Study of defects and microstructure of amorphous and microcrystalline silicon thin films and polycrystalline diamond using optical methods

Transcription

1 Study of defects and microstructure of amorphous and microcrystalline silicon thin films and polycrystalline diamond using optical methods Zdeněk Remeš PhD. thesis Faculty of Mathematics and Physics of the Charles University Institute of Physics of the Academy of Sciences of the Czech Republic Prague, 1999

2 c Zdeněk Remeš, 1999 I elaborated my thesis under supervision of Dr Milan Vaněček. The a-si:h, c-si:h and CVD diamond samples were prepared at National Renewable Energy Laboratory (NREL) in USA, at Neuchtel University in Switzerland and at Limburgs University in Belgium. The measurements were performed in the Institute of Physics, Academy of Sciences of the Czech Republic. Data were evaluated by the freeware system for numerical calculations Octave and my own programs written in the ANSI C, compiled by the GNU C compiler. The thesis was typeset in LATEX 2. Graphs were prepared by the program Gnuplot. The schematic pictures were drawn by the program Xfig. I declare that the thesis is my own work and that, to the best of my knowledge and belief. It contains no material previously published or written by another person nor material which to a substantial extent has been accepted for the award of any other degree or diploma of university or other institute of higher education, except where acknowledgement is made in the text. I also declare that the intellectual content of this thesis is the product of my own work, though I may have received assistance from others on style, presentation and language expression. A copy of the thesis is available in an electronic form by remes@fzu.cz website: remes The document is distributed in the hope that it will be useful, especially for students. If you will use it, give a reference i Z. Remes, Ph.D.Thesis, Charles University, Prague, 1999, remes/thesis/thesis.html. The printed original of my thesis is deposited in the library of Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic.

3 Thank you! I am greatly indebted to Dr Milan Vaněček for supervising my PhD. thesis. He has offered me the occasion to realize the present thesis in his research group; his advises and comments greatly helped me in my scientific life. I also appreciated his open mind and confidence, allowing me to propose and develop my own ideas. I thank all my colleagues from Institute of Physics, Academy of Sciences of the Czech Republic, for fruitful cooperation and pleasant atmosphere at the institute. I m glad that I could visit laboratories at University of Neuchtel in Switzerland and in the Institute for Material Research at Limburgs University in Belgium. I met there very friendly atmosphere. Especially, I thank following persons: Dr Jan Rosa, Dr Karel Polák, Dr Martin Nikl, Dr Aleš Poruba, Dr Eva Mihóková, Dr Antonín Fejfar, Ing. Tomáš Kouba, Dr Miloš Nesládek, Dr Pedro Torres and Dr Natalie Beck. I also thank my girlfriend Dáša who supported me during my postgraduate studies. ii

4 Preface The thesis deals with study of optical properties of amorphous and microcrystalline silicon thin films and polycrystalline diamond layers prepared from a vapor phase on a heated substrate by chemical vapor deposition process (CVD). My work follows the long-term investigation of optical properties of hydrogenated amorphous and microcrystalline silicon and polycrystalline diamond layers executed by Dr Milan Vaněček and his colleagues at the Institute of Physics, Academy of Sciences of the Czech Republic. The investigation has been done in cooperation with researchers from the Faculty of Chemistry, Technical University, Brno, Czech Republic, the National Renewable Energy Laboratory, Golden, USA, the Institute of Microtechnology, University of Neuchtel, Switzerland, and the Institute for Material Research, Limburgs University, Belgium. Increased interest is now being shown worldwide in developing thin-film technologies. Due to the capability of producing high quality layers on large deposition areas with reasonable growth rates, it is likely in the long term that thin-films will replace bulk crystalline materials in many applications, especially in large-area devices. Hydrogenated amorphous and microcrystalline silicon thin film technologies has been already successfully used in solar cells, displays and xerographic applications. Polycrystalline diamond layers have still their main applications as passive protective layers and substrates draining off the heat. However, it is expected that in future they will be applied also in optics and in electronics as active electronic devices. There are still many problems in practical applications of hydrogenated amorphous and microcrystalline silicon and CVD diamond layers. These problems arise mainly because of presence of defects in material structure and/or difficulties during the deposition process. Therefore, these layers are subjected to an intensive theoretical and experimental research. I briefly summarize the recent knowledge in this area in the Introduction chapter, focusing attention to those properties, which are related to the subject of my own research. The Introduction chapter begins with a section Electronic structure and optical properties, which is an overview of basic structural, electronic and optical properties of semiconductors. I review the investigated materials in more detail in the following three sections. Each section contains an overview of the deposition technology, used for the particular material, an overview of experimental techniques, used for material characterization, and a brief summary of my own results. The section Hydrogenated amorphous silicon consists of four subsections. The first subsection, Amorphous silicon, summarizes recent knowledge on unhydrogeneted amorphous silicon, a-si. The next subsection, Deposition of a-si:h films, deals with the deposition technologies used to grown a-si:h thin films, as plasma enhanced chemical vapor deposition (PECVD) and hot wire (HW) technology. The last two subsections,structure of a-si:h and Metastability of a-si:h, summarize recent knowledge on the microstructure and related metastability phenomena. iii

