A Dissertation Entitled Spectroscopic Ellipsometry Studies of Thin Film A

A Dissertation

entitled

Spectroscopic Ellipsometry Studies of Thin Film a-Si:H Solar Cell Fabrication by

Multichamber Deposition in the n-i-p Substrate Configuration

Lila Raj Dahal

Submitted to the Graduate Faculty as partial fulfillment of the

requirements for the Doctor of Philosophy Degree in Physics

______Dr. Robert W. Collins, Committee Chair

______Dr. Patricia Komuniecki, Dean College of Graduate Studies

The University of Toledo

May 2013

This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of

Spectroscopic Ellipsometry Studies of Thin Film a-Si:H Solar Cell Fabrication by Multichamber Deposition in the n-i-p Substrate Configuration

Lila Raj Dahal

Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Doctor of Philosophy Degree in Physics

The University of Toledo

May 2013

Real time spectroscopic ellipsometry (RTSE), and ex-situ mapping spectroscopic ellipsometry (SE) are powerful characterization techniques capable of performance optimization and scale-up evaluation of thin film solar cells used in various photovoltaics technologies. These non-invasive optical probes employ multichannel spectral detection for high speed and provide high precision parameters that describe (i) thin film structure, such as layer thicknesses, and (ii) thin film optical properties, such as oscillator variables in analytical expressions for the complex dielectric function. These parameters are critical for evaluating the electronic performance of materials in thin film solar cells and also can be used as inputs for simulating their multilayer optical performance.

In this Thesis, the component layers of thin film hydrogenated silicon (Si:H) solar cells in the n-i-p or substrate configuration on rigid and flexible substrate materials have been studied by RTSE and ex-situ mapping SE. Depositions were performed by

iii magnetron sputtering for the metal and transparent conducting oxide contacts and by plasma enhanced chemical vapor deposition (PECVD) for the semiconductor doped contacts and intrinsic absorber layers. The motivations are first to optimize the thin film

Si:H solar cell in n-i-p substrate configuration for single-junction small-area dot cells and ultimately to scale-up the optimized process to larger areas with minimum loss in device performance.

Deposition phase diagrams for both i- and p-layers on 2" x 2" rigid borosilicate glass substrate were developed as functions of the hydrogen-to-silane flow ratio in

PECVD. These phase diagrams were correlated with the performance parameters of the corresponding solar cells, fabricated in the Cr/Ag/ZnO/n/i/p/ITO structure. In both cases, optimization was achieved when the layers were deposited in the protocrystalline phase.

Identical solar cell structures were fabricated on 6" x 6" borosilicate glass with 256 cells followed by ex-situ mapping SE on each cell to achieve better statistics for solar cell optimization by correlating local structural parameters with solar cell parameters. Solar cells of similar structure were also fabricated on flexible polymer substrates in the roll- to-roll configuration. In this configuration as well, RTSE was demonstrated as an effective process monitoring and control tool for thin film photovoltaics.

To my Parents, Families, and Friends

Acknowledgements

First and foremost, I would like to extend my sincere gratitude to my thesis advisor Prof. Dr. Robert W. Collins for his expert mentoring with good advice, suggestions, and guidance throughout the course of this work. Without his innovative suggestions and continuous support, none of the works mentioned in this Thesis research would have been possible.

Next, I have to thank Dr. Nikolas J. Podraza for his continuous help and guidance on the ellipsometry data analysis. Also, I thank my dissertation committee members Dr.

Sanjay Khare, Dr. Song Cheng and Dr. Andre S. Ferlauto for their willingness to serve on the committee, despite their busy schedule.

I would also like to thank the staff and the faculty of the Department of Physics and Astronomy for their continuous support of this work. At this point, I would like to remember all of my Nepalese friends and their families in the Toledo area for their support and help to myself and to my family. I appreciate the help from all the members of the ellipsometry group at the University of Toledo. Also, I would like to thank all the agencies, NREL, DOE, Air Force, NIST, and Xunlight Corp. for the funding they provided to work in this area of ellipsometry for thin film photovoltaics.

At last but not the least, I want to acknowledge my parents, my wife, my two little sons and my other family members back home for their continuous support in every aspect of my life.

Table of Contents

Abstract ...... iii

Acknowledgements ...... vi

Table of Contents ...... vii

List of Tables ...... xi

List of Figures ...... xiii

1 Introduction ...... 1

1.1 Motivation and Background ...... 1

1.2 Thesis Organization ...... 7

2 Ellipsometry and Experimental Apparatus ...... 11

2.1 Introduction ...... 11

2.2 Experimental Methods in Thin Film Deposition ...... 13

2.2.1 Cluster Tool Deposition System ...... 14

2.2.2 Sputtering Chamber ...... 14

2.2.3 Plasma Enhanced Chemical Vapor Deposition

(PECVD) Chamber ...... 18

2.3 Theory and Experimental Methods in Spectroscopic Ellipsometry ...... 21

2.3.1 Theoretical Formalism in Spectroscopic Ellipsometry ...... 21

2.3.1.1 Propagation of Light in Thin Films ...... 21

2.3.1.2 Ellipsometry and Reflection ...... 24

vii 2.3.2 Instrumentation for Spectroscopic Ellipsometry ...... 32

2.3.2.1 Real Time Spectroscopic Ellipsometry (RTSE) ...... 32

2.3.2.2 Ex-Situ Mapping Ellipsometry ...... 37

2.3.3 Data Analysis Strategies in Spectroscopic Ellipsometry ...... 39

2.3.3.1 Multilayer Analysis of RTSE and

Ex-situ Mapping Data ...... 40

2.3.3.2 Virtual Interface (VI) Analysis ...... 46

2.3.4 Application of Spectroscopic Ellipsometry in Thin Film Growth

2.3.4.1 Effective Medium Theory ...... 51

2.3.4.2 Ag Bulk Film Modeling ...... 54

2.4 Experimental Methods in Solar Cell Characterization ...... 63

3 Si:H Layer Optimization for Solar Cell Application ...... 66

3.1 Introduction and Motivation ...... 66

3.2 Deposition Process and Phase Diagram Development ...... 68

3.3 i-layer Phase Diagram on 2" x 2" Glass Substrate ...... 80

3.4 i-layer Phase Diagram on 2" x 2" Glass Substrate ...... 91

3.5 Spatial Phase Diagram of p-layer on Polymer Substrate ...... 99

3.6 Summary ...... 111

4 Si:H Layer Optimization for Solar Cell Application ...... 114

4.1 Introduction and Motivation ...... 114

4.2 Deposition Processes of Ag/ZnO and Al/ZnO Back Reflectors ...... 117

4.3 Comparative Study of Al/ZnO and Ag/ZnO Interfaces ...... 125

4.4 Scattering Behavior of Ag/ZnO Back-Reflector...... 139

viii 4.5 Scattering by Al/ZnO Back-Reflector ...... 151

4.6 Improvement of the Back-Reflectors ...... 157

4.7 Summary ...... 161

5 Roll-to-Roll Deposition of Thin Film a-Si:H Solar Cell Structure

on Polymer Substrates ...... 163

5.1 Introduction and Motivation ...... 163

5.2 Deposition Processes ...... 166

5.2.1 ZnO:Al Layer ...... 166

5.2.2 a-Si:H i- and p-layers ...... 173

5.3 Experimental Details for Real Time Spectroscopic Ellipsometry ...... 178

5.4 RTSE of ZnO:Al Evolution on Ag Coated PEN ...... 179

5.5 RTSE of i-layer Evolution on Ag/ZnO/n-layer Coated PEN ...... 191

5.6 RTSE of p-layer Evolution on Ag/ZnO/n/i-layer Coated PEN ...... 203

5.7 Summary ...... 212

6 Correlation Between a-Si:H Solar Cell Performance and

Structural/Optical Properties ...... 214

6.1 Introduction ...... 214

6.2 Optical Properties of i-layer and p-layer Materials ...... 217

6.3 Correlation of the Parameters of Solar Cells Deposited on 2" x 2"

Borosilicate Glass Substrates with the i-layer Phase Diagram ...... 224

6.4 Correlation of the Parameters of Solar Cells Deposited on 2" x 2"

Borosilicate Glass Substrates with the p-layer Phase Diagram ...... 232

6.5 a-Si:H Solar Cell on 6" x 6" Borosilicate Glass Substrate ...... 235

ix 6.6 a-Si:H Solar Cell on Kapton® Polymer Substrate ...... 249

6.7 Summary ...... 254

7 Summary and Future Works ...... 257

7.1 Summary ...... 257

7.2 Future Works ...... 266

References ...... 273

Appendix ...... 284

A.1 Analytical Expressions ...... 284

A.2 Parameter Coupling of the Cody-Lorentz Oscillator for High

Quality PV Materials ...... 290

List of Tables

3.1 Deposition conditions of component layers used for the i-layer phase diagram

study of thin film Si:H n-i-p solar cells on 2" x 2" glass substrate...... 70

3.2 Deposition conditions of component layers for the p-layer phase diagram study of

thin film Si:H n-i-p solar cells on 2" x 2" glass substrate...... 77

3.3 Deposition conditions of the underlying layers for the spatial phase diagram of the

p-layer in roll-to-roll cassette deposition on PEN polymers...... 78

3.4 Oscillator parameters used to represent  for underlying layers in the i-layer phase

diagram study on glass substrates...... 83

3.5 Tauc-Lorentz oscillator parameters representing the dielectric function for

nanocrystalline Si:H...... 88

3.6 Oscillator parameters used to represent  for underlying layers in the p-layer

phase diagram study on glass substrates...... 93

3.7 Oscillator parameters used to represent the underlying layers for the p-layer phase

diagram study on PEN polymer substrate...... 101

4.1 List of measured and deduced quantities and their comparisons in studies of the

plasmonic behavior in Ag/ZnO and Al/ZnO back-reflectors...... 118

4.2 Oscillator parameters used to represent  for Al thin films deposited at various

substrate temperatures...... 122

xi 4.3 Measured and predicted quantities at the lowest photon energy scattering

maximum in Ag/ZnO back-reflectors...... 149

4.4 Comparison of the parameters describing the scattering behaviors for Al/ZnO and

Ag/ZnO back-reflectors...... 156

4.5 A comparison of the optical properties at 1.5 eV for four Ag/ZnO back-reflector

structures tabulated in order of interface layer thickness...... 157

5.1 Deposition conditions used for i- and p-layer growth on PEN polymer substrates

using a roll-to-roll cassette capability...... 174

5.2 Oscillator parameters representing the  for component layers in studying

ZnO:Al evolution on PEN polymer substrates...... 183

5.3 Oscillator parameters representing the  for component layers in studying i-layer

evolution on PEN polymer substrates...... 194

5.4 Oscillator parameters representing the  for component layers in studying p-layer

evolution on PEN polymer substrates...... 207

6.1 Deposition conditions of the individual layers of an a-Si:H based solar cell

consisting of Cr/Ag/ZnO/n/i/p on a 6" x 6" glass substrate...... 236

6.2 Deposition conditions of the individual layers of an a-Si:H based solar cell

consisting of Cr/Ag/ZnO/n/i/p on a flexible Kapton® substrate...... 250

xii

List of Figures

2-1 Cluster tool deposition system to deposit the component layers of thin film Si:H

solar cells on various substrates...... 15

2-2 Schematic of the rf magnetron sputtering process for metal and TCO depositions

on planar substrates...... 16

2-3 Schematic of the PECVD chamber used in the deposition of intrinsic and doped

Si:H layers used in thin film solar cells...... 19

2-4 Schematic representation of the electric field vector trajectory E(z0, t) for an

elliptically polarized light wave...... 24

2-5 Schematic of the plane of incidence along with the propagation vectors ki

(incident), kt (transmitted), and kr (reflected)...... 25

2-6 Schematic representation of plane wave reflection from a multilayer structure at

non-normal incidence...... 28

2-7 Schematic of the real time spectroscopic ellipsometry (RTSE) instrumentation

used to study the sputter deposition of metal/TCO layers...... 34

2-8 A single rotating compensator multichannel ellipsometer used for large area

mapping (AccuMap-SE)...... 38

2-9 Schematic of a four-medium (pseudo substrate / outerlayer / surface roughness /

ambient) model used in virtual interface analysis...... 49

xiii 2-10 Model dependent surface roughness and MSE evolution for the smoothest Ag

film deposited on a thermal oxide covered c-Si substrate...... 56

2-11 The complex dielectric function of the smoothest Ag film deposited on a thermal

oxide covered c-Si substrate...... 58

2-12 Model dependent surface roughness and MSE evolution for a moderately rough

Ag film deposited on a thermal oxide covered c-Si substrate...... 59

2-13 The complex dielectric function of a moderately rough Ag film deposited on a

thermal oxide covered c-Si substrate...... 60

2-14 Model dependent surface roughness and MSE evolution for a rough Ag film

deposited on a thermal oxide covered c-Si substrate...... 61

2-15 The complex dielectric function of a rough Ag film deposited on a thermal oxide

covered c-Si substrate...... 62

3-1 Surface roughness thickness versus bulk layer thickness for a Si:H i-layer film

deposited on an a-Si:H n-layer...... 74

3-2 Deposition rates of the i-layer as a function of the hydrogen dilution ratio R for

films on Cr/AgZnO/n-layer coated glass...... 84

3-3 Surface roughness thickness versus the bulk i-layer thickness for Si:H films

deposited at R = 10 and 30...... 85

3-4 Nanocrystalline volume fraction as a function of the bulk i-layer thickness for a

Si:H film deposited at R = 30...... 89

3-5 A deposition phase diagram for rf PECVD of i-layers fabricated on glass coated

with a Cr/Ag/ZnO/n-layer structure...... 90

xiv 3-6 Deposition rates of the p-layer as a function of the hydrogen dilution ratio R for

films on Cr/AgZnO/n/i-layer coated glass...... 95

3-7 Surface roughness thickness versus the bulk p-layer thickness for Si:H films

deposited at R = 75 and 250...... 97

3-8 A deposition phase diagram for rf PECVD of p-layers fabricated on glass coated

with a Cr/Ag/ZnO/n/i-layer structure...... 98

3-9 Evolution of the effective thickness of a thin film Si:H p-layer as measured by SE

during roll-to-roll deposition on a polymer substrate...... 103

3-10 Surface roughness evolution of the p-layers as measured by RTSE at different

web speeds on a polymer substrate...... 105

3-11 Maps of the p-layer surface roughness and bulk layer thickness deposited on a

polymer substrate at a web speed of v = 0.015 cm/s...... 107

3-12 Maps of the p-layer surface roughness and bulk layer thickness deposited on a

polymer substrate at a web speed of v = 0.020 cm/s...... 110

4-1 Complex dielectric function of the smoothest Al film deposited on a thermal

oxide covered c-Si substrate...... 120

4-2 Complex dielectric functions of the ZnO used in the Ag/ZnO and Al/ZnO RTSE

data analyses...... 123

4-3 Schematic of the specular and diffused reflectance measurement used to quantify

the tolar reflectance from a back-reflector...... 124

4-4 RTSE analysis of Al/ZnO interface layer formation during deposition of a ZnO

layer on a smooth Al film...... 128

xv 4-5 Complex dielectric function of the Al/ZnO interface layer formed while

depositing ZnO on a smooth Al layer...... 129

4-6 Complex dielectric function of the Ag/ZnO interface layer formed while

depositing ZnO on a moderately rough Ag layer...... 131

4-7 Correlation of surface roughness thickness from RTSE with rms roughness from

atomic force microscopy (AFM)...... 134

4-8 Resonance energy of the plasmon band and the interface layer thickness as

functions of Al surface roughness thickness...... 136

4-9 Resonance energy of the plasmon band and the interface layer thickness as

functions of Ag surface roughness thickness...... 137

4-10 Optical processes at the metal/TCO interface that result in reflection and

dissipation loss through plasmon mediated processes...... 140

4-11 Comparison of the reflectance deficit and predicted absorbance with the measured

scattering on smoothest Ag/ZnO back-reflector...... 143

4-12 Comparison of the reflectance deficit and predicted absorbance with the measured

scattering on a moderately rough Ag/ZnO back-reflector...... 144

4-13 Comparison of the reflectance deficit and predicted absorbance with the measured

scattering on a textured Ag/ZnO back-reflector...... 145

4-14 Comparison of the reflectance deficit and predicted absorbance with the measured

scattering on a ~100 Å rough Al/ZnO back-reflector...... 152

4-15 Comparison of the reflectance deficit and predicted absorbance with the measured

scattering on a ~100 Å rough Ag/ZnO back-reflector...... 153

xvi 4-16 Comparison of the imaginary parts of the complex dielectric function of

moderately rough Ag as roughened by two different methods...... 159

5-1 Schematic of normal speed and reduced speed roll-to-roll cassette deposition of

ZnO:Al and i-layer Si:H on a polymer substrate...... 165

5-2 Schematic of the monitoring configuration used for RTSE of thin film ZnO:Al

deposited by sputtering with the roll-to-roll cassette substrate...... 168

5-3 Schematic of the monitoring configuration used for RTSE of thin Si:H layer

deposited by PECVD with roll-to-roll cassette substrate...... 176

5-4 ZnO:Al complex dielectric function obtained using an analytical model and by

direct numerical inversion...... 181

5-5 Complex dielectric function of the Ag/ZnO interface as obtained using an

analytical model...... 182

5-6 Ag/ZnO interface layer thickness evolution during normal speed 0.0077 cm/s roll-

to-roll deposition of a ZnO:Al layer...... 184

5-7 Measured and simulated effective thickness evolution of the ZnO:Al layer during

normal speed roll-to-roll deposition...... 185

5-8 Measured and simulated effective thickness evolution of the ZnO:Al layer during

reduced speed, followed by normal speed, roll-to-roll deposition...... 187

5-9 Measured and simulated evolution of the ZnO:Al layer during normal and

reduced speed assuming a virtual source at the shutter position...... 189

5-10 Map of the effective thickness of ZnO:Al deposited at the normal speed of 0.0077

cm/s on Ag coated PEN at the leading edge...... 191

xvii 5-11 Complex dielectric function of the a-Si:H i-layer obtained using an analytical

model and by direct numerical inversion...... 193

5-12 Evolution of the layer thicknesses for the i-layer during normal speed roll-to-roll

deposition at 0.012 cm/s...... 195

5-13 Evolution of the layer thicknesses for the i-layer during reduced speed, followed

by normal speed, roll-to-roll deposition...... 197

5-14 Effective i-layer thickness evolution during normal and reduced speed roll-to-roll

deposition to study the deposition reproducibility...... 199

5-15 Measured and predicted thickness evolution for the i-layer in the saturation

region...... 200

5-16 Map of the effective i-layer thickness on the leading edge of the polymer substrate

as deposited at the normal speed of 0.012 cm/s...... 202

5-17 Map of the i-layer surface roughness thickness on the leading edge of the polymer

as deposited at the normal web speed...... 204

5-18 Map of the optical band gap of i-layer on the leading edge of the polymer as

deposited at the normal web speed...... 205

5-19 Complex dielectric function of the a-Si:H p-layer obtained using an analytical

model...... 206

5-20 Evolution of the effective, bulk, and surface roughness p-layer thicknesses during

normal speed roll-to-roll deposition at 0.20 cm/s...... 208

5-21 Evolution of the effective, bulk, and surface roughness p-layer thicknesses during

reduced speed including normal speed roll-to-roll deposition...... 210

xviii 5-22 Effective p-layer thickness evolution during normal and reduced speed roll-to-roll

deposition to study the deposition reproducibility...... 211

5-23 Evolution of the effective p-layer thickness when the plasma is ignited with the

help of a hot wire filament...... 212

6-1 Complex dielectric function for an amorphous Si:H i-layer at 200C, deposited at

R =10...... 220

6-2 Band gap energy as a function of R for i-layers on Cr/Ag/ZnO/n-layer coated

glass substrates...... 221

6-3 Band gap energy as a function of R for p-layers on Cr/Ag/ZnO/n-layer coated

glass substrates...... 223

6-4 Solar cell parameters for devices prepared on glass substrates versus R for i-layer

deposition to correlate with the i-layer phase diagram...... 226

6-5 Deposition phase diagram of the i-layer on glass substrate including a data point

at R = 20 obtained for growth on a c-Si substrate...... 228

6-6 Surface roughness evolution of i-layers deposited at R = 20 on a native oxide

covered c-Si wafer and c-Si wafer coated with an amorphous n-layer...... 230

6-7 Solar cell parameters for devices prepared on glass substrates versus R for p-layer

deposition to correlate with the p-layer phase diagram...... 233

6-8 Deposition phase diagram of the p-layer on Cr/Ag/ZnO/n/i-layer coated glass

substrate...... 234

6-9 Maps of solar cell performance parameters from 246 operating dot cells fabicated

on large area 6" x 6" glass substrate...... 238

xix 6-10 Maps of (a) bulk i-layer, (b) bulk p-layer, and (c) p-layer surface roughness

thicknesses on a large area solar cell structure...... 239

6-11 Optical band gap maps of (a) i- and (b) p-alyers on a large area solar cell structure

obtained from ex-situ mapping SE...... 240

6-12 Correlation of the solar cell performance parameters with i-layer thickness for

devices fabricated on a large area glass substrate...... 242

6-13 Correlation of the solar cell performance parameters with p-layer bulk and surface

roughness thickness...... 243

6-14 Correlation of solar cell performance parameters with i-layer optical band gap for

devices fabricated on a glass substrate...... 244

6-15 Correlation of open circuit voltage and efficiency with p-layer optical band gap

for solar cells fabricated on a glass substrate...... 245

6-16 Surface roughness thickness as a function of bulk layer thickness for the Si:H

p-layer deposited at R = 250...... 247

6-17 Large area (6.2" x 5") thin film a-Si:H n-i-p solar cell structure fabricated on a

flexible Kapton® substrate...... 252

6-18 Spatial distribution of operating and shunted dot cells on a large area (6.2" x 5")

flexible Kapton® polymer substrate...... 253

Chapter 1

Introduction

1.1 Motivation and Background

As the world’s population increases and the per capita energy consumption increases due to advances in the standard of living, the need for energy sources alternative to the conventional fossil fuels increases as well. This need is urgent because the world’s fossil fuel reserves are being depleted rapidly, and the adverse environmental impact caused by burning fossil fuels is threatening critical infrastructures of human civilization due to climate change. Moreover, tensions arising from disputes over the control of fossil fuel reserves have lead to considerable geopolitical instability. Thus, alternative distributed energy resources that can partially or completely replace conventional fossil fuels have the potential to support increases in the standard of living of the world’s population, stabilize the climate, and reduce global conflicts. Renewable energy sources such as hydropower, geothermal, wind, solar thermal and photovoltaics, among others, are desirable alternatives to reduce the dependence on conventional fossils fuels and provide energy that is more widely distributed over the world’s population.

Among the various renewable energy sources, solar derived sources can be implemented almost anywhere in the world. Solar radiation has been used over the

1 centuries as the source of light and heat that sustains life. After the industrial revolution, photovoltaics (PV), in which sunlight is converted directly into electrical energy, has become a more valuable approach for using solar radiation. Solar modules consist of arrangements of individual solar cells connected in series and parallel in order to increase voltage and current over that of single cells, and thus provide the most widely adaptable approach for widespread implementation of PV (Rose, 1979). PV modules have been applied for generating electricity, first for satellites, later for terrestrial use, and now even for planetary and space exploration. Since the sun is a virtually limitless, distributed source of clean energy with very high potential for widespread use, it is possible to implement solar as the primary source of worldwide terrestrial electrification for years to come. Quantitatively, the energy of solar radiation incident on the earth per day (~ 14 terawatt-years), is sufficient to supply the energy demand of the world for an entire year.

Hence the research and development of solar cells for PV applications has become a focus of intensive investigation in the fields of science and technology in recent years.

The largest portion (~ 90%) of the solar module market for terrestrial PV applications is based on bulk single crystalline and multicrystalline silicon materials, often referred to as first generation PV technology. This technology exhibits ~ 15 - 25% efficiency at the small area solar cell level (Green et al., 2004). Although solar modules made from crystalline materials give the highest conversion efficiencies, they can be more expensive to fabricate and process, and hence without government subsidization are less competitive relative to the conventional sources of energy. In attempts to reduce the cost of PV modules, solar modules based on thin films often referred to as second generation PV technology, have been introduced. The second generation solar modules

2 are based on thin film materials including hydrogenated silicon (Si:H), cadmium telluride

(CdTe), or copper indium-gallium diselenide (CuIn1-xGaxSe2 or CIGS). Since very little material is used in thin film solar modules relative to silicon in bulk crystalline silicon solar modules and high throughput thin film production processes such as magnetron sputtering, closed space sublimation (CSS), vapor transport deposition (VTD), plasma enhanced chemical vapor deposition (PECVD), among others can be used for deposition, these second generation solar modules have the potential for lower cost compared to the first generation modules. A discussion of the comparative economics of solar modules has been given by Luque and Hegedus (2003).

Hydrogenated silicon (Si:H) is among the first material systems to be incorporated as thin films into solar cell structures, the reason being that hydrogenated amorphous and nanocrystalline silicon are the most widely studied thin film semiconductors by scientists and engineers. Because amorphous Si:H (a-Si:H) is composed of abundant and non-toxic elements, it has an advantage over other thin film technologies. Furthermore small thicknesses of amorphous and nanocrystalline silicon, relative to bulk crystalline silicon, are sufficient to absorb the solar spectrum, yielding another advantage in solar cell applications. Finally, thin film Si:H deposition systems can be highly automated in fully integrated roll-to-roll or rigid substrate production lines with low operating cost including low source material consumption and low capital equipment depreciation (Schott, 2003). Projections that compare the price levels for different PV material technologies show that the break-even cost level of thin film Si:H based PV modules will be reached at ~ $1.15 per Watt peak (Wp) (USDOE, 2007). The calculated energy pay-back time for thin film Si:H based solar modules, i.e. the time it

3 takes to recover the energy required to produce the modules, lies in the range of one to three years (Alsema, 1999; Kato et al., 1998), whereas the functional lifetime of thin film

Si:H based modules is about 30 years (NREL, 1999).

The semiconducting behavior of a-Si:H was first demonstrated by Chittick et al.

(Chittick et al., 1969), who prepared the material in thin film form from a glow discharge of silane (SiH4) gas. In the mid 1970’s, the first doping of a-Si:H was reported by Spear and Lecomber (Spear and Lecomber, 1975), and in the following year, Carlson and

Wronski developed the first a-Si:H solar cell in the n-i-p substrate configuration (Carlson and Wronski, 1976). Over the years, the performance of the thin film a-Si:H solar cells was gradually improved by optimizing the passivation of electronic defect states associated with the dangling bonds using hydrogen atoms. Hydrogen incorporation relaxes the tetrahedral network and hence reduces the disorder due to the formation of an a-Si:H alloy with a lower average Si coordination number. Presently, the highest performing substrate type a-Si:H based solar cells are produced in the triple-junction configuration in which three n-i-p structures are stacked in the same device (Yang et al.,

1997; Deng et al., 2000). The intrinsic layer (i-layer) of a single junction solar cell is prepared from a-Si:H and the doped n- and p- layers can be either hydrogenated amorphous or nanocrystalline silicon.

Plasma enhanced chemical vapor deposition (PECVD) of SiH4 or Si2H6 and H2 gas is the most common technique used to deposit thin film Si:H layers at temperatures lower than 300oC. The optical and the electrical properties of these layers depend strongly on the deposition process and on the values of the deposition parameters such as total gas pressure, rf plasma power, substrate temperature, gas flows etc. Magnetron

4 sputtering is the most common deposition process for the back contact metal layers and the TCOs used in the thin film Si:H n-i-p solar cell. The goal of this research is to identify the best deposition conditions for the component layers of the a-Si:H based solar cell in the n-i-p substrate configuration based on a better understanding of the deposition processes.

The primary characterization tools in this work for optimization of the layers for a-Si:H solar cell applications include real time spectroscopic ellipsometry (RTSE) and ex-situ mapping spectroscopic ellipsometry. Both tools employ a rotating compensator multichannel ellipsometer for high accuracy and high speed. Being a non-invasive technique, RTSE is useful for exploring the fundamental relationships among the preparation and the structural parameters of thin film materials (Messier, 1986). This technique has been used to analyze the microstructural evolution of Si:H layers deposited on various bulk and thin film substrates ranging from microscopically smooth to rough, including native and thermal oxide coated crystalline silicon, glass, as well as a-Si:H and nc-Si:H, the latter two deposited under conditions different than the overlying thin film materials (Koh, 1998; Rovira 2000; Ferlauto 2001; Ferreira 2004). Also, these earlier

RTSE analyses have provided a number of deposition phase diagrams that provide guiding principles for the optimization of Si:H layers, even though film properties are highly system specific, depending on the size of the reactor cathode, the gas flow pattern, the cathode-to-substrate distance, etc. In these earlier reported phase diagrams, the optimum solar cell performance was observed with a protocrystalline i-layer (Koh et al.,

1998). In addition, a protocrystalline p-layer was found to produce the highest open circuit voltage Voc in the n-i-p substrate configuration (Koval et al., 2002).

5 Mapping spectroscopic ellipsometry, on the other hand, is used to evaluate the spatial uniformity of the component layers of the thin film Si:H solar cell over large areas. This measurement is performed ex-situ i.e. after the layer is deposited and removed from the chamber. In this work, the spatial phase diagram of the p-layer has been developed based on the observed roughening transition of the p-layer as it increases in thickness. Another impressive application of mapping spectroscopic ellipsometry involves the correlation of the layer structural parameters with the solar cell performance parameters so that optimization can be performed expeditiously from a single deposition.

Such studies are performed by fabricating a large number of small area dot cells across the full area of the solar cell structure such that a one-to-one correspondence is ensured between the structural parameters from the ex-situ mapping spectroscopic ellipsometry measurement and the solar cell performance parameters from the current-voltage measurement.

In short, this Thesis work describes a spectroscopic ellipsometry study of the component layers of the thin film Si:H n-i-p solar cell as deposited on a flexible substrate, and establishes a metrology to control layer thicknesses in real time. Phase diagrams of i- and p-layers have been developed for optimization of solar cells on rigid glass substrates and correlated with the corresponding solar cell performance. Spatial phase diagrams of p-layers on flexible substrates have also been developed. The overall goal of this work has been to optimize single junction a-Si:H solar cells on rigid as well as on flexible substrates and to develop strategies for fabricating tandem and even triple junction thin film Si:H solar cells.

6 1.2 Thesis Organization

This Thesis describes investigations of thin film Si:H solar cells in the n-i-p substrate configuration from the back contact through the active layer to the top p-layer contact. In most studies rigid glass substrates are used, however, some involve flexible substrates such as Kapton® plastic. Real time spectroscopic ellipsometry (RTSE) and ex- situ mapping spectroscopic ellipsometry (SE) are the main characterization methods applied to optimize the solar cell performance in this work. RTSE studies of the active intrinsic layer of the cell give the optical properties as functions of the photon energy obtained for different deposition parameters. The parameter of greatest interest is the hydrogen dilution ratio R (R = [H2]/[SiH4]), and for depositions at relatively high R, the material undergoes phase changes from amorphous-to-(mixed-phase) and eventually to single-phase nanocrystalline Si:H with increasing thickness. In back-reflector studies,

RTSE provides the evolution of the (i) surface roughness layer thickness on the metal film (Ag or Al), (ii) the transparent conducting oxide (ZnO) layer thickness, and most importantly (iii) the interface layer thicknesses (Ag/ZnO and Al/ZnO). These interface layers cannot be modeled by using simple effective medium approximations of the component layers. Ex-situ mapping ellipsometry is applied to study the large area uniformity of the layers on both rigid glass and flexible plastic substrates. Moreover, a unique methodology for correlating thin film structural properties with the performance of small area dot cells has been developed. In such analysis, the ex-situ mapping ellipsometry data are collected at one side of each dot cell and the results of this measurement are correlated with the corresponding dot cell performance parameters.

From this study, given sufficient non-uniformities, the best values of all the structural

7 parameters required for optimization of the single junction Si:H solar cells can be proposed.

Chapter 2 starts with a description of the experimental deposition equipment including magnetron sputtering and plasma enhanced chemical vapor deposition

(PECVD) systems. The second section focuses on spectroscopic ellipsometry starting with the theoretical background describing the interaction of light waves with matter and proceeding with the foundations of ellipsometry measurement for thin films having multilayer structure. The real time spectroscopic ellipsometry (RTSE) and the ex-situ mapping spectroscopic ellipsometry instrumentation and procedures are discussed in detail in this section as the main characterization methods. Next, this section provides an overview of data analysis strategies in RTSE as well as in ex-situ mapping spectroscopic ellipsometry. Described here are the methods developed to determine the complex dielectric functions and film thicknesses from the measured spectroscopic ellipsometry data based on multi-time analysis and on global -minimization analysis, both of which apply inversion and least square regression routines. Another important method is also discussed called virtual interface (VI) analysis, which is used to determine the evolution of the volume fraction of nanocrystalline silicon in Si:H thin films deposited at higher R values. To end the ellipsometry section, a description of effective medium approximations (EMA) is included and as an example, the EMA is applied to model the surface roughness layer on Ag films. Finally, the basics of solar cell operation are introduced.

Chapter 3 represents the main focus of this Thesis as it presents the phase diagram development for intrinsic and p-type Si:H depositions on rigid glass substrates based on

8 RTSE data collection and analysis. Also discussed is the spatial phase diagram of the thin but critical p-type Si:H layer (or p-layer) on flexible plastic substrates obtained from ex-situ mapping spectroscopic ellipsometry. The growth regimes of interest to achieve the most ordered protocrystalline i- and p-layers are identified from the deposition phase diagram. The dielectric functions of the i- and p-layer deposited at different R values are presented.

In Chapter 4, the back-reflector in the thin film Si:H solar cell is discussed. A comparative study of two types of back-reflectors, Ag/ZnO and Al/ZnO, is described based on their optical responses over the near infrared spectral range of operation.

Specular reflections as well as scattering are measured to understand the net absorption loss for back-reflectors with different metal/ZnO interface layer thicknesses. At the end of this Chapter, methods for optimization of the back-reflector in thin film Si:H solar cells are proposed.

Chapter 5 provides a detailed description of the roll-to-roll deposition of component layers of thin film Si:H solar cells on low-cost poly-ethyl napthalate (PEN) substrates. A suitable mathematical model has been developed to describe the sputter deposition of the ZnO layer at different speeds of the flexible substrate in roll-to-roll processing. Similar but simpler models are used to describe PECVD processing. Ex-situ mapping results in both cases have been correlated with the RTSE results. The overall concept of the Chapter 5 studies is to apply spectroscopic ellipsometry in a simulated production environments as a process control tool.

Chapter 6 includes solar cell results and discussion for solar cells on small area

2" x 2" glass substrates and on larger area 6" x 6" glass substrates. A smaller set of

9 results is provided for flexible Kapton substrates. The solar cell results on glass substrates are correlated with RTSE and ex-situ mapping spectroscopic ellipsometry results. A unique method for optimization of thin film Si:H solar cells in a smaller number of fabrication runs is presented. In this method, area non-uniformities in thicknesses and optical property parameters such as band gap can be characterized by ex- situ mapping spectroscopic ellipsometry and various component layers can be exploited in a single deposition in order to identify the parameter values that optimize solar cell performance.

Finally, