flexible solar cells, with flexible substrates such as metal or plastic foils (in polyethylene-naphtalate, PEN), a substrate texture has been proposed to scatter the light at each interface and to increase the light trapping in the active layer, together with the use of a buffer layer at the n/i interface [28]. TEM measurements have been used for investigating the relation between voids or nanocrack formations in the intrinsic layer and the textured substrate. An example of an obtained TEM micrograph of the interface is given in Fig. **22**.

Finally, interface characterization is essential in the fabrication of amorphous–crystalline silicon (a-Si:H/c-Si) heterojunctions [29, 30]. These cells present unique technological advantages with respect to homo-junction silicon cells such as low processing temperatures (below 230 °C) and the ability to rapidly deposit the thin amorphous emitter on large areas using PECVD. The a-Si:H passivates the silicon surface excellently, and cell efficiencies up to 22.3% have been recently

#### *Morphological and Structural Properties Silicon Based Thin Film Solar Cells* **165**

demonstrated by Sanyo, with a-Si:H/c-Si cells based on high-quality CZ-c-Si [31]. AFM and SEM [30] have been used together with surface photovoltage and photoluminescence measurements. As a consequence, the relation between structural imperfections at the structured silicon surfaces, energetic distribution of interface state densities, recombination loss at a-Si:H/c-Si interfaces and solar cell characteristics have also been investigated. It has been shown that the morphological and electronic properties of the substrate surface are strongly related to the preparation method.

**Figure 21:** SEM micrographs of surface morphology of gallium doped zinc oxide films on a-Si solar cell before (a) and after (b) 30 min roughening treatment by plasma etching. Reprinted with permission from La *et al.* [27], Copyright (2011), Elsevier.

**Figure 22:** Cross-sectional TEM micrograph of a microcrystalline silicon cell on textured substrate coated with 80 nm of sputtered ZnO. Reprinted with permission from Soderstrom *et al.* [28], Copyright (2004), American Institute of Physics.

Wet-chemical oxidation and etching steps have been carefully optimized to obtain textured silicon substrates, with randomly distributed Si (111) pyramids Fig. **23**. The preparation-induced surface micro-roughness and the density of electronically active defects have been reduced and significantly lower micro-roughness, densities of surface states and recombination loss at a-Si:H/c-Si interfaces have been achieved when compared to conventional pre-treatments.

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**Figure 23:** SEM micrographs (tilted by 30°) of silicon substrates with randomly distributed pyramids, (a) after H-termination by NH4F (48%), and (b) after subsequent wet-chemical oxidation in H2SO4/H2O2+HF dip (120 s). Reprinted with permission from Angermann *et al.* [30], Copyright (2008), Elsevier.

### **3.4. Growth Processes**

The growth of device-grade thin film silicon remains an active research topic, and different thin film structures have been proposed for solar cell fabrication. On one side, there is microcrystalline silicon (μc-Si:H), at the other amorphous silicon (a-Si:H), and in between a complex mixture of crystalline grains and/or columns, disordered material, cracks and voids, whose detailed structure strongly depends on preparation conditions. Much progress has been made in the past few years regarding the material performance and preparation, using plasma enhanced chemical vapour deposition (PECVD) processes. Nevertheless, a better understanding of the growth mechanisms and of the influence of deposition parameters on the performance of the final device is necessary. For this, the study of morphological and structural properties can be useful.

Hydrogenated microcrystalline silicon thin films are produced mainly by chemical vapour decomposition of SiH4+H2gas mixtures, by means of different processes such as PECVD, Very High Frequency PECVD, Electron Cyclotron PECVD and Hot-wire PECVD. Structural studies using electron microscopies (SEM and TEM) and X-ray diffraction [32, 33 and references therein] have been used for the interpretation of the growth mechanisms. The characteristic features of the growth of this material are the pronounced columnar structure and an initial amorphous layer. It has been demonstrated that such films grow in complicated heterogeneous and anisotropic structures, which depend on the film thickness and on the substrate type. By using a proper choice of the deposition parameters (a high substrate temperature, a low deposition rate) it is possible to influence the columns growth strongly and to avoid the amorphous layer formation. In Fig. **24** the columnar growth is evidenced by SEM and TEM micrographs of microcrystalline silicon film by ECR-CVD on glass and on Si(111) from [32]: the images show for both the substrates a fibre-like arrangement of crystalline columns, separated by incoherent boundaries with little variation in the typical column size from bottom to top.

In [34] large area microcrystalline silicon films grown by ECR-CVD have been measured with XRD characterization in thin film configuration, using an incident angle of 0.5°.

Each peak of the diffraction pattern was fitted with a pseudo-Voigt function and the full weight half maximum, FWHM, was used to calculate the grain dimension through the Scherrer equation. The percentage of the amorphous phase was calculated as the fraction of the areas of the two overlapped peaks of the amorphous and crystalline phases at above 27.4° and 28.4°, respectively. In Fig. **25** the XRD spectra of two samples deposited at a substrate temperature of 218°C and at different microwave power (800 W and 360 W respectively) are shown. It is possible to observe for the sample deposited at a microwave power of 800 W, the typical diffraction pattern of (111), (220) and (311) crystalline silicon. In contrast, the sample deposited at 360 W exhibits a broad band, which is typical of an amorphous silicon structure. It has been observed that both substrate temperature and microwave power strongly influence the crystallinity fraction and the crystal dimensions. TEM images have been performed by an electron microscope operating at 200 kV: the data of crystal dimensions for several orientations extracted from XRD have been compared to the average ones obtained by TEM micrographs and the results showed a good consistency.

**Figure 24:** SEM pictures of fractional area of microcrystalline silicon film (a) on glass and (b) on Si(111) and cross-sectional TEM micrographs (c) on glass and (d) on Si(111). Reprinted with permission from Sieber *et al.* [32], Copyright (2002), Elsevier.

Finally, morphological characterization is very useful for the experimental observation of the grain shape evolution during growth (the term 'grain' denotes that, in microcrystalline silicon films, the aggregates are composed of nanometer sized subgrains). The shape of the grains is often studied by cross section TEM [35] but it has also been deduced from the AFM topography of different series of samples with varying thickness [36].

**Figure 25:** Typical X-ray diffraction patters of amorphous and microcrystalline silicon films grown by ECR-CVD at different power (800 W for ECR56 and 360 W for ECR38). Reprinted with permission from Ferrero *et al.* [34], Copyright (2001), Elsevier.

**Figure 26:** Schematic picture of the specific shape of crystal grains based on AFM topography of microcrystalline silicon films with varying thicknesses. Reprinted with permission from Fejfar *et al.* [36], Copyright (2004), Elsevier.

In Fig. **26**, an interesting example of a model for the grain evolution with the film thickness is shown, taken from [36]. It was observed that the grains evolve in two distinct stages: an expansion stage and later an elongation stage. The shape of the grain cap is spherical. At the largest thickness the grains already collide and fill the whole surface, and the remaining surface of the grain is spherical.

It was observed that the grains evolve in two distinct stages: an expansion stage and later an elongation stage. The shape of the grain cap is spherical. At the largest thickness the grains already collide and fill the whole surface, and the remaining surface of the grain is spherical.

### **3.5. Crystallization Processes of Amorphous Thin Films**

The crystallization of silicon amorphous layers is a promising way for obtaining polycrystalline silicon thin films. Such films are of great interest for thin film transistors which are used in active matrix liquid crystal displays and active matrix organic light emission displays. They have also been employed for the fabrication of low-cost stable solar cells. By controling the parameters of the crystallization process as well as the structure, the composition and the thickness of the single layer, it is possible to control the resulting crystal and electronic quality of the polycrystalline film and thus the cell performance.

Different methods are used to develop thin poly-silicon films from amorphous silicon. These include annealing in the furnace, laser crystallization and rapid thermal annealing. Metal-induced crystallization has also been proposed to crystallize amorphous films at relatively low temperature: metals such as aluminium, nickel or palladium can lead to crystalline silicon grain formation of micrometric dimensions with considerable grain growth. In these grains the internal structure changes from the amorphous to crystalline structure resulting in a metal-induced phase transition.

The crystallization kinetics and the crystal quality of the films are studied by the combination of different techniques. These include Raman spectroscopy, Infrared absorption measurements, X-ray diffraction, optical, electronic and atomic force microscopies. In the following, some examples of morphological characterizations developed in order to understanding the crystal formation mechanisms will be examined. In Fig. **27** FESEM top-view images of amorphous silicon carbide (a-SiC:H) films with different C content are shown before and after laser annealing treatment [37, 38]. Although prior to laser treatment a weak increase in the roughness was noted with increasing carbon content, no substantial morphological differences were observed in the sample surfaces that appear quite smooth and homogeneous, as would be expected for amorphous films. By contrast, important morphological differences are observable in the images of the samples after the treatment, revealing the formation of structures on a sub-micrometric scale, which were attributed both to the presence of crystallites and of molten and re-solidified material. This is greatly influenced by the laser energy and the cooling velocity. Furthermore, the morphology of such structures appears to be strongly related to the carbon content, since the agglomerate dimensions appear to increase with *x*.

FESEM cross-sectional images of samples deposited on c-Si substrates, Fig. **28**, revealed that the crystallization process took place close to the top surface, and depended on the film composition. The depth of the annealed region increased with carbon content, and the topography changed from a compact, quite uniform crystalline zone to a structured region with agglomerates of increasing dimensions.

Atomic force microscopy (AFM) is often used to observe the surface morphology of the crystallized samples after annealing. In [39] a detailed investigation of laser crystallization of amorphous silicon thin films is presented which compares Raman spectroscopy and AFM results.

#### **170** *Silicon Based Thin Film Solar Cells Chiodoni and Tresso*

P-doping of the films strongly decreased the threshold of crystallization and a great deal of tensile stress remains as can be observed from the red-shift of the Raman peak intensity. Laser annealing at appropriate energy densities induces a considerable stress release and increases the crystalline fraction till to 82%. The disordered structure with defects induced by laser annealing were observed in AFM images and were found to be responsible for the degeneration of electron mobility in the film.

**Figure 27:** FESEM top-view images of a-SiC:H films with different C content, before and after laser treatment of the surface. Reprinted with permission from Coscia *et al.* [38], Copyright (2010), Elsevier.

In [40] annealed hydrogenated amorphous silicon films were analyzed using atomic force microscopy, Raman and FTIR spectroscopy. The crystalline formations and the shape of the film surfaces were found to be dependent on the annealing time as well as on the substrate employed during the deposition process.

*Morphological and Structural Properties Silicon Based Thin Film Solar Cells* **171**

**Figure 28:** FESEM cross-section images of a-SiC:H films deposited on Si substrates with different C content, after laser treatment of the surface.

### **3.6. Advanced Nanostructures for New Concepts in Silicon Thin Film Solar Cells**

In the design and fabrication of modern solar cells, different efforts are now being devoted to enhance the light absorption and to increase the efficiency. The different means currently in use are summarized under the term of "photon management". In particular, in amorphous siliconbased solar cells, the intrinsic low diffusion length of the holes limits the thickness of the light absorbing layers to a few hundred nanometers. As a consequence, these thicknesses are not sufficient for absorbing all incoming photons. Therefore, various modifications to the solar cell structure have been implemented. The main purpose is to elongate the path of the photons in the light absorbing layer and thus increase the absorption probability. Micro-and/or nanostructures are used, such as randomly textured surfaces, dielectric gratings, photonic crystals and suitably engineered metal nanostructures integrated to the cell designs [41].

All of the previously examined morphological characterization techniques have been proposed in order to study the nanostructured samples. Up to the present, the most compeling physical information about the existence of nanometric crystalline structures has been given by high

#### **172** *Silicon Based Thin Film Solar Cells Chiodoni and Tresso*

resolution transmission electron microscopy. The spacing of atomic lattice planes often apparent in such images also give clues to the associated chemical properties.

One example of how structures with nanoscale properties are used to increase the performance of thin film silicon solar cells is reported in [42]. Ultrathin film amorphous silicon solar cells were designed and constructed with nanostructured plasmonic back contacts. They demonstrated an enhanced short circuit current density compared to cells that had flat or randomly textured back contacts. The plasmonic light trapping patterns on the rear glass substrate have been made into a sol-gel silica layer by using substrate conformal imprint lithography. This layer was then overcoated with Ag and ZnO:Al to form the back contact. In Fig. **29** the SEM image of Ag overcoated patterns showing 290 nm diameter particles with 500 nm pitch is reported, while in Fig. **30** the comparison between the surface topography of nanopatterned and randomly textured solar cells is shown. Tapping-mode AFM images were obtained on the top ITO contacts for two cells.

**Figure 29:** SEM image of plasmonic patterns employed in ultrathin amorohous silicon solar cells: 290 nm diameter particles with 500 nm pitch. Reprinted with permission from Ferry *et al.* [42], Copyright (2010), Optical Society of America.

The AFM scan on the plasmonic cell revealed the underlying nanopatterns that were imprinted into the sol-gel glass layer, and transferred to the back contact of the cell at a pitch of 500 nm. By contrast, the randomly textured Asahi glass showed an uncorrelated distribution of height variations.

**Figure 30:** Surface topography of nanopatterned and randomly textured solar cells: (a) Patterned cell with 500 nm pitch, (b) Cell on randomly textured Asahi U-type glass substrate. Reprinted with permission from Ferry *et al.* [42], Copyright (2010), Optical Society of America.

In [43] a series of thin silicon films with different degrees of crystallinity were prepared by glow discharge. The crystallite size, shape, and the crystallinity fraction were investigated by highresolution transmission electron microscopy (HRTEM), selected area electron diffraction (SAED), Raman spectroscopy (RS), and X-ray powder diffraction (XRD). The crystallite fraction and the average crystallite size calculated from both XRD and HRTEM images, reported in Fig. **31**, were in accordance with the results estimated from Raman spectra. The mutual agreement of the results obtained by completely different physical phenomena shows that the vibrational properties of the investigated material are directly influenced by nanometric crystallite sizes due to quantum confinement.

Finally nanoparticles which are confined in all three spatial dimensions, referred to as the quantum dots, have been implemented in various photovoltaic applications. Novel materials consisting of silicon nanocrystals embedded in a dielectric matrix have attracted considerable interest in the field of third generation photovoltaics. When Si nanocrystals are made very small (*<*7 nm in diameter), they behave as quantum dots due to the three-dimensional quantum confinement of carriers. In [44] Si quantum dots were formed by the alternate deposition of silicon oxide (SiO2) and silicon-rich SiO*x*  with magnetron co-sputtering, followed by high-temperature annealing. The corresponding TEM images in both low and high magnification are reported in Fig. **32**.

**Figure 31:** HRTEM images and distribution of the measured crystallite sizes fitted to log-normal distribution. Reprinted with permission from Gajovic *et al.* [43], Copyright (2008), Elsevier.

**174** *Silicon Based Thin Film Solar Cells Chiodoni and Tresso* 

**Figure 32:** TEM images of Si QDs in a SiO2 matrix: (a) low-magnification image and (b) high-resolution image. Reprinted with permission from Cho *et al.* [44], Copyright (2008), IOP publishing.

#### **ACKNOWLEDGEMENT**

Declared none.

#### **CONFLICT OF INTEREST**

The author(s) confirm that this chapter content has no conflict of interest.

#### **REFERENCES**



#### **176** *Silicon Based Thin Film Solar Cells Chiodoni and Tresso*


© 2013 The Author(s). Published by Bentham Science Publisher. This is an open access chapter published under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/legalcode

# **CHAPTER 7**

## **Optical Properties of Semiconductors**

## **Marian Nowak\***

*Institute of Physics, Silesian University of Technology, 8 Krasińskiego, Katowice, PL-40019, Poland* 

**Abstract:** Optical properties of semiconductors, dielectrics and metals play a key role in the development of thin film solar cells. While these devices belong to photon photodetectors both the photon and wave nature of light affects their performance. Some of these problems are discussed in this chapter. The efficiency of photogeneration of free carriers by light as well as its spatial distribution is taken into consideration. This distribution is strongly affected by light interfering in a structure of many thin films. The possible geometrical and optical inhomogeneities of the solar cell structure are discussed. A few methods of determining surface and averaged overall film thickness refractive indices of semiconductor materials are presented. Techniques for determining different components of absorption of light in semiconductors are also reported. Examples of optical methods useful for determining essential parameters of semiconductors (*e.g.*, optical energy gap, carrier diffusion length, and parameters of electron states) are presented as well.

**Keywords:** Semiconductors, transmittance, reflectance, quantum efficiency of photogeneration, linear distribution of intensity of reflected and transmitted radiation, graded energy gap semiconductor, optical properties of multilayer structure, amorphous silicon, refractive index, absorption coefficient, spatial distribution of radiation intensity, photogeneration of free carriers, recombination, electronic states parameters, steady state photocarrier grating, photoconductivity, photoelectromagnetic effect, optical inhomogeneity.

### **1. INTRODUCTION**

While solar cells belong to photon detectors, both the photon and wave nature of light affects their performance. Therefore when optimizing the features of these devices different optical phenomena-for example, the penetration of light into a semiconductor, the spatial distribution of radiation in it (sometimes the cell can be equivalent to the so-called resonant cavity), and the efficiency of photogeneration of free carriers - must be taken into account. Construction of solar cells usually requires structure of many films. The radiation is divided into reflected and transmitted parts each time the beam strikes an interface (Fig. **1**).

To describe the optical phenomena mentioned above the following parameters are involved: coefficient of reflectivity of light; real part of refractive index of the investigated material, and absorption and scattering coefficients of light as well as quantum efficiency coefficients (QECs) for photogeneration of free electrons and holes. These parameters are discussed in many textbooks on optics (*e.g.* [1,2]) and semiconductors (*e.g.* [3,4]), as well as in monographs on photoelectric effects (*e.g.* [5,6]) and experimental methods of semiconductor investigations (*e.g.* [7-10]).

**Address correspondence to Marian Nowak:** Institute of Physics, Silesian University of Technology, 8 Krasińskiego, Katowice, PL-40019, Poland; Tel: 48-326034167; E-mail: marian.nowak@polsl.pl

**Figure 1:** Scheme of radiation propagation in a multilayer structure of a semiconductor and dielectric films.

The aim of this paper is to describe special aspects of the influence of optical and geometrical inhomogeneities on spatial distribution of light in a multilayer structure of semiconductor and dielectric films. Several techniques useful for determining surface and bulk values of optical parameters are reviewed. Methods applied to distinguish between different components of absorption of light in semiconductors are reported as well. To enhance efficiency of solar cells one should control, among others aspects, the carrier diffusion length and parameters of electron states in energy gap of the used semiconductor. Therefore, some optical methods suitable for determining these parameters are presented.

Owing to the limited length of this paper, the optical properties of the quantum nanostructures (*e.g.* [11,12]) as well as the Raman scattering (*e.g.* [13]), IR absorbance (*e.g.* [14]), luminescence (*e.g.* [15]), electroreflectance and electroabsorption (*e.g.* [16]) are not presented. Nor are the properties of anisotropic films (*e.g.* [17,18]) and radiative recombination of electrons and holes (*e.g.* [19,20]) reviewed in this chapter.

#### **2. OPTICAL PARAMETERS OF SEMICONDUCTORS**

Complex refractive index ܰ ൌ ݊ െ ݅ߢ) where ݅=√െ1) is the main optical parameter of a semiconductor. The real part of this index represents the ratio of electromagnetic wave velocities in a vacuum and in the investigated material [1]. The extinction coefficient ߢ describes the attenuation of the electric field of the wave in the material and determines the absorption coefficient of light

$$a\_f = \frac{\text{4m} \kappa\_f}{\lambda} \tag{l}$$

where ߣ is the wavelength of radiation. The value of the last parameter is an inverse of the material thickness that makes an intensity of light *e*-times smaller.

It should be noted that sometimes absorption of light is described by optical density of a sample (also called absorbance)

$$\text{Optical properties of Semiconductor}\newline\text{Sillicon Bases! Thin Film Solar Cells}\newline\text{179}$$

$$A\_{10} = \log\left(\frac{l\_0}{l}\right) = \log\left(\frac{1}{r\_0}\right) = -\log T\_o \tag{2}$$

where *I* is the transmitted light intensity, *I*0 is the incident light intensity, and ܶ represents the transmittance coefficient. The logarithm to the base of 10 applied here is commonly used in chemistry, while physicists usually adopt the natural logarithm.

According to the Bouguer-Lambert law

$$I = I\_0 e^{-a\_f y\_f} \tag{3}$$

the absorbance is proportional to the sample thickness ݓ and the absorption coefficient ߙ. Therefore, one can find

$$
\omega\_f = \frac{2.303}{w\_f} A\_{10} \tag{4}
$$

It should be noted that absorptance (not absorbance) is defined as the ratio of absorbed to incident radiation.

In some cases the complex refractive index is represented by the real (ߝ ᇱ ) and imaginary (ߝ ᇱᇱ) parts of the complex electric permittivity

$$N\_{l} = \sqrt{\varepsilon\_{l}^{'} - t\varepsilon\_{l}^{''}} \tag{5}$$

The Kramers–Kronig formulae are often used to relate the real and imaginary parts of refractive index. Therefore, one can find [3]

$$n\_{j}(\text{hv}) = 1 + \frac{c\hbar}{2\pi^{2}} \text{Pf} \int\_{0}^{+\alpha} \frac{a\_{j}(\text{f}')}{\left(\text{E}'\right)^{2} - (\text{hv})^{2}} dE' \tag{6}$$

where Ƥ denotes the Cauchy principal value, hν is photon energy, c is the light velocity in vacuum, and h is the Planck constant. One can estimate spectrum of ݊ in the range of strongly absorbed radiation from the known, full spectrum of light absorption.

Sometimes, values of optical parameters are described by the effective medium theory (EMT) as functions of the volume fractions ܸ of *j* components in a matrix [21, 22]

$$\begin{aligned} \, \_l\Sigma\_f \, V\_l \xrightarrow[\dot{\varepsilon}\_f + 2\dot{\varepsilon}\_\chi \,]{\dot{\varepsilon}\_f - \dot{\varepsilon}\_\chi} = 0 \end{aligned} \tag{7a}$$

$$\mathbf{a}\_{\mathbf{x}} = \sum\_{l} V\_{l} \mathbf{a}\_{l} \tag{7b}$$

where ߝ௫ <sup>ᇱ</sup> and ߙ௫ are so-called effective values of parameters for composite material. In the case of a rough surface one of the components is the surrounding ambient and the other one is consistent with the film material.

#### **2.1. Absorption Coefficient**

The measured absorption coefficient (ߙ௫ሻ usually is a sum of the (true) optical absorption coefficient (ߙ (and the scattering coefficient (ߙ௦) [22]

$$a\_{exp} = a\_{aj} + a\_{sc}$$

**(8)**

where ߙ௦ has units of inverse length (m-1). Despite the method presented in [22], the values of ߙ and ߙ௦ can be determined using the diffuse reflectance (DRS) and the diffuse transmittance (DTS) spectroscopy [23]. When a material, consisting of many particles, or nanoparticles, is illuminated, some of the impinging radiation penetrates the sample and some is reflected from its surface. The portion that penetrates the sample is scattered at a large number of points in its path as well as transmitted through the particles a number of times. Only the part of this radiation that is returned to the surface of the sample and comes back out is considered to be diffuse reflection [24]. DRS is a suitable, non-destructive, and simple method of investigation, especially important in examinations of porous, nanocrystalline materials and gels [25]. It is impossible to examine such materials applying specular reflection and it is also extremely difficult to determine their path length in an optical transmittance. The following factors are related to high spectral quality of diffuse reflectance: dilution of the sample with a nonabsorbing matrix ensures a deeper penetration of the incident beam into the sample, which increases the contribution of the scattered component in the spectrum and minimizes the specular reflection component; and smaller particles improve the quality of DRS spectra.

The diffuse reflectance ܴௗ ൌ ܫௗ ܫ ⁄ ௦௧ௗ (the ratio of intensities of radiation reflected in a diffuse manner from the sample and from the known standard) can be converted to the Kubelka-Munk function [24]

$$F\_{KM} = \frac{(1 - R\_d)^2}{2R\_d} = \frac{a\_{aj}}{a\_{sc}} \tag{9}$$

In some cases, ߙ௦ is constant (*e.g.* when thickness of the sample is much bigger than the individual particle [9]). The advantage of the Kubelka-Munk model is that the scattering and absorption coefficients may be directly expressed in terms of the measured ܴௗ and a diffuse transmittance (ܶௗ, *i.e.* the ratio of intensity of radiation transmitted in a diffuse manner through a sample, and *I*0) [23]

$$\alpha\_{sc} = \frac{1}{\nu\_f A\_Y} \ln \left[ \frac{1 - R\_d(A\_X - A\_Y)}{\tau\_d} \right] \tag{10a}$$

$$a\_{al} = (A\_x - 1)a\_{sc} \tag{10b}$$

$$\text{where } A\_\chi = \frac{1 + R\_d^2 - T\_d^2}{2R\_d} \text{ and } A\_\chi = \sqrt{A\_\chi^2 - 1}.$$

Various mechanisms of absorption of electromagnetic radiation can be observed in semiconductors, *e.g.* direct allowed (ߙ (or direct forbidden (ߙ (absorption, indirect allowed absorption with absorption and/or emission of phonons ሺߙூ), indirect forbidden absorption (ߙூ), Tauc absorption (ߙ்(, Urbach ruled absorption (ߙ(, free carrier absorption (ߙி), exciton absorption, intraband absorption, impurity absorption, lattice absorption, *etc.* (*e.g.* [3,4,26,27])

$$
\mu\_{Da} = A\_{Da} \sqrt{\text{hv} - E\_{gDa}} \text{ for hv} \ge E\_{gDa} \tag{11a}
$$

$$\mu\_{Df} = \frac{\mu\_{Df}}{\text{hv}} \left(\text{hv} - E\_{\text{g}}\right)^{3/2} \text{ for } \text{hv} \ge E\_{\text{gD}f} \tag{11b}$$

$$\mu\_{la} = A\_{la} \frac{\left(\text{hr} - \text{Egla} + \text{Egl}\right)^2}{\exp\left(\frac{\text{Egl}}{\text{k}\_B T}\right) - 1} \text{ for } \text{hv} \le \text{E}\_{gla} \tag{11c}$$

$$\alpha\_{Ia} = A\_{Ia} \left[ \frac{\left(\text{h}\prime - E\_{gla} + E\_{ph}\right)^2}{\exp\left(\frac{E\_{ph}}{k\_B T}\right) - 1} + \frac{\left(\text{h}\prime - E\_{gla} - E\_{ph}\right)^2}{1 - \exp\left(-\frac{E\_{ph}}{k\_B T}\right)} \right] \text{for h}\prime > E\_{gla} \tag{11d}$$

$$\mathbf{a}\_{\mathrm{lf}} = A\_{\mathrm{lf}} \left(\mathrm{hv} - \mathrm{E}\_{\mathrm{glf}}\right)^{3} \text{ for } \mathrm{hv} \ge \mathrm{E}\_{\mathrm{gff}} \tag{11e}$$

$$\mu\_T = \frac{\mu\_T}{\text{hv}} \left(\text{hv} - E\_g\right)^2 \text{ for hv} \ge E\_g \tag{11}$$

$$\alpha\_U = A\_U \exp\left(\frac{\text{hv}}{\varepsilon\_U}\right) \tag{11g}$$

$$
\mu\_F = A\_F \lambda^2 \tag{11b}
$$

where ܧ and ܧூ are direct and indirect allowed energy gaps (*e.g.* [3,4]), ܧ and ܧூ are direct and indirect forbidden energy gaps (*e.g.* [3,4]), ܧ is the Tauc energy gap in an amorphous semiconductor [26], ܧ is phonon energy (in general, the absorption can simultaneously involve phonons of different energies [28]), ܧ is so-called Urbach energy (that represents the widths of the exponential tail in the Urbach spectral dependence of absorption coefficient [27]), ܣ, ܣ, ܣூ, ܣ், ܣ, and ܣி are constants.

**Figure 2:** Spectral dependence of absorption coefficient of radiation of a-Si:H,F thin film [29] (1, હ܂ ;2, હ܃ ; 3, coefficient estimated for extrinsic photogeneration of carriers; 4, total absorption coefficient estimated from the optical transmittance of the film).

Various mechanisms of absorption of light can be observed in semiconductors; some of these can coexist in the same spectral range (Fig. **2**). The optical properties of amorphous semiconductors are dominated by the presence of a tail on the optical absorption which falls into the spectral region which is normally transparent in crystals. This tail is attributed to the presence of localized electronic states near the band edges in the amorphous semiconductors. Above the tail the absorption remains high due to the presence of interband electronic transitions identical to those which occur in crystals. Absent, however, are the singularities which are the result of the band structure in crystalline semiconductors. Rather, the amorphous materials exhibit much smoother absorption spectra in the interband region (Fig. **2**).

Therefore, the total absorption coefficient should be described as follows:

$$
\alpha\_{al} = \Sigma\_l \alpha\_l \tag{12}
$$

where ߙ describes various mechanisms of light absorption. A very important question is the mechanism of light absorption in a semiconductor. One of the best methods to determine it and the energy gap of the semiconductor is to perform the multiabsorption fitting of the spectrum of absorption coefficient (*e.g.* [25,30]). In this procedure one minimizes the following least square function

$$\chi^2 = \sum\_{l} \left[ a\_{aj}(h\nu\_l) - A\_a \Sigma\_l a\_l(h\nu\_l) \right]^2 \tag{13}$$

where *i* represents photons of different energy, ߙ describes various mechanisms of light absorption (*e.g.* Eq. (11)), and ܣఈ is the proportionality factor.

The different components in the total absorption coefficient as well as in refractive index are distinguishable due to their different spectral dependences (*e.g.* Eq. (11)), and due to their different influences on various optical and photoelectromagnetic (PEM) effects. Review [6] describes the firstorder PEM phenomenon which causes electromotive force parallel to the illuminated surface of a semiconductor owing to the charge separation by the magnetic field, of photogenerated carriers diffusing because of their different concentrations in various parts of a sample. This effect depends strongly on wavelength, intensity and polarization of radiation and magnetic field induction, as well as on the individual properties of the material investigated, and the configuration of the sample relative to the direction of applied magnetic field and optical illumination [6].

Contrary to photoconductivity (PC), the PEM effect occurs essentially in the case of interband (intrinsic) photoexcitation of electrons and holes. Therefore, PC and the PEM effect have attracted considerable interest as potential tools in investigations of many problems related to the fundamental properties of semiconductors [6]. They have been studied not only in many crystalline semiconductor materials but also in amorphous silicon. The first observation of PEM effect in a-Si:H, and the use of it for estimation of carrier mobility and lifetime, was reported by Moore [31].

#### **2.2. Determination of Optical Parameters Using QECs of Carrier Photogeneration**

In general, the PC and PEM responses are proportional to the following effective QECs for photogeneration of free carriers [6,29]

*Optical Properties of Semiconductor Silicon Based Thin Film Solar Cells* **183**

$$
\beta\_{PC} = \frac{\mu\_{\text{e}} r\_{\text{e}} \beta\_{\text{e}} + \mu\_{\text{h}} r\_{\text{h}} \beta\_{\text{h}}}{\mu\_{\text{e}} r\_{\text{e}} + \mu\_{\text{h}} r\_{\text{h}}} \tag{14a}
$$

$$
\beta\_{PEM} = \frac{n\_h \mathbf{r}\_e \beta\_e + n\_e \mathbf{r}\_h \beta\_h}{n\_h \mathbf{r}\_e + n\_e \mathbf{r}\_h} \tag{14b}
$$

where ߤ and ߤ are drift mobilities of electrons and holes, ߬ and ߬ represent lifetimes of photogenerated electrons and holes, ݊ and ݊ are electron and hole concentrations, and ߚ and ߚ are QECs for photogeneration of electrons and holes. In the case of an extrinsic semiconductor, measurements of PC has yielded information about the majority carriers because of trapping of the minority carriers (semi-insulating GaAs may be a rare exception). PEM effect is connected with a diffusion process, so it is controlled by the transport and recombination parameters of the minority carriers. Therefore, in the case of a strongly doped p-type semiconductor, the QEC for photogeneration of holes can be determined using the PC data

$$
\beta\_h = \frac{a\_h}{a\_{af}} \eta \tag{15a}
$$

where ߙ describes absorption processes in that free holes are photogenerated, and ߟ is the number of carriers generated by one photon (ߟ can be greater than one in the case of photon energies greater than the energy gap of the investigated semiconductor). In the case of PEM investigations in the same p-type semiconductor, the QEC for photogeneration of electrons can be determined

$$
\beta\_e = \frac{a\_e}{a\_{aj}} \eta \tag{15b}
$$

where ߙ represents the absorption processes in that free electrons are photogenerated.

**Figure 3:** Spectral dependence of quantum efficiency coefficients of radiation of a-Si:H,F thin film [29] (1, coefficient calculated with the assumption that free carriers are photogenerated due to Tauc absorption; 2*,*  coefficient calculated with the assumption that free carriers are photogenerated due to Urbach ruled absorption*;* 3, coefficient calculated for extrinsic photogeneration of carriers*;* 4, ࢼ ;5, ࢼ(.

The values of ߚ and ߚாெ (Fig. **3**) can be evaluated by applying normalized ratios of the measured responses to the theoretically evaluated values

$$\beta\_{\rm PC}(h\nu) = \frac{\sigma\_{\rm PCexp}(h\nu)}{\sigma\_{\rm PC}(h\nu)}\tag{16a}$$

$$
\beta\_{\rm PEM}(h\nu) = \frac{l\_{\rm PEMexp}(h\nu)}{l\_{\rm PEM}(h\nu)}\tag{16b}
$$

where ߪ௫ሺ݄ߥሻ and ݅ாெ௫ሺ݄ߥሻ are the measured photoconductivity and short-circuited current evoked by the PEM effect. The ߪሺ݄ߥሻ and ݅ாெሺ݄ߥሻ are calculated for the values of sample parameters obtained by fitting the experimental results with appropriate theoretical formulae in the range of a known or very probable value of the QEC (usually, it is assumed that ߚ=1 and ߚாெ=1 for photon energies slightly higher than that for which ߪ௫ሺ݄ߥሻ and ݅ாெ௫ሺ݄ߥሻ attain maxima, see [29,32,33]).

Using Eq. (14b), the determined values of ߚாெሺ݄ߥሻ, and the values of total absorption coefficients (derived from optical transmittance), one can calculate the absorption coefficients describing intrinsic photogeneration of carriers [29]. Fig. **3** presents the differences in the intrinsic and extrinsic spectra of QECs of radiation of a-Si:H,F thin film. If the values of ߚாெሺ݄ߥሻ are subtracted from ߚሺ݄ߥሻ, one obtains the values of QECs for the extrinsic photogeneration of free carriers [29]. Using these values, one calculates absorption coefficients related to extrinsic photogeneration of carriers (Fig. **2**).

**Figure 4:** Comparison of the spectra of absorption coefficients derived using optical transmittance (ࢻ(, the CPM method (ࢻ(, the method of Moddel *et al.* [37] (ࢻ (and the quantum efficiency coefficient (ࢼࢻ ( [32].

Contrary to traditional methods that are reliable only for larger values of ߙ, the PC and PEM methods are especially convenient to determine the low sub-band-gap absorption related to the density of state (DOS) distribution in the mobility gap of an amorphous semiconductor [34]. Fig. **4** shows the values of absorption coefficients derived using the optical transmittance method, the constant photocurrent method (CPM) [35,36], the method proposed by Moddel *et al.* [37], and the quantum efficiency coefficient. The absorption coefficients for weakly absorbed radiation can be determined applying classical CPM method

$$
\alpha\_{cpm} = \frac{\kappa\_{cpm}}{l\_f} \tag{17}
$$

where ܣ represents a constant normalized for a known value of absorption coefficient (obtained from optical transmittance measurements, see Fig. **4**), and ܫ is illumination intensity (in photons) that assures a constant photocurrent flowing through a sample for different values of photon energies.

The method of Moddel *et al.* [37] allows one to determine another absorption coefficient for weakly absorbed radiation

$$\alpha\_m = \alpha\_{0m} \frac{l\_{0m}}{l\_0} \left(\frac{\sigma\_{p\_{Cexp}}}{\sigma\_{m^{p\_{Cexp}}}}\right)^{1/\zeta} \tag{18}$$

where ߪ௫ represents photoconductivity measured for light intensity ܫ) in photons). Subscript 0*m* refers to reference photon energy at which the ߙ is directly measured (in optical transmittance measurements, see Fig. **4**). The ߞ is a power coefficient in the semi-empirical powerlaw formula

$$
\sigma\_{\text{PCexp}} = \mathbf{a}\_{\text{PC}} l\_0^l \tag{19}
$$

where a is the proportionality factor.

The evaluated values of ߙ and ߙ are different from the values of ߙఉ. However, it should be emphasized that they were evaluated without taking into account the possible influence of excess carrier concentration on recombination processes in the semiconductor. It must be noted that the optical energy gap increases with the electron concentration in the material (Burnstein-Moss shift). Hence, the energy-gap gradient can be caused by strong illumination of the sample [38]. Such illumination of a semiconductor can influence its optical parameters, too.

It should be emphasized that the PC and PEM methods can be used not only for measurements of absorption coefficients but also for investigations of real parts of refractive indices and thicknesses of dielectric films that cover the semiconductors (*e.g.* [6,39,40]). For example, the ratio of PEM responses, in the cases of oblique sample illumination with plane polarized radiation that has electric vector in and normal to the plane of incidence, is equal to the ratio of the intensities of variously polarized radiation which enters a sample. If the radiation intensity is low, this ratio of PEM responses is independent of the parameters of carriers in a semiconductor (*e.g.*, mobilities, lifetimes, and surface recombination velocities of carriers), and provides information on optical parameters of the investigated material. The ratio of PME responses for variously polarized radiation is independent of the distribution of light intensity over a sample surface. Hence, the spot-light method of PME investigation can be used for determining local properties of the sample [6].

Measurements of the ratio of PEM responses for plane polarized radiation were used [40] to determine values of refractive indices of SiO2 surface layers obtained by thermal oxidation of (100) oriented silicon in different gases (Fig. **5**). Such measurements are complementary to ellipsometry [7] but they should be more effective in investigations of samples with surface texturing (see Chapter 9 in this volume) because the intensity of radiation that enters a semiconductor through the investigated surface layer can be immediately determined.

**Figure 5:** Ratio of PEM responses for plane polarized radiation with electric vector in and normal to the plane of incidence *versus* angle of radiation incidence for different thicknesses of the surface film of SiO2 on n-type, (100) oriented Si, obtained by thermal oxidation in O2 with *2%* HCl [40] (●, =*121.5 nm*; +, =94 nm. Solid curves represent the theoretical dependences for different values of thickness and refractive index of the film: (1) =94 nm, =1.49) ;2 (=127.5 nm, =1.43, ࣅ=632.8 nm, )Si)= 3.9, ࣄ)Si)=0.02).

The need for electrical contacts is the main disadvantage of the known PC and PEM methods of measurements of the optical parameters (see, *e.g.* [39,40]). However, it is interesting to explore the application of contactless methods of PEM investigations (*e.g.* [41,42]) to determine the refractive indices of more sophisticated coating layers of solar cells.

#### **2.3. Interfaces and Optical Inhomogeneity**

The technology of the deposition process as well as the physical and chemical properties of the substrate can strongly influence values of optical parameters of thin films. Values of a real part of the refractive index and absorption coefficient can change substantially with the depth in a thin semiconductor film, *e.g.*, in the amorphous silicon (a-Si) films [43,44]. The changes are particularly great near the interfaces' air-semiconductor film and semiconductor-substrate. In so-called graded-gap semiconductors, for example in Si1-xGex structures with a position dependent energy band-gap [45,46], the values of optical parameters are also strongly dependent on the position in a sample.

**Figure 6:** Scheme of a semiconductor film with optical inhomogeneity (description in the text).

The optical inhomogeneity of the *j* film with thickness ݓ) Fig. **6**) can be characterized by different refractive indices ܰ=݊ െ ݅ߢ and ܰ=݊ െ ݅ߢ at front and rear surface [47], as well as by refractive index ܰ=݊ െ ݅ߢ averaged through the film thickness

$$n\_{aj} = \frac{1}{w\_j} \int\_0^{w\_j} n\_l(y) dy\tag{20a}$$

$$\kappa\_{al} = \frac{1}{w\_f} \int\_0^{w\_f} \kappa\_l(\mathbf{y}) d\mathbf{y} \tag{20b}$$

where *y* represents depth in the *j* film, ݊ሺݕሻ and ߢሺݕሻ are the local values of a real part of refractive index and extinction coefficient. The values of ݊ and ߢ determine the change in phase and intensity of the radiation transmitted through the film.

Values of ݊ െ ݅ߢ and ݊ െ ݅ߢ affect the Fresnel reflection and transmission coefficients (*i.e.*, ratios of electric fields of reflected/incident and transmitted/incident radiation) at an interface. Thus they determine intensity and phase of the radiation reflected and transmitted through the appropriate interface. For front illumination [from (j-1) to j medium] these coefficients are given by

$$r\_{sf} = \frac{(a\_{r(j-1)} - lb\_{r(j-1)}) - (a\_{ff} - lb\_{ff})}{(a\_{r(j-1)} - lb\_{r(j-1)}) - (a\_{ff} - lb\_{ff})} = |r\_{sf}|e^{-l\rho\_{sf}} \tag{21a}$$

$$r\_{p\bar{f}} = \frac{n\_{\tau(j-1)}^2 (a\_{f\bar{f}} - ib\_{f\bar{f}}) - n\_{f\bar{f}}^2 (a\_{\tau(j-1)} - ib\_{\tau(j-1)})}{n\_{\tau(j-1)}^2 (a\_{f\bar{f}} - ib\_{f\bar{f}}) + n\_{f\bar{f}}^2 \left(a\_{\tau(j-1)} - ib\_{\tau(j-1)}\right)} = |r\_{p\bar{f}}| e^{-l\rho p\_{p\bar{f}}} \tag{21b}$$

$$\mathbf{t}\_{sf} = \frac{\mathbf{z}^{\{a\_{r(j-1)} - lb\_{r(j-1)}\}}}{ (a\_{r(j-1)} - lb\_{r(j-1)}) - (a\_{fj} - lb\_{fj})} = |\mathbf{t}\_{sf}|e^{-l\beta\_{sf}} \tag{21c}$$

$$t\_{pj} = \frac{{}^{2N\_{\tau(j-1)} \aleph\_{fj}} {}^{N\_{fj}(a\_{\tau(j-1)} - ib\_{\tau(j-1)})}}{{}^{2}\_{\tau(j-1)} {}^{a}\_{\ell f} {}^{i - ib\_{fj}} + {}^{N\_{fj}^2 \left(a\_{\tau(j-1)} - ib\_{\tau(j-1)}\right)}} = |t\_{pj}| |e^{-i\beta\_{pj}} \tag{21d}$$

where

$$a\_{xj}^2 = \frac{1}{2} \left( n\_{xj}^2 - \kappa\_{xj}^2 - n\_0^2 \sin^2 \phi \right) + \sqrt{\frac{1}{4} \left( n\_{xj}^2 - \kappa\_{xj}^2 - n\_0^2 \sin^2 \phi \right) + n\_{xj}^2 \kappa\_{xj}^2} \tag{21e}$$

$$b\_{\mathbf{x}f} = \frac{n\_{\mathbf{x}f \mathbf{x}\_{\mathbf{x}f}}}{a\_{\mathbf{x}f}} \tag{210}$$

indices *p* and *s* represent plane polarized radiation with the electric vector in and normal to the plane of incidence; index *j=0* is used to describe the parameters of the surrounding ambient, and ߶ represents the angle of incidence of radiation upon the sample. Index ݔ must be replaced by indices ݂ and ݎ for front and rear interfaces of the film, respectively. If index *x* equals *a* in Eqs. (21e) and (21f), the ܽ and ܾ represent the effective refractive index and extinction coefficient of radiation in the bulk of a film.

In the case of a semi-infinite solid, ellipsometry is a direct technique which measures the complex reflectance ratio

$$\frac{r\_{p1}}{r\_{g1}} = \tan\psi \, e^{l\Lambda} \tag{22}$$

*Optical Properties of Semiconductor Silicon Based Thin Film Solar Cells* **187**

where ߰ and Δ are so-called ellipsometric angles (easily represented by formulae (21a) and (21b)). See [7] for an overview of this technique.

For back illumination [from (j+1) to j medium] the Fresnel reflection coefficients are ݎ̃ ௦ ൌ െݎ௦ and ݎ̃ ൌ െݎ, while the Fresnel transmission coefficients are given by

$$\tilde{t}\_{sf} = \frac{\mathbf{z}^{\{a\_{ff} - ib\_{ff}\}}}{(a\_{r(j-1)} - ib\_{r(j-1)}) - (a\_{ff} - ib\_{ff})} = |\tilde{t}\_{sf}| e^{-i\tilde{\beta}\_{sf}} \tag{23a}$$

$$\mathbb{E}\_{pj} = \frac{2\Big(n\_{r(j-1)} - \imath \kappa\_{r(j-1)}\Big) (n\_{ff} - \imath \kappa\_{ff})(a\_{ff} - l\flat\_{fj})}{n\_{r(j-1)}^2 (a\_{ff} - l\flat\_{fj}) + \imath \lambda\_{ff}^2 \Big(a\_{r(j-1)} - l\flat\_{r(j-1)}\Big)} = |\mathbb{E}\_{pj}| e^{-l\not\mathbb{B}\_{pf}} \tag{23b}$$

The losses from the specular light beam by scattering at the rough interface between media *j-1* and *j* can be described by the scattering factors. Thus, in comparison with a smooth interface, the reflection and transmission Fresnel coefficients should be reduced by the following factors [22]

$$\mathbf{s}\_f^r = \exp\left[-\frac{\left(4\pi n\_{b(f-1)}\sigma\_{RMS}\sin\phi\right)^2}{2\lambda^2}\right] \tag{24a}$$

$$s\_f^t = \exp\left\{ -\frac{\left[2\pi \left(n\_{b(j-1)} - n\_{ff}\right) \sigma\_{RMS} \sin \phi\right]^2}{2\lambda^2} \right\} \tag{24b}$$

where ߪோெௌ is the rms surface roughness of the boundary interface. Formulae (24) assume ߪோெௌ smaller than λ and small correlation length of the surface roughness.

### **3. OPTICAL TRANSMITTANCE AND REFLECTANCE**

After a summary of the electric fields of waves reflected from a single film (taking into account the waves internal reflected in it and transmitted back), one obtains the effective Fresnel reflection coefficient of the film

$$\varrho\_{\mathbb{V}\rangle} = \frac{r\_{\mathbb{V}} + r\_{\mathbb{V}(j+1)} \exp(-\mathbb{K}\_j) \exp(-l\Gamma\_{j0})}{1 + r\_{\mathbb{V}}r\_{\mathbb{V}(j+1)} \exp(-\mathbb{K}\_j) \exp(-l\Gamma\_{j0})} = |\varrho\_{\mathbb{V}\rangle}| e^{-l\theta\_{\mathbb{V}}} \tag{25a}$$

where index v must be replaced by indices p and s for plane polarized radiation with the electric vector in and normal to the plane of incidence, respectively, Γ ൌ 4ߨwj ܽ⁄ߣ is the change in phase of the beam on traversing twice a film, and K ൌ 4ݓߨܽߢ⁄൫ߣ݊൯ is the effective, dimensionless absorption coefficient that describes the attenuation of radiation intensity in the direction normal to the front surface of the film.

The effective reflection for reversed illumination (from *j* to *(j-1)* film) is given by

$$\left| \vec{\rho}\_{\eta} \right| = \frac{-r\_{\eta(j+1)} - r\_{\eta} \exp(-\mathsf{K}\_{f}) \exp(-l\Gamma\_{f0})}{1 + r\_{\eta}r\_{\eta(j+1)} \exp(-\mathsf{K}\_{f}) \exp(-l\Gamma\_{f0})} = \left| \vec{\rho}\_{\eta} \right| e^{-l\vec{\theta}\_{\eta}} \tag{25b}$$

The effective Fresnel transmission coefficients of the film (for front and back illumination) are described by

$$\tau\_{\mathsf{v}|\mathsf{I}} = \frac{\mathsf{t}\_{\mathsf{v}} \mathsf{t}\_{\mathsf{v}(j+1)} \exp\{-0.5 \mathsf{K}\_{j}\} \exp\{-l \mathsf{I}\_{j0}\}}{\mathsf{1} + r\_{\mathsf{v}} r\_{\mathsf{v}(j+1)} \exp\{-\mathsf{K}\_{j}\} \exp\{-l \mathsf{I}\_{j0}\}} = |\mathsf{t}\_{\mathsf{v}|\mathsf{I}}| e^{-l \mathsf{I}\_{\mathsf{v}}} \tag{26a}$$

$$\left| \vec{\tau}\_{\mathsf{V}} \right| = \frac{\mathsf{r}\_{\mathsf{V}} \mathsf{f}\_{\mathsf{v}(j+1)} \exp\{-0.5 \mathsf{K}\_{f}\} \exp\{-i\Gamma\_{f0}\}}{\mathsf{1} + \mathsf{r}\_{\mathsf{V}} \mathsf{r}\_{\mathsf{v}(j+1)} \exp\{-\mathsf{K}\_{f}\} \exp\{-i\Gamma\_{f0}\}} = \left| \vec{\tau}\_{\mathsf{V}} \right| e^{-i\tilde{\theta}\_{\mathsf{V}}} \tag{26b}$$

Formulae (25) and (26) can be used recurrently to reduce a system of multilayers to a single surface with appropriate effective reflection and transmission coefficient

$$\varrho\_{\rm vm\_{W}} = \Sigma\_{j=2}^{m\_{\rm W}} \frac{\varrho\_{\rm v(j-1)} + r\_{\rm v(j+1)} \exp(-\mathbb{K}\_{j}) \exp(-l\Gamma\_{j0})}{1 + \mathfrak{J}\_{\rm v(j-1)} r\_{\rm v(j+1)} \exp(-\mathbb{K}\_{j}) \exp(-l\Gamma\_{j0})} = |\varrho\_{\rm vm\_{W}}| \exp(-l\Theta\_{\rm vm\_{W}}) \tag{27a}$$

$$\left| \tau\_{\rm vm\_W} = \sum\_{j=2}^{m\_W} \frac{\tau\_{\rm v(j-1)} t\_{\rm v(j+1)} \exp(-0.5 \text{K}\_j) \exp(-l \Gamma\_{j0})}{1 + j \mathbb{I}\_{\rm v(j-1)} r\_{\rm v(j+1)} \exp(-\mathcal{K}\_j) \exp(-l \Gamma\_{j0})} \right| = \left| \tau\_{\rm vm\_W} \right| \exp\{-l \mathcal{O}\_{\rm vm\_W} \} \tag{27b}$$

where ݉௪ is the number of media in the multilayer structure. Index v must be replaced by indices p and s for plane polarized radiation with the electric vector in and normal to the plane of incidence.

The changes of amplitudes ห߷pೢห, ห߷sೢห, ห߬pೢห, and ห߬sೢห as well as the changes of phases ߠpೢ, ߠsೢ, ߴpೢ, and ߴsೢ of the electric fields of radiation reflected and transmitted through the ݉௪ film structure are dependent on wavelength and angle of light incidence. They can be determined applying, for example, the variable angle spectroscopic ellipsometry (VASE) [7]. However, an appropriate model must always be constructed on the assumed values of indices of refraction, layer thicknesses, alloy fractions, void fractions, roughness parameters, *etc.*

The energetic transmittance and reflectance of multilayer structure (*i.e.*, ratios of intensities of transmitted/incident and reflected/incident radiation) are squares of the appropriate Fresnel coefficients

$$T\_{\rm xv} = \left| \tau\_{\rm vm\_W} \right|^2 \tag{28a}$$

$$R\_{\rm xy} = \left| \varrho\_{\rm vm\_W} \right|^2 \tag{28b}$$

where index v must be replaced by indices p and s for plane polarized radiation with the electric vector in and normal to the plane of incidence, respectively.

Interference of radiation internally reflected in parallel-sided samples affects characteristic extrema in spectral distributions of optical transmittance ܶሺߣሻ and reflectance ܴሺߣሻ. The main feature, distinguishing these from absorbance extrema, is the correlation between maxima and minima in ܶሺߣሻ and ܴሺߣሻ (Fig. **7**). This is well described by the Eq. (28). The other feature consists in the relation between positions ߣ and ߣାଵ of the extrema in optical characteristics and the changes in phases of the beam on traversing twice the film of thickness ݓ:

$$\frac{4\pi w\_{\parallel}a\_{af}(\lambda\_m)}{\lambda\_m} - \frac{4\pi w\_{\parallel}a\_{af}(\lambda\_{m+1})}{\lambda\_{m+1}} = 2\pi \tag{29}$$

where *m* and *m+1* represent orders of extrema. Sometimes Eq. (29) is used to estimate sample thickness or refractive index of materials. However, the exact description of these parameters requires a more cumbersome approach. In the case of negligible absorption of radiation, the positions (m) of interference extrema are described by

$$2m\lambda\_m = 2n\_{af}\eta\_f\sqrt{1 - \frac{\sin^2\phi}{n\_{aj}^2}}\tag{30}$$

The wavelengths m of interference extrema decrease as the angle of light incidence and the order of interference fringes increase (*e.g.* [49]). In the case of an anisotropic medium the values of <sup>m</sup> depend on polarity of the used light and crystallographic orientation of the sample. Recently, the interference spectrogoniometric method [49] of investigations of anisotropic materials was based on Eq. (30). This method is very convenient in cases of relatively thick films.

**Figure 7:** Spectral distribution of transmittance (▼) and reflectance (▲) of a-Si:H film [48]. Solid curves show theoretical dependencies calculated for fitted =571.1 nm, =3.3 nm, and the parameters presented in Figs. **15** and **16**. Broken curves are envelopes of the experimental characteristics.

The additional layers of different materials which cover the semiconductor surfaces can be simply described as the interference filters [2]. Their effective reflectivities and changes in phase of radiation reflected by them depend on refractive indices of the film and the surrounding media as well as film thickness, angle of incidence and polarization of radiation. This problem is wellknown in thin film optics [2] and will not be discussed in detail in the present paper. The question of a surface texturing is discussed in Chapter 9 by M. Tucci *et al.* in this volume.

### **3.1. Influence of Uncertainty of a Change in Phase of the Beam on Transmittance and Reflectance**

Formulae (28) were derived for the case of perfect coherence of radiation interfering in the films, *i.e.*, for the strict values of Γ. This is an idealization of the experimental situation. In fact the radiation used in every experiment (even in experiments with laser illumination) has some

bandwidth Δߣ of the wavelengths. It is also probable that the real film is inhomogeneous or has non-parallel or rough surfaces. For example, Swanepoel [50] has analyzed the influence of linear, triangular, and rectangular surface roughness on a semiconductor film transmittance. A similar surface roughness of coating layers can be analyzed. In general, it creates some uncertainties ߪ and ߪ௪ of the real part of refractive index and thickness of the film over the illuminated sample area. All these factors can cause some uncertainty σ of the change in phase of the beam upon traversing the film:

$$
\sigma\_{\Gamma\!f} = \left(\frac{\sigma\_{wj}}{w\_j} + \frac{\sigma\_{naj}}{n\_{aj}} + \frac{\Lambda\lambda}{\lambda}\right) \Gamma\_f \tag{31}
$$

It is very probable [51] that the changes of semiconductor film and coating layers thicknesses as well as their refractive indices are random over the illuminated sample area. Also the distribution of radiation intensity over the wavelength range can be Gaussian. Thus the change in phase Γ of the beam on traversing a semiconductor or coating layer should be described by the Gaussian distribution with the average value Γ and standard deviation ߪ୨. Therefore, in the case of three films in a multilayer structure (Fig. **1**), the energetic transmission and reflection coefficients should be calculated using the triple integral

$$T\_{\rm xq\mathbb{G}}(\Gamma\_{2},\Gamma\_{1},\Gamma\_{3}) = \begin{pmatrix} \frac{1}{\sigma\_{\Gamma2}\sqrt{2\pi}}\exp\left[-\frac{(\Gamma\_{20}-\Gamma\_{2})^{2}}{2\sigma\_{\Gamma2}^{2}}\right].\\\\\int\_{\Gamma\_{2}=0}^{+\infty}\frac{1}{\sigma\_{\Gamma1}\sqrt{2\pi}}\exp\left[-\frac{(\Gamma\_{10}-\Gamma\_{1})^{2}}{2\sigma\_{1}^{2}}\right].\\\int\_{\Gamma\_{2}=0}^{+\infty}\int\_{\Gamma\_{3}=0}^{+\infty}\frac{\tau\_{\mathcal{H}}}{\sigma\_{\Gamma3}\sqrt{2\pi}}\exp\left[-\frac{(\Gamma\_{30}-\Gamma\_{3})^{2}}{2\sigma\_{\Gamma3}^{2}}\right]d\Gamma\_{3}d\Gamma\_{1}d\Gamma\_{2} \end{pmatrix}.\tag{32a}$$

$$R\_{\rm xq\mathbb{G}}(\Gamma\_{2},\Gamma\_{1},\Gamma\_{3}) = \begin{cases} \ast &\frac{1}{\sigma\_{\Gamma3}\sqrt{2\pi}}\exp\left[-\frac{(\Gamma\_{20}-\Gamma\_{2})^{2}}{2\sigma\_{\Gamma2}^{2}}\right].\\\\\int\_{\Gamma\_{2}=0}^{+\infty}\frac{1}{\sigma\_{\Gamma1}\sqrt{2\pi}}\exp\left[-\frac{(\Gamma\_{10}-\Gamma\_{1})^{2}}{2\sigma\_{1}^{2}}\right].\\\\\int\_{\Gamma\_{2}=0}^{+\infty}\int\_{\Gamma\_{3}=0}^{+\infty}\frac{\frac{\mathcal{R}\_{\rm{ge}}}{\sigma\_{\Gamma2}}}{\sigma\_{\Gamma3}\sqrt{2\pi}}\exp\left[-\frac{(\Gamma\_{30}-\Gamma\_{3})^{2}}{2\sigma\_{\Gamma3}^{2}}\right]d\Gamma\_{3}d\Gamma\_{1}d\Gamma\_{2} \end{cases} \tag{32b}$$

where ܶ௭v and ܴ௭v are given by Eq. (28), index v must be replaced by indices p and s for plane polarized radiation with the electric vector in and normal to the plane of incidence, respectively. For ߪଵ=ߪଶ=ߪଷ=0 the density of Gaussian distribution is represented by the ߜ െDirac and Eq. (32) reduce into the forms (28) for an ideal instance of perfect coherence of radiation interfering in the multilayer structure of thin films (see [2]).

The formulae (32) involve a few integrals and are rather time consuming for numerical calculations in cases of thick layers. The last situation occurs very often in investigations of amorphous thin films performed on a specific double layer structure: a thin semiconductor film of thickness ݓଵ covers a relatively thick, transparent, parallel-sided substrate of thickness ݓଶ ب ݓଵ. The sample is uniformly illuminated with radiation that has components in wavelength range Δߣ, and

$$\frac{\lambda^2}{2n\_{\text{d2}}w\_2} \ll \Delta\lambda \ll \frac{\lambda^2}{2n\_{\text{d1}}w\_1} \tag{33}$$

where ݊ଵ and ݊ଶ are real parts of refractive indices of the semiconductor film and the substrate, respectively. According to Eq. (33); the interference of internally reflected radiation occurs in a semiconductor film and is negligible in the substrate (*e.g.* [1]). In this case a simpler description of optical phenomena can be used because the phases of electric fields of beams internally reflected in the thick substrate are random. Therefore, the energetic transmission and reflection coefficients should be calculated by summing up intensities (no electric fields) of radiation of the multiple reflected beams

$$T\_{f\circ} = \frac{|r\_{\forall 1}|^2 |t\_{\forall 3}|^2}{1 - |\xi\_{\forall 1}|^2 |r\_{\forall 3}|^2} \tag{34a}$$

$$R\_{f\mathbf{v}} = |\varrho\_{\mathbf{v}1}|^2 + \frac{|\mathbf{r}\_{\mathbf{v}1}|^2 |\mathbf{r}\_{\mathbf{v}1}|^2}{1 - |\mathfrak{d}\_{\mathbf{v}1}|^2 |r\_{\mathbf{v}3}|^2} \tag{34b}$$

where |ݎv3|, |ݐv3|, |߷v1|, |߷v1|, |߬v1| and ห߬̃ ห are given by Eqs. (21), (25) and (26); index v must be replaced by indices p and s for plane polarized radiation with the electric vector in and normal to the plane of incidence, respectively; index *f* indicates that the sample is illuminated from the semiconductor side; for a sample immersed in air ܰ=ܰଷ=1.

To determine values of optical parameters at both interfaces of a thin semiconductor film, a double layer structure should be investigated under illumination from the free surface side as well as from the substrate side (*e.g.* [52]). In the case of incidence of radiation upon the back sample surface, the energetic transmission and reflection coefficients are given by

$$T\_{\rm bv} = \frac{|\mathbb{M}\_{\rm v1}|^2 |\mathbb{M}\_{\rm v3}|^2}{1 - |\tilde{\mathbb{M}} \boldsymbol{v} \boldsymbol{1}|^2 |\boldsymbol{r} \boldsymbol{q}|^2} \tag{35a}$$

$$R\_{\rm bV} = |r\_{\rm v3}|^2 + \frac{|t\_{\rm v3}|^2 |\bar{t}\_{\rm v3}|^2}{1 - |\mathbb{S}\_{\rm v1}|^2 |r\_{\rm v3}|^2} \tag{35b}$$

where symbols have their usual meanings.

Taking into account the possible Gaussian distribution of the change in phase of the beam upon traversing the semiconductor film in the double layer structure, one obtains

$$T\_{\rm divG} = \int\_0^{+\upsilon} \frac{\tau\_{\rm dv}}{\sigma\_{\Gamma1} \sqrt{2\pi}} \exp\left[-\frac{(\Gamma\_{10} - \Gamma\_1)^2}{2\sigma\_{\Gamma1}^2}\right] d\Gamma\_1 \tag{36}$$

$$R\_{\rm dvG} = \int\_0^{+\infty} \frac{R\_{\rm dv}}{\sigma\_{\rm I1}\sqrt{2\pi}} \exp\left[-\frac{(\Gamma\_{10} - \Gamma\_1)^2}{2\sigma\_{\Gamma1}^2}\right] d\Gamma\_1 \tag{37}$$

where index d must be replaced by indices f and b for the front and back illumination of the sample (the other symbols have the same meanings as in Eqs. (32), (34) and (35)).

Numerical calculations were done to analyze the influence of Gaussian distributions of Γ on the spectral characteristics of ܶௗvG. Fig. **8** presents the strong influence of ߪ௪ଵ on the ܶௗvG of a thin

semiconductor film. The calculations show that serious consideration must also be given to the wavelength bandwidth of radiation which illuminates the sample. When Δߣ increases with decreasing ߣ] 53[, the influence of wavelength bandwidth on ܶௗvG is stronger for higher ݄ߥ.

**Figure 8:** Spectral dependence of optical transmittance of a thin film calculated for different and ઢࣅ (chain curve, for =0 and ઢࣅ=0 ;broken curve, for =12.3 nm and ઢࣅ=0 ;solid curve, for =12.3 nm and ઢࣅሺࣅሻ taken from [53] for 2 mm output slot of the monochromator; =0.473 m, ሺࣅሻ and ࢻሺࣅሻ .(° ൌ ࣘ ,ࢻ=ࢻ=ࢻ ,== ,[51] from

**Figure 9:** Influence of thin-film thickness on spectral characteristics of optical transmittance (broken curve, =0.4 m, =20 nm; solid curve, =2 m; =20 nm; ==ሺࣅሻ taken from [29]; ࢻ=ࢻ=ࢻሺࣅሻ=0, = ઢࣅ=0, ࣘ ൌ °; ࣘ ൌ °; chain curves are envelopes of the characteristics).

It is obvious (Fig. **9**) that thin-film thickness and ݊ଵ influence the positions of interference fringes in the spectral characteristics of ܶௗvG*.* However, it does not influence the envelopes of the spectral characteristics (Fig. **9**). The shape of the envelope depends strongly on the standard deviation ߪ௪ଵ of the distribution of film thickness over the illuminated area of the sample (Fig. **10**). It is an advantage that in the case of Gaussian distribution of Γଵ values of maxima in the spectral characteristics of ܶௗvG decrease with decreasing ߣ, while values of minima increase, attain a maximum value and then decrease with decreasing ߣ) all in the range of negligible absorption of light in a sample), see Fig. **10**. This behavior of the spectral characteristics of ܶ is the main evidence for influence of the radiation wavelength bandwidth Δߣ and/or changes of thin film thickness ߪ௪ଵ and changes of refractive index ߪ on optical transmittance. This stated tendency of changing magnitudes of interference fringes with changing radiation wavelength is very often observed experimentally [50].

**Figure 10:** Influence of thickness changes in an illuminated area of thin film on spectral characteristics of optical transmittance (broken curve, =20 nm; solid curve, =40 nm; =2 m; other parameters are the same as in Fig. **9**; chain curves are envelopes of the characteristics).

**Figure 11:** Influence of real part of refractive index of thin film on spectral characteristics of optical transmittance (solid curve, ሺࣅሻ taken from [29]; broken curve, ሺࣅሻ from [29] increased by 0.1; = 40 nm, other parameters are the same as in Fig. **9**; chain curves, envelopes of the characteristics).

It is evident in the transmittance calculated for Gaussian distribution of Γଵ that the increase of standard deviation ߪ௪ଵ decreases the interference fringes in the spectral characteristics of transmittance (Fig. **10**). It does not influence the so-called averaged magnitude of optical transmittance. This magnitude strongly depends on the value of real parts of refractive indices ݊ଵ and ݊ଵ (Fig. **11**), and obviously it depends on the absorption coefficient ߙ. Increase of ݊ଵ affects the decrease of optical transmittance due to the increase of reflection coefficient. The same conclusions are true for reflectance (*e.g.* [48]).

**Figure 12:** Influence of the parameter of Gaussian distribution of ડ on optical transmittance of a thin other the; 10.23=ࣅ⁄ ,curve chain; 10.11*=*ࣅ⁄ ,curve broken; 10.0*=*ࣅ⁄ ,curve solid (film parameters are the same as in Fig. **10**).

Nevertheless, it is a great difference between the spectral characteristics of optical transmittance and reflectance calculated for linear and Gaussian distributions of the change in phase of radiation traversing a thin film (*e.g.* [48,51])*.* It is important to note that transmittance and reflectance are monotonic functions of ߪ௪ଵ (*e.g.* Fig. **12**) only in the latter case.

#### **3.2. Negligible Interference of Light in a Semiconductor**

In some cases the interference fringes are not observed in spectral characteristics of optical reflectance and/or transmittance. It can be evoked by strong absorption of light in a semiconductor (*e.g.* the ܶሺߣሻ and ܴሺߣሻ characteristics presented in Fig. **7** for larger photon energies). In this case one can pass over the components of light that are hypothetically internally reflected several times in a semiconductor. The second component of light (internally reflected) that contributes to the beam transmitted through a film is more diminished than the second component of light that contributes to the beam reflected from the film. The former traverses the film three times while the latter traverses the film only twice (Fig. **13**). Therefore, the interference fringes are evident in a reflectance spectrum in the photon energy range in which the spectrum of optical transmittance is relatively smooth (compare the ܴሺߣሻ and ܶሺߣሻ spectra presented in Fig. **7** for ݄ߥ 2.25 ܸ݁(.

In the case of relatively strong absorption of light, the transmittance and reflectance of a single semiconductor film are given by

$$T\_{f^\circ} = \frac{|t\_{v1}|^2 |t\_{v2}|^2 exp(\mathbb{K}\_1)}{1 - |t\_{v1}|^2 |r\_{v2}|^2 exp(-2\mathbb{K}\_1)}\tag{38a}$$

$$R\_{f\mathbf{v}} = |r\_{\mathbf{v}1}|^2 + \frac{|\mathbf{t}\_{\mathbf{v}1}|^2 |\tilde{\mathbf{t}}\_{\mathbf{v}1}|^2 |r\_{\mathbf{v}2}|^2 \exp(-2\mathbf{K}\_1)}{1 - |\mathbf{t}\_{\mathbf{v}1}|^2 |r\_{\mathbf{v}2}|^2 \exp(-2\mathbf{K}\_1)}\tag{38b}$$

$$\underbrace{\tilde{\mathbf{s}}\_{\mathbf{v}1}}\_{\tilde{\mathbf{s}}\_{\mathbf{v}1}} \times \underbrace{\tilde{\mathbf{s}}\_{\mathbf{v}1}^\*}\_{\tilde{\mathbf{s}}\_{\mathbf{v}0}} \cdot \left\langle \overbrace{\tilde{\mathbf{s}}\_{\mathbf{v}1}^\*}\_{\tilde{\mathbf{s}}\_{\mathbf{v}0}^\*} \right\rangle\_{\mathbf{v} = \mathbf{s}\_{\mathbf{v}0}} \cdot \underbrace{\tilde{\mathbf{s}}\_{\mathbf{v}1}^\*}\_{\tilde{\mathbf{s}}\_{\mathbf{v}0}^\*} \cdot \underbrace{\tilde{\mathbf{s}}\_{\mathbf{v} 0}^\*}\_{\tilde{\mathbf{s}}\_{\mathbf{v}0}^\*}$$

**Figure 13:** Scheme of radiation propagation and its electric field in a single film (XY is the coordinate system; description of the symbols in the text).

In the case of the double layer structure of a semiconductor film on a thick, transparent, parallelsided substrate as analyzed above, one should replace in Eqs (38) the values of |ݐv2| <sup>ଶ</sup> and |ݎv2| ଶ with

$$\overline{T}\_{f^\circ} = \frac{|t\_{\nu 2}|^2 |t\_{\nu 3}|^2}{1 - |t\_{\nu 2}|^2 |r\_{\nu 3}|^2} \tag{39a}$$

$$\vec{R}\_{f\mathbf{v}} = |r\_{\mathbf{v}2}|^2 + \frac{|t\_{\mathbf{v}2}|^2 |\mathbf{f}\_{\mathbf{v}2}|^2 |r\_{\mathbf{v}3}|^2}{1 - |r\_{\mathbf{v}2}|^2 |r\_{\mathbf{v}3}|^2} \tag{39b}$$

The other reason for the lack of interference fringes in spectral characteristics of optical transmittance and reflectance of a film is the incoherence of the beams internally reflected and superimposed on each other. This can occur in the case of relatively large uncertainty of the change in phase of the beam upon traversing the film (σ 2ߨ(, and consequently in the case of a relatively thick film, when ∆ߣ ب ߣଶ ൫2݊ݓ൯ൗ (see Eq. (31)). In such a situation the Eqs. (32) or (36) and (37) should be used.

#### **3.3. Method of Transmittance and Reflectance Data Treatment**

The treatment of transmittances and reflectances of a-Si:H film on a thick BK-7 substrate (presented in Fig. **7)** is presented step by step. Details of the experiment were given in [48]. Similar to the method of Swanepoel [50], the envelopes of the spectral dependences of optical transmittance and reflectance were determined. Then a few wavelengths ߣ*,* were chosen from the range of negligible absorption of radiation in the sample (Fig. **14**). The value ߪ௪ଵ=3.3 nm and the set of values ݊ଵ൫ߣ൯ (see Fig. **15**) were found by minimization of the following function

$$\begin{aligned} \chi^2 &= \Sigma\_l \left\{ \left[ T\_{\max} \{ \lambda\_l \} - t\_{\max} \{ \lambda\_l \} \right]^2 + \left[ T\_{\min} \{ \lambda\_l \} - t\_{\min} \{ \lambda\_l \} \right]^2 + \left[ R\_{\max} \{ \lambda\_l \} - r\_{\max} \{ \lambda\_l \} \right]^2 + \\ \left[ R\_{\min} \{ \lambda\_l \} - r\_{\min} \{ \lambda\_l \} \right]^2 \end{aligned} \tag{40}$$

#### *Optical Properties of Semiconductor Silicon Based Thin Film Solar Cells* **197**

where ܶ௫൫ߣ൯, ܶ൫ߣ൯, ܴ௫൫ߣ൯ and ܴ൫ߣ൯ are maximum and minimum values from the envelopes of optical transmittance and reflectance determined for wavelength ߣ*.* The ݐ௫൫ߣ൯, ݐ൫ߣ൯, ݎ௫൫ߣ൯ and ݎ൫ߣ൯ are the maximum and minimum values of ܶణൣߣ, ݊ଵ൫ߣ൯, ߪ௪ଵ, ݓଵ, ߴ൧ and ܴణൣߣ, ݊ଵ൫ߣ൯, ߪ௪ଵ, ݓଵ, ߴ൧ calculated for ߴ א ሺ0,2ߨሻ, where ܶణ and ܴణ are given for ߶ ൌ 0° by Eqs. (36) and (37) in which ܶௗv and ܴௗv are substituted by ܶ௦ and ܴ௦ after replacing Γଵ with Γణ ൌ Γଵ ߴ. In this approach the ߪଵ⁄݊ଵ was assumed to be negligible in comparison with the other components in Eq. (31). The spectral dependence of the wavelength bandwidth Δߣሺߣሻ was taken from [54] for the 2 mm output slot of the monochromator. The spectral characteristics of the refractive index ݊ଶ=݊ଶ=݊ଶ of the BK-7 substrate plate were assumed after [55]. It was assumed that ߙଵ=0, due to the treatment of the optical data for the spectral range of negligible absorption, *i.e.*, the spectral range in which the slopes of the envelopes of ܶ and ܴ are very small. In addition, in all the above calculations an optional value of ݓଵ was assumed. This is congruent with the statement made in the previous section: for negligible absorption the envelopes of ܶௗsG and ܴௗsG are independent of ݓଵ (Fig. **9**).

**Figure 14:** Parts of the spectral dependences of optical transmittance (▼) and reflectance (▲) from Fig. **7** (broken lines, parts of the envelopes of the data; dot and solid curves, first and secondary fitted spectral dependence of G and G; description in text).

Taking wavelengths ߣଵ and ߣଶ of two close maxima and minima and choosing the appropriate ݊ଵሺߣଵሻ and ݊ଵሺߣଶሻ, the film thickness was calculated using the classical formula

$$
\overline{\mathcal{W}}\_1 = \frac{\lambda\_1 \lambda\_2}{4[\lambda\_2 n\_1(\lambda\_1) - \lambda\_1 n\_1(\lambda\_2)]} \tag{41}
$$

The theoretical transmittance calculated for the found value ݓഥଵ=651 nm and the previously determined ݊ଵሺߣଵሻ, ߪ௪ଵ, and ߙଵ=0 is shown as the dot curve in Fig. **15**. In comparison with the experimental data the shift of the curve thus obtained is observed (as for every sample examined [51]). Hence, ݓഥଵ is taken only as the initial value of the thickness ݓଵ calculated numerically by minimization of the function

$$\chi^2 = \Sigma\_{\boldsymbol{\beta}} \left\{ \left[ T\_{\boldsymbol{\alpha}} \{ \boldsymbol{\lambda} \} - T\_{f \circ \mathbb{G}} \{ \boldsymbol{\lambda}\_{\boldsymbol{\beta}}, \boldsymbol{\omega}\_1 \} \right]^2 + \left[ R\_{\boldsymbol{\alpha}} \{ \boldsymbol{\lambda}\_{\boldsymbol{\beta}} \} - R\_{f \circ \mathbb{G}} \{ \boldsymbol{\lambda}\_{\boldsymbol{\beta}}, \boldsymbol{\omega}\_1 \} \right]^2 \right\} \tag{42}$$

where ܶ൫ߣ൯ and ܴ൫ߣ൯ are the optical transmittance and reflectance measured for wavelength ߣ (from the spectral range of negligible absorption), ܶ௦G൫ߣ, ݓଵ൯ and ܴ௦G൫ߣ, ݓଵ൯ are theoretical transmittance and reflectance calculated using Eqs. (37) and (38), and the previously determined ߪ௪ଵ and ݊ଵ൫ߣ൯. The value of ݓଵ=571.1 nm was obtained from the last minimization. The optical transmittance and reflectance calculated using this ݓଵ, ߪ௪ଵ, and ݊ଵ൫ߣ൯ are shown in Fig. **14** as the solid curves. The experimental points with these characteristics fit rather well (It appears that the value of the standard deviation of a film thickness determined using the method of investigations presented herein is comparable to the value of the mean surface roughness evaluated from the AFM studies [56]).

Using the known values of ݓଵ and ߪ௪ଵ, the values of ݊ଵ, ݊ଵ, ݊ଵ, and ߙଵ=ߙଵ=ߙଵ were found numerically by minimization of the following function (the ߙଵ and ߙଵ different from ߙଵ have rather small influence on ܶ and ܴ)

$$\begin{aligned} \chi^2 &= \Sigma\_l \left[ \left[ T\_o \{ \lambda\_j \} - T\_{fsG} \{ \lambda\_j \} \right]^2 + \frac{1}{2} \left[ T\_{\max} \{ \lambda\_j \} - t\_{\max} \{ \lambda\_j \} \right]^2 + \frac{1}{2} \left[ T\_{\min} \{ \lambda\_j \} - t\_{\min} \{ \lambda\_j \} \right]^2 + \\\ & \left[ R\_o \{ \lambda\_l \} - R\_{fsG} \{ \lambda\_l \} \right]^2 + \frac{1}{2} \left[ R\_{\max} \{ \lambda\_l \} - r\_{\max} \{ \lambda\_l \} \right]^2 + \frac{1}{2} \left[ R\_{\min} \{ \lambda\_l \} - r\_{\min} \{ \lambda\_l \} \right]^2 + \left[ \frac{1 - R\_{\delta} \{ \lambda\_j \}}{r\_{\delta} \{ \lambda\_j \}} - \{ \lambda\_j \} \right]^2 \right] \tag{43} \end{aligned} \tag{44}$$

where ܶ௦G൫ߣ൯ and ܴ௦G൫ߣ൯ are the theoretical transmittance and reflectance calculated using Eqs. (36) and (37) or (38) and (39) for ߣ, ݓଵ, ߪ௪ଵ, ݊ଵ൫ߣ൯, ݊ଵ൫ߣ൯, ݊ଵ൫ߣ൯, and ߙଵ=ߙଵ=ߙଵ൫ߣ൯. The ܶ௫൫ߣ൯, ܶ൫ߣ൯, ܴ௫൫ߣ൯, and ܴ൫ߣ൯ are the appropriate magnitudes from the envelopes of ܶ൫ߣ൯ and ܴ൫ߣ൯*.* The ݐ௫൫ߣ൯, ݐ൫ߣ൯, ݎ௫൫ߣ൯, and ݎ൫ߣ൯ represent values of the envelopes ܶ௦G൫ߣ൯ and ܴ௦G൫ߣ൯. Because the interference fringes are almost completely absent in ሾ1െܴሺߣሻሿ ܶ ⁄ ሺߣሻ function [57], it was also used to facilitate the numerical analysis. The values of the fitted refractive indices and absorption coefficients are presented in Figs. **15** and **16**, respectively. The theoretical transmittance and reflectance calculated for the fitted parameters are shown in Fig. **7**. The experiment data fit rather well with the theoretical transmittance and reflectance.

One can see (Fig. **15**) that the refractive index ݊ଵ averaged through the investigated a-Si:H film has values higher than the refractive index ݊ଵ near the free surface of the film. This can be explained by the possible penetration of oxygen into the imperfect layer of silicon, causing the decrease of the real part of refractive index from the value appropriate for the bulk a-Si:H to the value similar to the parameter of SiO2. Simultaneously, for almost all investigated wavelengths the values of ݊ଵ are lower than the refractive indices near the film-substrate interface. Such inhomogeneities and the no monotonic spectral dependences of ݊ଵ൫ߣ൯ and ݊ଵ൫ߣ൯ should be carefully investigated in the future. More reliable results should be obtained under illumination from the free surface side as well as from the substrate side of a sample (*e.g.* [52]).

The multiabsorption fitting (Eq. (13)) of ߙଵ൫ߣ൯ was performed. Fig. **16** presents the best theoretical dependence fit for the sum of Tauc absorption (Eq. (11f)), Urbach absorption (Eq. (11g)), and a constant absorption term that is considered as the sum of the scattering and absorption independent of hߥ near the absorption edge. Thus the optical gap ܧ=1.838)7 (eV and the Urbach energy ܧ=128)2 (meV of the investigated material have been determined.

**Figure 15:** Spectral dependences of refractive indices near the free surface ((, near the film-substrate interface ((, and averaged ( (over the thickness of a-Si:H thin film on a thick BK-7 substrate; , values determined with the assumption of negligible absorption; other details in the text.

**Figure 16:** Spectral dependence of absorption coefficient () of radiation in a-Si:H thin film on a thick BK-7 substrate (solid curve, the least square theoretical dependence fit for the sum of Tauc absorption, Urbach absorption, and a constant absorption term; description in the text).

#### **3.4. Linear Distribution of Intensity of Reflected and Transmitted Radiation**

Very often the parallel-sided substrates of thin films are transparent for radiation used in optical measurements and usually they are much thicker than the films. If the incident beam has a finite diameter, owing to multiple internal reflection for oblique illumination, there are series of parallel but displaced beams in both the transparent and reflected directions (Fig. **17**). This can evoke a specific linear distribution of intensity of reflected and transmitted radiation. This effect can be observed when the sample is illuminated with a laser beam (*e.g.* [58]). This effect is stronger in the case of reflectance than in transmittance (*e.g.* [59]). To simplify, one may assume the same double layer structure previously analyzed. Additionally it is assumed that the spatial distribution of

incident radiation intensity is Gaussian (ܫሺݎሻ ൌ ܫ݁ݔሾെ2ሺݎ ܾ⁄ ሻଶሿ where *r* is the distance from the beam axis, ܫ is maximum intensity of radiation, and *b* represents the beam radius at ܫ ൌ *.*(ሻ2ሺെݔ݁ܫ

**Figure 17:** Scheme of radiation propagation and distribution of intensity in laser beams reflected from and transmitted through a thin film on a thick parallel-sided plate (*x,* distance from axis of the beam reflected in the point of radiation incidence upon a sample; *z.* distance from axis of the beam incident upon a sample; the other parameters are described in the text).

Because no interference occurs between radiation of beams affected by internal reflection in the thick substrate (Eq. (33)), the total radiation intensity reflected from the sample is given by a simple sum of the radiation intensities of several components (Fig. **17**). Therefore the total intensity of reflected radiation is given by the following function of the distance *x* from the axis of the beam reflected in the point of radiation incidence upon a sample

$$I\_{\rm dvdG} = \int\_0^{+v} \frac{I\_{\rm dv}}{\sigma\_{\Gamma1}\sqrt{2\pi}} \exp\left[-\frac{(\Gamma\_{10} - \Gamma\_1)^2}{2\sigma\_{\Gamma1}^2}\right] d\Gamma\_1 \tag{44}$$

where

$$I\_{\rm dv} = I\_{d1} \exp\left[-2\frac{(\mathbf{x} - \mathbf{x}\_1)^2}{b^2}\right] + I\_{d2} \exp\left[-2\frac{(\mathbf{x} - \mathbf{x}\_2)^2}{b^2}\right] + \Sigma\_{l=3} I\_{dl} \exp\left[-2\frac{(\mathbf{x} - \mathbf{x}\_l)^2}{b^2}\right] \tag{45a}$$

$$I\_{dl} = |\tilde{\varrho}\_{\rm v1}|^2 |r\_{\rm v3}|^2 |\mathfrak{t}\_{\rm v1}|^2 I\_{l-1} \tag{45b}$$

$$\mathbf{x}\_{1} = \mathbf{0}, \text{and } \mathbf{x}\_{l} = \mathbf{x}\_{l-1} + \frac{\mathbf{w}\_{2} n\_{0} \sin \phi}{\sqrt{n\_{a2}^{2} - n\_{0}^{2} \sin^{2} \phi}} \tag{45c}$$

represent positions of maximum intensities in the successive beams (l=2,3,4,ڮ(. For front illumination of the sample

$$I\_{d1} = |\varrho\_{\rm v1}|^2 I\_o \tag{45d}$$

$$I\_{d2} = |\tau\_{\rm v1}|^2 |\tau\_{\rm v3}|^2 |\vec{t}\_{\rm v1}|^2 I\_o \tag{45e}$$

while for the back-illuminated sample

$$I\_{d1} = |r\_{v3}|^2 I\_o \tag{45}$$

$$I\_{d2} = |t\_{\upsilon3}|^2 |\tilde{\varrho}\_{\upsilon1}|^2 |\tilde{t}\_{\upsilon3}|^2 I\_o \tag{45g}$$

Formula (44) does not describe the influence of multiple internal reflection of radiation in the thin film on the spatial distribution of reflected radiation. This effect can be neglected owing to the very small thickness of this film in comparison with the thick substrate thickness. The Goos-Hanchen effect [60] is not taken into account because it is much smaller than the beam shift evoked by internal reflection in a thick substrate.

The spatial distributions of the reflected radiation can be examined using not only a linear photodetector but also a goniometer [58,61,62]. The angular distributions of the reflected radiation (ADIRR) can be described using the following relation

$$
\frac{\Delta x}{a} = \sin \Delta \theta\_d \cong \Delta \theta\_d \tag{46}
$$

where ∆ݔ is the linear shift of the reflected beam, *a* is the length of a goniometer arm on which a detector is placed to measure the radiation intensity, ߠௗ represents the angle between the goniometer arm and the direction of the beam incident on a sample, and ∆ߠௗ is the angular shift of the reflected beam. The last relation is correct for ∆ݔ ا ܽ.

Numerical calculations were performed to analyze the influence of optical parameters of a sample on ADIRR. Some results are shown in Fig. **18**. The typical parameters of a-Si thin films were used to perform the calculations (Table **1**) and *a*=0.25 m was assumed. To simplify the analysis, the standard deviation ߪଵ=0 of the change in phase of radiation traversing a thin film was also assumed.

Different values of the real part of refractive index at the surfaces and in the bulk of a thin film strongly influence the ratio of successive maxima in the ADIRR (Fig. **18**). Also, the inhomogeneous absorption influences the ADIRR (Fig. **18**). The changes in the values of surface and bulk optical parameters affect the ADIRR calculated for front and back illumination of the sample in different ways. The value of ߶ determines the intensities of the first and second component of reflected radiation differently (Fig. **18**). The influence of sample parameters on the ADIRR varies with the polarization of light incident upon a sample. All this suggests using the measured ADIRR to estimate the optical parameters of thin films on thick substrates.

**Figure 18:** Influence of the surface and bulk values of real part of refractive index and absorption coefficient on ADIRR calculated for an inhomogeneous thin film on a thick substrate [63] (curve values are shown in Table 1; =0.2 m, *na2*=1.5, *w2*=1 mm, =632.8 nm, ࣘ=50°, plane polarised radiation with the electric vector normal to the plane of incidence, *b*=1.3 mm).


**Table 1:** Values for the curves in Fig. **18**.

**Table 2:** Optical and geometrical parameters obtained by fitting ADIRR presented in Fig. **19**.


Fig. **19** presents the ADIRR reported in [63] for front-and back-illuminated sample of a-Si film on a 0.98 mm thick BK-7 substrate. The measurements were performed at room temperature for the p-and s-polarized radiation. The ADIRR was determined using the experimental set-up described in [58]. The samples were illuminated with a plane-polarized He-Ne TEM00 laser beam of wavelength ߣ=632.8 nm and beam radius *b=*1.5 mm. The ADIRR was measured with 0.01° steps. To make Fig. **19** clearer, only some of the results are shown (data scattering was almost negligible). The two separated reflected beams are well recognized. The first beam is reflected at a point of radiation incidence on the sample. The second beam leaves the sample due to internal reflection in the thick parallel-sided substrate (see Fig. **17**).

The experimental ADIRR data presented in Figs. **19** are at least in qualitative agreement with the results of theoretical calculations presented above. Therefore, the data have been least-squared fitted with formula (44). The determined parameters of the investigated sample are presented in Table **2**. One can recognize that the results obtained in different experiments correspond. The value of ݊ଵ is smaller than ݊ଵ but greater than ݊ଵ*.* The value of ߙଵ is similar to ߙଵ but greater than ߙଵ. It is possible that the low values of ݊ଵ and ߙଵ are affected by the oxidation of a-Si.

**Figure 19:** ADIRR of front-illuminated (A, B) and back-illuminated (C, D) ) film of a-Si (w1=198 nm) on a 0.98 mm thick BK-7 substrate plotted against angle of incidence ࣘ and the angle ࣂ between the incident beam and goniometer arm with the photodetector [63]. (A, C) s and (B, D) p polarized radiation; ࣅ=632.8 nm; =1.51)2 ;(points, the experimental results; solid curves, the fitted theoretical dependencies. The fitted semiconductor parameters are presented in Table 2.

Fig. **20** shows the dependences of maximum intensities of the components in ADIRR on angle of illumination incidence upon a sample composed of a-Si thin film on a thick BK-7 substrate. These dependences were [62] least-squared fitted with Eq. (44). The fitted parameters of the investigated

sample are presented in Table **3**. Parameters presented in columns A and B were obtained from simultaneous fitting of first and second maximum ADIRR components for s and p polarized radiation, respectively. The parameters obtained from simultaneous fitting of the angular dependencies of the first and second maximum ADIRR components as well as the s and p polarization are given in column A+B. It is recognized that the results obtained in different experiments and in different fittings correspond. Due to the greater number of fitted data, the values of parameters determined from simultaneous fitting of data obtained in experiments with s and p polarized radiation seem to be the more reliable. The fitted value of ݊ଵ is smaller than ݊ଵ but greater than ݊ଵ*.* The fitted value of ߙଵ is 22% greater than ߙଵ but only 18% greater than ߙଵ. It is possible that the low values of ݊ଵ and ߙଵ are affected by the oxidation of a-Si.

The same experimental data (Fig. **20**) were also fitted assuming optical homogeneity of the investigated sample (*i.e.* ݊ଵ=݊ଵ=݊ଵ, ߙଵ=ߙଵ=ߙଵ). However, the residual squares of the differences between the theoretical and experimental data are much greater in this case than those obtained for the model of optically inhomogeneous film (compare the solid and broken curves in Fig. **20**). Therefore, the investigated sample of a-Si seems to be optically inhomogeneous over its thickness. The investigations of optical inhomogeneity of thin films of a-Si should be taken into account in optimization of technological conditions.

**Figure 20:** Reflectivity measured for the first (■,●) and second (▼,▲) maximum intensities in ADIRR of a 198 nm thick a-Si film on a thick BK-7 substrate against angle of radiation incidence on a sample [62] (ࣅ=632.8 nm, =1.51)2(, =0.98 mm): (A) s and (B) p polarized radiation; points, the experimental results; solid and broken curves, the fitted theoretical dependencies for inhomogeneous and homogeneous films, respectively. The fitted parameters are presented in Table 3.

Simultaneous investigations of the angular dependence of radiation intensities of the two separated beams, reflected from a thin film on a thick, parallel-sided, transparent substrate, give more data and seem to be more accurate as well as more reliable than the standard variable angle reflectometry (VAR) method that takes into account the summarized intensity of the radiation reflected from a sample [62]. The presented method of investigations shares with the multiple angle ellipsometry and the VAR technique a common advantage over interference spectroscopy: measurements using these techniques are made at a single wavelength. Therefore, these techniques are free from the complications caused by refractive index dispersion.

Comparing the technique of angular investigations of radiation intensities of the two separated beams, reflected from a thin film on a thick substrate with the standard ADIRR method, the simpler interpretation and theoretical description of the experimental results should be evident. In fact, the intensity of the first component of the reflected beam can be described without taking into account the multiple reflections of radiation in the thin-film substrate. The spatial distribution of the incident light is not so crucial for the fitting of the maximum intensities of the reflected radiation.

**Table 3:** Values of optical and geometrical parameters obtained by fitting different components of reflected radiation (Fig. **20**).


### **4. SPATIAL DISTRIBUTION OF RADIATION INTENSITY IN A SEMICONDUCTOR FILM IN A MULTILAYER STRUCTURE**

Very often the intensity of radiation in parallel-sided semiconductor film that is part of a multilayer structure should be determined. To simplify the consideration we assume the following: An isotropic, parallel-sided semiconductor film (Fig. **6**) is part of a multilayer structure (Fig. **1**). It is infinite in the XZ plane and is bounded by two non-absorbing coating layers of thicknesses w1 and w3 for the front and back sides, respectively. The layer structure is bounded in Y direction by two semi-infinite layers of refractive indices n0 and n4-i4 for the front and back sides (Fig. **1**) (n0=1 and n4-i4=1 for a sample immersed in air). Radiation of wavelength , which propagates in the XY plane, hits the structure with the angle of incidence ߶. The radiation intensity is uniformly distributed over the sample surface.

The total electric vector ܧሬԦ of radiation in a semiconductor film can be obtained from summing up the multiple reflected elements

$$
\vec{E}\_{\text{vl}} = \sum\_{l=1}^{+\circ} (E\_{\text{vl}}^{+} + E\_{\text{vl}}^{-}) \tag{47}
$$

where ܧv ା-electric field of the *l-*th beam (see Fig. **13**) which propagates from the front to back side, and ܧv ି-electric field of the *l-*th beam which propagates from the back to front side. Index v must be replaced by indices p and s for plane-polarized radiation with electric vector in and normal to the plane of incidence. After elementary summing up one obtains:

$$\vec{E}\_{\rm{sf}} = \frac{\mathsf{E}\_{0}\mathsf{r}\_{\rm{sf}}\exp\left[\frac{2\pi\mathsf{i}}{\lambda}(\mathsf{c}t - x\mathsf{n}\_{0}\sin\phi)\right]}{1 - \mathsf{P}\_{\rm{bf}}\mathsf{v}\_{\rm{sf}(j+1)}\exp(-\mathsf{K}\_{j})\exp(-\mathsf{I}\mathsf{I}\_{j})} \begin{Bmatrix} \exp\left(-\frac{\mathsf{k}\_{j} + \mathsf{i}\mathsf{v}\_{j}}{2}\mathbf{y}\right) + \\\\ \mathsf{P}\_{\rm{sf}(j+1)}\exp\left[\frac{\mathsf{k}\_{j} + \mathsf{i}\mathsf{v}\_{j}}{2}\left(\mathbf{y} - 2\mathsf{w}\_{j}\right)\right] \end{Bmatrix} \vec{e}\_{\mathbf{z}} \tag{48a}$$

$$\begin{array}{c} \vec{E}\_{p\,l} = \\ \frac{E\_0 \pi\_{pj} \exp\left[\frac{2\pi i}{\lambda}(ct - xw\_0 \sin\phi)\right]}{1 - \vec{\upmu}\_{pj} \varrho\_{p(j+1)} \exp\left(-k\_f\right) \exp\left(-l\,\Gamma\_{j0}\right)} \left[ \begin{cases} \exp\left(-\frac{k\_f + i\nu\_f}{2}\chi\right) + \\ \left[\begin{array}{c} \exp\left(-\frac{k\_f + i\nu\_f}{2}\right) \\ \exp\left(\frac{k\_f + i\nu\_f}{2}\right) - \left[\begin{array}{c} \exp\left(-\frac{k\_f + i\nu\_f}{2}\right) \end{array}\right] \end{array} \right] \vec{E}\_x \cos\psi\_f + \left[\exp\left(-\frac{k\_f + i\nu\_f}{2}\right)\chi\right] + \\ \left[\begin{array}{c} \exp\left(\frac{k\_f + i\nu\_f}{2}\right) \left[\begin{array}{c} \exp\left(-\frac{k\_f + i\nu\_f}{2}\right) \end{array}\right] \end{array} \right] \vec{E}\_y \cos\psi\_f + \left[\exp\left(-\frac{k\_f + i\nu\_f}{2}\right)\chi\right] \end{array} \right] \tag{48b}$$

where ܧ is the amplitude of the electric vector of the wave incident upon the structure, ݁Ԧ௫, ݁Ԧ௬, ݁Ԧ௭ are the versors of the axis (Fig. **13**), ߰ ൌ ܽݎܿݏ݅݊ ቂ݊ ൫݊ <sup>ଶ</sup> sinଶ ߶ܽ <sup>ଶ</sup> ൯ ିଵ ଶ⁄ sin ߶ቃ is the angle of radiation refraction in the *j* film, ߛ ൌ 4ߨܽ⁄ߣ , ݇ ൌ ܽߙ⁄݊, t is the time, y is the distance from the front surface of the semiconductor *j* film. Other parameters retain their previous meanings.

Using Eqs. (48a) and (49b), the intensity of radiation (in photons) in the semiconductor film can be found from the Poynting vector

$$I\_{\rm v} = \frac{1}{r\_{em}} \frac{\lambda n\_{aj}}{\hbar c} \sqrt{\frac{\varepsilon\_0}{\mu\_0}} \int\_0^{T\_{em}} \left| \vec{E}\_{\rm v} \right|^2 dt \tag{49}$$

where the index v must be replaced by indices p and s for plane-polarized radiation with the electric vector in and normal to the plane of incidence; ܶ is the period of the electromagnetic wave; and ߝ and ߤ are the electric permittivity and magnetic permeability of free space, respectively.

For the plane-polarized radiation with electric vector in the plane of incidence, ܫሺݕሻ can be calculated numerically using Eqs. (48b) and (49). However, in the case of plane-polarized radiation with the electric vector normal to the plane of incidence it is relatively easy to find the following analytical formula

$$I\_s(\mathbf{y}) = I\_{s0} \begin{bmatrix} \exp\{-k\_l \mathbf{y}\} + \left| \varrho\_{s(j+1)} \right|^2 \exp\{k\_l \mathbf{y} - 2K\_l \} + \\ 2 \left| \varrho\_{s(j+1)} \right| \exp\{-K\_l \} \cos\{\mathbf{y}\_j \mathbf{y} + \theta\_{s(j+1)} - \Gamma\_{j0} \} \end{bmatrix} \tag{50}$$

where

$$I\_{s0} = \frac{\left(1 - \left|\varrho\_{5}\right|^{2}\right)l\_{0}}{1 + \left|\tilde{\varrho}\_{4}\right|^{2} \left|\varrho\_{5\left(j+1\right)}\right|^{2} \exp\left(-2K\_{j}\right) - 2\left|\tilde{\varrho}\_{4}\right| \left|\varrho\_{5\left(j+1\right)}\right| \exp\left(-K\_{j}\right) \cos\left(\tilde{\theta}\_{4\right)} + \theta\_{5\left(j+1\right)} - \Gamma\_{j0}\right)}}\tag{51}$$

is the so-called effective intensity of radiation (in photons) that enters the semiconductor, and ܫ is the intensity (in photons) of radiation incident upon the sample.

The spatial distribution of radiation intensity in a semiconductor film is a function of the sample geometrical and optical parameters, polarization and angle of incidence of radiation. However, it should be noted that by taking into account additional assumptions, the general formula (50) can be

reduced into some much simpler formulae, which apply to special experimental conditions (*e.g.* [64,65]). For normal radiation incidence upon a single semiconductor film surrounded by air, Eq. (50) is reduced to the expression presented in [66]. With the additional assumption, that the internal reflection of radiation is negligible, Eq. (50) is reduced to the Bouguer-Lambert law (see Eq. (3)).

Fig. **21** shows the effective intensity of radiation which enters a semiconductor film perpendicularly as a function of the reflection coefficient of a non-absorbing layer which covers the front surface of the semiconductor. The calculations were performed using Eq. (50). The curves in Fig. **21** represent different values of radiation reflectivity from the back semiconductor surface, different absorption of radiation in the semiconductor, and different changes in phase of the beam traversing the semiconductor film and reflected from its surfaces. It can be seen that the intensity of radiation in a semiconductor is very sensitive to all these parameters. Only in the case of negligible internal reflection does the radiation intensity in a semiconductor decrease linearly with the increasing reflection coefficient of the front surface film. The value of |߷v3| should be as high as possible. The highest intensity of radiation can be achieved in a semiconductor when the interference effect occurs and the sum of changes in phase of the beam traversing the semiconductor film and reflected from its surfaces is given by

$$
\tilde{\theta}\_{\text{s}\dagger} + \theta\_{\text{s}\{\text{j}+1\}} - \Gamma\_{\text{j}0} = 2m\pi \tag{52}
$$

where m=0,1,2,.

**Table 4:** Values for the curves in Fig. **21**.


The value of front surface reflection coefficient, for which the radiation intensity in a semiconductor can achieve the greatest value, depends on the back surface reflection coefficient and absorption of radiation in the investigated semiconductor

$$|\not{p}\_{v1}|^2 = |\varrho\_{v3}|^2 \exp\{-2K\_{\!\!/\!}{\!} \}\tag{59}$$

The value of front surface reflection coefficient selected in this way makes the internal reflection, and consequently the interference of internally reflected radiation, very effective. Simultaneously, an effectively large part of radiation which hits the multilayer structure can enter the semiconductor film. Authors of Chapter 9 of this eBook have presented special aspects of light trapping in thin silicon solar cells.

Radiative recombination of photogenerated carriers can influence the spatial distribution of radiation intensity in a semiconductor. One can say that part of the incident light is transformed into bandgap radiation, emitted in this process, for which the absorption coefficient is smaller. This effect is not discussed in this paper.

**Figure 21:** Effective intensity of radiation that enters a semiconductor film in a multilayer structure (Fig. **1**) *versus* the value of the reflection coefficient for back illumination of the front surface of the film, for different optical parameters of the sample (curve values are shown in Table 4).

### **4.1. Influence of Sample Parameters and Experimental Conditions on Radiation Intensity in a Semiconductor Film**

Formula (50) is an idealization of the experimental situation: it was derived for the study of the perfect coherence of radiation interfering in a semiconductor film. It was pointed out in cases of transmittance and reflectance changes in phase Γ of the beam on traversing a semiconductor and the coating layers can be described by Gaussian distribution with the average values Γଵ, Γଶ, and Γଷ, and with standard deviations ߪଵ, ߪଶ, and ߪଷ, respectively. Hence, the total intensity of radiation in a semiconductor film should be calculated using integral

$$I\_{GV}(\Gamma\_2, \Gamma\_1, \Gamma\_3) = \begin{pmatrix} \int\_{\tau\_{\ge 1}}^{+\alpha} \frac{1}{\sigma\_{\Gamma\_2} \sqrt{2\pi}} \exp\left[-\frac{(\Gamma\_{20} - \Gamma\_2)^2}{2\sigma\_{\Gamma\_2}^2}\right] \cdot \\\\ \int\_{\tau\_{\ge 0}}^{+\alpha} \frac{1}{\sigma\_{\Gamma\_1} \sqrt{2\pi}} \exp\left[-\frac{(\Gamma\_{10} - \Gamma\_1)^2}{2\sigma\_{\Gamma\_1}^2}\right] \cdot \\\\ \int\_{\Gamma\_2 = 0}^{+\alpha} \int\_{\Gamma\_3 = 0}^{+\alpha} \frac{\nu\_\Gamma}{\sigma\_{\Gamma 3} \sqrt{2\pi}} \exp\left[-\frac{(\Gamma\_{30} - \Gamma\_3)^2}{2\sigma\_{\Gamma 3}^2}\right] d\Gamma\_3 d\Gamma\_1 d\Gamma\_2 \end{pmatrix} \tag{54}$$

where ܫv is given by Eqs. (49) or (50). For ߪଵ=ߪଶ=ߪଷ=0 the density of Gaussian distribution is represented by the ߜ െDirac and ܫீvሺΓଶ, Γଵ, Γଷሻ ൌ ܫீvሺΓଶ, Γଵ, Γଷሻ. In this case formula (54) reduces into the forms (49) or (50) for the ideal instance of perfect coherence of radiation interfering in a semiconductor film.

To simplify, one might limit the analysis of ܫG୴ሺݕሻ to a double layer structure of a thin semiconductor film of thickness ݓଵ, which covers a relatively thick, transparent, parallel-sided substrate of thickness ݓଶ. As in the cases of transmittance and reflectance, it is assumed that the interference of internally reflected radiation occurs in a semiconductor film and is negligible in the substrate (Eq. (33)). Obviously, some part of radiation incident on the front surface of the double layer structure is transmitted through the semiconductor thin-film, and then internally reflected from the back side of the substrate entering into the semiconductor from its rear. One can call this part of radiation secondary illumination in contrast to primary (front) illumination. According to Eq. (33); the phases of waves incident upon the semiconductor from the back side are random in comparison to the phases of radiation which illuminates the semiconductor film from the front side. Due to multiple internal reflection of radiation in the substrate, the secondary illumination consists of a set of beams. By totaling the radiation of these beams, the total intensity of the secondary illumination of the film is obtained [67]

$$I\_{\rm v0}^{-} = \frac{|r\_{\rm v1}|^2 |r\_{\rm v3}|^2}{1 - |\langle \ell\_{\rm v1} \rangle^2 |r\_{\rm v3}|^2} I\_0 \tag{55}$$

where index v must be replaced by indices p and s for plane polarized radiation with the electric vector in and normal to the plane of incidence, respectively; all the other symbols retain their previous meanings. To calculate intensity of the p and s plane polarized radiation, the orientation of its electric field must be taken into account. For the primary illumination of the investigated thin semiconductor film on a thick substrate, the electric fields ܧሬԦ ௦ଵ ା and ܧሬԦ ଵ ା are given by Eq. (48). In the case of secondary illumination of the investigated film, one obtains

$$
\vec{E}\_{\rm i1}^{\rm i} = \frac{E\_0^- \vec{\epsilon}\_{z\to 2} \exp\left[\frac{2\pi i}{\lambda}(ct - x\_{\rm 10}\sin\phi)\right]}{1 + r\_{\rm 11}r\_{\rm 2}\exp(-\lambda\_1)\exp(-l\Gamma\_{10})} \left\{ \begin{aligned} \exp\left[\frac{k\_1 + l\nu\_1}{2}\left(y - \nu\_1\right)\right] -\\ r\_{\rm 11}\exp\left[-\frac{k\_1 + l\nu\_1}{2}\left(w\_1 + \nu\right)\right] \end{aligned} \right\} \tag{56a}
$$

$$
\vec{E}\_{\rm p1}^{\rm i} = \frac{\vec{e}\_0^{-\tilde{\epsilon}\_0}\exp\left[\frac{2\pi i}{\lambda}(ct - x\_{\rm 10}\sin\phi)\right]}{1 + r\_{\rm 11}r\_{\rm 2}\exp(-\kappa\_1)\exp(-l\Gamma\_{10})} \left[ \begin{cases} \exp\left[\frac{k\_1 + l\nu\_1}{2}\left(y - \nu\_1\right)\right] -\\ r\_{\rm 11}\exp\left[-\frac{k\_1 + l\nu\_1}{2}\left(w\_1 + \nu\right)\right] \end{cases} \right] \vec{e}\_x \cos\psi\_1 + \left\{\exp\left[\frac{k\_1 + l\nu\_1}{2}\left(y - \nu\_1\right)\right] - \right\} \tag{57b}
$$

$$
\left[\begin{aligned} \left[\left(w\_1\right)\right] + r\_{\rm 11}\exp\left[-\frac{k\_1 + l\nu\_1}{2}\left(w\_1 + \nu\right)\right] \end{aligned} \right] \vec{e}\_y \sin\psi\_1 \tag{57c}
$$

where the amplitude of the secondary illumination electric field is given by

$$\left|\vec{E\_0}^-\right|^2 = \frac{|\tau\_{\rm v1}|^2 |r\_{\rm v3}|^2}{1 - |\mathbb{Q}\_{\rm v1}|^2 |r\_{\rm v3}|^2} \left|\vec{E\_0}\right|^2 \tag{57}$$

One can find the intensity of p plane polarized radiation (in photons) in an ideal semiconductor film from the Poynting vector

$$I\_{\rm p}(\mathbf{y}) = \frac{1}{T\_{\rm em}} \frac{\lambda n\_{\rm e1}}{\hbar c} \sqrt{\frac{\varepsilon\_0}{\mu\_0}} \int\_0^{T\_{\rm em}} \left[ \left| \vec{E}\_{\rm p1}^{\rm +} \right|^2 + \left| \vec{E}\_{\rm p1}^{\rm -} (\phi) \right|^2 \right] dt \tag{58}$$

For the s polarized radiation, it is relatively easy to find the analytical formula describing distribution of radiation intensity in a thin film for the sum of primary and secondary illumination [67].

$$I\_s(\mathbf{y}) = I\_{s0} \begin{bmatrix} g\_1 e^{-k\_j \mathbf{y}} + g\_2 e^{-(k\_j \mathbf{y} + \mathbf{K}\_j)} \\ 2g\_3 e^{-\mathbf{K}\_j} \cos(\chi\_j \mathbf{y} + \boldsymbol{\psi}) \end{bmatrix} \tag{59}$$

$$\text{where } g\_1 = 1 + D|r\_{s1}|^2 e^{-K\_f} \tag{60a}$$

$$D = \frac{|\mathbf{r}\_{31}|^2 |r\_{33}|^2 \left(1 - |r\_{32}|^2\right)^2}{(1 - |r\_{31}|^2)^2 (1 - |\tilde{\mathbb{Q}}\_{\mathbb{T}^1}|^2 |r\_{33}|^2)}\tag{60b}$$

$$g\_2 = |r\_{s1}|^2 e^{-K\_f} + \mathcal{D}\tag{60c}$$

$$\sin\psi = \frac{|r\_{s2}|\sin(\wp\_{s2} - \Gamma\_{10}) - D|r\_{s1}|\sin\varphi\_{s1}}{\varrho\_3} \tag{60d}$$

$$\cos\psi = \frac{|r\_{\xi2}|\cos(\phi\_{\le 2} - \Gamma\_{10}) - \mathcal{D}|r\_{\xi1}|\cos\phi\_{\le 1}}{g\_3} \tag{60e}$$

$$g\_3 = |r\_{s2}|^2 + D^2 |r\_{s1}|^2 - 2D|r\_{s1}||r\_{s2}|\sqrt{\cos\{\varphi\_{s1} + \varphi\_{s2} - \Gamma\_{10}\}}\tag{60f}$$

$$I\_{s0} = \frac{(1 - |r\_{s1}|^2)l\_0}{1 + |r\_{s1}|^2 |r\_{s2}|^2 e^{-2K\_f} + 2|r\_{s1}||r\_{s2}|e^{-K\_f}\cos(\varphi\_{s1} + \varphi\_{s2} - \Gamma\_{10})} \tag{60g}$$

ܫ௦ is the so-called effective intensity of radiation (in photons) which enters the semiconductor, and ܫ is the intensity (in photons) of radiation incident upon the sample.

Taking into account the possible Gaussian distribution of the change in phase of the beam upon traversing the semiconductor film in the double layer structure, one should calculate

$$I\_{\rm vG}(\mathbf{y}) = \int\_0^{+\infty} \frac{l\_{\rm v}(\mathbf{y})}{\sigma \gamma \sqrt{2\pi}} \exp\left[-\frac{(\Gamma\_{10} - \Gamma\_1)^2}{2\sigma\_1^2}\right] d\Gamma\_1 \tag{61}$$

where index v must be replaced by indices p and s for plane polarized radiation with the electric vector in and normal to the plane of incidence; other symbols retain their previous meanings.

Fig. **22** shows ܫ୴ሺݕሻ calculated for a typical a-Si film in a double layer structure illuminated perpendicularly with radiation of different wavelengths. In the case of short wavelength and relatively strong radiation absorption (ܭଵ>>1), the radiation intensity decreases exponentially with increasing distance from the illuminated semiconductor surface (chain curve in Fig. **22**). However, in the case of radiation weakly absorbed in optically thin films (ܭଵ<1), a steady light wave occurs in the film (solid and broken curves in Fig. **21**) due to the interference of radiation internally reflected from its surfaces. This was first observed more than one hundred years ago by O. Wiener [68] in photographic emulsion that covered a mirror surface.

The period of interference changes of the radiation intensity in a sample equals

$$\mathbf{w}\_{\rm in} = \frac{\lambda}{2a\_{\rm at}}\tag{62}$$

**Figure 22:** Spatial distribution of radiation intensity in a thin film on a thick, transparent substrate for different wavelengths of the radiation [67] (solid curve, ߣ=0.8 ߤm, ݊ଵ=3.18, ߙଵ=2.48·10<sup>5</sup> m-1; broken curve, ߣ=0.6328 ߤm, ݊ଵ=3.29, ߙଵ=1.7·10<sup>6</sup> m-1; chain curve, ߣ=0.528 ߤm, ݊ଵ=3.45, ߙଵ=7.7·106 m-1; ߶=0°, ݓଵ=0.76 ߤm; ݊ଵ=݊ଵ=݊ଵ; ߙଵ=ߙଵ=ߙଵ; ߪଵ=0; ܰଶ=ܰଶ=ܰଶ=1.51; ܰ=ܰଷ=1).

**Figure 23:** Influence of standard deviation ߪଵ in the Gaussian distribution of the change in phase of a beam traversing a thin film on a thick, transparent substrate on the spatial distribution of radiation intensity [67] (solid curve, /=0; broken curve, /=0.05 (ߪଵ=1.49 ); chain curve, /=0.5 (ߪଵ=24.8 ); other parameters are the same as in Fig. **22**).

**Figure 24:** Spatial distribution of radiation intensity in a thin film on a thick transparent substrate for different thicknesses of the film [67] (solid curve, ݓଵ=2 ߤm; broken curve, ݓଵ=0.76 ߤm; chain curve, ݓଵ=0.5 ߤm; ߣ=632.8 nm, ݊ଵ=3.29, ߙଵ=1.7·106 m-1, other parameters are the same as in Fig. **22**).

and decreases with the decreasing wavelength and angle of incidence of radiation. Thus, the ߣ is important for the spatial distribution of radiation intensity in a semiconductor film not only because of its influence on values of optical parameters of a semiconductor but also because of its direct influence on the spatial distribution of the steady light wave in a sample (Fig. **22**).

When 0<ߪଵ<2 the characteristic fringes in ܫ୴ሺݕሻ decrease with increasing ߪଵ. The decrease is stronger near the front surface of a semiconductor (Fig. **23**). The periodicity of the spatial oscillations remains practically the same as for ideal interference. However, for ߪଵ>2ߨ the amplitudes decrease as the distance from both film surfaces increases. In this case spatial distribution ܫ୴ሺݕሻ becomes relatively smooth in the middle of the film. Yet, even for great ߪଵ there are relatively large changes of ܫ୴ሺݕሻ with increasing distance from semiconductor surfaces, especially near the rear surface (Fig. **23**). It is a consequence of the total of the electric fields of incident and reflected waves close to the surface. It is not disturbed by the wave front deformation in the bulk of a semiconductor film. This effect cannot be described by the formulae derived in [66,69] for negligible interference of radiation.

The number of interference fringes of radiation intensity in the film is proportional to its thickness (Fig. **24**) and is inversely proportional to the radiation wavelength. The depth of interference oscillations vanishes with increasing film thickness (Fig. **24**) and with absorption coefficient of the radiation.

It should be emphasized that when a semiconductor is bounded by a rear medium which has smaller optical density (݊ଶ<<݊ଵ), the radiation intensity is relatively high near the rear semiconductor sample surface (Figs. **22-24**).

**Figure 25:** Influence of ડ in the Gaussian distribution of the change ડ in phase of a beam traversing a semiconductor film on a thick transparent substrate on the spectral dependencies of the ratio of absorbed to incident photons for semiconductor films of different thicknesses [67] (A: =0.76 ࣆm; solid curve, /=0; broken curve, /=0.03; chain curve, /=0.1; B: =2 ࣆm, solid curve, /=0; broken curve, /=0.01; chain curve, /=0.03; ሺࣅሻ and ࢻሺࣅሻ taken from [29], other parameters are the same as in Fig. 22).

The ratio F of the number of photons absorbed in the whole semiconductor to the number of photons incident upon it equals:

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$$F = \frac{1}{l\_0} \int\_0^{\nu\_f} a\_f l\_v(\mathbf{y}) d\mathbf{y}.\tag{63}$$

It must be emphasized that the thickness of a semiconductor film strongly influences not only the spatial distribution (Fig. **24**) but also the total energy of radiation in it (Fig. **25).** In general, the spectral characteristics of F are very complicated due to simultaneous contributions of interference effects in semiconductor film and in the coating layers. Typical for these are oscillations that vanish with the increasing semiconductor thickness and absorption coefficient of radiation (thus increasing hν). The period of these oscillations depends on ߣ and ݊ଵ*,* and decreases with increasing ݓଵ*.* Due to different thicknesses of a semiconductor film and the coating layers, the appropriate periods of oscillations in spectral characteristics may differ. For some values of sample thickness, F can be comparable to its value where absorption of radiation in a very thick sample is strong (*e.g.* [70]).

**Figure 26:** Spatial distribution of radiation intensity in a thin film on a thick, transparent substrate for different polarization and angle of incidence of radiation [67] (chain curve, ߶ ൌ 0°; broken curve, ߶ ൌ 60°, p plane polarized radiation with the electric vector in the plane of incidence; solid curve, ߶ ൌ 60°, s plane polarized radiation with the electric vector normal to the plane of incidence; ݓଵ=0.76 ߤm, other parameters are the same as in Fig. **22**).

Increase of the standard deviation ߪଵ does not influence the positions of the interference fringes in spectral characterisics of F (Fig. **25**). However, it does decrease the magnitude of the fringes. For a fixed ߣ the ratio F increases or decreases with increasing ߪଵ (Fig. **25**) depending on the fact that ߣ can be appropriate for destructive or constructive interference of light in the sample.

The dependence of the spatial distribution of radiation intensity on polarization and the angle of incidence of radiation (Fig. **26**) is caused by two agents. First, by changing the angle of incidence and polarization of radiation, the intensity of radiation that enters the semiconductor structure is changed due to the change of ݎvଵ. Second, the value of the effective absorption coefficient ߙଵ increases with increasing angle ߶. The angular dependence of ߙ can be relatively strong in semiconductors with small ݊ or bounded by an optically dense medium (݊ሺିଵሻ*<*݊*<*݊ሺାଵሻ) in which radiation propagates in high degree to the semiconductor surface.

**Figure 27:** Ratio of absorbed to incident photons *vs.* angle of incidence for different film thicknesses and different polarization and wavelengths of radiation [67] (broken curve, ݓଵ=0.76 ߤm, ߣ=0.6328 ߤm (݊ଵ=3.29, ߙଵ=1.7·106 m-1); solid curve. ݓଵ=2 ߤm, ߣ=0.7 ߤm (݊ଵ=3.23, ߙଵ=5.78·10<sup>5</sup> m-1); p, s: values for plane polarized radiation with the electric vector in and normal to the plane of incidence; other parameters are the same as in Fig. **22**).

Due to the increase of the period ݓ of changing radiation intensity in a film with increasing ߶ (Fig. **26**), the radiation intensity near the front semiconductor surface can attain the maxima and minima with an increase in the angle of incidence. If the period ݓ is much smaller than the film thickness, the angular dependencies of *F* can be non-monotonous (Fig. **27**) or even oscillatory as observed experimentally, for example, in [71]. These oscillations are more evident for plane polarized radiation with the electric vector normal to the plane of incidence. If the radiation is strongly absorbed in a sample, the interference effect does not occur and the angular dependence of F becomes monotonous.

The interference peaks in spectral characteristics of F are shifted to shorter wavelengths with an increase in the angle of radiation incidence (Fig. **28**). In the case of non-normal illumination of a single semiconductor film, which strongly absorbs radiation, the intensity ܫ) for plane-polarized radiation with the electric vector in the plane of incidence) is always greater than intensity ܫ௦ for radiation with electric vector normal to the plane of incidence. It is because of the smaller reflectivity of such polarized radiation from the front surface of the semiconductor. However, in the case of interference of weakly absorbed radiation this is not always true (see Fig. **28**). It occurs because s-polarized radiation is more strongly internally reflected from the sample surfaces. This dependence may be strongly influenced by the optical and geometrical parameters of surface coating layers [70]. For a relatively thick coating layer the oscillatory angular dependence of ܫ୴ should be also observed but such experimental conditions are less probable.

Assuming the same parameters as those presented in descriptions of Figs. **22**-**28**, the appropriate calculations of ܫv and *F* were done [67] using the general theory represented by Eq. (54). These calculations were performed taking into account substrate thickness ݓଶ=1 ݉݉ and the standard deviation *=*10 of the change in phase of a beam traversing the thick substrate. This value of standard deviation represents relatively small /=10-4 variation of the change in phase of the beam traversing the substrate. However, *=*10 is greater than 2ߨ and it is sufficient for discounting the interference effect in the substrate (see [70]). The results obtained in this case were

[67] exactly the same as those presented in Figs. **22-28**. Therefore, Eq. (61) can be applied as a good approximation of the general theory for a thin semiconductor film on a thick, transparent, parallel-sided substrate. Using this approximation makes the calculation about fifty times faster, so it is very important, for example, for the least square fitting of spectral PC or PEM characteristics with theoretical dependences.

**Figure 28:** Spectral dependencies of the ratio of absorbed to incident photons for different polarizations and angles of incidence of radiation [67] (solid curve, ߶ ൌ 0°; chain curve, ߶ ൌ 60° and p plane polarized radiation with the electric vector in the plane of incidence; broken curve, ߶ ൌ 60° and s plane polarized radiation with the electric vector normal to the plane of incidence; ݓଵ=0.76 ߤm; /=0; other parameters are the same as in Fig. **25**).

Due to the interference effect, the change of the real part of the semiconductor refractive index with some of the experimental parameters (*e.g.*, electric field, magnetic field, temperature or illumination intensity) can cause an oscillatory dependence of *F* (*e.g.* [72]). This mechanism is similar to those that cause the oscillatory dependencies of *F* on ߣ,߶ , and ݓଵ*.*

**Figure 29:** Energetic model of carrier photogeneration in a graded-gap semiconductor ( is the width of the effective absorption region where the energy gap is smaller than the photon energy, V and C are the top of the valence band and bottom of the conduction band, respectively).

#### **4.2. Spatial Distribution of Radiation Intensity in Graded Energy Gap Semiconductors**

To simplify the analysis we assume that the energy gap gradient is parallel to the y-direction, and it is also parallel to illumination (߶=0°). In this case the absorption of radiation and photogeneration of excess carriers take place only in this part of a semiconductor film, where the semiconductor energy gap is smaller than photon energy (see Fig. **29**). Of course, the thickness ݓ of this part of a semiconductor can be much less than the thickness ݓ of the whole semiconductor film (Fig. **29**). Thus, due to the weak absorption of radiation in a relatively thick, parallel-sided semiconductor film, the interference of radiation internally reflected from the sample surfaces can extremely influence the spatial distribution of radiation intensity in this part of the sample where carrier photogeneration occurs. Using the presented above approach, the intensity of radiation in a graded energy gap semiconductor can be described with Eq. (54), but the spatial distribution of radiation intensity ܫv in that equation must be replaced by

$$I\_s(\mathbf{y}) = I\_{s0} \begin{bmatrix} \exp\left(-\int\_0^\mathbf{y} a \, d\xi \right) + \left| \varrho\_{s(j+1)} \right|^2 \exp\{-2K\_l \} \exp\left(-\int\_0^\mathbf{y} a \, d\xi \right) + \\\\ 2\left| \varrho\_{s(j+1)} \right| \exp\{-K\_l \} \cos\left(\int\_0^\mathbf{y} \frac{4\pi}{\lambda} n \, d\xi + \Theta\_{s(j+1)} - \Gamma\_{\uparrow 0} \right) \end{bmatrix} \tag{64}$$

where ܫ௦ is given by Eq. (51) with ห߷sjห, ห߷sjห, and ߠsሺାଵሻ described by Eq. (25). The other symbols retain their previous definitions.

For a single film bounded by semi-infinite, non-absorbing layers and for ߪଶ=0, Eq. (54) with (64) is reduced into formula presented in [73]. In general, equation (54) with (64) has no analytical solution. However it is possible to calculate ܫீvሺΓଶ, Γଵ, Γଷሻ numerically using the appropriate spatial dependences of ݊ሺݕሻ and ߙሺݕሻ. It was done, for example, in [73] for a single graded-gap CdxHg1 xTe film.

#### **4.3. Spatial Distribution of Radiation Intensity in a Semiconductor Illuminated with Two Beams**

One of the most promising methods of determining values of diffusion length of carriers in amorphous semiconductors is based on the steady state photocarrier grating (SSPG) model [75,76]. This technique uses an interference pattern obtained over the illuminated sample surface when two coherent radiation beams hit the sample at different angles of incidence (Fig. **30**). Due to this interference effect, the sample area between two electrodes consists of many regions of varying concentrations of free carriers. In places of constructive interference, if the incident photons have energy exceeding the energy gap of investigated semiconductors, they are likely to generate excess carriers in contrast to sites of destructive interference, where such excess carriers are not generated. Therefore, in a rough approximation the electrical conductivity (ߪ (of the sample in the direction normal to the interference fringes is represented by a sum of several components, characterizing areas of photoconductivity (ߪ (and so-called dark conductivity (ߪ (

$$
\sigma\_{coh}^{-1} = \sum\_{l} \frac{l\_l}{l} \sigma\_{Pl}^{-1} + \sum\_{l} \frac{l\_l}{l} \sigma\_{Dl}^{-1} \tag{65}
$$

where ݈ and ݈ are lengths of the areas of constructive and destructive interference, and ݈ ൌ ∑ ݈ ∑ ݈ is the distance between electrodes.

**Figure 30:** Graph illustration of the two beams showing an interference pattern in the case of steady state photocarrier grating technique of carrier diffusion length investigations [74].

After the changing polarization of radiation in one of the beams incident upon the sample under constant illumination, the interference effect vanishes and the concentration of free carriers is homogeneous. In this case, the electric conductivity (ߪ (of the sample is simply represented by its photoconductivity evoked by the sum ሺܫଵ ܫଶሻ of the intensities of light in the beams incident upon the sample. In the SSPG method of investigations, the ratio ߪ⁄ߪ of the conductivities of the sample with and without the interference of radiation incident upon the sample depends on the carrier diffusion length L [75]

$$\frac{\sigma\_{\rm coh}}{\sqrt{\sigma\_{\rm Incoh}}} = \sqrt{1 - \frac{c\_0}{\left[1 + \left(\frac{2\pi L}{\Lambda}\right)^2\right]^2}}\tag{66}$$

$$\text{where } \mathcal{C}\_0 = 4\zeta^2 \eta\_0^2 \frac{l\_{10} l\_{20}}{(l\_{10} + l\_{20})^2} \tag{67}$$

Λ ൌ ߣ sin ߶ ⁄ represents the grating period, ߶ is the angle between the beams, ߞ is a power coefficient in the semi-empirical power-law formula (19), and ߟ is a quantity representing an empirical factor [75] between zero and unity that describes the fringe visibility reduced due to partial coherence between the beams, light scattering and mechanical vibration. The other symbols retain their previous definitions.

The sample used in SSPG measurements usually consists of the double layer structure: a thin, isotropic, semiconductor film on a thick, parallel-sided, uniform, isotropic, transparent substrate (Fig. **31**). It is located in the *XZ* plane and is bound in the *Y* direction by two semi-infinite layers. The sample is illuminated with two beams of plane-polarized radiation of wavelength that has components in the wavelength range . The planes of light polarization of the two beams can be parallel or perpendicular, respectively. One of the beams illuminates the sample normally and the second beam impinges upon the sample with an angle of incidence ߶ (Fig. **30**)The radiation intensity of each of the beams is uniformly distributed over the sample surface. The reflections from the air-semiconductor, semiconductor-substrate and substrate-air interfaces are specular. Owing to the variation in thin film thickness ݓଵ, surface roughness, variation in the real part of refractive index ݊ଵ over the illuminated sample area, and the distribution of radiation intensity over the wavelength range, the change Γଵ in the phase of radiation traversing a semiconductor film has the Gaussian distribution (*e.g.* [70,76]) around the most probable value of Γଵ with a standard deviation ߪଵ over the illuminated sample area. Interference of internally reflected radiation occurs in the thin semiconductor film and is negligible in the substrate.

Some part of the radiation incident on the front surface is obviously transmitted through the semiconductor thin-film and then internally reflected from the rear side of the substrate (Fig. **31**). We call this part of the radiation a 'secondary illumination' in contrast to the 'primary (front) illumination'. Assuming that no interference of radiation takes place in the semiconductor substrate, the phases of the waves incident on the semiconductor from the rear are random in comparison to the phases of radiation which illuminate the semiconductor from the front. The sum of the radiation of the multiple reflected beams gives the total intensity ܫv ି of the secondary illumination (Eq. (55)).

**Figure 31:** Schematic representation of radiation propagation in a sample used in a SSPG technique of carrier diffusion length investigations [76] (A, electrode; B, thin film of the investigated material; C, thick, parallelsided, transparent substrate; solid and dashed arrows represent the two beams of light incident on and passing through the sample; the different shadows in the semiconductor film (B) show the relative intensity of the radiation).

To calculate the intensity of the *p* and *s* plane polarized radiation (*i.e.*, with the electric vector in and normal to the plane of incidence) the orientation of its electric field must be taken into account. For the primary illumination of the investigated thin semiconductor film on a thick substrate, the electric fields ܧሬԦ ௦ଵ ା and ܧሬԦ ଵ ା are given by the Eqs. (48). The adequate electric fields ܧሬԦ ௦ଵ ି and ܧሬԦ ଵ ି are described by Eq. (56). The intensity of radiation (in photons) in an ideal semiconductor film illuminated with two beams (incident upon the sample with angles of incidence ߶ and 0°) can be found from the Poynting vector:

$$I\_{\rm v}(\mathbf{x}, \mathbf{y}) = \frac{1}{\tau\_{\rm em}} \frac{\lambda n\_{\rm d1}}{\hbar c} \sqrt{\frac{\varepsilon\_0}{\mu\_0}} \int\_0^{\tau\_{\rm em}} \left[ \left| \vec{\vec{E}}\_{\rm v1}^+(\boldsymbol{\phi}) + \vec{\vec{E}}\_{\rm v1}^+(\mathbf{0}^\circ) \right|^2 + \left| \vec{\vec{E}}\_{\rm v1}^-(\boldsymbol{\phi}) + \vec{\vec{E}}\_{\rm v1}^-(\mathbf{0}^\circ) \right|^2 \right] dt \tag{68}$$

where indices v and v*'* describe the polarization direction of the two incident beams. These indices should be replaced with *p* or *s* for the appropriate polarization direction.

Taking into account the Gaussian distribution of the phase of radiation traversing a semiconductor film, the total intensity of radiation in a semiconductor film illuminated with two beams must be calculated using (68) in the following integral:

$$I\_G(\mathbf{x}, \mathbf{y}) = \int\_0^{+\alpha} \frac{l\_0(\mathbf{x}, \mathbf{y})}{\sigma\_{11}\sqrt{2\pi}} \exp\left[-\frac{(\Gamma\_{10} - \Gamma\_1)^2}{2\sigma\_{11}^2}\right] d\Gamma\_1 \tag{69}$$

Numerical calculations were done [76] to analyze the influence of the optical and geometrical parameters of the sample as well as the experimental conditions on the spatial distribution of radiation intensity in a sample examined with the SSPG method of determining carrier diffusion length. Some of results are shown in Figs. **32** and **33** (values of parameters essential for different sections of the figures are given in Tables **5** and **6**). The values of the optical parameters of amorphous silicon [51] were used to describe the semiconductor film. The value of ܰଶ=ܰଶ=ܰଶ=1.51 was assumed as the refractive index of the substrate.

To simplify the analysis, one can distinguish two important results of the SSPG tests: (A) The two beams that hit a sample have the same polarization. (B) The two radiation beams are plane polarized in normal directions. In the former instance, there is interference of the electromagnetic fields of the two beams, affecting the interference pattern in the illuminated surface of the sample (Fig. **32**). In the latter, no interference occurs between the two beams and the sample is uniformly illuminated at its surface with radiation intensity equaling the sum of the two components (Fig. **33B**).

**Figure 32:** Influence of optical and geometrical parameters of a thin semiconductor film on spatial distribution of radiation intensity in a sample examined with the SSPG method in the case of interference of radiation internally reflected in a semiconductor film [76] (values of parameters essential for different sections of the figure are given in Table 5; s polarized radiation, = 633nm, =0, photons/(m2 1== ,mm 1=2w 1.51,=== ,(s

Fig. **32** shows the influence of the optical and geometrical parameters of a thin semiconductor film on spatial distribution of radiation intensity in a sample examined with the SSPG method in the interference example. The steady light wave is well recognized. To make the figure clearer, the thickness of a semiconductor film was assumed relatively small. The period of this steady light wave and consequently the number of extrema depends on the semiconductor thickness (compare Figs. **32A** and **32B**) and obviously the real part of the refractive index (compare Figs. **32A** and **32D**). The position of maxima or minima of the steady light wave at the semiconductor interface should be especially important if the surface recombination of electrons and holes is faster than the bulk recombination process. The last case is important for photoconductivity [5].


**Table 5:** Values for the curves in Fig. **32**.

The steady light wave vanishes with the increase of the standard deviation ߪ௪ଵ of the thickness of semiconductor film (Fig. **32C**) as well as with the increase of the absorption of light (Fig. **32F**). However, in the first case the decrease of the characteristic spatial oscillations of radiation intensity is stronger near the front surface of a semiconductor (Fig. **32C**). The periodicity of the spatial oscillations remains essentially the same as for ideal interference. For greater values of ߪ௪ଵ the amplitudes decrease with increasing distance from both film surfaces. In this case the spatial distribution of radiation intensity in the *Y* direction becomes relatively smooth in the middle of the film. Yet, even for large ߪ௪ଵ there are relatively large changes of ܫீሺݔ, ݕሻ with increasing distance from the semiconductor surfaces, especially near the back surface (Fig. **32C**). This is a consequence of the accumulation of electric fields of incident and reflected waves close to the surface. This effect cannot be described by the formula derived for the case of negligible interference of radiation internally reflected in a thin film.

An increase of the real part of refractive index of a semiconductor affects the change in intensity of radiation that enters the semiconductor film (compare Fig. **32A** and **32D**). The same is observed in the case of the increase of absorption coefficient for the semiconductor (compare Fig. **32A** and **32F**). In both cases a lower photoconductivity is expected. The spatial distribution and magnitude of radiation intensity in a semiconductor film examined with the SSPG method is sensitive to the ratio of radiation intensities in the two beams that illuminate the sample (compare Fig. **32A** and **32F**). Therefore, the polarization of the oblique illumination beam is also important.

Fig. **33** presents the influence of polarization and angle of incidence ߶ on the spatial distribution of radiation intensity in a sample examined with the SSPG method. Comparing Figs. **32A** and **33C** one recognizes the influence of the high reflection support of the sample (see description of the figures) on the spatial distribution of radiation intensity in a semiconductor film. The increase of ߙଷ must also consider the shadow of the electrode for *x=*115.6 ߤ݉*.* Such a shadow is more

important in cases where there is no interference of the two beams of perpendicular polarization (Fig. **33B**). The position (in *X* dimension) of this shadow depends on the angle of incidence of radiation upon the sample (compare Fig. **33A** and **33C**) as well as on the thickness of the semiconductor film substrate [76] and its refractive index. An increase of the angle between the two beams incident upon a sample decreases the period of the steady-state light grating in the *X*  dimension (compare Figs. **32A** and **33A**). This is an essential feature of the SSPG measurement [74-77].

**Figure 33:** Influence of polarity and angle of radiation incidence on spatial distribution of radiation intensity in a sample examined with the SSPG method [76] (values of parameters essential for different sections of the figure are given in Table 6; photons/(m2 s), n=3.5,=10<sup>6</sup> m-1, w=0.2 m, w=0, n3=1, m-1; other parameters are the same as for Fig. **32**

**Table 6:** Values for the curves in Fig. **33**.


It should be emphasized that even in cases of different polarizations of illumination beams, the spatial distribution of radiation intensity in a semiconductor film can be inhomogeneous both in the *X* and *Y* dimensions (Fig. **33B**). It is worth noting that the steady light wave occurring in homogeneously illuminated film is important for the magnitude of the observable photoconductivity (*e.g.* [70]). The increase of substrate thickness influences the spatial distribution of the radiation intensity in both the *X* direction (Fig. **33A**) and in the *Y* direction. Obviously the wavelength determines the values of optical parameters of the examined material and also strongly affects the interference phenomenon. Therefore the spatial distribution of radiation intensity in a semiconductor film is also strongly dependent on ߣ.

#### **5. PHOTOGENERATION OF FREE CARRIERS**

One can describe the ambipolar transport of photocarriers in a semiconductor in a phenomenological manner [4-6]. In this approach the concept of drift mobility is used, which is an average mobility of all carriers involved in the transport and is thus model independent. The phenomenological theory is based upon the solution of Maxwell's equations, the Poisson equation, the continuity equations and the transport equations. The solution can be obtained analytically only

for special cases. To simplify the consideration one assumes that: a homogeneous semiconductor is placed in a uniform, steady magnetic field; the magnetic field induction ܤሬԦ is so weak that in the dependence of electrical conductivity on ܤሬԦ, the terms with second and higher orders of ܤሬԦ are negligible; all parts of the semiconductor have the same temperature and the carriers are described by the Boltzmann statistics. The aforementioned assumptions are justified in most of the experiments on PEM effect. Some exceptions have been discussed in detail in [6].

The transport through a semiconductor in the presence of a static electric field intensity ܧሬԦ and steady ܤሬԦ under bulk photogeneration is described by the following equations

$$\vec{f}\_e = e\mu\_e n\_e \vec{E} + eD\_e grad(n\_e) - \mu\_{He} \{\vec{f}\_e \times \vec{B}\} \tag{70a}$$

$$\vec{f}\_h = e\mu\_h n\_h \vec{E} - eD\_h grad(n\_h) + \mu\_{hh} \{\vec{f}\_h \times \vec{B}\} \tag{70b}$$

$$\frac{\partial n\_e}{\partial t} = G\_e - R\_e + \frac{1}{e} d \text{l}\nu(\vec{j}\_e) \tag{71a}$$

$$\frac{\partial n\_h}{\partial t} = G\_h - R\_h - \frac{1}{e} d\text{div} \{\vec{j}\_h\} \tag{71b}$$

where ଔԦ and ଔԦ represent the electron and hole current densities, ߤ, ߤு, ߤ and ߤு are drift and Hall mobilities of electrons and holes, respectively, ݊ and ݊ are concentrations of electrons and holes, ܦ and ܦ are the diffusion constants for electron and holes, *e* is the electronic charge, ܩ, ܴ, ܩ, and ܴ are photogeneration and recombination rates of electrons and holes.

In Eq. (70), phenomenological distinction is made between Hall and drift mobilities of electrons and holes, scattering models not considered. In case of degenerate energy bands in the investigated semiconductor, the same equations still apply; however, the Hall and drift mobilities as well as diffusion coefficients for holes are certain weighted averages, as used, for example, in Refs. cited in [6]. It is worth mentioning that relatively few fast holes can make a large contribution to the PEM current or voltage.

The photogeneration rates are given by:

$$G\_e = \beta\_e a\_e l\_v(\mathbf{y}) \quad \text{and} \quad G\_h = \beta\_h a\_h l\_{v(\mathbf{y})} \tag{72}$$

where ܫvሺݕሻ represents the local intensity of radiation (in photons). Such intensity is described, *e.g.*, by Eqs. (54) and (61). The other parameters are the same as in Eq. (15).

In the so-called small-signal approach, a simple model for the recombination mechanisms states that ܴ and ܴ are proportional to the excess carrier density. It acknowledges the fact that no recombination takes place if the carrier density equals the thermal equilibrium value. The resulting expressions for the recombination rates of electrons and holes are given by:

$$R\_e = \frac{\Delta n\_e}{\tau\_e} \quad \text{and} \qquad R\_h = \frac{\Delta n\_h}{\tau\_h} \tag{73}$$

where Δ݊ ൌ ݊ െ ݊ and Δ݊ ൌ ݊ െ ݊ are concentrations of the excess carriers, and ݊ and ݊ are equilibrium concentrations of electrons and holes, respectively. The electron and hole lifetimes ߬ and ߬ can be interpreted as the average times after which excess minority carriers recombine.

In the cases of arbitrary illumination intensities, the recombination rates are represented by much more complicated formulae different for various recombination mechanisms, *e.g.*, for the Auger recombination and for the trap-assisted Shockley-Hall-Read recombination (*e.g.* [4,5]). Additionally, recombination at semiconductor surfaces and interfaces can have a significant impact on the photoelectric and PEM effects. This is because surfaces and interfaces typically contain a large number of recombination centers because of the abrupt termination of the semiconductor crystal which leaves a large number of electrically active dangling bonds. In addition, the surfaces and interfaces are more likely to contain impurities since they are exposed during the device fabrication process.

For cases of small, steady illumination, the boundary conditions at the front and back semiconductor surfaces must be taken into consideration to solve the transport equations. For a parallel-sided sample, which is infinite in the XZ plane, the boundary conditions are:

$$f\_{\rm ey} = e \mathbf{s}\_{1\epsilon} \Delta \mathbf{n}\_{\mathbf{e}} = e \mathbf{s}\_{1\hbar} \Delta \mathbf{n}\_{\mathbf{h}} \quad \text{for } \mathbf{y} = \mathbf{0} \tag{74}$$

$$f\_{\rm ey} = -es\_{2e} \Delta n\_e = -es\_{2h} \Delta n\_h \quad \text{for } \mathcal{y} = \mathcal{W}\_l \tag{75}$$

where ݏଵ, ݏଵ, ݏଶ, and ݏଶ represent recombination velocities for electrons and holes at the front and back surfaces of the *j* semiconductor film, ݆௬ is the *y* component of electron current density.

When the semiconductor sample is placed in a magnetic field ܤሬԦ(0,0,B), the radiation propagates in the XY plane, and if the sample ends in X-direction are short-circuited externally, the so-called short-circuit PEM current which flows through the sample is given by:

$$\mathrm{Id}\_{\mathrm{PEM}} = (\mu\_{\mathrm{He}} + \mu\_{\mathrm{Hh}}) \mathrm{Bl}\_{\mathrm{z}} \int\_{0}^{w\_{f}} \mathrm{j}\_{\mathrm{ey}} \mathrm{dy} \tag{76}$$

where ݈௭ is the width of a sample.

The PC of the sample is described by

$$\sigma\_{\rm PC} = e l\_{\rm z} \int\_{0}^{w\_{\rm j}} [\mu\_{\rm e} \Delta n\_{\rm e}(\rm y) + \mu\_{\rm h} \Delta n\_{\rm h}(\rm y)] d\rm y \tag{77}$$

One can find the solutions for the PEM and PC responses solving Eqs. (70)-(73) with the boundary conditions (74) and (75) after assuming an adequate spatial distribution of light in the investigated sample. For example, in [29] the PEM and PC responses have been analysed in the double layer structure of a single, parallel-sided homogeneous, and isotropic semiconductor film of thickness ݓଵ on transparent, parallel-sided substrate of thickness ݓଶ ب ݓଵ (the conditions (33) have been assumed, too). In this case, for normal illumination of a sample, the distribution of radiation in the

semiconductor film is given by Eq. (59). Hence, the following formulae have been derived (for :(്1ܮଵܭ

$$\begin{split} i\_{PEM} &= (\mu\_{He} + \mu\_{Hb}) Bew\_1 I\_2 \beta\_{PEM} I\_{\mathbb{S}0} \left[ \frac{g\_1}{(K\_1^2 - W^2)R\_P} \{ [W + \mathbb{S}\_2 + (W - \mathbb{S}\_2)e^{-2W} - 2We^{-W}] (\mathbf{X}\_1 + \mathbf{Y}\_1) \} \right. \\ &\left. \begin{split} S\_1 &+ [W + \mathbb{S}\_1 + (W - \mathbb{S}\_1)e^{-2W} - 2We^{-W}] (\mathbf{K}\_1 - \mathbb{S}\_2)e^{-K\_1} - (1 - e^{-K\_1})R\_P \} - \\ \frac{g\_2 K\_1 e^{-W\_1}}{(K\_1^2 - W^2)R\_P} \{ [W\_{\xi 1} (\mathbf{K}\_1 + \mathbf{S}\_2) + W\_{\xi 2} (\mathbf{K}\_1 - \mathbf{S}\_1)e^{-K\_1}] (1 - e^{-W}) - (1 - e^{-K\_1})R\_P \} - \frac{g\_2 K\_1 e^{-K\_1}}{(K\_1^2 - W^2)R\_P} \langle (1 - e^{-W})(1 - e^{-W}) - (1 - e^{-W})R\_P \rangle \\ (1 - e^{-W}) \{ [\Gamma\_1 \sin(\Gamma\_1 - \psi) - \mathcal{S}\_2 \cos(\Gamma\_1 - \psi)] \} W\_{\xi 1} + (\mathcal{S}\_1 \cos\psi - \Gamma\_1 \sin\psi) W\_{\xi 2} + R\_p [\cos(\Gamma\_1 - \psi) - (\mathcal{S}\_2 \cos(\psi))] \\ \cos \psi [\} \} \end{split} \tag{78}$$

ߪ ൌ ሺߤு ߤுሻ݈݁௭ߚ߬ܫ௦ ൴ ௐభ൫ଵିషೈ൯ ൫భ మିௐమ൯ோು ሼ݃ଵሾܹ௦ଶሺܭଵ ܵଵሻ െ ܹ௦ଵሺܭଵ െ ܵଶሻ݁ିభሿ ݃ଶሾܹ௦ଵሺܭଵ ܵଶሻ െ ܹ௦ଶሺܭଵ െ ܵଵሻ݁ିభሿሽ െ భ మ൫ଵିష಼భ൯ భ మିௐమ ሺ݃ଵ ݃ଶ݁ିభሻ యభష಼భ ൫Γభ మାௐమ൯ோು ۃܹሺ1 െ ݁ିௐሻሾΓ<sup>ଵ</sup> sinሺΓ<sup>ଵ</sup> െ ߰ሻ െ ܵଶ cosሺΓ<sup>ଵ</sup> െ ߰ሻሿܹ௦ଵ െ ሺܵଵ cos ߰ െ Γ<sup>ଵ</sup> sin ߰ሻܹ௦ଶۄ െ ܴΓଵሾsinሺΓ<sup>ଵ</sup> െ ߰ሻ sin ߰ሿ ሺߤு ߤுሻ݈݁௭ߚ߬ܫ௦ ቄሺ1െ݁ିభሻሺ݃ଵ ݃ଶ݁ିభሻ యభష಼భ ଶΓభ ሾsinሺΓ<sup>ଵ</sup> െ ߰ሻ sin ߰ሿቅ **(79)**

$$\text{where } R\_P = \{\mathcal{W} + \mathcal{S}\_1\} \{\mathcal{W} + \mathcal{S}\_2\} - \{\mathcal{W} - \mathcal{S}\_1\} \{\mathcal{W} - \mathcal{S}\_2\} e^{-2\mathcal{W}},\tag{80a}$$

$$\mathcal{W}\_{\rm s1} = \mathcal{W} + \mathcal{S}\_1 - (\mathcal{W} - \mathcal{S}\_1)e^{-\mathcal{W}},\tag{80b}$$

$$W\_{s2} = W + \mathbb{S}\_2 - (W - \mathbb{S}\_2)e^{-W},\tag{80c}$$

the ambipolar carrier diffusion constant is given by

$$D = \frac{(n\_d + n\_h)D\_e D\_h}{\left(1 + \mu\_{hh}^2 B^2\right)D\_h n\_d + \left(1 + \mu\_{He}^2 B^2\right)D\_h n\_h} \tag{80d}$$

the effective carrier lifetime deduced from the PEM is represented by

$$\tau\_{PEM} = \frac{n\_a x\_h + n\_h x\_e}{n\_a + n\_h} \tag{80e}$$

the effective carrier lifetime deduced from PC is given by

$$
\pi\_{PC} = \frac{\mu\_a \tau\_e + \mu\_h \tau\_h}{\mu\_a + \mu\_h} \tag{800}
$$

ܹൌݓଵ⁄ܮெ is the dimensionless thickness of a sample, ܮெ <sup>ଶ</sup> ൌ ܦ߬ாெ is the square of effective ambipolar carrier diffusion length that is determined in PEM investigations, and ܵଵ ൌ ெܮ ଵݓ߬ଵݏ <sup>ଶ</sup> ⁄ and ܵଶ ൌ ݏଶ߬ݓଵ ܮெ <sup>ଶ</sup> ⁄ are dimensionless front and back surface recombination velocities. All the other symbols retain their previous meanings.

The spectra of photoconductivity reported in [29] depicted correlation with the interference fringes observed in transmittance of the same sample (Fig. **34**). Therefore, formulae (78) and (79) have

been used in [29] to determine the spectral dependences of QECs (Fig. **3**) and to determine the spectral distributions of different components of absorption coefficient of a-Si:H,F (Fig. **2**). Values of carrier lifetime, diffusion length, and surface recombination velocity have been estimated, too. However, the influence of radiation intensity on optical and recombination parameters of the material has been observed [29]. The same situation has been observed in many experimental cases. For example, Fig. **35** presents the typical amorphous silicon non-linear dependencies of PC on illumination intensity. Fitting of ߪሺܫሻ with the semi-empirical power-law formula (19) allows one to determine the power coefficients (Fig. **35**). Usually, the ߞ depends on photon energy (Figs. **36** and **37**).

**Figure 34:** Optical transmittance (+) and PC current (ൈ) of a 0.76 ߤm thick film of a-Si:H,F *vs.* photon energy (PC responses measured for ܫ=1018 photons/m2 s). Dashed curve-theoretical transmittance calculated for σଵ=0, ݊ଵ=݊ଵ=݊ଵሺߣሻ and ߙଵ=ߙଵ=ߙଵሺߣሻ determined in [29]. Solid curve-effective intensity of radiation which enters the semiconductor.

**Figure 35:** Photoconductivity *vs.* illumination intensity for =632.8 nm () and =488 nm (); solid curves represent semi-empirical relation (19) with ࣀ*=*0.806)6 (for =632.8 nm and ࣀ=0.859)9 (for =488 nm [74].

Knowledge of ߞ is necessary not only in the standard approach to SSPG measurements (*e.g.* [75]) but also in any investigations of photoconductivity. Usually, the PC responses measured for

various photon energies correspond to different illumination intensities (Fig. **36**). Therefore, the PC responses are normalized to different values of constant illumination intensity. The normalized PC can have different spectral characteristics (Fig. **37**). Such differences suggest the influence of illumination intensity and photon energy on values of surface recombination velocities and on carrier lifetimes (Fig. **38**). It is because the recombination rate is a nonlinear function of concentration of the excess carriers; simultaneously the penetration of light into a semiconductor changes with increasing hν. In general, the values of ߞ്1 proof the necessity of using non-linear description of PC (*e.g.* the next Section).

**Figure 36:** Photoconductivity of a 5.694 ࣆm thick film of sputtered a-Si:H *vs.* wavelength and intensity of illumination [32].

**Figure 37:** The power coefficient from the power-law dependence (19) and normalized photoconductivity *vs.*  photon energy [32] (pointed curve, ࣀ ;solid curve, for =3·1017 photons/m2 s, =1.89·10-8 m-1; broken curve, for =5·1015 photons/m2 s, =2.5·10-9 m-1).

### **6. SSPG METHOD OF DETERMINING ELECTRONIC STATES PARAMETERS OF AMORPHOUS SEMICONDUCTORS**

In SSPG investigations of electronic states parameters in semiconductors [74,77], it is convenient to describe the PC of a sample in the form

$$\sigma\_{PC} = \frac{e}{w\_1} \left. \int\_0^{w\_1} \frac{\Lambda}{\int\_0^{\Lambda} \frac{dx}{\mu\_\text{eff} n\_\text{f}(\mathbf{x}, \mathbf{y}) + \mu\_\text{fl} n\_\text{f}(\mathbf{x}, \mathbf{y})}} dy \right. \tag{81}$$

where Λ ൌ ߣ sin ߶ ⁄ represents the grating period.

**Figure 38:** Carrier lifetime *vs.* illumination intensity for different photon energies [32].

The concentrations of excess electrons and holes can be found by solving numerically the set of charge-neutrality condition and the generation-recombination equality. In steady state the following simplification of latter equality is adopted [74]

$$D\_{\varepsilon} \left[ \frac{\partial^2 \ln\_{\varepsilon} \langle \mathbf{x}, \mathbf{y} \rangle}{\partial x^2} + \frac{\partial^2 \ln\_{\varepsilon} \langle \mathbf{x}, \mathbf{y} \rangle}{\partial y^2} \right] + G\_{\varepsilon} = \sum\_{l} \int\_{E\_{\mathbf{v}}}^{E\_{\mathbf{f}}} \{n\_{\varepsilon} K\_{\mathrm{leA}}(E) [1 - f\_{l\Lambda}(E)] - e\_{l\Lambda} f\_{l\Lambda}(E)\} N\_{l\Lambda}(E) dE + \sum\_{l} \int\_{E\_{\mathbf{v}}}^{E\_{\mathbf{f}}} \{n\_{\varepsilon} K\_{\mathrm{leD}}(E) [1 - f\_{l\Lambda}(E)] \} N\_{l\Lambda}(E) dE \tag{82}$$
 
$$\sum\_{l} \int\_{E\_{\mathbf{v}}}^{E\_{\mathbf{f}}} \{n\_{\varepsilon} K\_{\mathrm{leD}}(E) [1 - f\_{k\mathcal{D}}(E)] - e\_{k\mathcal{D}} f\_{k\mathcal{D}}(E)\} N\_{k\mathcal{D}}(E) dE \tag{82}$$

where ܩ is given by Eq. (72), ܰሺܧሻ is the density of states (DOS) per unit energy of the *l*-th species of acceptor-like states at energy E, and ܰሺܧሻ is the DOS per unit energy of the *k*-th species of donor-like states at energy E, as measured upward from the valence-band edge ܧv to the conduction-band edge ܧ. The acceptor-like state can be electrically neutral or negatively charged when it is occupied by electron. The donor-like state can be electrically neutral or positively charged when it is empty for electron.

The coefficients ܭሺܧሻ and ܭሺܧሻ in (82) are the energy-dependent capture-rate constants for electrons to the *l*-th and *k*-th donor species, respectively. Sometimes the capture rates are represented by multiplication of thermal velocity v or v of electrons and holes and the capture cross sections ߪௌ and ߪௌ of the traps for electrons and holes (where idex *i* should be replaced with *l* and *k*, and index *S* must be replaced with *A* and *D* for the acceptor-like and donor-like states, respectively).

For example

$$K\_{\rm leA}(E) = \mathbf{v}\_e \sigma\_{\rm leA} \tag{83a}$$

$$K\_{\rm l\&A}(E) = \mathbf{v}\_e \sigma\_{\rm l\&A} \tag{83b}$$

where ܭ is the rate constant of free hole recombination with captured electron at the *l*-th acceptor-like state.

The coefficients ݁ௌ in (82) are the thermal-emission rates for electrons at *i*-th species (where index *i* should be replaced with *l* and *k*, and index *S* must be replaced with *A* and *D* for the acceptor-like and donor-like states, respectively). For example, the probability of electron emission from the *l*-th acceptor-like trap equals

$$\mathbf{e}\_{le\mathbf{A}} = K\_{le\mathbf{A}}(\mathbf{E}) N\_{\mathbb{C}} \exp\left(\frac{\mathbf{E} - \mathbf{E}\_{\mathbf{C}}}{k\_B \mathbf{T}}\right) \tag{84}$$

where ܰ is the effective density of states at the conduction-band edge.

Under nonequilibrium steady-state conditions, the trap-occupancy function ݂ௌሺܧሻ (*i.e.* the probability of occupation of the *i*-th acceptor-like or donor-like trap by electron, for *S* replaced with *A* or *D*, respectively) is given by the Simmons-Taylor statistics [78,79]

$$f\_{lS}(E) = \frac{n\_e \kappa\_{lieS}(E) + e\_{lhS}(E)}{n\_a \kappa\_{lieS}(E) + n\_h \kappa\_{lhS}(E) + e\_{leS}(E)e\_{lhS}(E)} \tag{85a}$$

where

$$\mathbf{e}\_{h\mathbf{i}\mathbf{S}}(E) = K\_{h\mathbf{i}\mathbf{S}}(E) N\_{\mathbf{V}} \exp\left(\frac{-\mathbf{r}}{k\mathbf{g}\tau}\right) \tag{85b}$$

represents the thermal-emission rate for holes at *i*-th species, ܰ is the effective density of states at the valence-band edge.

In [79] it was shown that (85) is mostly a general statement and is independent of the energy distribution of the traps. It was shown that ݂ௌሺܧሻ can be multivalued at a particular energy without being irregular. For example, if we have three traps positioned at the same energy having different cross sections, then clearly ݂ௌሺܧሻ will take three different values.

The total concentrations of free electrons and holes are given by

$$m\_e(\mathbf{y}) = N\_C \exp\left[\frac{\mathbb{E}\_{F\_C}(\mathbf{y}) - \mathbb{E}\_c}{k\_B T}\right] \tag{86a}$$

$$m\_h(\mathbf{y}) = N\_V \exp\left[\frac{\mathbb{E}\_{\mathbf{y}} - \mathbb{E}\_{Fh}(\mathbf{y})}{k\_B T}\right] \tag{86b}$$

where ܧிሺݕሻ and ܧிሺݕሻ are quasi-Fermi levels for free electrons and holes at the depth *y* in the semiconductor, respectively. Thus, the conduction and valence bands may be regarded, to this

approximation, as single levels with degeneracy ܰ and ܰ placed at the bottom of the conduction-band and at the top of valence-band, respectively.

The equilibrium concentrations of electrons and holes are given by

$$m\_{e0} = N\_C \exp\left(\frac{E\_{F0} - E\_c}{k\_B T}\right) \tag{87a}$$

$$m\_{h0} = N\_V \exp\left(\frac{E\_V - E\_{P0}}{k\_B T}\right) \tag{87b}$$

where ܧி is the equilibrium Fermi energy.

Simultaneously, the charge-neutrality condition is given by

$$n\_h(\mathbf{y}) - n\_e(\mathbf{y}) = \sum\_{l} \int\_{E\_{\mathbf{v}}}^{E\_{\mathbf{f}}} f\_{l\mathbf{A}}(E) \, N\_{l\mathbf{A}}(E) dE - \sum\_{k} \int\_{E\_{\mathbf{v}}}^{E\_{\mathbf{f}}} [1 - f\_{kD}(E)] N\_{kD}(E) dE \tag{88}$$

In the case of discrete trap levels, the DOS per unit energy ܰሺܧሻ and ܰሺܧሻ must be replaced by ܰሺܧሻ ൌ ܰߜሺܧሻ and ܰሺܧሻ ൌ ܰߜሺܧሻ, where ߜሺܧሻ represents the Dirac function, ܰ and ܰ are the total numbers of states in the *l*-th acceptor-like and in *k*-th donor-like state, respectively.

The set of generation-recombination (82) and charge-neutrality (88) equations can be solved at least numerically for the assumed model of the state distributions in mobility gap of a semiconductor. The most generally accepted DOS for undoped or lightly doped a-Si:H includes two exponential band tails arising from the disorder of the continuous random network and the correlated states associated with the dangling bonds (DB) states situated around midgap. The DB center plays an essential role in the recombination of excess carriers in a-Si:H because of its amphoteric nature and its location in energy around midgap. The peculiarity of this defect is that, at equilibrium, it may be neutral, or positively or negatively charged according to the position of the Fermi level. The effective correlation energy of the DB in a-Si was shown to be positive (*e.g.* [80]).

Fig. **39** presents the model structure of energetic gap (so-called mobility gap) of an amorphous semiconductor [81,82]. In [74] it was assumed after [82] that the total density of states *N(E)*  consists of:

exponential tails from conduction and valence bands

$$N\_{1A}(E) = N\_{ct}(E) = \frac{N\_{ct0} \exp[(E - E\_c)/E\_{ct}]}{E\_{ct} \left[1 - \exp\{-E\_g/E\_{ct}\}\right]} \tag{89a}$$

$$N\_{1D}(E) = N\_{\rm vt}(E) = \frac{N\_{\rm vt0} \exp[(E\_{\rm v} - E)/E\_{\rm vt}]}{E\_{\rm vt} \left[1 - \exp\left(-E\_{\rm g}/E\_{\rm vt}\right)\right]} \tag{89b}$$

where ܰ௧ and ܰv௧ are total densities of acceptor– and donor-like states in exponential tails, ܧ௧ and ܧv௧ are characteristic energies of exponential decays of distribution of these states, and ܧൌ ܧ െ ܧv is energy gap.

Gaussian distributions of localized states of donor-like and acceptor-like states of *e.g.*, dangling bonds

$$N\_{2D}(E) = \frac{N\_{2D0}}{E\_{2D}\sqrt{2\pi}} \exp\left[-\frac{(E - E\_{2D0})^2}{2E\_{2D}}\right] \tag{90a}$$

$$N\_{2A}(E) = \frac{N\_{2A0}}{E\_{2A}\sqrt{2\pi}} \exp\left[-\frac{(E - E\_{2A0})^2}{2E\_{2A}}\right] \tag{90b}$$

where ܰଶ and ܰଶ are the integrated DOS in the Gaussian distribution of donor-like and acceptor-like states, ܧଶ and ܧଶ are standard deviations of the Gaussian distributions, and ܧଶ and ܧଶ represent energies to that the Gaussian distributions are pinned.

**Figure 39:** Model of density of electronic states in the mobility gap of a-Si:H (D- , D0 , D+ and U have the same meaning as in [81]).

According to [82] one can assume that capture-rate constants for trapping of free carriers in band tail regions are given by

$$K\_{\rm ct}(E) = \mathbf{v}\_{\rm e} \sigma\_{\rm ct0} \exp[\{E - E\_{\rm c}\} / E\_{\rm ct}] \tag{91a}$$

$$K\_{\rm vt}(E) = \mathbf{v}\_e \sigma\_{\rm vt0} \exp[\left(E\_\rm V - E\right)/E\_{\rm vt}] \tag{91b}$$

where ߪ௧ and ߪv௧ are maximum capture cross-sections of the traps for electrons in the tail of conduction band and valence band, respectively.

The solution of Eqs. (82) and (88) was found in [74] using iterative method of numerical calculations [83,84] assuming the following boundary conditions

$$
\Delta n\_e(\mathbf{x}, 0) = \text{const} \quad \text{for } \mathbf{y} = \mathbf{0} \tag{92a}
$$

݁ܦ݃ݎܽ݀ሾ݊ሺݔ, ݓଵሻሿ ൌ 0 for ݕ ൌ ݓଵ **(92b)**

$$
\Delta n\_e(\mathbf{x}, \mathbf{y}) = \Delta n\_e(\mathbf{x} + \Lambda, \mathbf{y}) \tag{92c}
$$

The value of Δ݊ሺݔ, 0ሻ has been estimated by solving for ݕൌ0 the set of Eqs. (82), (88) and

$$\int\_0^\Lambda \Delta n\_e(\mathbf{x}, \mathbf{0}) d\mathbf{x} = \text{const} \tag{93}$$

The ratio ߪ⁄ߪ of photoconductivities is essential for the SSPG technique because fitting its dependence on angle ߶ between the incident beams allows one to determine the carrier diffusion length [75,76] or DOS parameters of electronic states in semiconductors [74,77]. The numerical calculations were done in [74] to analyze the influence of DOS parameters as well as experimental conditions on ߪ⁄ߪ. The optical parameters of a-Si at *T=*293 K [51] have been used to describe the semiconductor film. The value of ݊ଶ=1.51 was assumed as the refractive index of the substrate. Table **7** presents the values of DOS parameters taken after [82] to the calculations.

The evident influence of Ncto, Nvto, Ect, and Evt of the exponential tails of electronic states in energy gap of the semiconductor on the angular dependence ߪ ߪ ⁄ ሺ߶ሻ was reported in [74]. Each of these parameters affects the range ߶ א ሺ0, ߶ெሻ of angles ߶ such that the nonlinear changes of ߪ ߪ ⁄ ሺ߶ሻ are observed. Values of these parameters also affect the nearly constant ߪ⁄ߪ observed in the wide range of medium ߶.


**Table 7:** Parameters of the DOS distributions of a-Si:H [82].

One can recognize (Fig. **40**) that changes of 2hA and 2hD evoke variations of ߪ ߪሺ߶ሻ⁄ similar to those evoked by Ncto, Nvto, Ect, and Evt. Above all, changing 2hD produces a relatively wide range of angles (߶ெ ൌ 10°) so that the ߪ⁄ߪ ratio increases with the increase of ߶. Meanwhile the two orders of magnitude changes of 2eA and 2eD do not effect significant variations in the ߪ ߪሺ߶ሻ⁄ characteristics. Comparing influences of N2A0 and E2A0 on ߪ ߪሺ߶ሻ⁄ , the dominant significance of N2A0 has been found. Fig. **41** shows the evident influence of both N2D0 and E2D0 on ߪ ߪሺ߶ሻ⁄ *.*

Fig. **42** presents the strong influence of illumination intensity on angular dependence of ratio ߪ⁄ߪ. The parameter ߶ெ (where *i=*1,2,.) in this figure represents the angle for which ߪ⁄ߪ equals 95% of its saturation value. Therefore, magnitude of this parameter describes the range of strong dependence of SSPG results on the angle ߶. The value of ߶ெ increases with increasing illumination intensity (Figs. **42** and **43**). The influence of the illumination intensity on ߶ெ depends on the DOS parameters (Fig. **43**).

**Figure 40:** The influence of the capture cross sections of the traps for electrons and holes 2eA, 2hA2eD, 2hD on angular dependence of ratio coh/incoh [74] (▬▬, 2eA=10-20 m2 , 2eD=10-20 m2 , 2hA=10-21 m2 , 2hD=10-21 m2 ; , 2eA=10-18 m2 , 2eD =10-20 m2 , 2hA=10-21 m2 , 2hD=10-21 m2 ; , 2eA=10-20 m2 , 2eD=10-18 m2 , 2hA=10-21 m2 , 2hD=10-21 m2 ; , 2eA=10-20 m2 , 2eD=10-20 m2 , 2hA=10-19 m2 , 2hD=10-21 m2 ; , 2eA=10-20 m2 , 2eD=10-20 m2 , 2hA=10-21 m2 , 2hD=10-19 m2 ; values of other parameters are given in Table 7).

**Figure 41:** The influence of density N2D0 of DOS in Gaussian distribution, energy E2D0, to which the distribution is pinned and standard deviation E2D on angular dependence of ratio coh/incoh [74] (▬▬,

N2D0=11·1021 m-3, E2D0=0.85 eV, E2D=80 meV; , N2D0=11·1021 m-3, E2D0=1.15 eV, E2D=80 meV; , N2D0=11·1021 m-3, E2D0=0.85 eV, E2D=40 meV; , N2D0=11·1022 m-3, E2D0=0.85 eV, E2D=80 meV; values of other parameters are given in Table 7).

**Figure 42:** The influence of illumination intensity on angular dependence of ratio coh/incoh [74]: ▬▬, 1016 photon/(m2 s); , 1018 photon/(m2 s); , 1020 photon/(m2 s); , 1022 photon/(m2 s); values of parameters describing DOS are given in Table 7; description in the text.

**Figure 43:** Upper limit of range of the angles for that the SSPG results strongly change *vs.* illumination intensity for different values of the integrated DOS in the Gaussian distribution of donor-like states [74] (- N2D0 = 11·1021 m-3; -N2D0 = 11·1022 m-3; values of other parameters are given in Table 7).

Analyzing the results of SSPG measurements one should take into serious consideration the influence of the values of energy gap of the investigated amorphous material (see [74]). In addition, the higher mobility of one type of carrier can have substantial impact on the observed ߪ ߪሺ߶ሻ⁄ dependence. The results of performed calculations did not show evident influence of Nc, Nv, cto, vto, Eac and Eav on the angular dependence of ߪ ߪሺ߶ሻ⁄ .

#### **6.1. Method of Experimental Data Treatment**

Fig. **44** presents the diagram of the apparatus used in [74] for SSPG measurements. Direct current measurements were performed using the Keithley 617 electrometer at room temperature. The samples were illuminated with HeNe (ߣ=632.8 nm) or Ar+ (ߣ=488 nm) lasers. The laser light intensity was changed using neutral filters.

**Figure 44:** Experimental set-up for measuring the diffusion length using SSPG technique [74]: L-laser, Fneutral density filter, BS-beam splitter, R-half wavelength retardation plate, Z1, Z2-mirrors, P-prism, Ssample, U-voltage source, A-electrometer Keithley 617, RK-resistor coupled mechanically with prism, multimeter Keithley 196, PC-computer IBM PC with IEEE-488 card.

Obviously a large number of parameters describing the investigated material cannot be determined using data obtained from one experiment alone. Therefore, taking into account the conclusions presented above, fitting of the angular dependence of the results of SSPG measurements with appropriate theoretical formulae has been used [74] to determine energy levels and densities of acceptor and donor-like states (N2A0, N2D0, E2A0, E2D0) in a-Si:H. Other parameters describing optical properties, recombination and mobilities of carriers, and DOS have been be taken in [74] from other experiments performed on the same semiconductor, *e.g.*, from investigations of optical transmittance and reflectance. Some parameters have been determined by standard investigations of the dependence of PC in uniformly illuminated samples on temperature, wavelength and intensity of radiation [85]. In some cases it was necessary to use typical values of semiconductor parameters measured by other investigators. In [74] the values of parameters given in [82] and [85] have been used.

Fig. **45** presents the evident influence of the optical properties of the back surface of the investigated sample on SSPG results. When radiation was relatively weakly absorbed in the investigated a-Si:H (for ߣ=632.8 nm, ߙଵ=1.9·106 m-1, ߙଵݓଵ=2.69), the metallic foil covering the back side of the sample had reflected the radiation traversing a-Si:H film and the BK-7 substrate. This reflection has an important impact on the measured ߪ ߪሺ߶ሻ⁄ . For strongly absorbed radiation (ߣ=488 nm, ߙଵ=10.6·106 m-1, ߙଵݓଵ=14.84) this effect was not observed. Results shown in Fig. **45** prove that the suggested [74,76] spatial distribution of radiation internally reflected in the sample must be taken into account.

The number of fitted parameters depends on the non-linearity of the measured signal on controlled, independent variables. To obtain relatively strong non-linearity of the ߪ ߪሺ߶ሻ⁄ characteristics, all SSPG results (see Fig. **46**) have been simultaneously least-square fitted with the theoretical dependence

$$\chi^2 = \Sigma\_j \Sigma\_k \Sigma\_l \left[ \frac{\sigma\_{\text{Emb}}(l\_{1kj} l\_{2kj} \lambda\_k \phi\_l)}{\sigma\_{\text{Emb}}(l\_{1kj} l\_{2kj} \lambda\_k \phi\_l)} - \frac{\sigma\_{\text{coh}}(l\_{1kj} l\_{2kj} \lambda\_k \phi\_l \eta\_{0k} D \text{OS})}{\sigma\_{\text{incoh}}(l\_{1kj} l\_{2kj} \lambda\_k \phi\_l \eta\_{0kj} D \text{OS})} \right]^2 \tag{94}$$

**Figure 45:** The influence of illumination wavelength on angular dependencies of coh/incoh of a-Si:H samples with different back support [74] (, =488 nm, backAl foil, L=79(5) nm; , =632.8 nm, backAl foil, L=26(3) nm; , =488 nm, backair, L=81(4) nm; , =632.8 nm, backair, L=44(2) nm).

where index *i* represents different angles ߶ between the two beams incident on the sample*,* index *k* represents different wavelengths ߣ of radiation incident upon the sample, and index *j* describes various illumination intensities ܫଵ and ܫଶ of these parts of radiation that illuminates the sample perpendicularly and obliquely. ߪா and ߪா represent the measured photoconductivities for cases of the same and different polarizations of the beams incident upon the sample. ߪ and ߪ represent the ratio of the photoconductivities (with and without interference of radiation incident upon the sample) calculated using the theoretical model presented above. The theoretical calculations are performed for the suitable values of ܫଵ, ܫଶ, ߶, ߣ, ߙଵሺߣሻ, ݊ଵሺߣሻ, ݓଵ as well as values of parameters describing DOS. Using ߟ) see description of Eq. (67)) the corrected radiation intensity was described as [74]

**Figure 46:** Influence of wavelength and intensity of illumination on angular dependencies of coh/incoh for a-Si:H sample [74] (A, =632.8 nm; B, =488 nm; , I1+I2=4.64·1021 photon/(m2 s); , I1+I2=4.08·10<sup>20</sup> photon/(m2 s); , I1+I2 = 2.66·1019 photon/(m2 s); , I1+I2=4.64·1018 photon/(m2 s); , I1+I2=6.5·1021 photon/(m2 s); , I1+I2=1.72·1021 photon/(m2 s); , I1+I2=7.34·1020 photon/(m2 s); , I1+I2=1.36·10<sup>20</sup> photon/(m2 s); , I1+I2=8.2·1019 photon/(m2 s); , I1+I2=6.04·1019 photon/(m2 s); , I1+I2=1.02·10<sup>19</sup> photon/(m2 s); Solid curves: the fitted theoretical dependence, the values of the fitted parameters are given in Tables 8 and 9).

$$I\_D(\mathbf{x}, \mathbf{y}) = I\_a(\mathbf{y}) + \eta\_0 [I\_G(\mathbf{x}, \mathbf{y}) - I\_a(\mathbf{y})] \tag{95}$$

$$\text{where } I\_a(\mathbf{y}) = \frac{1}{\iota} \int\_0^l I\_G(\mathbf{x}, \mathbf{y}) \, d\mathbf{x} \tag{96}$$

Minimization of ߯<sup>ଶ</sup> was done in [74] numerically using the stepping method in a multidimensional space [86]. The appropriate calculations were done using the HP-UX Zeus B. 10.20 C 9000/800 machine. The success of using the least square method for non-linear problems depends on the choice of good starting points. In the described case [74], the information about some of the material parameters obtained from other measurements mentioned above were used. Table **8** presents the used initial values of the fitted parameters. Solid curves in Fig. **46** represent theoretical dependencies ߪ ߪ ⁄ ሺ߶ሻ calculated for the fitted values of semiconductor parameters presented in Table **8**, too. Table **9** includes the fitted values of ߟ that decrease with decreasing illumination intensity. It can be interpreted as follows: For weak illumination, the ratio of signal to noise decreases.


**Table 8:** Values of DOS parameters determined in the presented SSPG measurements.

**Table 9:** Values of empirical parameters 0 obtained from simultaneous fitting of all the experimental results represented in Fig. **46** with theoretical dependences described in the text.


The values from Table **8** have been used to calculate the energetic distribution of electronic states in mobility gap of the investigated a-Si:H (Fig. **47**). Such calculated DOS (solid curve in Fig. **48**) is somehow different from the DOS evaluated from the standard photoconductivity measurements [85] (*i.e.*, the measurements of PC as a function of temperature, wavelength and intensity of

radiation). However, it should be noted that the last DOS parameters (used as initial values in our minimization procedure) give ߪ ߪሺ߶ሻ⁄ characteristics different from the experimental data (Fig. **49**).

**Figure 47:** The energetic spectrum of density of electronic states in the mobility gap of a-Si:H obtained from SSPG measurements [74]: (▬▬, the exponential acceptor-like conduction-band tail, , the Gaussian distribution of acceptor-like states, , the Gaussian distribution of donor-like states, , the exponential donor-like valence-band tail).

**Figure 48:** Total energetic spectrum of electronic states in the investigated a-Si:H [74] (▬▬, density of electronic states determined using SSPG methods; , density of electronic states determined using the standard PC method of investigations [85]).

**Figure 49:** Comparison of the experimental () angular dependencies ofcoh/incoh for sample of a-Si:H with the theoretical dependencies calculated for different parameters [74] (▬▬, the fitted parameters that values are given in Tables 8 and 9; , the initial values of parameters presented in Table 8 and 0=0.97; I1+I2=6.5·1021 photon/(m2 s); =488 nm).

**Figure 50:** Diffusion length of excess carriers *vs.* illumination intensity for different wavelengths of the radiation incident upon the a-Si [74] ( = 632.8 nm () and = 488 nm (); description in the text).

Fig. **50** presents values of the diffusion lengths evaluated using Eq. (66) applied in the standard method of SSPG measurements. This evaluation is possible because in [87] it has been shown that the dc measurements can be applied in the SSPG technique.

It should be underlined that values of *L* calculated using the standard SSPG technique differ even more than 40% when the a-Si:H sample has different supports (see the results for ߣ=632.8 nm in Fig. **50**). The obtained decrease of *L* with increasing illumination intensity is rational and can be easily explained by the increase of recombination processes with the increase of excess carrier concentration.

Therefore, the spatial distributions of light intensity in semiconductors used in solar cells as well as inhomogeneities of their optical parameters as mentioned above should be taken into consideration.

#### **ACKNOWLEDGEMENT**

The author is indebted to Dr. M. Kępińska of the Silesian University of Technology, Katowice (Poland) for helpful discussions and her aid in preparing this paper.

### **CONFLICT OF INTEREST**

The author(s) confirm that this chapter content has no conflict of interest.

#### **REFERENCES**






© 2013 The Author(s). Published by Bentham Science Publisher. This is an open access chapter published under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/legalcode

## **Electrical Properties of Semiconductors**

**Nicola Pinto\* , Marco Ficcadenti<sup>+</sup> and Lorenzo Morresi**

*University of Camerino, School of Science and Technology, Physics Division, Via Madonna delle Carceri 9, Camerino, 62032, Italy* 

**Abstract:** The accurate measure of semiconductor electrical properties is a fundamental step for the design and the correct operation of any electronic device. The electrical performance of any device will depend on how the carriers move inside the semiconductor lattice. The measure of the resistivity, the concentration of shallow and deep states, the charge carrier mobility, *etc.*, allow for the design of new and advanced functionalities and for improvement in current device technology. In this chapter we will give a brief overview of the main electronic transport coefficients and experimental techniques used to investigate semiconductor materials and the main solar cell parameters. We have limited our attention to the most common and reliable techniques. Our work has been organised into seven sections. The first and second sections define the conductivity and the mobility of any material in terms of its band structure and looks at some semiconductor properties and the material doping. The third and fourth sections illustrate the main scattering mechanisms of charge carriers in a semiconductor and several experimental techniques to measure thin film resistivity, respectively. The fifth section introduces the Hall effect and defines the Hall coefficient and the Hall mobility, with a description of an experimental method to measure these. In the sixth section we report a brief analysis of deep state defects and we describe the DLTS technique to reveal them in a semiconductor lattice. Finally, in the seventh section we describe the current-voltage technique commonly used to measure the main solar cell parameters.

**Keywords:** Electrical Conductors, Resistance measurement, Conductivity tensor, charge carrier scattering, Hall mobility, Hall coefficient, van der Pauw geometry, Deep Level Transient Spectroscopy, Current-voltage, Solar cell electrical parameters.

### **1. INTRODUCTION**

One of the main physical properties of any material is its ability to conduct an electrical current. Depending on the nature of the material, its temperature, dimension and shape, applied electric field, *etc.* the current can span several orders of magnitude.

A parameter used to classify the attitude of materials to conduct a current is the electrical conductivity, , (-1cm-1 or Scm) expressed as a function of the charge carrier density, *n*, (cm-3) the electron charge, *e*, (C) the effective electron mass, *m\** , by the relation [1]:

$$
\sigma = n e^{2} \left< \tau\_{\;m} \right> \Big/ \stackrel{\*}{m} = n e \mu
$$

**(1.1)** 

**\*Address correspondence to Nicola Pinto:** University of Camerino, School of Science and Technology, Physics Division, Via Madonna delle Carceri 9, Camerino, 62032, Italy; Tel: +48 0737 402515; Fax: +48 0737 402853; E-mail: nicola.pinto@unicam.it

+ Now at CESI SpA, Via Rubattino 54, 20134 Milan, Italy.

 This unit is preferentially used instead of (m)-1 or Sm, this last being the unit of measure in the SI.

> **Roberto Murri (Ed) © 2013 The Author(s). Published by Bentham Science Publishers**

where *<sup>m</sup>* is the average value of the momentum relaxation time of the carrier, and (cm2 /Vs) is the so called drift mobility, related to the above mentioned quantities by:

$$\mu = e \left< \tau\_m \right> / m^\* \tag{1.2}$$

The mobility represents the average velocity gained by a charge carrier in an applied electric field of 1 V/cm. The mobility is another relevant electronic transport coefficient which may provide important physical information about the scattering mechanisms active in the semiconductor material, as will be detailed in the section 3.

According to the value of the conductivity, materials are conventionally divided into three groups: conductors, semiconductors, and insulators (or dielectrics). The room temperature conductivity of different kinds of materials spans more than 25 orders of magnitude. In fact, taking into account the conductivity of superconductors, measured at low temperatures, the conductivity can cover about 40 orders of magnitude1 . This is the largest known variation in a physical property.

The electrical behaviour exhibited by the three classes of materials can be explained in terms of their band structure [2]. In particular, according to quantum theory, an electric current can flow thorough a material if it has a partially filled electron band (the so called conduction band). Electrons can then be lifted slightly above the Fermi energy into an allowed and unfilled energy state. This permits them to be accelerated by an electric field, thus producing a current. However, only those electrons that are close to the Fermi energy can participate in the conduction process. The number of electrons near the Fermi energy depends on the density of available electron states. In terms of a quantum mechanic description, the conductivity yields the following equation:

$$
\sigma = \frac{1}{3} e^2 \mathbf{v}\_F \pi N \left( E\_F \right) \tag{1.3}
$$

where *<sup>F</sup> v* is the velocity of the electrons at the Fermi energy (the so called Fermi velocity) and *N E <sup>F</sup>* is the density of filled electron states (called the population density) at the Fermi energy.

#### **1.1. Behaviour of Insulators and Semiconductors**

Insulators and semiconductors at very low temperatures (ideally at 0 K) have a completely filled valence band (VB) and a completely empty conduction band (CB), which results in a virtually zero population density (Fig. **1**).

Thus, in insulators, the conductivity is virtually zero at all but very high temperatures. A similar result holds for semiconductors near absolute zero.

Focussing attention on the behaviour of semiconductors, their unique and technologically relevant properties can be deduced by their band structure (Fig. **1**).

<sup>1</sup> For superconductors conductivity a value of 1020 Scm has been assumed.

**Figure 1:** Schematic of a band diagram showing the energy levels filing for a semiconductor, near 0 K, and for an insulator. *Eg* represents the amplitude of the energy gap of the material.

At 0 K, the VB, completely filled with valence electrons, is separated by a gap, *Eg*, (called energy gap or forbidden band) from the completely empty conduction band. Quantum mechanics prevents electrons from residing in the gap between these bands.

The *Eg* values range from few tenths of eV (*e.g.* for compound materials of groups IV-VI) to more than 3 eV (*e.g.* GaN, ZnS, ZnO, *etc.*) depending on the semiconductor material.

Since at 0 K the valence band is completely filled (electrons are not allowed to move in empty energy states), while the conduction band contains no electrons at all (empty states), the semiconductor material behaves as an insulator.

Raising the semiconductor temperature above 0 K causes a sizeable change in conductivity. In fact, some electrons may be thermally excited across the band gap, passing from states near the edge (top) of the VB to empty states available in the CB. The number of these electrons is generally extremely small and will depend exponentially on the temperature and energy gap values of the semiconductor. Specifically, about one out of every 1013 atoms contributes an electron at room temperature. Nevertheless, this number is large enough to cause some conduction and the conductivity increases according to the relation (1.1). The mobility of electrons is substantially impaired by interactions with impurity atoms, crystallographic defects and phonons.

Hence, the conductivity for semiconductors increases exponentially with rising temperature due to the exponential increase of the charge carrier concentration in both bands. This is in marked contrast to metals and alloys, for which the conductivity decreases with temperature.

However, the conduction process in semiconductors is not uniquely due to electrons. In fact, as a consequence of thermal excitation of valence electrons from the VB to the CB, some empty states have been left behind, which allows additional conduction to take place in the valence band. The empty states are called electron holes or simply holes. From a quantum mechanical point of view

these holes are considered, and indeed effectively behave like, positively charged carriers. They can freely move in the VB providing there is some conduction. This hole current is directed in the opposite direction with respect to the electron one.

The total conductivity is a sum of both contributions and the process is called intrinsic conduction. The material involved is termed an intrinsic semiconductor since no foreign (impurity) elements are involved.

The Fermi energy of intrinsic semiconductors is located near the centre of the gap since it can be considered the average of the electron and the hole Fermi energies.

#### **1.2. Semiconductor Doping**

For the useful and correct operation of any electronic device based on a semiconductor material, a relatively high charge carrier concentration (either electrons or holes) is required. This can be achieved by adding impurity atoms to the semiconductor lattice host. For example, very few atoms of Group-V elements, called donors, added to the silicon can significantly lower its conductivity. Donor dopants such as phosphorous (P) or arsenic (As) are commonly utilized as substitutional atoms in a ratio of about 1 dopant every 10<sup>5</sup> ÷ 10<sup>7</sup> atoms of the host semiconductor (Fig. **2**).

**Figure 2:** Two-dimensional representation of a silicon lattice (covalent bonds) with a phosphorus atom substituting a regular lattice atom.

Since phosphorous has five valence electrons, that is, one more than silicon, the extra electron called the donor electron is only loosely bound. The binding energy of an electron of a dopant element will depend on the semiconductor host material [3]. For example, phosphorous donor electrons in a silicon matrix have a binding energy of about 0.045 eV. Thus, the donor electrons can be disassociated from their nuclei by only a slight increase in the thermal energy. In fact, at room temperature all donor electrons have already been excited into the conduction band.

#### *Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **247**

Similar arguments can be used to explain the *p*-type doping in a semiconductor. For example adding a Group-III element (B, Al, Ga, *etc.*) to silicon or germanium will cause an excess of free holes in the material and then an increase of the semiconductor conductivity. The *p*-type dopant, called acceptor, will introduce empty energetic levels just above the VB edge. At RT the acceptor levels, occupied by thermally excited electrons coming from the VB, will leave empty states in the VB. These last will behave as positively charged carriers (*i.e.* electron holes) which can contribute to the conduction process.

It is worthwhile noting that electrons and holes differ not only for the sign of the electric charge. In fact, their effective mass2 :

$$m^\* = \hbar^2 \left| \frac{d^2 E\left(k\right)}{dk^2} \right. \tag{1.4}$$

will depend on the semiconductor band structure, with electrons having an effective mass generally lighter than that of holes. Hence, the mobility of electrons will be generally higher than that of holes in the same material.

For example, the gallium arsenide (GaAs) is a compound semiconductor, made of Group-III and Group-V elements, exhibiting interesting properties with respect to the Group-IV materials like silicon or germanium. In fact, its larger electron mobility aids in high-speed applications. Moreover, GaAs is of some technological interest since it is a direct band gap material, with a wider band gap than Si and Ge, allowing for the fabrication of optoelectronic devices like LED, lasers, *etc.*

Further, the ionization energies of donors (acceptors) impurities in GaAs are one order of magnitude smaller than in silicon, which ensures complete electron (hole) transfer from the donor (acceptor) levels into the conduction (valence) band even at relatively low temperatures. However, GaAs is about ten times more expensive than Si and its thermal conductivity is smaller. Other compound semiconductors include II-VI combinations, such as ZnO, ZnS, ZnSe, or CdTe, and IV-VI materials such as PbS, PbSe, or PbTe. Silicon carbide, a IV-IV compound with a band gap of about 3 eV, can thus be used in devices operating at high temperatures (up to 700°C) before intrinsic effects set in.

#### **2. CONDUCTIVITY TENSOR**

If we consider a weak electric field applied to a semiconductor, with or without a magnetic field, the current density, *j* , induced in the material [4, 5] will follow the microscopic relationship:

$$\left| \vec{J} \right|\_{l} = \sum\_{m} \sigma\_{lm} \left( \vec{B} \right) \left| \vec{E} \right|\_{m} \tag{2.1}$$

<sup>2</sup> Strictly speaking, the effective mass is a tensor with components 2 2 . *m Ek k k ij i j*

where *lm* are the components of the electrical conductivity tensor, , depending on the magnetic field *B* eventually applied. The electrical conductivity is a second-rank tensor, symmetric since its components *lm* obey the Osanger relation [6]:

$$
\sigma\_{lm}\left(\vec{B}\right) = \sigma\_{lm}\left(-\vec{B}\right) \tag{2.2}
$$

However, for semiconductors with a cubic symmetry, and at low fields, the conductivity tensor reduces to the form [1]:

$$
\underline{\sigma} = \begin{pmatrix}
\sigma\_{\text{uv}} & \sigma\_{\text{vy}} & 0 \\
\sigma\_{\text{uv}} & \sigma\_{\text{vy}} & 0 \\
0 & 0 & \sigma\_{\text{zu}}
\end{pmatrix}
\tag{2.3}
$$

assuming that *B* has been applied in the *z* direction. We note that the conductivity component in the z direction is unaffected by the field *B* , as it does not generate any force in its own direction. The other two diagonal components *xx* and *yy* are equal to each other due to symmetry. Also, the non diagonal components *xy* and *yx* would be odd functions of the magnetic field because the forces in the cross directions due to the magnetic field are proportional to it. Considered that *xy* and *yx* are odd functions of *B* and holding the Osanger relation (2.2), it follows that:

$$
\sigma\_{xy} = -\sigma\_{yx} \\ \tag{2.4}
$$

The current density *j* may be expressed as follows:

$$\begin{aligned} \dot{j}\_x &= \sigma\_{xx} E\_x + \sigma\_{yy} E\_y\\ \dot{j}\_y &= -\sigma\_{xy} E\_x + \sigma\_{yy} E\_y\\ \dot{j}\_z &= \sigma\_{zz} E\_z \end{aligned} \tag{2.5}$$

where *Ex*, *Ey* and *Ez* are the components of the electric field in the three directions. Since, in an actual experiment the sample is generally rectangular in shape, with the current flowing along one direction (*e.g. x* direction), we can assume that *jy* = 0. Hence from the (2.5) we get:

$$E\_y = \sigma\_{xy} E\_x \Big| \sigma\_{yy} \tag{2.6}$$

However, considering that the current direction is more easily measured than the field direction (*e.g.* by means of a long thin sample with leads at the ends), the resistivity is another physical quantity of interest. The resistivity tensor, , is the inverse of the conductivity tensor:

$$
\underline{\underline{\sigma}} = \underline{\underline{\sigma}}^{-1} \tag{2.7}
$$

whose components are defined by:

$$E\_l = \sum\_{m} \rho\_{lm} j\_m \tag{2.8}$$

#### *Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **249**

An exception is the Corbino disk geometry [7] in which the components of the conductivity tensor are measured directly.

In general, for several practical reasons it is not always possible to identify the different components of the conductivity of a semiconductor material. Therefore, the experimental measure of the conductivity (or resistivity) is an average value characteristic of the investigated material under well-defined parameters of measure (temperature, voltage o current applied, *etc.*) In these cases, the sample conductivity (or resistivity) is considered as a scalar quantity and holds the following relations:

$$
\Box f = \sigma E \tag{2.9}
$$

$$
\sigma = 1/\rho \tag{2.10}
$$

with the relations (1.1) and (1.2) are still valid.

In real semiconductors, electrons and/or holes can contribute to the conduction process simultaneously.

If this condition is present, and we assume that both the charge carriers in different bands do not interact with each other and that the magnetic field eventually applied has a weak intensity, the conductivity is independent of the magnetic field intensity and is expressed by the relation:

$$\sigma = ne\mu\_e + pe\mu\_h$$

where *n*, *p*, *e* and *<sup>h</sup>* are the electron and hole concentration, and electron and hole mobility, respectively. The general relations accounting for the thermal effects and the magnetic field are reported in the reference [8].

### **3. SCATTERING MECHANISMS OF CHARGE CARRIERS**

In any conducting material, the motion of charge carriers is hampered by several collision processes with crystalline "imperfections" [9-11] which will limit their average drift velocity and then the carrier mobility. The collision process (also known as scattering mechanism) is the result of an interaction between the carrier wave function and the potential associated with the imperfections.

The nature of these collision processes can be very different and their contribution to the overall mobility will be generally dependent, among other factors, on the temperature range considered. Hence, a measure of the charge carrier mobility as a function of the temperature affords greater knowledge of the electronic transport mechanisms active in the semiconductor material. In the following sections a summary of the main scattering mechanisms will be briefly outlined.

### **3.1. Neutral Impurity Scattering**

Collisions of charge carriers with impurity atoms are those most commonly found in a semiconductor. The presence of impurities in the material lattice must be considered an

**(2.11)** 

unavoidable consequence of their growth process. In fact, any growth or deposition process creates imperfections in the lattice structure such as crystallographic defects (dislocations, stacking faults, point defects, *etc.*) and impurities (neutral or ionized). These last can be formed either as substitutional (*i.e.* in a crystal position of the host lattice) or interstitial atoms (*i.e.* in any place inside the lattice structure).

From an energy point of view, defects and impurities will introduce energy levels in the energy gap of the material. At very low temperatures (around liquid helium temperature) these impurities are neutral and the carrier mobility is independent of the temperature [12]:

$$
\mu = \frac{e}{20a\_\text{g}\hbar\varepsilon N^\circ} \frac{m^\circ}{m\_\text{o}} \tag{3.1}
$$

where <sup>B</sup> *a* is the Bohr radius, the dielectric constant and *N* the impurity atom density, *m\** the effective electron mass (see Eq. 1.4) and *m*0 the electron mass.

The scattering mechanism caused by neutral impurities is difficult to detect experimentally because it is generally accompanied by other collision processes, such as ionized impurity scattering and phonon scattering. The cyclotron resonance technique is generally used to get information by this scattering mechanism [1].

#### **3.2. Ionized Impurity Scattering**

Above few Kelvin of temperature, the atoms of impurities have a finite probability for ionization and the carrier concentration will increase with the temperature increase. An electron approaching a charged impurity will be deflected from its trajectory, *i.e.* it will undergo a scattering process caused by ionized atoms.

Depending on the model used, several expressions for mobility have been found [1]. In any case, independently of the model used, the temperature dependence of the mobility is always the same and expressed by the relation:

$$
\mu\_i = aT^{\frac{9}{2}}\tag{3.2}
$$

where *a* is a quantity almost independent of the temperature but inversely dependent on the total ionized impurity concentration [1].

At impurity concentration values ranging from 1017 to 1018 atoms/cm3 , the different theoretical expressions can differ markedly [1]. A review of the collision processes by ionized impurities scattering can be found in reference [13].

#### **3.3. Scattering by Phonons**

Charge carriers can also be subject to another relevant scattering mechanism produced by lattice vibrations. As we know from quantum mechanics [14], the lattice vibration can be described as lattice particles called phonons whose nature will depend on vibration types. The scattering of charge carriers by phonons will differ depending on the phonon types.

#### *Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **251**

The phonons are quasi particles which follow Bose-Einstein statistics and are divided into two branches, acoustical and optical. They interact with electrons as particles obeying the principles of momentum and energy conservation.

For the acoustical branch, both longitudinal (LA) and transverse (TA) acoustic vibrations can set; these phonons are called acoustic phonons. Similarly, in the optical branch both longitudinal (LO) and transverse (TO) optical vibrations can be found; the corresponding phonons are called optical phonons.

#### **3.4. Acoustic Deformation Potential Scattering**

In this specific interaction of acoustic phonons with electrons, phonons generate a perturbing potential, changing the distance among the lattice atoms and then affecting both the energy gap and the edges of the conduction and valence bands. These changes from site to site of the crystal will produce a potential discontinuity, called deformation potential, whose magnitude is proportional to the lattice strain caused by the phonons. Consequently, the interaction of the charge carriers with phonons will be called acoustic deformation potential scattering.

The temperature dependence of the electron mobility is expressed by the relation:

$$\mu = A \left( m^\* \right)^{-\frac{\beta}{2}} \left( k\_\text{\text{\textquotedblleft}t} T \right)^{-\frac{\beta}{2}} \tag{3.3}$$

where *A* is constant quantity, depending on the semiconductor material considered. The relation shows a mass dependence of the mobility. Hence, high mobility values will be obtained by semiconductors with smaller effective mass. For example, in an *n*-type Ge sample at 100 K, the mobility attains a value of 3×104 cm2 /Vs. In any case, at higher temperatures the contribution to the collision processes by optical deformation potential scattering (see the next subsection) modifies the exponent of the temperature in the mobility expression. It has been found on experimentation that the mobility is proportional to 1.67 *T* [9].

Even if acoustic deformation potential scattering is essentially an elastic process, at high intensity electric fields the mobility becomes field strength dependent [9, 11].

#### **3.5. Piezoelectric Scattering Mechanism**

The second perturbing potential caused by acoustic phonons involves compound semiconductors having different atoms (*e.g.* SiC) with a partial or a complete ionization. In this case, a piezoelectric field will be created by the periodic displacement of the lattice atoms. Field intensity, depending on both the position of the atoms in the crystal and the system symmetry, will be stronger in lower symmetry systems. This kind of collision process is called piezoelectric scattering and is relevant for compound semiconductors, below RT in the low-medium range of temperature (Fig. **3**).

The mobility for non degenerate thermal carriers is expressed by [15]:

$$
\mu = A \left( m^\* \right)^{-\frac{3}{2}} \left( k\_\text{B} T \right)^{-\frac{1}{2}} \tag{3.4}
$$

where ' *A* is a quantity depending on the semiconductor material.

In a temperature range of around 100 K, piezoelectric scattering competes with the acoustic (nonpolar) collision process, this last being the main scattering mechanism in semiconductors with partly ionic bonds.

**Figure 3:** Mobility as a function of the temperature for a sample of *n*-type GaAs. Triangles: experimental data; continuous line: theoretical contributions to the overall (combined) mobility taking into account different scattering mechanisms (After [16]).

In a pure polar semiconductor, such as GaAs with a very low density of dislocation and crystallographic defects, the piezoelectric scattering may be the dominant process at low temperatures (about 10 K) resulting in a mobility value about five times lower than that dominated by acoustic deformation potential scattering (Fig. **3**).

#### **3.6. Optical Deformation Potential Scattering**

In non-polar semiconductors, charge carriers may be scattered by longitudinal optical phonons. Due to the higher values of the phonon energies which are comparable to the thermal carrier energies, this kind of collision process must be treated as inelastic. Therefore, scattering rates for transitions from a state *k* to a state *k q* or to a state *k q* must be considered different.

In general, the expression for the mobility will depend on different parameters such as the electric field intensity and a function of the ratio between the Debye temperature and the sample temperature [9, 11].

#### **3.7. Polar Optical Scattering**

The scattering process between carriers and optical phonons takes place in polar semiconductors (*e.g.* GaAs), similar to piezoelectric scattering for acoustical phonons. As mentioned above, the inelastic nature of the electron-phonon interaction should not allow for a momentum relaxation time. However, using an approximation [9, 11] it is possible to derive an expression for depending on the Debye temperature, :

$$
\mu = \vec{A}'\vec{e}^T\tag{3.5}
$$

where *A"* is a constant quantity for a given material. The computed values of the mobility are comparable to the experimental values, although at temperatures lower than 100 K, the main scattering mechanisms in GaAs, and in general in compound materials, is still due to impurity scattering, making it difficult to check the equation (3.5).

The experimental behavior of the mobility *vs. T* for a GaAs crystal has been reproduced in the Fig. **3***,* in the range from about 4 K to about 100 K. The figure also reproduces the contribution to the overall mobility of several different scattering mechanisms as outlined in the previous subsections.

### **4. METHODS OF MEASUREMENT**

The measurement methods for electrical conductivity can be divided into two main classes: methods that use contacts and those that do not (contactless).

Reviews of the electrical characterization of semiconductors, both for majority and minority carriers, can be found in [17-19].

In general, contact methods require suitably prepared samples with ohmic contacts fabricated on the sample surface or the use of point probes.

The contactless methods do not generally require electrical contacts. However, each method presents advantages and drawbacks. Although electrical characterization is considered a non destructive technique, ohmic contacts and probe methods may render the sample unsuitable for further use. This is especially the case with ohmic contacts, which require a very good mechanical adhesion of the metallic alloy onto the sample surface. Such adhesion is frequently assured by thermal treatment of the contacted specimen. The contactless methods have no deleterious effects.

Among the probe methods, spreading resistance has a much higher spatial resolution ( 10 m) than the four-point probe techniques (~ 1 mm), but is not an absolute method (*i.e.* it requires calibration using standard samples) [18]. In several cases, the resistivity and the Hall effect measurements are combined in the same experimental set up, allowing for the evaluation of different physical parameters of the investigated material.

By extending the measurements over a wide temperature range, from few Kelvin to about several hundreds of Kelvin above RT, sample parameters can be derived, such as the concentration of electrically active donor, *ND*, and acceptor, *NA*, dopants and their energy levels, *D* and *A*, respectively. One common assumption concerns the spatial uniformity of the electrical properties. In practice, considerable attention must be devoted to the methods of measuring the spatial variation of carrier density and mobility, establishing their "profiles".

Depending on the application, the measurement techniques involve different sample geometry and/or experimental approaches. The bar geometry (Fig. **4**) (or bridge samples) and the van der Pauw geometry [20] belong to a first group. The four-point probe and the spreading resistance methods [18] belong to a second group.

**Figure 4:** Schematic of a Hall bar samples. Current is sourced along the bar length while the voltage is measured along the side arms. The six arms Hall bar geometry allows for annuling the voltage offset eventually measured in absence of any current applied. The same bar geometry allows to measure the Hall coefficient by applying a magnetic field orthogonal to the sample surface.

Finally, a third group involves contactless methods using power dissipation from radio frequency or microwave sources [18].

On measurements and data interpretation involving thin epitaxial films careful consideration must be given to corrections for conduction in the substrate, while the interpretation of the probe measurements requires a reconstruction of the current distribution [21].

"Ohmic" contacts are required when one is using two terminals, but even with four terminals, it is advisable to use good ohmic contacts wherever possible. A comprehensive review of ohmic contacts is given in [22].

Finally, it is worthwhile mentioning that cracks and voids in the material lead to a local change in conductivity which can be detected by conductivity probes.

#### **4.1. Contact Methods**

#### *4.1.1. Bar Geometry*

A geometry to directly measure the semiconductor resistivity makes use of a bar sample (Fig. **4**) having a uniform cross-section along its length. A constant current, *I*, is supplied through the bar length by way of ohmic contacts covering the two ends of the bar and, under the assumption of uniform current distribution, the voltage drop, *V*, is measured between two facing side arms. This geometry avoids arithmetical corrections in converting measured resistance into resistivity, using Ohm's law.

The resistance *R* is then calculated according to Ohm's law:

$$R = V \left| I \right. \tag{4.1}$$

#### *Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **255**

The semiconductor material conductivity is determined by the measured value of *R* and its dimensions (length *l,* width *w,* and thickness *ts*). From these data the value of can be directly obtained [1]:

$$
\sigma = l / R \text{wt}\_s \tag{4.2}
$$

#### *4.1.2. Van der Pauw Geometry*

Several steps are required for the preparation of bar-shaped samples. The theorem published by van der Pauw [20] provides resistivity measurements in an arbitrarily shaped, uniform and plane sample, with four line contacts placed on its edge. The location of the contacts along the sample border is arbitrary. The theorem also assumes a uniform thickness and a homogeneous doping level. Moreover, the material must not contain holes.

With reference to Fig. **5**, the sample resistivity can be obtained by supplying a constant current between two adjacent contacts (*e.g.* 1 and 2) and then measuring the voltage *V* between another two contacts (*e.g.* 3 and 4). To obtain a more accurate value and minimize contribution from non perfectly ohmic contacts, up to 8 measures are collected (Fig. **5**) [23]. The voltage is measured twice on the same couple of contacts considering the two possible current directions for the same contact set (Fig. **5**). The current supplied and the measure voltage configuration are cycled around "90°" (Fig. **5**).

Two values of resistivity, *<sup>A</sup>* and *<sup>B</sup>* are then computed as follows:

$$\begin{aligned} \rho\_A &= \frac{\pi}{\ln 2} f\_s t\_s \frac{V\_2 + V\_4 - V\_1 - V\_3}{4I} \\\\ \rho\_B &= \frac{\pi}{\ln 2} f\_d t\_s \frac{V\_6 + V\_8 - V\_8 - V\_7}{4I} \end{aligned} \tag{4.3}$$

where: *ts* is the sample thickness; *V*<sup>1</sup> *V*8 represents the voltages measured by the voltmeter; *I* is the current intensity through the sample; *fA* and *fB* are geometrical factors based on sample symmetry. The *fA* and *fB* values are related to the two voltage ratios *QA* and *QB*, whose values depend on the measured voltages, as follows:

$$\mathcal{Q}\_A = \frac{V\_2 - V\_1}{V\_4 - V\_3} \quad \text{and} \quad \mathcal{Q}\_B = \frac{V\_6 - V\_s}{V\_8 - V\_7} \tag{4.5}$$

For perfect symmetry: *fA* = *fB* = 1. In the other cases the *f* value can be computed by solving the implicit function relating *Q* to *f*:

$$\frac{Q-1}{Q+1} = \frac{f}{0.693} \arccos \mathbf{h} \left(\frac{e^{\frac{0.693}{f}}}{2}\right) \tag{4.6}$$

**Figure 5:** Schematic of a van der Pauw geometry for the resistivity measurement. The numbers in the squares represents the 4 ohmic contacts on the sample border. For each combination of contacts, the current is reversed (After [23]).

It is worthwhile noting that if *<sup>A</sup>* and *<sup>B</sup>* are not within 10% of one another, the sample is not sufficiently uniform to determine an accurate value of the resistivity, and their values should be discarded [23].

Once *<sup>A</sup>* and *<sup>B</sup>* are known, the average resistivity ( *AVG* ) can be determined as follows:

$$\left| \begin{array}{c} \rho\_{AVG} = \left( \rho\_A + \rho\_B \right) \end{array} \right| \tag{4.7}$$

The van der Pauw geometry can also be used to determine the Hall coefficient by applying a magnetic field orthogonal to the sample surface. The measured values of the sample resistivity and Hall coefficient provide the Hall mobility (as will be explained in the section 5). Therefore, this

#### *Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **257**

kind of geometry has been used extensively for several semiconductors such as III-VI layered materials, amorphous silicon and amorphous gallium arsenide [24-29].

A differential measurement may be required if the sample resistance is of the same magnitude as the isolation of the voltmeter. Electronic equipment has been specifically designed to measure the resistivity and Hall coefficient of semiconductor materials applying the van der Pauw and Hall bar geometry [23]. The current source and the voltmeter are automatically switched to all sides of the sample by using a high isolation card controlled by a PC. Special features, such as built-in unitygain buffers, allow differential measurements on high resistivity samples. The addition of a magnetic field, whose insertion and field reversion is PC controlled, provides the measure of the Hall coefficient for the same sample [23].

Equations (4.3) and (4.4) are essentially concerned with the sheet resistance of the sample, defined as the resistance between opposite edges of a square of size, *L*. This resistance is independent on *L* and is therefore a property of the sheet. Its dimensions are simply "ohms", even if, to avoid confusion, they are commonly referred to as "ohms per square". The concept of sheet resistance is important for thin films where typical lateral dimensions are much greater than the film thickness, *ts*.

To obtain a van der Pauw measurement, samples can be rapidly contacted by spring-loaded tips. However, in many cases this form of contact may show resistance that is too high and it then becomes necessary to use planar contacts deposited on the sample surface. However, due to a non-ideal van der Pauw geometry, alternative contact geometries are generally taken into account [1, 17].

Errors can also arise from a number of causes in addition to the sample non-uniformity and contact problems: Joule heating, photo-effects, current leakage through the substrate and surface; interface depletion effects (for epitaxial films). The first two can be eliminated by taking measurements in the dark as a function of the measuring current. The latter two are more difficult to control. For example, a semi-insulating substrate may conduct significantly at elevated temperatures showing activation energy of half the band gap. Possible *p-n* junction substrate break-down can be eliminated by reducing the measured voltage with a reduction of the supplied current. Surface leakage can introduce serious errors in these measurements and requires strong control [1].

#### *4.1.3. Four Points Probe*

A local determination of the DC conductivity can be obtained by the so-called four-point probe technique. The four-point probe technique represents a development of the "bar" method.

The technique uses four-point electrodes (probes) pressed on the semiconductor material surface. In this technique, the voltage measuring arms are replaced by point-contact probes. The need for ohmic contacts is no longer critical since no current flows in the voltage arms. A resistivity in the range of about 10-1 ÷ 103 cm can be easily measured with a standard accuracy of less than 1% [1, 18, 21].

A typical implementation is the linear four-point probe configuration (Fig. **6**) [18, 21]. Four spring-loaded needles, at an equal distance, *s*, (*e.g. s* = l mm), are pressed onto the semiconductor surface. The system head applies enough pressure to ensure good near-ohmic contacts, but soft

enough to avoid sample damage. In the two outer probes (Fig. **6)** the measurement current, *I*, is supplied by a constant current generator, with a high impedance output, while the voltage, *V*, is read between the inner pair of probes by a high impedance input voltmeter.

The resistivity is computed from the Ohm's law, introducing a right proportionality constant, *c*, dependent on the sample dimensions and the distance among the needles:

$$\rho = \mathbf{c}V/I\tag{4.8}$$

Practical problems concern the type of probe, the spring loading, the accuracy of probe spacing, the contact between probes and the material surface, its preparation, *etc.* Several sources of error and various factors can affect the accuracy of the sample resistivity such as: minority carrier injection, heating by the measurement current, leakage current in the voltmeter circuit, sample geometry, *etc.* [1].

**Figure 6:** Four point probe on a semi-infinite semiconductor wafer, with a resistivity .

**Figure 7:** Linear four point probes technique applied to a sample of finite dimensions, on a semi-insulating substrate. The sample must be isolated from the substrate.

Experimentally, four point probe measurement on thin films is no different from that on bulk materials. Practical expressions for the bulk and thin film cases are reported in the reference [18, 21], while some specific cases will be detailed in the next sections.

An additional complication arises when the film is supported by a substrate of high resistivity which, because it is thicker, has a sheet resistance similar to that of the layer. A correction factor

#### *Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **259**

depending both on the ratio (*ts*/*s*) and the substrate resistivity must be used to calculate the actual resistivity of the layer [18]. In practice, there are many possible combinations of resistivity and layer thickness.

Despite the practical difficulties mentioned above, the method is widely used and the correction factor, *c*, has been calculated for different sample geometries, some of which are reported in the next paragraphs.

### *4.1.4. Thin Film on an Insulating Substrate*

In this case, it is assumed that a thin layer of thickness, *ts*, extended infinitely in the other two dimensions, is deposited on a semi-insulating substrate. The semiconductor film should be homogeneous with a specific resistance, .

The film resistivity can be computed by using the following relation:

$$
\rho = \frac{V}{I} t\_s \frac{\pi}{\ln 2} \tag{4.9}
$$

A typical error of about 1% in the value is obtained when *ts* is about one half of the probe distance *s*. For higher values of *ts*, the error would increase and in the case of *ts* = *s*, it is 8 %. For typical layer thicknesses (1 10 m) and probe distances ( 1 mm) the error can be neglected.

The previous relation is also applicable in all cases where the sample lateral dimensions are much larger than *s* and the probes are distant from the sample border.

#### *4.1.5. Bulk Material*

Finally, we should mention the case of a homogeneous bulk semiconductor such as an ingot of silicon with a planar surface. The technique provides the resistivity value by using:

$$
\rho = 2\pi d \frac{V}{I} \tag{4.10}
$$

if the condition *d* > 3.5*s* if fulfilled, where *d* represents, in this case, the radius of a hemispherical volume centred in the middle of the inner probes and extending in the bulk semiconductor volume.

#### *4.1.6. Small Sample of Rectangular Shape*

For a small slab of rectangular shape with finite dimensions *a* and *b* (see Fig. **7**), different approaches and solutions have been proposed. The equation relating the specimen resistivity to the sample dimensions (*a*, *b* and *ts*) and to the probe spacing, *s*, has been found by *Hansen* [30] by an analytical approach, solving the Laplace equation and applying standard boundary conditions on the doubled sample (see dotted lines in Fig. **7**) without changing the field and current line conditions in the original sample. The resulting expression is:

$$\rho = \frac{V}{I} \left( \frac{s}{bt\_s} + \frac{8}{bd} \sum\_{n=0}^{n} \sum\_{n=0}^{n} F \right)^{-1} \tag{4.11}$$

where:

$$F = \frac{\cosh \beta \left(l - \frac{3s}{2}\right) \sinh \left(\frac{\beta s}{2}\right)}{\left(1 + \delta\_{0,m}\right) \left(1 + \delta\_{0,u}\right) \beta \cosh \left(\beta l\right)}$$

(*m*, *n*) is unequal to (0, 0);

$$\beta = \frac{2\pi}{b} \left[ m^2 + \left( \frac{nb}{2t\_s} \right)^2 \right]^{\frac{1}{2}}$$

and 0,*m* = 1 (if *m* = 0) and 0,*m* = 0 (for *m* > 0).

#### **4.2. Contactless Methods**

These methods are based on the physical absorption of power from a radiation field by free charge carriers in the semiconductor material. Depending on the frequency radiation excitation, three bands are generally involved: radio frequency (RF; 10<sup>7</sup> Hz); microwave (MW; 1010 Hz) and optical ( 1014 Hz). The experimental methods as well as the spatial resolution will depend on the frequency band considered.

The RF methods provide an average resistivity value over the area of the investigated film up to a thickness of the order of the skin depth. Examples of experimental setup are reported in literature [31-33].

The MW methods are based on waveguide techniques and generally require well-shaped specimens since the wavelengths used are comparable to the sample size. Several approaches in different frequency bands have been proposed [19, 34-39].

Finally, the optical techniques may offer some advantages with respect to those previously considered because they allow for investigation of local properties of the sample, such as inhomogeneity, focusing the beam on area of order the 10 m. For a general review and experimental details see the reference [19].

All these methods have in common the problem of deriving the theoretical relationships between the sample resistivity and the measured parameters. In practice, a reliable value of the resistivity requires calibration of the experimental setup. Further drawbacks are the possible non linearity between resistivity and measured parameters and the reduced range of resistivity that can be measured. The above-mentioned difficulties and range of applications make contactless methods suitable only for specific applications.

#### **5. HALL EFFECT**

The Hall effect was discovered for the first time in 1879 by E.H Hall [40] in a conducting material. It is largely used to measure important electronic transport coefficients such as charge carrier concentration and Hall mobility, this last in conjunction with the measurement of the sample resistivity.

#### *Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **261**

The mathematical relationships involving the main physical quantities of the Hall effect can easily be found by considering a slab of a conductor, in the shape of a parallelepiped.

**Figure 8:** The classical Hall effect. Both electrons and holes are deflected by the Lorentz force ( () () , *Fu Fu <sup>L</sup> y Ly* respectively) in two opposite direction as shown by the large arrows. The Hall field, *E*<sup>H</sup> *E uy y* , has the direction of the positive *y* axis.

In a cartesian system (see Fig. **8**), if a current density *x xx j ju* flows along the *x* axis direction and an induction magnetic field *B Bu z zz* is applied parallel to the z axis, orthogonal to the current flow direction, an electric field *E Eu y yy* (called Hall field) is set up, mutually perpendicular to the directions of *xj* and *Bz* . The intensity of *Ey* is proportional to *xj* and *Bz* by a quantity *R*, called Hall coefficient:

$$E\_y = Rj\_xB\_z\tag{5.1}$$

The Hall effect can be physically explained by considering that charge carriers, forming the electrical current, *xj* , will experience a Lorentz force *FL evu B x z* in a direction orthogonal to the plane formed by the vectors *Bz* and *x x j nqvu* , where *n* is the concentration of the charged particles.

This force will deflect the charge carriers towards the edges of the slab and will create an electric field, *E Eu* <sup>H</sup> *y y* , whose force, *y y eE u* , will counterbalance the Lorentz force and, then, the further build up of charge:

$$e\vec{v}\_x \wedge \vec{B}\_z = e\vec{E}\_\text{H} \tag{5.2}$$

With reference to Fig. **8** and considering the definition of the current density, the (5.2) can be written:

$$
\mathbf{v}\_x \mathbf{B}\_z = E\_y \tag{5.3}
$$

Hence, the magnitude of the field *Ey* can be expressed as:

$$E\_y = \frac{1}{me} B\_z j\_x \tag{5.4}$$

The expression for *R* can be derived by comparing the (5.4) with the (5.1):

$$R = \frac{E\_y}{B\_z j\_x} = \frac{1}{ne} \tag{5.5}$$

The convention governing the sign of *R* is to take it as negative when the electric charge, *e*, is negative.

The measure unit of *R* in the SI is m3 /C but generally the unit cm3 /C is preferred.

The Hall coefficient is a powerful investigative tool for the study of the transport properties of conductors and semiconductors due to its simple relationship to the electric charge concentration, *n*. The measurement of *R* provides a direct estimate of the carrier concentration contributing to the transport process.

A more general expression for the Hall coefficient for a simple isotropic band can be found in reference [1].

#### **5.1. Hall Mobility**

Another relevant electronic transport coefficient can be obtained by combining the Hall coefficient with the resistivity (or conductivity) of the material. This coefficient is known as Hall mobility, <sup>H</sup> , and is related to the other two quantities as follows:

$$
\mu\_{\rm li} = \left| \frac{R}{\rho} \right| = \left| R \sigma \right| \tag{5.6}
$$

In general, for the same material, the Hall mobility and drift mobility (see equation (12)) assume different values. A more correct expression for the Hall coefficient is [1]:

$$R = -\frac{\mu\_{\rm H}}{\mu} \frac{1}{ne} = -\frac{r\_{\rm H}}{ne} \tag{5.7}$$

where the adimensional ratio of the Hall mobility to the drift mobility is called the Hall factor, <sup>H</sup>*r* . This quantity is of great interest in a discussion of the electronic transport properties of semiconductors; its theoretical and experimental determination is extremely difficult, <sup>H</sup>*r* depending on the temperature and band structure of the semiconductor. Its value ranges from about 1 to about 2, for most semiconductors [18]. Knowledge of the <sup>H</sup>*r* value is important because from a direct measure of *R* the carrier concentration, *n*, can be derived from the equation (5.7).

Where there is doubt as to the most probable value of H*r* , setting it equal to unity is not likely to introduce an error greater than 20 30 % in the *n* value [18].

#### *Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **263**

*x*

In the presence of electrons and holes, with concentration *ne* and *nh* respectively, the Hall coefficient can be rearranged in the following way:

$$R = \frac{r\_{\rm th}}{e} \frac{n\_h - n\_e \left(\frac{\mu\_e}{\mu\_h}\right)^2}{\left(n\_h + n\_e \frac{\mu\_e}{\mu\_h}\right)^2} \tag{5.8}$$

Finally, another useful quantity can be derived by observing Fig. **8.** In fact, in the presence of a magnetic field, the direction of the electric field, *E* , ( *EE E <sup>x</sup>* <sup>H</sup> , see the Fig. **8**) and the current density, *j* , differ. In fact, considering the (5.4), the expression of *xj* and *<sup>x</sup> j E* , it follows:

$$E\_{\,\,\,v} = \frac{1}{nq} B\_{\,\,z} j\_{\,\,x} = \frac{1}{nq} B\_{\,\,z} \sigma E\_{\,\,x} = R B\_{\,\,z} \sigma E\_{\,\,x}$$

then:

tan *<sup>y</sup> z H x E RB E* **(5.9)**  

The equation (5.9) is valid in the limit of small H, *i.e.* if the intensity of *B* is so low that does not depend on *B* [1].

#### **5.2. Experimental Measure of the Hall Effect**

The Hall effect can be measured in a semiconductor by a DC method using different geometries. One possibility is the bar (see the Fig. **4**).

A requirement for a correct determination of the Hall coefficient value is that the side arms for the four or six contacts must be narrow enough to ensure a uniform voltage drop along the bar. The ratio of the bar length to its width must be at least 4, to avoid the end contacts shorting the Hall voltage. These end contacts must also be either non-injecting or sufficiently far from the other side arms to avoid injected minority carriers recombining before reaching them. Experimentally, the voltages measured for both directions of current are generally averaged to minimize errors arising from misalignment of the facing Hall side arms and from thermo-electric effects due to temperature gradients within the bar [1]. A uniform current distribution and a well-defined electric field are assured by the geometrical regular bar sample.

Ultrasonic cutting for bulk material, or "sandblasting" with alumina powder for epitaxial films, is commonly used to prepare samples. Epitaxial films must be isolated either by growth on semiinsulating substrates or by using a *p-n* junction. In this last case, attention must be paid to the effect of the depletion regions on the effective sample thickness.

An alternative approach to the bar geometry is van der Pauw's [20]. With respect to the resistivity, the Hall coefficient measurement requires the additional application of a magnetic field, orthogonal to the sample surface, while a constant current must be sourced by using diagonal pairs of contacts (see Fig. **9**).

A total of eight voltage values are measured to obtain two values of the Hall coefficient for a better control of the homogeneity of the film properties [23]. These are the result of the two permutations of the diagonal contacts and the reversal of the current direction for each set and of the magnetic field direction (see Fig. **9**).

**Figure 9:** Schematic of the van der Pauw geometry for the Hall coefficient measurement. The numbers in the corners represent the 4 ohmic contacts on the sample border. For each combination of contacts, the current is reversed. The magnetic field, not shown in the figure, is orthogonal to the sample surface. The sequence shown, is repeated again with the magnetic field applied in the reverse direction. The corresponding measured voltages are shown in the brackets.

The average of the two measured Hall coefficient values is taken as the best estimate of *R* for the sample. The Hall coefficient is measured using diagonal pairs of contacts rather than adjacent pairs:

$$R\_a = \left(2.5 \times 10^7 t\_s \, / \, I B\_z\right) \left(V\_2 - V\_1 + V\_3 - V\_6\right)$$

$$R\_b = \left(2.5 \times 10^7 t\_s \, / \, I B\_z\right) \left(V\_4 - V\_3 + V\_7 - V\_8\right)$$

where *Ra* and *Rb* are two independent Hall coefficient values and the *Vi* (*i* = 1÷ 8) are the measured voltages (see the Fig. **9**).

The Hall coefficient for the sample is the average of *Ra* and *Rb*. Finally, the Hall mobility is then given by the equation (5.6) if the sample resistivity has been measured.

An accurate knowledge of sample thickness is necessary when measuring carrier density, while the value derived for Hall mobility is independent of sample thickness, if the electric field inside the material is uniform. The importance of the Hall effect as a characterization method lies in its ability to measure the free carrier density, (see the Eq. 5.7), when current is carried by a single type of carrier.

**(5.10)** 

### **6. DEEP STATES IN A DEPLETION LAYER**

Impurity and defect levels in semiconductors are usually classified as shallow and deep. To the first classification belong the so called hydrogenic impurities such as the substituitional atoms used for semiconductor doping. These states are located in the forbidden gap near the CB or the VB edge. On the contrary, deep states are energetically located in the forbidden gap at several tens or hundreds of meV from band edges.

Deep states are important because they affect some material properties such as forward and reverse current in devices, reduce minority charge carrier recombination lifetime (*e.g.* in photovoltaic cells), increase the noise in photodiodes and transistors, or can quench the storage time in charge coupled devices.

Deep states can be intentionally introduced in the semiconductor host matrix to control some properties3 or more frequently are the unwanted result of the preparation technique (growth, deposition and/or post deposition processing) of the semiconductor material. Thus, the study of deep state properties is important both to evaluate their influence on carrier recombination and as a means of identifying and labeling defects.

Deep states are also referred to as deep levels and traps depending on their electrical behavior. In detail, deep levels generally may interact with both the conduction and valence band, while traps exchange their carriers mainly with one of the two bands. This fact is evident in a different energy position of deep states in the semiconductor gap. In fact, deep levels are located closer to the midgap, while the trap states are shifted from the midgap towards one of the two bands.

Due to their position, deep levels act as recombination centers to extract charge carriers from both bands under non-equilibrium excitation conditions. Conversely, traps will capture carriers from the band which they are closer to, in a very short time constant (of the order of few ns), re-emitting carriers to the same band after a delay time (emission time constant of the order of ms or more).

From an experimental point of view, deep states properties cannot be accessed directly. In fact, it is not infrequent that their concentration is several orders lower than that of shallow impurities which control the density of free charge carriers and the Fermi level position in the semiconductor. Therefore, in this case, the Hall effect measurement will be inadequate to determine the energy position and concentration of deep states because the Hall coefficient value will be affected only by charge carriers coming from the shallow levels [18].

The study of deep states requires measurement techniques which are both sensitive to very low concentration of these centers (in presence of a great concentration of shallow impurities), and are capable of revealing recombination processes at deep level centers. These techniques are based on the observation of transient phenomena related to charge carriers capture and emission only at deep states. The time constant of transient is controlled by the rate of the capture or emission process, while its amplitude provides information about the concentration of the deep traps.

<sup>3</sup> For example, Au is introduced in the Si matrix to control the lifetime in thyristors.

One of the most sensitive techniques for investigation of deep states properties in a semiconductor is the Deep Level Transient Spectroscopy (DLTS) [41].

The technique uses a diode structure to investigate the time dependent change of the depletion region capacitance due to the capture and emission of charge carriers after the application of a suitable pulse to charge the deep states. Monitoring this capacitance change as a function of time will produce trap states properties. Several different techniques have been developed, known as capacitance spectroscopy [42].

Different possibilities can be found for trap location in a semiconductor material, as shown in Fig. **10**.

Looking at Fig. **10**, if a trap is located closer to the CB than to the VB (top left and bottom right) the electron emission rate, *en*, will be higher than the hole emission rate, *eh*. Likewise for traps located closer to the VB.

A further distinction is made in majority or minority carrier traps depending on the main trap interaction with the majority or minority carrier band4 .

The electron capture rate, *cn* (*ch* for the holes), is related to other characteristic trap parameters such as the capture cross section, *n* (*<sup>h</sup>*), the electron thermal velocity, *vth*, and the electron concentration, *n* (*p*), by the following relation:

$$
\sigma\_n = n \sigma\_n \nu\_{th} \tag{6.1}
$$

$$\text{and } \mathcal{c}\_h = p \sigma\_h \nu\_h$$

**Figure 10:** Energy location of main processes for majority and minority carrier traps in a *n* and a *p* type semiconductor. The thick arrows indicate the dominant transition process.

for the holes. The electron emission rate, *en* (*eh*), process, following the carrier capture, is also related to the trap level position with respect to the CB edge, *i.e., EC* - *ET* (*ET* - *EV*, for the VB) by the equation:

<sup>4</sup> A trap interacting mainly with the conduction band is called an electron trap. Similarly, a hole trap will interact dominantly with the VB.

*Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **267**

$$\mathbf{e}\_{n} = \sigma\_{n} \mathbf{v}\_{h} N\_{\mathcal{C}} \mathbf{g} \exp\left[ - \left( E\_{\mathcal{C}} - E\_{\mathcal{T}} / k\_{\mathbb{B}} T \right) \right] \tag{6.2}$$

where *NC* and *g* are the effective density of states of the CB and the trap degeneracy, respectively. A similar relation holds for *eh*.

According to the Shockley, Read, Hall theory [43, 44], the minority carrier lifetime, *eff,* can be deduced from the generation rate, *U*, and the intrinsic carrier concentration in the semiconductor:

$$
\pi\_{\rm eff} = \mathfrak{n}\_i \not\!\!\!\mathcal{U} \tag{6.3}
$$

$$U = n\_i \frac{\sigma\_h \sigma\_n \mathbf{v}\_{th} N\_T}{\sigma\_u \exp\left(E\_{\nu \alpha \rho} / k\_B T\right) + \sigma\_h \exp\left(-E\_{\nu \alpha \rho} / k\_B T\right)}\tag{6.4}$$

where *Etrap* is the energy position of the trap with respect to the intrinsic energy 2 *E EE i CV* of the semiconductor.

It is worthwhile noting that deep levels located around the midgap cause large *U* values (see eq. 6.4) and then lower *eff* values (see eq. 6.3) with respect to trap states.

All the above reported relations can be used to obtain the main trap parameters, *i.e., NT*, *ET Ei*, *<sup>n</sup>* and *h*.

#### **6.1. The DLTS Technique**

The exploitation of the DLTS technique requires a *p-n* junction, or a Schottky structure (of the semiconductor to be investigated), kept in a state of reverse biasing. A repetitive pulse is applied to the structure (see Fig. **11**a) resulting in a capacitance transient due to the capture and subsequent emission of charge carriers from the traps (see Fig. **11**b). This transient is induced in the structure by applying a slight forward bias (a short duration pulse of few s) into deep depletion for a longer time (duration from ms to s), see the Fig. **11**a.

The pulse fills the traps repetitively and the resulting series of emission transients are processed to generate a "spectrum" as the sample is slowly heated, with peaks in the system output corresponding to each trap species. The pulse repetition allows for the collection of more transients to be averaged, since their amplitudes are generally low.

Hence, the process is carried out at several fixed temperatures in a wide range, from about 77 K to about 400 K in order to detect trap states with energy levels ranging from near band edge to midgap.

The principle of the DLTS technique can be explained considering the case of a majority electron trap.

The diode structure is held under reverse biasing by applying a voltage *Vr*. Then a pulse, of duration *tf*, reduces the reverse bias almost to zero causing traps to be filled by majority electrons. This pulse is repeated with a *tr* interval (see the Fig. **11**a).

Between two consecutive pulses (interval *tm*, see the Fig. **11**a) the trapped electrons will be emitted at a rate *en* and an exponential transient will be observed in the recorded capacitance *C*(*t*):

$$C\left(t\right) = A\sqrt{b\left(N\_D^\* + N\_T\left[1 - \exp\left(-t/\tau\right)\right]\right)}\tag{6.5}$$

where *A* is the area of the diode structure; <sup>0</sup> 2 *r bi r <sup>q</sup> <sup>b</sup> V V* ; *Vbi* is the built-in voltage and *ND* the concentration of the ionized shallow donors. The transient is shown in the Fig. **11**b.

**Figure 11:** Working principle of the DLTS technique. (a) Repetitive pulse sequence for filing (duration *tf*) and reverse biasing (duration *tm*). (b) Diode structure capacitance transient as a function of time. (c) Variation of the transient time constant <sup>1</sup> *t n t e* vs *T*-1 for two different traps. (d) Deep level spectrum obtained by a reference time constant, *ref*, considering the capacitance transient shown in (b).

For practical reasons, due to the need to observe emission rates covering many orders of magnitude (more than 10) by using standard electronic equipments5 , the transient is analyzed in a given time window, called rate window, *rw* (*rw* = *t*<sup>2</sup> *– t*1). For a given *rw* value, the capacitance variation will be maximum when the time constant, <sup>1</sup> *t n t eT* , is equal to a known reference time constant, *ref*, related to *rw*. This condition is fulfilled at a given temperature value, *Tpk*, while at low and high temperatures the capacitance transient in *rw* will be practically constant. In fact, for low *T* the emission process will be low and the capacitance change will be negligible during the

<sup>5</sup> A fast response electronics is required, with enough resolution to appreciate very small change in the capacitance value.

#### *Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **269**

observation time window (*rw*). For high temperatures the transient is almost complete even before the first sampling time *t*1, and then the capacitance remains constant during the interval *rw*. However, within the temperature range used for the investigation, there will be a narrow *T* region where the capacitance transient will be highest. In this state, the electron trap emission rate will fit the selected rate window (*t*2 - *t*1), *i.e.* the condition <sup>1</sup> *t n ref t eT* will be satisfied (Fig. **12**). The quantity *ref* is related to *rw*. In case of a shallow trap, relatively low temperatures are requested to obtain a maximum DLTS signal.

**Figure 12:** Capacitance transients collected at different temperatures. The abscissa shows the *t*1 and *t*<sup>2</sup> sampling times (rate window) for the construction of the DLTS signal *C*(*t*1) - *C*(*t*2) (right curve) (after [21]).

It is not infrequent to find semiconductors containing two different traps, each characterized by a clear trap signature in the form of a linear dependence of <sup>1</sup> ln *<sup>n</sup> e vs. T*  -1, with different values of *Etrap* and *<sup>n</sup>*. Increasing the system temperature, a peak will occur (at *Tpk*), as <sup>1</sup> *n e T* passes through *ref*, for each trap (see the Fig. **11**d).

For a given *ref* the *Tpk* values (*e.g. T*1 and *T*2) are characteristic of each trap.

Repeating the scan with different values of the rate window (and then of *ref* ), sets of *en* and *Tpk* values can be obtained.

An Arrhenius plot of 1 2 ln( ) *<sup>n</sup> e T* vs <sup>1</sup> *T* allows to get the *Etrap* and *<sup>n</sup>* values for each trap. However, great care must be taken in the physical interpretation of the results [18].

Typical DLTS signals for an Au donor trap in *n*-type Si is shown in Fig. **13**. The DLTS peaks shift towards higher *T* with the increase of the rate window. The trap concentration can be determined from the DLTS signal amplitude. An Arrehnius plot of 1 2 ln( ) *<sup>n</sup> e T vs.* 1000/*T* provides the trap activation energy while the extrapolation of the line to 1000/T 0 allows for the extraction of the capture cross section, see Fig. **14**.

A more detailed treatment of the physics of deep states in a depletion region and the DLTS technique is reported in reference [18].

**Figure 13:** DLTS measurement of the Au trap in *n*-type Si doped with 3.5×1017 cm-3 atoms. The structure is reversed biased at 13.3 V. The rate windows of the shown curves are (from left to right): 20/s, 50/s, 80/s, 200/s, 400/s and 1000/s. The depletion capacitance is 100 pF (after [21]).

**Figure 14:** Arrhenius plot of the DLTS signal reported in the Fig. **13**. The measurement is the full line. Dashed lines are data from a trap library for Au in *n*-type Si. The measured activation energy is 340 meV. The dotted lines are used for extrapolation of the capture cross section for 1000/*T* 0 (after [21]).

#### **7. CURRENT- VOLTAGE CHARACTERIZATION OF SOLAR CELLS**

Solar cells performance can be measured by several electrical characterization techniques which are performed as part of research and development of photovoltaic materials and cells, as well as a standard test tool during the manufacturing process.

#### *Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **271**

Electrical tests usually performed on PV cells, involve measuring capacitance and/or current as a function of several parameters such as an externally applied DC voltage; the illumination intensity; the wavelength of a monochromatic illumination; the illumination position; device temperature, *etc.* [45]. Relevant device parameters, such as output current and voltage; energy conversion efficiency; maximum power output; doping density; resistivity, *etc.* can be extracted from currentvoltage (I-V) and capacitance-voltage (C-V) measurements, carried out either in DC or in pulsed mode. Additional information can be derived by the measurement of the device impedance as a function of frequency or voltage, by applying alternating voltages [45].

Among the available characterization methods a fundamental one is the measurement of the illuminated current - voltage (I-V) curves carried out under standard conditions, *i.e.* at 25°C and by using an AM1.5G spectrum.

A simplified equivalent electrical circuit of a single *p-n* junction solar cell (see Ficcadenti and Murri in the chapter 1) is represented in Fig. **15**, which consists in a light-induced current source (*IL*), a diode that generates a saturation current, a series resistance, *rs*, and a shunt resistance, *rsh*.

The series resistance is due to the resistance of the metal contacts, ohmic losses in the front surface of the cell, impurity concentrations, and junction depth. The *rs* limits both the maximum shortcircuit current and the maximum power output of a cell. The ideal value for *rs* should be zero. The shunt resistance represents the loss due to the surface leakage along the edge of the cell or to the crystal defects. The ideal value for the shunt resistance should be infinite.

**Figure 15:** Simplified equivalent electrical circuit of a bulk or a thin film solar cell.

**Figure 16:** Typical current – voltage curve of a solar cell, having a reversed current sign (see the text). The figure shows the main cell parameters: short-circuit current (*ISC*); maximum output current (*Imax*) and voltage (*Vmax*) on an external load; maximum output power (*Pmax*); open circuit voltage.

The total current flowing through an illuminated solar cell, when a load resistor (*rload*) is connected to its output terminals, can be approximated by the following relation:

$$I = I\_S \left[ \exp \left( qV / k\_B T \right) \right] - I\_L \tag{7.1}$$

Fig. **16** illustrates a typical I-V curve of a forward biased solar cell under illumination. We note that in an actual I-V characteristics, the curve passes through the fourth quadrant and allows power to be extracted from the device (*V <sup>+</sup>* , *I* - ). For convention, considered that a PV cell is an active device, the measured current is reversed in sign and the I-V curve is plotted in the first quadrant, as in the Fig. **16**.

The electrical parameters commonly used to characterize the solar cell efficiency are: the short circuit current, *ISC*; the maximum current, *I*max; the open circuit voltage, *VOC*; and the maximum voltage, *V*max.

The maximum power point, *P*max, is the product of the *I*max*V*max and it represents the knee of the I-V curve. The *P*max value corresponds to the area of the largest rectangle (whose sides are *I*max and *Vmax*) under the I-V curve. Another important parameter of a PV cell is the fill factor (*FF*), defined as:

$$FF = \frac{P\_{\text{max}}}{I\_{\text{sc}}V\_{\text{oc}}} = \frac{I\_{\text{max}}V\_{\text{max}}}{I\_{\text{sc}}V\_{\text{oc}}} \tag{7.2}$$

The *FF* represents how far the I-V characteristics of an actual solar cell differs from that of an ideal one. The *FF* is always lower than one, due to the losses from series and shunt resistances. From a geometrical point of view the *FF* is also equal to the area ratio between the two rectangles shown in the Fig. **16**.

Finally, the conversion efficiency, *η*, is defined as the ratio of the maximum power output, *P*max, to the power input, *Pinc*, this last being the total radiant energy incident on the surface of the PV cell:

$$
\eta = \frac{P\_{\text{max}}}{P\_{\text{loc}}} \tag{7.3}
$$

#### **7.1. Experimental Measure**

In general, the measurement is carried out under standard testing conditions, *i.e.,* usually keeping constant the cell temperature at 25 °C and illuminating the cell by means of a AM1.5G spectrum (for non concentrating solar cells) that resembles the solar spectrum as much as possible [46]. This kind of spectrum is usually realized combining a W-halogen lamp with a Xe-lamp to get a close match to the solar spectrum. Details about the measurement of I-V characteristics under illumination of solar cells can be found in references [47, 48].

To extract the solar cell parameters, the I-V characteristics is measured with a load resistance connected to the cell, under illumination with a standard AM1.5G spectrum. The voltage and current are measured during the voltage sweep with a four-point probe technique (see the section 4) in order to eliminate the lead resistance. By using a set of leads, a voltage sweep, ranging from 0 V to *VOC*, will source the PV cell with a current ranging from *ISC* to 0, respectively. The voltage drop across the cell is measured by a second set of leads, allowing to calculate all the characteristic solar cell parameters [45].

Several apparatus are now commercially available in order to simplify electrical testing and analysis of material and PV cell parameters. These last can be measured sourcing and measuring both current and voltage, (four-quadrant source capability), *i.e.* the measuring instrument can sink the cell current as a function of the applied voltage.

A method for the determination of the series resistance in PV cells, with a voltage-independent charge carrier collection in the *p-n* junction, is the comparison between dark and illuminated I-V curves, since the difference between dark and illuminated I-V curves is not a constant, when *rs* > 0, even when the actual charge carrier collection process is not voltage dependent [45].

Now, if the I-V curve measured under illumination by the AM1.5G spectrum, *IL*, is shifted by the short-circuit current *ISC* (at exactly this AM1.5G illumination) the resulting current (*IL* + *ISC*) voltage characteristics will show the same voltage behaviour as the unshifted one.

The value of *rs* can be obtained by the following relation:

$$r\_S = \frac{V\_d - V\_L}{I\_{3C}}\tag{7.4}$$

where *Vd* and *VL* are the dark and under illumination voltages at a given current intensity, respectively, while *Isc* is the short circuit current intensity measured under AM1.5 G spectrum. *VL* is the voltage value obtained by the (*IL* + *Isc*) - V curve [45].

However, this method is only suitable as long as the series resistance is independent on illumination conditions. For this situation, Aberle *et al.* [49] proposed to use the *VOC* measured at different illumination conditions yielding the so-called *Isc* - *VOC* curve. Then the *rs* value can be derived by the following relation:

$$r\_S = \frac{V\_{OC} - V\_L}{I\_{SC} - I\_{SC}^{AM1.8}} \tag{7.5}$$

where *VL* and *ISC* are the variable voltage and short circuit current at various illumination intensities.

It is worthwhile mentioning that *VL* is the value measured at a given current intensity, in the far forward region of the I-V curve, while *VOC* is completely independent on *rs* because no current flows at open-circuit conditions. Then the *Isc* - *VOC* curve is a series-resistance free I-V curve [45].

The value of shunt resistance *rsh* and leakage current can be derived from the reverse-biased I-V characteristics carried out in the dark. A voltage sweep applied to the cell is sourced from 0 V, up to a value near the break down of the device. The resulting current is measured and plotted as a function of the voltage. The *rsh* is determined from the slope of the reverse-biased I-V curve of a PV cell, as shown in Fig. **17**. From the linear region of this curve, the shunt resistance can be calculated as:

$$r\_{sh} = \frac{\Delta V\_{RB}}{\Delta I\_{RB}}\tag{7.6}$$

$$\underbrace{\mathbf{r}\_{SH}^{r} = \frac{\Delta V\_{RB}}{\Delta I\_{RB}}\tag{7.7}}\_{\Delta V\_{RB}}\tag{7.8}$$

$$\underbrace{\mathbf{r}\_{\Delta V\_{RB}}^{r} \times \cdots \times \mathbf{r}\_{\Delta V\_{RB}}^{r}}\_{\Delta V\_{RB}}\tag{7.9}$$

**Figure 17:** Current – voltage characteristics of a reverse polarized solar cell. The curve allows to calculate the value of the shunt resistance, *rsh*, as shown in the figure.

#### **ACKNOWLEDGEMENT**

Declared none.

#### **CONFLICT OF INTEREST**

The author(s) confirm that this chapter content has no conflict of interest.

#### **REFERENCES**


#### *Electrical Properties of Semiconductors Silicon Based Thin Film Solar Cells* **275**



© 2013 The Author(s). Published by Bentham Science Publisher. This is an open access chapter published under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/legalcode

**SECTION III - PHOTOVOLTAIC DEVICES** 

**CHAPTER 9** 

## **Heterojunction for Silicon Photovoltaics**

**Mario Tucci1,\*, Luca Serenelli1 , Massimo Izzi<sup>1</sup> , Enrico Salza1 , Simona De Iuliis1 , Pietro Mangiapane<sup>1</sup> , Giampiero de Cesare2 and Domenico Caputo<sup>2</sup>**

*1 ENEA, Research Center Casaccia, via Anguillarese 301, 00123 Roma Italy and <sup>2</sup> DIIET, University "Sapienza", Via Eudossiana 18 00184 Rome, Italy* 

**Abstract:** The amorphous/crystalline silicon heterojunction solar cell fascinated the researchers since the beginning as a way to improve the efficiency of silicon based solar cell and to reduce the cost of the PV. Indeed with the aid of a heterojunction it is possible to achieve higher built-in voltage and higher cell open circuit voltage with respect to the homojunction. Moreover thin amorphous film technology, using low temperature processes (below 300°C), in principle allows the use of thinner silicon wafer that could suffer of high temperature step required in the homojunction approach to the cell efficiency. Many efforts have been spent by several research groups to address the main problems of the HJ device related to the silicon surface cleaning, defects at the interface, thin film doping, metal contact and device architecture. From '90 years the progresses of SANYO results have driven the scientific community to achieve higher cell efficiency. Actually SANYO has demonstrated the possibility to fabricate heterojunction cell on c-Si wafer thinner than 100 m, leading the amorphous crystalline silicon heterojunction concept toward thin film solar cell.

In this chapter we overview the heterojunction cell concept out lighting the problems encountered and the current understanding of the fundamental device physics to achieve highest efficiency.

**Keywords:** Amorphous silicon, cleaning, doping, heterojunction, lifetime, numerical model, plasma treatment, screen printing, solar cell, silicon, texturing, thin film, transparent conductive oxide.

### **1. INTRODUCTION**

Basically the amorphous/crystalline silicon (a-Si:H/c-Si) heterojunction solar cell cannot be considered as a thin film cell, since, up to now, the silicon wafer act as a base. Nevertheless all the technologies involved in the HJ cell fabrication are more related to the thin film than to the conventional silicon based cell. This allows in the near future reducing the silicon wafer thickness thus approaching the thin film cell. Therefore in this chapter we propose a brief overview of the HJ cell.

Hydrogenated amorphous/crystalline silicon (a-Si:H/c-Si) heterojunction (HJ) has been widely studied since 70 years [1]. Even though a stacked a-Si:H/c-Si tandem junction has been reported in 1983 [2] and several years have been spent on understanding transport mechanism and band

**Address correspondence to Mario Tucci:** ENEA, Research Center Casaccia, Via Anguillarese 301, 00123 Rome Italy; Tel: +39 630484095; Fax: +39 30486405; E-mail: mario.tucci@enea.it

discontinuity at the heterointerface [3-9], the first efficient cell comparable with the c-Si based top cell [10] has been demonstrated in 1992 when the HIT cell [11] has been presented to the scientific community. A cross section of the HIT cell first release is depicted in Fig. **1**. The thin intrinsic layer between the doped a-Si:H film and the c-Si base works as an effective silicon surface passivation that strongly reduces the interface recombination, leading to an efficiency of 18.1% using temperature lower than 200 °C in the cell manufacturing process. In particular that cell had not only the a-Si:H front side emitter, but also the rear side a-Si:H base contact. Due to a-Si:H emitter poor conductivity the front side contact has been formed by TCO deposition and the rear side contact has been ensured by Al evaporation. In 1994, SANYO ltd. overcame 20% efficiency with heterojunction solar cell based on a n-type Czochralski silicon textured absorber [12, 13]. In 2009 SANYO achieved 23% efficiency on practical size of 100 cm2 and 22.8% on c-Si wafer thinner than 100 m [14, 15]. Even though SANYO patent on HIT cell has limited the industrial application from other solar cell manufacturing companies, many research groups worldwide have investigated HJ approach to achieve silicon based solar cell using low temperature processes needed for the a-Si:H film deposition as well as TCO fabrication. Indeed the possibility to reduce the thermal budget in cell manufacturing has been considered as a way to reduce the solar cell cost. A qualitative comparison of the thermal budget needed for the homojunction c-Si conventional and a-Si:H/c-Si heterojunction cell fabrication processes in Fig. **2** are reported. Actually the SANYO patent has been expired therefore a growing interest on this technology is rising up from solar cell manufacturing companies [16].

**Figure 1:** Schematic cross section of the HIT cell first release.

All the other research groups involved in the HJ investigation have reached lower efficiency with respect to the impressive SANYO results, despite to their strong efforts. Fig. **3** shows the SANYO progress in conversion efficiency with respect to the other competitors.

**Figure 2:** Qualitative comparison of the thermal budget needed for the homojunction c-Si conventional and a-Si:H/c-Si heterojunction cell fabrication processes.

*Heterojunction for Silicon Photovoltaics Silicon Based Thin Film Solar Cells* **279**

**Figure 3:** Progress in conversion efficiency of HIT and other institutions' results for heterojunction solar cells.

We can summarize a series of advantages and related to the HJ technology:


Nevertheless several drawbacks still affect the market breakthrough of this technology:


### **2. DEFECTS AT THE HETEROJUNCTION**

The heterointerface is the heart of the HJ device; the photogenerated carriers within the c-Si absorber material have to cross the interface to be collected by the emitter and during this path they survive only if recombination at interface is lower than collection probability. This general concept becomes critical when one of the two materials is amorphous. Indeed, the crystalline silicon edge represents a strong discontinuity of atoms network that in the well known Tham-Shockley theory can be represented by a defect density distribution laying around one third of energy gap from the valence band. The number of states has been estimated as two third fraction of the atomic density within the volume [19, 20]. A schematic picture of p-type doped c-Si edge discontinuity is depicted in Fig. **4(a)**. The Fermi level moves toward mid gap since a pinning occurs on the defect distribution. On the other side a-Si:H is a well known defective atom network even if hydrogen introduction helps to reduce the defect density amount [21]. The defect density is so high that the energy band theory, based on the crystal network periodicity and the thigh binding model, can be approximated on a short range periodicity and still survives introducing a pronounced density distribution along the forbidden gap as depicted in Fig. **4(b)** for an intrinsic material. Due the high defect density the edge of a-Si:H layer not differ too much from the bulk material in terms of energy band distribution. Therefore it is likely imaging that the probability of an electron to recombine crossing the interface formed jointing the two band diagrams and their density distributions, is high as depicted in Fig. **4(c)**. The decision to immediately escape from this game could be understandable, but the challenge in finding a strategy to overcome the difficulties and then producing low cost solar cells still based on c-Si absorber fascinated many research groups for long time and still now several aspects are under debate.

**Figure 4:** (a) Band bending at the c-Si surface due to Tamm Shokley states. (b) Schematic band diagram of a-Si:H material. (c) Energy band distribution at c-Si/a-Si:H interface.

#### **2.1. Nature of Defects in a-Si:H**

In this paragraph we focus on the nature of the interface defect density and the possibility to reduce their impact on the recombination by introducing the silicon surface passivation concept. In c-Si when N tetravalent atoms combine into solid they modify their orbitals to four hybrid sp3 disposing in a tetrahedral shape. Taking into account Pauli principle they form 2N bonding orbitals (valence band) and 2N anti-bonding orbitals (conduction band), as depicted in Fig. **5(a)**, where the bandgap between the two bands is empty. When the atom network is disordered and a great

#### *Heterojunction for Silicon Photovoltaics Silicon Based Thin Film Solar Cells* **281**

amount of bonds are weak and stressed, as in a-Si:H, two tails of states appear in the forbidden bandgap. If the bonds are not saturated but dangling within the network, then a distribution of states appears at midgap of the forbidden bandgap. They determine the position of Fermi level and act as recombination centres. Hydrogen, introduced during the a-Si formation in order to reduce the dangling bond density, alters the tetrahedral structure of Si and modifies the energy band distributions. If a Si atom is bonded to three Si atoms and to one H atom a distribution as depicted in Fig. **5(b)** is obtained. Since the Si-Si bonding energy is 3.4 eV while the Si-H that is 2.4 eV, a wider separation between bonding and anti-bonding orbitals occurs. The 1s H orbital is at energy lower than that sp3 therefore the resulting bonding orbital lies within valence band, while the antibonding, due to the wider separation, lies at the bottom of conduction band. This reduces the density of states (DoS) close to the band edge, thus increasing the energy bandgap of the semiconductor (1.72eV). A more precise description of the localized states should include the Coulomb effect between electrons.

If two electrons with opposite spin are on the same energy state they repulse each other inducing an energy variation U (correlation energy) of the state [21, 23]. If the state is in the extended bands, U can be neglected and the one-electron approximation is still valid. If the state is localized (gap), the average distance between the two electrons can so short that U cannot be neglected since it assumes value of tens meV. This means that the density of states depends on their occupation. The most common defect in a-Si network is the dangling bond (DB), denoted as Tz q in which z is the coordination number and q is the state of charge. Therefore the Si atom tetrahedric bonded in the network is T4 0 , while a T3 0 is a neutral DB. This atom still assumes a tetrahedric configuration, but introduces two states within the gap: one empty at higher energy and one filled at lower energy as depicted in Fig. **4(c)**. These states are separated by the energy U. If T3 0 loses an electron it becomes T3 + thus altering the hybridization orbitals from sp3 to sp2 and forming planar molecules having 120° angles between each other. As a result an increment of energy related to the DB occurs. In other words, if the centre T3 0 captures a hole has a more stable energetic situation. On the contrary, if T3 0 captures an electron, becomes T3 and a de-hybridization occurs towards p orbitals, having 95° between each other. Also this effect produces an energy reduction of the DB. Therefore both cases produce bond relaxation leading to correlation energy Ueff lower than U that can also assume negative values [24]. A schematic view of the density of states with Ueff > 0 and Ueff < 0 is reported in Fig. **5(d)**. If Ueff > 0 the states under the Fermi level are occupied with one electron and then a strong Electron Spin resonance signal appears. If Ueff < 0 the states under the Fermi level are occupied with electron pair having opposite spin and then there is no evidence from ESR measurements. Therefore if the ESR signal is lower with respect of expected DoS; this probably means that states with Ueff < 0 and Ueff > 0 are simultaneously in equilibrium [23].

This DB behaviour is referred as amphoteric nature and the resulting defect density distribution is referred as defect pool model [25, 26]. The model proposes the existence of a pool of defect from which the density of dangling bond states are determined by a chemical equilibrium process, leading to a minimum of the system free energy. In the different presented defect pool models, the equilibration process involves breaking of weak Si-Si bonds, diffusion of hydrogen as well as reformation of Si-H bonds. Winer [25] developed a suitable framework for the description of the defect pool model, where the chemical equilibrium between dangling bonds and weak Si-Si bonds is similar to the equilibrium between vacancies and interstitial defects in crystalline silicon. In particular, the neutral defect formation in intrinsic a-Si:H is described by the reaction:

#### SiH + SiSi D<sup>0</sup> + SiHSi **(1)**

where SiSi are the weak Si-Si bonds (valence band tails), SiH group provides that hydrogen atom that enables the equilibration, D0 are the neutral (*i.e.* occupied by one electron) dangling bonds and SiHSi group traps the hydrogen released by the SiH. This equation establishes that the system free energy minimum is determined by the equilibrium between the entropy produced by defect creation and the enthalpy cost of transferring hydrogen atoms from SiH group to trapping H sites.

**Figure 5:** (a) Si bonding and antibonding; (b) tails formation in a-Si:H energy gap due to H; (c) DB related states within energy gap; (d) simultaneously presence of states with U > 0 and U < 0 within a-Si:H energy gap.

Applying the law of mass action and assuming that the pool of defect energies is expressed by a Gaussian distribution with peak at Ep, Winer derives a defect density with Gaussian shape with width equal to and centered at Ep-<sup>2</sup> /E0 if kT<E0 or at Ep-<sup>2</sup> /kT if kT>E0. is the standard deviation of the Gaussian defect pool distribution that can be identified with the concentration of bonded hydrogen, whose variable back bond strain determines the broad distribution of potential defect sites. therefore is a measure of the disorder of a-Si:H material as well as E0 that represents the slope of the valence band tail states.

The shift of the defect distribution with respect to the defect pool means that the free energy system minimum does not coincides with the energy at which the potential defect sites are most numerous.

In the Winer's theory these considerations apply to undoped a-Si:H materials. In order to take into account the effect of dopant atoms, Winer considers that in a n-type material, the following reaction occurs:

$$\mathbf{D}^0 + \mathbf{e}^\* \leftrightarrow \mathbf{D} \tag{2}$$

where D- is the concentration of defects that have captured one electron from the conduction band. An analogous reaction involving holes has to be considered for p-type materials. From a qualitative point of view, the above equilibrium equation says that the presence of electrons determines a larger defect concentration in reaction 1 and that in n-type films the most likely defect are Dstates. Mathematically speaking, the increase of defect concentration is caused by the reduction of the enthalpic cost to form a defect due to the difference between the energy gained in dropping an electron from the Fermi level to the defect level and the energy spent (correlation energy U) in bringing two electrons in the same defect state. This energy variation determines a variation of the defect chemical potential that becomes Fermi level dependent and shifting of the maximum defect distribution that now occurs at Ep+U-2<sup>2</sup> /E0. From this equation derives that if is sufficiently large, *i.e.* the defect pool is sufficiently wide, D- in a-Si:H material lies deeper than D0 in undoped materials even though the correlation energy is positive. These results are summarized in Fig. **6**, where the gap-state distribution for n-type, intrinsic and p-type a-Si:H materials are calculated basing on the above theoretical considerations. Powell and Deane [26] improved the defect pool model proposed by Winer, including in their theory the simultaneous presence of defects in all three charge states in all material types, the weak bond depletion due to defect formation and the hydrogen entropy. The microscopic model assumed by these authors for the defect formation is described by the following three chemical reactions:

$$\mathbf{W} \mathbf{B} \leftrightarrow (\mathbf{\mathcal{D}}) \tag{3}$$

$$\text{SiH} + \text{WB} \leftrightarrow (\text{D} + \text{Si} \cdot \text{H}) + \text{D} \tag{4}$$

$$\text{2SiH} + \text{SiSi} \leftrightarrow (\text{D} + \text{Si-H-H-Si}) + \text{2D} \tag{5}$$

As a starting point for the calculation of the defect density they determined a general expression for the defect chemical potential taking into account the energy of electron (or electrons) of the defect, the entropy associated with the electron occupancy of the defect and the entropy associated with the location of the defect on alternative hydrogen sites. For the calculation of the defect density D(E) at energy Et from weak bond states they derive the following expression:

$$D(E) = \int \frac{P(E)D(E\_\prime)}{1 + \exp\left\{2\left[E\_\prime(E) - Et\right]/kT\right\}} dE\tag{6}$$

where P(E)gt(Et) is the density of weak bonds at energy Et that lead to potential defect sites at energy E, d is the defect chemical potential and the integral is extended over the all weak bond energies. Assuming that D(Et) is given by the valence band tail states with an exponential behavior and that P(E) has a Gaussian distribution with pool width and maximum Ep, they calculated the density of positive (D<sup>+</sup> ), neutral (D<sup>0</sup> ) and negative (D- ) defect distribution by:

**Figure 6:** Gap state defect distribution for n-type, intrinsic an p-type doped a-Si:H with the appropriate defect chemical potentials (U = 0.25eV) [25].

where *f <sup>+</sup>* , *f <sup>0</sup>* and *f-*are respectively the occupancy functions of the amphoteric dangling bonds occupied by zero, one or two electrons, respectively and D(E) is calculated from equation.

The main results are reported in Fig. **7** for intrinsic material, and in Fig. **8(a)**, **(b)** for n-type and ptype respectively.

As for the Winer model the Gaussian distribution are shifted with respect to the pool of potential sites by energy dependent on for the neutral defect and by a linear combination of s and U for

#### *Heterojunction for Silicon Photovoltaics Silicon Based Thin Film Solar Cells* **285**

charged defect states. However, it is important to underline that both charged states are present even for undoped material and that their density is approximately four times higher than density of neutral defects.

**Figure 7:** Defect pool in intrinsic a-Si:H at different temperatures [26].

**Figure 8:** Defect pool in n-type (a) and p-type (b) doped a-Si:H [26].

#### **3. RECOMBINATION** *VIA* **DEFECTS**

As pointed out in section 2, the carrier transport in the HJ is dominated by the defect density distribution at the interface. Surface recombination has to be considered to evaluate the junction quality. Shockley-Read-Hall theory is always used to describe bulk recombination *via* defects [27], [28] even if it considers defect as discrete level in the gap having two states: neutral or charged. This concept can be extended to continuous distribution in disordered semiconductors, as in aSi:H, as suggested in [29]. Moreover the states located between the quasi Fermi levels work as recombination centers and their re-emission probability is almost negligible. In turn, the states between quasi Fermi levels and bandgap edges act as trap centres with a re-emission probability toward the band edge. Concerning the DB, Olibet *et al.* [30] showed that the recombination rate through defect density within the a-Si:H is linearly dependent on density of states at the interface:

$$R\_{D8} = \frac{n\sigma\_{\nu}^{0} + p\sigma\_{\rho}^{0}}{p\sigma\_{\rho}^{0}} \text{v}\_{\text{th}} N\_{D8} \tag{7}$$

where n and p are the free carriers, NDB is the total density of DB, vth is the thermal velocity, <sup>0</sup> p,n are the capture cross section for neutral states and <sup>+</sup> n, p are the capture cross section for charged states. Of course to reduce the recombination a neutralization of the NDB is needed, but the equation (7) also states that recombination *via* DB can be determined by the largest free carrier density. This is opposite to the SHR recombination rate which is limited by the lowest carrier density [27, 28]:

$$R\_{\rm SIR} = \frac{np}{\frac{P}{\sigma\_n} + \frac{n}{\sigma\_p}} \mathbf{v}\_{th} N\_{DB} \tag{8}$$

If doped a-Si:H is considered, the equation (7) reduces to SHR case since one type of charged dangling bond is dominant. Indeed in n-type doped a-Si:H the majority of DB are negatively charged. To describe the surface recombination rate a similar approach in HJ, as in equation (7), can be followed since the a-Si:H dominates the defect density:

$$U\_{S\omega} = \frac{n\sigma\_{\nu}^{0} + p\sigma\_{\rho}^{0}}{\frac{p\sigma\_{\rho}^{0}}{n\sigma\_{\nu}^{+}} + 1 + \frac{n\sigma\_{\nu}^{0}}{p\sigma\_{\rho}^{-}}} \mathbf{v}\_{h} N\_{S} \tag{9}$$

where NS is the density of states at the c-Si surface. Then it is possible to calculate the effective surface recombination velocity Seff [31]:

$$\mathbf{U\_{Sur}} = \mathbf{S\_{eff}} \Delta \mathbf{n\_s} \tag{10}$$

ns is the carrier density at the edge of space charge region within the c-Si, formed by the band bending that neutralizes the built-in potential at the junction. Calculated Seff on c-Si lightly pdoped (130 cm) surface as a function of the charge generation for different values of Ns and surface charge distribution Qs and different ratio between capture cross sections are reported in Fig. **9**. The proposed model has been validated on both n-type and p-type doped c-Si surface passivated by different kind of passivation layers. a-Si:H passivation is due to the low NS and the symmetrical neutral capture cross section for both carriers. Moreover a-Si:H passivation performs better on n-type c-Si surface with respect to p-type, because holes have a larger capture cross section than electrons <sup>0</sup> p > <sup>0</sup> n.

In c-Si the effective carrier lifetime *τ*eff can be determined by recombination in the bulk and at the surfaces according to [32]:

$$\frac{1}{\tau\_{\text{eff}}} = \frac{1}{\tau\_{\text{bulk}}} + 2\frac{S\_{\text{eff}}}{W\_{\text{eff}}} \tag{11}$$

Therefore we can summarize that two mechanism can be used to passivate the silicon surface: 1) reducing the density of states; 2) induce a field effect able to deplete one carrier in c-Si close to interface by varying the state of charge of the DB

**Figure 9:** Measured and calculated Seff for the lightly n-type doped c-Si surface passivated by stacks of intrinsic plus doped layers. Empty symbols and dotted lines replicate the microdoped layers passivation for comparison purpose. The symbols show the measurements, and the lines the fits [30].

being at the a-Si:H/c-Si interface. This effect causes a repulsion of electrons or holes from the surface states. The first may be accomplished by hydrogenation of silicon dangling bonds at the c-Si surfaces [33] that can be easily performed and monitored by flash test while dipping the c-Si substrate into HF bath [34]. Intrinsic *a*-Si:H films are known already for some decades to yield good *c*-Si surface passivation [35-37] Experimentally, such films are commonly prepared by plasma-enhanced chemical vapor deposition (PECVD) with SiH4 as precursor gas, possibly diluted in H2. For the plasma-excitation frequency 13.56 MHz is often chosen [38, 41], although the successful use of very high frequencies (*e.g.*, 40 MHz [42, 43] or 70 MHz is reported too [44]). For device-grade films, usually the deposition temperatures are about 200°C and the system is kept at a relatively low pressure (0.1-1 Torr). Other techniques reported to give good results are directcurrent PECVD [44] and hot-wire or catalytic CVD [46, 47].

#### **4. HYDROGEN AND THERMAL ANNEALING**

It has been well established that hydrogen plays a role in the c-Si surface passivation. From infrared attenuated total reflection spectroscopy (ATR) [48], the authors have found that for a-Si:H thickness lower than 20 nm the SiH2 content is higher with respect to the SiH. This indicates a poor network formation and islands growth. After 4 nm of a-Si:H growth, a certain steady state equilibrium is reached in which the amount of both SiH2 and SiH species is roughly similar, as reports in the upper side of Fig. **10**. From that point the DB amount becomes lower. Then, as reported in lower part of Fig. **10** the best thickness for the buffer intrinsic layer in HJ solar cell can be defined. a-Si:H thinner than 5 nm reduces the HJ cell efficiency due to defect while a-Si:H thicker than 5 nm introduce just a filtering effect.

It has been found that low-temperature annealing is beneficial for the passivation quality. It has been observed that annealing can yield an extremely low interface recombination activity, even at temperature below 180°C [44]. Carrier injection dependent recombination calculations suggest that the origin of this phenomenon is related to dangling bond reduction at the interface instead of to a field effect. This behaviour is similar to the SiO2/c-Si passivation [49].

**Figure 10:** (a) Depth profile of hydrogen contents; (b) HJ solar cell efficiency, as a function of a-Si:H buffer layer thickness [48].

To evaluate the effect of thermal annealing several HJ samples have been prepared starting from 300 mm thick 3cm n-type doped (100) FZ c-Si with mirror polished surface. After a cleaning in HF 4% bath for 45s the a-Si film has been deposited in a RF 70MHz PECVD system in the following conditions: 300mTorr, 15mW/cm2 , 11 sccm SiH4 and 29 sccm H2. Before a-Si:H deposition 50 sccm H2 has been fluxed over the substrate to stabilize its temperature [44]. 50 nm thick a-Si:H layers have been deposited on both side of the c-Si wafer to evaluate the surface passivation quality. Minority carrier effective lifetime eff changes over thermal annealing time of bifacial a-Si:H passivated c-Si wafers is reported in Fig. **11**. It is quite surprising to note that low temperature deposited sample (T = 130 °C) shows an as grown poor lifetime eff = 12.2 s (measured with a flash lifetime Sinton Consulting WCT100 tester at injection level of 1x1015 cm-3 [50]) that, after prolonged thermal annealing reach a lifetime value of 4 ms. The experimental data can be fitted by the stretched exponential function helpful to describe the relaxation of disordered systems towards equilibrium [51, 53]. Hydrogen diffusion, arising from a distribution of energies for trap states and barrier heights, was argued to assume the stretched-exponential relaxation [54].

**Figure 11:** Minority carrier effective lifetime as a function of thermal annealing time. Symbols refer to measurements, curves refer to stretch exponential fit. In the inset an HRTEM picture is reported for a-Si:H deposited at 200°C, over (100) 3cm FZ c-Si [44].

$$\tau\_{\rm eff} \left( t\_{\rm ams} \right) = \tau\_{\rm eff}^{\rm SS} \left[ 1 - \exp \left[ - \left( \frac{t\_{\rm ams}}{\tau} \right)^{\rho} \right] \right] \tag{12}$$

where sseff is the saturation value for eff, and the dispersion parameter (0 < < 1) and effective time constant, respectively.

Fig. **12** shows in detail the evolution of eff related to the sample deposited at 130°C during the thermal annealing time as a function of injection level. The uppermost curve represents the maximum bulk lifetime based on Auger recombination [55]. The experimental data curves can be explained with the model expressed before, in which the recombination mechanism at the HJ is due to DB having amphoteric nature. To fit the data at different thermal annealing time (solid line in Fig. **12**), it is sufficient to vary NS in the recombination mechanism reported in equation (7) (<sup>0</sup> p/<sup>0</sup> n=20 and <sup>+</sup> n/<sup>0</sup> n= p/<sup>0</sup> p = 500). Qs has been kept constant at-2.2x1010cm-2 [55]. This assumption means that the charge does not vary during the thermal annealing exposure leading to the conclusion that the a-Si:H passivation is not promoted by any field effect at the interface. Hydrogen passivation of DB at c-Si surface is a more convincing explanation for the observed improvement. For bulk a-Si:H, relaxation is governed by release of hydrogen from trap sites [54]. In case of few nm a-Si:H thinner films, typically higher DB densities are measured, compared to thicker layers [56]. This is related to the hydrogen content within the first layer of the growth. The most relevant condition for the improvement under annealing of the intrinsic a-Si:H(*i*)/c-Si interface passivation is to avoid epitaxial film as depicted in the inset of Fig. **11** [44]. In this experiment several 50 nm thick a-Si:H films have been grown at different temperatures on HF 5% oxide free (100) p-type 3cm FZ c-Si wafer, by RF 13.56MHz PECVD system using the following conditions: 20sccm SiH4, 500mTorr, 12 mW/cm2 . The imaginary part of the pseudo dielectric function <1> + i <2>, as obtained from spectroscopic ellipsometry, for thin a-Si:H layers deposited at different temperature on c-Si is reported in Fig. **13**.

**Figure 12:** Measured (symbols) values for eff as function of the carrier injection level for films deposited at 130 °C. Each curve is measured at different thermal annealing time exposure. Solid lines represent the calculated recombination-model [44].

Since samples deposited at T > 200 °C show the crystalline signature, they can be considered epitaxial. In turn samples deposited at lower temperature are more amorphous. Films deposited at very low temperatures show initial poor eff value that increase after thermal annealing. The c-Si surface passivation quality improves for samples deposited at higher temperature up to 180°C. After 30 min of thermal annealing al temperature of 260 °C the eff rises up to 1ms. Sample deposited at 205°C has higher eff as grown value and is not affected by the annealing. Samples deposited at higher temperature show a strong detrimental of eff after annealing procedure. Therefore 200 °C as the deposition temperature can be used to discriminate the two phases of the deposited a-Si:H layer: below amorphous, upper epitaxial. Epitaxial material grown at such low temperatures is known to be defective at the interface. Clustered H-related defects such as Hplatelets [57] may be present at the interface with increasing density as decreasing deposition temperature [58]. For deposition temperature below 550 °C, breakdown of the epi-Si into an amorphous phase often occurs, which depends on the precise deposition conditions [59]. At the brink of epi-breakdown, these films are usually very defective [60]. At breakdown itself, a mixedphase transition region consisting of a-Si:H cones embedded in a c-Si matrix exists [61]. The detrimental effect of low-temperature annealing on the passivation quality can be related to the low hydrogen content of the interfacial epitaxial layer. Indeed, this contains about 30-100 times less hydrogen than a-Si:H [62]. During thermal annealing, hydrogen effuses from higher hydride states, leaving a dehydrogenated DB at the a-Si:H/c-Si interface. In turn, when the amorphous phase is dominant at the a-Si:H/c-Si interface, a larger hydrogen source is present to guarantee repassivation of the interface states. Several deeper investigations concerning the buffer layer deposition conditions, remarked the role of the silane depletion fraction in the plasma [43], rather than film deposition-rate or ion-bombardment before a-Si:H deposition [11, 63, 64]. High-quality interface passivation has been associated with highly-depleted plasmas, close to the microcrystalline silicon (µc-Si) growth regime [43]. These observations show that even though epi-Si is undesired, the film growth conditions that guarantee highly quality passivation are quite related to those yielding epi-Si interfaces. Deposition temperatures lower than 150 °C in the initial amorphous layer growth are also suggested in [65, 66] to avoid detrimental epilayer formation. However the epilayer can be completely avoided reducing the deposition temperature down to 70°C [67].

**Figure 13:** Imaginary part of the pseudo dielectric function <1> + i<2>, as obtained from spectroscopic ellipsometry, for thin a-Si:H layers deposited at different temperature on c-Si [38].

To complete the overview on the intimate interface between a-Si:H and c-Si we report on the use of epilayer instead of amorphous at the interface. According to [68] epitaxial growth has been obtained depositing a-Si:H layer over 14 cm p-type doped (100) c-Si deoxidized by HF dip wafer, in the following conditions: 200 °C substrate temperature; 10 mW/cm2 RF power density; H2/SiH4 = 2. Then n-type a-Si:H has been deposited and the top contact has been ensured by ITO. From HRTEM reported in Fig. **14** the presence of the epi-Si at the c-Si edge is evident. After 6nm a mixed phase appears and a completely amorphized phase is formed close to ITO layer. Quite high open circuit voltage of 664 mV and a cell efficiency of 17% have been reached. Therefore the authors argued that the loss in Voc is not due to the presence of epilayer. Moreover the epilayer itself deposited on c-Si wafer did not perform a good surface passivation. Since this Voc value is lower than that reported in [30] it is possible to conclude that amorphous phase show better performances to passivated the c-Si surface with respect to epi-layer but the epi-layer can be used too in solar cell application. The relevant point is that mixed phase must be avoided and the abrupt junction must be preferred and performed to fabricate an effective HJ solar cell. To complete the concerning on thermal annealing of a-Si:H layer to enhance the c-Si surface passivation, it is interesting to introduce a particular technical procedure proposed in literature that differs from the commonly used quartz tube or hot plate in nitrogen environment. In practical the authors of [69] suggested to expose the HJ sample to a commercial 2.45GHz magnetron generated microwave (MW) radiation. They operated the MW at 700W also controling the power transferred to the sample by inserting a defined quantity of water (200 ml) as additional absorber. The MW heating coefficient of the sample has been used as 114 ±1.6 K/s. To evaluate the effectiveness of this technique a comparison is reported with respect to a hot plate (HP) procedure settled at 210°C. Two reported with respect to a hot plate (HP) procedure settled at 210°C. Two nominally identical samples have been respectively exposed to MW for 1.6 s and HP for 10 s to reach the same peak

temperature as reported in the inset a) of Fig. **14**. Several cycles have benn performed and compared in terms of lifetime eff and reported in the inset c) of Fig. **15**. Moreover it is worth to note that using deposition temperature of 130°C for the HJ formation Seff lower than 3 cm/s corresponding to a eff > 4 ms has been achieved. As expected the MW resulted much faster, indeed after 2 cycles the passivation saturation has been achieved, while the same results needed 20 cycles with HP. This effect is due to MW absorption mechanism in a-Si:H, which selectively affects the polar Si-H bonds thus enhancing the release of H from the reach hydrogenated surface leading a better surface passivation. From FTIR measurements performed on the samples after several annealing cycles it has been observed an enhancement of Si-H on the c-Si surface as a consequence of reconfiguration and decrease of both Si-H peaks at 2000 cm-1 and H-Si-H peak at 2090 cm-1 in a-Si:H layer thus resulting in a surface passivation enhancement. Of course the prerequisite for this is a hydrogen rich a-Si:H layer at the interface, even if very low hydrogen relocation would be needed to reduce the defect density at the interface [70].

**Figure 14:** HRTEM image of a mixed phase silicon layer (c-Si and a-Si:H) grown on p-type 14Wcm (100) c-Si [68].

**Figure 15:** Passivation of nominally identical samples being pulse-annealed with similar temperature profiles. (a) T profiles for a 10 s contact with the HP at 210 °C (black line) and for a 1.6 s MW exposure [gray (red) dashed line]. (b) Comparison of S upon successive pulse annealing steps with T profiles shown in (a) on the HP (black) and in the MW [gray (red)]. (c) Linear plot of Seff with stretched-exponential fit for HP data [69].

### **5. DOPING AND DEFECTS**

While post-deposition thermal annealing has a beneficial effect on c-Si/a-Si:H interface passivation, this may not be the case for a few nanometers thin a-Si:H/p<sup>+</sup> a-Si:H stacked structures deposited on c-Si surfaces. Indeed the H transfers from a-Si:H film into H2 state creating defects within the material. Moreover presence of such doped layers may result in lowered Si–H bond rupture energies in underlying a-Si:H buffer. Both effects are attributed to the particular energetic position of the Fermi level in the amorphous material rather than on the actual dopants [71]. The same mechanism has been attributed as well to doping dependent hydrogen desorption in such material [72]. Since the a-Si:H layer is only a thin buffer before doped film growth, it is relevant to evaluate the effect of doping layer deposited over this film to form the emitter layer of the HJ solar cell. Indeed it has been demonstrated that boron doped a-Si:H film deposited on top of intrinsic a-Si:H promotes a hydrogen effusion even at low temperature [73]. According to [74], different eff have been obtained using different stacked structure on c-Si wafer as reported in Fig. **16**. For a-Si:H/c-Si interface passivation, doping has been observed to produce very similar trends: postdeposition annealing of p-type passivation layers yielded at much lower temperatures already losses in passivation, compared to their n-type counterparts. Hydrogen effusion occurs at higher temperature for i/n-type a-Si:H stacked layer with respect to the i/p-type a-Si:H stacked layer, and this reflects to the c-Si passivation as reported in Fig. **16**. The hydrogen diffusion energy *E*<sup>D</sup> \* , defined by *D*H = *D*<sup>0</sup> \* exp(-*E*<sup>D</sup> \* /k*T*), in *a*-Si:H and *c*-Si is displayed as function of *E*F in Fig. **17** [75]. The diffusion coefficient, *D*H, describes the motion of hydrogen in the silicon matrix, where *D*0 \* = 10-3 cm2 s -1 is the theoretical diffusion coefficient unaffected by traps [76], k is the Boltzmann constant and T is the temperature. The diffusion activation energy *E*<sup>D</sup> \* equals *E*S-H, where *E*S is the saddle point for interstitial H migration and H the chemical potential of H atoms [77, 78].

**Figure 16:** Influence of stepwise annealing treatment on the c-Si surface passivation quality, expressed by eff (evaluated at 1.0 x1015 cm−<sup>3</sup> ), for doped a-Si:H stacks as shown in the inset sketches. Open symbols represent doped single films, closed symbols represent stacks, featuring an intrinsic buffer layer. Symmetric structures have been deposited on both wafer surfaces. Results for as deposited material are indicated in the abscissa by the label a.d. Symbols represent experimental data; the lines are guides for the eye [74].

**Figure 17:** H diffusion energy *E*<sup>D</sup> \* in *a*-Si:H (stars), *c*-Si:H (open circles) or *c*-Si:H (closed circles) as a function of *E*F, at *T*ann = 350°C. The superposed straight lines represent the dependence of the formation enthalpy *H* of defect in the respective charge states *q* = +, 0 and-on *E*F. *E*M represents the middle of the bandgap [74].

When *E*F is closer to the VB maximum (VBM, *i.e. p*-type doping) this results in decreasing values for *E*<sup>D</sup> \* (see region with label (1)). For *n*-type doping, *E*F must be brought relatively closer to the CB minimum (CBM) to yield a similar drop (region with label (3)). Since doping of a-Si:H films occurs by incorporation of substitutional impurities [79], it may induce additional localized states in the film [80].

A schematic model of donor and defect bonding states is depicted in Fig. **18**. The sp3 hybridized states of P4 donor are split into bonding and antibonding donor levels, while the silicon defect has three bonding states and a DB at midgap (the antibonding is not shown). The transfer of the electron from the donor onto the DB gives energy of Ep-Ed2 that is 0.5-1eV. This energy transfer leaves the both the defect and dopant pair to lower energy configuration. Therefore in a-Si:H defect and DB are not independent consequence of the doping, but are intrinsically linked. Substitutional doping in a-Si:H does not occur without defect.

**Figure 18:** Schematic energy diagram of the donor and DB, showing the energy gain by the transfer of an electron from donor to DB.

The defect-formation in a semiconductor mainly depends on the energetic position of its Fermi level rather than on the physical nature of a dopant. Therefore dangling bond formation enthalpy can change in the intrinsic absorber layer depending on its position within the gap [81]. When intrinsic is grown close to doped material Ef has the maximum deviation from midgap moving toward energy position where larger T3 density is expected. Due to the asymmetry in U energy, larger density of T3<sup>+</sup> is generated when Ef is close to VBM with respect to the T3 density generated when Ef shifts toward to CBM, as evident from Fig. **17**. This reflects in hydrogen effusion at lower temperature when i a-Si:H is a buffer sandwiched between doped materials whit respect to the bulk intrinsic [74]. This means that the doped layer plays a role in defect creation in the intrinsic layer underneath. Also this suggests the reason for poorer passivation of i/p a-Si:H with respect to i/n a-Si:H. Indeed in this last the shift of EF in the buffer layer towards CBM is not sufficient to overcome the energy barrier U (see Fig. **18**). Therefore i/n a-Si:H is able to passivated the c-Si surface at the same level of the intrinsic alone. Then we can conclude that doping of a-Si:H films may result in Fermi-energy dependent defect generation in the layer, detrimentally affecting its passivation properties. p-type films passivate worse than their n-type counterparts due to positive correlation energy of DB in a-Si:H. Therefore an intrinsic buffer layer is needed to decoupling passivation and doping properties. p-type films may still generate defects in the intrinsic buffer layers underneath promoting hydrogen effusion. For optimal device performance, a careful assessment of the deposition conditions of doped films is thus strongly needed. Directly deposit doped a-Si:H on c-Si substrate has been not the best suggestion since, as we detailed discuss in the following paragraphs, the first layers of doped a-Si:H result highly defected due to the presence of dopant atoms at the beginning of the a-Si:H layer growth [11, 82]. The poor c-Si surface passivation of doped a-Si:H film suggested the insertion of few nanometres of intrinsic a-Si:H layer before doped layer [11].

### **6. MEASURING THE DIT(E)**

Constant final state yield spectroscopy CFSYS is interesting way to investigate the a-Si:H/c-Si interface as proposed in [67]. The technique is based on the photoemission of a semiconductor irradiated by monochromatic photons (*i.e.* generated by UV light of a Xenon lamp filtered by a monochromator) having energy in the range 4-7 eV, keeping 0.1-0.2 eV higher than the material under test vacuum level. Nevertheless some limitation in the accuracy [83], the photoemission provides a signal directly proportional to the DoS, under the assumption that it is constant. Since the escape depth of an electron increases at low kinetic energies, a thicker layer (4-5 nm) under the surface can be investigated. The photoemitted electrons can be collected as a function of the photon energy.

The valence band edge can be determined by the slope of a straight line in a plot of √Y(E) as a function of E, Y(E) being the photoelectron quantum yield. The number of occupied states at the valence band, evaluated as 2 x 1021 cm-3eV-1 [84], can be used as reference in the photoemitted electron numbers at different energies. A comparison of DoS for p-type (10<sup>4</sup> ppm B2H6), n-type doped (2x10<sup>4</sup> ppm B2H6) and intrinsic a-Si:H films growth at 180 °C on p-type doped c-Si substrate is reported in Fig. **19** [85].

**Figure 19:** N(E) distribution in the bandgap of p-type (104 ppm B2H6), n-type doped (2x10<sup>4</sup> ppm B2H6) and intrinsic a-Si:H films growth at 180°C on p-type doped c-Si. The arrows remark the position of the Fermi level. The vertical line is the valence band edge [85].

The position of Fermi level from the valence band edge can be evaluated as follows: 1.22 eV for undoped a-Si:H (confirming the n-type behavior of the intrinsic film); 1.56 eV for n-type doped a-Si:H (0.18 eV from conduction band if 1.74 eV is assumed as a-Si:H bandgap); 0.8 eV for p-type doped a-Si:H film (confirming the difficulties to reduce the Eatt in p-type doped a-Si:H). If n-type a-Si:H thin films (~10 nm) are grown at 170°C directly on c-Si wafer, even at different PH3 dilution ratio with respect to SiH4, the defect density is one order of magnitude higher with respect to intrinsic film as evaluated by near ultraviolet photoemission spectroscopy in the constant final state yield mode (NUV-PES-CFSYS) and reported in Fig. **20**. From the data it is evident the shift of Fermi level toward the conduction band with increasing dopant concentration [86].

**Figure 20:** CFSYS measurements, normalized to a density of states, on a-Si:H layers with varying gas phase doping [PH3]/[SiH4] = 0, 0.1, 0.3, 1 and 2 x10<sup>4</sup> ppm. a-Si:H film thickness 10 nm, Tdep = 170 °C. Arrows mark the Fermi level, the vertical line is the valence band mobility edge [86].

The CFSYS method has been also used to evaluate the effect of deposition temperature, in the range between 65°C and 300°C, of 10 nm thick undoped a-Si:H layers grown on 1cm p-type doped c-Si wafer. Urbach energy dependence of valence band edge, Fermi level position and

integrated defect density are reported in Fig. **21** as a function of deposition temperature [87]. From the data it is observed an order of magnitude enhancement of defect density in these thin film layer with respect to bulk a-Si:H [88]. The shift of Fermi level toward valence band for sample deposited near 200°C is indicating a less pronounced pinning of Fermi level close to midgap resulting in a better a-Si:H quality material with respect to other deposition temperature. Moreover N(E) is not correlated to the Urbach energy E0V due to the constrain imposed by the c-Si substrate that can alter the film growth as expected and previously mentioned. Indeed voids and large hydrogen content (SiH2) at the interface degrade the network formation thus resulting in higher defect density due to dangling bonds enhancement [39]. In this frame the thinner the a-Si:H film the higher the occupied defect density [86]. As suggested in [89], this is due to incomplete annealing of the thin film during short growth. Indeed the growth of thicker layer induces a prolonged thermal annealing on the first layers that, since at beginning, are more defected than the bulk material.

Surface photovoltage (SPV) is an helpful tool to determine the surface states Dit by measuring the photovoltage of a MIS structure formed by a TCO, a dielectric transparent mica foil and a a-Si:H/c-Si HJ sample back contacted with a metal, [90, 91]. A scheme of SPV measuring set-up is depicted in Fig. **22**. The surface potential can be shifted through the gap applying an external field. When a pulsed light with energy lower than a-Si:H gap crossing through the TCO/mica/a-Si:H window hit the c-Si surface, an excess of carriers is generated close to the c-Si surface that can recombine *via* defect density at the a-Si:H/c-Si interface. If the short light pulse flattens the band, the related surface photovoltage pulse can be capacitively measured at each applied bias voltage. Then it is possible to obtain the surface potential-field voltage relation, even subtracting the Dember voltage [90], from which the distribution of surface states can be evaluated [90], under the hypothesis that the defects do not change their charge state during the light pulse. It is worth to note that Dit,min = 1011cm-2eV-1 can be assumed as the lowest density of states of thermally oxidized well passivated c-Si surface [91].

**Figure 21:** Urbach energy dependence of valence band edge, Fermi level position and integrated defect density as a function of deposition temperature [87].

**Figure 22:** Scheme of surface photovoltage measuring set-up. When the laser pulse with photon energy lower than a-Si:H energy gap, hit the c-Si the band bending at the a-Si:H/c-Si interface become flat and a photovoltage pulse can be detected.

A comparison of the Dit(E) on c-Si/SiO2 and a-Si:H/c-Si on both n-type and p-type doped c-si wafer interfaces is shown in Fig. **23**. In particular the SiO2 is a thermally oxide grown at 1100°C in dry O2 followed by 30 min forming gas annealing procedure at 450°C. It is worth to note that sample temperature during the SPV measurements has been kept as low as 120 K to reduce recharging effect of the a-Si:H layer during the laser pulse excitation, therefore the measure Dit(E) can be assumed as the upper limit of the interface density distribution [92]. Starting from a flat DoS at interface, independent from energy position within the gap and able to reproduce a 1011cm-2eV-1 Dit(E), the HJ n+ a-Si:H/p-c-Si/p+ a-Si:H cell structure has been simulated with the aid of numerical program [93] to evaluate the photovoltaic performances. The simulations verified that increasing the Dit(E) both the Voc and Isc reduce as well as the cell efficiency as reported in Fig. **24** [94].

**Figure 23:** Dit(E) for 10 nm a-Si:H(i)/c-Si(p,n, (111)) structures resulting from SPV measurements, carried out at 118 K. For comparison Dit(E) of 100 nm thermally grown oxide (1000 °C) on c-Si(n, (100)) measured at 295 K is reported [92].

*Heterojunction for Silicon Photovoltaics Silicon Based Thin Film Solar Cells* **299**

**Figure 24:** Photovoltaic parameters evolution as a function of Dit(E) at the interface of n+ a-Si:H/p-c-Si/p+ a-Si:H cell structure as obtained by numerical simulations [94].

#### **7. CLEANING**

Open circuit voltage values over 740 mV can be obtained by using the HITTM structure [14], which permits to drastically reduce the defect level at the crystalline silicon surface by implementing a high quality intrinsic amorphous silicon layer [13]. By inserting a buffer layer the tunneling effect due to the presence of many localized defect states in the doped layer can be suppressed and an excellent interface properties can be obtained. To attain a high quality intrinsic layer and excellent a-Si/c-Si interfaces has to be implemented [95].

The electronic interface properties of Si devices are strongly influenced by the chemical integrity and morphological structure of the substrate surface prior to the preparation. Conventional wetchemical treatments were developed decades ago to remove particles, organic and metallic contaminants from the polished wafer surface [96]. However, the fabrication of efficient HJ requires not only extremely clean and undamaged interfaces but also a surface texture to enhance antireflection properties. Furthermore the textured surface directly becomes part of the electronic interface because the *a-Si:H/c-Si* interface is used to form the emitter junction. Additionally, due to the texturing, the interface area is increased and consequently interface defects become more critical for the quality of subsequent processing. The recombination losses are mainly controlled by surface charge, and interface trap densities *Dit* [97, 98]. These electronic interface states result from dangling bond defects localised in a very small interlayer extended over only a few Å. Therefore, the density of these states is strongly related to the surface morphology and microroughness. Different approaches have been investigated to reduce interface recombination losses: (i) wet-chemical smoothing of the silicon surface after saw damage removal and texturing [99], (ii) the saturation of dangling bonds at the surface and near surface region by hydrogen (Htermination) [100] or other substituent's [101, 102], and (iii) the engineering of the surface band

bending to separate the electronic junction from the crystallographic interface [103]. The final aim of the wafer cleaning and surface conditioning is the removal of damaged regions and the defect passivation at the interface/surface.

The relevance of clean substrate surfaces in the fabrication of semiconductor devices has been recognized since the dawn of solid state device technology in the 1950s. It is now well known that the device performance, reliability, and product yield of Si devices are critically affected by the presence of chemical contaminants and particulate impurities on the wafer surface. As a consequence, the preparation of ultraclean Si wafers has become one of the key technologies in the fabrication processes. The term *"ultraclean"* may be defined in terms of the concentration of both chemical contaminants and particles on the wafer surface. The term *"surface conditioning"* may need some clarification. In recent years one has become to realize that the process of cleaning may do more than just remove impurities from the surface. It can prepare the surface chemically for the next process step. For example, immersing a Si wafer with a contaminated native (ambient) SiO2 layer in dilute HF (DHF) solution not only removes the contaminants with the oxide film but also leaves a hydrogenated Si surface, an important prerequisite for subsequent thin film layer growth from the gas phase. Thus, the cleaning step has also conditioned the Si surface by a chemical reaction in preparation for the next process step.

Surface micro-contamination detection is an important topic to address. If we can prevent contamination during the entire device manufacturing process by creating and maintaining superclean conditions in equipment, materials, and environment, there would be little need for wafer cleaning. Therefore, avoiding contamination must be the first priority, and strict contamination control should be exercised throughout device manufacturing. Methods for the analysis of trace impurities on Si surfaces are available to monitor the results of cleaning processes [104, 105], [105]. Wafer cleaning and surface conditioning processes are based on the use of aqueous chemicals, organic solvents, or mixtures of the two. If aqueous chemicals are used the process is properly called *"wet-chemical"*. The mechanism of liquid cleaning can be purely physical dissolution and/or chemical reaction dissolution. Chemical etching occurs when materials are removed by a chemical transformation to soluble species. Traditionally, chemical etching is expected to remove substantial quantities of a material, however, certain chemical cleaning processes may result in the removal of only a few atom layers of material and by above definition should also be considered chemical etching; perhaps the term "*micro-etching"* would be a more appropriate description.

### **7.1. Hydrofluoric Acidic Solutions**

Silicon dioxide, silicate glasses and silicon nitride have been widely etched using HF, either diluted with DIW, or pH buffered using NH4F, known as buffered HF (BHF) or buffered oxide etch (BOE). Concentrated HF is actually a 49 wt% solution of HF in DIW. Dilutions ranging from 5:1 to 200:1 are commonly used in the industry. The chemical dissolution reactions have been identified and described in the literature [106]. The etching rate increases with temperature and concentration. Typically room temperature is used, while time and concentration determine the amount of film removal. The thin layer of native oxide on Si, typically 1.0–1.5 nm thick, is removed by dipping the wafers in ultrapure and filtered DHF solution at room temperature. The change of the wetting characteristics of the initially hydrophilic to a hydrophobic surface, which strongly repels aqueous solutions, can visually indicate when the oxide dissolution is complete. The effect is due to the H-passivated Si surface that results from exposure to HF. The resulting oxide-free, H-terminated Si surface strongly attracts oppositely charged particles and is very sensitive to organic contaminants from DIW and ambient air. Therefore, etching with HF solutions that leave the Si surface bare must be carried out with very dilute, ultrapure (Fe-free), and ultrafiltered HF solution in a very low-particle atmosphere. In addition to etching, HF solutions can desorb metallic impurities from the Si surface. If desired, a pure SiO2 film can be re-grown by surface exposure to an oxidizing solution.

Mixtures of DHF and 40 wt% NH4F solutions, results in a more stable etch rate. The NH4F dissociates to provide F- ions that stabilise etch rate by replacing ions consumed in the SiO2 etch reaction. Surfactants may be added to the solution to improve the wettability and to prevent Si attack, namely in preventing surface micro-roughness [104]. Whereas the free acid is the major etching species in DHF, the ionized F species HF2 is the major etchant component in BHF. Commonly used BHF volume ratio of (7:1=NH4F:HF) has a pH of about 4.5 and appears to contain only HF2 - and F- , with very little free HF. The SiO2 etching rate of HF2 - is four to five times as fast as that for free HF in DHF [104]. Addition of NH4F increases the pH, maintains the F concentration, stabilizes the etching rate, and produces the highly reactive HF2.

#### **7.2. Sulphuric Acid/Hydrogen Peroxide Mixtures**

Removal of gross organic materials from Si wafers can be accomplished by using mixtures of 98 wt% H2SO4 and 30 wt% H2O2. Volume ratios of 2:1–4:1 are used at a temperature of 100–130 °C for 10–15 minutes. Organics are destroyed and eliminated by wet-chemical oxidation, but inorganic contaminants, such as metals, are not desorbed. What is worse, the Si surface after this cleaning step is strongly contaminated with sulphur residues [104]. These *"sulphuric-peroxide mixture"* (SPM), which is also known as *"piranha etch"* is extremely dangerous to handle and is not commonly used in the fabrication process. Anyway it would have been employed it should be the first cleaning process to prepare grossly contaminated Si wafers for subsequent treatments. Vigorous rinsing with DIW is required to completely remove the viscous liquid. Finally, it is advantageous to strip the impurity-containing formed oxide film on Si by dipping the wafers for 15 seconds in 1:50 DHF, followed by a DIW rinse. By adding a small amount of HF to the SPM several beneficial can be obtained: better removal of sulphur compounds, shorter rinsing times, and improved particle removal [104]. Some alternative oxidants are sometimes used instead of H2O2 to improve the mixture stability. These alternative additives include (NH4)2SO4; H2S2O8; and DIW/O3 [106].

### **7.3. RCA Cleaning Process**

The first successful process for wet-cleaning Si wafers was systematically developed at Radio Corporation of America, (RCA), and published in 1970 [107, 110]. The process consists of two, SC-1 and SC-2, consecutively applied hot solutions known as *"RCA Standard Clean"*. The SC-1 solution consists of a mixture of NH4OH, H2O2, and H2O; also known as *"APM"* for *"ammonia/peroxide mixture"*. The SC-2 solution consists of a mixture of HCl, H2O2, and H2O; also known as *"HPM"* for *"hydrochloric/peroxide mixture"*. The originally specified composition for the SC-1 solution ranges from 5:1:1 to 7:2:1 parts by volume of: H2O:H2O2:NH4OH. Filtered DIW or quartz distilled H2O is used. The 30 wt% H2O2 is electronic grade and un-stabilized (to exclude contaminating stabilizers). The NH4OH is 27 wt%. The originally specified composition for the SC-2 solution ranges from 6:1:1 to 8:2:1 parts by volume of: H2O:H2O2:HCl; the H2O and H2O2 are as noted above, while the HCl concentration is 37 wt %. Cleaning in either mixture is carried out at 75–85 °C for 10–20 minutes followed by a quench and overflow rinse in running DIW. After rinsing the wafers are spun dried and immediately transferred to an enclosure flushed with pre-filtered inert gas for storage, if they cannot be processed immediately. The SC-1 solution was designed to remove from Si, oxide and quartz surfaces organic contaminants that are attacked by both the solvating action of the NH4OH and the powerful oxidizing action of the alkaline H2O2. The NH4OH also serves to remove by complexing some periodic group IB and IIB metals such as Cu, Au, Ag, Zn, and Cd, as well as some elements from other groups such as Ni, Co, and Cr. SC-1 dissolves the thin native oxide layer on Si at a very low rate and forms a new oxide on the Si surface by oxidation at approximately the same rate. This oxide regeneration is now believed to be an important factor in the removal of particles and chemical impurities [111]. The SC-2 solution was designed to dissolve and remove from the Si surface alkali residues and any residual trace metals (such as Au and Ag), as well as metal hydroxides, including Al(OH)3, Fe(OH)3, Mg(OH)2, and Zn(OH)2. The solution does not etch Si or SiO2 and does not have the beneficial surfactant activity of SC-1 for removing particles. SC-2 has better thermal stability than SC-1 so that the treatment temperature does not need to be as closely controlled. The thermal instability of H2O2 in SC-1 (and to a lesser extent in SC-2) necessitates the use of freshly prepared mixtures. The effects of H2O2 depletion and of fluoride ion addition were also investigated in terms of Si and SiO2 etch rates. Several improvements to the original RCA cleaning procedure were employed during the last 20 years. The most influential of these changes was the introduction of the RCA megasonic cleaning system for cleaning and rinsing of wafers [112]. Mega-sonic treatment in an SC-1 bath is especially advantageous for physically dislodging particles from the wafer surface due to the high level of kinetic energy. It allows a substantial reduction in solution temperature and offers a much more efficient mode of rinsing than immersion tank processing. Other important improvements include the simplification of the composition ratios for both SC-1 and SC-2 to 5:1:1 and a reduction of treatment temperature and time to 70–75 °C for just 5–10 minutes. The use of fused silica vessels instead of Pyrex glassware was introduced to eliminate contamination from leached glass components. The separation of SC-1 from SC-2 processing stations in two dedicated exhaust hoods was recommended to avoid contamination from airborne colloidal NH4Cl generated from NH3 and HCl vapours. No gross etching of Si or SiO2 was shown to occur with SC-1 even if the H2O2 concentration is reduced by a factor of ten. Finally, an optional process step was introduced by stripping the hydrous oxide film formed after SC-1 with high-purity particle-free, 1:50 DHF-dipping for 10 seconds so as to re-expose the Si surface for the subsequent SC-2 step. The employment of surfactant additives to aqueous solutions has become widely accepted. Surfactants increase the Si wafers wettability, can prevent surface micro-roughness generation, and improve the overall cleaning efficiency [107].

#### **7.4. Wafer Rinsing, Drying and Storing**

The last steps in wet-chemical wafer cleaning are rinsing and drying, both are extremely critical because clean wafers can become re-contaminated very easily. Rinsing should be done with flowing high-purity and ultra-filtered high-resistivity DIW at room temperature. *Mega-sonic rinsing* is advantageous and is the most effective technique for reducing the critical boundary layer between the wafer surface and the rinse H2O. Wafer drying after rinsing must be done by physical removal of the H2O, rather than by allowing it to evaporate, which would leave residues. *Spin drying* accomplishes this and has been one of the most widely used techniques, although

recontamination tends to occur. *Forced air or N2 drying* using warm and filtered gas is a preferred technique with less chance for particle recontamination. *Solvent vapour drying* starts with wet wafers being moved into the hot vapour of a pure, H2O-miscible solvent, usually IPA, which condenses and thereby displaces the H2O. The wafers dry particle-free when the cassette is withdrawn above the vapour zone. IPA vapour drying in its various modifications has become the preferred method in batch processing. Extreme care must be taken to avoid recontamination of clean wafers during storage if immediate continuation of processing is not possible. Wafers should be placed ideally in chemically cleaned, closed glass containers or stainless steel enclosures, while being flushed with high-purity filtered N2 in a clean room. However, this is rarely feasible in a production line; the usually used plastic containers will always cause organic surface contamination. Metal tweezers must never be used to handle wafers since they will invariably cause contamination by traces of metals. The final criteria of the success of all wafer cleaning operations are the purity of the wafer surface after the last treatment and eventually the device yield. No matter how effective the various cleaning steps may be, improper rinsing, drying, and storing can ruin the best results. Wafer carriers are an integral part of all wafer processing operations due to the need of handling and transfer of wafers in batches. Wafer carriers are designed to hold wafers in slots of 25 or more wafers. A variety of plastic materials are available for their manufacturing. They can be a critical source of particle contamination, their proper use and specialized cleaning are very important for preserving wafer cleanliness.

#### **7.5. Saw Damage Etching, Texturing and Cleaning**

Wet-chemical surface preparation is used in solar cell manufacturing mainly for three purposes: (*i*) saw damage etching, (*ii*) texturing and (*iii*) wafer cleaning/surface conditioning for the subsequent passivation and/or junction and contact formation.

So far in HJ manufacturing alkaline wet-chemical etching procedures are preferred to remove saw damage and texture the as-cut wafers. A well-established process in Si solar cell fabrication is the anisotropic etching of <100>Si in KOH/IPA solution at 80°C to obtain randomly distributed pyramids, thus improving the light trapping properties [113, 114]. To reduce manufacturing expense it should be advantageous to combine saw damage removal and texture formation in a single step process by using KOH/IPA solution at 80°C and extending the etching time or by using an acidic texturing process [115, 116]. The completed removal of saw damage is a crucial precondition to reduce recombination losses on solar cell substrates. SEM micrographs show saw damaged regions (Fig. **25(a)**) and cracks (Fig. **25(b)**) typically observed on as-cut Si substrates. The thickness of the damaged surface layer is dependent on the wafer saw technology. Fig. **26** depicts the energetic distributions of interface states *Dit(E)*, obtained by field depended SPV measurements [92], [93] of commercial p-type CZ wafers after standard alkaline saw damage etch and texture. For comparison the *Dit(E)* of a neighbouring as-cut substrate is also shown. The very high *Dit,min* (≥ 2·1013cm-2eV-1) is drastically reduced to a value ≤ 2·1012cm-2eV-1 by employing a typical saw damage etching due to removal of crystallographic defects in the near surface range of about 30 μm. The KOH etched surface is characterised by flat, extended (20 to 50 µm) <100>Si structures (see Fig. **25(c)**). Once the random pyramids are formed the *Dit,min* rise up to value ≤ 25·1012cm-2eV-1 due to the texturing process that generates randomly distributed pyramids on <111>Si crystal facets (see Fig. **25(d)**), thus increasing the surface roughness, namely the interface traps density. The anisotropic etching in KOH/IPA changes the initial surface orientation of the <100>Si substrate to <111>Si orientation to well-ordered pyramid facets.

**Figure 25:** Scanning electron micrographs (tilted view) of: (a) as-cut wafer, (b) cracks on as-cut wafer surface, (c) saw damage etched wafer in KOH solution (d) textured wafer in KOH/IPA solution [119].

**Figure 26:** Interface state density comparison for CZ wafers obtained by SPV measurements on (a) as-cut wafers, (b) after saw damage etch in KOH solution and (c) after texturization by anisotropic etching KOH/IPA [119].

The formation of pyramids increases *Dit,min* and results in significantly narrowed energetic distributions by additional appearance of states near the band edges and in the lower half of the gap, *i.e.* closer to the valence band edge. These states, typically observed on microscopically rough surfaces, are related to strained bond defects and defects on Si atoms of lower stage of oxidation, Si+1 (Si2O≡Si<sup>−</sup> ) *e.g.* formed by hydroxyl groups [117]. It was demonstrated [118] that the strongest decrease in surface reflectance can be achieved by anisotropic etching of in KOH/IPA solution.

Moreover, surfaces texturisation by acid solutions, generally lead to higher light reflectance and interface state densities, compared to the alkaline etched substrates. Up to now, the acid based texture etch yields a roughened surface by isotropic etching that exhibits less light absorption than the alkaline process and produce higher surface micro-roughness, resulting in high recombination losses. Further investigations are required to optimize the isotropic texturization process and subsequent wet-chemical treatments, to make it possible to combine saw damage removal and surface texturization. Therefore, for high efficient HJ, normally anisotropic etched substrates with random pyramids should be preferred.

#### **7.6. Wafer Cleaning and Surface Conditioning**

Values of *Dit,min* as well as that obtained after the texturing process (see above Fig. **26**) do not allow to deposit a high quality buffer layer needed to produce high efficiency solar cells. It is evident that a wafer cleaning followed by a surface conditioning has to be applied prior to the thin film layer growth.

Several groups are hardly working trying to reproduce HITTM performance. One of the technological keys is the wafer cleaning combined with a surface conditioning. Comparing standard RCA cleaning with others wet-chemical treatments once again confirmed that the better is the standard one. However a wet-chemical surface conditioning has to be applied prior to the *a-Si:H* growth to obtain *Dit* values suitable for high efficiency HJ. Wet-chemical surface conditioning consists of wet-chemical oxide formation followed by an oxide removal step to smooth the surface roughness; thus avoiding microscopical irregularities that would otherwise represent fertile spots acting as recombination centres. The effect of different combination of wetchemical wafer cleaning and surface conditioning on the interface state density and minority carrier lifetime has been extensively studied and recently published by Laades *et al.* [119]. They reported that the wet-chemical surface conditioning has to be carefully optimised with respect to the different substrate configurations by means of μW-PCD [120] and SPV measurements [92, 93] to determine the spatially resolved effective minority carrier lifetime and the energy distribution of the interface states respectively. They fabricated several samples starting from commercial (3-6 Ωcm) p-type CZ wafers, and investigated the interface properties of two surface morphology (saw damage etched and textured surfaces) when different wet-chemical surface conditioning are applied soon after a standard RCA cleaning. To measure and compare the *τ*eff the samples have been passivated by iodine/ethanol (I/E) solution. Because of passivation by I/E is based on saturation of dangling bond defects, the choice has been taken to obtain similar results for n-and ptype substrates. Fig. **27** depicts results of lifetime measurements. For almost all pre-treatments, as expected, the KOH etched surface shows higher values of effective lifetime. On KOH etched surfaces using just DHF for oxide removal (RCA+HF) higher values of lifetimes were obtained compared to the cleaning procedure (RCA+HF+DIW). In contrast, on textured surfaces the omission of DIW rinsing leads to lower lifetimes. Both can be explained by the counteracting effects of two processes caused by DIW rinsing: (*i*) the removal of chemical reaction products, which leads to a clean, hydrogen-terminated surface and (*ii*) the subsequent initial oxidation of this clean surface. On the pyramids of textured substrates, a clean surface with higher lifetime can only be achieved by employing DIW rinsing. On the comparatively flat surface of KOH etched substrates however, the rinsing leads to oxidation-induced defects, higher density of states and

**Figure 27:** Lifetime distribution over the area of representative p-type samples obtained on wafer with the two surface structures, saw damage etched and textured, after different sequences of wet-chemical steps and subsequent passivation with iodine ethanol solution [119].

lower lifetime values. In order to decrease surface micro-roughness at atomic scale, for the first oxide removal step the DHF-dip was replaced by NH4F treatment. Without rinsing in DIW this treatment results in a drastic decrease of the lifetime probably due to surface contamination by ammonium salts [121]. To dissolve these contaminations the substrates have been subsequently treated in hot water for 6 min followed by a DHF-dip to remove the water-induced surface oxide. The highest lifetime values have been obtained applying these treatments followed by a final short DIW rinsing at room temperature: (RCA+NH4F+Hot DIW+HF+DIW).

The influence of different combination of wafer cleaning and surface conditioning has been extensively investigated for randomly pyramids textured surfaces, obtained from polished p-type FZ samples in order to eliminate bulk effects, by means of *Dit(E)* measurements [122]. As demonstrated, the microscopic surface roughness, typically obtained after alkaline texturing (KOH/IPA) and standard cleaning (RCA+DHF-dip) treatments, can be stepwise reduced by wetchemical smoothing applying sequences of oxidation in H2SO4/H2O2 and oxide removal in (1%)DHF or in (48%)NH4F solutions.

NH4F containing solutions are commonly used to passivate atomically flat smooth <111>Si surfaces by H-termination, on the other hand also produce various compositions of ammonium salts by the reaction with Si and SiO2 [100]. This reaction results surface irregularities, which seems to start particularly on surface particle contaminations, or on crystallographic irregularities of the structured surfaces (Fig. **28(a)**). These contaminations cannot be removed even by intensive water rinse, because of the poor solubility of (NH4)2SiF6 in water. As expected this behaviour leads to a strong increase in *Dit,min* compare to the minimum value obtained for the initial rough

RCA treated surface as shown in Fig. **29** curve 1. The application of NH4F solution after formal smoothing in H2SO4/H2O2 leads to a reduction in *Dit,min*, mainly in the lower half of the gap. Best results were obtained by smoothing in NH4F solution with a subsequent wet-chemical oxidation step in H2SO4/H2O2, followed by DHF-dip (120 s), which obviously dissolves these contaminations, as shown in Fig. **28(b)**. When (1%) DHF was used as final etching solution, the *Dit* near the band edges and in the lower half of the gap, *i.e.*, closer to the valence band edge, were found to be significantly reduced. These states, typically on microscopically rough surfaces, are related to strained bond defects and defects on silicon atoms of lower stage of oxidation, Si+ (SiO2≡Si−) formed by hydroxyl groups [123]. Wet-chemical smoothing procedures using H2SO4/H2O2 subsequent to NH4F treatment (Fig. **29** curve 4) or DHF-dip (Fig. **29** curve 5) results result in lower densities of these states, with respect to the standard RCA process plus DHF-dip (Fig. **29** curve 2,3). The density of states in the upper half of the gap, *i.e.* closer to the conductivity band edge, results from dangling bond of the next higher stage of oxidation Si+2(SiO2≡Si−) and were found to be strongly related to the stage of Si surface oxidation [123]. In order to further elucidate the influence of wet-chemical oxide removal, the HF treatment times were systematically stepped up after RCA as well as after H2SO4/H2O2. The extension of the HF treatment time from 60 s to 90 s and to 120 s leads to a stepwise reduction in *Dit* in the upper half of the gap, and to a *Dit(E)* broadening. The chemical and physical conditions of the Si substrate surfaces can be modified by dry or wet specific process steps. For example, remote hydrogen-plasma *in situ*  cleaning and surface conditioning of the Si surface to produce smooth and atomically clean surfaces with controlled Si H-termination-bonds immediately prior to Si growth can be achieved by activated hydrogen plasma processing in a remote plasma reactor [124]. Wet-chemical cleaning processes for Si wafers can be classified according to the final surface condition into two groups: the surface passivation (i) by H-passivation (H-terminated surface) or (ii) by thin wet-chemical oxide layers, resulting in hydrophobic and hydrophilic surfaces, respectively [125, 127]. Which substrate surface conditioning can successfully be applied to Si solar cells largely depends on the details of the device structure and the kind of subsequent layer deposition.

**Figure 28:** Scanning electron micrographs (tilted by 30°) of silicon substrates with randomly distributed pyramids: (a) after H-termination by NH4F and (b) after subsequent wet-chemical oxidation and oxide removal in H2SO4/H2O2+HF-dip (120 s) [122].

**Figure 29:** *Dit(E)* of p-type Si substrates with randomly distributed pyramids, obtained after two types wetchemical pre-treatment: (i) standard RCA process and subsequent oxide removal by NH4F (curve 1), or HFdip for 90 and 120 s (curves 2,3) and (ii) wet-chemical smoothing by H2SO4/H2O2 and subsequent oxide removal by HF-dip for 60 s (curve 4) and 120 s (curve 5), respectively [122].

#### **7.7. Surface Passivation Stability**

The stability of surface passivation on wet-chemically treated wafers with the time of the subsequent layer preparation step is an important parameter in the technological process. The Hterminated Si surface predominantly limits oxidation in clean room air but does not completely inhibit native oxidation. The stability of hydrogen passivation was shown to be influenced mainly by substrate morphology and the employed wet-chemical preparation method. A strong influence of various etching and smoothing procedures on the stability of the H-terminated vicinal <111>Si surfaces under ambient atmosphere was recently shown by M. Kolibal *et al.* [128]. Highest stability (48 h) was found on the atomically smooth mono-crystalline surface. Thereby a completed removal of RCA oxides was achieve after 3 min treatment time on polished p-type <111>Si substrates, compared to 6 min on alkaline textured substrates. A rapid decrease in the effective minority carrier lifetime was observed during the initial phase of oxidation in air, corresponding to an increase in surface states. A significantly shorter duration of the initial phase of oxidation in air was found on the polished <100>Si surfaces in contrast to that observed on textured surfaces [129]. These experimental results indicate a strong influence of surface morphology on native oxidation growth in air. The initial oxidation reactions start on atomic defects and steps, because various species of Si(−H)2, Si−OH and dangling bond defects are localised there. Oxidants, such as oxygen and water in air, are expected to preferentially break the Si back-bonds on atomic defects and polarised back-bonds of the silanol groups Si≡Si−OH, on the atomically rough surface, rather than the Si≡Si−H bonds on the atomically flat <111>Si terraces. Thus, the insertion of oxygen, results in a strong polarization of Si≡Si−O back-bonds, which leads

#### *Heterojunction for Silicon Photovoltaics Silicon Based Thin Film Solar Cells* **309**

to further nucleophilic reactions with their neighbouring Si atoms forming the first monolayer of native oxide. Whether all Si atoms of the top layer are oxidized, the Sibulk≡Sibulk−O back-bonds of the second monolayer are broken by subsequent insertion of oxygen and a layer-by-layer growth of native oxide films takes place on Si surfaces exposed to air at room temperature. In this way, a layer-by-layer growth of native oxide films takes place on Si surfaces exposed to air at room temperature. The over-layer structure converts to the amorphous phase. The remaining O−Sis(−H)2 bonds on the top-layer cause the hydrophobic behaviour of the surface, which can be observed during the initial phase of native oxidation in air. The Si−H bonds on the surface are oxidized only after completion of the back-bond oxidation, resulting in the formation of silanol groups Si−OH. By this oxidation mechanism, the dependence of the first oxide monolayer growth rate on the initial density of interface states can be explained. To inhibit native oxide growth, H-terminated substrates are often stored in dry nitrogen atmosphere. A very slow initial native oxidation, however was also observed in N2 atmosphere, probably due to the fact that water molecules adsorbate or not completely H-terminated surface defects [130]. Summarising these results the duration of initial phase of oxidation, which can be used as measure for the stability of Hterminated Si surfaces in ambient atmosphere, was found to be not only influenced by the clean room conditions and the handling procedures, but also by the substrate bulk properties, surface morphology and the preparation-induces surface micro-roughness and surface coverage. The reoxidation of H-terminated Si surfaces can be slowed down for a short time by excellent smoothing and complete saturation of the dangling bonds by hydrogen or by storage in dry N2 atmosphere until subsequent layer deposition. Other surface passivation methods, however, are required to inhibit completely the native oxidation of substrate surface for longer time duration as recently published by organically modified Si surfaces [131, 132].

#### **7.8. Influence of Optimised Wet-Chemical Treatment on Test HJ Solar Cells**

Several groups are hardly working to individuate the effect best wet-chemical pre-treatment to improve HJ solar cells performances. One recent work [133] showed the influence of optimised surface pre-treatment for amorphous/crystalline heterojunction solar cells (ZnO/*a*-Si:H/*c*-Si/BSF/Al) prepared on p-type substrates with random pyramids texturing. Two groups of samples, consisting of 24 cells of 1 cm2 each, were processed and characterised. Both groups received a standard RCA cleaning followed by a DHF-dip to etch the silicon oxide. For the second group a subsequent wet-chemical smoothing by H2SO4/H2O2+(1%)DHF-dip was applied. Fig. **30** shows the distribution of the obtained solar cell characteristics. In addition to the histograms, the results of fitting normal (Gaussian) distributions to the data are shown. The histograms over cells demonstrate that the samples with the smoothened *a*-Si:H/*c*-Si interface shows much narrower distributions of the respective parameters around the mean value. Further a pronounced increase in efficiency was achieved by the group with optimised surface conditioning. The increase in efficiency is mainly due to a higher *Jsc* (mean improve 5.0%) and to a less pronounced extent, an increased fill factor (2.2%), while the change in the *Voc* is rather small (0.5%). Because of a previous simulation studies [134], have shown that the increasing front side interface state density from 1010 cm-2 to 1012 cm-2 leads to a reduction in *Voc* of 90 mV, and the rear side recombination acts as a loss mechanism on *Jsc* and reduces *Voc* by 40 mV at maximum additional investigations are under way to clarify the reason for this behaviour. Similar results were also obtained for test solar cells prepared on textured n-type substrates [135]. Those results indicate not just a better performance but also a better reproducibility when textured substrates are processed by an additional smoothing step and optimised wet-chemical oxide removal.

**Figure 30:** Histogram of the basic solar cell parameters: short cut current density *Jsc*, open circuit voltage *Voc*, fill factor and efficiency *η*, for two groups of 1 cm2 (n)*a*-Si:H/(p)*c*-Si solar cells The black bars denote conventional HF treatment after cleaning of the c-Si substrate; red bars: additional smoothening of the textured substrate surface; lines: normal distributions fitted to the data [134].

### **8. ELECTRICAL TRANSPORT AND TRAPPING IN A-SI:H/C-SI**

In general the current voltage in HJ solar cell can be expressed using the common double diode expression plus series and shunt resistances (Rs, Rsh):

$$J(V) = J\_d(V) - J\_{ph} = J\_{01} \left( e^{\frac{q(V - J R\_3)}{nkT}} - 1 \right) + J\_{02} \left( e^{\frac{q(V - R\_3)}{nkT}} - 1 \right) + \frac{V \text{ -} J R\_3}{R\_{sh}} - J\_{ph} \tag{13}$$

where Jd is dark current; Jph is photogenerated current; Rs, Rsh are series and shunt resistance respectively; n1,2 are ideality factors; T is the temperature; k is the Boltzmann constant.

However in a-Si:H/c-Si HJ device the carrier transport can be affected by several issues as defect density at interface, barriers due to band alignment mismatch and defect within bulk material. Therefore the use of the diode model with recombination in the space charge region, commonly used in homojunction diode [136, 137] should be reconsidered [5, 6, 138, 139] taking into account tunneling mechanisms.

Basically the current voltage still follows the high forward regime written above (J01 diode), of course affected by the series resistance for forward bias. According to the Shockley theory [95] and with the assumption of single side junction, J01 can be expressed as the prefactor of the diffusion current within c-Si base:

$$J\_{\neq 1} = \frac{qn\_i^2 D\_{p|n}}{L\_d N\_{D/A}}\tag{14}$$

where Dp/n is the c-Si minority diffusion coefficient, ND/A is the c-Si doping type and concentration; Ld is the diffusion length. This last can be evaluated from lifetime measurements performed on passivated c-Si wafer before HJ device fabrication [140] or from quantum efficiency when the device is completed [141, 142]. Commonly for a very good HJ cell J01 should be in the order of 10-13 A/cm2 as for the Sanyo HIT cell [11] in which the Seff is lower than 5 cm/s after a-Si:H deposition on both sides of the c-Si wafer. This of course reflects in open circuit voltage:

$$V\_{oc} = \frac{n\_i kT}{q} \ln\left(\frac{J\_{sc}}{J\_{o1}} + 1\right) \tag{15}$$

that is weakly affected by the low forward bias regime. Instead at low bias voltage (< 0.5V) regime, the current flowing through the device can be written as follows:

$$\mathbf{J}\_d(\mathbf{V}) = \mathbf{J}\_0 \ e^{\mathbf{A}\mathbf{V}} \tag{16}$$

where A is constant.

Current voltage measurements in dark condition of n-type a-Si:H/a-Si:H/c-Si p-type HJ sample for different temperature is reported in Fig. **31**.

**Figure 31:** Current voltage measurements in dark condition of n-type a-Si:H/a-Si:H/c-Si p-type HJ sample for different temperatures.

According to [143] most of tunneling take place at peak of conduction band mismatch (path A of Fig. **32**).

Since the density of states is high at the energy below that peak, by the a-Si:H layer side, also path B of Fig. **32** should occur. J0 is:

$$J\_0 = B\mathfrak{e}^{\left(-\Lambda E/kT\right)}\tag{17}$$

where B is constant. Now the energy related to the tunneling E should be lower than the pick height, but experimentally has been found the opposite [4, 7]. Path C in Fig. **32** can be considered small with respect to path D and E due to large amount of DoS within the a-Si:H. Path D is a multi-step tunneling that can be expressed as follows according to [4, 145]:

$$\mathbf{J}\_0 = \mathbf{B} \mathbf{e}^{h\mathbf{T}} \tag{18}$$

If hopping mechanism through the defects [146] at energy Et close to the Fermi level density could prevail then J0 becomes [7]:

$$J\_0 = B \left[ \sigma\_p \mathbf{v}\_{th} N\_v \exp\left(-\frac{E\_t - E\_v}{kT}\right) + \sigma\_s \mathbf{v}\_{th} N\_c \exp\left(-\frac{E\_c - E\_f}{kT}\right) \right] \tag{19}$$

or

$$J\_0 = B \left[ \sigma\_n \mathbf{v}\_{th} N\_c \exp\left(-\frac{E\_c - E\_t}{kT}\right) + \sigma\_n \mathbf{v}\_{th} N\_c \exp\left(-\frac{E\_f - E\_v}{kT}\right) \right] \tag{20}$$

where p.n are the capture cross sections, Ef, Et,Ec,Ev are the Fermi level, the trapping level, the valence band and the conduction band respectively. The use of (17) or (18) depends on the c-Si doping type choice on which the HJ is formed.

**Figure 32:** Schematic overview of HJ band bending in low forward bias regime and tunneling mechanisms.

**Figure 33:** Exponential dependence of the current from T, in dark condition, for different samples listed in Table **1**. Note that the current of samples 3-5 have been scaled 100 times to be comparable with the other samples.

Now it is interesting to note that J0 expressed as (18) or (19, 20) for low forward bias such as 0.3V are quite similar in a certain range of temperature as evident from the IV data of different samples collected from different references [7, 147, 148] and reported in Figs. **33, 34**. The structure of the different samples are listed in Table **1**. In general current voltage characteristics under sunlight exposure are the common way to evaluate solar cell performances. Since in these measurements all carrier transport mechanisms and recombination phenomena are averaged, it is very difficult to extract detailed information on specific part of the cell from these characteristics. Quantum efficiency and current voltage profiles in dark condition can help to this aim, but also from them it is critical to select the details. The amphoteric nature of DB within the a-Si:H and their not homogeneous distribution along the energy gap and along the interface make difficult to evaluate in details. The generation mechanism within depletion region seems to dominate the current in reverse bias condition as reported in Fig. **35**, in which the dependence of current on the square root of reverse bias is highlighted (Vbi refers to built-in voltage) [7]. Details on transport mechanism are widely discussed and a complete analytical model is under construction in [148].


**Table 1:** Sample structures of Figs. **33** and **34**.

Capacitance voltage measurements as a function of frequency (CVf) have been used as a tool to evaluate defect density distribution in a-si:H either solar cell p-i-n structures [149, 150] or in stacked photo-detectors [151], since capacitance is highly sensitive to the trapping kinetics depending on the trap state position in the gap close to the junction and test signal frequency. Capacitance indeed depends on the variation of state occupancy around the Fermi level, for each temperature the lower the test signal frequency, the higher the number of states involved in the trapping kinetics process and the higher the exchanged charge and then the capacitance value [152]. The dependence of the capacitance on the bias voltage is related to different position of Fermi levels in the space charge region of the junction and to different minority carrier density. Moreover the temperature parameter can be introduced to further improve the capacitance measurements sensitivity (CVfT). Indeed the dependence of capacitance on temperature is related to the freezing of trapping kinetics that occurs by lowering the temperature described by the steeping of the Fermi function.

**Figure 34:** Exponential dependence of the current from-1/T, in dark condition, for different samples listed in Table **1**. Note that the current of samples 3-5 have been scaled 100 times to be comparable with the other samples.

The amplitude of the capacitance variation from low to high temperature is related to the number of states involved in the trapping kinetics and to their distribution along the thickness of the involved layers. Even though the capacitance measurements are relatively easy to perform, their interpretation requires a carefully analysis that cannot be performed by analytical models. To this aim, numerical simulations of the device structure under measurements can be helpful to reproduce the measurements, even if sometimes it is difficult to rightly establish the values of a large number of free parameters within the model.

Here we report the CVfT measurements used to evaluate the defect density at interface of two HJ p-type c-Si based in which dry cleaning wafer treatment before the a-Si:H layer deposition have been applied:

**Figure 35:** Current voltage measurements of n-type a-Si:H/a-Si:H/c-Si p-type HJ sample for different temperature in dark condition [148].

H2 plasma in the following conditions: 200 mTorr working pressure, 100 sccm gas flow, 28 mW/cm2 RF 13.56MHz power density, and 280°C substrate temperature for 5 minutes;

CF4/O2 with 8% oxygen content with the follow parameters: 200 mTorr working pressure, 30 sccm gas flow, 98 mW/cm2 RF 13.56 MHz power density, and 240 °C substrate temperature for 90 seconds [153].

We compared the capacitance values with the output of numerical simulation able to solve both the DC and AC problem in the stacked structure. We used one dimensional approximation dividing the structure in a grid of points, each characterized by a set of parameters [154]. Comparing Fig. **36(a)**, **36(b)** we noted also an increase of defect density in number and extension in the crystalline silicon side in case of H2 treatment. This was absolutely needed to model the experimental capacitance values. We related this behavior to damages in crystalline layer during plasma treatments. Then we can argue that, due to high mobility of hydrogen atoms, H2 plasma treatment on p-type crystalline silicon induced hydrogen diffusion inside crystalline wafer.

In Fig. **37** current voltage measurements performed at room temperature and dark conditions were reported as dot. They highlight that sample treated with H2 plasma was strongly affected by recombination mechanism.

In Fig. **37** line curves refers to simulations obtained starting from the same defect density and distribution as used in capacitance calculation were reported. The good agreement of the measurements and the simulation remarked the validity of parameters chosen in numerical model.

**Figure 36:** (i) CVfT measurements (symbols) and model (lines); (ii) band bending at 0V (dark) and-1V (grey) as obtained by the simulation of the CVfT values; (iii) defect distributions in the three region of the HJ used to fit the experimental data. (a) HJ treated with plasma dry etching of CF4/O2 before a-Si:H layer depositions: (b) HJ treated with plasma dry etching of H2 before a-Si:H layer depositions.

**Figure 37:** Measured (symbols) and simulated (lines) current voltage characteristics in dark and room temperature conditions of HJ p-type c-Si base 1cm2 area.

### **9. DEVICE DESIGN**

The cell structure of a-Si:H/c-Si solar cell is basically fabricated starting from a c-Si wafer (Floating Zone FZ; Chocralsky CZ; multicrystalline mc-Si) which needs a previously saw damage removal and texturing that are commonly used in c-Si based solar cell manufacturing. Before a-Si:H deposition particular care must be paid to clean the silicon surface in order to reduce contamination. Then thin doped a-Si:H can be deposited by plasma enhanced chemical vapour deposition (PECVD) or hot-wire chemical vapour deposition (HW-CVD). Even if the emitter layer has higher bandgap (1.7eV) with respect to the c-Si base (1.124eV) and then it should work just as a window layer for the c-Si absorber, it shows strong a-Si:H absorption in the short wavelengths spectrum. Since the emitter layer is a doped a-Si:H film, does not contribute to the carrier generation due to the high recombination within the material that strongly limits the diffusion length [155, 156]. Therefore the emitter thickness should be optimized to reduce its filtering effect to the c-Si base absorber. The choice of doping type of c-Si base is crucial for the device configuration. In principle, since the c-Si is an absorber thicker than the depletion region that can be formed on one side of the wafer, most of carriers are generated inside the neutral region where they move by diffusion mechanism. Therefore electron should be preferred as minority carriers and then p-type doped c-Si should be adopted (electron diffusivity in 1cm p-type doped c-Si: Dn = 26.88cm2 /s; hole diffusivity in 1cm n-type doped c-Si: Dp = 11.64 cm2 /s at room temperature). Also industrial considerations can support this choice such as the abundance of p-type doped c-Si in the PV market historically driven by microelectronic in which the p-type doped is commonly used. But for the HJ solar cell this choice has several drawbacks:


3) the band diagram of the HJ shows a higher mismatch in valence band with respect to the conduction band [159], therefore the p-type c-Si/p-type a-Si:H base contact not easily forms a ohmic junction as well as back surface field (BSF) as, in turn, the counterpart n-type c-Si/n-type a-Si:H junction.

To evaluate the valence band discontinuity offset between a-Si:H and c-Si several methods have been proposed in literature [7, 160, 163]. The most interesting is once again the constant final state yield spectroscopy CFSYS proposed in ref [67]. The evolution of the CFSYS for several HJ with different a-Si:H thicknesses is reported in Fig. **38**. The progressive reduction of the substrate signal increasing the a-Si:H layer is clearly visible and it is also possible to evaluate the DoS from a clean hydrogenated p-type c-Si surface to thicker a-Si:H layer. 0.44 eV offset in valence band with a standard deviation of 0.02 eV has been evaluated from the data reported in Fig. **38**.

The basic band diagram of the HJ cells is depicted in Figs. **39, 40** for p-type and n-type c-Si base respectively. These band bending distributions are plotted on the base of finite difference simulation program able to describe the carrier transport in stacked structure by solving Poisson, continuity and current equations in each layer described by a set of parameters imposed to define semiconductor properties [164]. In particular these simulations have been performed taking into account the energy gap: Eg, electron affinity: and the activation energy: Eatt of each material. The lowest Eatt that doped a-Si:H films can achieve [11] is reported in Table **2**.

**Figure 38:** CFSYS spectra of HJ at different a-Si:H thicknesses, starting from c-Si wafer.

**Table 2:** Dopant activation energy Eatt, electron affinity , energy gap Eg.


Higher built-in potentials and then higher cell efficiency can be obtained with the HJ structure with respect to the c-Si based homojunction with the same doping concentration in the c-Si bulk, but defect density can strongly affect and reduce this potentiality [165].

**Figure 39:** Band bending simulations in dark and 0V. p-a-Si:H/i-a-Si:H/n-type-c-Si/i-a-Si:H/n-aSi:H double heterostructure cell.

**Figure 40:** Band bending simulations in dark and 0V. n-a-Si:H/i-a-Si:H/p-type-c-Si/i-a-Si:H/p-aSi:H double heterostructure cell.

If same defect density is chosen at the interface both HJ structure on p and n-type doped c-Si show the same built-in potential value of 1.03V.

If HJ not affected by defect density at the interface are simulated without BSF, simply taking into account the Eatt of doped a-Si:H emitters, as reported in Table **2**, and the Eatt = 0.2 eV of 1cm doped c-Si (p on n-type), a built in potential of 0.94V and 0.79V for n-and p-type c-Si based is respectively obtained. This is merely due to the band alignment between the two semiconductors. In turn the higher valence band offset with respect to the conduction band offset affects the carriers collection as evident from Fig. **41**, in which the sun lighted IV characteristics of HJ, not affected by defect density at the interface, and simulated without BSF, are reported. While the p-type c-Si HJ is not affected by the band offset, in turn the n-type c-Si HJ is strongly dominated by barrier against the hole flow toward the emitter layer and an undesired S shape appears. Moreover the depletion region is more pronounced within HJ on p-type c-Si than in HJ on n-type c-Si. Indeed the simulations report that capacitance values at 100 kHz and 0V are higher in HJ on n-type c-Si (660 nF/cm2 ) with respect to that on p-type c-Si (125 nF/cm2 ). If defect density at the interface is introduced the S shape in HJ on n-type c-Si would be more pronounced. This unwanted effect almost disappears if microcrystalline silicon (c-Si) emitter is used instead of a-Si:H [166]; in that case the valence band offset is reduced due to narrow Egap of c-Si, but the unwanted epilayer that forms during microcrystalline growth reduces the cell performance as already discussed.

#### **9.1. n-Type Doped c-Si**

On n-type doped c-Si substrate several studies have been reported in literature to evaluate the potentiality of this heterostructure, but the efficiency obtained were always much lower than the Sanyo results. This was mainly due to the choice of the device architecture. One of the relevant part of the cell as the rear side contact was always neglected by the authors, since they mainly focus on the front junction of the cell to investigate the transport and the role of the intrinsic a-Si:H buffer layer [167, 169]. In that approach part of the built-in potential of the entire structure proposed by Sanyo is lost due to the lack of back surface field. Increasing the doping of the c-Si base the S shape seen in Fig. **41** become less pronounced and almost disappear if a n<sup>+</sup> c-Si (1x10<sup>19</sup> cm-3) is added to the rear side of HJ cell. Better situation is achieved introducing i/n a-Si:H as BSF. The lighted IV characteristic reported in Fig. **41** reveals a very high efficiency (almost fitting the Sanyo's best results). Then it is quite surprising that the same emitter that produced S shape lighted I-V characteristic now is working almost perfectly.

**Figure 41:** Comparison of simulated lighted IV characteristics of HJ on p-(black) and n-type doped c-Si (red) without BSF and defects at the interface.

This effect is described in Fig. **42** comparing the band bending and the quasi Fermi levels, at 0.4V and sunlight exposure, related to the two structure with and without n a-Si:H BSF. It is worth to note that all the material involved in the simulation are the same and the defect densities at the interfaces have been chosen very low to affect the quasi Fermi level distribution along the structure. Indeed also now the valence band offset is still working as a barrier against hole collection from the emitter side. But now the end point of the entire carrier equilibrium is fixed by

#### *Heterojunction for Silicon Photovoltaics Silicon Based Thin Film Solar Cells* **321**

the i/n a-Si:H BSF. The hole quasi Fermi level is almost free within the c-Si (no defects have been added yet that could pin it) assuming a value closer to the valence band almost everywhere along the c-Si. This effect is due to the edge condition at the surface from which the carriers are extracted. Indeed at that surface the mass law (np = ni 2 ) must be always satisfied. This condition implies a reduction of hole in the semiconductor underneath the surface as well described by the jointing of the two quasi Fermi levels at the surface. If this happens on n a-Si:H (as in case of n c-Si/n a-Si:H BSF) the n c-Si is safe and there the hole amount can remain higher with respect to the case in which the carrier extraction is performed from directly from the n c-Si surface. The quasi Fermi levels are indeed more splitted at the c-Si surface than in c-Si BSF. Then if the hole amount in the c-Si is higher the hole collection from the emitter side is less affected by the valence band offset thus enhancing the total current as evident from lighted IV curves in Fig. **41**. Moreover the splitting of quasi Fermi levels during sunlight exposure is larger along the c-Si and thus the cell Voc value is higher. This has another relevant consequence: wider the Fermi levels splitting lower the sensitivity to the interface defects. The right dopant amount and thickness, as well as the choice of metal work function of this layer have needed an optimization process. Indeed the n-type a-Si:H should be sufficiently thin to avoid series resistance enhancement and sufficiently doped to avoid depletion by the metal contact due to its work function.

**Figure 42:** Comparison of simulated band bending at 0.4V under sun light exposure related to the two HJ structure with (a) and without n a-Si:H BSF (b).

To better evaluate this concept a comparison of band bending distributions at the rear side of the cell is reported in Fig. **43**, as obtained by numerical simulations, in which two different work function 4.2 eV and 4.6 eV have been applied at the rear side metal contact keeping the same doping and density of state distribution within the n a-Si:H layer. The Wf has been simulated fixing the Fermi level at the edge of the n a-Si:H layer where the metal contact would be. The thickness of the n a-Si:H layer has been fixed at 27 nm. As evident from Fig. **43**, depletion occurs in the n-type c-Si and this reflects in a barrier formation for the electrons being collected by the metal contact. This barrier reflects again in a "S shape" in the sun-lighted current voltage characteristic as reported in Fig. **44** as continuous lines. This unwanted effect has been experimentally observed on sample with TCO rear contact (see Fig. **44** red dots) and has been almost recovered by TCO removal and subsequent Al contact evaporation (see Fig. **44** black dots). The good agreement between simulation and experiments can be considered as proof of the effect of metal contact Wf on thin n-type a-Si:H layer. Indeed the rear side c-Si/a-Si:H interface refers to the same sample. But the use of Al to ensure an ohmic contact at the rear side of the n-type c-Si wafer, even if suggested by the Al work function (Wf) able to align the Fermi level close to the conduction band, is not the best choice since also small amount of Al diffusion into c-Si wafer enhance the recombination process. Indeed Al is a p-type dopant for c-Si and, therefore no BSF can be formed in any way.

**Figure 43:** Numerical simulations of band bending distributions of n c-Si/n aSi:H rear side of HJ solar cell, in which the work function of the metal contact to the n a-Si:H has been varied from 4.2 eV (black) to 4.6 eV (red).

Now it is intuitive that reducing the doping density within the n-a-Si:H layer the current voltage sun-lighted characteristics will assume a behaviour similar to that reported in Fig. **44**. To confirm the effectiveness of the a-Si:H BSF, two similar HJ cells have been compared: the first with a-Si:H BSF and the latter with P diffused BSF (n<sup>+</sup> region). Different Voc values have been obtained: 690 mV and 630 mV respectively. Inserting an intrinsic a-Si:H buffer layer 710 mV of Voc value has been achieved [170]. Actually Sanyo has two best results on HJ n type doped c-Si based cell [171]. Their photovoltaic parameters are listed in Table **3**.

**Figure 44:** Comparison between experimental and numerically simulated IV characteristics under sun-light of n c-Si/n aSi:H rear side of HJ solar cell in which the workfunction of the metal contact to the n a-Si:H has been varied from TCO = 4.6 eV (red) to Al = 4.2 eV (black).

**Table 3:** Photovoltaic parameters of the actually Sanyo's best HJ cell.


Starting from the simulation of the best cell produced by Sanyo, reported as black curve in Fig. **45**, and introducing defects within the c-Si up to 1x1018 cm-3 in a thin layer close to the interface, the shape of the current-voltage lighted characteristic shows an S shape that strongly reduces the cell Fill Factor as already seen in [172]. If the defect density is introduced at both side of the cell very similar results occur.

**Figure 45:** Numerically simulated IV characteristics under sun-light of n c-Si/n aSi:H rear side of HJ solar cell in which the DoS has been increased up to up to 1x1018 cm-3.

As discussed in the previous paragraphs, the introduction of 5 nm thin intrinsic buffer layer at beginning only at the front side interface and then at both the interfaces of the HJ, resulted in higher silicon surface passivation and then in higher cell performance mainly due to a Voc enhancement. The thicknesses of p-type a-Si:H emitter layer and n-type a-Si:H BSF have been fixed at 5 nm and 15 nm respectively [173] even if thicker n-type a-Si:H and n-type c-Si has also been reported in literature [174].

In [94] high efficiency on n-type c-Si base has been reported with the following performances: Voc = 639 mV, Jsc = 39.3 mA/cm2 , FF = 78.9%, eff = 19.8% on 1cm2 area FZ 1-2cm n-type c-Si.

Voc as high as 713mV has also been obtained using 70 MHz VHF-PECVD, as reported in [175].

#### **9.2. p-Type Doped c-Si**

In the past, to form the back surface field, various groups have used diffused junctions [175], [177]. Currently, an a-Si:H BSF also formed by PECVD/HWCVD has to be considered as state of the art, both because the diffused BSF diffusion is not in line with the low temperature approach, and due to the excellent passivation of the c-Si surface that can be obtained by a-Si:H. Surface recombination velocities as low as 3 cm/s have been reported [178].

The main advantage in the use of n-type doped a-Si:H emitter is due to its conductivity that is two order of magnitude higher with respect to the p-type a-Si:H layer as shown in Fig. **46** in which the dark and light conductivities as well as the doping activation energies of both n-type and p-type doped a-Si:H films as a function of PH3 and B2H6 dilution in SiH4 are respectively reported [179]. These conductivity have been measured on 500 nm thick a-Si:H films deposited on 7059 corning glass using 13.56 MHz RF glow discharge with a power density of 28 mW/cm2 , SiH4 flow of 40 sccm, gas pressure of 300 mTorr, substrate temperature of 200 °C and dopant gas concentrations ranging between 0% and 1%. On the other hand the optimum n-type doping concentration should be carefully considered in order to also form a good ohmic contact with a metal avoiding Schottky barrier formation. Fig. **47** reports the current*-*voltage characteristic for the n-a-Si:H/Al junction for two different doping concentrations of the amorphous film. In particular, open and dark symbols correspond to a dopant/silane ratio equal to the saturation value 10-2 %, and 1%, respectively. It is evident that doping ratio equal to 10-2 % interface induces a rectifying Schottky barrier at the metal interface. Then higher dopant concentration is needed to have a good ohmic contact [82]. It is worth to note that the a-Si:H film conductivity decrease as the film thickness reduces as remarked in [180] and reported in Fig. **48**. This effect cannot be compensated introducing more dopant during the thin layer deposition since higher defect density would be formed strongly affecting the electronic transport within the doped layer as previously discussed.

Therefore the emitter thickness and the dopant amount is a compromise between conductivity, filtering effect and recombination. An example of this trade-off is reported in ref [82] and summarized in Fig. **49 (a**), **(b)** in which are reported photovoltaic performances of several HJ cells fabricated on p-type doped c-Si base with same thickness of n-type doped a-Si:H emitter deposited at different PH3 doping concentration. Nor TCO neither antireflection coating has been used as a top contact. The maximum efficiency value was obtained at a ratio equal to 0.12% (1700

**Figure 46:** (a) Dark and lighted conductivities, activation energy for n-doped films *vs.* phosphine percentage in the gas mixture. (b) Dark and lighted conductivities, activation energy for p-doped films *versus* diborane percentage in the gas mixture [179].

**Figure 47:** Current *vs.* voltage characteristics of n-doped a-Si:H/Al contact for two different dopant concentrations in the amorphous layer [82].

**Figure 48:** Electrical activation energy of n-type doped a-Si:H as a function of film thickness. Same PH3 amount is used during the deposition of each sample [180].

[PH3]/[SiH4] ppm), corresponds to the conductivity saturation value found for the single doped layer as reported in Fig. **46**. A reduction of the doping concentration in the buffer layer determines a shift of the Fermi level toward midgap and thus a reduction of the electric field at the interface. On the other hand at higher doping concentration the increase of defect density at the interface layer causes recombination and a reduction of the conversion efficiency of the device. This effect is also confirmed in Fig. **49(c)** in which the HJ external quantum efficiency is reported at 460 nm of wavelength as a function of doping dilution in the emitter layer. This wavelength has been chosen since it is absorbed mainly at the heterointerface [82]. Quite similar results, in terms of [PH3]/[SiH4] ppm, are reported in [181]. Also the depletion region within the crystalline side of the HJ follows the same trend as a function of doping dilution as demonstrated in Fig. **49(d**) by the capacitance measurements performed at frequency of 10 kHz where there is no contribute to the capacitance value from the capture-emission kinetic of the defects present at heterojunction and the device behaves as a capacitor in which the depletion region is the dielectric [149]. Voc improvement up to 635 mV has been obtained by introducing an intrinsic buffer layer on front side interface. Then a compromise of 5 nm thick n-type emitter and 5 nm thick intrinsic buffer layer has been reached [182].

Photoluminescence (PL) measurements, reported as IPL (PL-intensity) as the transient PL signal over time, can be used to evaluate the a-Si:H/c-Si interface quality. Indeed the higher the defect density at the interface the lower is the IPL signal due to higher recombination [92]. A comparison between HJ cell efficiencies and IPL as a function of deposition temperature and a comparison between HJ cell efficiencies and IPL as a function of [PH3]/[SiH4] doping ratio are respectively reported in Figs. **50, 51**. In both comparisons the IPL can be considered as the signature of the lowest defect density at the interface, thus suggesting 210-230°C as the best temperature deposition range and the doping ratio of 2000 ppm as the best choice to enhance the built-in voltage taking into account the interface defect density. Even if lower doping ratio should reduce the defect density, in this case the position of Fermi level moves toward the midgap at the a-Si:H/c-Si interface where the defect density is more effective in recombination mechanism.

**Figure 49:** (a) Voc, Isc (sample area 1cm2 ); (b) FF, Eff; (c) Quantum Efficiency at 460 nm; (d) Capacitance of n-aSi:H/p-cSi HJ solar cell [82].

**Figure 50:** (a) IPL of a-Si:H/c-Si HJ and (b) HJ cell efficiency, both as a function of deposition temperature [92].

In order to fabricate a full low temperature HJ cell on p-type doped c-Si wafer the base contact cannot be formed by high temperature diffusion process.

**Figure 51:** (a) IPL of a-Si:H/c-Si HJ and (b) HJ cell efficiency, both as a function of emitter doping ratio[92].

**Figure 52:** Band bending simulations in dark and 0V. (a) p-type-c-Si/i-a-Si:H/p-aSi:H heterostructure; (b) ptype-c-Si/i-a-Si:H/p-aSi:H/p+ -aSi:H heterostructure.

The use of heterojunction on the rear side of the cell, as suggested in Fig. **39**, needs particular care. The valence band discontinuity between p-type c-Si and p-type a-Si:H reduces the hole collection at the rear side contact. Moreover the high Eatt in p-type a-Si:H does not allow a strong bending of valence band. On the other hand it is very difficult to reduce the p-type a-Si:H Eatt by simply adding more dopant gasses in the gas mixture during the plasma deposition [183]. Indeed the more the B2H6 the more the defect density [184].

The numerical simulations performed on this heterostructure remark that, if the Eatt of p-type a-Si:H layer is chosen on the base of data reported in Table **2**. If the p-type a-Si:H is high doped (p<sup>+</sup> ), the band bending at the heterointerface changes from that reported in Fig. **52(a)** into a more helpful configuration, as reported in Fig. **52(b)** and this reflects in a better hole collection as evident in Fig. **53(a)** (red curves). Indeed the hole collection is dominated by recombination process, as evident in Fig. **53(b)** (blue curves).The IV simulated characteristics related to the two band distribution of Fig. **52** are reported in Fig. **54**. The S shape that strongly affects the cell FF can be almost removed by the p<sup>+</sup> a-Si:H introduction [185]. In neither these simulations nor hopping at the Fermi level, neither tunneling through the barrier mechanisms are included. In principle they can help the hole collection from the p-type c-Si toward the rear side electrode, but are difficult to control of course.

A way to enhance the p-type a-Si:H conductivity thus producing a kind of p<sup>+</sup> is represented by the formation of CrSi thin layer on top of the p-type a-Si:H. This can be accomplished by Cr evaporation and subsequently wet removal [186]. CrSi layer results in lowering the p-type a-Si:H Eatt as reported in Table **2** as p<sup>+</sup> layer. This approach has been successfully used also in HJ fabricated on p-type multicrystalline silicon (mc-Si) wafer [187, 188]. The CrSi has been applied successfully also on front side of the cell to enhance the n-type a-Si:H conductivity, thus reducing the Eatt as reported in Table **2** as n<sup>+</sup> a-Si:H. With this approach HJ cell efficiency as high as 17% has been achieved [177].

The problem of the BSF formation on p-type c-Si has been almost solved as follows:


To confirm the effectiveness of the a-Si:H BSF, two similar HJ cells have been compared: the first with a-Si:H BSF and the latter with Al diffused BSF (p<sup>+</sup> region). Different Voc values have been obtained: 680 mV and 650 mV respectively [170]. Concerning the doping of the p-type c-Si wafer several simulations have been performed and reported in [191]. The authors suggested better performances if 0.5 cm substrate resistivity is adopted as p-type doped base wafer.

**Figure 53:** Holes and recombination distributions at the heterojunction at 0.65 V in dark condition.

**Figure 54:** Simulated current voltage characteristics under AM1.5G sunlight conditions.

*Heterojunction for Silicon Photovoltaics Silicon Based Thin Film Solar Cells* **331**

**Figure 55:** Solar cell parameters, short-circuit current (a), open-circuit voltage (b) and efficiency (c), as a function of the thickness of the a-Si:H(p) layer, da-Si:H(p), in a-Si:H(n)/c-Si(p)/a-Si:H(p) cell structure [181].

**Figure 56:** Temperature dependence of PV parameters of the HIT cell with different a-Si:H buffer layer thicknesses [192].

#### **9.3. Temperature Coefficient**

One of the most particular features of the HIT solar cell is its temperature dependence. Indeed the temperature coefficient is lower than c-Si base homojunction, thus reducing the detrimental effect on the photovoltaic performance due to heating under sunlight exposure. This temperature dependence is mainly characterized by the high Voc due to the lower J0, with respect to the c-Si based homojunction, and by FF dependence related more to the a-Si:H layer conductivity. The temperature dependence of the photovoltaic parameters of the HIT cell fabricated with different a-Si:H buffer layer thickness (half, normal, double, triple) is reported in Fig. **56**. The temperature coefficient can be summarised as -1.78 mV/°C. It increases in absolute value increasing the a-Si:H buffer layer thickness [192].

### **9.4. TCO**

These best performance of HJ solar cells have been achieved by a continuous effort in a-Si:H quality, interface quality, in terms of cleaning and pre-treatment before a-Si:H deposition, dopant optimization and TCO optimization. In particular this last has allowed enhancing cell efficiency in the near infrared region of the sunlight spectra as reported in Fig. **57**.

Details about the TCO used by Sanyo are not completely discloused, but some ideas are maturing to establish its role within the HJ cell. As seen before concerning the a-Si:H doping efficiency as well as the metal contact, it is relevant to use particular care to chose the correct contact having the right Wf to avoid built-in potential reduction as well as S-shape formation.

In general the need of TCO is mainly due to the poor conductivity of the a-Si:H layer. Moreover the possibility to deposit it at low temperature (< 300°C) forming at the same time an antireflection coating for the impinging sunlight, has made the TCO material one of the relevant part of the HJ cell. The electrical and optical properties of TCO films are critically process dependent. Transparency and conductivity of this highly degenerate and wide band-gap oxide semiconductor film can be varied by adjusting the deposition conditions. To obtain the best solar cell performances the ability of depositing highly conductive and transparent ITO films is crucial. However, the optical and electrical properties of this material are inversely related so that a larger conductivity in the ITO film is accompanied by a larger light absorption and opacity. For this reason, a compromise in performance must be made for the intended application.

**Figure 57:** IQE spectra of HIT cell, with optimized TCO (solid line) and not optimized TCO (dashed line) [171].

**Figure 58:** Band bending simulation of the n-type c-Si doped based a-Si:H/c-Si heterojunction cell with two different TCO work functions: 5.2 eV for front and 4.2 eV for the back side. At the left side the band bending at the edge between TCO and p-type doped a-Si:H is magnified to remark the undesired band bending distribution (red) when TCO work function lower than 5.2 eV is used for the cell front side.

Actually the majority of TCO are n-type doped, as indium thin oxide, (ITO) ZnO:Al (AZO), SnO2; while very few p-type doped TCO are under development. However their resistivity is almost one order of magnitude lower than their n-type counterpart. The physical mechanism for the contact formation at the TCO/p-a-Si:H interface is a tunneling effect, as shown in the Fig. **58**. By modeling the bifacial heterojunction device using numerical simulator [164], the band bending at the amorphous/crystalline silicon interfaces and the electronic affinity distribution can be evaluated, and the minimum value of the TCO work function can be estimated as 5.2 eV for the emitter side of the cell, while 4.3 eV are sufficient for the rear side of the heterostructure cell.

Thus we can conclude that to avoid a built-in reduction due to the presence of the TCO/p-a-Si:H contact a TCO with an associated work function more than 5 eV should be designed as suggested by literature [193, 194]. If this rule is neglected and a TCO work function lower than 5eV is used for the front side of the heterostructure cell a band bending at the TCO/p type doped a-Si:H interface can reduce the built-in potential as shown in left side of Fig. **58**. One of the most used in the HJ fabrication process is the ITO film [196]. It is used as both front and back contacts and has been optimized by combining experimental and computer simulation results, determining also which deviation from the optimal ITO thicknesses can be tolerated. The ITO films useful for heterostructure solar cells have been deposited using a low temperature RF 13.56 MHz magnetron sputtering. The sputtering process temperature has been chosen after several trials varying the temperature from 50°C to 300°C. In Fig. **59** are reported, as points, the values of resistivity and effective transmittance (Teff) from 350 nm to 1200 nm. In this graph Teff is defined as:

$$T\_{eff} = \frac{\int\_{390um}^{1200um} T(\mathcal{L}) \cdot AM1.SG(\mathcal{L}) d\mathcal{L}}{\int\_{390um}^{1200um} T(\mathcal{L}) d\mathcal{L}} \tag{21}$$

where T () is the transmittance and AM1.5G() is the number of photons per unit wavelength ().

The deposition process parameters have been optimized in order to obtain a good compromise between the film conductivity and transmittance. Nevertheless the ITO is not sufficient to collect the photo generated current without introduce a great amount of series resistance. Indeed, to reduce this power lost mechanism the HJ cell still needs a front metal grid. In the HJ solar cell technology high temperature steps are detrimental for the cell, due to the low temperature process used to deposit a-Si:H films. Specific silver pastes have been developed from different screen printable paste manufacturers, able to be sintered at temperatures ranging from 120°C to 250°C.

**Figure 59:** Sputtered ITO resistivity and transmittance as a function of deposition temperature.

Longer thermal annealing time and higher temperatures improve adhesion and bulk resistivity [197, 198]. The actual application of this kind of pastes requires an accurate optimization of printing parameters to obtain a fine-line printing, aspect ratio, non-interrupted fingers. At the same time adequate curing in air atmosphere has to be chosen to obtain good conductivity of front grid without damaging the cell performances or modifying the TCO properties. The best condition we have used in the HJ cell manufacturing for the screen printing process has been settled as follows: low temperature sintering Ag paste (Dupont PV410); double wet printed through a 350 mesh screen; drying in a conveyor IR belt furnace at 250°C for 15 minutes; 15 micron thick fingers. A resistivity of 2.92. 10-5 cm has been determined on screen printed silver after this curing process [188]. It has to be mentioned that the ITO sheet resistance increases from 45 / up to 60 / during the procedure while ITO reflectance and transmittance have been almost unaffected. Also the rear side of the cell has been formed by a screen printed metal grid in order to reduce the amount of Ag and thus the cost as well as to perform bifacial cell configuration cell. Actually ZnO is one candidate to replace the ITO due to difficulties in managing the ITO Wf to obtain a good material for front and back contact, as well as availability and cost. Indeed boron doped ZnO has been used for the rear side of the cell followed by an Al foil. This approach is justified by the lower workfunction of the ZnO (around 4.1 eV) with respect to the sputtered ITO (around 5 eV).

Indeed a work function of 4.1 eV aligns better with the Fermi level of n-type doped a-Si:H layer as indicated in Fig. **58**. In Fig. **60** the sun-lighted I-V characteristic of the best cell is reported together with the photovoltaic parameters. Series resistance of 0.95 cm2 and shunt resistance higher than 1 Mcm2 have been evaluated. Reducing the edge effects by cutting the cell area to 100 cm2 the efficiency has been raised up to 20% as reported in Fig. **60**.

**Figure 60:** Current Voltage characteristic of the a-Si:H/c-Si heterostructure best cell under AM 1.5G sunlight simulator before and after the area reduction from 148.5 cm2 to 100 cm2 [195].

Amorphous P-I-N Solar cells have poor stability under sunlight exposure, due to a-Si:H light induced degradation by the Staebler-Wronski effect [17]. Thus using a-Si:H in heterojunction solar cells could be detrimental to the stability of such devices. Instead of heterojunction cells have shown good stability to light-soaking and high temperature exposure tests measured over periods of hours [200, 201]. The performance of HJ cells have been evaluated stable on both p-and n-type [199] even with light soaking of few months.

### **10. INTERDIGITATED BACK CONTACT HJ CELL**

Once the recombination processes have been limited, the main limitation to the short circuit current is the front grid shadowing which is, in average, 8-10% of the cell area. This issue has been overcame by Sunpower which developed the Interdigitated Back Contact (IBC) solar cells, initially proposed by Lammert and Schwartz [202] in which the sunward side is completely exposed, so maximising the absorption. Both the emitter and base contact, produced with alternate diffusing processes at high temperature, are located at the back side following an interdigitated pattern. The Sunpower record cell, based on n-type FZ wafer, shows 24.2% efficiency, having Voc above 720 mV [203]. In Fig. **61** is illustrated the schematic of an IBC solar cell.

The idea to apply the IBC concept to the HJ cell, to take advance of low temperatures budget process and high Voc together with a fully exposed sunward side proposed a new challenge. Taking into account the high FF that can be obtained by IBC cells, it is possible to consider an IBC-HJ cell as one of the most attracting and promising technology for Silicon solar cell production to reach up to 26% efficiency.

**Figure 61:** General schematic of an Interdigitated Back Contact solar cell.

On this considerations basis, several research groups have recently started to find the best approach to produce IBC-HJ. In this section we report an overview of different approach as well as results obtained by different groups: University of Delaware (USA); University of Toronto (Canada); Helmholtz Zentrum (Germany); IMEC (Belgium); CEA-INES (France); ENEA (Italy). Several patents have been deposited in Europe [205-207]. Actually the highest efficiency result to date for IBC-HJ, it is still on small area (1 cm2 ) and involves photolithography steps as well as high temperature steps like diffusion for FSF and oxidation for passivation. Nevertheless we will show two IBC-HJ structures produced all at low temperature and avoiding photolithography, even if their efficiencies are still lower than the expectation.

#### **10.1. University of Delaware**

The earlier publication on IBC-HJ solar cells from university of Delaware, by Lu *et al.* are dated 2007 [208]. The developed cells are based on polished 2.5 cm n-type FZ 300 m thick wafer. Both emitter (p-type a-Si:H) and base contact (n-type a-Si:H) are placed at the back side of the cell, in an interdigitated structure, separated by a narrow non-diffused and non-passivated region.

**Figure 62:** IBC HJ at University of Delaware [208].

Both doped layers, 20 nm thick each, are deposited in a multi-chamber PECVD system at temperature of 200°C, followed by 200 nm thick e-beam evaporated Al layer. The interdigitated

pattern, consisting of 1.2 mm wide strips for emitter and 0.5 mm for base contact, is produced by a two-step photolithography processing; the 2 m wide separation region is the natural product of the etching processes undercutting.

**Figure 63:** Schematic of IBC-SHJ cell having the i-a-Si buffer layer between substrate and doped layers.

The sunward side is passivated with 20 nm intrinsic a-Si:H layer, finished with Indium Tin Oxide (ITO) and MgF2 double layer as antireflection coating (ARC).

It has been found the current and the IQE strongly affected by front surface recombination Seff. Reducing the Seff from 300 to 82 cm/s by means of thermal annealing, the overall response of the cell enhanced in the range of 600-900 nm from an average of 0.55 to 0.8, thus ramping up the efficiency to 11.8% on 1.32 cm2 area, having a Voc of 602 mV.

Numerical simulations have shown the possibility to get device over 24% [204] if: 1) the Voc is enhanced up to 700 mV inserting an intrinsic a-Si:H layer between doped amorphous layer and crystalline base; 2) the Jsc is enhanced up to 26.7 mA/cm2 by applying Silicon Nitride (SiNx) to the front surface substituting the used structure for both passivation and antireflection purpose; 3) the Fill Factor (FF) is improved by optimizing the doped amorphous layers, their covering fractions and the metallization process. While the introduction of (i) a-Si:H buffer helps to enhance the cell Voc, in turn has detrimental effect in cell FF resulting in a "S shape" in the lighted I-V characteristic, as shown in Fig. **64**. The "S shape" curve, similar to those of standard HJ when intrinsic buffer is too thick, is assumed to be not dependent by shunting between p and n regions because of the flat behaviour in reverse bias condition. From Fig. **63** can be noted that the interspacing between doped regions are larger than that in Fig. **62**, and it is formed with an additional photolithography step. Since the front i-a-Si:H passivation/ARC structure resulted not effective, it has been replaced by 75 nm thick Silicon Nitride, to improve both passivation and optical properties. Two dimensional (2D) simulations have been performed [209] with the aid of Sentaurus software from Synopsys. A particular care have been spent in considering the (i) a-Si:H buffer layer properties and the interface with c-Si. It has been found the lower the thickness the higher the FF. Moreover the simulations have evidenced a monotonically dependence between FF and increasing B dopant concentration (*i.e.* the p-type a-Si:H conductivity), without affecting the Voc. In particular moving the concentration by one order of magnitude, 78% FF without any "S shape" is achievable. However both Voc and Jsc are lower in this case. Simulations suggest the increased recombination velocity at the rear side is due to high doping level, both under emitter and in the gap region: increasing Seff by 30 times lead to decrease of 30 mV and 3 mA/cm2 on Voc and Jsc respectively, without affective the FF, neither in negative nor in positive. From simulations it has been shown also the Egap has its influence. When using intrinsic amorphous silicon with decreasing Egap, the FF is enhanced, due to modification in band alignment and offsets. The reason is the less the barriers for the minority carrier (hole) for the lower bandgap, the more the Fill Factor.

Following simulations suggestions, new cells have been fabricated with narrower bandgap back surface buffer layer by decreasing the RF power in the (i) a-Si:H plasma deposition process, obtaining a thickness of 5 nm. Cell efficiency of 13.5% has been reached with Voc and Jsc values lower than the expected.

**Figure 64:** I-V characteristic of previous IBC-SHJ cell (straight line) and with reduced bandgap (*via* reduced RF power) a-Si:H buffer layer [209].

However from simulations it is possible to evaluate the potentiality of this structure. If the front surface recombination velocity is limited to 5 cm/s, the base contact width is reduced to 200 m with simultaneous emitter enlargement, and a light trapping scheme is adopted it is possible to achieve 26%.

### **10.2. BACH Cell**

Recently at University of Toronto has been presented the Back Amorphous-Crystalline silicon Heterojunction (BACH) cell, based on n-type 300 m thick FZ wafer having resistivity around 20 cm. Also in this case the fabrication process consists of different photolithographic steps with at least 4 photo masks. The process sequence comprises also initial oxidation of the n-type wafer to have surface passivation and electrical isolation between emitter and base contacts at the back side. The efficiencies of IBC cells having area of circa 1 cm2 are quite low, with a maximum of 8.1%, having Voc below 600 mV, and low short circuit current density below 20 mA/cm2 , nevertheless the front textured surface. However Fill Factors are appreciably higher than 75% [210]. The major limiting factor for both Voc and Jsc is recognized to be surfaces passivation.

#### **10.3. Helmholtz Zentrum**

The first papers published by this group talking about RECASH (Rear Contacted Amorphous/crystalline Silicon Heterojunction) cells are dated to 2007 [211].

This device is a particular kind of heterostructure, which is not a proper interdigitated heterojunction, but an heterojunction with interdigitated. It consists of a base contact on p-type (FZ, 240 m thick, 1 cm resistivity) silicon substrate made by an e-beam evaporated Al grid (structured by photolithography) covered by an insulator, such as PECVD deposited SiO2. The structuring of this oxide is done by HF etching, assisted with photolithography step.

Over the whole back surface but the busbar of the base contact, the a-Si:H n-type doped emitter, 30 nm thick, is deposited, followed by an e-beam Al evaporation to make the emitter contact. A 3rd photolithography step has been used to isolate the cells, to a final size is 1 cm2 . The sunward side, alkaline textured, is passivated by Silicon Nitride, which also acts as ARC.

**Figure 65:** Sketch of RECACH and PRECACHcells in cross-section (left) and in longitudinal section (right), The inner arrows sketch the average traveling path of the absorber minority/majority excess carriers towards the contacts [213].

The point contacted version (PRECASH) instead consists of a textured front surface passivated by means of SiNx. The whole back surface is instead covered by the a-Si emitter layer (n-type doped) contacted by e-beam evaporated Aluminium. Then a structuring with point-like opening is produced by photolithography and electrically insulated by using SiO2. Then p-type a-Si is deposited and contacted by e-beam evaporated Aluminium. In this way the most back surface is covered by the emitter, while the point contacts are just for the base [212]. In Fig. **65** the scheme of both cell structures are shown.

The authors (Stangl *et al.)* remark the photolithography has been used to provide a proof of concept and other technologies for base grid burying and patterning can be used, like Oxides growth by electrochemical oxidation or screen printing or inkjet. However, at the moment none of this technologies have applied to the RECASH cells [214].

The cells optimization and limits understanding have been done comparing the PRECASH structure with a reference cell having front emitter, with the aid of AFORS-HET software simulation [93]. The model is in 1D, with an approximation: the base back contact Al grid is modelled with a fictive front contact with S=30 cm/s due to SiNx passivation. The BSF p-type layer is similar in both cell structures chosen to give a similar passivation level. The main differences are the side of minority carrier collection (front for reference, back for RECASH) and the absence of TCO front absorption and front shadowing for the back contact cell. Depending on the wafer quality in terms of diffusion length, the RECACH cell has higher efficiency if > 130 s for 275 m wafer thick. In particular if the diffusion length higher than 2 mm then 24% is achievable. However, using wafers with 1 ms bulk lifetime, and the n-a-Si:H actual parameters (as measured from deposited layers) this limit does not exceed 21% [211]. The efficiencies obtained so far, with I-V characteristics reported in Fig. **66**, are of 8.1% for PRECASH and 13.9% for RECACH [214].

**Figure 66:** Measured I-V characteristic under AM1.5 of PRECASH and RECACH cell compared to a standard SHJ cell [213].

Very recently, in early 2011, a group form the same institute together with ISFH group have reached a 20.2% IBC-SHJ cell [215] based on the same structure proposed by Lu *et al.* [208] on ntype 3 cm FZ substrate. The front side is textured and phosphorous diffused to form a Front Surface Field, then passivated by means of Silicon Oxide and SiNx. The back side has 60% area coverage by emitter strips (p-type), 28% BSF strips (n-type) and 12% of gap space between these,

#### *Heterojunction for Silicon Photovoltaics Silicon Based Thin Film Solar Cells* **341**

passivated by a SiO2/SiNx stack, with pitch in the range of millimetres. The metal contact is Aluminium for both emitter and BSF regions.

Two different approaches have been considered: with or without intrinsic buffer layer just under the emitter, obtaining in both cases nearly 20% efficiency. In the first case Voc is 40 mV higher (673 mV), but he FF is nearly 3% absolute less (75.7%); due to the short circuit current density (39.7 mA/cm2 ) the efficiency s 20.2%. Without any buffer the Voc is less (633 mV) but the FF of course is higher (78.8%) with the same current, so that the efficiency is 19.8%. Both cell structures and I-V curves are depicted in Fig. **67**.

**Figure 67:** New cell structure produced at Helmholtz Zentrum and their results in term of I-V curves and PV parameters [215].

### **10.4. IMEC**

They started from CZ n-type, 3-4 Ω.cm (100) silicon, with thickness of either 150 or 280 μm.

Different front side passivation have been adopted: n+ diffusion (POCl3) and HJ on both textured and flat surface. Then on the rear side of the wafer the (i) a-Si:H passivation layer, and doped (p+) emitter have been deposited by PECVD at temperatures less than 200°C. An indium tin oxide (ITO) transparent conductive oxide has been deposited on the a-Si:H layers. Photoresist has been spun on both sides of the wafer, and patterned on the rear side, before etching through the ITO. Openings through the a-Si:H have been performed by wet etching, and immediately prior to Al base deposition, an HF dip has been performed. Aluminium base contacts has been deposited by ebeam evaporation, and following Al lift off/resist removal (in acetone and IPA), the emitter contact Ti/Pd/Ag has been deposited on the ITO layer using shadow masks during e-beam evaporation. A final anneal has been performed in N2 at low temperature. In Fig. **68** the schematic cross section of the cell is reported in Fig. **68** together with the photovoltaic sunlighted I-V characteristic of each cell.

**Figure 68:** Schematic cross section of the cell (left) and relative I-V characteristic (right) [216].

Textured front side has ensured higher Jsc of course, but the Voc as well as the FF are quite low to reach the expected high efficiency, maybe due to poor c-Si surface passivation by low quality a-Si:H layer. Nevertheless 15.2% efficiency has been achieved on 1cm2 area [216].

#### **10.5. CEA-INES**

The earlier publications of CEA-INES about this topic are dated to 2008 [217, 218]. The solar cell architecture is very similar to those illustrated for University of Delaware. It is based on n-type wafers, with back interdigitated heterojunction and contacts. The difference is in the cell size (25 cm2 ) and of course in the processing which completely avoid both high temperature and photolithography steps.

Before producing solar cells, the structure, illustrated in Fig. **69**, has been numerically simulated by means of ATLAS software from Silvaco [217, 219, 220]. It has been found a series of relationships between absorber and amorphous silicon properties and geometries and the final performances. As the base doping concentration increases (*i.e.* less resistive substrate) the short circuit current decreases because of the degradation of carrier lifetime. On the contrary, the Fill Factor increases because of the higher conductivity. Then an optimum doping concentration lays between 5x1016 and 1x1017 cm-3. The bulk lifetime has a strong influence mainly to the Jsc and Voc so that passing from 1.8 ms to 0.36 the efficiency drop is from 23.6 to 14%, keeping all other parameter fixed. The front surface passivation is the most critical parameter even for p-type substrates, having detrimental effect on both Jsc and Voc. The BSF width (in the case of p-type substrate a p-type doped a-SI) is related to the Jsc, which increases when the BSF region decreases. The gap region between emitter and BSF strongly influences the current: the larger the gap, the lower the Jsc. Of course this effect is more pronounced for the lower passivation level achieved on this area. The coverage fraction of the emitter affects the FF linearly, so that the whole emitter area should be covered by the metal, and the contact resistance has to be, of course, as low as possible. Indeed decreasing from 1 to 0.1 /cm2 the FF can increase of 30% absolute. Passing to a n-type substrates the picture is similar. In this case several difficulties have to be considered in the device design essentially due to the poor lateral conductivity of the emitter, since is p-type doped a-Si:H. Therefore in this case the use of high conductive layer on top of amorphous emitter, such as TCO, is mandatory to achieve cell efficiency.

Simulations with the ATLAS software have been performed also on a structure based on 300 m n-ype wafer, with p-type a-Si:H emitter and n-type a-Si:H base contact/BSF with a gap region between them of circa 100 m, as sketched in Fig. **69**. The results are similar to those obtained for p-type c-Si based cell. The Voc's, higher for higher bulk quality, increases with decreasing c-Si resistivity, but with a lower limit of 0.5 cm. Jsc slightly decrease with increasing c-Si doping, but dramatically reduces, as also Voc, below 0.5 cm. The FF shows an opposite behaviour, but the decrease for higher bulk resistivity is not so pronounced as for Voc and Jsc. The result is that Efficiency, depending on the bulk material quality, can stay well above 20% for substrate resistivity in the range 0.6-30 cm.

**Figure 70:** Cross section and sun lighted I-V characteristic of the IBC cell based on n-type c-Si wafer [223]. **((**

It is mandatory the Dit(E) at interface between c-Si and doped a-Si:H stays below 5x1011cm-2 to avoid any strong reduction in all photovoltaic parameters [221].

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The presence of a Front Surface Field, produced with a Front diffusion or either a n-a-Si deposition is very important. It allows to obtain 20% efficient IBC-HJ cells even if the front surface recombination velocity S is up to hundreds cm/s [222]. Based on the simulations, the fabricated solar cells [223] started from high quality FZ 300 m n-type wafers. Front ITO as ARC over a Front Surface Field produced by a n-type a-Si:H layer, reduces the Seff down to 20 cm/s. On the back side an interdigitated pattern has been produced, with the base contact formed by a n-type a-SI:H layer directly deposited on the n-type c-Si and followed by a stack of 80 nm ZnO and 3 m of Al. The emitter consists of an intrinsic a-Si:H as buffer layer and p-type doped a-Si:H layer, deposited at temperature around 200°C. To reduce the problem of poor lateral conductivity of ptype doped a-Si layer an emitter stack consisting in a-Si:H (i)/a-Si:H (p)/ZnO/Al has been chosen for the IBC structure. Then the emitter layer has been patterned in an interdigitated comb shape configuration using a screen-printing etching step, followed by a n-type a-Si:H base contact deposition. Finally a mask assisted process has been used to deposit a metal sheet on top of n-type a-Si:H base contact. This patterning process has not completely reduced the wafer surface passivation. On a 25cm2 area an efficiency of 15.7 % (Voc = 678 mV and Jsc = 32.4 mA/cm2 ) has been achieved as reported in Fig. **70**. In the same figure the scheme of the device cross section is reported on the left side, together with the photovoltaic parameters of the IBC.

#### **10.6. BEHIND Cell**

At ENEA the work on interdigitated back contact heterojunction cells has started in 2006 and presented for the first time in 2007 [224]. The novel scheme for heterojunction has been named BEHIND: Back Enhanced Heterostructure with INterDigitated contact solar cell. What makes BEHIND cell different from other IBC-HJ is the fabrication method which do not involve chemical step for the patterning, neither photolithography nor etching. The back contact structuring is formed by using metallic mask assisted process, in which the alignment is self-mechanically achieved by adopting a specifically designed holder for the substrate and the masks. In principle this kind of concept can be scaled up in area and volume so that it has more appealing for industrial application with respect to other IBC approach reported above. The BEHIND concept can be applied to both pand n-type substrates, however it has been optimized on the first one, renouncing on the benefits of ntype silicon, but taking advance of higher lateral conductivity of n-a-Si:H emitter, allowing to avoid TCO. While the earlier BEHIND cell used just one metallic mask to produce the interdigitated pattern after a rotation of 180 degrees within the holder [224], the best results have obtained employing two masks, one for the depositions and one for the metallization, with narrower finger [224]. It has been fabricated starting from a 200 µm thick, 1 cm p-type, one side polished CZ mono-crystalline silicon wafer. After front side alkaline texturing and cleaning, the front side antireflection and passivation coating and the rear side emitter and back contact have been deposited in a 13.56 MHz direct Plasma Enhanced Chemical Vapour Deposition (PECVD) system. In particular for the front side a double layer stack of a-Si:H/SiNx has been deposited [226] because of its demonstrated good passivation level, despite to a small absorption in the UV part of the sun spectrum. Then on the whole polished backside of the wafer, the emitter n-type doped a-Si:H layer has been deposited over an (i) a-Si:H buffer layer. A Chromium evaporation and following removal has been used to increase the emitter conductivity by formation of CrSi [227].

At this stage part of the emitter has been removed by using a plasma assisted dry etching procedure using NF3 gas through the apertures of a metallic mask, fabricated from a 100 m thick

#### *Heterojunction for Silicon Photovoltaics Silicon Based Thin Film Solar Cells* **345**

Molybdenum foil. Subsequently, keeping the mask in the same position, the cell base contact has been formed by an intrinsic a-Si:H buffer and a p-type a-Si:H layers, followed by a n-a-Si:H deposition useful to increase the conductivity of the a-Si layer [227]. Both doped a-Si have been deposited in a three-chamber having each chamber devoted to a specific doping type. Then another comb shaped aperture mask, having narrower fingers (halved) with respect to the previous mask, has been held and fixed on the rear side of the device. Through these apertures, a 30 nm thick Cr layer followed by 4 m Al layer have been e-beam evaporated. Finally, the mask has been rotated 180 degrees and 4 m of Ag have been evaporated to contact the emitter region, creating the interdigitated shape with respect to the base contact. The total area of the solar cell is 6.25 cm2 . A schematic cross section of the BEHIND cell is depicted in Fig. **71**, together with the experimental I-V characteristic measured at room temperature, under Class A calibrated to 100 mW/cm2 AM1.5G sun simulator.

**Figure 71:** Schematic cross section of the BEHIND cell (left) and relative I-V characteristic (right) [228].

The solar cell efficiency, 15%, is the highest known at the moment on p-type based IBC-HJ. However it is limited by a low Fill Factor. The very high open circuit voltage Voc = 695 mV confirms the effectiveness of the a-Si:H/c-Si heterojunction as the way to improve the silicon based solar cell efficiency. This result also confirms that the uniformity of the deposited amorphous silicon layers is not influenced by the mask-assisted deposition process even when multiple masks are used in the fabrication process. Indeed the alignment between masks and substrate is feasible and the regions where the doped layers can unfortunately overlap are isolated by the intrinsic a-Si:H. The key issues to obtain high Jsc depends on diffusion length, Ld, and front surface recombination velocity, Sn,p. In particular Ld and Sn,p have been respectively estimated of 680 m and 80 cm/s from a fitting procedure of the IQE reported in Fig. **72** [228] together with reflectance and EQE of the cell.

The weak point of this technology is the relatively high number of steps required to complete the cell.

Therefore a new simplified version of the BEHIND cell has been investigated in order to reduce the number of steps needed in the cell fabrication procedure and presented recently as BEHIND 2.0 [229]. This kind of structure also avoids the dry etching steps through masks, which are critical

in terms of reliability and reproducibility. The new scheme is based on the idea to deposit both the emitter and base amorphous contact on the same passivating intrinsic amorphous layer. The absorber is a p-type 1cm CZ 200 m thick double side polished c-Si wafer, having on the sunward side the same a-Si:H/SiNx double layer shown before, having thicknesses of 10 nm and 65 nm respectively. After the deposition of 7 nm thick intrinsic a-Si:H buffer layer on the whole rear side of the wafer the interdigitated structure have been deposited in two steps by using two different metal (Molybdenum foil based) masks: "n-mask" for the emitter and "p-mask" for the base contact on purpose designed. The masks are in turn ensured in contact to the rear side of the wafer by using a specific designed holder. To form the n-type emitter it has been deposited the amorphous emitter layer and evaporated 100 nm of Cr to form the CrSi. Then, after un-set the "nmask", the "p-mask" is used to deposit the amorphous base contact layer, an amorphous delta-n layer and finally evaporated the Cr to form the CrSi. To enhance the metallization thickness, instead of metal evaporation, a low temperature sintering (250°C for 15 minutes) Ag screen printing process for both contacts has been developed. The mask alignment is not critical since the n-type a-Si:H emitter width is three times wider than the p-type a-Si:H region. Finally a SiNx layer has been deposited over the entire rear side (except the two cell bus bars) to enhance the of the region not covered by emitter or base contact [199] A sketch of the new structure, together with picture of the screen printed interdigitated metal electrodes is reported in Fig. **73**. Despite of the simplified process, two main point has to be addressed:


To exploit these two points 2D numerical simulation have been performed with ATLAS software [219]. In particular the doping density of each layer has been chosen taking into account the activation energies of doped amorphous films as already mentioned in Table **1**. The intrinsic layer thickness has been varied in the range from 3.5 nm to 14 nm. It has been found that increasing the i-a-Si:H layer thickness the lighted I-V characteristics, simulated under standard AM1.5G condition, has been strongly affected resulting in a fill factor reduction. This effect is related to the recombination at the a-Si:H/c-Si interface. Indeed when the (i) a-Si:H layer becomes thicker, the p-type a-Si:H base contact is not able to collect the holes due to the valence band offset at the edge of a-Si:H/c-Si interface These holes can recombine through a-Si:H/c-Si interface defects with electrons generated in the c-Si side of the device and diffusing also toward the rear side of the device. This reflects in a barrier against carrier collection from the base contact that can be regarded as a double diode (in anti-series) [229]. From the simulated lighted I-V characteristics as a function of intrinsic layer thickness it has been understood that increasing the (i) a-Si:H layer thickness an S shape curve in the I-V characteristic occurs. Indeed also several interdigitated structures have been simulated having different distance between the two doped contacts, varied from 4 m to 90 m. These simulations remarked that to achieve the best efficiency the distance between doped contacts should be as short as possible; otherwise a reduction of fill factor occurs. This effect is due to the absence of electric field in crystalline region covered only by the intrinsic a-Si:H layer which favorites the recombination Indeed if the density of states in the i-a-Si:H layer

#### *Heterojunction for Silicon Photovoltaics Silicon Based Thin Film Solar Cells* **347**

were increased from 1017 cm-3 to 1018 cm-3 the recombination would be stronger and its effect on the I-V characteristic would be dramatic with the presence of a S shape. Unfortunately in practice it is evident the difficulty to obtain a distance between the two doped contacts as short as 4 m without any photolithographic process.

**Figure 72:** Reflectance, Internal and External Quantum Efficiency of the BEHIND Cell [228].

**Figure 73:** BEHIND 2.0 structure, with a picture of interdigitated screen printed silver electrodes.

Nevertheless several experiments have been performed to evaluate the proposed structure and to validate the simulations. The experimental I-V characteristic in this study have been measured at room temperature, calibrated to 100 mW/cm2 and AM1.5G illumination and are shown in the Fig. **74**. The difference between the two samples consists of spacing width between the n and p type regions, in case of A-sample this width is 100 m, while for the B-sample this distance is 200 m. Moreover the SiNx deposition over the rear side of the structure, proposed to enhance the surface passivation in the gap region, even if is able to enhance the Voc of 10 ÷ 15 mV with respect to the values measured before the SiNx deposition, is not sufficient to recover the S shape of the I-V characteristic, probably due to its positive charges that recall electrons close to the c-Si/a-Si:H interface.

**Figure 74:** Sun lighted I-V as a function of distance between base and emitter contacts. Front side of the cell is not textured [229].

I-V characteristic of sample A seems not affected by the barrier against carrier collection and thus is free from the S shape, but the fill factor of sample A is far from the ideality. This effect can be related to two main reasons. The first to the a-Si:H/c-Si interface defects that affect the transport mechanism toward the doped contacts. The latter to shunt effect arising from screen printing process not perfectly aligned with the underneath Cr contacts. Nevertheless the cell efficiencies have not exceeded the 12%, so it can be concluded that the gap between the base and emitter contact is the main limitation of the simplified cell design.

#### **ACKNOWLEDGEMENT**

Declared none.

### **CONFLICT OF INTEREST**

The author(s) confirm that this chapter content has no conflict of interest.

#### **REFERENCES**

[1] Fhus W, Niemann K, Stuke J. Heterojunctions of amorphous silicon and silicon single crystals. Proceedings of AIP Conference; 1974 Mar 20-22; Yorktown Heights, NY, USA 1974; pp. 345-350.









[196] Plà J, Tamasi M, Rizzoli R, *et al.* Optimization of ITO layers for applications in a-Si/c-Si heterojunction solar cells. Thin Solid Films 2003; 425: 185-192.


<sup>[197]</sup> Available from: DuPont:http://www2.dupont.com/Photovoltaics/en\_US/news\_events/article20090325.html

[219] Available from: http://www.silvaco.com/products/device\_simulation/atlas.html


© 2013 The Author(s). Published by Bentham Science Publisher. This is an open access chapter published under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/legalcode

## **Micromorph Cells**

## **Maurizio Acciarri\***

*Department of Materials Science and Solar Energy Research Center (MIB-SOLAR), Università degli Studi Milano Bicocca, Via Cozzi, 53-20125 Milan, Italy* 

**Abstract:** The photovoltaic (PV) industry is growing, with rates well in excess of 30% a year over the last decade. World solar photovoltaic market installations are expected to reach 17.5 Gigawatt in 2010; however, PV contribution to global electricity generation is still negligible. The main challenge for a major contribution demands incremental reductions in €/Wp costs of PV modules. The traditional development of photovoltaics was based on crystalline-silicon wafer technology. However, the early 1970's witnessed a new approach based on the possibility of growing silicon in the form of a thin-film on a given substrate. Several techniques are currently used to achieve this deposition, and they are mainly based on the chemical vapour deposition (CVD) technique. While amorphous siliconbased PV modules have dominated the thin-film market for over 20 years, recent industrial developments include tandem solar cells based on stacks of amorphous (a-Si:H) and microcrystalline silicon (μc-Si:H) film ("micromorph cells"). A basic question that already awaits an answer concerns the link between the microstructure of the material, transport properties of the intrinsic absorbing layers, as well as the electrical performance of solar cells. μc-Si:H is a complex material with a wide range of microstructures, depending both on deposition conditions and on the substrate material. This chapter will report on the state of the art and several aspects of material properties. Device physics will also be presented.

**Keywords:** Absorption coefficients, amorphous superconductors, impurity and defect levels, chemical vapor deposition, electronic structure, electrical conductivity, optical properties, photovoltaic thin films, semiconductors and insulators, thin films.

### **1. INTRODUCTION**

The photovoltaic market has grown quickly in recent years at a rate well in excess of 30% a year. The market is dominated by bulk mono-and multi-crystalline silicon (c-Si) solar cells, which account for about 85% of the total production. However, the wafer-based technology has still not proven its capability of making the cost of electricity produced by PV competitive against that produced by fossil fuels. One reason for this, though not the only one, is the high cost of raw material (silicon). PV industries are making an intensive effort to reduce consumption of the material by diminishing the thickness of solar cells. Thin-film technologies allow for important reductions in semiconductor thickness through the capacity to absorb most of the incident sunlight within a few microns of thickness. In addition, thin-film technology has an enormous potential in terms of cost reduction by offering the opportunity to use large area monolithic modules with a fully automated manufacturing procedure. The GBI Research [1] recently reported the increase in

**Address correspondence to Maurizio Acciarri:** Department of Materials Science and Solar Energy Research Center (MIB-SOLAR) Università degli Studi Milano-Bicocca, Via Cozzi, 53-20125 Milan, Italy; Tel: +390264485136; Fax: +390264485400; E-mail: maurizio.acciarri@unimib.it

thin-film production from 14 MW in 2001 to 2141 MW in 2009. Considering production in 2009, thin-film technologies represented 25% of total global production and were expected to increase their share to 38% by 2020. However, silicon thin-film technology lost its leadership in the thinfilm PV market because of the steep rise of CdTe modules. In 2010 the market share for siliconbased thin-film technology dropped to 32% *vs.* 60% in 2005 [1]. This reduction may also be associated with the inability of the modules based on amorphous silicon to overcome certain limitations in their photovoltaic performance. In particular, the efficiency of an amorphous silicon module is considerably less than levels reached by crystalline silicon modules. This means that, despite the lower production cost of amorphous silicon modules, the market is dominated by crystalline silicon, and interest is growing in new materials like CdTe or Cu (In, Ga)Se2. But the recent use of microcrystalline silicon for tandem junctions with amorphous silicon has aroused interest in enhancing construction efficiency while maintaining low costs. This chapter will discuss the deposition methods of microcrystalline silicon thin-film, its structural and electrical properties and photovoltaic devices based on this material.

### **2. MICROCRYSTALLINE SILICON THIN-FILM: AN OVERVIEW**

Reducing material consumption by diminishing thickness was one of the reasons that triggered the introduction of thin-film technology in the PV market. However, the low absorption coefficient of crystalline silicon limits this solution. Therefore new materials were studied in view of their potential use as an active layer in solar cells. Amorphous silicon was the first to draw the interest of researchers.

Amorphous silicon PV history [2, 3] starts in 1965, when Sterling *et al.* [4] reported deposition of silicon onto a substrate using a silane glow discharge. In 1969, Chittick *et al.* [5] obtained an intrinsic amorphous silicon film of acceptable quality through plasma Enhanced Chemical Vapor Deposition (PECVD).

The PE-CVD technique consists in gas decomposition by plasma. Gases used for the deposition of intrinsic silicon thin-films are silane (SiH4) and hydrogen (H2). The amorphous or microcrystalline nature of the deposited material depends on the various deposition parameters that have to be adjusted.

Another important date is 1975 when Spear and LeComber [6] demonstrated the possibility of doping (both n-and p-type) amorphous silicon. This paved the way for solar cell development.

In 1976 Carlson and Wronski announced the first experimental a-Si:H solar cell made at the RCA Laboratory [7]. This single junction p-i-n a-Si:H solar cell deposited on a glass substrate exhibits 2.4% conversion efficiency. It took some years to realize that plasma-deposited amorphous silicon contains a significant percentage of hydrogen atoms bound to the amorphous silicon structure. Hydrogen is essential to increase the electrical quality of the amorphous growth film. Due to the presence of hydrogen, this amorphous silicon film was named hydrogenated amorphous silicon (a-Si:H). The development of a monolithically integrated type of a-Si:H solar cell was of the utmost importance for industrial production [8]. Integration of the monolithic series made it easy to achieve the desired output voltage from a single substrate. In 1980, the integrated type a-Si:H solar cells were commercialized by Sanyo and Fuji Electric, and used in consumer electronics such as

calculators and watches. In the 1980s the initial cell efficiency was increased to around 11-12% [3], which dropped to 7-8% after stabilization. Three decades later, the highest confirmed stable efficiency for a single-junction a-Si:H cell at lab level is 10% obtained in 2010 at the Oerlikon Solar Lab, Neuchatel [9].

Always in the 1980s, industry addressed its interest to off-grid power generation. Modules chosen for this application were single junction p-i-n a-Si:H solar cells. The typical area of the modules ranged from 0.1 to 0.3 m2 and they were designed to deliver a power of around 14 W with up to 5% stabilized efficiency. However, the strong interest in a-Si:H modules cooled down owing to certain limitations that were detected at the time.

The main problem was light-induced degradation known as the Staebler–Wronski effect [10]. This effect is responsible for a typical 15–30% decrease in the initial performance of an a-Si:H solar module. Moreover, inadequate protection and framing of these modules against moisture resulted in the corrosion of contacting electrodes. These problems and the difficulty in further increasing cell (module) efficiency directed researchers to pursue new paths.

In 1983, Matsuda [11] produced both p-and n-type microcrystalline silicon (µc-Si). This new material was used in 1987 by Hattori *et al.* [12] to make the first thin-film silicon solar cell that had microcrystalline-silicon emitters (µc-Si). µc-Si cells attracted general interest mainly because they presented no light-induced degradation. The interest in microcrystalline silicon continued in the 1990s as the market demanded more stable absorbing material, higher output power modules and lower manufacturing costs for thin-film silicon solar cells. New deposition techniques were explored and in 1992 Faraji *et al.* [13] used very-high-frequency PECVD (VHF-PECVD), and in 1997 Rath *et al.* [14] proposed the hot-wire CVD (HW-CVD).

In the 1990s it became quite clear that a-Si:H single junction alone could not compete with low cost crystal silicon and, more recently, with CIS and CIGS-based solar cells. In fact, singlejunction technology is expected to hit its practical efficiency peak (8% to 8.5%) for many producers by 2012, and it will phase out thereafter [1].

To overcome the efficiency limit of amorphous single junction solar cells, industries developed tandem and even triple layer devices containing p-i-n cells stacked one on top of the other. Several a-Si:H based alloys were tested for a better match of the solar spectrum. Hydrogenated amorphous silicon carbide (a-SiC:H) was used as top cell (window layer) [15]. Hydrogenated amorphous silicon germanium (a-SiGe:H) became an attractive low bandgap material for stacked solar cells [16]. Surface textured substrates were also introduced to enhance optical absorption [17].

Some industries transferred these new materials and devices to production lines. For example, a-SiGe:H alloy was used in a tandem solar cell structure by BP Solar [18], Sanyo [19] and Fuji Electric [20], and in a triple junction by United Solar [21]. However, better performances are expected if a higher electrical quality material like µc-Si is used.

In 1994 [22, 23] the "micromorph tandem cell" concept was introduced at the "Institut de Microtechnique" in Neuchatel (Switzerland). It was a new promising thin-film solar cell that used the same deposition technology as amorphous silicon-based devices. The use of the a-Si:H cell combined with microcrystalline silicon (µc-Si:H) leads to the so-called "micromorph" (microcrystalline/amorphous) tandem solar cells.

Because of the difference in bandgap, a-Si layer is suitable for the use of shorter wavelengths and a µc-Si:H layer is suitable for the use of longer wavelengths (Fig. **1**). Therefore a-Si:H/µc-Si:H tandem structure absorbs the sunlight effectively. This technology makes a 30% or more increase possible in output power.

**Figure 1:** Spectral distribution of the AM1.5 solar spectrum incident on the Earth's surface. The spectral ranges which are absorbed by a-Si:H and μc-Si:H, respectively, are indicated.

Moreover, compared to other thin-film technologies currently under development and industrialization (CIGS, CdTe), silicon thin-films have the key advantage of using silicon as raw material which is non-toxic and widely available.

Although the first microcrystalline thin-film was introduced into solar cell fabrication something like 20 years ago, these cells/modules have still not achieved an important increase in conversion efficiency. However, the amorphous/microcrystalline silicon solar cells are still a topic of research and new progress is expected.

### **3. MICROCRYSTALLINE SILICON THIN-FILM DEPOSITION**

Considering that the principal techniques used nowadays for microcrystalline deposition are the same as those used for amorphous deposition, and that they have already been mentioned in this eBook, the easy deposition process will be briefly described below along with the evolution from amorphous silicon to the "micromorphous" concept.

Starting from the initial amorphous silicon deposition and then from the evolved family of semiconductors based on different forms of silicon alloys or crystallinity (nano, micro or poly), all

the various deposition techniques have in common deposition in the form of thin-film at low temperatures (below 600°C and often around 300°C). The general idea of research on µc-Si:H deposition is to understand and control the deposition process in order to achieve the best material quality at the lowest feasible preparation cost. A broad range of vacuum techniques has been employed to work towards this goal.

The three methods commonly used for manufacturing a-Si are electron beam evaporation, rf sputtering and deposition from silane (SiH4) in a radio frequency discharge. Electrical and optical properties of the resulting film depend on the method of deposition.

In these deposition techniques, film growth takes place through sequential sticking of reactive silicon-containing species called growth precursors, which may originate either from a source gas or from a solid target. A common feature of all µc-Si:H deposition techniques is that H2 gas is present to tune the material ranging from a-Si:H to highly crystallized µc-Si:H, as illustrated in Fig. **2**. Crystalline growth starts at nucleation centers near the film/substrate interface. The columnar grains can be several 100 nm wide and several μm long. Atomic hydrogen is believed to play the decisive role in structuring the Si-Si bonds to form a more crystallized matrix [24, 25]. The crystallization process evolves in a transient way, giving rise to a substrate-dependent structural evolution ranging from an initial amorphous incubation zone to the more crystalline thicker parts of the film [26, 27] (Fig. **2**).

**Figure 2:** Schematic diagram showing the prominent microstructural characteristics of µc-Si:H, after Vetterl *et al.* [28]. The left-most region corresponds to highly crystallized material deposited in hydrogen-rich conditions whereas the right-most region corresponds to highly amorphous material deposited in hydrogenpoor conditions (reproduced with permission of Elsevier).

The space between these crystalline grains is filled with amorphous silicon and/or voids. The crystalline volume content of the film depends on deposition conditions, in particular on the silane concentration in the gas mix. The regime around 6% silane concentration is called the "transition region" and yields the best μc-Si:H solar cells [29].

The terms 'micro-crystalline silicon' (μc-Si:H) or, alternatively 'nano-crystalline silicon' (nc-Si:H) are usually adopted to indicate layers that are deposited at low temperatures (below 400°C). The low deposition temperature allows the application of flexible substrates (stainless steel or polymer) that are useful for building integration [29].

Industry was initially drawn to the a-Si:H PV technology as it is a low-T silicon deposition process and the material deposited does not require any post-deposition treatments (such as hydrogenation). This cuts down the thermal budget and saves time.

However, the limited efficiency obtained with amorphous silicon in the 1990s pushed research along new paths which, maintaining these features, could produce solar cells with higher stable efficiency.

Hydrogenated microcrystalline silicon was prepared by Veprek and Marecek for the first time in 1968 by chemical transport method [30]. The fabrication of μc-Si:H using PECVD was introduced in 1980 [31]. The first application of the PECVD technique in microcrystalline deposition was limited to the p type window layers in p-i-n type amorphous silicon solar cells [32]. Hydrogen dilution ratio r = H2/SiH4 > 15 was conventionally used to form μc-Si:H.

The introduction of microcrystalline silicon (μc-Si:H) as i-layer in the 1990s by Wang *et al.* [33] initiated the production of solar cells that possessed higher and more stable efficiency. This material is a heterogeneous blend of a-Si:H, voids and 10 nm c-Si grains. Regardless of the deposition technique used, the resulting material had a very high density of defects.

In 1994 Meier *et al.* prepared solar cells with μc-Si:H i-layer that suffered no light-induced degradation. Later, Klein *et al.* demonstrated that μc-Si:H may show some light-induced degradation with significant a-Si:H volume fractions of 40% or more [34]; however, this degradation is much less pronounced than in a-Si:H and shows improved electronic properties. For this issue, the crystalline volume fraction is a crucial property for materials. Vetterl *et al.*  demonstrated in 2000 that there is an optimum in solar cell performance for material consisting of about 60% c-Si grains, 40% a-Si:H and a minimum amount of voids [28].

The PECVD deposition of silane (SiH4) and silane-containing mixtures ensured better material quality as the result of the incorporation of hydrogen in the silicon matrix that diminishes defects [39]. These features have made PECVD the most widely used preparation technique for thin-film silicon.

**Figure 3:** Diagram of a parallel plate capacitively coupled plasma deposition set up.

The most widespread preparation CVD configuration is parallel plate capacitively coupled plasma deposition using an SiH4 + H2 gas mixture. The parallel plate plasma source consists of two planar electrodes (Fig. **3**). One of the electrodes is the substrate itself on which the silicon film is to be deposited. The other electrode is supplied with an oscillating voltage signal at a typical frequency of 1-100 MHz. The breakdown voltage for plasma ignition strongly depends on the pressure and electrode gap.

For H2 the breakdown voltage shows a minimum of approximately 100 V (about 1 Torr cm). For voltages above the breakdown voltage, ionization reactions ensure the creation of free electrons with a temperature in the range of 104 K and a density in the range of 1010 cm<sup>−</sup><sup>3</sup> . Due to the inefficient thermal coupling between electrons and the much heavier neutral atoms and molecules, the substrate and background gas temperatures are hardly affected by the hot electrons. The fast electrons create plasma potential compared to grounded walls and substrate over which positively charged ions can gain energy amounting to several tens of eV leading to ion bombardment of the substrate. Moreover, the hot electrons induce chemical reactions that create the reactive precursors involved in film growth. The general growth mechanism and the contribution of the various precursors to µc-Si:H growth is an active area of research.

More details about CVD deposition can be found in dedicated literature but the brief description given here has the sole purpose of underscoring the fact that material properties like crystalline volume fraction are a result of precursor fluxes during deposition. Plasma properties such as electron density and temperature are the result of complex processes like RF power dissipation, inelastic collisions, gas-phase chemistry and surface chemistry. These processes can be empirically influenced by changing process parameters, such as pressure, substrate temperature, RF power, RF frequency, electrode gap, electrode area, gas flow and gas mixture.

Considering the experience developed, it became clear that the guidelines for forming high quality microcrystalline silicon from plasma CVD are very simple as long as a sufficient quantity of hydrogen atoms can be supplied to the substrate during crystallization without causing any damage (most of it is ion damage). Then film fabrication speed can be improved without deteriorating cell characteristics.

Throughput is an important parameter to be considered for mass-production, and it is, therefore, essential to develop a method for high speed film deposition over large areas.

In the case of μc-Si:H, the deposition rate is definitely an issue regarding industrialization as, at present, the thickness of μc-Si:H solar cells is about 5 to 10 times higher than that of a-Si:H solar cells. μc-Si:H solar cells require a thick intrinsic layer (2.0–3.5 μm) to absorb a sufficient amount of sunlight because of its indirect optical transition.

However, thin-film silicon solar cell technology works at relatively low deposition rates, and a high hydrogen dilution condition can limit the growth rate of μc-Si at some A/s. The deposition of a 2 μm thick μc-Si:H film might take 5 h in "standard conditions".

Therefore, high-rate-growth of μc-Si:H film is a crucial matter for low-cost production of thin-film solar cells.

The introduction of very-high-frequency (VHF) PECVD techniques (*i.e.* plasma excitation frequencies well above the standard industrial frequency of 13.56 MHz) has increased growth rates and offers high-quality materials.

The use of plasma excitation frequencies in the Very High Frequencies (VHF) range (70 to 130 MHz) was pioneered by Curtins *et al.* in 1987 [35].

The VHF-PECVD method enabled researchers at the University of Neuchatel to manufacture the first hydrogenated microcrystalline silicon (μc-Si:H) cells at 200°C with reasonable efficiency indexes [36]. These new cells presented maximum efficiency levels of 4.6% and were stable under light soaking conditions. This last feature convinced researchers that it could be possible to produce modules with more stable efficiency levels than the a-Si:H modules.

When a higher excitation frequency is used (typically in the range of 30-300 MHz), electrons in plasma have a much higher thermal velocity than positive ions. This induces a positive potential in the bulk plasma to maintain charge neutrality. The plasma sheath near the substrate leads to the acceleration of positive ions and also to electron confinement within plasma with enhanced dissociation of silane and reduced energy of ions impinging on the growing surface [37]. The use of VHF plasma is a consequence of the improved formation of microcrystalline silicon and higher deposition rate as compared to conventional plasma deposition at 13.56 MHz [38].

In the VHF-PECVD deposition technique the quality of film growth can be controlled by adjusting some deposition parameters.

The thermal budget is another crucial point in crystalline silicon solar cell production. An advantage of PE-CVD is that it allows relatively low deposition temperatures (below 400°C).

During the plasma gas phase, pressure and Silane Concentration (SC):

$$\text{SC} = \text{SiH} \sqrt{(\text{SiH}\_4 + \text{H}\_2)}$$

strongly affect the crystalline and electrical properties of the μc-Si:H film. The structure of the deposited layer changes from amorphous (at high SC-values) to microcrystalline (at low SCvalues). The most efficient solar cells are grown near the μc-Si:H/a-Si:H transition point (SC= 4- 9%).

However, high-rate deposition of device grade μc-Si:H has been generally difficult because of such problems as ion bombardment and powder formation that are often encountered during the high-rate plasma process [40]. In fact, high efficiency μc-Si:H solar cells reported so far can be achieved at limited deposition rates, typically as low as 0.5 nm/s.

An alternative promising deposition technique for the parallel plate plasma deposition of µc-Si:H is the so-called "high pressure depletion" (HPD) regime, [38, 40, 41]. Using this regime, the maximum efficiency of 9.13% has been achieved at an i-layer deposition rate of 2.3 nm/s [42] without important material quality deterioration, and up-scaling to m2 substrate sizes [43] has been demonstrated. Key aspects of the regime are a "small" electrode gap (~1 cm or less), "high"

pressure (~5 Torr or more), "high" power density (~0.5 W/cm2 or more) and "high" H2 dilution (~10% SiH4 in H2 or less). A qualitative view of the µc-Si:H deposition process has been developed to describe the HPD deposition regime. According to this view, dilution in H2 produces sufficient atomic hydrogen for the crystallization process. A high RF power and corresponding high degree of dissociation in the plasma allows high deposition rates to be obtained, but too high RF power gives rise to energetic ion bombardment inducing defects in the deposited material. A high pressure and corresponding short mean free path ensures multiple collisions of ions as they are accelerated towards the substrate, thereby reducing ion energy and preventing defect formation. A small electrode gap is required for plasma operation at high pressure.

Besides the parallel plate plasma deposition, several other deposition methods are being studied.

Growth rates of 3–5 nm/s, which are compatible with industrial applications, can be obtained with the Low Energy Plasma Enhanced Chemical Vapor Deposition [44] techniques see Fig. **4**. This technique is based on a low-voltage, high-current arc discharge which has been so far very successfully applied, in terms of material quality, in the field of Si–Ge hetero-structures grown epitaxially on Si [45].

Preparation of µc-Si:H from a solid silicon target has been reported using reactive sputtering from an Ar + H2 gas mixture [46] or etching and re-deposition (chemical transport) using H2 plasma [30]. Preparation from an SiH4 + H2 gas mixture has been reported using various methods to dissociate the gas, *e.g.* hot wire [47], expanding thermal plasma [48], inductively coupled RF plasma [49], microwave plasma [50-52] and a DC arc [53]. Preparation of µc-Si:H from source gases besides SiH4 + H2 has been reported for *e.g.* SiCl4 + H2 [54], SiH2Cl2 + H2 [55] and SiF4 + H2 [56].

**Figure 4:** Diagram of a LEPECVD deposition system.

Recently, Shinohara [57] reported a variation implemented to the CVS technique, the so-called Localized Plasma Confinement CVD (LPC-CVD) method [58]. The concept of LPC-CVD is to generate a large amount of small plasma by using pyramidal nozzles under very high-pressure conditions, instead of generating uniform large plasma through parallel plane electrodes under conventional conditions. This concept makes it easier to deposit uniform µc-Si:H film with a high deposition rate, because the overlap of the localized plasma can form uniform high-density silane radicals even under high-pressure conditions (>1,000Pa). A maximum deposition rate of 4.1 nm/s was obtained. This feature also helps to increase gas utilization. An a-Si:H/µc-Si:H solar panel with a conversion efficiency of 11.1% (Voc=161.7 V, Isc=1.46 A, F.F.=72.4%, Pmax=171 W), and stabilized efficiency corresponding to 10.0%, was obtained with this technique. The size was 1,100 mm x 1,400 mm and the deposition rate of µc-Si:H was 2.4 nm/s.

However the advantages and disadvantages compared to parallel plate plasma deposition are not clear to date, and more work on these preparation techniques is necessary.

In the laboratory, deposition rates up to 10 Ǻ/s can be obtained for state-of-the-art solar cells with some of these methods, and regular large scale production at such high rates has not been reported as yet, with the exception of Kaneka Corp.

### **4. STRUCTURAL, OPTICAL AND ELECTRICAL PROPERTIES**

The intrinsic layer of a p-i-n (or n-i-p) silicon thin-film solar cell plays two important roles in the functioning process of the device. On the one hand, it must have good light absorption properties in order to generate as many electron-hole pairs as possible for a given incident light intensity and, on the other hand, it must have good electrical transport properties in order to enable the free electron and holes to exit the device before recombining.

Only under certain conditions microcrystalline silicon is suitable for solar cell applications. For instance, it is claimed that favorable conditions for high efficiency pin solar cells are obtained by depositing the μc-Si film at growth conditions near the μc-Si:H/a-Si:H phase transition [62] or close to the transition to amorphous silicon [34].

Other conditions, which must be complied with for high efficiency, are described below:


 the growth rate should be around 1–3 nms-1 to be compatible with industrial applications [40].

In the following paragraph we shall describe the main physical characteristics of undoped and doped μc-Si:H layers in view of their incorporation into solar cell devices.

For such μc-Si:H material, the microstructure varies while the growth of the film proceeds: an amorphous incubation layer has frequently been observed at the bottom (*i.e.* in the initial growth stage) of layers grown with deposition conditions close to the μc-Si:H/a-Si:H transition. Thereafter, the microcrystalline phase follows, consisting of conical conglomerates made of nanocrystals the size of a few tens of nanometers (See Fig. **5**) [59].

The microstructure of μc-Si:H is actually a "mix" between that of amorphous silicon (*i.e.* no periodicity and no long-range order) and that of crystalline silicon (*i.e.* fully regular network of atoms). In fact, three main length scales for disorder can be identified in microcrystalline silicon (see Fig. **5**):


**Figure 5:** Hydrogenated microcrystalline silicon (μc-Si:H). Schematic illustration of a μc-Si:H layer: pencillike conglomerates (D) formed by a multitude of nanocrystals (d), plus their corresponding boundaries.

**Figure 6:** Cross-sectional TEM image of the μc-Si/SiO2/Si region.

Experimental methods allowing the evaluation of i-layer crystallinity are, therefore, of practical importance for the characterization of μc-Si:H. Transmission electron microscopy (TEM) is a very powerful technique that allows for direct observation of the presence of amorphous and microcrystalline phases.

Figs. **6** and **7** show the typical microstructural features of films deposited at low temperature, as obtained from TEM. They present a typical columnar structure that is orthogonal to the substrate surface and a distribution of elongated nanocrystals, with a section of about 5–6 nm, inside the amorphous phase.

**Figure 7:** Cross-sectional HRTEM image of a particular region of μc-Si film. Some stacking faults and some crystalline regions with different crystallographic orientation can be noticed.

Information about the orientation and size of the nanocrystals can be obtained from XRD measurements. Some typical XRD spectra of μc-Si:H samples at different dilutions are reported in Fig. **8**.

In an XRD spectrum of randomly oriented Si powder, a peak intensity ratio of 1:0.55:0.3 among the (111), (220) and (311) peaks is observed.

In this example, the (220) peak intensity is, like the (111) peak intensity, indicative of a preferred (220) orientation of nanocrystallites.

**Figure 8:** X-ray diffraction spectra obtained for a series of μc-Si:H layers deposited on silicon (a) and glass (b) substrates at various silane, d percentage, dilutions. The curves are shifted for clarity. The three main diffraction peaks corresponding to the (111), (220) and (311) silicon crystallographic planes are indicated [60].

The grain size φ along different crystallographic directions can by calculated using the Debye– Scherrer equation:

$$\boldsymbol{\upphi} = (0.9)\,\lambda \langle \text{[K } \cos(2\theta)] \,\text{]}$$

where λ is the X-ray beam wavelength and K is the broadening of the X-ray diffraction line expressed in radiants.

Raman spectroscopy measurements do provide additional information about the microstructural features of the films [61]. Fig. **9** gives an example of the Raman spectrum of sample growth at different dilutions.

By their deconvolution, one could detect the presence of two bands of which the one at about 520 cm-1 is the position of the transverse optical mode in monocrystalline silicon, and the integrated area is associated with the crystalline fraction (IC).

The peak at about 480 cm-1 is associated with the amorphous phase. The integrated intensity of this peak IA is proportional to the amorphous volume fraction in the excited volume.

**Figure 9:** Raman depth profile of a typical CZ set sample grown at d>30%. The crystallinity obtained from each spectrum is reported on the right side. The spectra are vertically shifted for better clarity [60].

The crystalline phase volume fraction χc could be obtained from the Raman spectrum by using the equations:

$$\mathbf{x}\_{\mathbf{c}} = \mathbf{I}\_{\mathbf{C}} (\mathbf{I}\_{\mathbf{C}} + \sigma \mathbf{I}\_{\mathbf{A}})$$

where σ is the ratio between the cross-sections of c-Si and a-Si.

Structural properties have a strong impact on the electrical and optical properties of μc-Si:H films which, again, are closely related to hydrogenated amorphous silicon (a-Si:H), as both materials are deposited by similar techniques. As previously reported, a-Si:H or μc-Si:H material can be

obtained by working on the deposition parameters (such as temperature, silane concentration, power, frequency, pressure…).

μc-Si:H can be considered as something like a (complex) mixture between crystalline silicon (c-Si) and a-Si:H. So it is useful to consider the basic electronic characteristics of a-Si:H before studying μc-Si:H.

As reported in other chapters of this eBook, a-Si:H is a solid-state material made of silicon atoms which are arranged on a lattice that has a certain short range order, but no long range order. Compared to crystalline silicon (c-Si), the average bond angles between neighboring atoms are distorted. Some bonds are even broken and result in so-called "dangling bonds". The presence of hydrogen during the fabrication of amorphous silicon material enables one to passivate a large part of these dangling bonds. These two main "defects" of the lattice of a-Si:H-bond distortion and dangling bonds-give rise to an electronic band structure containing localized states within the socalled "mobility" bandgap (see Fig. **10**). Note that the value of the "optical" bandgap, which is extrapolated from optical measurements, can be slightly different from that of the resistivity or mobility gap.

**Figure 10:** Density of states N(E) for intrinsic a-Si:H. The states are localized (dangling bonds and bandtails) within the mobility bandgap (delimited by EC and EV).

The bond distortion results in band-tails near the valence and conduction bands. In these bandtails, the electrons (or holes) are localized in space and do not participate (directly) in electron transport. The (non-passivated) dangling bonds create deep states near the middle of the bandgap. They can either be positively charged (*i.e.* absence of electron), neutral (*i.e.* one electron) or negatively charged (*i.e.* two electrons). The dangling bonds act as recombination centers for the free electrons and holes. They can also affect electron transport by influencing the total electric charge. In a-Si:H as well as in μc-Si:H, hydrogen has the important role of reducing the number of dangling bonds, or "defects" and, therefore, of making the material "device-grade", *i.e.* suitable for use in optoelectronic devices like solar cells and detectors.

Coming to μc-Si:H films, the co-presence of amorphous and crystalline silicon is mirrored by electrical and optical properties which are a mix of the two materials.

The difference in the absorption range of a-Si:H and μc-Si:H is due to different bandgap energy (Eg) values. For a-Si:H material, Eg ≈ 1.75 eV, whereas for highly microcrystalline silicon Eg ≈ 1.1 eV, similarly to c-Si. Due to its indirect gap, the absorption of μc-Si:H is lower than that of a-Si:H (Fig. **11**).

In addition to the enhanced light absorption, related to its lower bandgap, microcrystalline silicon has an enhanced scattering property due to the natural texture of its surface, which increases effective absorption.

We have already reported that one of the main advantages of μc-Si:H was its stability under light exposure. Works are reported in literature which confirm no light-induced degradation in the transport properties of μc-Si:H layers [63] as well as in the efficiency of μc-Si:H solar cells [22]. In the past, mainly "highly microcrystalline" material, *i.e.* material deposited far from the μc-Si:H/a-Si:H transition, was studied.

However, solar cells exhibiting the highest efficiencies are fabricated near the μc-Si:H/a-Si:H transition. Therefore, light-induced degradation is an important argument for this material and contrasting data can be found in literature. In 1986 Liu [64] reported a light-induced degradation effect for μc-Si:H films containing grain sizes smaller than 120 Å [64]. On the other hand, Fonrodona *et al.* [65] reported the different behavior of nanocrystalline solar cells deposited by HW (hot wire)-CVD at different silane concentrations. In fact, a variation in dangling bond density under illumination was detected for a solar cell deposited at a SC-value of 6.2%. Conversely, they obtained stable solar cells at SC-values of 5 and 5.6%.

**Figure 11:** Typical curves for the optical absorption coefficient of photon energy, for (mono)crystalline silicon (c-Si), as well as for hydrogenated amorphous silicon (a-Si:H) and hydrogenated microcrystalline (mc-Si:H) silicon thin-films [62] (reproduced with permission of Elsevier).

Klein *et al.* [34] have reported up to 10% relative degradation in the efficiency of μc-Si:H HW-CVD solar cells containing a high amorphous volume fraction, after 1000 hours of exposure to light at an intensity of 100 mW/cm2 and a temperature of 50°C.

However, if it seems that the μc-Si:H films are more stable compared to light degradation, on the other hand, μc-Si:H is very sensitive to the incorporation of oxygen, both during deposition and after deposition (post-oxidation). This is why a gas purifier must be used during deposition in order to get "device-grade" microcrystalline silicon material [66]. Fortunately, once incorporated into complete solar cells, μc-Si:H is usually not subjected to post-oxidation. On the other hand, the electrical properties of single intrinsic layers can be dramatically affected by post-oxidation [67], the latter depending on the deposition conditions (especially on the power applied to the plasma). Therefore, the interpretation of transport measurements performed on layers can be a problem.

**Figure 12:** Conductivity as a function of the crystalline volume fraction.

Charge transport in microcrystalline silicon is strongly influenced by its heterogeneous microstructure composed of crystalline grains and amorphous tissue. An even bigger effect on transport is their arrangement in grain aggregates or possibly columns, separated by grain boundaries, causing transport anisotropy and/or depth profile of transport properties.

An example of the impact of crystalline fraction and hydrogen can be seen in (Fig. **12**). Low conductivity values are requested for p–i–n junction fabrication. A decrease in conductivity with increasing crystallinity can be clearly noticed in the figure. This behavior can be explained by the increased presence of grain boundaries inside the film.

Instead, the increase in hydrogen content induces a conductivity increase. This last behavior can be explained assuming a passivation effect of grain boundaries induced by dissolved hydrogen.

Indeed, unlike a-Si:H, where transport models have been successfully developed (see *e.g.* [68]), no simple generally accepted transport model is so far available for mc-Si:H.

Kocka *et al.* [69] recently analyzed electron transport in microcrystalline silicon thin-film and proposed a transport model which considers the columnar structure of this film [70]. A schematic picture of a microcrystalline film is given in Fig. **13**.

**Figure 13:** Schematic drawing of the uc-Si:H film structure and the density of states [69]. (reproduced with permission of Elsevier).

Authors concluded that it is necessary to know the transport path inside the film in order to correctly interpret conductivity. The microstructure of mc-Si:H, namely of the grain boundaries, plays an important role in electron transport. They also formulated a transport model that is based on the idea that there are at least two kinds of c-Si grains, small and LGs. Whenever potential barriers related to "LG boundaries" are formed, the transport properties deteriorate. The detrimental role of LG boundaries on transport stands in contrast with the beneficial optical effect of light trapping *via* scattering on the column heads. This raises the question about what kind of mc-Si:H microstructure is optimal for solar cells, LGs and/or columns. The question is still open.

#### **5. SOLAR CELLS**

### **5.1. Microcrystalline Silicon Solar Cells**

Just like amorphous solar cells, microcrystalline silicon solar cells are usually designed with a p-in structure. The p-i-n structure is necessary as µc-Si:H films have a shorter lifetime than singlecrystal cells. The three layers are a very thin (typically 20 nm) p-type layer, a much thicker undoped intrinsic (i) layer and a very thin n-type layer.

We have already seen that there are, however, some main important differences between μc-Si:H and a-Si:H solar cells; they are summarised below:

 The bandgap of μc-Si:H is about that of monocrystalline silicon (≈1.1 eV at room temperature) whereas that of a-Si:H is significantly higher, *i.e.* around 1.75 eV;


Although μc-Si:H films have these advantages on amorphous silicon material, the higher conversion efficiency so far reached by single junction μc-Si:H solar cells in the laboratory is comparable with that reached by the best single junction a-Si:H cells after degradation (stabilized efficiency) [71].

Moreover, due to the reduced absorption coefficient of μc-Si:H films, a higher thickness is required for optimal light absorption but the deposition of μc-Si:H solar cells takes much longer than that of a-Si:H solar cells and is, therefore, more expensive.

The introduction of the micromorph tandem cell concept [36] has opened new potential. The 1.1 eV (microcrystalline Si) and 1.75 eV (amorphous Si) bandgap combination is very near to the ideal 'theoretical' bandgap combination needed to obtain maximum efficiency under AM1.5 illumination [72, 73].

Single junction μc-Si:H solar cells will be described in the following sections, giving the state of the art for this technology. Then the application of μc-Si:H films in silicon hybrid solar cells will be presented with a tandem structure made of microcrystalline and amorphous silicon thin-films.

*Single junction microcrystalline silicon solar cells*. Thin-film μc-Si:H solar cells can be divided into p-i-n and n-i-p types according to the film deposition order, although the window layer of the solar cell is the p-type layer in both cases. This is done in order to enhance the collection of holes, which are collected at the p-layer, and whose mobility is smaller than that of electrons. A detailed analysis of the transport process in thin-film amorphous silicon solar cells is reported by Deng and Shiff [74]. The asymmetrical drift of electrons and holes explains why amorphous silicon–based pin solar cells are more efficient when illuminated through their p-layers.

Fig. **14** (pin) also reports the two totally different designs for the solar cells involved, corresponding to transparent and opaque substrates connected to the use of the p-i-n or n-i-p configuration.

The n-i-p substrate configuration processing starts with the n-layer, which is normally grown on a metallic back contact. The first n-i-p cells were developed at Kaneka PV Research Division [75] in 1994. These cells had an initial conversion efficiency of 10.1% [75] for a film thickness of 2 µm (surface area 1 cm2 ).

The characteristics of a cell which has a p-i-n structure prepared with the very high frequency glow discharge method were first reported by researchers at Neuchatel University [22]. An initial efficiency of 4.6% and short circuit current densities of up to 21.9 mA/cm2 were obtained.

 (a) (b)

A typical diagram for a p-i-n cell is given in Fig. **14**.

**Figure 14:** Schematic illustration of the structure of p-i-n (a) and n-i-p (b) solar cells.

In the "superstrate" design (Fig. **14(a)**), sunlight enters through the transparent substrate, which is usually glass or a transparent plastic. A conducting layer, typically a "transparent conductive oxide" (TCO) such as SnO2, is deposited on the insulating substrate. The thin-film silicon layers are then deposited on the TCO, starting with a p-type window layer. Finally, a "back" reflector is deposited, which acts as an electrode for the n-type film layer. The "superstrate" configuration is adopted for the p-i-n structure. PV thin-film module manufacturers use soda-lime glass substrates coated with transparent conductive oxide. Soda-lime glass is used for its low cost but this glass has a negative impact on overall cell efficiency due to its absorption in the near infrared. In this spectral region μc-Si:H solar cells still have significant conversion efficiency. A solution could be the introduction in the production line of the more expensive low iron content glass.

In the "substrate" (n-i-p) design (Fig. **14b**), sunlight enters the cell before it reaches the substrate. Starting with the substrate, the cell is manufactured in reverse order, compared to the superstrate design: first a back reflector, then the film layers (starting with an n-type layer), and finally a TCO layer to act as an electrode to the topmost, window layer of the cell.

The main difference between the two configurations is that the underlying layer of a p-i-n cell is the transparent electrode, whereas the underlying layer of a n-i-p cell is the back electrode.

These two designs allow a very wide range of applications for amorphous silicon solar cells. The superstrate design (light enters through the substrate) is particularly suited for building-integrated solar cells in which a glass substrate can be used as an architectural element. The "substrate" design has generally been applied to solar cells using flexible, stainless steel (SS) substrates. The detailed construction of a deposition facility of course depends on whether the substrate is rigid or flexible. Finally, it turns out that the substrate has a profound effect on the properties of the first layers deposited upon it; this effect has led to fairly different cell structures for the "superstrate" and "substrate" designs.

In the thin-film deposition process, the need to keep the device at temperatures not higher than the highest temperature attained during the previous steps is of particular importance throughout the manufacturing process. This means that the "superstrate" configuration allows cheap deposition of SnO2:F by spray pyrolysis (involving temperatures of 600°C to 800°C) at the beginning, so that the 200 to 300°C PECVD process is performed afterwards.

Moreover, the "superstrate" geometry includes an easy encapsulation process and, usually, higher conversion efficiency. In this case, enhanced η values are a common consequence of the relatively simple application of light confinement strategies [76].

Generally, transparent electrodes are made of oxides and there is a risk of these oxides being reduced by the hydrogen atoms used during growth. In the p-i-n structure the oxide window process must be thinner but the reduced film thickness increases contact resistance. The "superstrate" configuration adopted for p-i-n cells has the advantage that cell integration into the modules can be achieved with well consolidated techniques resembling those used for amorphous silicon.

For n-i-p cells, it should be possible to make integrated structures with methods that are equivalent to those used for Cu(In,Ga)Se2-based solar cells [77]. At present, it is hard to determine which is better.

Historically the n-i-p configuration is connected to flexible substrates because it was used on opaque substrates or poorly transparent substrates like steel foils or high temperature polymers. However, the configuration is not limited to this choice. It is, in fact, compatible with any kind of substrates, such as rigid or flexible, transparent or opaque. Nevertheless, flexible substrates are still the main application for n-i-p cells because roll-to-roll processing makes them highly attractive for cutting down production costs as well as energy payback time, particularly when low cost substrates like polyethylene are used. Use of metal substrate requires substrate insulation as, for example, SiO2 films, and this topic is still the focus of research [78, 79].

The schematic band diagram of a p-i-n device is illustrated in Fig. **15**. As with the a-Si:H-based solar cell, a particularly important conclusion that must be drawn is that the absorber layer, the intrinsic one, is indeed the space-charge zone. This means that:

 carrier transport is performed by drift, and not by diffusion; the mobility-lifetime product (µτ) is now the key parameter that determines effective carrier recombination; the average distance covered by a carrier before recombining is given by µτE, where E is the electric field present,

charge zone is not valid. " #

the usual hypothesis (in wafer-based PV) of a negligible recombination in the space-

**Figure 15:** Band diagram of a p-i-n thin-film silicon solar cell.

As already mentioned, by using the AMPS-1D computer program [80] and a set of optimized parameters to describe a-Si:H [81], Schropp demonstrated that it is possible to design electronic levels such as band edges and to gain insight into device physics.

The electric field E(x) within the device causes all electron level energies such as EC and EV to vary in space in the same way. When the device is assembled, these Fermi energies must be equalized to create thermal equilibrium. Electrons are donated from the n-layer to the p-layer, which generates a built-in electric field; while level positions such as EC and EV now vary. The Fermi energy level remains constant.

Carriers are mainly generated in the intrinsic layer, where incoming light generates electron/hole pairs. Both electrons and holes are separated by the internal electric field (drift current), which is built by the doped layers (p-and n-type) on each side of the intrinsic material. Electrons are drifted to the n-type layer, whereas holes, which exhibit lower mobility, are driven towards the p-type one. The geometry presented favors an increased production of electron-hole pairs near the p-i interface, so that hole collection is facilitated by reducing their mean collection distance. It is important to note that carriers generated in the doped layers do not contribute toward the measured current, as the doped material density of defects is too large to allow carrier transport. As a consequence, light absorption in the p-type is to be minimized.

Thus, the electrical, optical and structural properties of the intrinsic layer strongly influence the PV performance of the cell.

Although short circuit current, open circuit voltage and fill factor are all important parameters to be optimized in terms of IV cell characteristics, the open circuit voltage is used here as a guide to overall cell characteristics as it is directly related to the lifetime of the cell. The current is mainly related to light trapping effects and cell film thickness.

In μc-Si:H-based thin-film solar cells, improved performance is achieved [82, 83] when i-layers contain a substantial amount of amorphous tissue but are still in the microcrystalline regime [84]

(a-Si:H/μc-Si:H transition). Bailat *et al.* [59] clearly demonstrated the correlation between the open circuit voltage (Voc) and crystallinity.

Nath *et al.* [85] have reported the dependence of open-circuit voltage (Voc) on crystallinity. Precisely, open-circuit voltage diminishes as the crystalline volume fraction (Fc) increases (Fig. **16**). Authors have identified three contributing factors to the decrease in Voc with increasing Fc, namely an increase in both mid-gap and tail defects as well as a decrease in the mobility gap.

**Figure 16:** The Voc of silicon solar cells with varying Raman crystallinity [86] (reproduced with permission of Elsevier).

The same authors have also [86] reported a deviation to this general rule in fluorinated µc-Si:H solar cells when grain dimensions increase. The large grain fluorinated films grown with high crystalline volume fraction and large grain exhibit an increased performance. They explained this behavior with a reduction in midgap defects and effective density of states at band edges.

The impact of grain dimension was already studied by Werner *et al.* [87]. According to Werner *et al.* the reason why a microcrystalline silicon cell exhibits a typical 10% or more regardless of its small grain size is because of the very low recombination speed at its grain boundaries. This low recombination speed originates from the small barrier height at the grain boundaries, which is guaranteed by (a) the passivation of hydrogen at grain boundary defects, (b) uncharged intrinsic grains (low oxygen density), and (c) the (110) orientation of crystal grains. These hypotheses are in agreement with results obtained by Nath *et al.*

By the close of the 1990s, low-T fabricated μc-Si:H solar cells on glass had reached stable efficiencies of up to 8.5%. However, due to the low deposition rate (<40 nm/min) of the μc-Si:H film and technical difficulties with the development of industrial-scale VHF PECVD systems, μc-Si:H single-junction solar cells do not seem to be commercially viable at present. The same conclusion appears to apply to the 2 μm thick, 10% efficient μc-Si:H STAR solar cell developed at Kaneka using intermediate-T (~550 °C) and standard 13.56-MHz PECVD [88]. Nevertheless, these results showed that a c-Si thickness of merely 2 μm is all that is needed for obtaining a shortcircuit current density Jsc of >24 mA/cm2 .

### **5.2. Contact Layers**

Generally, all thin-film silicon solar cells use a transparent conductive oxide (TCO) layer as front contact, whereas a reflective contact material is needed at the back.

Various transparent conducting oxides have been reported for their solar cell applications. Among the reported TCOs, ZnO [89], ITO [90], and SnO2 [91] are most widely used in the PV area. The PV market requires low-cost solar cells for the widespread use of PV, which can be achieved by introducing low-cost materials and processes for solar cell production. ZnO has been considered as the most promising TCO material in view of cost and properties. Several deposition techniques, such as spray pyrolysis [92], CVD [93] and sputtering [94], have been successfully employed to produce ZnO films. Sputtering has been the preferred method for its production. The window layer in solar cells must be well optimized so that it has low absorption and critical resistivity. The interface properties with underlying layers have to be carefully considered in preparing the window layer.

Very high quality transparent and back reflecting films can reduce the total thickness required for the absorbing layer and, subsequently, the cell cost.

TCO films are strongly affected by deposition parameters (argon ambient pressure and substrate temperature).

For thin-film solar cells based on amorphous (a-Si:H) or microcrystalline silicon (µc-Si:H) with absorber layer(s) in the micrometer range, efficient light trapping is of the utmost importance. Light trapping and effective light incoupling are important aspects for optimized utilization of the solar spectrum. The use of transparent conductive oxides (TCO: ZnO) with a randomly textured surface is a common approach to meet both requirements [95].

As previously reported, two basic cell configurations are used, in practice, for thin-film silicon solar cells: substrates and the p–i–n or 'superstrate' configuration. We shall now see which solution has been proposed to form contact layers for the two configurations.

## p–i–n or 'superstrate' configuration

In the case of a p–i–n deposition sequence, light enters the cell through the glass substrate on which the TCO layer has been deposited as contact layer. We have seen that the p-layer is the first film crossed by incoming light. However we have also seen that the electrical and optical properties of this layer are low. So, this layer should be relatively thin (about 10 nm) and have a low absorption coefficient in order to allow light to reach more efficient layers. The light then crosses the much thicker i-layer (the active layer) and, finally, the relatively thin n-layer (20 nm typical thickness), and reaches (if not yet absorbed) the reflective back contact layer. This last reflective back contact can be a TCO and/or a metal layer. Actual reflectivity is determined by the combination of the TCO interlayer and the metal.

In this 'superstrate' configuration, not only are the electrical and optical properties of the TCO film important, but it is also essential to ensure that it remains chemically stable during plasma

deposition of the other layers. The use of SnO2:F is quite common for a-Si:H solar cells, but must be avoided for single-junction μc-Si:H cells, as it is partly chemically reduced in the H2-rich plasmas that are necessary in this case. Current research also focuses on ZnO, deposited either by sputtering [96] or by low-pressure CVD (LPCVD) [97].

The higher electrical and optical property quality indium-tin-oxide (ITO) film cannot be used in this application as it can be chemically reduced, even without any hydrogen dilution, *i.e.* already by hydrogen formed by silane decomposition during the PECVD process.

A very important aspect for the back contact is its capacity to reflect whatever light reaches this far back into the intrinsic absorber layer. An appropriate combination of a thin TCO layer with a thicker metallic layer (Al or Ag) provides both the desired optical properties (high value of reflectivity) and high electrical conductivity.

## n–i–p or 'substrate' configuration

This configuration has the advantage of using lightweight, unbreakable substrates, such as stainless steel, polyimide or PET. These are generally either opaque, as in the case of stainless steel, or, if they are transparent, they are often easily damaged by ultraviolet light, like most plastics.

Therefore, the substrate/n–i–p configuration is generally used in this case, and lets light enter the device through the semiconductor layer deposited as last layer, *i.e.* still through the p-layer. The top TCO layer is the critical layer, and both ITO and ZnO are used in this case.

Although the deposition sequence differs from the superstrate configuration, the electrical and optical properties required for these films remain stringent.

*Electrical TCO properties* Electrical properties are determined by the sheet resistance of the TCO film, which is related to specific resistivity ρ and film thickness d, *i.e.* Rsheet = ρ/d. Sheet resistance is practically important for integrated serial connection of cells to a solar panel; it gives rise to a series resistance and, hence, to electrical losses.

Obviously, sheet resistance should be minimized; this is achieved by:


Thus, TCO sheet resistance is inherently related to the absorption of near-infrared light within the TCO film. In fact, increasing carrier mobility is the only way to decrease sheet resistance without

**Figure 17:** Example of the impact of Ar pressure and substrate temperature on TCO resistivity. More details about the deposition procedure can be found in the reference [98] (reproduced with permission of Elsevier).

generating a rise in optical absorption of the TCO layer in the near-infrared. The latter may, on the other hand, significantly contribute toward TCO-related optical losses (see below) already at cell level, while sheet resistance causes electrical losses practically only at module level, as a consequence of the integral serial connection of cells.

Considering the mentioned relationship between sheet resistance and TCO absorbance, it follows that efficiency considerations imply a trade-off between these two TCO quantities.

As mentioned, deposition parameters can have a strong effect on the electrical properties of the film. For example, Lee *et al.* [92] have reported the effect of temperature and Ar pressure on film resistivity (See Fig. **17**).

*Optical TCO properties* Apart from the optical absorption that is directly related to sheet resistance, the TCO should have additional optical properties:


Both functions may be achieved by a suitable surface texture of the TCO, with feature sizes comparable to the wavelengths (divided by the refractive index of the corresponding layer).

For shorter wavelengths, the difference in reflectance is due to index grading at the front TCO/player interface. For longer wavelengths penetrating to the back contact, the reduced reflectance stems from both index grading and light trapping.

**Figure 18:** Typical transmission spectrum of TCO film.

A typical transmission spectrum of TCO film is reported in Fig. **18**.

An important aspect should be mentioned here. During the multiple passes of trapped light, light goes through the TCO several times and is reflected by the back contact. Hence, all absorption losses will accumulate, and this makes the need for very low light absorption in contact layers more severe. It is in this field of contact layers and light trapping that most progress is to be expected in cell research, whereas the photoactive absorber layer, the i-layer, has been well optimized.

### **5.3. Micromorph Tandem Silicon Solar Cells**

Although microcrystalline silicon cells formed at low temperatures have a potential for high efficiency, their efficiency in single-cell structures is much lower than that of bulk mono or multicrystalline cells. New concepts have been researched to achieve a substantial improvement in efficiency. In an attempt to achieve this, different groups introduced the concept of two-stacked (hybrid) structures (Fig. **19**) in which multiple cells with different light absorption characteristics are stacked together.

This device structure, as already mentioned, was pioneered by the University of Neuchatel in the 1990s [22].

**Figure 19:** Schematic device structure of the micromorph tandem cell in the 'superstrate' configuration, *i.e.* in the configuration glass/TCO/p-i-n a-Si:H/p-i-n μc-Si:H.

This approach allows better characteristics to be obtained with existing materials and processes. There are different advantages in using a layered structure: it enables a much better use of the solar spectrum; it enables to obtain a higher open-circuit voltage and, it allows, to some extent, suppression of the rate of reduction in cell performance, which is caused by optical degradation phenomena that are observed when using amorphous silicon-based materials (Staebler–Wronski effect). Hence, in principle, higher PV efficiency can be achieved.

Microcrystalline and amorphous silicon are quite good for tandem cells. It can be proven that the bandgap combination of 1.1 eV with 1.75 eV to is very near the ideal combination for tandem solar cells (See Fig. **20**).

*Micromorph Cells Silicon Based Thin Film Solar Cells* **387**

**Figure 20:** Semi-empirical upper limit of efficiency g as a function of the energy gap Eg of the bottom and top cells of a tandem solar cell [99] (reproduced with permission of Elsevier).

Practically speaking, the double layer thickness must be optimized in order to match the current of the two sub cells.

The preliminary structure studied was composed of stacked (tandem) cells in which an amorphous silicon cell was combined with a microcrystalline silicon cell (Fig. **19**).

The low Jsc of stable a-Si:H cells ensures that the thickness of the μc-Si:H cell in the stack does not have to be increased significantly, compared to a stand-alone μc-Si:H cell. Thus, using PECVD, a high PV module efficiency can be achieved with an economic process.

The research team at the University of Neuchatel has coined the term "micromorph" for this tandem cell and reported initial (*i.e.* non-stabilized) efficiencies of up to 13.1% [22].

The "micromorph" concept has also been considered by various organizations, including Kaneka [100]. In 2001 this company started a pilot production of their so-called "hybrid" thin-film PV technology.

The production line is based on low temperature deposition (13.56-MHz PECVD) onto a large (~0.85 m2 ) TCO-coated soda lime glass. The μc-Si:H cell is about 2 μm thick, whereas the a-Si:H top cell is about 5 times thinner.

This company introduced an intermediate thin TCO layer between the amorphous silicon layer of the top cell and the microcrystalline silicon layer of the bottom cell [101].

In this configuration, a transparent intermediate layer reflects part of the light that has not been absorbed while passing through the amorphous silicon layer of the top cell.

As a result, the effective light sensitivity of the top cell is higher than that of a top cell with the same thickness in a conventional hybrid structure. Hence, an improvement can be expected in the short-circuit current Jsc of the overall hybrid cell. The cell with a transparent intermediate layer is more sensitive at shorter wavelengths (top cell).

The presence of the transparent intermediate layer enables to reduce the top cell thickness needed to obtain the same current compared with a conventional hybrid cell. If the thickness of the amorphous silicon film in the top cell can be reduced, then it should also be possible to reduce photo-degradation of the cell.

Quite good initial efficiency rates (aperture area) of over 12% were reported for these large (0.41m2 ) all-silicon modules. The best cell (area 1 cm2 ) made so far has an initial efficiency of 14.5% [102].

Due to the thinness of the a-Si: H cell in the stack, micromorph (or hybrid) PV devices are expected to decay very weakly in the field. The best stable efficiency confirmed as yet is 11.7% for a sub-module [103] produced by Kaneka in 2004 [104], and 11.9 for a cell manufactured by the Neuchatel group in collaboration with industrial partner Oerlikon [105].

These technologies promise high stable average efficiency of about 10% for large-area massproduced modules using large-area low-T processing equipment from the LCD industry.

However, they require a textured TCO layer and a high capital cost of the deposition tool for the ~2 μm thick μc-Si:H cell, which can be a limitation for high throughput production lines.

### **CONCLUSIONS**

The introduction of microcrystalline silicon in thin-film silicon solar cells is relatively recent. The interest in microcrystalline silicon issued from the need to overcome some intrinsic limitations of amorphous solar cells. However the results so far obtained are still unsatisfactory and, in fact, incorporating μc-Si:H is, thus, still a topic of research.

Several deposition techniques have been tested, and the PE-CVD ones have achieved the best results so far. PE-CVD equipment is already used for a-Si:H deposition with a mixture of silane and hydrogen, and increasing the hydrogen to silane ratio in the feed gas easily obtains microcrystalline growth with reduced variation of equipment.

This technique has many advantages, such as low temperature deposition, use of non-toxic materials and deposition on large substrates. All these features offer the potential for future cost reduction of photovoltaic modules based on this material. Hydrogenated microcrystalline silicon is a complex material composed of a mixture of crystalline and amorphous silicon that can be more easily doped than a-Si:H. On the other hand, it is also more sensitive to contaminants than a-Si:H (for example, oxygen). This material exhibits a wide range of microstructures that depend both on deposition conditions and on the substrate material.

It is quite clear that the best solar cells are obtained when the deposition conditions (hydrogen dilution, temperature,) are tuned in order to approach the microcrystalline/amorphous transition.

The strong interest in μc-Si:H also comes from the quite different optical properties of μc-Si:H compared to a-Si:H. Although μc-Si:H has an indirect optical bandgap at 1.1 eV and has, therefore, a relatively low optical absorption, this optical gap matches the higher bandgap of a-Si:H (about 1.75 eV) for a tandem cell quite well.

The electron transport properties of μc-Si:H resemble those typical of a-Si:H but with increased conductivity. The carrier transport mechanism can be explained considering the amorphous/disordered material present in μc-Si:H layers.

Although the electronic properties are quite better, lifetime is reduced and a p-i-n type or n-i-p type device structure is used also for microcrystalline silicon-based devices. In such devices, carrier collection is enhanced by drift, *i.e.* by the internal electric field that prevails in the i-layer. Currently, the conversion efficiency of the best single junction μc-Si:H solar cell is around 10%.

Microcrystalline silicon was initially introduced in single junction μc-Si:H solar cells due to the reduced electrical performance degradation associated with the Staebler–Wronski effect. However, the conversion efficiency achieved so far by the best single junction μc-Si:H solar cell is around 10%.

One expects a further increase in the efficiency of μc-Si:H single junction solar cells mostly by implementation of improved light trapping schemes and by a corresponding increase in short circuit current density. Improved light trapping will be based on the development of new and better suited transparent conductive oxides, structured substrates (periodic gratings or rough random substrates).

More improvements are expected using microcrystalline silicon in tandem cells consisting of a stack with a top a-Si:H cell and a bottom μc-Si:H cell. This combination of materials can be shown theoretically to possess bandgaps that are very near to the best combination of bandgaps for optimum conversion of the AM1.5 spectrum. For reaching maximum efficiency, an intermediate reflector is used between the bottom and the top cell. Such tandem devices generally suffer less from light-induced degradation in the amorphous top cell. In general, the microcrystalline bottom cell inside the tandem is stable (as it is only exposed to the long wavelength part of the solar spectrum). In order to gain both in conversion efficiency and in device stability, one should reduce the thickness of the amorphous top cell and further optimize light trapping. This may hopefully lead to solar cells with stabilized efficiencies of 13–14%. The industrial production of tandem modules has currently been started by a Japanese module manufacturer.

Several other firms (mainly Japanese) are carrying out research on this subject and a few of them have even developed prototype modules.

Thin-film silicon offers interesting applications in building-integrated photovoltaics through its esthetical appearance and the versatility provided in the choice of a substrate material. On the other hand, the 'micromorph' tandem concept allows for an increase in module efficiency towards a stabilized value above 10%. Because of these factors, one may reckon that the industrial development of thin-film silicon tandem modules based on a combination of amorphous and

microcrystalline silicon will be intensified during the next few years, leading to a clear reduction in module costs, probably down to values below 1\$/Wp.

### **ACKNOWLEDGEMENT**

Declared none.

### **CONFLICT OF INTEREST**

The author(s) confirm that this chapter content has no conflict of interest.

#### **REFERENCES**






© 2013 The Author(s). Published by Bentham Science Publisher. This is an open access chapter published under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/legalcode

**CHAPTER 11** 

## **Light Trapping in Thin Silicon Solar Cells**

**Mario Tucci1,\*, Luca Serenelli1 , Simona de Iuliis1 , Domenico Caputo<sup>2</sup> and Giampiero de Cesare2**

*1 ENEA, Research Center Casaccia, Via Anguillarese 301, 00123 Roma Italy and <sup>2</sup> DIIET, University "Sapienza", Via Eudossiana 18 00184 Rome, Italy* 

**Abstract:** Light trapping plays a key role in solar cell to enhance light confinement and then light absorption within the cell. The reduction of the optical losses reflects in photovoltaic solar cell efficiency enhancement. To this aim different and combined strategies can be adopted. Firstly a reflectance reduction of sunlight impinging on the cell is mandatory. Then a cell surface texturing can be very helpful to reduce the reflection by increasing the chances of reflected light bouncing back onto the surface rather than surrounding air. To this purpose different approach can be followed such as substrate and/or single layer texturing. Moreover particular care should be paid to the rear side of the cell where the introduction of a reflecting mirror can produce an optical path length enhancement over a wide wavelength spectrum. Rightly combining the front side texturing and the rear side mirroring it is possible to enhance this pathlength up to 50 times the device thickness indicating that light bounces back and forth within the cell many times performing a light confinement. To this purpose Bragg reflector formed using thin film technology is one of the most promising approach to the back side reflector. Also multi-junction cell, such as tandem micromorph, can receive benefit to the light management by the introduction of inner reflector within the two cells to enhance the spectral separation between the two cells and reduce the front cell thickness where the metastability problem still remain an open request.

In this work we overview all these concepts as applied to thin film cell and to silicon based cell that actually are speedily moving toward thinner substrate making the light confinement a key point to cell efficiency enhancement and PV cost reduction.

**Keywords:** Amorphous silicon, antireflection coating, heterojunction, lifetime, numerical model, optical properties, reflector, scattering, solar cell, texturing, thin film, transparent conductive oxide, plasma process, light trapping, thin wafer, quantum efficiency, bragg reflector, haze, reactive ion etching, laser treatment, silicon.

### **1. INTRODUCTION**

To enhance the solar cell efficiency in recent years, researchers have experimented with approaches to capture the sunlight photon impinging on the device and forcing it to collaborate instead of being reflected away. This is done by changing the basic structure of solar cells, so that photons become trapped when they arrive in contact with the cell, thus providing a greater chance that they will be absorbed and converted into electrons. To this aim a light-trapping scheme introduction is mandatory. Light trapping allows cell to absorb sunlight using an active material

**<sup>\*</sup>Address correspondence Mario Tucci:** ENEA, Research Centre Casaccia, *Via* Anguillarese 301, 00123 Rome Italy; Fax: 0044 1740 644146; E-mail: mario.tucci@enea.it

layer thinner than the material's intrinsic absorption length. This can reduce the amount of materials used in PV cells, cutting cell cost that are mainly based on less abundant or expensive purified materials. It is well known that the largest part in cost production of industrial silicon solar cells is actually referred to the base silicon substrates. Hence reducing the amount of involved silicon, by means of thinner wafer, is a key point in limiting the overall PV cost, making the price of energy from solar cells competitive with the conventional production systems [1]. Moreover, light trapping can improve cell efficiency, since thinner cells provide better collection of photo-generated charge carriers [2]. Historically the theory of light trapping was developed for conventional cells in which the optical path length is several times the actual device thickness, where the optical path length of a device refers to the distance that an unabsorbed photon may travel within the device before it escapes out of the device [2, 3]. For example, a solar cell with no light trapping features may have an optical path length of one device thickness, while a solar cell with good light trapping may have an optical path length of 50 times the device thickness, indicating that light bounces back and forth within the cell many times. Basically conventional light trapping exploits the effect of total internal reflection between the semiconductor material, such as silicon, and the surrounding medium commonly assumed to be air. Simply by texturing the semiconductor surface it is possible to couple light obliquely into the medium, thus giving a longer optical path length than the physical device thickness and also it is possible to randomize the light propagation directions inside the material. Achieving a total internal reflection results in a much longer propagation distance inside the material and hence a considerable absorption enhancement. Indeed the light can be trapped inside the cell and make multiple passes through the cell, thus allowing even a thin solar cell to maintain a high optical path length. The standard theory for this light-trapping scheme was developed by Yablonovitch [3] and applied to silicon based solar cell several years later [4]. To further enhance the absorption of light penetrated into the device a rear side reflector is needed to avoid light escape from the rear side of the cell. This allows the light to bounce back into the cell for possible absorption. This allows an optical path length of approximately 50 times the physical devices thickness and thus is an effective light trapping scheme. For thin film cells with thicknesses comparable or even smaller than wavelength scale, the ray-optics representation and some of the basic assumptions adopted in the conventional theory are no longer applicable. Recently in literature several numerical [5-8] and experimental [9-17] works reported considerable improvement beyond the Yablonovitch limit.

In this chapter a description of light management at the front and rear side of the solar cell is reported. In this description not only thin film cell are considered, but also silicon base cells that are going beyond thinner silicon wafer to reduce PV cost. Indeed in this case several approaches can be helpfully transferred from thin film technologies to wafer based technology. In this direction the best silicon based cell candidate is the amorphous/crystalline heterostructure. To exploit this argument a particular section is dedicated to a dielectric reflector and its related manufacturing technology helpful to improve thin solar cell performances. All the technologies that can be proposed to the light confinement must fit with industrial manufacturing facilities otherwise can only represent academic speculations not useful to reduce the cost per watt produced by the sunlight photovoltaic conversion. Therefore the use of sophisticated technology such as photo-lithographic steps, not easy to transfer to very large area device, used to produce particular features on front or rear side of the cell to enhance the light confinement are not extensively exploited in this overview.

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **397**

In this chapter a detailed description of cell design is reported concerning the use of antireflection coating and texturing of both thin films and silicon wafer based device in order to manage at the best the light impinging on a solar cell. After an overview of light scattering promoted by texturing a detailed description is proposed on rear side reflector in which a Bragg scheme is detailed and experimented.

### **2. ANTIREFLECTION COATING**

Optical losses are responsible for the short circuit lowering in solar cells. They are mainly caused by the parts of incident light escaping from the cell and the part reflected from the cells surface or metal front contacts. To maximise the percentage of light to be converted in electron-hole pairs it is important to maximise the light penetrating into the cell. This can be done modifying the surfaces morphology producing the so-called texturing and applying to the front surface an Anti Reflection Coating (ARC) [18]. The idea behind anti-reflection coatings is that the creation of a double interface by means of a thin film gives you two reflected waves.

**Figure 1:** Schematic of Anti Reflection Coating principle of operation for a single layer ARC.

If these waves are out of phase, they partially or totally cancel. In practice a thin layer of dielectric material having a precise refractive index is deposited with a specific thickness on a substrate, so that interference effects in the coating cause the wave reflected from the anti-reflection coating top surface to be out of phase with the wave reflected from the semiconductor surfaces. In particular when the light reflected from the second interface arrives back at the first interface 180° out of phase with that reflected from the first interface, there is no net light coming out, at least for a chosen wavelength. The schematic situation is sketched in Fig. **1**, where *n0*, *n1* and *n2* are surrounding ambient, dielectric film and semiconductor refractive index respectively. The expression for the fraction of the energy in a normally incident beam of light reflected from the surface of a material covered by a transparent layer of thickness *d1* is [19, 20]:

$$R = \frac{r\_1^2 + r\_2^2 + 2r\_1r\_2\cos 2\theta}{1 + r\_1^2r\_2^2 + r\_1r\_2\cos 2\theta} \tag{1}$$

with:

$$r\_1 = \frac{n\_0 - n\_1}{n\_0 + n\_1} \ r\_2 = \frac{n\_1 - n\_2}{n\_1 + n\_2} \ \ \ \theta = \frac{2\pi n\_1 d\_1}{\lambda} \tag{2}$$

In this case the reflectance has its minimum value:

$$R\_{\rm min} = \left(\frac{n\_1^2 - n\_0 n\_2}{n\_1^2 + n\_0 n\_2}\right)^2 \tag{3}$$

which can be driven to zero when 1 2 0 2 *n nn* , for a specific wavelength *λ0*, due to the dependence of the refraction index on wavelength.

**Figure 2:** Reflectance profiles simulations of Silicon Nitride on flat silicon as a function of silicon thin film thickness. The Black continues line is the AM 1.5 G spectrum, expressed in arbitrary units.

However the sun spectrum is of course made by multiple wavelength photons, so the choice of material, refractive index and thickness of the dielectric film needs to be done considering the best reflection reduction around the wavelength corresponding to the maximum of the sun spectrum intensity. For photovoltaic applications, the refractive index and thickness are chosen in order to minimise reflection for a wavelength of 600 nm [21]. At the present one of the most widely used material is Silicon Nitride deposited *via* Plasma Enhanced Chemical Vapour Deposition (PECVD) which refractive index can be varied from 1.5 and 2.3 circa, evaluated at 633 nm [22]. In Fig. **2** we show simulations made with the aid of NKDGEN software [23] of how the reflectance profile (in term of % of incident light) varies with the thickness of a silicon nitride film (as deposited on a flat

silicon surface) having a refractive index of 2 at 633 nm. It is appreciable the best profile giving the lower reflectance around 600 nm is around 60-70 nm thickness.

Such a kind of behaviour can be enhanced with the introduction of a multi-layer as ARC (see Fig. **3**), varying the refractive indexes and thicknesses to obtain a low reflectance profile over a wider range of wavelengths. The equations for multiple antireflection coatings are more complicated than that for a single layer [20]. Any film combination composed of two dielectric layers on a semi-infinite substrate has a reflectance given by:

$$R = \frac{r\_1^2 + r\_2^2 + r\_3^2 + r\_1^2 r\_2^2 r\_3^2 + 2r\_1 r\_2 (1 + r\_3^2) \cos 2\varphi + 2r\_2 r\_3 (1 + r\_1^2) \cos 2\varphi + 2r\_1 r\_3 \cos 2(\varphi + \varphi) + 2r\_1 r\_2^2 r\_3 \cos 2(\varphi - \varphi)}{1 + r\_1^2 r\_2^2 + r\_1^2 r\_3^2 + r\_1^2 r\_3^2 + r\_2^2 r\_3^2 + 2r\_1 r\_2 (1 + r\_3^2) \cos 2\varphi + 2r\_2 r\_3 (1 + r\_1^2) \cos 2(\varphi + \varphi) + 2r\_1 r\_2^2 r\_3 \cos 2(\varphi - \varphi)} \tag{4}$$

with:

$$r\_1 r\_1 = \frac{n - n\_1}{n + n\_1}, \ r\_2 = \frac{n\_1 - n\_2}{n\_1 + n\_2}, \ r\_1 = \frac{n\_2 - n\_3}{n\_2 + n\_3}, \ \ \wp = \frac{2\pi n\_1 d\_1}{\lambda} \quad \ \ \wp' = \frac{2\pi n\_2 d\_2}{\lambda} \tag{5}$$

where *n* is the refractive index, *d* the film thickness and the wavelength. This expression is quite cumbersome and can be solved only by approximate numerical methods, unless the two layers are restricted to be of equal optical thickness at 550nm. In this case the above equation can be simplified to:

$$R = \frac{r\_1^2 + r\_2^2 + r\_3^2 + r\_1^2 r\_2^2 r\_3^2 + 2r\_2(r\_1 + r\_3)(1 + r\_1 r\_3)\cos 2\varphi + 2r\_1 r\_3 \cos 4\varphi}{1 + r\_1^2 r\_2^2 + r\_1^2 r\_3^2 + r\_2^2 r\_3^2 + 2r\_2(r\_1 + r\_3)(1 + r\_1 r\_3)\cos 2\varphi + 2r\_1 r\_3 \cos 4\varphi} \tag{6}$$

For the equal optical thickness of quarter-wavelength coatings (*i.e.* 11 2 2 0 *nd nd* / 4 ) and in terms of the indices media *n0* of ambient, *n1* and *n2* for two coatings and *n3* for substrate, R at λ<sup>0</sup> becomes

$$R = \left(\frac{n\_1^2 n\_3 - n\_2^2 n\_0}{n\_1^2 n\_3 + n\_2^2 n\_0}\right)^2 \tag{7}$$

and it can be found that zero reflectance can be obtained in this case with a double quarter-wave coating if the refractive indexes of the two layer satisfy the following relation:

$$\frac{n\_2}{n\_1} = \sqrt{\frac{n\_3}{n\_0}}\tag{8}$$

In Fig. **4** is shown an experimental reflectance profile of a double ARC made by MgF2 and ZnS over a flat silicon surface, having effective reflectance equal to 8.1%, good if compared to the one of a single SiN ARC, which is around 13%. However, this treatment is usually too expensive for most commercial solar cells, but it finds application in very high efficiency solar cells designed to operate in concentration. The ARC concept illustrated till now for silicon solar cells is actually

totally general and can find application on thin film cells and modules. For instance it is possible to use Silicon Nitride as ARC for thin film cells CdS/CuInSe2 [24].

**Figure 3:** Schematic of Anti Reflection Coating principle of operation with two equal thickness coating.

**Figure 4:** Experimental reflectance profile of double ARC (blue) compared with flat silicon (red).

#### **2.1. Dielectric Layers**

Dielectric layers have wide applications in photovoltaics due to their different optical and electrical properties useful for passivation, antireflection and even masking purposes.

The former two are keys to increase solar cell performances since the passivation level strongly influences the Voc, the Jsc, and in minor part the FF, while according to paragraph above the antireflection coatings are very important to drastically reduce the optical losses, and so influence the Jsc. However, not all dielectrics employed in PV are appropriate to both purpose, or suitable on all kind of processes.

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **401**

Before the wide diffusion of Silicon Nitride (SiNx) deposition *via* remote plasma [25], leading the overall silicon solar cell processing throughput at the present level, the main way to passivate the front of silicon solar cells was Silicon Oxide (SiO2) grown by thermal wet or dry oxidation in which ultra clean water vapour or oxygen respectively are entered in a quartz tube at high temperature (in the range 800-1200 °C) to oxidise the Silicon wafers. Such high temperatures are one of the drawbacks of using SiO2 in solar cells processing. Indeed metallization of cells when using silicon oxide would involve low throughput steps of lithography, since metal contacts cannot be deposited prior to high temperatures step because of the consequent lifetime degradation in the base wafer and metal contacts extra-penetration through the formed emitter [26]. Moreover since the hardness of SiO2 films, common firing through processes are not effective in this case, so an opening procedure (*via* laser or chemical processing) is mandatory. Of course silicon oxide is not suitable for thin film applications.

Sputtered or evaporated dielectric films, like Titanium Oxide (TiO2) [27] or Magnesium Fluoride (MgF2), or Zinc Sulphide (ZnS) are suitable for antireflection purpose and have been used previously in photovoltaic industry but with poor passivation quality. Plasma deposited films, like non-stoichiometric Silicon Oxide (SiOx) [28], Silicon Nitride (SiNx) also coupled with amorphous silicon (a-Si) [29] have shown both good passivation quality and optical characteristic suitable to be employed as ARC. Also they are such to be easily penetrated by common Silver screen printable paste to perform good firing through during metallization processes.

Finally, due to their low process temperatures, they are suitable also in low temperature application, like thin film [24] and heterojunction [30].

In the following paragraph we will focus on silicon nitride, which is at the present the most widely diffused dielectric employed in solar cell processing.

#### **2.2. Silicon Nitride**

The application of Silicon Nitride, deposited *via* Plasma Enhanced Chemical Vapor Deposition (PECVD), to photovoltaic represents an important step toward the enhancement of conversion efficiency, especially for c-Si based cells. Indeed its electric properties make it an excellent passivating dielectric, due to the relevant surface recombination velocity reduction, while it is a natural good candidate for Anti Reflection purpose because it is possible to continuously move the refractive index from 1.7 to 2.3 (evaluated at 633 nm), depending on deposition condition [31]. These are the main reasons to adopt this material in solar cells processing, giving a double contribute in a single step deposition. For historical reasons we report that Silicon Nitride can be deposited using high temperature process approach, but the one utilized for photovoltaic applications is deposited by the low temperature techniques (< 400 °C), like PECVD, suitable to be industrially adopted, because of low cost of ownership, high throughput and high reliability. One of the mostly interesting characteristics is the possibility of good interfacing in terms of electrical and optical properties of Silicon Nitride with different materials, like amorphous silicon [29], or Silicon Oxides [32]. Depending on deposition conditions it is possible to vary the stoichiometry composition and the Hydrogen content, that affect the fixed and mobile charge content, which are responsible of the film passivation properties. Indeed there are two main mechanisms to passivate silicon surface: the dangling bonds saturation by means of Hydrogen

atoms and a field effect due to the charge present in the film [33], better explained in the following.

Silicon Nitride can be grown in different ways that we can group in three classes:


In the two former cases the obtained film are perfectly stoichiometric (Si3N4) but, despite a long deposition process and at high temperature (circa 900 °C), very thin (< 10 nm). This low deposition rate is the main reason for abandoning this growth method toward other techniques using reaction in gas phase [34].

CVD deposition happens in a pressure and temperature controlled chamber, called reactor, because of the dissociation of gas species molecular bonding after an excitation. Depending on gas mixture, excitation source, pressure and process temperature, it can be distinguished between different CVD types [35].


Generally all these techniques use reactant gases containing Hydrogen, easily incorporated in the film. Moreover the particular deposition condition of a single solid phase from a gas one, in condition far from the thermodynamic equilibrium lead to the formation of an amorphous and nonstoichiometric material. This is the reason why, referring to silicon nitride deposited in CVD systems, they are defined as amorphous and hydrogenated silicon nitride, a-SiNx:H, (or simply SiNx) where *x* is the atomic ratio N/Si [36], equal to 1.33 for perfectly stoichiometric nitride. Both APCVD or LPCVD are based on the reaction of silane (SiH4) and ammonia (NH3) happening at the substrate surface due to the high temperature (700-1000 °C) or the low pressure in the reactor (0.01-1 Torr), with a deposition rate of around 2.5-5 Å/min [26]. Both methods are quite obsolete, due to the low growth rate and process conditions, not suitable for high throughput production in industrial environment, especially when compared to plasma assisted CVD. Similar drawbacks are typical of HWCVD, in which the gas mixture is excited by a wire kept at high temperature by current flow, which does not ensure a homogenous deposition on large area wafer surface, even with low deposition rate [37]. The main advantage of plasma assisted CVD (Plasma Enhanced CVD-PECVD) compared to the APCVD or LPCVD is the low process temperature, since the

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **403**

reaction is started by means of an external source, like an electric field in radiofrequency. In this case the electric field gives energy to electrons in the external shells of reactant gases atoms in the reactor, ionizing them, while electrons are free to travel into the gas mixture. In this way the collisions they experience with other molecules lead to new ions and radicals formation, which are then free to combine with other reactant species. During these collisions, electrons loose kinetic energy, with light emission. All this complex of ions, radicals, light and free electrons in gas phase is the so-called plasma [26]. The second strength of PECVD is the high deposition rate, which allows to grow hundreds nanometres thick film in few minutes. In summary PECVD is a fast and low temperature process, allowing the deposition of different kind of materials controling both optical and electrical properties by means of deposition parameters. PECVD systems differ by working frequencies (Low Frequency, High frequency, Very High Frequency [38], and microwave [39]), and applied plasma (direct or remote [25]). The system choice is mainly related to the application and required final properties.

As reported before, silicon Nitride properties depend strongly on the deposition method.

In APCVD and LPCVD cases the film is purely stoichiometric, very strong and poor of Hydrogen content. The material structure is made by Silicon atoms in tetrahedral coordination with Nitrogen atoms, in turn placed on a plane.

In PECVD case, instead, the ratio N/Si and the Hydrogen content are strongly dependent on the process parameters, like the precursor gases flux ratio, the RF power, the substrate temperature. Despite the non-stoichiometric and amorphous nature of the so obtained film, experiments show the tetrahedral coordinated structure for silicon and trivalent for Nitrogen is still valid [26]. The Hydrogen content increases with deposition temperature decreasing, and this is the reason why Silicon Nitride produced *via* PECVD has higher Hydrogen content with respect the ones deposited *via* APCVD or LPCVD. This phenomenon is correlated with the cross linking between Si and N atoms, because of the correspondence between the Hydrogen content and film density, in turn related to the Si-N bonding. Such a kind of behaviour can be confirmed by means of IR absorbance spectra, where depending of peaks position and intensity it can be estimated both Hydrogen content and structural properties of film, such as refractive index, related to Si-N bonds. Moreover depending on the stoichiometry of deposited material, SiNx can be classified in Silicon rich (N/Si<1.2) or Nitrogen rich (N/Si>1.4). In the former, Si-Si and Si-N bonds are definitely prevalent with respect to N-H bonds,; while in the latter, or even near the stoichiometry, Silicon can form several bonding and Nitrogen is able to establish bonds with both H and Si. N-N bonds are very difficult to be formed, even for Nitrogen rich film, due to the bonding energy (38.4 kcal/mol), lower with respect to both Si-N (50 kcal/mol) and N-H (93.4 kcal/mol). This suggests, for Nitrogen rich films, more N-H bonding than Si-H, since bonding between N atoms are less favourite, obtaining higher Hydrogen contents [40], which increases with N/Si ratio. The stoichiometric silicon nitride (Si3N4) electronic structure was calculated by Robertson [41] and shows the non-saturated bonds of trivalent Silicon (≡Si•) introduce a paramagnetic state in the middle of its bandgap (estimated to be 5.3 eV), while the defects introduced by nitrogen dangling bonds (=N•) are located just above the valence band edge. This is still valid for silicon rich SiNx (x<1.1), where trivalent silicon bonding can be saturated with different configurations, like Si3≡Si•, Si2N≡Si•, SiN2≡Si•, N3≡Si•. The bonding density is controlled by the equilibrium with weak Si-Si bonding, forming states near the band edges, while the level caused by Nitrogen

dangling bonds are not present. This happens because the high silicon content in SiNx moves the conduction and valence band edges toward midgap, reducing its value till 1.7 eV. Silicon induced defects still remain around midgap, while those due to Nitrogen disappear into Valence band. Actually the more the Silicon content, the more SiNx behaves like a-Si:H, where Nitrogen atoms act as donors, when they are less than 2%, and SiNx is, in practise, n-type a-Si [42]. From FTIR spectra it is possible to obtain an absorption spectrum as function of IR radiation wave number (expressed in cm-1) where peaks or distribution are related to the energy corresponding a particular vibration or stretching mode of a molecule, whose values are reported in literature [22, 43] and the most important indicated in Fig. **5**.

**Figure 5:** Example of FTIR spectrum for Silicon Nitride, with most important explicit peaks.

Analysing such spectra is possible to understand the material composition. In particular it can be found a relation between the presence of certain bonds with the optical and electrical material, like the refractive index and the charge inside the film [40]. The eventual peaks related to CO2 presence, around 653 and 2340 cm-1 have been reduced by software interpolation. If in silicon rich Nitride the only states at midgap are due to Silicon, different is for Nitrogen rich Silicon Nitride. In this case, also the states due to Nitrogen dangling bonds are inside the gap, and the prevalent effect is due to N3≡Si• groups, the so-called K centres of recombination.

They are diamagnetic and neutral, but introduce a large amount of instable charge in the film, since they are able to capture both electron and holes, becoming positively or negatively charged (K+ , K- ). This charge state formation can happen also after the film exposure to high energy radiation, like UV, which breaks some Si-H and SiN-H bonds around the K centre, forming new radicals and mobile charges inside the Nitride film [44]. Of course the silicon or nitrogen rich behaviour is determined by the deposition parameter, like the reactant gas flux ratio R=ΦNH3/ΦSiH4. The correspondence between deposition parameter, film properties, and atoms bonding can be appreciated in Fig. **6(a)**. We report the

**Figure 6:** a) Comparison of refractive index and N-Si3 peak intensity in FTIR spectra of Silicon Nitride deposited with different Ammonia/Silane gas flux ratio. b) comparison of refractive index and lifetime of Silicon Nitride deposited with different Ammonia/Silane gas flux ratio.

variation of refractive index (evaluated at 633 nm) as a function of R. When the film is deposited with less Silane the refractive index start to reduce, because the equilibrium between Silicon and Nitrogen atom content move their availability to form bonds with Hydrogen. Then N-Si bonding is less favourite and the film become less dense, with lower n. This behaviour is confirmed measuring IR spectra. In particular the intensity of peak located around 850 cm-1 shows the same trend of refractive index. At the same time the opposite trend in N-H and Si-H bonds is reflected in lifetime trend, as reported in Fig. **6(b)**. Indeed the higher charge content due to K centres and hydrogen is responsible of Field effect passivation on crystalline silicon: the charge inside the film can accumulate electrons near

the silicon wafer surface avoiding recombination or also inverting the silicon locally, obtaining an effective passivation. For instance in case of SiNx with high positive charge in the film, when deposited on p-type silicon, there are electrons recalled from the substrate close to the surface. This causes a band bending which moves the Fermi Level away from midgap, where the most important defects (through which electrons and holes can recombine, lowering the overall lifetime) are located [32]. This effect together with the saturation of dangling bonds at the surface defect state density can led to very high effective lifetime, in the order of milliseconds [26] both for mono and multicrystalline silicon.

**Figure 7:** Field effect: the positive charge in the SiNx recalls electron from the substrate close to the surface, avoiding recombination *via* midgap defects.

### **3. TCO AND SURFACE SCATTERING**

In thin film silicon solar cells and modules incorporating amorphous (a-Si:H) or microcrystalline (c-Si:H) silicon as absorber materials, light trapping, *i.e.* increasing the path length of incoming light, plays a decisive role for device performance. All these cells commonly have a Transparent Conductive Oxide (TCO) as top electrode deposited on low cost glass substrate. In Fig. **8** schematic sketch of the cross section of thin film solar cell is reported. The light trapping is illustrated by the arrows representing incoming/reflected and scattered sun light at different interfaces: glass/TCO, TCO/absorber layers, absorber/TCO and TCO/back reflector.

Not all device configurations include the TCO before the metal electrode but often this layer is introduced to enhance the chemical compatibility between thin films and metal electrode. In a particular kind of silicon wafer based solar cell, TCO is also applied on both sides of the cell, such as the a-Si:H/c-Si/a-Si:H heterostructure cell [45].

When TCO is applied at the cell front side, it needs high transparency in the spectral region where the solar cell is operating. Therefore refractive indexes are relevant and have to be well designed for coupling of light into the absorber materials. TCO also should have high carrier mobility and high electrical conductivity properties to reduce electrical losses. This last property is mandatory due to the poor lateral conductivity of doped emitter thin films composing the front junction. Of course the minimum requirements for the optical and electrical properties of the TCO depend on the structure and the absorber material adopted to fabricate the solar cell. Typically values of 10 /sq as a sheet resistance and a transmittance around 93-94% in the range 350-1100 nm are valuable for solar cell applications. A high transparency for visible light (wavelength from 350 nm up to 750 nm) is sufficient for amorphous silicon absorber layers [46], while for solar cells integrating c-Si:H or a-Si:H/c-Si the TCO has to be highly transparent up to the near infrared (NIR) region (1100 nm). This reflects in certain restrictions on the carrier density n of the TCO

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **407**

material. Indeed higher the free carrier absorption, lower is the IR transmittance [47, 48]. However the success of the TCO films is mainly determined by the physical-chemical properties for the growth of the thin film material on top of it. For example it has to be inert to hydrogen-rich plasmas or act as a good nucleation layer for growth of nano-or microcrystalline material. A brief summary of the relevant properties of the most common TCO for photovoltaic applications, such as ZnO, SnO2 and ITO is listed in the following section.

**Figure 8:** Schematic cross section (not in scale) of thin film cell with rough interfaces. The light trapping is remarked by the arrows representing impinging and scattered sun light at the rough interfaces.

## **3.1. ZnO**

ZnO films is n-type semiconductor due to oxygen deficiencies with an energy gap of 3.3eV, commonly doped by adding aluminium, gallium, boron or indium [49].

In Fig. **9** resistivity as a function of impurities is reported on the base of [50]. In the same work it is shown that a film with low resistivity (5.10-4 cm) and high optical transmission (greater than 85% between 400 and 800 nm) can be produced on low-temperature substrates with a relatively high deposition rate in particular RF magnetron sputtering configuration. The sheet resistance and Hall mobility of the film are 10 /square and 120 cm2 /Vs respectively [50].

**Figure 9:** Dependence of ZnO resistivity () on impurity/Zn ratio in the target. Film with B(▲), Ga (∆), Al(●), In(□) have been experimented [50].

Theoretical work [51] has identified also hydrogen as a possible n-type dopant although an enhancement of conductivity by hydrogen treatment has been known for long time [52].

Various methods are commonly used for TCO preparation. The methods involve spray pyrolysis, vapour and liquid phase or sol–gel deposition, pulsed laser deposition and sputtering. Zinc oxide is often prepared by CVD processes (using, *e.g.*, Zn(C2H5)2 as a precursor gas) or sputter deposition [53]. Substrate temperatures differ quite significantly in these two deposition techniques. Indeed, for ZnO prepared by CVD, temperatures near 150 °C are applied [53, 54], while for ZnO prepared by sputtering, typical process temperatures are near 300 °C.

Recently doped ZnO has been established as a successful alternative to the ZnO also on large area module as demonstrated by Oerlikon [55]. Examples are boron doped ZnO prepared by lowpressure chemical vapour deposition (LPCVD) [56, 57] or aluminium-doped films deposited by expanding thermal plasma CVD [58]. A very helpful approach is the use of magnetron sputtering together with a post-deposition chemical etching step. The sputtering process leads to highly conductive and transparent but smooth ZnO:Al films. Typical sheet resistance values of 5–8 /sq for film of 650 nm thicknesses and absorption of only 5–6% in the wavelength range from 350 nm to 1100 nm proof the high quality of these films. A surface texturing can be performed by a simple chemical etching step in diluted hydrochloric acid (typically 0.5% HCl) to improve the light scattering as well as the light trapping of the ZnO film. This etch yields a textured surface which can be adjusted to give optimal light scattering over a wide wavelength range. Fig. **10** shows scanning electron microscope (SEM) images of an (a) as deposited and (b) etched ZnO:Al film. Sputtered ZnO:Al is initially smooth. With increasing etch time, the roughness of the surface increases from 7 nm to 162 nm [49].

ZnO electrical properties are sensitive to the working pressure and the deposition temperature as demonstrated in Fig. **11** [48].

**Figure 10:** SEM images of RF sputtered ZnO:Al surface before (a) and after wet chemical texturing (b) [49].

It should be noted that film properties depend also strongly on film thickness. In Fig. **12** the Hall mobility, carrier densities and conductivities of Al doped ZnO films are reported according [48] as a function of deposited thicknesses and for different doping density related to the concentration of Al2O3 in the target (referred as TAC).

**Figure 11:** (a) resistivity (), (b) carrier concentration (N) and mobility (), of Al:ZnO layers as a function of working pressure during film deposition [48].

**Figure 12:** (a) Resistivity (), (b) mobility (), (c) carrier concentration (N) of Al:ZnO layers as a function of film thickness [48].

Also the optical properties can be affected by the deposition temperature as evident from the transmittance spectra of ZnO films deposited at different temperature and different doping densities reported in Fig. **13**.

Electronic transport parameters such as sheet resistance *Rsh*, resistivity , carrier concentration *N*, mobility , and the optical gap for ZnO:Al films deposited with different target doping concentration TAC and deposition temperature are listed in Table **1**.

**Table 1:** Thickness; Sheet resistance, Rsh; Resistivity, ; Carrier concentration, N; Mobility, and Optical gap, E Gap for ZnO:Al films deposited with different target doping concentration ( TAC) and deposition temperature, T.


When viewing the electrical parameters it can be seen that the lowest resistivities and the highest mobilities have not changed in the last 15 years, despite a lot of technological effort in this period [53]. The lowest resistivities reported are in the range of 1.4 to 2×10<sup>−</sup><sup>4</sup>cm, independently of the deposition method. Carrier concentration of 5.1020 cm−<sup>3</sup> and mobility of about 40 cm2 V<sup>−</sup><sup>1</sup> s −1 , can be considered as an upper limit. It seems reasonable to suppose, that resistivities less than 1.10<sup>−</sup><sup>4</sup> cm for doped polycrystalline zinc oxide films are hard to achieve, due to a general limitation by ionized impurity scattering. This assumption is further supported by the fact that heavily n-doped single crystalline silicon also exhibits mobilities in the same range as polycrystalline ZnO films [59].

**Figure 13:** Transmittance and reflectance of different doping films (Ts =100°C and film thickness d=600-725 nm) deposited from different percentage Al content in the target [48].

Conducting p-type ZnO has recently been realized [60]. Even if the conductivity still remains on open request ( around 300 cm), a promising way to enhance the light trapping in thin film cell using ZnO film, concerns the formation of surface nanostructures. They exhibit a high crystalline quality. Fig. **14(a)** shows a tilted SEM image of the ZnO nanorods synthesized on the fluorine thin oxide substrate by chemical solution deposition (CSD). The SEM image in the inset of Fig. **14(a)** shows a cross-sectional view of the ZnO nanorods. The length and average diameter of the ZnO nanorods were about 1.5 μm and 80–90 nm, respectively. Each ZnO nanorod has a hexagonal shape. The SEM images of Al n-doped p-type ZnO thin film coated ZnO nanorods are depicted in Fig. **14(b)**. The thickness of the ZnO thin film coating the nanorod is about 200 nm [61].

Very helpful ZnO nanorods for antireflection coating in solar cell application is also reported in ref [62] where the authors achieved a weighted global reflectance of 6.6% on silicon surface.

## **3.2. SnO2**

As a front transparent conducting oxide (TCO) layer for thin-film solar cells, ZnO:Al has a lot of advantages over the conventional SnO2:F, *e.g.*, high stability under the hydrogen plasma environment and high electro-optical properties [63]. In turn, due to the higher contact potential of ZnO:Al/p a-SiC:H compared with SnO2:F/p a-SiC:H, the contact properties of n-type ZnO:Al with adjacent p-type a-SiC:H can be limiting factors for a-Si:H solar cell performances, since the a-Si:H solar cells prepared on ZnO:Al suffer from reduced fill factor and Voc [64].

**Figure 14:** (a) SEM image of ZnO nanorod synthesized on F:SnO2 substrate. Inset shows the cross sention view. (b) Tilted SEM image of the p-type ZnO thin film coated ZnO nanorod [61].

Fluorine-doped tin oxide films (SnO2:F), which fulfil these requirements up to a large extent, have been developed by Asahi Glass (Asahi Type U, [65]) by chemical vapour deposition CVD process using SnCl4 precursor gas [56, 57]. It is also the most commonly used TCO material for thin film Si solar large area module manufacturing [65].

Accurate optical constants (n and k) of textured SnO2 films have been reported in the range of 0.85–4.6 eV using spectroscopic ellipsometry on Ashai U type SnO2 on glass substrate [66]. In Fig. **15** is reported the transmission spectrum of the SnO2 film deposited on glass substrate.

In Fig. **16** are reported the refractive index n as well as the extinction coefficient k of the textured SnO2 on glass measured at different angles. For comparison the n and k of SnO2 flat surface are also reported.

SnO2:F can also be fabricated by spray pyrolysis technique as referred in [67]. In that experience SnO2:F films were deposited from a solution comprising 23 ml of SnCl4, 7 ml of H2O, and 920 ml of methanol solution 6. Fluorine was added in the form of HF, instead of NH4F, to give the solution a doping level of F/Sn in the range of 0–180 atomic per cent.

**Figure 15:** Measurements and fit of the transmission measured on SnO2 deposited on glass substrate [66].

Deposition was performed on borosilicate glass substrates at a temperature of 490 °C-525 °C and from a distance of approximately 18 cm using a spray bottle with a nozzle diameter of 0.5 mm. The carrier gas was nitrogen and the spray rate was 12 ml/min. , N as a function of doping level expressed as F/Sn atomic percentage are reported in Fig. **17**.

**Figure 16:** Refractive index n and extinction coefficient k of the textured SnO2 on glass measured at different angles. For comparison dashed line refers to n and k of SnO2 flat surface [66].

The transmission spectra of doped (n = 7.2.1020cm-3, = 4.7 10-4cm thickness = 0.25 m) and undoped (n = 3.2.1020cm-3, = 63.4 10-4cm thickness = 0.28 m) SnO2 films are reported in Fig. **18**.

## **3.3. ITO**

Basically the ITO is a degenerate n-type doped semiconductor that can be fabricate by thermal evaporation [68] or by sputtering system [69, 70]. Here we briefly report on the ITO films as fabricated by the authors for amorphous crystalline heterojunction solar cell solar cell applications.

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **413**

Concerning the first technique, the ITO was deposited using a Balzers BA510 electron gun system starting from a self-made target of Indium and Tin alloy. Films of 150 nm thickness have been deposited on Corning 7059 in oxygen atmosphere setting a chamber pressure of 2·10-4 mbar. Temperature was measured directly on the substrate using a K thermocouple. Sn/(Sn+In) (wt%) target ratio and substrate temperature were varied to obtain minimum resistivity and best transmittance in the visible range.

**Figure 17:** , N as a function of doping level expressed as F/Sn atomic percentage [67].

**Figure 18:** The transmission spectra of doped and undoped SnO2 films [67].

The variation of resistivity and averaged transmittance from 400 to 800 nm as a function of Sn/(Sn+In) ratio for a fixed substrate temperature are reported in Fig. **19**. The variation of resistivity and averaged transmittance from 400 to 800 nm as a function of substrate temperature for a fixed Sn/(Sn+In) ratio are reported in Fig. **20**.

The ITO films useful for a-Si:H/c-Si heterostructure solar cells [71, 72] have been deposited using a low temperature RF 13.56 MHz magnetron sputtering. In Fig. **21** are reported, as a function of deposition temperature, the values of resistivity and effective transmittance from 350 nm to 1200 nm defined as:

$$T\_{\eta^{\text{c}}} = \underbrace{\int\_{10^{\text{c}}}^{10^{\text{c}}} T(\lambda) \cdot AM \, 1.5G(\lambda)d\lambda}\_{\text{(c)}^{\text{(L)}}} \underbrace{\int\_{10^{\text{c}}}^{10^{\text{c}}} T(\lambda) \cdot AM \, 1.5G(\lambda)d\lambda}\_{\text{(L)}^{\text{(L)}}} \tag{9}$$

**Figure 19:** Resistivity and optical averaged transmittance (400-800 nm) of ITO *vs.* percent of Tin in the Tin+Indium solid source for films deposited at 260°C of temperature substrate [68].

Sn/(Sn+In) (wt %)

**Figure 20:** Resistivity and optical averaged transmittance (400-800 nm) of ITO *vs.* substrate temperature of deposition for fixed target composition (60% Sn content) [68].

where T() is the transmittance and AM1.5G() is the number of photons per unit wavelength ().

**Figure 21:** Sputtered ITO resistivity and transmittance as a function of deposition temperature.

**Figure 22:** Sputtered ITO resistivity and transmittance as a function of oxygen flux at a deposition temperature of 80°C.

The deposition process parameters have been optimized in order to obtain a good compromise between the film conductivity and transmittance. In particular, the sputtering conditions have been fixed as follows: the RF power to 200 W, the process pressure to 2.25 mTorr, the Ar content to 25 sccm. It is worth to note that no oxygen has been used in order to reduce the film resistivity. For comparison the effective transmittance and resistivity as a function of oxygen flux during the sputtering process at a fixed temperature of 80°C are reported in Fig. **22**.

## **3.4. Texturing**

Basically light trapping is an interesting technique to increase absorption of the incident light in the active layers of solar cells. This is particularly true in all thin film cells where the absorber layer thickness is chosen on the base of the orthogonal light absorption. To enhance the optical path of the refracted light impinging onto the cell, a texturing technique is commonly adopted producing roughness on the window layer of the device. Moreover to further enhance the internal absorption a rear side textured reflector is used, thus producing several light round trip within the absorber layer. These concepts can be successfully extended also to solar cell involving thicker absorber layer, such as silicon wafer based cell, even more when wafer thinning is mandatory to reduce the PV cost. In this paragraph we focus on texturing techniques used in thin film and in c-Si based solar cell also going toward thinner silicon wafer.

Thin film cells are commonly based on different kind of architecture depending on the choice of mechanical support as substrate. If a hard substrate such a glass is used, then a top down configuration is adopted in the cell manufacturing, thus the glass is the cell window layer [73]. On the other hand if a flexible substrate is preferred such as stainless steel, then the cell fabrication process has a bottom up development during the growth [74]. These are the most common configurations, even if mixed approach are possible such as flexible transparent plastic foil [75] or hard metallic substrates. Except for the CdTe and CIS/CIGS cells, in which the TCO is used just for the front side contact, the other device commonly use TCO for both front and rear side contacts. In Fig. **23** a schematic overview of the different configuration is reported. To enhance the cell absorption by the texturing technique, two strategies can be adopted and eventually merged: TCO texturing and substrate texturing. Both introduce light scattering at the rough interfaces in the solar cell. In this way the average length of the optical light path in a layer is increased and the light absorption enhanced. Scattering at rough interfaces not only leads to enhancement of the absorption in the active layer of the cell but also influences the absorption in all other layers.

**Figure 23:** Different thin film cell configurations.

Now we will consider the scattering promoted by a rough surface of TCO deposited on flat glass surface as depicted in Fig. **24**.

**Figure 24:** Light scattering at a thin film with one roughly textured surface deposited on glass surface.

For an optimal optical design of thin film solar cells it is important to know the light absorption profile in the whole solar cell. Since it is not easy to determine this profile experimentally, computer modeling has often reported in literature to study the absorption in thin film solar cells [76-78]. The model is based on the first order Born approximation [79] and on Fraunhofer scattering. A rough interface can be described taking into account the root mean square (rms) roughness,rms and the scattering data including the haze parameter and the angular distribution of diffuse light. The rms is defined as follows:

$$
\sigma\_{r\text{nu}} = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} \left(\eta\_i - \bar{\eta}\right)^2} \tag{10}
$$

Where is the height of the i-th scanned point, the average height of the scanned point and N is the total number of point collected during an atomic force microscopy (AFM) scan. 

The haze for transmitted light normally incident to the glass side and crossing a rough surface as depicted in Fig. **24** is defined:

$$\mathbf{H}\_{\rm T} = \mathbf{T}\_{\rm diff} / \mathbf{T}\_{\rm tot} \tag{11}$$

where Ttot is the total and Tdif is the diffused optical transmittance measured by a photospectrometer equipped with an integrating sphere. The total and diffused transmittance of a fluorine doped tin oxide (FTO) SnO2 glass coated, deposited using atmospheric pressure chemical vapour deposition APCVD, commonly available on market as Ashai U-type [65], having around 40 nm, is reported in Fig. **25**.

To simulate the haze of TCO it is possible to use the following equation:

$$H\_T(\mathcal{Z}) = 1 - \exp\left[ - \left( 4\pi\sigma\_{mu}C\_T \left| n\_1(\mathcal{Z})\cos\theta\_{m} - n\_2(\mathcal{Z})\cos\theta\_{out} \right| \mathcal{\lambda} \right)^{\rho} \right] \tag{12}$$

are fitting parameters. While a square dependence ( = 2) is reported by the scalar scattering theory [80], other research group found better agreement for large wavelength as cubic dependence [76].

The meaning of CT is quite controversial: it is dependent from and it is strongly needed to have reasonable results. Physically might be related to the shadowing effect of scattered light [81]. Power factors larger than 3 for ZnO:Al layers textured by post-etching in HCl is also reported in [82, 83].

**Figure 25:** Total and diffused transmittance together with haze of FTO Asahi U-type.

**Figure 26:** AFM scan image over a 3x3 m2 of F:SnO2 Ashai U-type.

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **419**

Moreover is not easy to evaluate the rms because, if atomic force microscopy (AFM) is used, the rms can depend on the scanned area, becoming higher for larger scanned area. This would indicate that the roughness varies more than the range of one micron as a typical AFM scan. Therefore large area should be investigated with AFM to estimate reasonable rms values.

After deposition of absorber layer on rough TCO surface a smoothening occurs that reduces the rms. Indeed, in case of P-I-N amorphous silicon solar cell deposited onto Asahi U-type covered corning glass, while the very short p-type doped layer almost does not affect the TCO roughness, after 300 nm intrinsic layer deposition the rms reduces to 33 nm [77]. An AFM scan image over a 3x3 m2 of F:SnO2, Ashai U-type is reported in Fig. **26** [83]. A SEM picture remarking the pyramidal surface of this textured TCO is reported in Fig. **27** [76].

**Figure 27:** The SEM picture of the rough surface of the glass/SnO2 Asahi U-type substrate [76].

A haze comparison of three different ZnO textured surfaces in case of ZnO/air and ZnO/c-Si interfaces are respectively reported in Fig. **28(d), (e)**, together with the simulations obtained using equation (12). The thicknesses, the rms and the shape of these Al doped TCOs are listed in Table **2**. Moreover the shape of the three different Al ZnO textured surfaces are depicted in SEM images reported in Fig. **28(a), (b), (c)** [84].


**Table 2:** Parameters related to the Al doped textured ZnO.

**Figure 28:** SEM pictures (a), (b, (c) of typical type-A,-B and-C ZnO layers respectively. Experimental (symbols) and calculated (lines) haze in transmission in air (d) and at the ZnO/Si interface for the type-A,-B and-C front ZnO layers (e) [84].

Basing on the experience reported in [77], now we report about the use of model related to the equation (12) to evaluate the reflectance and transmittance of a Ashai U-type F:SnO2 used for p-in a-Si:H solar cell.

In case of rough interface, having rms smaller than /n of the medium incidence, the scalar scattering theory is applicable to determine the specular reflectance of an interface. The total reflectance Rs can be modelled using the following equation reported in [77]:

$$R\_S(\mathcal{A}) = R\_0(\mathcal{A}) \exp\left[ - \left( 4\pi \sigma\_{\rm rms} n\_0 / \lambda \right)^2 \right] \tag{13}$$

where R0 is the reflectance of a flat surface. Assuming that:

$$R\_0(\mathcal{Z}) = R\_i(\mathcal{Z}) + R\_d(\mathcal{Z}) \tag{14}$$

where *Rd()* is the diffused reflectance, we obtain

$$R\_d(\mathcal{A}) = R\_0(\mathcal{A}) \left( 1 - \exp\left[ -\left( 4\pi \sigma\_{mu} n\_0 / \lambda \right)^2 \right] \right) \tag{15}$$

Fig. **29(a** and **b)** show the ratio *Rd/R0* as calculated from equation (15) for light incident at a rough interface through Asahi U-type TCO and n-type a-Si:H, respectively, for several values of rms. It

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **421**

is important to note in Fig. **29** that the back contact interface acts as a nearly perfect diffuser for the reflected light in the wavelength range of interest when rmsis larger than 30 nm [77].

**Figure 29:** The *Rd*/*R*0 ratio as a function of wavelength for several values of the rms roughness of the rough interface: a) Asahi U-type TCO material and b) *n*-type *a*-Si:H [77].

To evaluate the diffused transmittance Td() of the rough Ashai U-type TCO it is possible to use a relation similar to equation (15):

$$T\_d(\mathcal{A}) = T\_0(\mathcal{A}) \left( 1 - \exp \left[ -\left( 4 \pi \sigma\_{ms} C \left| n\_0(\mathcal{A}) - n\_l(\mathcal{A}) \right| / \, \lambda \right)^3 \right] \right) \tag{16}$$

where C depends on the two media and in particular when |n0-n1| increases C tends to 1. Fig. **30** shows the ratio of Td to T0 for TCO/p and p/i interfaces for different values of rms assuming C = 1.

By using the modelled transmittance and reflectance and the values of rms at each interfaces it is possible to evaluate how the interfaces within the TCO/p/i/n/Ag structure affect the Quantum Efficiency of the solar cell. Indeed a Quantum Efficiency can be seen as the sum of optical and electrical contributes arising from each scattering interface and each layer respectively.

$$\underline{QE}(\lambda) = \sum\_{\text{hyp}} \underline{QE}\_{op}(\lambda) \underline{\eta}(\lambda) \underline{QE}\_{el}(\lambda) \tag{17}$$

QEop is the optical quantum efficiency measuring the probability of a photon to be absorbed; () is the carriers generation per photons; QEel is the collection probability.

**Figure 30:** The *Td/T*0 ratio as function of wavelength for several values of rms for: a) the TCO/*p* interface and b) the *p*/*i* interface [77].

The texturing effects on front and rear contact on experimental QE of four different TCO/p/i/n/Ag cells are reported in Fig. **31** as points. The cells have different intrinsic layer thicknesses. For each of them four different simulations are reported in the same figure as lines. Each of them refers to: (1) all interfaces are flat; (2) only TCO/p is a rough interface; (3) only n/Ag is a rough interface; (4) all interfaces are rough. For each case it is possible to evaluate the short circuit current (Jsc) integrating the QE values over the wavelength range from 350 nm to 900 nm and taking into account the photon number per wavelength of sunlight AM1.5G spectrum. This value is also reported in Fig. **31** for each simulation as Jph. The simulation clarifies that the scattering enhances the absorption in the intrinsic layer leading to a gain up to 2.3 mA/cm2 . This enhancement is slightly dependent on the intrinsic layer thicknesses. The simulation also states that the roughness close to the rear contact has a strong effect in the spectral region of wavelength higher than 650 nm and has no effect on front side of the cell then does not affect the QE in the spectral range from 350 nm to 550 nm. Moreover the front rough interface strongly affects the QE in the spectral range between 450 nm and 650 nm slight, while introduces a slight decrease of the QE below 450 nm.

Introducing a TCO layer with rough surface in between n/Ag interface it is possible to further enhance the QE in the spectral range above 650 nm, leading to a Jsc improvement up to 2.9 mA/cm2 .

As expressed before, the angular distribution of diffused light is a relevant parameter to evaluate the scattered light in transmission IT and then to extract information on the surface roughness of the investigated medium. A very helpful tool to determine IT is the Angular reflectance transmittance Analyzer (ARTA) [86] depicted in Fig. **31**. This instrument uses monochromatic

light coming from a spectrophotometer. The detector is located in a little integrating sphere and can be moved along the sphere for an angle between-165° and 165°. The sample under test is placed in the centre of the sphere and can be rotated with respect to the incident light from 0° (normal incidence) to 90° (parallel incidence). At normal incidence the reflected light cannot be collected due to restriction of the detector

**Figure 31:** Experimental (■ points) and simulated (lines) QE of the four single junction *a*-Si:H solar cells each with a different thickness of the intrinsic layer: (a) 150 nm, (b) 300 nm, (c) 450 nm, and (d) 600 nm. The simulated QE curves refer to: (□) all flat interfaces; (∆) only the front interfaces TCO/*p* and *p*/*i* are rough; (o) only the back interfaces (*i*/*n* and *n*/metal) are rough; (full line) all interfaces are rough. The rms roughness of the front and rear interface of the cell and the Jph values are reported for each cell [77].

The absorbance A of the sample is related to the incoming light intensity I0 as follows:

<sup>0</sup>10 *<sup>A</sup> I I* **(18)** 

In this way the IT can be measured over a wide range of wavelengths.

Several textured substrates have been evaluated as reported in Table **3** where the surface structure and the rms values are listed. The FTO has been already described.

**Figure 32:** Schematic cross section of the ARTA [85].

**Table 3:** Morphology and rms of different textured TCOs.


**Figure 33:** AFM scan image of Al:ZnO etched surface.

The Al:ZnO (AZO) has been deposited in condition so that it resulted flat after the deposition and then has been etched in 0.5% HCl bath for 40 s to form a crater like surface morphology as depicted by AFM scan image reported in Fig. **33** [87].

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **425**

Boron depod ZnO (BZO) has been deposited by LP-CVD. The transmitted light angular distributions of samples listed in Table **4** are reported in Fig. **34(a),(b)** for 450 nm and 700 nm monochromatic incident light respectively. To compare these intensities each other they are normalized to the total transmittance Ttot(). From the measurements reported in Fig. **34** it is evident that at 700 nm the higher the rms, the stronger the scattering; moreover the AZO sample shows a stronger scattering at smaller angles than BZO. On the contrary, for both wavelengths, the specular part of the transmittance decreases with increasing rms.

**Figure 34:** Scattered light angular distribution at = 450 nm (a) and 700 nm (b) for the samples listed in Table **3** [85].

Now we report about an interesting study on the scattering properties of ZnO useful for thin film solar cells [87]. They have used the most common way to fabricate ZnO films by 13.56MHz rf magnetron sputtering system using a ZnO:Al2O3 target. Four different kinds of ZnO films have been prepared on 1737 Corning glass by varying the Al2O3 weight percentage (TCA) of the target as: 0.2, 0.5, 1 and 2%. 0.3 Pa deposition pressure has been used for three kinds of film, while 1 Pa has been adopted in case of 2%. Different films have been deposited at different temperature in the range between 60 and 490 °C. After deposition a wet chemical etch in 0.5% HCl bath has been performed on top of the film initially smooth to texture the surface. By varying the deposition conditions the ZnO films can assume different optoelectronic properties. Briefly we summarize the most relevant, such as carrier concentrations-mobilities as a function of deposition temperature for different TAC, reported in Fig. **35**, and transmission-absorption in the wavelength range between 300 nm and 2500 nm, reported in Fig. **36**.

**Figure 35:** Carrier concentration and mobility of Al:ZnO films as a function of deposition temperature for different TAC. Reprinted with permission from [87]. Copyright (2007), American Institute of Physics.

To evaluate the roughness rms, AFM scans have been performed after wet chemical treatment and the relevant results are depicted in Fig. **37**. From the data it is evident a certain activation temperature that increases with decreasing the TAC. Depending on the temperature and TAC, different surface morphologies appear. Three features can be found: (i) very rough surface with lateral feature size of about 300 nm and with rather steep edges, as in case of TAC = 0.2% and T = 290 °C; (ii) large craters that uniformly cover the surface, as in case of TAC = 0.5-1% and T =300- 375 °C; (iii) shallow craters with diameters of 1-3 m and depth of about 150-400 nm, as in case of TAC = 0.5-1%. Increasing the deposition temperature the surface changes from (i) toward (iii).

These data are useful to evaluate the haze of samples as reported in Fig. **38**. Also in this picture a transition temperature can be identified and it corresponds with the transition from feature (i) to (ii). To evaluate the PV performance of these TCO as top contact of thin film solar cell several c-Si:H cells, with 1 m of absorber layer, have been manufactured and different results have been obtained using different featured Al:ZnO films. In case of type (i) features (TAC = 0.2%, T = 290 °C) the cell reached only 22.1 mA/cm2 due to poor electrical properties of Al:ZnO and relatively low scattering effect.With the same amount of TAC but increasing the deposition temperature up to 460°C a transition to features (ii) appears forming craters over the Al:ZnO surface able to enhance the light scattering thus increasing the Jsc to 22.9 mA/cm2 . Even though the features of type (iii), such as obtainable in case of TAC = 2%, T = 375 °C, produce less scattering effect resulting in 17.2 mA/cm2 , the relatively smooth surface, able to reduces the shunt effects together with better electrical properties, enhances the cell Voc. With the TAC of 2%, increasing the Al:ZnO deposition temperature the scattering effect strongly reduces toward non-textured front contact. Since features of type (ii) are the most interesting from the light scattering point of view, deeper investigation have been carried out in this direction [87]. With increasing the intrinsic c-Si:H layer thickness up to 1.9 m the influence of parasitic losses, produced using the ZnO surface features of type (ii), reduces at both top and bottom interfaces with doped p and n layers. This effect, together with absorption along the thicker intrinsic layer produces a strong enhancement of Js up to 26.8mA/cm2 [87].

**Figure 36:** Transmission and absorption of Al:ZnO deposited at 370 °C for different TAC. Reprinted with permission from [87]. Copyright (2007), American Institute of Physics.

**Figure 37:** Calculated rms roughness data points using AFM measurements of texture-etched Al:ZnO films with different TACs. Lines are Guide-to-the-eye Reprinted with permission from [87]. Copyright (2007), American Institute of Physics.

**Figure 38:** Haze values at wavelength of 1m. Reprinted with permission from [87]. Copyright (2007), American Institute of Physics.

Using a similar approach it is possible to evaluate the role of the scattering at each interface of a micromorph tandem solar cells deposited on two different kinds of LPCVD textured TCO type A and C of Table **2**. In these cells a Silicon Oxide Intermediate Reflector (SOIR) has been introduced [88]. Four different cells have been deposited on type A and type C ZnO with and without SOIR. Their External Quantum Efficiencies are reported in Fig. **39(a)**. Taking into account that the top cell is the limiting factor of the total device, from the figure is evident that the gain in Jsc is larger when the SOIR is introduced and the cell is formed starting from type-A ZnO compared to type-C ZnO. Also the top cell is strongly affected by the presence of SOIR but is less affected by the ZnO substrate. ΔJsc, top *vs.* the thickness of the SOIR layer inserted in devices with top and bottom cell thicknesses of 180 nm and 1.8 μm, respectively, is plotted in Fig. **39(b)**. In turn a decrease of total reflectance of the cell is observed when SOIR is applied, as indicated by the Jsc values [88]. Nevertheless micromorph tandem cell deposited on type-C ZnO layer having a 3 m thick bottom cell reached initial efficiency of 12.6% with Jsc of 12.7mA/cm2 ,Voc of 1.38 V and FF of 72.2%. This efficiency is, up to now, the state of art of this tandem micromorph cells.

**Figure 39:** (a) EQEs of micromorph cells with and without a 150 nm thick SOIR deposited on type-A and type-C front ZnO layers; (b) Gains obtained in Jsc of top cell for a thickness series of SOIR layers [84].

The balance of scattering in micromorph tandem a-Si:H/mc-Si:H solar cell is quite critical since the two cells work as series of current generator. Then the tandem cell current is the lowest current generated by the two cells. This means that every kind of scattering enhancement introduced to the front will result in limited efficacy if also the rear cell is not sufficiently enhanced at the same time. On the other hand the top cell should be as thin as possible in order to reduce light induced degradation [89, 90]; therefore it limits the tandem cell current. To overcome this problem an intermediate reflecting layer (IRL) has been proposed [91]. To be effective this layer should have a refractive index lower than silicon (nSi = 3.8 at 600 nm) to produce a step index at the interface able to reflect part of incident light. At same time this layer must be quite conductive to avoid series resistance enhancement. ZnO has been proposed [91, 92] and an increment of 2.8mA/cm2 has been obtained using 110 nm thick ZnO with a80 nm thick top cell [93]. At the industrial scale this approach requires a significant trouble related to the deposition of ZnO layer in a different system with respect to the PECVD used to deposit the tandem cell layers. Recently a n-type doped

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **429**

SiOx intermediate reflector layer (SOIR) has been proposed instead of ZnO [94]. It can be deposited by a 110 MHz RF PECVD using a PH3/SiH4 = 0.024 and CO2/SiH4 = 2.7 at 250°C using a power density in the range between 0.01 and 0.1W/cm2 . With reducing the CO2/SiH4 ratio from 6 to 0.5 it is possible to change the refractive index from 2 to 3. Moreover its conductivity grows from 10-14-1cm-1 up to 1-1cm-1 reducing the CO2/SiH4 ratio from 3.2 to 1.6 and increasing the PH3/SiH4 ratio from 0.008 to 0.024. Nevertheless its conductivity still remains two order of magnitude lower than ZnO layer (102 -1cm-1), even if when the SOIR is deposited in a tandem cell unexpected growth of microcrystalline Si grains appears from Raman measurements that penetrate through the SOIR thus enhancing its conductivity and suggests a percolation mechanism for the current flowing through is. The effect of SOIR introduced as IRL in a tandem cell is reported in Fig. **40** where both the EQE and absorbance are plotted for different SOIR thicknesses. Introducing this layer a relative enhancement of 8% in cell efficiency has been obtained reaching an efficiency of 12.2% [94].

**Figure 40:** EQE and absorbance of tandem micromorph cell for different SOIR thicknesses [94].

An alternative approach to the texturing of window layer to enhance the light scattering effect is represented by the design of periodic surface texture on the substrate before contact deposition [95, 96]. To this aim the technology mutated from CD and DVD manufacturing can be really helpful. Here we briefly report an example of periodic pattern formed on top of polycarbonate substrate by embossing procedure [97] and covered by a thin Al layer (100 nm). Over this structure a single junction 200 nm thick a-Si:H cell has been deposited. The periodic structure, as monitored by AFM scan, together with the profile and the cell structure are depicted in Fig. **41**. The proposed structure induces optical interferences due to the periodic structure of the substrate. These interferences enhance the absorption in the a-Si:H layer and strongly reduce the total reflectance.

The cell has fabricated with the following structure and thicknesses: ZnO:Al (500 nm)/p-type a-SiC:H (10 nm)/intrinsic a-Si:H (300 nm)/n-typea-Si:H (20 nm)/ZnO (80 nm)/Ag (300 nm). Using a numerical simulator program (FEMOS [98]) it has been possible to find the optimum combination of the height h and the periodicity P of the periodic structure in terms of interferences. In particular values of P = 300 nm and h = 300 nm are able to optimize the cell QE as well as the Jsc. The effect of pattern duty cycle on the cell Jsc values for two different couple of P and h parameters is reported in Fig. **42**. As evident from the data reported in Fig. **42** a duty cycle of 50% allows reaching the maximum Jsc of 15 mA/cm2 that is 3.5 mA/cm2 higher than the Jsc obtainable starting from flat substrate. A drawback of this approach is represented by the increasing absorption in the Ag layer with higher vertical features (h). No absorption within front side ZnO has been found in comparison with cell fabricated on flat substrate, since very less light is reflected back at the metal back contact.

The above texturing approach can be also performed on top of cell if the periodic pattern is transferred on a glass substrate. Further enhancement can be achieved if the glass substrate is subsequently covered by ZnO, later textured by wet chemical bath as demonstrated in [99].

**Figure 41:** AFM scan of periodic texture formed by embossing procedure on a polycarbonate substrate and after covered by Al and a-Si:H layers [97].

#### **4. SILICON SURFACE TEXTURING**

Silicon is the most important of the available photovoltaic energy conversion materials. Crystalline silicon solar cells currently comprise more than 80% of all solar cells produced worldwide, with multi-and mono-crystalline approximately sharing the market. The solar cell industry currently obtains its silicon base material from the by-products of hyperpure poly-Si production and from remelted Czochralski (CZ) and Float-Zone (FZ) material originating from the microelectronics industry. As-cut silicon substrates are typically 180 µm thick, with approximately 200 µm thick saw kerf losses, but significant cost and energy reduction can also be achieved if thinner wafers are used. For this reason, the general trend is towards the use of still thinner silicon wafers. An important consequence of reducing the cell thickness arises due to the low absorption coefficient of crystalline silicon. An increasing proportion of light of longer wavelengths will not be fully absorbed on its first passage through the cell thickness, so that very effective light trapping schemes have to be built in. A way to reducing reflectance is by applying a randomizing or geometrical surface texture to the front surface of the silicon. This can be done mechanically, by

**Figure 42:** Effect of pattern duty cycle on the Jsc [97].

laser assisted processing, by plasma, or (electro-) chemically, by etching the silicon in an alkaline or acidic solution. Texturing the front surface of a solar cell generally results in improved performance, mostly due to an increase in the short-circuit current. This increase arises from three distinct mechanisms, all of which are related to the fact that the incident photons strike the cell surface at an angle. Firstly, some light rays will be reflected from one angled surface merely to strike another, resulting in an improved probability of absorption, and therefore reduced reflection.

Secondly, photons refracted into the silicon will propagate at an angle, causing them to be absorbed closer to the junction than would occur with a planar surface. This is especially relevant in material with diffusion lengths comparable to or less than the cell thickness, such as many multi-crystalline silicon wafers. Thirdly, long-wavelength photons which are reflected from the rear surface back to the front will encounter an angled silicon surface, improving the chance of being internally reflected, either at the silicon interface or at the glass surface, and providing another chance for absorption. This final process is referred to as light-trapping, and gives an improved response to infrared light. The anti-reflection properties pertaining to the geometry of the texture are demonstrated for a simple two-dimensional structure shown in Fig. **43**. Light incident normally to the silicon wafer falls upon the grooves at a point *a*. About 70% of this light is transmitted into the silicon and the rest is reflected. However, the reflected light is now angled downwards towards a neighboring groove, instead of away from the silicon surface as would be the case of a planar cell. Thus the light falls re-incident at the silicon surface for a second chance of transmission into the silicon at point *b*. In this way, light is more efficiently coupled into the silicon, leading to reflection reduction. The number of bounces upon the front surface for such a periodic symmetrical texture depends upon the facet angle of the texture with respect to the wafer surface. Minimal facet angles of 30° and 54° are required for double and triple bounce reflectance respectively. For the double bounce, case shown in Fig. **43**, the light reflected away from the silicon at *b* is lost. However, if the silicon is encapsulated under the glass, it is possible to totally internally reflect light arriving at the glass-air-interface at above the critical angle of 42°, whereby it will be re-directed towards the silicon yet again for possible incidence.

**Figure 43:** Reflection reduction and light trapping in geometrically textured silicon [100].

#### **4.1. Texturing of Si Wafers**

Texturing of crystalline silicon has been adopted for the development of high efficiency monocrystalline silicon solar cells. Inverted pyramids (Fig. **44**) on the c-Si surface produced with photolithography and anisotropic wet etching steps have resulted in reflectance values as low as 8%, leading to a record efficiency of 25% in c-Si solar cells [101, 102]. The standard inverted pyramid scheme shown in Fig. **44** is non optimal in terms of its light trapping capabilities [103]. Specifically, as shown in Fig. **45**, weakly absorbed light incident on one face of the inverted pyramid will be reflected from the rear reflector upwards. From the symmetry of this situation, light, which then falls internally on a face of opposite orientation from that coupling it in, will exit immediately from the cell.

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **433**

However, the light, resurfacing at the two other possible faces it can strike, will be totally internally reflected and trapped within the cell. To maximize this trapped component, the relative spacing between the inverted pyramid structures can be varied as indicated by the arrow on the plan view of the process in Fig. **45**. This component could be increased even further if the pyramid positioning in the perpendicular direction could also be varied. One way of doing this is to use the bi-dimensional screw structure shown in Fig. **46**. In this geometry, two different pyramid sizes have been incorporated which provides an additional degree of freedom in optimizing the overall design. Ideally, the difference in the two pyramid sizes would be very small to minimize the criticality in pyramid size to wafer thickness ratio. This scheme is a development of the idea originally proposed by Campbell and Green [103]. An example of a fabricated structure is shown in Fig. **47**.

**Figure 44:** Scanning electron microscope of a textured silicon surface: "inverted pyramids" [100].

**Figure 45:** Path of rays in inverted pyramid structure [102].

Also by numerical three dimensional simulations it has been found that inverted pyramids with periodicity of around 1 mm resulted in high quantum efficiencies close to the theoretical limit [104]. However, the use of photolithography steps for producing such structures is a time consuming and costly process. Photolithography-free texturing processes are currently used by industry, employing wet chemical solutions such as KOH/IPA or NaOH/IPA among others. Random pyramids formation on the surface of (100) c-Si is a very effective way to reduce the reflectivity of the front surface of c-Si solar cells [105-107].

**Figure 46:** Improved light trapping scheme using a bi-dimensional screw caused by incorporating two different sizes of inverted pyramids [102].

**Figure 47:** Scanning electron microscope of a textured silicon surface: "random pyramids" [100].

Potassium hydroxide combined with isopropyl alcohol (KOH/IPA) is widely used in order to obtain normal pyramid structures with reflectance values around 15%, however it produces contamination due to potassium, which causes a detrimental in the electrical characteristics of semiconductor devices and as a consequence an extensive wafer cleaning is required. Sodium hydroxide based etchants (NaOH/IPA) have also been investigated for obtaining pyramid structures without the use of KOH, however those processes are not cost-effective, because of the

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **435**

use of IPA. Thus despite the low reflectance, due to pyramid structures, that is achieved with wet processes, they have several drawbacks. These processes cannot be performed just in the front wafer surface where required, since texture in the back surface reduces the quality of the dielectric rear surface passivation [108]. For large volume production in PV industry the relative high amount of chemicals and de-ionized water (DI), which are employed in wet processes, represent an important environmental and financial issue. Recently attention has been focused on dry texturing processes in order to obtain highly textured surfaces, without the use of photolithography steps, DI water, or chemicals. It is known that fluorine radicals easily etch silicon, and more over the addition of oxygen to fluorine enhances the plasma texturing [109]. In particular SF6 and O2 plasmas have been used for texturing silicon in a micro-wave (MW) reactor, obtaining reflectance values below 20%; however no details on the process parameters have been reported [110-112]. Reactive ion etching (RIE), which is a standard process in microelectronics industry, has been used for texturing c-Si, for solar cells fabricated by doping diffusion [113]. However the needlelike structures reported are not suitable for a reliable solar cell process. Thus, despite the efforts made so far on plasma texturing, to our knowledge, there are no reports in literature about obtaining of normal or inverted pyramids by a dry etching process until the work [114] was recently published. It reports important results on the study of texturing c-Si wafers using SF6/O2 plasma in a RIE system. They focused on the combined effects of the RF plasma power and the SF6/O2 ratio. They found that by varying the RF power with an optimized SF6/O2 ratio it is possible to produce normal or inverted pyramid-like structures, with very low reflectance values, as low as 6%. They also studied the evolution from normal to inverted pyramids by increasing the RF power. Texturing was performed using p-type c-Si (100), with resistivity s in the range of 14– 22 Ω cm. For reliable texturing it was found that the gas ratio should be adjusted to 3 (SF6/O2=99sccm/33sccm). With an optimized gas ratio, the most interesting structures produced were obtained when the RF power was adjusted to 25, 50, 100, and 150 W. All the processes were performed for 15 min at a fixed pressure of 100 mTorr. Before each texturing process, an oxygen plasma was applied for 5 minutes. The addition of O2 to SF6 plays an important role on the plasma texturing process. It is believed that two opposite effects take place on the SF6/O2 plasma: an etching process due to fluorine radicals which are very efficient for etch silicon, and a deposition process due to residual SiOxFy radicals, which produce a masking effect [109]. Those micro-masks enhance the texturing of the c-Si surface. Experimentally, authors found that the SF6/O2 ratio determines the density of micro-masks, and a ratio equal to 3 improves the density of the structures produced on the c-Si wafers. On the other hand the RF plasma power determines the shape of the produced structures. By varying the RF power using an optimized gas ratio (SF6/O2=3), it is possible to produce very different structures such as pyramid-like or inverted pyramid-like structures. They found that the RF power has a critical effect on the c-Si texture. At low RF power the formation of normal pyramid-like structures is achieved, where texturing is governed by an anisotropic process, while at high RF power the inverted pyramid-like structures were obtained, where texturing is mainly governed by an isotropic ion assisted process. Normal pyramid-like structures in the c-Si surface resulted in an average reflectance around 18%, while inverted pyramid-like structures resulted in an average reflectance as low as 6%, without any antireflection coating. SEM images and reflectances of textured surfaces at different RF power are respectively reported in Figs. **48-50**.

The University of New South Wales has held the world record for silicon solar cell efficiencies for the last 15 years, initially with the Passivated Emitter solar cell (PESC) and more recently with the Passivated Emitter and Rear Locally diffused (PERL) solar cell. Despite the performance and achievements of these two technologies, neither has been used commercially, apart from for space cells, primarily due to the sophistication, cost and complexity of the processes involved. The photolithographic based processing is probably the main contributor to this. Recently the group has been developed inkjet printing techniques [115] for patterning low cost resist layers as a simple, much cheaper alternative to photolithographic based processing. Figs. **51** and **52** show images of the structures and reflectance results achieved with this new technology.

**Figure 48:** SEM images of textured c-Si surfaces, for different RF power: (A) P=25W; (B) 50W with SF6/O2=3 [114].

**Figure 49:** SEM images of textured c-Si surfaces, for different RF power: (C) 100W and (D) 150W with SF6/O2=3 [114].

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **437**

These new approaches appear capable of achieving similar device performance levels but with the greatest challenge being to match the dimensions of features in the resist patterning achievable with photolithography. Test devices to date based on inkjet technology have achieved feature dimensions such as holes of 30-40 microns diameter. However, these dimensions need to be reduced to about 10 microns diameter to fully match the performance levels demonstrated with photolithographic based processing. New and innovative inkjet printing techniques have been recently developed for further reducing the resist patterning dimensions. This work is being greatly assisted by the recent availability of the new 1 picolitre inkjet heads. The described dielectric patterning capabilities *via* inkjet patterning can not only be used for defining localized diffusion regions and locations for metal contacts, but also for the formation of textured surfaces and light trapping schemes. Examples of the latter are shown below as well as corresponding reflectance curves.

**Figure 50:** Reflectance of the textured c-Si surfaces without anti-reflection coating, when RF power is varied in 25, 50, 100 and 150 W, with SF6/O2=3. Also included as reference is the reflectance of a flat c-Si wafer, which was not exposed to plasma [114].

Commercial multicrystalline silicon cells have lower efficiencies than their single-crystal counterparts. One of the major performance limitations with the use of multicrystalline silicon is the inability to effectively texture the front surface, a process that is relatively straightforward in single-crystal cells. Anisotropic alkaline etching techniques, commonly used to texture monocrystalline wafers, are ineffective on the randomly oriented grains that make up a multicrystalline wafer. The random nature of the crystal orientation of multicrystalline silicon wafers makes such techniques much less effective for this material because only a handful of grains are properly orientated. It is therefore necessary to develop a texturing technique that will isotropically shape the front surface, regardless of crystallographic orientation. In addition, alkaline solutions can cause unwanted steps and crevasses between the grains. To be useful in the fabrication of solar cells, the texture must perform well both electrically and optically. There have

been many techniques proposed to texture multicrystalline silicon solar cells, masked and maskless wet acidic texturing, masked and mask-less reactive ion etching, mechanical scribing and masked isotropic etching, laser texturing followed by wet etching, and the so called black silicon etching.

**Figure 51:** Top: optical Microscope photograph of ink jet patterned lines in a SiO2 layer and bottom: Scanning Electron Microscope photograph of the inverted pyramids (left) and grooves (right) formed in the silicon surface following KOH etching of [115].

**Figure 52:** Reflectance of silicon wafers with different surface finish (i) inverted pyramids formed by photolithography, (ii) inverted pyramids patterned by ink jet printing and (iii) v-grooves patterned by ink jet printing [115].

## **4.2. Wet Acidic Texturing**

Industrial multi-crystalline silicon solar cells are textured using a technique based on isotropic etching with acidic solutions [116, 117]. The acidic solution consists of a mixture of nitric acid, hydrofluoric acid and some additives. In the etching reaction of silicon, nitric acid acts as an oxidising agent, while the created silicon-oxides are removed from the surface by hydrofluoric acid. The additives reduce the initiation-time required to start the reaction, and ensure good wet ability, resulting in uniform surface etching. For example H2SO4, or NaNO2 can be added to the etching solution, the role of the sulphuric acid is to stabilise the reaction, while by adding a tiny amount of NaNO2 the reaction starts before and control the etch speed. The removal of saw damage from the wafer surface is part of the texture etching, thus it requires only one single short chemical step to create the surface texture, starting from as-cut wafers. Wet acidic texturing can result in features with rounded surfaces, as opposed to flat-sided features which arise from anisotropic etches [118]. These rounded features produce a scalloped surface that can have good antireflection properties. An important issue with this technique is that the feature growth needs to be 'seeded' in some way, otherwise a planar surface will result. This seeding can be provided by surface damage caused during wafer sawing (mask-less acidic etching), or, in more complex methods, by defined holes through protective layers such as oxides, nitrides or polymers (masked acidic etching). Such a technique does not provide the extremely low reflection of some other methods, but does have the advantages of being relatively easy to implement and low-cost.

**Figure 53:** SEM photograph of an isotextured multi-crystalline silicon wafer [118].

On the other hand, this technique has some drawbacks such as making the substrates fragile (this can be avoid adding surfactants to the solution even though this increases the texturing process cost dramatically) and using a large amount of chemicals which is not good for the environment. During etching of silicon, the composition of the solution will change due to the ongoing chemical reaction: nitric acid and hydrofluoric acid are consumed while water is created, resulting in an expected decrease of the etch-rate. Furthermore, it should be noted that temperature-control during this exothermic reaction is desired as well, since a temperature rise drastically increases the etch-

**Figure 54:** SEM images of various mc-Si surfaces with different magnifications. From top to bottom: as-cut (left 1000x·, right 5000x·), alkaline-etched (both 500x·, different grains), acidic textured (left 500x·, right 5000x·), maskless RIE textured (left 1000x·, right 5000x·) and masked RIE pyramids [122].

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **441**

rate. Finally the isotexturing technique does not develop grain boundaries, but some dislocations are partially developed by increasing the etching rate (see Fig. **53**). For industrial application of the isotexturing technique some requirement need to be taken into account such as respecting the temperature-window in which the etching should take place by employing a temperature controlled etching bath and providing at regular intervals replenishments cycles to prevent depletion of the solution.

## **4.3. Plasma Texturing**

Reactive ion etching (RIE) is a method for 'dry' etching of silicon without the use of large quantities of liquid solutions. It is based on placing wafers in a plasma of highly reactive ions. Under certain conditions, the etching dynamics produce deep surface features that have excellent antireflection properties. Like wet acidic etching, RIE can be performed in a mask-less fashion that produces somewhat randomly placed features, or in conjunction with a masking layer to produce more even features. Masked RIE texturing was created by etching through photo-lithographically defined holes in a metal layer which is subsequently removed [119]. The mask-less RIE texturing was performed at Sandia laboratories in the USA using a proprietary 'metal-assisted' process [120, 121]. Both of these techniques offer promise for very low reflectance surfaces with minimal chemical waste, an issue that will become increasingly important in the photovoltaic industry. However, they are likely to be more costly to implement than wet chemical methods.

Fig. **54** shows scanning electron micrographs (SEMs) of multi-crystalline silicon wafers with various surfaces. In the as-cut wafer (top two images), the heavy surface damage is evident as deep fissures and cracks, resulting in reasonable reflection control but high recombination. The next two images are of a standard industrial alkaline-etched wafer. It appears to have some texturing, but this is both shallow and highly grain-dependent, and when averaged over many grains is almost as reflective as a perfectly flat wafer. The following two images are of an acidic textured wafer, which was performed with a HF/HNO3 solution. A wetting agent was added to produce more uniform texturing. Approximately 5–10 µm of silicon was removed from each surface. Although the surface damage is removed, its original presence is nevertheless critical, since it acts as a seeding layer for the texturing. The resulting surface contains smooth sided, bowllike features. Fig. **54** also shows images of the mask-less RIE texturing performed at Sandia. These wafers have somewhat randomly placed but nevertheless deep features with steep sides, which provide very low reflection. Note that the features of these RIE textured wafers are much smaller than those of the acidic textured sample (the two images on the right have the same magnification, 5000·). Finally, a masked RIE textured wafer is also shown at the bottom Fig. **54**. These features are very regular and steep-sided, with a distance of 7 µm between pyramid peaks. The pyramids are approximately the same size as the features on the wet acidic textured wafer. Fig. **55** shows the results of reflectance measurements on the three types of textured wafers, plus alkaline etched and as-cut samples.

While the results of the bare wafers give a good indication of the effectiveness of the various texturing methods, in a real cell the surface will have an encapsulated antireflection coating (ARC), which will further change the overall reflection properties. Therefore, we have measured the reflectance of the textured surfaces coated with a plasma-enhanced chemical vapour deposited (PECVD) SiNxfilm, both before and after encapsulation. A major advantage of PECVD SiNxfilms

is that they also electronically passivate the surface, leading to reduced recombination losses. Hence there are two separate issues to consider here: firstly, the optical properties of the SiNxcoated textured surfaces, and secondly, how well the SiNx film passivates the textured surfaces. The quality of the surface passivation is revealed by lifetime measurements, which are presented in the next section. Firstly though, we present reflectance results on SiNx coated wafers. The results for the un-encapsulated wafers show that the difference between the various textures

**Figure 55:** Reflectance measurements of bare alkaline-etched, as-cut acidic textured, masked RIE and maskless RIE textured multi-crystalline silicon wafers [122].

and the alkaline etched surface has been reduced. Initially, this appears to diminish the relative benefit of the texturing processes. However, this does not accurately represent the real case of a finished solar cell inside a module. When encapsulated under glass, and with a rear reflector in place, the samples with more textured surfaces will have relatively improved reflectance values due to light-trapping. These encapsulated measurements were taken with a 90% reflective mirror behind the wafer. This reasonably closely simulates the case in a finished cell which has a rear reflectivity of about 70% due to the Al back surface field. At wavelengths greater than 1000 nm, the benefits of light-trapping in the textured wafers as opposed to the alkaline-etched sample are clear. The RIE textured wafer in particular exhibits good light-trapping. The reflectivity curves shown in the previous figures cannot be interpreted in this way, since no mirror at the rear was used, and there was no planar glass surface at the front. We found that the reduction in reflection in the UV region after encapsulation is caused by absorption within the encapsulating material. The results certainly show that both the mask-less RIE and wet acidic texturing methods give a significant reduction in reflectance in comparison to the alkaline-etched wafer after encapsulation. Comparable results for the masked RIE process were not available, but it is reasonable to assume that they would be lower even that the mask-less RIE value of 7.6%. One important observation is that the difference between the acidic and RIE process has been further reduced after encapsulation. In comparison to the alkaline-etched wafer, the acidic wafer gives a 3.7% reduction

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **443**

in reflectance, while the mask-less RIE wafer yields a gain of 5.3%. It may be that the extra cost of RIE processes is warranted by this extra gain. All three texturing methods examined, wet acidic texturing, and masked and mask-less RIE texturing, significantly reduce reflection losses in solar cells. The reduction in reflection is greatest for masked RIE pyramids, followed by mask-less RIE, and then acidic texturing and this is likely to also be the order of greatest improvement in cell performance. However, the relative difference between the methods is substantially reduced after antireflection coating and encapsulation. Also, the cost of implementation is likely to be substantially less for acidic texturing then for either RIE process, especially masked RIE.

## **4.4. Laser Texturing**

Laser ablation is an isotropic process that will sculpt the surface of a silicon wafer, regardless of its crystallographic orientation. When combined with isotropic etching techniques, the process is able to effectively texture the silicon surface. The technique of using a laser to texture multicrystalline silicon solar cells was first published by Zolper *et al.* [123]. Initial attempts employed overlapping grooves to create an approximation of an upright pyramid texture. This provided a reduction in reflection, a boost in current and a decrease in open-circuit voltage and fill factor. It was concluded that the technique was limited by excessively deep grooves at cross-over points and dislocations penetrating the junction region. It was speculated that these dislocations may have been caused either by laser damage of the front surface or generated during the oxidation occurring after re-crystallization process of the nonplanar front surface. It was suggested that future work be done to develop a better post-scribe etching technique to remove the laser damage and further smooth the surface to reduce the oxidation-induced stress. A modified technique for the laser scribing was suggested that would incorporate the use of a matrix of individual laser-ablated pits, thereby removing the overlapping sections. A work of the UNSW group [124] demonstrates that laser texture is as good as the upright random pyramid technique and that the laser can be used to texture silicon solar cells and concludes that, if this process could be performed economically, it would be of benefit to the solar cell. Texture features are formed in a two-step process. The surface of the silicon is first sculpted by laser ablation, which removes the bulk of the silicon required for texturing. The laser ablation is performed using a Q-switched, Nd:YAG laser at a wavelength of 1064 nm. Pulse triggering is synchronized with the position of the sample stage, allowing the texture spacing to be easily controlled, regardless of the stage speed. A nitrogen shield gas protects the laser optics and removes some of the slag from the ablation pits. The ablated pits are arranged in the interlocking pattern shown in Fig. **57** by scanning the laser across the silicon surface. Next, the surface is chemically etched to remove the slag, smooth the surface and etch away any residual laser damage. The etching is performed in two stages. Initially a low-temperature, high-concentration NaOH etch is used to clear away surface slag blocking the holes. This is followed by an isotropic etch consisting of nitric, acetic and hydrofluoric acid that removes remaining slag from the holes and the layer of laser damaged silicon. The etching process is illustrated in Figs. **56**-**58**.

The optimum laser parameters were determined experimentally by creating textures with different laser settings and the optimal process parameters are illustrated in the reference [124]. Textures on high lifetime wafers were surface passivated with a phosphorus diffusion and dry thermal oxidation, then measured using the generalised photoconductance decay technique. This provided information on the effect the texture may have on the electrical properties of the cell. The carrier lifetime and implied open-circuit voltage after texturing are higher than 3 ms and 690 mV respectively, indicating the efficiency potential of laser textured surfaces for multi-crystalline silicon wafers.

## **4.5. Honeycomb Texturing**

Record performance multicrystalline silicon cells have in the past benefited from photolithographically defined "honeycomb" texturing using an acidic isotropic etch. Such structures have also been demonstrated recently using inkjet technology as shown in Fig. **59**. Such techniques appear to have significant commercial appeal.

**Figure 56:** SEM Images of laser texture fabrication: (a) immediately after ablation; (b) after NaOH etch [124].

**Figure 57:** SEM Images of laser texture fabrication: (c) finished texture after isotropic etch; (d) cross-section of finished texture viewed at an angle [124].

*Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **445**

**Figure 58:** Laser texture on multi-crystalline wafers: (a) FIB image of surface; (b) SEM image of crosssection on an angle [124].

**Figure 59:** Honeycomb texturing (left) and macro-groove texturing (right) of multi-crystalline silicon wafers through the use of inkjet technology. Direct Etching Via Aerosol Jetting [115].

## **4.6. Black Si Etching**

An appealing approach to minimize reflectivity utilizes a fine surface texture, comprising features on the nano-meter scale. Stephens and Cody [125] have proposed a model assuming that a textured surface with features smaller than the wavelength of light is an effective medium with gradually varying optical constants. The model predicts that the reflectivity of such a boundary layer is vanishing for wavelengths below a cut-off threshold, which depends on the complex refractive index of the bulk material as well as on the density profile and depth of the textured layer. Accordingly, the reflectivity cut-off for textured silicon surfaces with a linearly increasing density should appear at a wavelength four to six times larger than the depth of the textured layer, *i.e.*, a fine texture of only 200–300 nm in depth should be enough to suppress the reflectivity of a Si surface in the whole usable spectral range of photon energies above the band gap. These predictions have been confirmed experimentally *via* the preparation of randomly textured Si surfaces with nano-scale features by sputtering etching [126]. Similar techniques based on reactive ion etching RIE have been developed recently, employing selective etching through discontinuous SiO2 micro-masks [127] or utilizing the catalytic action of various metals during the ion etch

process [128]. However, the ion damage associated with RIE, difficulties with obtaining a uniform texturing on area above 100 cm2 , and the complexity of the plasma processes involved are of concern regarding a large scale solar cell production. In 2006 Svetoslav Koynov *et al.* [129] presented a method for nano-scale texturing of silicon surfaces, which utilizes simple wet chemical etching, facilitated by the presence of small metal clusters. Three kinds of silicon samples were used to demonstrate the universality of the method with respect to surface structure and doping: n type single crystalline Si p type multi-crystalline Si, and thin films of intrinsic hydrogenated amorphous silicon (a-Si:H). They demonstrated that the optical losses due to surface reflection can be reduced to below 5% throughout the entire usable spectrum, from 350 to 1000 nm wavelength for crystalline Si. The samples are first cleaned in acetone and isopropyl alcohol, followed by a HF dip to remove the natural oxide from the surface. The texturing process, referred to as "black etch" in the following, is performed in three steps.


Fig. **60** illustrates the ability of the black etch treatment to produce the desired optical antireflection properties on different silicon surfaces. Three silicon samples with different morphologies crystalline, multi-crystalline, and amorphous and doping n type, p type, and intrinsic are shown. Initially, all three samples had polished or smooth surfaces. The major part of each sample surface bottom parts in Fig. **60(a)** has been modified, while the rest remained untreated for direct comparison. The treated areas of all samples appear similarly black, even under non-normal incidence. Small differences in the reflectivity of the crystallites in the cast-Si sample are visible after treatment, indicating a slight variation in the textures obtained. In distinct contrast, all

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **447**

untreated areas have a high reflectivity, as seen by the mirror images of the labels above them. The spectra in Fig. **60(b)** quantify the similar, uniformly suppressed reflectivity of as little as 2%–5% in the high absorption ranges of all three samples.The amount of absorbed light is significantly increased after the surface treatment. The increase at wavelengths below the absorption edge obviously originates from the suppressed reflection.

**Figure 60:** (a) Photograph of black etched Si samples of different crystal structure and doping. "c-Si n" denotes a bulk single crystalline silicon sample with(100) orientation, n-type doping, and 2.5 Ω cm resistivity; "cast-Si p" a bulk multi-crystalline silicon, p-doped sample also with 2.5 Ω cm resistivity; and "a-Si:H i" a nominally un-doped thin film of amorphous hydrogenated a-Si:H on a glass substrate, with a thickness of 500 nm. For comparison with the initial surfaces, the upper part of each sample is left untreated. (b) Total hemispherical reflection spectra of the treated areas of the samples from a. The data for a-Si:H are shown as measured and after removal of the interference fringes [129].

### **5. REAR SIDE REFLECTOR**

The rear side reflectance inward the absorber layer is very relevant to enhance the cell absorption and then the efficiency. High reflection of the rear cell surface reduces absorption in the rear cell contacts or transmission from the rear, allowing the light to bounce back into the cell for possible absorption. Randomising the direction of light allows much of the reflected light to be totally internally reflected. Light reaching the top surface at an angle greater than the critical angle for total internal reflection is reflected again towards the back surface. Light absorption can be considerably increased in this way, since the pathlength of the incident light can be enhanced by a factor up to 4n2 where n is the index of refraction for the semiconductor [130, 131]. This allows an optical path length of approximately 50 times the physical devices thickness even if a more realistic value of 10 is achievable [132]. This allows the use of thinner absorption layer and then, in case of c-Si wafer, PV cost reduction that is strongly related to the cost of silicon of course. Light impinging with angle less than the critical angle escapes the cell, but light having incident angle greater than the critical angle is totally internally reflected inside the cell. From the rear reflection point of view, the Lambertian reflector is the theoretically preferred scheme to enhance the internal light absorption as depicted in Fig. **61**.

Even with textured rear side surface, part of the light impinging the rear contact can be absorbed by the metal. With the aid of optical simulation software (XOP [133]) it is possible to evaluate the optical properties of different back reflecting scheme of the solar cell. Most of the actual rear side

contacts on p-type c-Si wafer are formed using single metal, such as Al in case of, or passivating coating, such as SiO2 or SiNx followed by Al metal [131, 134, 135], in case of point contacts [136], or a-Si.H-ZnO/Al [137].

**Figure 61:** Randomize reflected rear side surface able to form a Lambertian reflector.

**Figure 62:** Reflectance inward the c-Si bulk for different kind of rear c-Si surface coating as simulated using XOP software.

A comparison of reflectances inward the c-Si bulk of the solar cell due to different kind of rear surface coatings are reported in Fig. **62**. As evident, the Al reflector shows a pronounced reduction of reflectance in the near infrared spectrum. Other schemes using passivating layers show less absorption. In the simulations reported in Fig. **64** the optimum thicknesses values for the thin films to ensure the maximum inner reflectances have been assumed.

## **5.1. Bragg Reflector**

To enhance the reflectance (R) inward the Si substrate from the rear side of the cell it is possible to form a Dielectric Bragg Reflector (DBR) instead of the commonly adopted full Al contact. A DBR can be fabricated using a multilayer-stack of alternate high-and low-index films. Referring to our experiment, those films are respectively a-Si:H and SiNx and their thickness (t) can be dimensioned as one quarter wavelength thick: t = /(4 n) taking into account the refractive index (n) of a-Si:H and SiNx and the centre wavelength of the DBR (. Introducing the DBR in the rear side of our cell its scheme can be fabricated referring to Fig. **63**, in which a cross section scheme of the device is depicted.

Keeping in mind this structure we can evaluate the reflectance R() toward the Si substrate as [138]:

$$R(\lambda) = \left[ \frac{n\_{\rm Si} \left( n\_{a-\rm Si \cdot H} \right)^{2\pi} - n\_{\rm \cdot M} \left( n\_{\rm Si \rm Ni \cdot \rm Ni} \right)^{2\pi}}{n\_{\rm Si} \left( n\_{a-\rm Si \cdot H} \right)^{2\pi} + n\_{\rm \cdot M} \left( n\_{\rm \cdot \rm Si \cdot H} \right)^{2\pi}} \right]^2 \tag{19}$$

where nSi, na-Si:H, nSiNx, nAl are the refractive indexes of the materials respectively. # is the number of couples a-Si:H/SiNx.The bandwidth Δ of the photonic stopband can be calculated by:

$$
\Delta\lambda = \frac{4\lambda\_0}{\pi} \cdot \arcsin\left(\frac{\mathbf{n}\_{\text{a-Si:H}} \cdot \mathbf{n}\_{\text{SiNx}}}{\mathbf{n}\_{\text{a-Si:H}} + \mathbf{n}\_{\text{SiNx}}}\right) \tag{20}
$$

**Figure 63:** Schematic Cross section view, not in scale, of the cell with DBR.

**Figure 64:** Reflectance at 1050 nm inward the c-Si bulk as a function of a-Si:H/SiNx couples number in DBR [17].

To obtain high reflection in the infrared region of the sun spectrum,1050 nm as the DBR centre wavelength can be chosen. At that wavelength the thicknesses of a-Si:H and SiNx films become 66 nm and 130 nm respectively, taking into account their refractive index as 3.65 and 2.01 respectively.

The higher the a-Si:H/SiNx couples number, the higher the mirror reflectance, as reported in Fig. **64** where the inward Silicon wafer reflectance, as expressed by equation (10), is exploited. As evident from this figure, four couples of a-Si:H/SiNx can be considered sufficient to obtain a reflection higher than 95%. A comparison of reflectances spectrum, in the range between 400 nm and 1200 nm, inward the c-Si bulk of the solar cell due to different number of a-Si:H/SiNx couples forming the DBR is reported in Fig. **65**.

**Figure 65:** XOP numerical simulations of reflectance inward the c-Si bulk for single couple aSiH/SiNx/Al, 4 couples aSiH/SiNx/Al and 4 couples aSiH/SiNx/Al after fitting procedure of experimental data [17].

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **451**

The four couple of DBR/Al shows higher reflectance values in the same spectral region with respect to single couple of a-Si:H/SiNx/Al as well as simple Al contact used as reference.

To verify the presence and the consistence of the DBR structure after its growth on the rear side of c-Si wafer, we have measured the reflectance profile from the rear side of this multilayer before the SOD and Al deposition. To extract information from this measurement we have optically modelled our structure using XOP software [133] taking into account the sequence, the refractive index and the expected thicknesses of each layer in our stack over a c-Si substrate. We have fitted the reflectance experimental data using those thicknesses as free parameters as reported in Fig. **66**. From the good agreement between experimental data and simulation we have found several differences between the expected and the evaluated thicknesses of each layer in the DBR, as reported in Table **4**. Even if the deposition time has been set equal for each kind of film at the beginning of the PECVD process, an unpredictable enhancement of SiNx growth rate occurs increasing the number of subsequent depositions. On the contrary the a-Si:H growth rate seems to be underestimated from the beginning of the process.

**Figure 66:** Experimental (symbols) and optical model of reflectance collected from the rear side of the DBR deposited onto a c-Si wafer [17].

**Figure 67:** Effect of DBR on the reflectance in the infrared region of the impinging light spectrum [17].


**Table 4:** Comparison of expected and evaluated thicknesses of each layer inside the DBR.

Taking into account the evaluated thickness data we have calculated a new reflectance profile of the DBR inward the c:Si bulk, as reported in Fig. **65** as green line. Comparing the two curves of expected DBR and fabricated DBR\* we can remark that even if the multi-layer deposited shows different thicknesses with respect to the expected one, only an helpful left shift of the reflectance curve occurs. This effect confirms that the DBR can be easily formed despite to its complexity.

To have a better vision of the DBR effect on rear side of the solar cell structure, a comparison of the front side reflectance of the two different structures: ARC/c-Si/DBR and ARC/c-Si is reported in Fig. **67**. From the reflectance in the near infrared region of the front side impinging spectrum the mirror effect imposed by the DBR is evident if compared with the a-Si:H/SiNx surface coating layer. Mirror like surface of the silicon wafer is used to remark the effectiveness of the DBR. The wafer front side is covered by SiNx thin film working as sunlight antireflection coating.

### **5.2. Bragg a-Si:H/c-Si Solar Cell**

As an example of the reflector efficiency in solar cell, we have applied the DBR as a back side mirror in a-Si:H/c-Si heterojunction solar cell. The success of a-Si:H/c-Si hetero-structure has been first demonstrated by SANYO ltd, which have reported efficiency above 20% with very high open circuit voltage (Voc = 746 mV) [139] on heterojunction solar cells based on n-type Czochralski silicon. In particular the good performances of this kind of cell relies on the introduction of a thin intrinsic buffer layer between the n-type a-Si:H layer and the c-Si absorber for the improvement of interface properties. a-Si:H/c-Si heterostructure solar cells have been also fabricated on commercial p-type substrates and on multicrystalline silicon (mc-Si) achieving 17% and 15% efficiency respectively [140, 141]. However heterostructure itself is not enough to ensure good performances on thin wafers. Indeed also back surface passivation and Back Surface Field (BSF) play a fundamental role in enhancing open circuit voltage. It has already been demonstrated the feasibility of BSF on n-type c-Si based a-Si:H/c-Si heterostructure using the n-c-Si/i-a-Si:H/na-Si:H/ITO structure [139]. Several difficulties, instead, occur in the p-c-Si/i-a-Si:H/p-a-Si:H/structure in the formation of the rear contact, due to a band offset in valence band between amorphous and crystalline materials. The band bending distribution of heterojunction rear contact formed on p-type heterojunction contact is reported in Fig. **68** in dark and short circuit conditions. The simulation, made using a finite difference numerical simulator [140] has been performed taking into account the energy band gaps EgaSiH = 1.72eV, EgcSi = 1.12eV the electron affinities

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **453**

aSiH = 3.9eV, cSi = 4.05eV, the activation energies Eatt= 0.2 eV of p-type 1 cm c-Si, the lowest Eatt that doped a-Si:H films can assume [141] of 3.4 eV and the density of states (DoS) within each layer (lower than 1017cm-3). An intrinsic buffer layer has been introduced between the a-Si:H and c-Si doped materials in order to reduce defect density and thus the recombination at the interface [139].

**Figure 68:** Band bending simulations in dark and 0V conditions of the p-type-c-Si/i-a-Si:H/p-aSi:H heterostructure.

**Figure 69:** Holes and recombination distributions at the hetero-junction simulated at 0.65 V in dark condition.

As evident from the band diagrams, the pronounced valence band offset is a critical point for holes flowing toward the metal electrode. In the simulations the carrier collection at the amorphous silicon edge has been supposed not influenced by the metal electrode workfunction. Indeed any depletion within amorphous layer can be neglected due to the high defect density at the metal/a-Si:H interface. This unwanted effect is mainly due to the valence band offset at the edge of the c-

Si wafer that forms a barrier against the carrier collection from the metal electrode as can be deduced from Fig. **69**. In this figure the hole distribution along heterojunction p c-Si/i a-SiH/p a-Si:H at the cell rear side, simulated at 0.65 V in case of 5 nm and 10 nm of intrinsic buffer and doped p-type a-Si:H thicknesses respectively, strongly drops at the edge of the a-Si:H/c-Si heterojunction due to recombination, as reported in the same figure. As reported in literature, this problem can be overcome with a low temperature BSF formation process, which requires a back surface passivation, obtained depositing a-Si:H/SiNx stacked layers. Then a Nd:YAG pulsed laser treatment, used to promote a local and simultaneous Al & B diffusion through the passivation layers [142], allowed to achieve Voc higher than 630 mV [143, 144] on substrates having thicknesses in the order of 250-300 m. The efficacy of this approach is also exploited in [145, 146].

Even though hetero-structure solar cells coupled with laser promoted BSF give the possibility to get a full low temperature process suitable to obtain high efficiency thin wafer solar cells, their performances can be still enhanced because the near infrared components of the sun spectrum is not completely absorbed in a thin wafers. This enhancement can be obtained using a mirror on the back side of the solar cell. Indeed merging a perfect dielectric mirror with an ohmic semiconductor metal contact on the rear side of a cell means to adopt a particular scheme in which the rear area of the cell would be divided in two regions where both mirror and contact would coexist. Different kind of point contact technologies have been reported in literature [147]. Even though some of them resulted in highest efficiency solar cells, often they adopt several technology steps merged from microelectronic, such as photolithography, that are not easy to transfer to mass production. A very promising technology, able to form effective metal contact on semiconductor material through dielectric film, is represented by Laser firing contact technology developed in the last few years [146]. Moreover different kinds of surface passivation layers have been reported in literature such as SiNx and/or SiOx [148] on which the laser process can be applied.

a-Si:H/SiNx DBR and single couple of a-Si:H/SiNx structures have been compared as back side mirror of identical hetero-structure solar cells fabricated on 250 m thick FZ monocrystalline 0.5 cm p-type wafers with one side polished. After RCA standard cleaning procedure and 1% HF bath, the front cell emitter has been deposited in a Plasma Enhanced Chemical Vapor Deposition (PECVD) system as an intrinsic-type a-Si:H/n-type a-Si:H stacked structure. Then a 30 nm thick chromium layer has been evaporated on the top of the heterostructure and subsequently wet removed to form a high conductive CrSi layer [141]. The four couples of the a-Si:H/SiNx structure of the DBR has been formed on the rear side of the wafer after a 1% HF bath. The PECVD parameters of the emitter and of the DBR structure, together with the estimated thicknesses, are reported in Table **5**. Each material couple of the DBR has been deposited without interruption of the glow discharge process in order to reduce the stress at the a-Si:H/SiNx interface. Between two subsequent couple depositions, a N2 purge and adequate vacuum conditions have been recovered to avoid ammonia residua during the a-Si:H layer depositions.

Then the front side of the cell has been completed by an ITO layer, deposited in a sputtering system at 150 °C, 200 W RF power using 25 sccm of Ar. Its final thickness has been fixed at 65 nm, which is also ideal for antireflection purpose. After a Filmtronics B200 Boron spin-on dopant (SOD), spinned at 2000 round/min for 30 sec on the DBR, has been deposited and cured at 250 °C for 15 min. The SOD annealing temperature has been chosen as the one sufficient to hard the SOD avoiding at the

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **455**

same time boron contaminations in the underneath amorphous layers. Subsequently a 2 m thick Al layer has been e-beam evaporated on the whole rear surface of the mirror. To form the rear side contact of the solar cells a laser treatment has been locally performed by a Q-Switched Nd-YAG pulsed laser working at 1064 nm of wavelength in TEM00 mode with power 320 mW, pulse burst of 100 ms at 1kHz repetition rate, in order to induce a simultaneous diffusion of Al and B inside the silicon wafer, through the amorphous multilayer [144]. The front contact of the cell is ensured by a silver grid deposited by screen printing of low temperature sintering DuPont Ag paste. The paste has been then dried and simultaneously sintered at 200 °C for 10 minutes in a conventional IR dryer belt furnace. Finally the cell area has been limited to 4 cm2 cutting the wafer with a dicing machine. An identical procedure has been followed for the fabrication of solar cells having only one couple of a-Si:H/SiNx in the rear side. In particular the a-Si:H/SiNx mirror has been deposited with the same parameters reported in Table **5** for the four couples of the DBR structure. To evaluate the efficacy of both the mirror and the Back Surface Field we have characterized the heterostructure solar cells measuring the Internal and External Quantum Efficiency (IQE, EQE) as well as the Reflectance profiles as a function of wavelength. Results are reported as symbols in Figs. **70**, **71** for the DBR and for the single a-Si:H/SiNx respectively. As predicted by the simulation results, the reflectance values of the DBR, in the spectral range from 1000 nm to 1200 nm, are higher than in case of the a-Si:H/SiNx. This effect immediately reflects on the IQE of both samples, leading to a higher IQE values when DBR is adopted as back reflecting mirror.


**Table 5:** PECVD parameters used in the deposition of the a-Si:H, and a-SiNx layers of the emitter and DBR structures. PD is the process pressure; PRF is the power density of the plasma discharge; TD is the substrate temperature.

To extract quantitative information from the quantum efficiency measurements, the experimental QE data have been modelled with the numerical program PC1D [149]. The heterostructure has been divided in three regions:




**Table 6:** Parameters used in PC1D simulations for fitting the experimental data of EQE, IQE and current voltage curves. The front coating and the back inner reflectances fit the reflectance curves in the range 800- 1200 nm.

These better performances have been confirmed by the measurement of the minority carriers lifetime eff, that quantifies the effectiveness of the back side mirrors as surface passivation

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **457**

structure. Measurement have been performed on two 0.5 cm p-type silicon wafers, passivated on both side by the DBR or the single a-Si:H/SiNx respectively, by monitoring the Quasi Steady State Photoconductance decay in a Sinton System [151]. The experimental values are reported in Table **7**. The higher eff found in case of DBR is mainly due to the increase of the positive charge content at the a-Si:H/SiNx interfaces of stacked structure with respect to the single couple of a-Si:H/SiNx layers. Indeed higher the positive charge amount, stronger the field effect close to the a-Si:H/c-Si interface due to inversion layer formation that keeps away the minority carriers from the silicon surface [29].

**Figure 70:** Reflectance profile (stars), External (open circles) and Internal (filled circles) Quantum Efficiencies for a-Si:H/c-Si heterojunction solar cell with the DBR/Al back structure. Lines refer to the simulation results obtained using PC1D software with the parameters reported in Table **6** [16].

**Figure 71:** Reflectance profile (stars), External (open circles) and Internal (filled circles) Quantum Efficiencies for a-Si:H/c-Si heterojunction solar cell with the a-Si:H/SiNx/Al back structure. Lines refer to the simulation results obtained using PC1D software with the parameters reported in Table **6** [16].

**Figure 72:** Measured (symbols) and modeled (lines) current-voltage characteristics measured under AM1.5G for solar cells with DBR/Al (filled symbols) and a-Si:H/SiNx/Al (open symbols) as mirror [16].

**Table 7:** Minority carrier lifetime value of the c-Si surface passivation structures as measured from photoconductance decay method.


The photovoltaic performances of the solar cell with the DBR result once again better than the ones with the single couple. A high Voc of 681 mV and a Jsc of 34.96 mA/cm2 have been achieved, which confirm the DBR efficacy as rear side dielectric mirror in laser fired point contacted cell. The current voltage characteristics, measured under Class A AM1.5G sunlight simulator, of both kind of heterostructure solar cells is reported as points in Fig. **72**. In the same figure the lines are related to the PC1D numerical simulations. The same set of parameters, used to reproduce QE data, allow to accurately model the current voltage curves collected under standard AM 1.5G. The overall efficiency at 16.1% is limited by the Fill Factor (67.8%), which can be increased by an optimization of the screen printed front grid and of the pitch of laser point contact.

Taking into account the proposed model it is possible to apply the DBR idea to thinner silicon wafer to enhance the near IR cell response also choosing the centre wavelength of the DBR accordingly.

#### **5.3. Thin c-Si Wafer**

In order to reduce the PV cost the most promising approach concerns to the use of thinner silicon wafer, indeed half of the cell cost is due to the base material. In case of multicrystalline silicon (mc-Si) the actual wafer thickness has been thinned from 300 m of five years ago, to the actual 180 m. Further improvement can be obtained using thinner saw wire and a reduction to 120 m is expected. In turn, the thinner mc-Si wafer becomes more fragile since is very large area

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **459**

156x156 mm2 . Therefore the manufacturing production yield actually is not competitive with the actual production line. Further investments are needed to replace some old technologies and facilities to approach those thinner wafers. On the other hand, it is difficult to image mc-Si wafer thinner than the saw wire. To this aim different approach to wafer cutting are needed. In case of monocrystalline silicon (c-Si) a very promising technique to cut the wafer thinner than 100 m is now arriving on market as presented by SiGen [152]. The solution presents itself by combining advanced layer transfer cleaving methods with efficient, high-energy ion accelerator technology. The convergence of these two technologies allows a thickness of silicon made from a CZ silicon ingot to be directly detached using a high energy light ion beam with near-zero kerf loss and with low overall process cost. The process is called Direct Film Transfer (DFT) and shown conceptually in Fig. **73**. The thin wafer produced in this way result flexible and then less fragile with respect to thicker one. Moreover it is free from saw damages, therefore can be directly textured saving a costly wet chemical. On this wafer high temperature steps, such as emitter diffusion and high temperature sintering screen printed fired contact should be replaced by different approach using low thermal budget. Thin film technologies are suitable to this aim. Indeed one of the most promising way is the use of a-Si:H/c-Si technology in order to form both the front and the rear side contact of the cell. Then TCO should be used to form large area contact followed by Ag grid shaped metal electrodes. This approach has been successfully demonstrated by Sanyo [139] on silicon wafer thinner as thin as 98 m, achieving the record efficiency of 22.8% (Jsc = 38.96 mA/cm2 ; Voc = 743 mV; FF= 79.1% area 100 cm2 ).

**Figure 73:** Direct Film Transfer (DFT) process to form a kerf free CZ thin silicon wafer.

Thinning the wafer with the same cell fabrication method, such as heterostructure, several aspects have to be carefully considered to maintain the same efficiency. To this aim we performed numerical simulation, by using PC1D software [149], to evaluate the effect of thinner wafer on the solar cell performances.

The cell under test was a n-type c-Si based heterostructure in which both the front emitter and the back surface field were formed by a-Si:H/c-Si heterojunction. To better evaluate the effect of wafer thickness in the range between 200 m and 20 m, we also considered an ITO layer as antireflection coating. The cell structure and parameters used in the simulations are listed in Table **8**. The photovoltaic parameters of the simulated heterostructure cell as a function of silicon wafer thicknesses, normalized to the initial value, are reported in Fig. **74**. The photovoltage (Voc) enhancement is expected due to recombination reduction along the wafer that reflects in higher built-in voltage reducing the wafer thickness. In turn, the thinner the wafer, the lower the photocurrent. From the Fig. **74** it is evident that the photocurrent reduction is stronger than the photovoltage enhancement thus affecting the cell efficiency that reduces as the wafer becomes thinner. These results are in good agreement with SANYO report [139]. This remarks that the use of thinner wafer ensures a cost reduction because of less material, but also produces a cell efficiency reduction. To overcome this undesired condition it is possible to introduce the mirroring effect, such as proposed with the use of DBR concept reported above. To do this in the simulation we use the internal light reflectance parameters as indicated in Table **7**. The evolution of photovoltaic parameters by reducing the wafer thickness is reported in Fig. **75**. Now the cell efficiency remains almost constant from thickness in the range between 200 m and 60 m.

**Figure 74:** Normalized photovoltaic parameters of the heterojunction cell as a function of the wafer base thickness.

**Table 8:** Parameters used in PC1D simulations to describe the heterojunction solar cell in which the base wafer thicknes is used as parameter.


#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **461**

*Table 8: cont….* 


Very similar approach to the rear side mirroring has been reported in [153], in which the authors suggest the use of a distributed Bragg reflector made by a stacks of Si/Si3N4 having refractive indexes: *n*1/*n*2 = 3.5/2.0 or Si/SiO2*n*1/*n*2=3.5/1.46 achieving a reflectivity of 99.8% in the wavelength range between 800 and 1100 nm. By the unique combination of grating and DBR, light is tightly trapped within the solar cell, effectively changing the optical path length from the thickness of the cell to its lateral dimension. The schematic cross section of the distributed Bragg reflector is reported in Fig. **76**.

**Figure 75:** Normalized photovoltaic parameters of the heterojunction cell as a function of the wafer base thickness after the introduction of mirroring effect.

**Figure 76:** Distributed Bragg reflector for solar cell [153].

**Figure 77:** IV characteristics for solar cell with different distributed Bragg reflecting mirror [153].

**Figure 78:** (a) Schematic solar cell cross section with antireflective coating and distributed Bragg reflector and SiO2 grating layer with amorphous silicon cylinders in background. (b) Top view of the cell [154].

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **463**

Different materials have been used resulting in different efficacy, as demonstrated by the IV characteristics under AM1.5G sunlight simulator reported in Fig. **77**. This concept can be transferred to amorphous thin film solar cell as reported in ref [153]. The authors have made several simulations using the mirror structure as depicted in Fig. **78** in which both the schematic cross section and the top view of the cell are reported. The mirroring effect has been modelled to enhance the absorption at wavelengths longer than 650 nm. An optimal structure consisted of a = 600 nm, R/a = 0.38, d1 = 50 nm, d2 = 500 nm, d3 = 50 nm and d5 = 120 nm. The thickness of ITO d0 is expected to range from 500nm/4nITO= 64 nm to 775nm/4nITO = 100 nm.

**Figure 79:** Non specular reflection/transmission/absorption in the absorber layers for the two designs with d0 = 65 nm, d1 = 50 nm, d2 = 500 nm and (a) a-Si layer with SiO2 cylinders (b) SiO2 layer with a-Si cylinders [154].

The optimized solar cell with SiO2 cylinders inside the a-Si layer (Fig. **79a**) and the complementary structure of a-Si cylinders in the SiO2 matrix (Fig. **79b**) both demonstrate very high absorption (A > 0.8) through most of the optical wavelengths (0.4-0.7 μm), accompanied by small reflection. The enhanced absorption improves the near-IR solar response. Wavelengths larger than 0.775 μm are largely reflected from the cell in both configurations, but these are above the bandgap and do not contribute to photocurrent. A comparison of the light trapping in the optimized solar cell with a bare a-Si:H film, an a-Si:H film with antireflective coating and an a-Si:H film with DBR and antireflective coating is reported in Fig. **80**.

Even though the efficacy of these last two presented structures, sometimes recalled as "photonic crystals", is out of doubt, nevertheless it is not easy to image how to precisely control the grating sizes over a large area device as required by the PV application.

#### **6. INNOVATIVE CONCEPT**

As pointed out in the previous sections, in conventional solar cells where the active absorbing layer is much thicker than the impinging wavelengths, light trapping is usually based on texturing the front solar cell surface in order to randomize the light propagation direction within the cell structure and obtain a total internal reflection between the active material with high refractive index and the external surrounding material with low refractive index. In this way the fraction of the light lying within the escape cone for refraction out from the substrate toward the external material is reduced and a much longer propagation distance inside the active material of the solar cell is achieved.

**Figure 80:** Comparison of absorption of a bare a-Si:H film, a-Si:H film with AR coating only, a-Si:H film with AR coating, and DBR, a-Si:H film with AR coating and DBR and optimized grating [153].

For these textured structures, it has been demonstrated [3, 4] that the light absorption can increase, with respect to a non-textured surface, up to a factor 4n2 /sin2Φ where n is the refractive index of the active material and Φ is the angle of the emission cone in the external medium. This limit [3] cannot be exceeded in standard solar where the thickness of the active layer is much larger than the wavelength range. However, in the nanophotonic regime when the thickness is comparable or even smaller than the impinging wavelengths, the absorption enhancement can overcome this limit if a proper design of the solar cell structure is considered. The basic concepts for this enhancement are:


The absorption spectrum of film satisfying the first requirement is constituted by a sequence of sharp peaks, one for each guided resonance as reported in Fig. **81**. Since the incident radiation useful in photovoltaic applications has a bandwidth much larger of the bandwidth associated with each resonance, the total absorption is given by the sum of the absorption peak of each resonance,

#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **465**

and can be demonstrated that it is linearly dependent on the number of resonances and inversely proportional to the number of the plane waves that couple to the resonance.

**Figure 81:** Light-trapping with the use of aperiodic grating on a back-reflector (yellow). *d* = 2m. *L* = 250 nm.

When the solar cell structure has a thickness and periodicity of the grating much larger than the incident radiation, the absorption enhancement factor does not overcome the 4n2 limit and nanophotonic effects are absent. They can occur only if the active layer thickness is much smaller than the impinging wavelength and/or the design structure determines a group index much larger than the refractive index of the active material.

**Figure 82:** Uper Part: The scattering layer consists of a square lattice of air groove patterns with periodicity L = 1200nm. The thicknesses of the scattering, cladding, and active layers are 80nm, 60nm, and 5nm respectively. The mirror layer is a perfect electric conductor. Lower Part: The profile of electric-field intensity for the fundamental waveguide mode. Fields are strongly confined in the active layer. To obtain the waveguide mode profile, the scattering layer is modelled by a uniform slab with an averaged dielectric constant [154].

The structure proposed by the authors in [154] is reported in Fig. **82** and consists of four layers. Starting from the bottom, the first is a perfect conductor layer and acts as a mirror for the guided wavelength that propagates into the 5nm thick active material which has a refractive index equal to (2.5)1/2. This layer therefore has a thickness lying in the deep-subwavelength range and satisfies the second requirement. The cladding layer, with thickness equal to 60nm, has a refractive index equal to (12.5)1/2. These characteristics ensure:


The 80 nm thick scattering layer designed with a periodicity larger than the investigated wavelengths ensures the coupling of the incident radiation into the nanoscale guided modes. Simulations of the entire structure show that the absorption enhancement factor reaches 119 which is well above the 4n<sup>2</sup> limit for both the active and cladding material demonstrating that nanophotonic light trapping effect can greatly enhance the light absorption, increase the solar cells performance and decrease their costs due to the reduced amount of utilized material.

#### **ACKNOWLEDGEMENT**

Declared none.

### **CONFLICT OF INTEREST**

The author(s) confirm that this chapter content has no conflict of interest.

#### **REFERENCES**


#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **467**



#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **469**



#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **471**



#### *Light Trapping in Thin Silicon Solar Cells Silicon Based Thin Film Solar Cells* **473**


© 2013 The Author(s). Published by Bentham Science Publisher. This is an open access chapter published under CC BY 4.0 https://creativecommons.org/licenses/by/4.0/legalcode

# **INDEX**

### **A**

*a*-Si 15-21, 37-42, 44-7, 164-6, 277-83, 286-99, 310-18, 320-4, 326-33, 337-9, 344-6, 359-66, 372-7, 386-9, 446-61 bare 463-4 c-Si/i 330 c-Si/i a-SiH/p 454 c-Si/n 321 deposition of 36, 38, 47-8 device quality 37, 128 edge of 280, 346 function of 288, 450 homogeneous deposition 49 investigated 198, 234, 236-7 mobility gap of 230, 237 n-type c-Si/n-type 318 obtained depositing 291, 454 oxidation of 203-4 p-type c-Si/p-type 318 protocrystalline 18, 21 single 455, 457 single couple of 451, 454, 457 stable 38, 387 thick 38, 288-9, 324, 429 thin 289, 291, 293 *a*-Si/c-Si interfaces, excellent 299 *a* -Si cell 12, 164 *a* -Si cylinders 463 *a* -Si emitter layer 339 *a* -Si film 202-3, 288 *a* -Si layer 345, 362, 463 doped 344 *a* -Si network 16, 281 *a* -Si solar cell 165 *a* -Si structures 117 *a* -Si1-xCx 108, 110, 117, 127, 130, 133, 136, 138 *a* -SiC 16, 40, 169-71, 361, 410, 416 *a* -SiGe 16, 361 *a* -SiH 328, 330, 453 Absorbance 130, 178-9, 423, 429 Absorber materials 10, 406 Absorbing layers 171, 382 Absorption 21, 41, 104, 109, 177, 180-2, 198, 317, 335, 368, 374, 416-17, 426-7, 429-32, 463-4

*Index Silicon Based Thin Film Solar Cells* **475**

Absorption coefficients 16-17, 41, 117-18, 134, 177-82, 184-6, 195, 198-9, 202, 208, 212-13, 220, 225, 359 low 10, 41-2, 46, 382 total 181-2, 184 Absorption processes 183 Acid, hydrofluoric 439, 443, 446 Acidic texturing, wet 438-9, 443 Activation energy 41, 43, 257, 318, 325, 346 Active layer 41, 137, 164, 360, 382, 416, 464-6 Active material 395, 463-5 ADIRR 201-4 AFM scan image 418-19, 424 Alloy triple-junction solar cell processor 52 AM1.5G spectrum 271-3 Amorphous 3-4, 10, 15, 19-21, 42-3, 125-7, 131-2, 140, 159, 167-9, 279-80, 290-1, 359-61, 402, 446-7 Amorphous films 161, 169, 324 Amorphous layers 19, 158, 325, 453, 455 doped 337, 346 Amorphous materials 17-18, 118, 140, 150, 159, 182, 293, 363, 369, 455 Amorphous matrix 91, 150, 159-60 Amorphous phase 11, 33, 43, 131, 134, 158, 160-1, 167, 290-1, 309, 370, 372 Amorphous semiconductors 182, 184, 216, 226, 229 Amorphous silicon 4, 9, 11, 15-16, 20, 29, 39, 117, 164, 166, 169, 360, 362-4, 368-9, 401 hydrogenated 108, 117, 158, 360, 372, 374 Amorphous silicon films 9, 360, 388 Amorphous silicon layer 21, 387 Amorphous silicon material 373, 377 Amorphous silicon modules 360 Amorphous silicon solar cells 157, 164, 379, 419 Amorphous silicon structure 167, 360 Amorphous solar cells 18, 376, 388 Amorphous superconductors 359 Amorphous thin films 169 Amorphous tissue 40, 369, 375, 380 Amorphous top cell 389 Amount 5, 9, 43, 45, 75-6, 281, 287, 300, 334, 365, 380, 396, 426, 439, 446 Analysis of thin films 157 Angle 85, 87, 99-100, 154-5, 201, 203, 206, 212-13, 215, 221, 231-3, 411-12, 431-2, 444-5, 447 Angle of incidence of radiation 187, 206, 212-13, 221 Angle of light incidence 189-90 Angular dependence 204, 213-14, 231, 233-4 Angular dependencies 204, 214, 235, 237 Angular reflectance transmittance Analyzer (ARTA) 422, 424 Annealing 18, 127, 132, 136, 169, 288-90 Annealing temperature 97, 132, 136-7

#### **476** *Silicon Based Thin Film Solar Cells Roberto Murri*

Anode 60, 62-3, 65-6, 70-1 Anti Reflection Coating (ARC) 5, 337, 339, 344, 397, 399-401, 441 Arrival rate 92-3, 95 Ashai U-type 417, 419-20 ASi, c-Si/n 322-3 ATLAS software 342-3, 346 Atmosphere 127, 129, 132, 309 Atmospheric Pressure Chemical Vapour Deposition (APCVD) 402-3 Atomic 94, 104, 146-7, 153, 169, 411, 417, 419 Atomic defects 308 Atomic force microscopy (AFM) 104, 146-7, 153, 157, 161, 165, 169-70, 198, 369, 417, 419 Atoms 14, 29, 35, 43, 58-62, 69, 79, 92-5, 99-101, 116, 245-6, 250-1, 281, 369, 402-3 anion 102-3 average number of 58, 60 element 102 single 94-5, 152-3 sputtered 59-60, 70, 74 surface binding energy of 58, 60 Average crystallite size 158, 160, 173 Average grain dimension 108

### **B**

Back amorphous-crystalline silicon heterojunction (BACH) 338 Back surface field (BSF) 318-22, 324, 329, 342, 442, 452, 455-6, 460 Band gap 10-11, 15-17, 109, 245, 247, 257, 445 graduated 3 Band structure 182, 243-4, 262 Barrier 310, 319-20, 322, 338, 346, 348, 454 Base contact 278, 318, 328, 335-9, 344-6 Basis 31, 152-5, 336 Beam splitter (BS) 114-16, 124 Beams diffracted 88, 152, 155 reflected 201, 205 Beams incident 217, 221, 235 Bending simulations 319, 328, 333, 453 Bias voltage 76, 314 BK-7 substrate, thick 196, 199, 202-4 Bonding 4, 37, 281, 294, 403 Bonds 37, 43, 77, 91, 116-17, 127, 131-3, 281, 292, 308-9, 373, 403-5 Boron 17, 34, 40, 164, 293, 334, 407-8 Boron depod ZnO (BZO) 425 Bottom cells 46, 158, 387 Boundary conditions 223, 230 Boundary layer 32, 445

Bragg reflector 395, 449 Breakdown 22, 62-3, 290 Breakdown voltage 365 Buffer layer thickness 288, 331-2 Buffer layers 32, 35, 133-4, 157, 164, 295, 299, 320, 322, 326, 338, 344, 346 i-a-Si 337 intrinsic 293, 295, 326, 341, 453 Built-in 286, 319-20, 332-3, 380 Bulk a-Si 198, 289, 297 Bulk materials 14, 125, 147, 155, 258-9, 263, 280, 297, 310, 445 Bulk plasma 39, 366

### **C**

C-Si 40-1, 43-6, 127-30, 134, 280, 286-7, 289-94, 298, 317-18, 320-4, 330-3, 362-6, 368-78, 380-1, 385-9 inward 448, 450 C-Si/a-Si 280, 293, 348 C-Si absorber 280, 317, 452 C-Si absorber material 280 C-Si base 311, 317, 320, 455 C-Si BSF 320-1 C-Si bulk 318, 448-50 C-Si cells 41 C-Si films 44-5, 368, 370 C-Si grains 364, 376 C-Si layers 41, 43-4, 46 C-Si photovoltaic layers 44 C-Si solar cells 42, 44, 46, 133, 310, 432, 434 C-Si solar cells series 133 C-Si substrate 159, 169, 287, 295, 297, 310, 451 doped 295, 320 C-Si surface 280, 286-7, 289, 291-3, 295, 297, 321, 324, 432, 435 doped 286-7 C-Si surface passivation 287, 291, 295, 342 C-Si surface passivation quality 290, 293 C-Si wafer 279, 288, 291, 293, 296, 311, 317-18, 322, 435, 447, 451 doped 296, 328 passivated 288, 311 C-Si wafer thinner 277-8 Cadmium telluride 3 Calculations 31, 193, 197, 201, 207, 214-15, 231, 236, 283 numerical 191-2, 201, 219, 230-1 Capacitance 269, 314, 316, 327 Capacitance transients 267-9 Capacitance values 268, 314-15, 320, 326

Capacitor 66-7, 326 Carbon content 117, 135-9, 169 Carceri 3, 81, 243 Carrier collection 346, 348, 389, 453-4 Carrier concentration 250, 262, 383, 409-10, 426 Carrier diffusion length 177-8, 217, 219, 231 Carrier photogeneration 182, 215-16 Carriers 8, 51, 109, 173, 183-5, 216, 221-2, 233-4, 244, 252, 264-5, 286-7, 297, 317, 379-80 extrinsic photogeneration of 181, 183-4 Cathode 58-9, 62-7, 70-1, 79 Cathode sheath 64-5, 69 Cell based 277, 279, 322, 343, 395, 401, 416 best 323, 335, 388 heterojunction 277-8, 335, 460-1 new 338, 366 real 20, 441 single-crystal 376, 437 Cell absorption 416, 447 Cell area 22, 335, 455 Cell characteristics 365, 380 Cell cost 382, 396, 458 Cell designs 171, 397 Cell efficiency 45, 164, 277, 291, 298, 338, 343, 348, 378, 396, 429, 460 higher 277, 318 Cell efficiency values, good 146 Cell front side 333, 406 Cell manufacturing 278-9, 416 Cell parameters, main solar 243 Cell performances 133, 169, 320, 334, 386, 443 c-Si Solar 133 Cell structures 24, 298-9, 317, 331, 340-1, 379, 429, 460, 463 Cell thickness 431-2 Cell window layer 416 Chain curve 193-5, 210-13, 215 Chamber 36, 38, 40, 66, 75, 78, 83-4, 149, 345 Characteristics, spectral 104, 192-5, 197, 213-14, 226 Charge 51, 67, 69, 261, 265-6, 281, 287, 289, 402, 404-5 Charge carriers 40, 82, 243-4, 249-52, 261, 265-7 Chemical vapor deposition (CVD) 3, 14, 29-36, 45, 53, 82, 133, 140, 158, 287, 359-60, 367, 374, 382, 401-2 Chemical solution deposition (CSD) 410 Chemical vapour deposition, enhanced 108 CIS and CIGS-based solar cells 361 Clusters 13, 40, 92, 94-5, 103 Coating layers 186, 191, 208, 213

*Index Silicon Based Thin Film Solar Cells* **479**

Coatings 29-30, 32-3, 35, 68, 115, 399, 456, 460 Coefficients 177, 180-1, 183, 187, 217, 227-8, 262 extinction 130-1, 178, 187, 411-12 relevant electronic transport 244, 262 thermal accommodation 93 Collisions 34, 37, 58, 61-2, 71, 77, 83, 403 inelastic 61-2, 365 Component system 93 Components 10, 77-9, 83-4, 93, 179, 182, 191, 195, 197, 200, 203, 205, 216-17, 219, 247-9 Components of absorption of light 177-8 Composition 29, 31, 68, 77, 81, 147, 150, 152, 169, 301-2, 439, 446 Compound semiconductors 81, 84, 92, 247, 251 Concentration 37, 40, 42, 182, 216-17, 222-3, 226-7, 243, 253, 261, 263, 265, 268, 283, 300-2 bond 116-18, 133 Conduction 17, 228-9, 245-7, 251, 254, 265, 404 Conduction band (CB) 6, 16, 103, 215, 230, 244-6, 265-7, 280-3, 296, 312, 318, 322, 373 Conduction process 17, 244-5, 247, 249 Conductivity 154, 217, 243-6, 249, 254, 262, 278, 324-5, 329, 332, 337, 345, 375-6, 408, 429 lighted 325 Conductivity tensor 243, 247-9 Configuration 47-51, 67, 90, 147, 155, 164, 182, 329, 377-9, 382-3, 386-7, 403, 416, 463 cluster 29, 51-2 cluster PECVD 52 in-line 29, 51 plasma box 47 superstrate 378-9, 382-3, 386 thin film cell 416 Constant 53, 62-3, 67-8, 93, 127, 153, 180-1, 185, 231, 254-5, 258, 268-9, 272-3, 295-6, 311-12 Constant photocurrent method (CPM) 184 Construction of solar cells 177 Contact layers 17, 382, 386 Contacts 17, 19, 157, 164, 172, 253-8, 263-4, 292, 333-4, 339-40, 342, 344-6, 382-3, 385-6, 448-9 doped 346-8 rear 8, 422, 447, 452 Contaminants 38, 51, 101-2, 300, 388 Contaminations 41, 43, 50, 53, 77, 83, 300, 302-3, 306-7, 317, 434 Convergent beam electron diffraction (CBED) 151 Conversion efficiency 3, 5, 8, 18-19, 23, 129-30, 272, 278-9, 326, 360, 362, 368, 389, 401 higher 3, 9, 377, 379 Copper indium diselenide 3 Copyright 117, 126, 128-32, 134-8, 149, 152-4, 159-63, 165-8, 170, 172-3, 426-7 Corning glass 138-9, 324, 425 Correlation energy 281, 283 Couples 154, 255, 430, 450-1, 454-5, 465 Cracks 42-3, 166, 254, 303-4, 441 Craters 135, 424, 426

#### **480** *Silicon Based Thin Film Solar Cells Roberto Murri*

Critical thickness hcrit 97 Crystal nucleation 3 Crystalline 10-11, 22, 33, 100, 109, 125-6, 130, 150, 156, 249, 366, 388 Crystalline silicon 17, 167, 281, 360, 369, 373-4, 405, 432 Crystalline silicon solar cells 5, 431 Crystalline volume fraction 42-3, 108, 126, 133, 135, 137-8, 364-5, 375, 381 Crystallinity 4, 11, 21, 44, 133-6, 173, 362, 372, 381 Crystallites 42, 44, 79, 100, 126-7, 139, 155, 159-60, 169, 446 Crystals 19, 81, 97, 99-102, 121, 160, 182, 251 Current density 63, 73, 172, 222-3, 247-8, 261, 311, 313-15, 320, 323, 330, 338, 341, 377, 389 Current voltage measurements 311, 315 Curves, broken 190, 193-5, 204, 210-15, 226 CVD coatings 32-3 CVD processes 30-3, 408 CVD reaction 29-30, 32-3 CVD techniques 30, 33, 35

### **D**

Damage 153, 303-6, 315, 365, 439, 459 Dangling bonds (DB) 37, 45, 90, 109, 127, 229-30, 280-2, 286-7, 289, 294-5, 307, 309, 313, 369, 373 Dark 6-7, 133, 257, 273, 310, 316-17, 319, 324-5, 328, 452-3 Dark condition 7, 313-15, 330, 453 DBR/Al 451, 456-8 DBR structure 451, 454-6 DC Diode 75 DC glow discharges 63, 66 DC sputtering 69, 78 Debye temperature 252-3 Deep level transient spectroscopy (DLTS) 16, 243, 266, 268 Deep states 16, 243, 265-6, 270, 373 Deep states properties 265-6 Defect concentration 283 Defect density 20, 40, 44, 133, 280, 283, 286, 292, 296-7, 310, 315, 318-20, 323, 326, 329 Defect distribution 280, 283-4, 316 Defect formation 283 Defect pool 281, 283, 285 Defects 16, 18, 20, 32, 41, 45, 83, 97, 100-1, 280-1, 283-5, 293-5, 320-1, 368-9, 373 interstitial 101, 281 neutral 284-5 self-interstitial 101 Deformation, acoustic 251-2 Degradation, light-induced 46, 108, 361, 364, 374, 389 Density 11, 14, 16, 18, 23, 45, 61, 65, 76, 165, 184, 230, 244, 284-5, 435

Density of states (DoS) 3, 11, 16-18, 20, 154, 184, 227-9, 232-6, 280-1, 284, 286-7, 295-8, 312, 316, 323, 453 Dependence 119-20, 136, 203, 213-14, 216, 222, 231, 233-4, 294, 309, 313-14, 332, 337, 381, 398 Depletion region 17, 263, 270, 313, 317, 320, 326 Deposit 16, 23, 42, 53, 60, 68, 77, 164, 295, 305, 332, 344, 346, 368, 428 Deposited layers 19, 39, 340 Deposition 10-11, 23, 34-5, 38-40, 44-5, 83-4, 98-9, 278, 344-6, 359-60, 363, 365, 375, 388, 401-3 epitaxial 102-3 high quality 47 ion-assisted 77 large area 15, 46, 49-50, 162 low temperature 29, 387-8 n-a-Si 344 sputter 59, 66, 68, 78-9, 408 uniform 37-8, 47, 49 Deposition chambers 31, 33, 47, 51, 82, 102 Deposition conditions 11, 14, 16, 36, 43, 158, 163, 290, 295, 332, 359, 363, 369, 388, 401 Deposition kinetics 31 Deposition parameters 3, 10, 15-16, 19-20, 33, 50-1, 166, 366, 373, 382, 385, 403-4 Deposition process 15, 29, 45, 50-1, 59, 77, 79, 81, 84-5, 170, 186, 250, 362-3, 367, 435 Deposition process parameters 334, 415 Deposition rates 29, 35-6, 38-9, 44-5, 48, 69, 71-2, 89, 92-3, 365, 368, 402 higher 38-9, 46, 75, 366 low 36, 38, 75, 166, 381, 402 very high 39-40 Deposition sequence 382-3 Deposition system, in-line 51 Deposition techniques 3, 22, 29-30, 35, 38, 47, 133, 363-4, 366, 382, 388, 408 Deposition temperature 22, 35, 162, 287, 290-1, 296-7, 334, 403, 408-9, 415, 426 Depth 104, 135, 158, 169, 186-7, 212, 228, 426, 445 Design 3-4, 16, 19, 22, 31, 47, 52, 121, 163-4, 171, 243, 377-80, 429, 433, 463-4 Development 3, 10-11, 22, 29-30, 34-5, 46, 51, 53, 119, 177, 257, 270, 333, 360, 432-3 Device thickness 395-6 Devices 3, 7, 9, 23, 35, 129-30, 177, 272-3, 311, 326, 344-6, 368, 379-80, 395-6, 416 electronic 4, 10, 243, 246 optoelectronic 247, 373 photovoltaic 5-6, 9, 21, 35, 360 DHF 300-1, 305-7 DHF-dip 306-7, 309 Dielectric bragg reflector (DBR) 449-52, 454-8, 461, 463-4 Dielectric films 178, 185, 397-8, 454 Diffraction patterns 19, 89, 151-2, 155, 159-60, 167 Diffusion coefficient 93-4, 101, 222, 293 Diffusion energy 94, 294 Dilution 20, 31, 36, 38, 42-3, 45, 180, 324, 329, 367, 371-2 Dilution ratio 3, 19-20

Dimensions 14, 103, 113, 221, 243, 255, 257, 259, 437 Direct film transfer (DFT) 459 Direction 91, 97, 120-1, 182, 188, 201, 205, 216-17, 220-1, 248, 261, 263, 396, 426, 447 Discharge 63, 65-7, 69, 71, 73 Distance, increasing 210, 212, 220 Distribution 17, 48, 173, 177, 184-5, 193, 223, 229, 232, 237, 281, 283, 296-7, 309, 314-15 energy band 280-1 spatial 177, 199, 201, 205, 212-13, 220-1, 238 Dit values 305 DIW 300-1, 305-6 DIW rinsing 305 DLTS signal 269-70 DLTS technique 243, 267-8, 270 Donor-like states 227-9, 233-4, 237 Donors 17, 246-7, 294, 404 Doped a-Si 40-1, 229, 278, 284-6, 293, 295-6, 317-19, 324, 326, 333, 335, 342-5, 453 Doped c-Si 296, 317, 319-20, 322, 324 Doped layers 38, 287, 293, 295, 299, 324, 336-7, 345, 380, 419 Doping 15-17, 40-1, 81, 102-3, 146, 277, 293-4, 320, 322, 329, 360, 446-7 Doping concentrations 318, 324, 326 Doping level 280, 411-13 Doping of a-Si 294-5 Doping ratio 135-6, 324, 326 DOS parameters 231-2, 236 Drying 302-3, 334 Dual Beam Photoconductivity (DBP) 20

#### **E**

E-beam 339-40, 345, 455 Effect, mirroring 460-1, 463 Effective lifetime 288-9, 292, 305 Efficacy 454-5, 463 Efficiency of photogeneration of free carriers 177 Effusion cells 82, 84-5 Electric field 11, 61-6, 70-2, 76-7, 119-20, 147, 187-9, 192, 205, 209, 218, 261, 263-4, 379-80, 403 Electric vector 185-9, 191-2, 205-6, 209-10, 213-15, 218 Electrical conductivity 40, 46, 216, 222, 243, 248, 253, 359 Electrical properties of semiconductors 243, 245, 247, 249, 251, 253, 255, 257, 259, 261, 263, 265, 267, 269, 271 Electrode gap 365 small 366-7 Electrode spacing 37-8 Electrodes 29, 34, 36, 39, 45, 47-9, 60, 62-5, 67, 69-70, 216-18, 220, 361, 365, 378 ladder-shaped 47-8 transparent 378-9

Electron beam 86-7, 89, 147-8, 152 high-energy 147, 150 Electron beam evaporation 77, 363 Electron concentration 185, 86-7, 266 Electron density 61, 65, 365 high 38, 44 Electron Energy Loss Spectroscopy (EELS) 152 Electron gun 87 Electron holes 245, 247 Electron mobility 170, 245, 247, 251 Electron sources 78, 147 Electron states 177-8, 244 Electron transport 373, 376 Electron trap 266 Electronic properties 16, 165, 389 Electronic states 121, 230-1, 236-7 density of 237 Electronic states parameters 177, 226 Electrons 4-6, 60-7, 70-1, 75, 77, 147-52, 222-3, 227-8, 244-7, 249-51, 280-4, 294-5, 373, 380, 403-6 backscattered 147, 149 donor 246 drift mobilities of 183, 222 equilibrium concentrations of 223, 229 hot 14, 365 photogenerated 40, 183 photogeneration of 183 recombination rates of 222 valence 245-6 Emitter contacts 339, 348 Emitter layer 293, 317, 320, 324, 326, 344 Encapsulation 441-3 Energy adsorption 93-4 binding 58, 60, 246 free 31, 96, 281 potential 62 unit 227, 229 Energy gap 3, 6, 41, 43, 178, 181-3, 215-16, 231, 233, 245, 250-1, 280, 282, 298, 318 Energy gap values 233, 245 Energy input 10, 63 Energy pay-back time (EPBT) 10 Energy position 265, 267, 295, 298 Entropy 103, 282-3 Envelopes 190, 193-4, 196-8 Epi-layer 291

#### **484** *Silicon Based Thin Film Solar Cells Roberto Murri*

Epi-Si 290-2 Epilayer 96-9, 291, 320 Epitaxial films 81, 96, 99, 257, 263, 289 Epitaxial layer 4, 32, 82, 89, 97 Equilibrium 14, 66, 136, 229, 281-2, 288, 403, 405 Equivalent circuit 6, 8-9 Estimate sample thickness 190 Etched surface 303, 305, 424, 442 Etching 45, 58, 159, 301, 341, 344, 367, 431, 441, 443, 446 Evaporation 10, 68, 86-7, 278, 339 Excitation frequency 23, 36, 38, 44-5, 47-8 Excitations 61, 118-19, 121, 135, 402 Experimental conditions 32-3, 35, 214, 219, 231 Experimental data 103, 197, 204, 237, 252, 288, 293, 316, 450-1, 456 External reflectance thickness 456, 460

### **F**

Fabrication of semiconductor devices 102, 300 Fermi energy 244, 380 Fermi level 17, 46, 229, 280-1, 283, 293, 295-7, 312, 314, 322, 326, 329, 406 quasi 286, 320-1 Field 29, 47, 61, 66, 70-1, 73, 87, 146, 158, 173, 248, 259, 262, 303, 367 Fill Factor 8, 337-8, 342, 458 Film growth 21, 37, 76, 81, 87, 95, 159, 297, 363, 365-6 Film structure 3-4, 16, 19, 189, 376 Film thickness 19, 47, 166, 168, 177, 186, 190, 193, 197-8, 214, 257, 296, 324, 326, 408-10 Films air-semiconductor 186 based 108-9, 133 deposited 18-19, 68, 76, 79, 401 doped 40, 295 evaporated 68, 78 growing 37, 69, 79, 81, 93 hydrogenated amorphous silicon carbon 117, 129 intrinsic 40-1, 128, 296 investigated 209, 260 multilayer 132, 137 obtained 402-3 polycrystalline 4, 169 protocrystalline 3, 19 relatively thick 190, 196 resulting 74, 363 rich 403 semiconducting 157-8 silicon-based 158, 160-1

 single 188, 196, 216 thick 225-6, 403 thicker 96 uniform 13, 37 Films for solar cells 128 Films growth 295-6 Filter 121-2, 124 Flow rates 29 Fluorescence 121, 123-5 Fluxes 77, 79, 85-6, 92, 329 Focused ion beam (FIB) 104 Formation 10, 34, 38, 43, 45, 60-2, 73, 82, 91, 94, 100, 104, 127, 131-3, 136 Forward bias 267, 311, 313-14 Fourier spectroscopy 111 Fourier transform 108-10, 113-15 Fourier transform spectroscopy 110, 112-13 Free carriers 6, 16-17, 110, 177, 183-4, 216-17, 221, 230, 286 Free electrons 73, 103, 177, 183, 228, 365, 368, 373, 403 Frequencies 21, 29, 39, 44, 47, 66, 109-11, 113, 115-16, 119, 123, 271, 314, 326, 373 plasma excitation 366 radio 21, 34-5, 61, 63, 254, 260 Front cell thickness 395 Front contact layer 162, 164 Front surface 5, 24, 188, 206-9, 212, 214, 218, 220, 271, 337, 397, 431-2, 434, 437, 443 Front surface reflection coefficient 207 Front ZnO layers 420, 428 FTIR 108-10, 127 FTIR and Raman spectroscopy 108-10 FTIR spectroscopy 109-15, 117, 127, 129, 133 FTIR technique 110-11 Function of doping dilution 326 Function of film thickness 326, 409 Function of oxygen flux 415 FWHM 118, 129-32, 156-7, 167 FZ c-Si 288-9

### **G**

Gap region 338, 342-3, 348 Gas 3, 15, 36, 38, 58-63, 68, 104, 162, 164, 185, 247, 360, 363, 367, 402 reactive 60, 68, 74-5 Gas atoms 60-1 Gas flow sputtering 78 Gas mixture 34, 39, 325, 329, 365, 367, 402-3 Gas precursors 31, 33, 162 Gaussian distribution 132, 191-3, 195, 208, 211-12, 218, 230, 232, 283-4 Geometries 36, 72-3, 90-1, 155, 254, 257, 263, 342, 380, 432-3 Glass 4, 9, 11, 20, 23, 35, 50, 68, 160, 166-7, 279, 371, 378, 411-12, 416 Glass substrate 4, 11, 49, 157, 360, 379, 382, 411-12, 430, 447 Glow discharge 34-5, 58, 60-3, 173 Glow region, negative 63-5 Graded energy gap semiconductors 177, 216 Grain boundaries 23, 41, 100, 109, 125, 128, 152, 158, 368-9, 375-6, 381, 441 Grain dimensions 167, 381 Grains 43, 100, 167-9, 369, 437, 440-1 Growing 36, 44, 77, 97, 359-60 Growth heteroepitaxial 92 layer-by-layer 69, 95 Growth chamber 83, 89 Growth conditions 14, 16, 81, 103, 368 Growth mechanisms 3, 21, 30-2, 82, 89, 166 Growth modes 96 Growth of high-quality a-Si 37-8 Growth parameters 104 Growth processes 10, 15, 18, 87, 93-5, 146, 157, 166, 250 Growth rate 38, 44-5, 82, 86, 365, 367, 369, 451 Growth techniques 81-2 Growth temperatures 98, 104 GZO films 164

### **H**

H/a-Si 311, 315, 366, 368-9, 374 H-based solar cell 379 H/c-Si 159, 164, 277, 298, 310, 406 H/c-Si/a-Si 406, 451, 458 H/c-Si cells 165 H/c-Si heterojunction 345, 454, 460 H/c-Si heterojunction cell 333 H/c-Si heterojunction cell fabrication processes 278 H/c-Si heterojunction solar cell 452, 457 H/c-Si heterostructure 335, 452 H/c-Si heterostructure solar cells 414, 452 H/c-Si HJ 327-8 H/c-Si HJ sample 297 H/c-Si interface 165, 287, 290, 295, 297-9, 309, 326, 346, 457 H/c-Si interface defects 346, 348 H/c-Si p-type HJ sample 311, 315 H/c-Si Solar Cell 317, 452 H/i-a-Si 319 H/p-a-Si 330, 452

*Index Silicon Based Thin Film Solar Cells* **487**

H/p-cSi HJ solar cell 327 H/SiC multilayers 108, 133 H/SiNx 344, 346, 450-1, 454-8 H/SiNx/Al 450-1, 456-8 H/SiNx structures 454 H-terminated Si surfaces 301, 308-9 H/μc-Si 362, 368 Hall coefficient 243, 254, 256-7, 261-4 Hall coefficient measurement 264 Hall coefficient value 263, 265 Hall effect 243, 260-1, 263-4 Hall mobility 243, 256, 260, 262, 264, 407-8 Haze 395, 417-18, 420, 426 Heterojunction 3-4, 10, 164, 277, 280, 326, 329-30, 339, 344, 395, 401, 454 Heterostructure 320, 328-9, 339, 452-5, 459 Heterostructure cell 333, 406 double 319 HF-dip 307-8 High deposition rates 21, 23, 39, 44-5, 47-8, 367-8, 403 High frequency 29 High-quality a-Si 37-8 High resolution (HR) 112, 122, 124, 159 High-resolution transmission electron microscopy (HRTEM) 173, 291 High stretching mode (HSM) 128 High substrate temperatures 43, 166 High temperature deposition 22-3 High temperatures 127, 247, 268-9, 314, 335, 342, 401-2 HJ cell efficiencies 288, 327-8 HJ cell efficiencies and IPL 326 HJ cells 277, 318, 320, 324, 332, 334-5 similar 322, 329 HJ n-cSi 320 HJ samples 288, 291 HJ solar cell 288, 293, 310, 317, 322-3, 332 HJ solar cell efficiency 288 HJ solar cell technology 334 HJ solar cells performances 309 HJ structure 318-19, 321 Hole collection 320-1, 329, 377, 380 Holes 5-6, 104, 177-8, 182-3, 222-3, 227-9, 245-7, 266, 286-7, 321, 346, 373, 377, 380, 443 Homojunction c-Si 278 Hot plate (HP) 291-2 Hot wire (HW) 30, 33-4, 133, 367, 374, 402 Hot wire chemical vapor deposition (HWCVD) 34-5, 133-4, 402 HWCVD solar cells 133, 375 HWCVD solar cells series 134

Hydrogen 15-16, 18, 20, 90, 109, 129, 135, 281-2, 287, 292-3, 360, 373, 388, 401-2, 405 Hydrogen content 288-9, 375, 401, 403 Hydrogen dilution 15, 20-1, 126, 136, 140, 161, 383, 388 Hydrogen effusion 293, 295 Hydrogenated microcrystalline silicon films 117 Hydrogenated silicon films 158, 160

### **I**

I-a-Si 346, 455 I-layer 38, 134-5, 364, 380, 386, 389 IBC cells 335, 338, 343 IBC-HJ solar cells 336 IBC-SHJ cell 337-8, 340 IBC solar cell 335 Ideal solar cell 6-7 IL 7, 271, 273 Illumination 6-7, 18, 151, 185, 188-9, 192, 198, 201, 208-9, 216, 218, 226, 235, 272-3, 374 Illumination conditions 273 Illumination intensity 185, 215, 223, 225-7, 232-3, 235, 238, 271 Imperfections 249-50 Impinging wavelengths 463-5 Impurities 9, 47, 69, 81, 84, 101, 109-10, 117, 223, 246-7, 249-50, 265, 300, 359, 407 Impurity and defect levels 265, 359 Incidence 87, 89, 187, 206, 212-13, 221 angle of 24, 87, 155, 190, 203, 205, 213-14, 217, 220 plane of 185-9, 191-2, 202, 205-6, 209-10, 213-15, 218 Incident 76, 88, 119, 121, 218, 417-18 Incident light 119, 205, 207, 397-8, 416-17, 423, 428, 447 Incident photons 118, 212, 214-16 Incident radiation 110, 179, 464-6 Indium tin oxide (ITO) 162-3, 291-2, 333-4, 337, 341, 382-3, 407, 412-14, 416, 463 Industrial multi-crystalline silicon solar cells 439 Influence, evident 231-4 Influence of Optimised Wet-Chemical Treatment on Test HJ Solar Cells 309 Influence of Sample Parameters and Experimental Conditions 208 Information 110, 140, 146-7, 152-5, 158, 185, 236, 250, 265, 271, 313, 371-2, 443 Inset 117, 130-1, 160-1, 289, 292, 410-11 Insulators 75, 81, 244-5, 339, 359 Interact 81, 249, 251, 265-6 Interaction 13, 18, 61, 116, 120, 147, 152-3, 245, 249, 251 Interdigitated Back Contact (IBC) 335-6, 344 Interdigitated contact solar cell 344 Interface 21, 146, 164, 186-7, 223, 280, 285-92, 297-9, 319-20, 322-4, 326, 333, 420-3, 428, 453 first 397 rough 188, 407, 416-17, 420, 422 Interface plane 97

Interface state densities 165, 305 Interference 87, 192, 200, 207, 209, 214, 218-19, 221, 238, 429-30 Interference effects 207, 213-16, 397 Interference fringes 190, 193-6, 198, 212-13, 216, 224, 447 Interferogram 110, 114-15 Interferometer 110-11, 113-16, 121 Interlayers 21 Intermediate layer, transparent 387-8 Intermediate reflecting layer (IRL) 428-9 Intrinsic a-Si 40, 281, 285, 287, 289, 293, 295-6, 320, 322, 337, 344-6, 373, 429 Intrinsic layer 11, 18, 21, 38, 41-2, 50, 129, 140, 164, 288, 295, 299, 368, 380, 422-3 Intrinsic semiconductors 246 Ion-assisted deposition (IAD) 77 Ion-beam sputtering (IBS) 77 Ion bombardment 45, 79, 365-6 Ionization 58-9, 61, 65, 71, 155, 250 Ions 34-5, 58-61, 63-6, 69, 77-9, 301, 367, 403 positive 59-60, 366 IPL of a-Si 327-8 IQE 337, 345, 347, 455-7 IR radiation 116 IR spectra of hydrogenated microcrystalline silicon films 117 ITO films 163, 332-3, 412, 414 IV characteristics, lighted 319-20

### **J**

Jsc 134, 164, 309, 323-4, 329, 335, 337-8, 342-5, 400, 422, 426, 428, 430-1, 458-9 Junction 3, 5-6, 10, 40-1, 263, 267, 273, 286, 291, 303, 314, 318, 432

### **K**

Kaufman source 77-8 Kinetic energy 62, 87, 302, 403

### **L**

Large areas 29, 43, 46-8, 50, 52, 164, 365, 419 Large scale thin films deposition 47 Laser treatment 169-71, 395, 455 Lasers 23, 30, 116, 119, 121, 123-5, 233, 247, 401, 431, 443, 454, 456, 458 visible 121, 123-4 Lattice 40, 92, 100-1, 119, 373 Lattice atoms 251 Lattice parameters 94, 97-8 Lattice structure 250

Lattice vibrations 250 Layer-by-layer 96 Layer depositions 22, 50, 315-16, 329, 454 subsequent 307, 309 Layer growth 41, 295 subsequent thin film 300 Layer Parameters 456, 460 Layer structure, double 191-2, 196, 199, 208-10, 217, 223 Layer thickness 98, 133, 189, 259, 329, 346, 426 intrinsic 46, 346, 422 Layer transfer processes 22-3 Layers a-SiNx 455 dielectric 399-400 extra 99-100 first 96, 162, 289, 295, 297, 379 textured 445 thicker 96, 289, 295, 297 topmost 91 type 40 Lenses 122, 148-9, 151 electromagnetic 147, 150-1 objective 124, 148-9, 151-2 Lifetime 17, 182-3, 185, 265, 277, 288, 292, 305-6, 376, 380, 389, 395, 405-6 Light 3-5, 7, 10-11, 23-4, 118-19, 171, 177-8, 182, 194-5, 325, 382-3, 396-7, 416-17, 431-3, 447 inelastic scattering of 118-19 reflected 5, 421, 423, 432, 447 scattered 109, 119-22, 124, 418, 422 scattered sun 406-7 second component of 195 wave nature of 177 Light absorption 3-4, 24, 162, 171, 177-9, 182, 220, 380, 395-6, 416, 447, 464, 466 Light confinement 395-6 Light incidence 189-90 Light intensity 185, 238 Light scattering 162, 217, 385, 397, 408, 416-17, 426 Light soaking 3 Light trapping 23-4, 164, 207, 376, 382, 385-6, 389, 395-6, 406-8, 410, 416, 432, 463 Light-trapping 432, 442, 465 Light trapping mechanisms 23-4, 34 Limitations 66, 122-4, 295, 360-1, 388 Longitudinal 125, 251-2 Losses 9, 108, 122, 124, 188, 271-2, 291, 293 Low temperature process, using 277-8 Low temperatures 15, 34, 40, 244, 252, 288, 290, 293, 332, 336, 341, 363-4, 370, 386 LPCVD (Low Pressure Chemical Vapor Deposition) 33-4, 383, 402-3, 408, 428

LSM (low stretching mode) 128

### **M**

Magnetic field 70-1, 74, 77, 182, 215, 223, 247-9, 254, 256-7, 263-4 Magnetrons 70-2, 76-7 Market 3, 9-10, 46, 121, 359-61, 417, 431, 459 Material properties 14-15, 158, 265, 359, 365 Material SiH4 455 Materials 3-6, 10, 16, 67-8, 108-9, 146-7, 154-5, 243-7, 283, 300, 317-18, 359-60, 364, 372-4, 396-8 a-Si alloys 15 crystalline structure of 154 device grade 128-9 investigated 173, 177-8, 185, 198, 218, 234, 249, 253 nanocrystalline 81 new 140, 360-1 sputtered 68, 77 undoped 283, 285 Matrix 101, 109, 129, 132, 136, 138, 179, 443 Matter 116, 118, 152, 154, 303, 365 Maximum intensities 88, 129, 156, 200-1, 203, 205 Mc-Si 329, 374-6, 452, 458 Mean free path (MFP) 14, 62, 69, 71, 78-9, 83, 367 Measurements, c-Si layer 46 Medium range order (MRO) 108, 133, 140 Metal contacts 271, 277, 321-3, 332, 341, 401, 437 Metal electrode 406, 453-4, 459 Metal-Organic Chemical Vapor Deposition (MOCVD) 35, 82 Methods, contactless 186, 253-4, 260 Michelson interferometer 110, 113-16 Micro-wave (MW) 36, 39, 45, 260, 291-2, 360, 435, 455 Microcrystalline 3, 16, 19-20, 41-4, 109, 126-7, 129, 131, 146, 366, 377, 386, 389, 406 Microcrystalline films 15, 45, 375 Microcrystalline phases 19, 21, 131, 369-70 Microcrystalline silicon 29, 36, 39, 46, 108, 117, 127, 140, 166, 290, 320, 359-62, 364, 374-5, 388-9 Microcrystalline silicon cell 165, 381, 386-7 Microcrystalline silicon films preparations 37 Microcrystalline silicon layers 46, 127, 387 Microcrystalline silicon solar cells 108, 140, 376 Microcrystalline silicon thin film solar cells 11 Microcrystallinity 19-21 Microelectronic 29, 34-5, 317, 454 Micromorph cells, tandem 428-9 Micromorph tandem cell 12, 386, 428 Micromorph tandem cell concept 361, 377

Micromorph tandem silicon solar cells 386

Microscope 124-5, 147, 150-2, 154


Microstructure evolution 15, 45

Microstructure factor 108, 128


 moving 114-16 Misfit dislocations 96-8


vibrational 108


### **N**

N-a-Si 319, 322, 324, 340, 344-5, 455 N-type 17, 41-3, 186, 279, 283-8, 295-6, 298, 317, 319-20, 324, 326, 333, 335, 338-40, 428 N-type a-Si 11, 41, 291, 296, 315, 318, 321, 324, 329, 336, 343-4, 346, 404, 420-1, 452 dark condition of 311 N-type c-Si 318, 320, 322, 324, 333, 344, 452, 460 N-type c-Si base 318, 324 N-type c-Si wafer 279, 322, 343 N-type doping 102-3, 294, 447, 456, 461 N-type layers 18, 378, 380 N-type semiconductor 266, 407 N-type Si 269-70 N-type wafers 338, 342, 344 Nano-crystalline silicon films 140, 159 Nanocrystalline silicon films 125-7, 133, 140 Nanocrystalline silicon solar cells 140 Nanocrystals 104, 109, 125, 136, 157, 369, 371

Nanostructured films 109, 136 Nanostructured silicon carbon films 108, 127, 133, 136 Nanostructures 14, 146-7, 157, 171 Native oxide films, layer-by-layer growth of 309 Nc-Si 4, 158, 364 Negative glow 63-6 NH4F solutions 301, 306-7 Nitrogen 36, 38, 403-4, 412 Normalized photovoltaic parameters 460-1 Nowak, Marian 177-8, 180, 182, 184, 186, 188, 190, 192, 194, 196, 198, 200, 202, 204, 206 Nucleation 15, 19, 43, 81, 92-5 Numerical model 277, 315, 395

### **O**

Ohmic contacts 253-7, 264, 322 good 254, 324 Open circuit voltage 24, 39, 164, 271-2, 277, 311, 380-1 Optical absorption 10, 21, 180, 182, 361, 383, 385 Optical inhomogeneity 177, 186, 204 Optical parameters 178, 185-6, 201, 206, 208, 219, 231, 238 values of 179, 186, 192, 212, 221 Optical properties 76, 109, 163, 177-8, 182, 234, 332, 337, 359, 363, 372-3, 382-3, 385, 389, 446-7 Optical Properties of Semiconductor 179, 181, 183, 185, 187, 189, 191, 193, 195, 197, 199, 201, 203, 205, 207 Optical properties of semiconductors 177, 238 Optical transmittance 180-1, 184, 188-9, 193-5, 197-8, 225, 234 spectral characteristics of 193-6 Optoelectronic applications 34-5 Oscillations 63, 89, 153, 213-14 Oxidation, initial phase of 308-9 Oxide removal 90, 305-8 Oxides, p-layer/tin 138-9 Oxygen 38, 43, 46, 68, 109, 117, 127, 132, 198, 308-9, 388, 401, 415, 435 Oxygen impurities 108-9, 127

### **P**

P-layer 40, 137, 377, 380, 382-3 P-type 11, 17, 41, 136, 280, 284-6, 289, 291-2, 295-6, 317-18, 324, 333, 339-40, 342-6, 380 P-type a-Si 11, 41, 283, 317-18, 324, 329, 336-7, 340, 343, 345-6 P-type a-SiC 17, 429 P-type c-Si 279, 318, 320, 329, 343 P-type-c-Si/i-a-Si 328, 453 P-type c-Si wafer 329, 448 P-type doping 102-3, 247, 294, 456, 461

#### **494** *Silicon Based Thin Film Solar Cells Roberto Murri*

P-type layer 376-7 P-type semiconductor 183, 266 P-type substrates 309, 342 Pairs, electron-hole 3, 6, 149-50, 368, 380, 397 Parallel plate plasma deposition 366-8 Parameter Initial Values 236-7 Parameters fitted 198, 203-4, 234-7 geometrical 202, 205, 214, 219-20 measured 260 values of 21, 204, 219, 221, 233-5 Parameters of electron states 177-8 Parasitic resistances 3 Particles 13, 32, 62-3, 65, 180, 299-300, 302 Passivated Emitter solar cell (PESC) 436 Passivation 41, 286, 288-9, 292-3, 295, 305, 336-7, 400 Path 62, 171, 180, 280, 312, 339 Path difference 114-16 Path length, optical 396, 447, 461 Pauw geometry 243, 254-7, 264 PC 16, 182, 223-6, 234, 257, 457 PC responses 225-6 PD 455 Peak intensity 371, 405 Peak position 125, 129-32 Peaks 16, 115-18, 125-7, 137, 155, 157, 160-1, 167, 267-9, 283, 291-2, 312, 371-2, 404-5 PECVD solar cells 134 PECVD system 29, 36-7, 138, 140, 288, 403 PECVD technique 18, 23, 41, 364, 366 PEM effect 182-4, 222-3 PEM responses, ratio of 185 Performance 20, 103-4, 123, 157, 164, 166, 172, 177, 310, 324, 329, 332, 335, 436, 454 Permission 117, 126, 128-32, 134-9, 148-9, 152-4, 159-63, 165-8, 170, 172-3, 363, 374, 376, 381, 426-7 Phases 19-21, 109, 115, 125, 128-9, 187-92, 195-6, 201, 207-12, 214, 218, 290, 361, 397 mixed 19, 21, 291 Phonons 118-19, 125, 180-1, 245, 250-1 optical 118, 251-2 Photoconductivity 16, 18, 41, 43, 177, 182, 185, 216-17, 220, 224-6, 231, 235 Photothermal deflection spectroscopy (PDS) 20 Photogeneration 41, 177, 183, 216, 222 Photolithographic 436-7 Photolithography 339-40, 344, 432, 437-8, 454 Photolithography steps 336-7, 339, 342, 434-5 Photon energies 3, 16, 179, 183-5, 215-16, 225-7, 291, 295, 298, 374, 445

Photons 5-6, 10, 16, 61, 118, 147-8, 171, 177, 182-3, 185, 206, 209-10, 212, 218, 421

*Index Silicon Based Thin Film Solar Cells* **495**

 low-energy 104 scattered 118 Photovoltaic parameters 22, 322-3, 332, 335, 343-4, 460 Photovoltaics 24, 29, 34, 46, 81, 108, 140, 341, 359, 400-1 Physical properties 4, 9-10, 14, 19, 41, 43, 118, 244 Physical sputtering 58, 60, 79 Physical vapor deposition (PVD) 59, 79 Pitch 71, 104, 172, 341, 458 Plane 101, 160, 185-9, 191-2, 202, 209-10, 213-15, 217-19, 261, 403 Plasma 29-30, 32-5, 37-40, 42-4, 47, 49, 58, 60-2, 65-7, 70-1, 73, 315-17, 365-7, 382-3, 401-2 Plasma deposition 10, 29, 329 conventional 44, 366 Plasma enhanced chemical vapour deposition (PECVD) 3-4, 15-16, 18-19, 21, 23, 34-6, 40, 82, 133-4, 158-9, 166, 287, 317, 360, 398, 401-3, 454 Plasma etching 164-5 Plasma process 395 Plasma texturing 435, 441 Plasma treatment 277, 315 Plasmonic thin-film solar cells 466 Point defects 101, 250 Polarization 201, 204, 206, 213-15, 219-21, 235 Polarized radiation 185-9, 191-2, 203-4, 209-10, 213-15, 218-19 Powder, silicon polyhydride 38 Pressure 14, 18, 31, 33, 37, 69, 71, 73, 78, 83, 85, 257, 365-7, 373, 402 total 74-5, 82 working 315, 408-9 PRF 455 Probability 61-2, 71, 77, 228, 280, 421 Probes 147, 152-3, 257-9 Process temperatures, low 401-2 Processes collision 61-2, 249-52 wet 435 Processing, based 436-7 Production system 29, 47, 50, 396 Properties, optoelectronic 39-40, 425 Protocrystalline 3, 18, 20 PV cells 271-3, 396 Pyramid structures, inverted 433 Pyramids 103, 304-6, 441 distributed 166, 303, 307-8 inverted 432-5, 438

## **Q**

Quality

#### **496** *Silicon Based Thin Film Solar Cells Roberto Murri*

 best microcrystalline solar cells 43 high 46, 48, 299, 408 Quantum dots 14, 81-2, 109, 173 Quantum Efficiencies 457 Quantum efficiency 177, 311, 313, 327, 395, 421 Quantum efficiency coefficients (QECs) 177, 183-4, 225

### **R**

Radiation 109-12, 114, 116, 119, 177-8, 180, 185, 187, 189-93, 199-201, 204-18, 220-3, 225, 234-5, 237 absorbed 179, 184-5, 214 absorption of 207, 213, 216 interference of 210, 216, 218-19 perfect coherence of 190-1, 208 plane-polarized 205-6, 214, 217 reflected 192, 200-1, 205, 207, 209, 218 transmitted 177, 199 Radiation incidence 186, 192, 200, 203-4, 214-15, 221 Radiation incident 5, 206, 209-10, 218, 235, 238 Radiation intensity 185, 188, 200-1, 204-8, 210-14, 216-18, 220-1, 225, 234-5 spatial distribution of 177, 206-7, 211-13, 216, 219-21 Radiation of a-Si 181, 183-4 Radiation traversing, phase of 218 Radiation wavelength bandwidth 193-4 Radicals 37-8, 40-1, 79, 403 Radio frequency (RF) 21, 34-5, 38, 61-3, 66, 69, 76, 254, 260, 288, 363 Raman scattering 108, 118-21, 123, 133-4, 178 Raman signal 120-2 Raman spectra 125-6, 136-8, 140, 173 Raman spectra of samples 139 Raman spectroscopy 108-10, 119, 121-5, 127, 133, 135-6, 140, 169, 173 Raman spectroscopy apparatus 121-2 Raman spectrum 118, 372 Rate electron emission 266 high 44-5, 47, 49, 69, 368 Rate window 268-70 Ratio 11, 14, 22, 24, 29, 66, 93, 112-14, 178-80, 185, 187, 212-15, 231-2, 235-6, 413-14 angular dependence of 232-3 Reaction 29-30, 32, 35, 281, 283, 306, 402-3, 439 Reactive sputtering 69, 74-5 Reactor 18, 32, 35-7, 44, 50, 402-3, 435 Rear side 218, 320, 322, 329, 333-4, 338, 341, 345-6, 348, 395-6, 416, 449, 451-2, 454-5 Rear side c-Si/a-Si 322 Rear side of HJ solar cell 322-3

Recombination 61, 66, 177, 222-3, 229, 234, 280, 285-7, 310, 324, 326, 330, 346-7, 404, 453-4 Reduction 22-3, 30, 39, 41, 44-5, 71, 109, 124, 137, 257, 283, 302, 307, 326, 442-3 Reevaporation 93-5 Reflectance 177, 188-90, 195-9, 208, 234, 345, 347, 385, 398-400, 410, 420-1, 437, 441-3, 448-52, 457 average 435 diffuse 180 Reflectance measurements 441-2 Reflectance profiles 398, 451, 455, 457 Reflectance values 432, 434, 455 Reflection coefficients 191-2, 195, 207-8 value of front surface 207 Reflectivity 177, 204, 383, 434, 445-6, 461 Reflector 395 Refractive index 24, 177, 179, 186-7, 190-1, 194, 197-8, 201-2, 218-21, 397-9, 403-6, 411-12, 428-9, 449-51, 464-6 Refractive indices 177, 185-6, 190-2, 195, 198-9, 205, 418 Regime 95, 311, 363, 366 Regions 63-6, 73, 100, 115, 128, 134, 150, 216, 269, 294, 316, 322, 329, 345-6, 454-5 infrared 116-17, 332, 450-2 inhomogeneous 96 visible 123-4 Remote Plasma Enhanced Chemical Vapour Deposition (RPECVD) 402 Resistance 8-9, 67, 108, 253-4, 257, 259, 271, 273 shunt 8-9, 271-2, 310, 335 Resistivity 76, 243, 248-9, 253-4, 256-60, 262, 264, 271, 333-4, 338-9, 373, 383, 409-10, 413-15, 447 values of 255, 333, 414 Resistivity measurements 255-6 Resolution 111-12, 115, 152-3, 155, 268 Resonance 121, 123, 464-5 RF-PECVD 36, 38, 43-4, 134 RF plasma power 435 RF power 36, 39, 48, 338, 365, 403, 415, 435-7, 454 RF power density 37-8 RF sputtering 69-70, 363 RHEED patterns 88-9 RIE (reactive ion etching) 79, 395, 435, 438, 441-2, 445-6 RIE processes 442-3 Rinsing 302, 305-6 Roll-to-roll 29 Room temperature 61, 84, 104, 109, 202, 233, 245-6, 300, 302, 306, 309, 315, 317, 345, 347 Roughness 146, 169, 408, 417, 419, 422, 426 Rs value 273

Sample back-illuminated 201-2 investigated 203-4, 223, 234 nanostructured 171 parallel-sided 189, 223 Sample area 216, 327 illuminated 191, 218 Sample atom 58, 60 Sample border 255-6, 259, 264 Sample chamber 77 Sample dimensions 258-9 Sample geometries 254, 258-9 Sample parameters 184, 201, 208, 253 Sample resistivity 255-6, 258, 260, 264 Sample surface 153, 155, 169, 185, 192, 205, 214, 216-17, 253-4, 256-7, 264 rear semiconductor 212 Sample temperature 252, 298 Sample thickness 179, 213, 255, 264 effective 263 Saturation value 232, 289, 324 SC-1 301-2 SC-1 solution 301-2 SC-2 301-2 SC-2 solution 301-2 SC-values 374 Scanning electron microscopy (SEM) 146-9, 157-8, 163, 165-6, 408, 433-4, 438, 441 Scanning probe microscopy (SPM) 152, 301 Scattering 109, 118, 180, 188, 198, 250, 376, 395, 416, 422, 425, 428, 465 Scattering layer 465 Scattering mechanisms 244, 249-50, 252-3 Scattering process 118, 120, 250, 252 Screen 87-9, 148, 151, 334, 346, 458 Screen printing 277 Se2-based solar cells 379 Secondary electrons (SE) 63, 66, 147-9 Secondary electrons, generation of 64-5 Selected area electron diffraction (SAED) 159-60, 173 SEM images of hydrogenated silicon films 158 SEM images of textured c-Si surfaces 436 SEM pictures 419-20 Semiconductor devices 102, 238, 300, 434 Semiconductor film 81, 186, 191-3, 196, 205-10, 212-13, 216-21, 223-4, 231, 259 parallel-sided 205, 216 thin 186, 191-2, 215, 218-20 Semiconductor industry 32, 34, 68, 127

*Index Silicon Based Thin Film Solar Cells* **499**

Semiconductor lattice 243 Semiconductor material conductivity 255 Semiconductor materials 5-6, 17, 177, 243-6, 249, 251-2, 257, 260, 265-6, 396, 454 Semiconductor parameters 234, 236 Semiconductor properties 243, 318 Semiconductor sample 223 Semiconductor-substrate 186, 217 Semiconductor surfaces 190, 207, 212-13, 220, 223, 257, 396-7 Semiconductor thickness 220, 359 Semiconductors 5-6, 34-5, 177-83, 185, 195, 205-23, 225-9, 231, 233-5, 237-8, 243-5, 247-9, 251-3, 261-3, 265-7 polar 252 Series resistance 8, 271, 273, 311, 334-5, 383 Shadow 218, 220-1 Sheaths 39, 63-6 Sheet resistance 257-8, 383, 385, 406-7, 409 Short range order (SRO) 140, 373 Si atoms 281, 309 Si-based solar cells 104 Si films 11, 18 Si layers 10, 22-3, 103 Si-rich a-Si1-xCx 132, 136 Si-Si bonds, weak 281-2 Si solar cell fabrication 303 Si solar cells 12, 133, 307, 466 Si substrates 9, 171, 303, 308, 446, 449 Si surfaces 300-2, 306-9, 445 Side mirror 452, 454, 456 Signal-to-noise ratio 111-12, 121, 123-4 Silane 20-1, 23, 35, 135, 360, 363-4, 366, 388, 402 Silane concentration 134, 363, 366, 373-4 Silicon (hydrogenated) thin films 108 Silicon, etching of 439, 441 Silicon carbon (hydrogenated) thin films 108 Silicon films 16, 21, 23, 365 annealed hydrogenated amorphous 170 nanostructured 126 thin 23, 173 Silicon layers 23, 45 Silicon nanocrystallites 108, 136 Silicon nitride 5, 300, 339, 398, 400-3, 405 Silicon oxide 173, 309, 401 Silicon oxide intermediate reflector (SOIR) 428-9 Silicon photovoltaics 277, 279, 281, 283, 285, 287, 289, 291, 293, 295, 297, 299, 301, 303, 305 Silicon samples 446 Silicon solar cell production 335

Silicon solar cells 381, 399, 401 Silicon substrates 159, 166, 307, 339 Silicon surface 164, 277, 287, 299, 317, 399, 410, 432, 438, 443, 446, 457 textured 433-4, 445 Silicon thin films 15 Silicon wafers, multi-crystalline 432, 441, 443, 445 Simulation results 455, 457 Simulations 298, 315-16, 318, 320, 322-3, 329-30, 337-8, 343-4, 346-7, 398, 419, 422, 449, 451-3, 460 Single junction 45, 360-1, 377, 389, 429 Single junction solar cells efficiencies 44 SiO2 films 301, 379, 401 Sites 101-2, 216, 251, 282 potential defect 283-4 SnO2 films 411-12 SOIR layers 428 SOIR thicknesses 429 Solar cell applications 146, 291, 368, 382, 406, 410 amorphous crystalline heterojunction solar cell 412 Solar cell architecture 342 Solar cell characteristics 165 Solar cell conversion efficiency 163 Solar cell cost 278 Solar cell design 8 Solar cell development 29, 360 Solar cell devices 369 Solar cell efficiency 34, 164, 178, 272, 345, 395 Solar cell efficiency tables 23 Solar cell industry 431 Solar cell junction 9 Solar cell manufacturing 303 Solar cell manufacturing companies 278 Solar cell optimization 110 Solar cell parameters 272, 331 Solar cell performances 38, 45, 313, 364, 400, 410, 459 Solar cell process, reliable 435 Solar cell processing 401 Solar cell production 3, 33, 364, 382 large scale 446 Solar cell production scale 46 Solar cell research 4, 140 Solar cell results, best 44 Solar cell simulation 20 Solar cell structure 21, 171, 177, 452, 464-5 Solar cell substrates 303 p-type CZ Si 304

Solar cells 3-12, 16-18, 40-3, 45-6, 127-8, 133-5, 270-2, 359-61, 363-6, 373-4, 376-9, 381-3, 389, 395-7, 416-17 actual 272 all Si tandem 109, 129 amorphous/crystalline heterojunction 309 amorphous/crystalline silicon heterojunction 277 amorphous/microcrystalline silicon 362 based 277-8, 396, 406, 416 based multi-junction 158 based thin film 34-5 based thin films 147 best 388 building-integrated 379 complete 375 conventional 463 developing thin-film 10 effective HJ 291 efficient 16, 109 efficient photovoltaic 68 efficient terrestrial 10 fabricated 10, 129, 344 fabrication of 35, 108, 437, 455 finished 442 first thin-film silicon 361 flexible 164 forward biased 272 generation 127 hetero-junction 164 hetero-junction microcrystalline silicon 163 hetero-structure 454 heterojunction 277-9, 335, 452, 460 heterostructure 333, 455, 458 high efficiency 305 high efficiency mono-crystalline silicon 432 high efficiency pin 368 highest efficiency 454 hphP 135 hybrid 377 identical hetero-structure 454 illuminated 272 industrial silicon 396 intermediate band 104 junction 3-5, 271 large area 46 low-cost 382 low-cost stable 169

 lplP 135 manufacture 41 micromorph 19 micromorph tandem 428 modern 171 most commercial 399 most efficient 366 multijunction 108, 137 nanocrystalline 374 new generation 136 obtained stable 374 optimized 463 prepared 364 producing 342 producing low cost 280 real 8 silicon-based 146, 171 silicon-based pin 377 silicon-based thin film 36 silicon-based thin-film 35 silicon-based thin films 146 single junction 361, 389 single-junction 381 stacked 39, 361 stacked quantum dot 83 state-of-the-art 368 tandem 9, 46-7, 359, 362, 386-7 test 309 texture multicrystalline silicon 438, 443 texture silicon 443 textured 172 thick 135 thin-film 10, 41, 361, 368, 380, 382, 410 thin-film amorphous silicon 377 thin film silicon 46, 172, 406 thin-film silicon 41, 140, 361, 380, 382, 385, 388 thin wafer 454 triple junction 109 triple junction amorphous Si 12 type 40, 43 type amorphous silicon 364 typical amorphous silicon 158 ultrathin amorohous silicon 172 very high efficiency 399 Solar cells parameters 108, 133 Solar cells performance 40, 270, 466

 better 38 Solar cells processing 401 Solar cells structures 19 Solar energy mater & solar cells 140 Solid curves 186, 190, 193-5, 197-9, 203, 211-15, 225-6, 235-6 Source field effect 147 ion 58, 60, 77 Source material 14, 59, 68, 82 Source spectrum 114 Spatial distribution of radiation intensity 211, 213 Specimen 147, 150, 152-3, 159 Spectra 111-13, 117-18, 125, 136, 154, 195, 224, 369, 372, 404, 447 Spectral range 111, 115, 124, 182, 197, 422, 445, 455-6 Spectrometer, dispersive 113, 121 Spectroscopy dispersive 111-13 infrared 108-10 Spectrum 8, 109-12, 114-17, 125, 129, 136-7, 155, 179-80, 182, 195, 267, 272-3, 372, 398, 446 Sphere 61, 417, 423 Spherical 61, 157, 168-9 Sputtered ITO resistivity 334, 415 Sputtering 3, 10, 14, 58-9, 61, 67-9, 73-5, 77-9, 382-3, 402, 408 Sputtering process 58, 60, 69, 73, 76-7, 408, 415 Sputtering systems 70, 73, 75, 412, 454 Sputtering techniques 58, 72, 75-6, 79 SPV measurements 298, 304-5 SSPG measurements 217, 221, 225, 233-4, 236-8 SSPG method 219-21, 226 SSPG results 232-4 Stability 38, 108, 308-9, 335, 374 Stacked cell 3 Stacked layers 4, 293, 454 Stacked structure 21, 293, 315, 318, 454, 457 Stacking faults 99-100, 250, 370 Stacks 287, 293, 344, 359, 387-9, 451, 461 Stainless steel 35-6, 157, 364, 379, 383, 416 Standard effusion cells 84 STAR solar cell 381 States 16-17, 30, 63, 78-9, 184, 227-30, 237, 245, 252, 280-2, 285-6, 304, 307, 314, 403-4 charged 17, 285-6 density of 3, 16-18, 20, 227, 281, 286-7, 296, 307, 312, 346, 376, 453 effective density of 228, 267, 381 empty 245, 247 trap 265, 267, 288 Steady state photocarrier grating (SSPG) 177, 216-17

Sticking coefficient 93 Strain 96-7, 104, 157 Stress 32, 34, 75-6, 157, 454 Stretching modes 117, 127-9, 404 Structural changes 110, 129 Structural characterisations 146 Structural properties 19, 108-9, 146-7, 149, 151, 153, 155, 157, 159, 161, 163, 165-7, 169, 171, 173 Structures basic 157, 395 diode 266-8 electronic 162, 359, 403 fragmented island 13 interdigitated 336, 346 layered 23, 386 periodic 429 Substrate 13-15, 18-19, 22-4, 34-6, 38-40, 47-8, 50-1, 59-60, 76-7, 81-2, 84-5, 92-9, 136-8, 365-7, 378-9 etched 305 flat 430 flexible 53, 164, 364, 379, 416 insulating 65-6, 259, 378 opaque 377, 379 polycarbonate 429-30 semi-insulating 257-9, 263 textured 164-5, 305, 308, 310, 361, 424 thick 192, 200-2, 204, 209, 214, 218 Substrate configurations 305, 383 Substrate designs 379 Substrate material 162, 359, 388-9 Substrate resistivity 259, 330, 343 Substrate surface 13, 22, 32, 39, 79, 83, 94, 96, 165, 299, 309, 370, 402 Substrate temperature 14, 29, 37-8, 89, 92-3, 160-1, 163, 167, 291, 315, 324, 365, 382, 384, 413-14 given 92 low 38, 43, 45, 68 Sunlight 4, 279, 119, 323, 362, 365, 378, 395 Sunlight exposure 313, 317, 320-1, 332, 335 Surface, rough 179, 191, 304, 307-8, 416-17, 419, 422 Surface atoms 58, 60, 90-1 Surface conditioning 300, 305-7 wet-chemical 305 Surface morphology 163-5, 169, 299, 305, 308-9, 424, 426 Surface passivation 307-8, 338, 348, 442, 452, 454, 456 Surface photovoltage 165, 297-8 Surface reconstruction 81, 84, 89-90 Surface temperature 93-5

*Index Silicon Based Thin Film Solar Cells* **505**

### **T**

Ta, annealing temperature 130-2 TAC 408-9, 425-7 Tails 16, 182, 230, 281-2 exponential 181, 229, 231 Tandem cell layers 428 Tandem cells 4, 157, 164, 386-7, 389, 428-9 Target atoms 58, 60 Target surface 58, 60, 70, 73, 75, 77 TCO films 162, 332, 382-3, 385-6, 407 TCO layer 378, 382, 385, 422 TCO material 332, 382-3 TCO/p-a-Si 333 TCO work function 333 Techniques experimental 14, 119, 243 isotexturing 441 TEM images 152, 158-9, 167 Temperature higher 251, 290, 293, 334 lower 290, 293, 295 Temperature coefficient 332 Temperature dependence 250-1, 332 Texture 79, 146, 154, 303, 425, 432, 435, 437, 443, 446 Textured c-Si surfaces 436-7 Textured surfaces 171, 299, 305-6, 308, 338, 382, 408, 417, 419, 435, 437, 441-3, 445 Texturing 24, 164, 277, 299, 303, 317, 395-7, 416, 429, 431, 435, 441, 443, 463 Texturing process 303, 305, 435, 442, 446 Texturing technique 416, 437 Theory 108, 110, 113, 119, 283, 396 Thermal annealing 108, 127, 129-30, 133, 136, 287-8, 290-1, 337 Thermal annealing time 288-9, 334 Thermal budget 278, 364, 366 Thermodynamics 13, 30 Thickness 19, 167-9, 185-6, 211-13, 220-1, 318-19, 321-4, 359-60, 387-9, 396-9, 408-10, 412-13, 449-54, 459-61, 464-6 actual 24 effective 22, 24 epilayer 97 equal optical 399 evaluated 451-2 finite 88-9 largest 168-9 parallel-sided substrate of 191, 208, 223 silicon wafer 277, 460

**506** *Silicon Based Thin Film Solar Cells Roberto Murri* 

 wafer base 460-1 Thin film cells 277, 279, 395-6, 400, 407, 410, 416 Thin film geometry 155-6 Thin film hydrogenation 3 Thin film layer growth 305 Thin film silicon 3, 166 Thin film solar cells 3-5, 7, 9, 11, 13, 15, 17, 19, 21-3, 35, 39, 50-1, 140, 417, 425-6 Thin film solar cells technology 46 Thin film structures 3, 166 Thin film technologies 10, 396, 459 Thin-film technologies 359-60, 362 Thin-film thickness 193 Thin films 3-4, 10, 12-16, 37-9, 45-9, 58-61, 67-9, 81, 108-9, 146-7, 159-61, 193-5, 199-204, 209-11, 257-9 based 36, 108 deposited 76 doped 21 producing 46 un-doped 447 Thin films a-Si 48 Thin films epitaxial growth 87 Thin films solar cells 3 Thin layer 5, 81, 259, 300, 323, 329, 397 Thin Silicon Solar Cells 4, 23, 207, 395, 397, 399, 401, 403, 405, 407, 409, 411, 413, 415, 417 Thin solid films 238 Thinner 96-7, 288, 297, 379, 387, 460 Thinner silicon wafer 277, 396, 416, 431, 458 Thinner wafers 10, 396, 431, 459-60 Throughput, silicon solar cell processing 401 Top cell 39, 46, 361, 387-9, 428 Total energetic spectrum of electronic states 237 Transfer, local energy 61 Transfer function 62 Transparent conductive oxide (TCO) 395 Transient 265, 267-9 Transition 15, 19, 21, 43, 131-3, 252, 368-9, 374, 381, 426 Transmission electron microscopy (TEM) 109, 146-7, 150-2, 157, 166, 369-70, 455 Transmission, energetic 191-2 Transmittance 177, 180, 190, 195-6, 199, 208, 224, 334, 385, 406, 410, 414-15, 418, 420, 425 effective 333-4, 414-15 theoretical 197-8 Transparent substrate 204, 211, 213, 217-18, 378-9 thick 211-12 Traversing 188-9, 191-2, 196, 208, 210 Treatment temperature 302 TTC 162-3

Type a-Si 318

### **U**

U-shaped electrode 49, 51 Ultra-violet (UV) 121, 123, 125, 404 Ultra high vacuum (UHV) 46, 82 Uncertainties 16, 82, 190-1 Undoped a-Si 283, 296

### **V**

Vacuum system 33, 36, 82, 84 Valence band 6, 17, 102, 215, 228-30, 245, 251, 265, 280-1, 295, 297, 312, 318, 321, 329 Valence band edge 295-6, 304, 307, 403-4 Valence band offset 320-1, 346, 453 Values curve 202, 208 evaluated 183, 185 fitted 204, 236 higher 19, 44, 252, 259, 305 ideal 271 low 134, 203-4 measured 255-6 Vapor deposition 29 chemical 29, 31, 359 plasma-enhanced chemical 140, 287 Variable angle spectroscopic ellipsometry (VASE) 189 VBM 294-5 Very high frequency (VHF) 23, 36, 38, 48, 166, 366, 377, 403 VHF-PECVD 38-9, 44, 47, 361 VHF plasmas 44, 47, 366 Voc of silicon solar cells 381 Voc values 291, 322, 329 Voids 164, 166, 254, 297, 363-4 Voltage 4, 8-9, 35, 63, 69, 73, 77, 154, 222, 249, 254-5, 257-8, 263, 271-3, 323 Voltage distribution, non-uniform 47 Voltage sweep 272-3 Voltage values 264, 273 Voltmeter 255, 257-8

### **W**

Wafer surface 293, 300, 302-3, 432, 439 Wafer thickness 460 Wafers 3, 10, 90, 300-3, 305-6, 317, 329, 340-1, 344, 346, 396, 434, 441-2, 454-5, 459-60

as-cut 303-4, 439, 441 textured 304, 441-2 thin 395, 452, 454, 459 Wavelength range 191, 217-18, 385, 408, 421-2, 425, 461, 464 Wavelengths 109-11, 115-16, 122, 130, 151, 189-91, 196-8, 210-11, 214, 234-6, 362, 385, 397-400, 445-8, 450-1 function of 421-2, 455 Wavenumber 109-11, 114, 117, 130 higher 117, 131-2 Waves 115, 178, 188, 206, 397 steady light 210, 212, 220-1 Wet-chemical smoothing 299, 306, 308 Window layer 40, 317, 361, 377-8, 382, 416, 429 Work function 147, 321-2, 335

## **X**

X-rays 151, 154-5 X-ray diffraction (XRD) 109, 132-3, 146-7, 154, 157-8, 160, 166-7, 169, 173, 369

### **Z**

ZnO films 382, 407-9, 425-7 ZnO layers 409, 420, 428-9

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