5 PREFACE iv Semiconducting a-si:h thin films can be grown with fever then cm neutral three-fold-coordinated Si dangling-bond defects. The introduction of excessive carriers through moderate irradiation or electronic injection increases the density of dangling bonds to nearly cm. These excess carrier-induced dangling bonds are metastable. They are annealed out in a few hours at 150 C. However, their rapid formation limits application of a-si:h as an inexpensive material for photovoltaic and electronic application. Since its discovery by Staebler and Wronski in 1976, the metastability of a-si:h remains an open problem. Both phenomena are discussed in a close relation with experimental techniques, used for their characterization. The most important experimental techniques used for microstructural characterization are infrared absorption spectroscopy, nuclear magnetic resonance (NMR) and small angle X-ray scattering (SAXS). Some information can be also obtained from transmittance and reflectance spectra, particularly about the incorporation of hydrogen into an amorphous network. The structural defects can be monitored by electron paramagnetic resonance (EPR) and by sub-gap absorption, measured by constant photocurrent method (CPM) 1. An important part of the subsection dealing with metastability phenomena is a survey of theoretical models. Despite the fact, that the low sub-gap absorption cannot be seen in transmittance and reflectance measurements on thin films, these measurements can still give us important information about hydrogen interaction with the amorphous network. The next section, Hydrogenated microcrystalline silicon deals with intensly studied material which can replace a-si:h in many applications. This material was discovered by S. Vepřek in Hydrogenated microcrystalline silicon ( c-si:h) is composed of microcrystallites embedded in an amorphous tissue. Material is prepared by PECVD from silane strongly diluted by hydrogen. In contrast to a polycrystalline silicon, c- Si:H is deposited in the same low temperature region as a-si:h. The great advantage of c-si:h over a-si:h is that c-si:h shows no metastability. On the other hand, c-si:h was considered for a long time as a defect-rich material. This opinion was supported by a strong n-type character generally observed in as-deposited undoped c-si:h. However, recent progress in a very high frequency glow discharge (VHF-GD) technology, developed at University of Neuchtel, Switzerland, has culminated into a new c-si:h with significantly improved properties. In the section CVD diamond I summarize recent knowledge on diamond wafers, deposited by Chemical Vapor Deposition (CVD). This material is of high importance for future applications in electronics and optics. However, the defects induced during CVD growth represent the limiting factor for many applications and also for the recently reported n-type doping. Generally three types of defect are always present in low concentration in CVD wafers: residual carbon in non-carbon configuration (sp carbon), nitrogen impurities and the hydrogen induced defects. The exact picture of defects is not complete yet, despite various attempts to characterize defects states in the forbidden gap. The defects are usually measured by photothermal deflection spectroscopy (PDS) or photocurrent spectroscopy (CPM constant photocurrent method) in combination with electron paramagnetic resonance (EPR). Currently, a successful reduction of the sp carbon content has been reported. The chapter Experimental has four sections. The section Description of spectrometer describes in detail the spectrometer setup used for the transmittance and reflectance measurements in near ultra-violet, visible and near infra-red region of electromagnetic 1 CPM was pioneering by Dr M. Vaněček in 1981 in Prague

6 PREFACE v spectrum. The details about transmittance and reflectance measurements are discussed in the section Transmittance and reflectance measurements. Despite of conventionality of the method, I was able to receive new experimental results, mainly due to the fact that I did not use the conventional spectrometer, but I built a special one, which suited my particular requirements. Two main advantages of the spectrometer are the reduced illuminated area (0.5 1 mm) and a possibility to measure transmittance and reflectance spectra without moving the sample. Furthermore, I completed the transmittance and reflectance measurements with the angle resolved reflectance and scattering measurements and the constant photocurrent method measurements. They are described briefly in sections Angle resolved reflectance and scattering and Constant photocurrent method (CPM). The more details about these methods can be found in references. The chapter Theory has three sections. The most important between them is the first section Optics of rough thin films. General aspects about propagation, reflection and scattering of electromagnetic waves I discuss in the subsection Introduction. In the subsection Transmittance and reflectance of rough thin films I describe a theory of transmittance and reflectance spectra of rough thin films deposited on thick transparent substrate. The theory for the first time includes interference effects and surface scattering. The method used for evaluations of optical parameters from the transmittance and reflectance spectra is presented in the subsection Determination of optical constants of thin rough films. The angle resolved reflectance is discussed in the section Angle resolved reflectance. The angle resolved reflection from homogeneous medium is described by Fresnel formulas. However, the situation is more complicated in the case of reflection from inhomogeneous medium. Here I study the optical properties of a stratified media. In the stratified medium model, the inhomogeneous layer is considered as a multilayer, composed of an infinite number of infinitesimally thin layers with a constant index of refraction. The last section Modeling of optical properties is divided into two subsections. In the subsection Effective media approximation I discuss how to model the dielectric function of mixture of two or more materials in the Effective media approximation. In the subsection Optical properties and mass density of a-si:h and c-si:h I show how to calculate the mass density of a-si:h and c-si:h from their index of refraction using the Claussius Mossoti equation. The chapter Results and Discussion: c-si deals with optical properties of smooth thin crystalline silicon deposited on sapphire substrate. The chapter has been included in the thesis to verify the validity and precision of evaluated optical parameters. The chapter Results and Discussion: a-si:h has five sections. In the first section, The optical absorption edge of a-si:h as a function of hydrogen content and deposition conditions, I study how the optical absorption edge depends on hydrogen content and deposition conditions. It is well known that the incorporation of hydrogen into amorphous network generally leads to an expansion of the optical gap. I discuss this effect as measured on a-si:h samples deposited by glow discharge and hot wire methods. The hydrogen content in these samples varied from 0 to 20.5 at.%. It the section Investigation of the mass density of a-si:h as a function of hydrogen content and deposition conditions, I study the mass density of a series of nanovoid-free samples prepared by a hot wire technology with different deposition temperature. The density is calculated from the index of refraction using Claussius-Mossoti equation. The aim of this study is to show how the mass density depends on hydrogen content, and if

7 PREFACE vi there is some relevance for the metastability. The average gap between valence and conduction bands is discussed in the section Single oscillator energy of a-si:h as a function of hydrogen content and deposition conditions. It is well known that the average gap of a-si:h is smaller than that of c-si, and increases by increasing the hydrogen content. The evaluation of average gap in my thesis is based on the analysis of the dispersion of the index of refraction and application of Wemple-DiDomenico model. I identify the average gap with the single oscillator energy, introduced by Wemple and DiDomenico. The purpose of the section is to compare the single oscillator energy of hot-wire (HW) and glow discharge (GD) a-si:h with a different hydrogen content. The next section, Silicon network relaxation in a-si:h due to H diffusion, concerns the annealing experiments. I answer the fundamental questions: is the matrix of Si atoms really rigid at the temperatures well below the amorphous-crystalline transition or is there a true equilibrium of the whole silicon-hydrogen network? What happens when the hydrogen is very slowly driven out? Will a significant lattice reconstruction occur? Is there a measurable shrinking of the thin film? I show that there is a measurable shrinking of the amorphous network when hydrogen concentration decreases at elevated temperature. In the last section I conclude our present understanding of metastability in a-si:h based on many experiments done in the Institute of Physics in Prague. The chapter Results and Discussion: c-si:h has five sections. In the section Light scattering in c-si:h I verify the method of evaluation of optical parameters from transmittance and reflectance measurements on rough layers. The experimental results obtained on rough samples I compare with results obtained on the same samples after polishing. In this part I also analyze the presumptions of the theory of evaluation of optical parameters, namely the presumption of randomness of the surface roughness verified by angle resolved scattering measurements. The next three sections deal with three different series of hydrogenated microcrystalline silicon samples, prepared at IMT, University of Neuchtel, Switzerland. The aim is to show how the optical parameters reflect the transition from the amorphous to microcrystalline deposition depending on the deposition parameters. The first series, discussed in section Dilution series at 70 MHz and 7 W plasma power, is a concentration series (silane concentration at.% in hydrogen) of hydrogenated amorphous and microcrystalline silicon thin films prepared by VHF-GD at plasma excitation frequency 70 MHz, plasma power 7 W and substrate temperature 225 C. This series is well documented by X-ray, Raman, infrared absorption and elastic recoil detection measurements. The next two series were prepared with the aim to optimize the deposition condition and to enhance the deposition rate. The second series, discussed in section Power series at 130 MHz and 5% silane concentration, is a power series (! W) of hydrogenated microcrystalline silicon thin films prepared by VHF- GD at plasma excitation frequency 130 MHz, silane concentration 5% and substrate temperature 230 C. Since the samples of this series displayed no significant differences in the index of refraction and the absorption coefficient evaluated from transmittance and reflectance spectra, I executed complementary measurements of sub-gap absorption using the constant photocurrent method. The last series, discussed in the section Power series at 130 MHz and 7.5% silane concentration is a power series (! "$#% W) of hydrogenated amorphous and microcrystalline silicon thin films prepared by VHF-GD at frequency 130 MHz, silane concentration 7.5% and substrate temperature 230 C.

8 PREFACE vii In the last section Model of the absorption coefficient of c-si:h I apply the effective media approximation model to explain the spectral dependence of absorption coefficient of c-si:h. It is well known that the residual amorphous fraction in c-si:h increases the absorption of c-si:h with respect to c-si. However there is some enhancement of absorption that cannot be described by these contributions. Thick CVD diamond layers are discussed in chapter CVD diamond. These layers do not have a homogeneous depth profile of the index of refraction. It is supposed that the index of refraction increases from the silicon substrate CVD diamond layer interface and saturates in the bulk of CVD diamond layer. In the section Study of optical inhomogeneity (depth profile) of CVD diamond layer I estimate the inhomogeneity by the angle resolved reflectance measurements. In the chapter Conclusions I summarize the particular results contained in previous chapters. The results of my work were presented at several international conferences and some of them were also published. Here is a survey of my contributions and papers. 1. M. Vaněček, Z. Remeš, J. Fric, R. S. Crandall and A. H. Mahan, On the microscopic origin of the higher stability of amorphous silicon prepared by hot wire technique, in Proceedings of the 12th European Photovoltaic Solar Energy Conference (R. Hill, W. Palz, and P. Helm, eds.), (H. S. Stephens and Associates, Bedford, UK), pp , M. Vaněček, Z. Remeš, J. Fric, E. Šípek, A. Fejfar, J. Kočka, U. Kroll, A. H. Mahan and R. S. Crandall, Light-saturated defect density in amorphous silicon with different oxygen content, microstructure and hydrogen bonding, in Proceedings of the 13th European Photovoltaic Solar Energy Conference (W.Freiesleben, W. Palz, H. A. Ossenbrink and P. Helm, eds.), (H. S. Stephens and Associates, Bedford, UK), pp , N. Beck, J. Meier, J. Fric, Z. Remeš, A. Poruba, R. Flückiger, J. Pohl, A. Shah and M. Vaněček, Enhanced optical absorption in microcrystalline silicon, Journal of Non-Crystalline Solids, vol , pp , N. Beck, P. Torres, J. Fric, Z. Remeš, A. Poruba, Ha Stuchlíková, A. Fejfar, N. Wyrsch, M. Vaněček, J. Kočka and A. Shah, Optical and electrical properties of undoped microcrystalline silicon deposited by the VHF-GD with different dilutions of silane in hydrogen, in Materials Research Society Symposium Proceedings Volume 452 (R. W. Collins, P. M. Fauchet, I. Shimizu, J.-C. Vial, T. Shimada and A. P. Alivisatos, eds.), (Pittsburgh, Pennsylvania), pp , Z. Remeš, M. Vaněček, A. H. Mahan and R. S. Crandall, Silicon network relaxation in amorphous hydrogenated silicon, Physical Review B, vol. 56, pp. R , A. Poruba, Z. Remeš, J. Fric, M. Vaněček, J. Meier, P. Torres and N. Beck, Microcrystalline silicon thin films cells: Differences in the cell and material properties, in Proceedings of the 14th European Photovoltaic Solar Energy Conference (H. A. Ossenbrink, P. Helm, and H. Ehmann, eds.), (Bedford, UK), pp , H. S. Stephens and Associates, 1997.

9 PREFACE viii 7. J. te Nijenhuis, G. Z. Cao, P. C. H. J. Smits, W. J. P. van Enckevort, L.J. Giling, P. F. A. Alkemade, M. Nesládek and Z. Remeš, Incorporation of lithium in single crystal diamond: diffusion profiles and optical and electrical properties, Diamond and Related Materials, vol. 6, pp , Z. Remeš, M. Vaněček, U. Kroll, A. H. Mahan and R. S. Crandall, Optical determination of the mass density of amorphous and microcrystalline silicon layers with different hydrogen contents, Journal of Non-Crystalline Solids, vol , pp , M. Vaněček, A. Poruba, Z. Remeš, N. Beck and M. Nesládek, Optical properties of microcrystalline materials, Journal of Non Crystalline Solids, vol , pp , A. Poruba, Z. Remeš, J. Špringer, M. Vaněček, A. Fejfar, J. Kočka, J. Meier, P. Torres and A. Shah, Light scattering in microcrystalline silicon thin film cells in Proceedings of the 2nd World Conference on Photovoltaic Solar Energy Conversion (J. Schmid, H. A. Ossenbrink, P. Helm, H. Ehmann and E. D. Dunlop, eds.), (European Commision, Italy), pp , Z. Remeš, M. Vaněček, K. Meykens, M. Nesládek, C. Quaeyhaegens and L. M. Stals, Study of optical inhomogeneity (depth profile) of CVD diamond layer, grown on Si substrate, presented at 9th European Conference on Diamond, Diamond-Like Materials, Nitride and Silicon Carbide, Crete, September A. Poruba, Z. Remeš, J. Špringer, M. Vaněček, A. Fejfar, J. Kočka, J. Meier, P. Torres and A. Shah, Optical absorption and light scattering in microcrystalline silicon thin films and solar cells, submitted to Journal of Applied Physics.

10 Contents Thank you! Preface Contents List of symbols and abbreviations ii iii ix xi 1 Introduction Electronic structure and optical properties Hydrogenated amorphous silicon (a-si:h) Amorphous silicon Deposition of a-si:h films Structure of a-si:h Metastability of a-si:h Hydrogenated microcrystalline silicon ( c-si:h) CVD diamond Experimental Description of our spectrometer Transmittance and reflectance measurements Angle resolved reflectance and scattering Constant photocurrent method (CPM) Theory Optics of rough thin films Introduction Transmittance and reflectance of rough thin films Determination of optical constants of thin rough films Angle resolved reflectance Modelling of optical properties Effective media approximation Optical properties and mass density of a-si:h and c-si:h Results and Discussion: c-si Transmittance and reflectance of c-si thin film in UV and visible region Transmittance and reflectance of c-si thin film in visible and IR region Angle resolved reflectance of thick c-si ix

11 CONTENTS x 5 Results and Discussion: a-si:h The optical absorption edge of a-si:h as a function of hydrogen content and deposition conditions Investigation of the mass density of a-si:h as a function of hydrogen content and deposition condition Single oscillator energy of a-si:h as a function of hydrogen content and deposition conditions Silicon network relaxation in a-si:h due to H diffusion Conclusions on metastability Results and Discussion: c-si:h Light scattering in c-si:h thin films Introduction Scattering factors Angle resolved scattering The influence of the surface scattering on the optical spectra Dilution series at 70 MHz and 7 W plasma power Power series at 130 MHz and 5% silane concentration Power series at 130 MHz and 7.5% silane concentration Model of the absorption coefficient of c-si:h CVD diamond Introduction Study of optical inhomogeneity (depth profile) of CVD diamond layer.. 86 Conclusions 88 Useful websites 90 Bibliography 91

12 ) * / / = G F List of symbols and abbreviations AFM atomic force microscope a-si amorphous silicon a-si:h hydrogenated amorphous silicon & speed of light in vacuum &(' hydrogen content CPM constant photocurrent method c-si crystalline silicon CVD chemical deposition process thickness *+ normalized detectivity *-, neutral dangling bond *. positively charged dangling bond negatively charged dangling bond * ' diffusion coefficient of H energy, electric field vector, single oscilator energy /10 activation energy of H motion /32 dispersion energy in Wemple-DiDomenico formula /14 optical gap /15 migraton energy EMA effective media approximation /16 phonon energy, plasma energy /1798;:<: Penn gap EPR electron paramagnetic resonance ERDA elastic recoil detection analyses focal length => amorphous volume fraction =? crystalline volume fraction =A@ void volume fraction FWHM frequency width at half maximu B Landé factor of the electron C * D$E glow discharge hot wire intensity of light IR infra-red light IS integrating sphere imaginary part of index of refraction!!jk L J/K Boltzmann constant GIH xi

13 j t M V ` LIST OF SYMBOLS AND ABBREVIATIONS wavelength N mass c-si:h hydrogenated microcrystalline silicon ' chemical potencial O real part of index of refraction P volume density NMR nuclear magnetic resonance PDS photothermal deflection spectroscopy PECVD plasma enhanced chemical vapor deposition QSR /UT bond polarizability reflectance V1W reflectance from film side V 4 reflectance from substrate side V1X reflectance of p-polarized light VZY reflectance of s-polarized light []\_^ reflection amplitude coefficient screening factor `9acbed, `9fhgid, `9d scattering factors SAXS small angle X-ray scattering SEM scanning electron microscope transmittance, temperature jk5 envelope around transmittance maxima jkl envelope around transmittance minima m \n^ transmission amplitude coefficient UV ultra-violet light VHF-GD very high frequency glow discharge VIS-NIR visible or near infra-red light o absorption coefficient o 8 extinction coefficient o Y volume scattering coefficient p dielectric function q quantum efficiency r phase factor s mass density angle of incidence tvu Brewster angle w rms roughness xii

14 Chapter 1 Introduction 1.1 Electronic structure and optical properties The electrical and optical characteristics (conductivity, carrier diffusion length, mobility, lifetime, index of refraction, absorption coefficient, etc.) of solid-state material are influenced by its structure. The structure describes the geometric framework to which the material is referred and the arrangement of atoms or electron-density distribution concerning that framework. According to a quantum theory, the energy states of an electron in a condensed matter form a continuous distribution in the allowed energy bands. Whereas the inner electron states are affected very little by the neighboring atoms, the outer states are spread over certain bands. These states are delocalised. In semiconductors, the quantum states of the valence electrons form the valence band, which is separated by a forbidden energy gap from the conduction band. At absolute zero temperature the valence band is fully occupied by electrons while the conduction band is empty. At nonzero temperature some states near the top of the valence band are vacant, while same states near the bottom of the conduction band are occupied. Many features of semiconductors are caused by the fact that the number of electrons in the conduction band increases rapidly with increasing temperature, especially if the forbidden gap is narrow. In practice, there are many irregularities even in crystals the defects are always present in solids, especially in thin films. The defects create quantum states in the forbidden energy gap. Vacancy in silicon crystal structure is an example of the erosion of crystal symmetry. The displacement of one silicon atom from the crystal lattice creates dangling bonds at four neighboring atoms by breaking their bonds. The dangling bonds are also in an amorphous network, where they represent the dominant recombination centers [1]. In hydrogenated amorphous silicon they are responsible for a low lifetime of electrons excited to the conduction band. The other defects in regular structure are the local bond length and bond angle distortions, and impurities. Local stresses caused by distortions induce variations in the binding energy and thus influence the electronic states. Donor impurities are the atoms that have more valence electrons than required to complete the bonds with neighboring atoms. These atoms create new quantum states in the forbidden gap, right below the conduction gap. In contrast to donors, acceptor impurities are the atoms that have fewer valence electrons than required to complete the bonds with neighboring atoms. They accept electrons to complete the bonds. These extra electrons are almost as tightly bound to the atom as the valence electrons. Thus, the presence of acceptor impurities results in 1

15 p x p p p p p H y / CHAPTER 1. INTRODUCTION 2 α (cm -1 ) Abs. coeff c-si a-si:h µc-si:h Photon energy (ev) Figure 1.1: Absorption coefficients of typical c-si, a-si:h and c-si:h. the states just above the valence band edge. The electronic excitation spectrum is described by an energy-dependent complex dielectric function p H. The imaginary part zy { p of the dielectric function can be approximated within the one-electron approximation at zero temperature by [2] R i R /? /UT (1.1) Here is the dipole matrix element connecting the valence and conduction band states and the delta function expresses the conservation of energy. The sum runs over all initial and final states. The matrix elements in a crystalline semiconductor are non-zero only for the states of the same crystal momentum G. The optical transitions connected to those energy levels that conserve both energy and momentum are called direct transitions. Indirect transitions to a state of different crystal momentum is accompanied by the absorption or emission of a phonon to conserve the total momentum. Such transitions are generally weak and only observed at the energies where the direct transitions are forbidden. In an amorphous semiconductor, allowed transitions can occur between any two states for which energy conservation applies. The matrix elements therefore reduce to an average V R /UT over all pairs of states separated by the energy /. Then the imaginary part of the dielectric function can be expressed as Here R /-T respectively. and P? R /-T The real part p Kramers-Kronig relation } V R /-T ˆ, R /Š TiP? R / /Œ TL k/œ (1.2) is the density of states in the valence and conduction band, of the dielectric function is related to the imaginary part p R /-T Ž z, / p R / T k/ / via (1.3)

16 / / H œ p H p, H y y /, / T T CHAPTER 1. INTRODUCTION 3 Here denotes the principal part of the integral. It is useful to approximate the general theoretical expression for p R /UT in a way that displays explicitly certain physically meaningful parameters. These parameters depend on the particular approximation being made. For example, Penn [3] proposed a simple two-band model with an average bandgap / 798;:<: (known as the Penn gap) to account for p<r in a semiconductor or insulator. In this sense zero energy means an energy low compared to interband electron is given by transitions but higher than phonon energies. In Penn model p<r p<r T R T H R / X% / 798;:]: T (1.4) where / X is the plasma energy of the valence electrons. Plasma energy is proportional to the electron density. Whereas Penn model describes the static dielectric constant of semiconductor, Wemple and DiDomenico [4] used a single-oscillator model to show that below the forbidden gap the dielectric function in covalent and ionic materials can be expressed as p<r /-T" R /-T H / 2/, (1.5) where /, is the single oscillator energy and / 2 is the dispersion energy. The parameter / 2 is related to chemical bonding and the nearest-neighbor atomic-like quantities, and it is a measure of the strength of interband transitions. It does not significantly depend on either the bandgap or the volume density of valence electrons. According to Wemple and DiDomenico, the parameter / 2 follows the simple empirical relationship /32 H P?L > P 8, where P? is a coordination number, > is a formal chemical valence and P 8 is an effective number of valence electrons per atom. For diamond type semiconductors these values are: P?ƒHš, >Hš and P 8 H J. The multiplication factor varies from 0.32 in Ge to 0.39 in diamond. Thus, / 2 is related to the charge distribution within nearest-neighbor atomic vicinity, and closely related to chemical bonding. Furthermore, Wemple and DiDomenico related Penn gap / 798;:]: and single-oscillator energy, to p R /UT spectrum using moment integrals œ. œ R T / œ p R /UT k/ ž Ÿ (1.6) Here /z is the absorption threshold energy. The whole class of average gaps can be defined by the general relation / œ œ. Then / 798;:<: is simply the ratio of the 798;:<: H, is +1 to the -1 moments ( / ), whereas the single oscillator energy / the ration of the -1 to the -3 moments ( / ). Both parameters / 798;:]: and, are independent of the scale of p and both can be used to describe an average gap. Wemple and DiDomenico showed that / /, / 7 8 :<:. Consequently, Penn gap / 798;:<: weights the p R /UT spectrum at higher energies more heavily than single-oscillator energy /,. In addition to the single-oscillator parameterization given by (1.5), many other curve fitting forms involving three or more parameters have been used to describe the real part of dielectric function. In general, no physical significance has been attached to the parameters, and the expressions serve primarily as interpolation formulas. The wavelength of light in near-uv, visible and IR regions is much larger than the lattice constant or other relevant dimensions of the semiconductor structure. Thus, the

17 O G G o p H p CHAPTER 1. INTRODUCTION 4 optical measurements of homogeneous material are sensitive to macroscopic properties of solid state. When photons excite electrons from the filled to empty energy states, the intensity of an electromagnetic radiation is exponentially reduced during the passage through the material and this reduction is given by the absorption coefficient. Thus the absorption measurements are powerful tools that help us to understand the electronic structure of a material. Photons can also interact with lattice vibrations and with electrons localized on defects, making the optical techniques useful for studying these excitations The optical properties of a material are described by the complex index of refraction ( O ) [5]. The real ( yª{ O ) and imaginary ( G ) part of complex index of refraction are related to the complex dielectric function yk«p as follows: y «O H GIH p yž± y²± p y p y p p (1.7) (1.8) The imaginary part of the complex index of refraction G is related to the optical absorption coefficient o by equation G M (1.9) where M is a wavelength of light in vacuum. There is a tight relationship between the distribution of electronic states and the optical absorption spectrum [6, 7, 8, 9]. The presence of the forbidden gap in electron energy spectrum causes an abrupt discontinuity ( absorption edge ) in the graph relating the absorption coefficient with the photon energy of the radiation. The absorption edge defines the optical gap ( / ), which is the photon energy related to the forbidden gap between valence and conduction bands. Thus, the most direct and perhaps the simplest method for evaluation of the energy gap is to measure an absorption edge by inserting a layer of semiconducting material into a monochromatic light beam and studying the changes in transmitted optical intensity as a function of photon energy ( / ). The energy dependence of absorption coefficient allows us not only to determinate the optical gap, but also the nature of the optical transitions. Experimental and theoretical examination of the absorption edge of crystalline semiconductors led to the distinction between two kinds of optical transitions between the filled valence band and the unoccupied conduction band. In the semiconductor where the direct transition is allowed, the excitation of an electron by a photon satisfies the conservation of energy and crystal momentum. For instance, GaAs is a type of semiconductor known as a direct-gap semiconductor with the absorption coefficient proportional to R / /z %T ³. On the contrary, c-si and diamond are indirect-gap semiconductors with phonon assisted absorption of photons. In the indirect-gap semiconductor, excitation to the lowest energy electron state is forbidden by the failure of conservation of crystal momentum, and additional phonon momentum is necessary to conserve the crystal momentum. Their absorption coefficient is proportional to R / / µ / X T, where / X is energy of the phonon involved in the absorption. In contrast to crystalline semiconductors where the optical transitions are dominated by the long range symmetry of crystal lattice, there is no conservation of electron momentum in the disordered amorphous semiconductors. They introduce a new category

18 CHAPTER 1. INTRODUCTION 5 of optical transition a non-direct transition [2]. The optical absorption in an amorphous semiconductor was first described by J. Tauc in 1966 [10], and his model is still generally accepted. The model starts with a virtual crystal derived from the real crystal into which positional disorder is introduced. This model presumes a parabolic density of states for the conduction and valence bands, and an energy independent dipole matrix element between the states involved in a transition. Tauc model of optical transitions in amorphous semiconductor leads to an absorption coefficient proportional to R / / %T /. While the absorption spectrum associated with a defect free semiconductor terminates abruptly at the absorption edge, in an amorphous semiconductor an absorption tail extends into the gap region [2]. In the range of absorption coefficients below % cm, the optical absorption is exponential over three or more orders of magnitude ( Urbach edge ) [11], see figure 1.1. The Urbach edge in the optical absorption spectrum arises as a result of optical transitions involving the exponential tail states with their density exponentially decaying into the gap. These tail states are induced by the local bond length and bond angle distortions. Experimentally, it is found that the Urbach edge broadens with increased thermal and structural disorder [2], whereas the optical gap is insensitive to the disorder [12, 13]. Defects induce the localized states within the energy gap. Such states determine the position of the Fermi energy, which controls the free-carrier concentrations at the thermal equilibrium. They also act as the trap and/or recombination centers that determine the kinetics for restoration of equilibrium after any perturbations in carrier concentrations. The absorption is often used to obtain information about the density of sub-gap states, taking an advantage of the sensitivity of special measuring techniques such as constant photocurrent method (CPM) [14] and photothermal deflection spectroscopy (PDS) [15]. The main experimental techniques used for measuring the optical constants of bulk materials are transmittance and reflectance measurements, polarimetry and ellipsometry. They can be, in modified forms, applied also for thin films. Many books concerning the measurement of the optical properties of thin films have been published [7, 9]. They believed that normal incidence transmittance and reflectance measurements, based on measurements of ratio of intensity of reflected or transmitted light to incident radiation, were preferable, because of the generally nonhomogeneous nature of the films. The surface roughness and the presence of a transition layer at the film-air interface make interpretation of results in polarimetry and ellipsometry too difficult. Combining transmittance and reflectance measurements with special techniques for low absorptance values, it is possible to obtain a complete picture of the optical properties of a semiconductor for photon energies in a broad spectral range. Additional information about surface properties can be obtained by measuring an angular dependency of polarized reflectance the angle resolved reflectance (ARR), and angular dependency elastically scattered light the angle resolved scattering (ARS). 1.2 Hydrogenated amorphous silicon (a-si:h) Amorphous silicon In contrast to a crystalline structure, the amorphous structure lack the regular arrangement of their atoms. The structure of amorphous silicon (a-si) is generally believed to be

19 H CHAPTER 1. INTRODUCTION 6 a random network with four-coordinated atoms in their local bonding configurations [1]. Amorphous silicon is homogeneous on nm length scale, as no voids were detected within a sensitivity of 0.1 vol.% in SAXS [16]. However, the amorphous network is not continuous within an atomic-scale structure; it contains vacancies. The vacancies in a-si were directly observed by Mossbauer spectroscopy like two different line shapes of ¹ Sb incorporated in a-si, which has been interpreted to correspond to the site substitutions and vacancy complexes of Sb [17]. The local bond lengths and bond angles are slightly deviated from an ideal tetrahedral structure. On the average, the bond angles in a-si are deviated by 11.4 from a perfect tetrahedral bond angle. The average bond length in a-si is about 1.9% longer then that of crystalline silicon. It leads to a volume expansion and lower mass density a-si is about 1.8% less dense than c-si [16]. The large strain in the amorphous network introduces point defects. The dangling bonds formed at the three-coordinated sites are believed to be the dominant point defects in a-si. They are characterized by their B -factor value, B º»!, as observed in the electron paramagnetic resonance (EPR) experiments [18]. The dangling bonds in a-si form deeply localized gap states in [19]. The amorphous structure has a higher free energy than crystalline structure and therefore it exists as a kinetically frozen metastable phase. Heating at elevated temperature usually induces solid phase transition of amorphous into the thermodynamically stable crystalline phase. Properties of amorphous materials have been found to depend critically on the thermal history and/or preparation conditions. These changes have been attributed to structural relaxation [20], a process in which the whole amorphous network rearranges upon annealing to decrease its free energy. The structural relaxation decreases the bond-angle distortion, and increases short range ordering. The process can be reversed by degradating previously relaxed amorphous material. The structural relaxation and degradation are always connected with annihilation and creation of bond defects Deposition of a-si:h films Silicon thin films are now used in various large area devices instead of crystalline silicon (c-si) [1]. In contrast to the fabrication of crystalline silicon wafers, amorphous thin films technologies do not require the costly and delicate crystal traction and saving. The thin film technology is based on a simple and inexpensive deposition process on glass or other lowcost substrate at deposition temperatures well below the melting point of c- Si [21]. Nevertheless, the unhydrogeneted a-si thin films, prepared by sputtering or by thermal evaporation, have a very high defect density that prevents doping and reduces the mobility and lifetime of free carriers three desirable characteristics of a useful semiconductor. In 1975 W E. Spear discovered that hydrogen incorporated into the material during the deposition process reduces the density of localized states in the band gap [22]. The reaction of hydrogen with a growing amorphous silicon layer plays a crucial role there is an evidence [23] that during plasma deposition SiH radicals directly insert into strained Si-Si bonds. At present the most common method of depositing device quality a-si:h is plasma enhanced chemical vapor deposition (PECVD), based on plasma decomposition of silane gas, SiH¼. In the standard technology silane dissociates between two parallel electrodes in a radio frequency (13.56 MHz) glow discharge (GD) [1]. The plasma containing ions and other reactive species allow silicon to be deposited on the substrate at temperatures

20 CHAPTER 1. INTRODUCTION C, so hydrogen could be incorporated in amorphous silicon structure during the growth process. Increasing the discharge frequency (Very High Frequency Glow Discharge, VHF GD) to MHz brings an advantage of a higher deposition rate. In hot wire (HW) technology silane dissociates thermally in near heated tungsten filament placed close to the substrate. Filament temperature is around 2000 C [24]. Mahan et al. produced by this technology intrinsic a-si:h films with electronic properties equal to or better than GD a-si:h, particularly for low H-content films deposited at the substrate temperature above 360 C [25]. In all technologies, the deposition is complicated due to the fact that there are many variables in the deposition process which must be controlled to produce a good material. For example, the gas pressure determines the mean free path for collisions of the gas molecules and influences whether the reactions occur on the growing surface or in the gas [1]. The temperature of the substrate controls the chemical reactions on the growing surface and the hydrogen content in thin film. Discharge power controls the rate of dissociation of the gas and therefore the film growth rate. Other parameters are gas flow, gas dilution by hydrogen in inert gas, electrode self bias, reactor design, outgasing, gas purity, etc. Details about mechanisms influencing hot wire deposition of a-si:h are discussed in [26]. It is obvious, that proper choice of all technological parameters and the use of non-destructive and sensitive characterization techniques are essential for the material optimization Structure of a-si:h Structural disorder, inhomogeneities and the presence of hydrogen bonded to the amorphous network are specific features of a-si:h. This subsection summarizes several methods of their characterization. Although the amorphous network cannot be analyzed in details by the conventional X-ray or electron diffraction method, Raman spectroscopy [27] provides a lot of information on the amorphous network, because all the vibration modes are Raman active. The technique comprises the inelastic scattering of light by simultaneous excitation of lattice vibrations. Excitation of optical phonons then yields information about the phonon dispersion. By means of Raman spectroscopy it is possible to measure quantitatively the bond length and angular distortions, which are the characteristics of an amorphous network. For example it was found, that the bond angle distortion in a-si:h is typically about 10% of the normal bond angle of crystalline silicon. Distortions induce internal stress and variations in the binding energy and force constants of the silicon bonds and thus affect the electrical and optical properties of a-si:h. The behavior of hydrogen in a-si:h is quite complex and not fully understood. Investigation of a-si:h prepared by ion implantation has shown [28] that only a limited concentration of hydrogen atoms can be accommodated in the Si network. This hydrogen concentration defines the solubility for hydrogen in a-si, which has been found to be about 4%. When this hydrogen concentration is exceeds, the alloy structure is unstable and, upon annealing, nanoscale H-rich defects nucleate and grow in size. Since hydrogen content in device quality GD a-si:h excess of the solubility limit, the material is therefore unstable to inhomogeneity formation. Thus, upon annealing at 400 C, hydrogen precipitates into nanoscale complexes [29]. Hydrogen clusters are formed also in material with less then 4% H, as will be discussed below. The thermal desorption spectroscopy is an analytical method used for analysis of hy-

21 5 0 CHAPTER 1. INTRODUCTION 8 4 E ~ ev D E ~ ev A E ~ 0.5 ev M Hydrogen density of states Energy 0 Figure 1.2: Schematic hydrogen density of states distribution in c-si and a-si:h according to [33]. 0 represents energy level of H in free space, 1 - mobile H, 2 - isolated interstitial hydrogen in c-si, 3 - ' - H chemical potential, 4 - H strongly bonded in Si-H bond. ½ is the activation energy of H diffusion, ½z¾ is the dangling bond formation energy and ½ is the migration energy. drogen chemical binding in a-si:h. The common way of measuring temperature regions of hydrogen evolution is based on measurement of the pressure of gas released into a certain volume, for samples heated at a constant rate [1]. In these experiments, a large amount of evolved hydrogen was observed near 400 C and further near 600 C. Hydrogen is completely removed from a-si:h if heated above 600 C. The lower temperature peak is explained by the releasing of weakly-bonded hydrogen captured at weak Si-Si bonds, whereas the temperature peak near 600 C is explained by the releasing of strongly bonded hydrogen in Si-H bonds. It was also found that the weakly-bonded hydrogen captured can diffuse easily through the amorphous network [30]. The detailed analysis of the peaks on differential scanning calorimetry curves shows that the low-temperature effect is connected to the relaxation of weak Si bonds. The high-temperature effect is connected to the hydrogen effusion with subsequent relaxation of the microstructure [31]. The research group in Brno obtained similar results using thermal desorption spectroscopy [32], which is based on the mass spectroscopy of thermally evolved hydrogen under the constant temperature growth rate. The bonding energy of the Si-H bond in a-si:h is influenced by its local environment. The figure 1.2 shows schematically the energies of various configurations of hydrogen in a silicon network [33, 34, 35], examined using first principle density-functional-pseudopotential calculations. The hydrogen chemical potential ( ' ) determines the occupation of various configurations. The states with energies below the chemical potential are in thermodynamic equilibrium. These states are mostly occupied by hydrogen, whereas those above are mostly empty. The chemical potential is at the minimum of the hydrogen density of states, i.e. at a level where the energy cost for creation of a Si dangling bond is zero. The energy difference between the mobile H and chemical potential (the activation energy of H motion ( / 0 )) determines the number of hydrogen atoms that can participate in diffusion. The motion of H through a-si:h at the temperature j can be described by / 0 G jœt. The activation energy /10 in undoped a diffusion coefficient * ' H *,9ÀÁÂ R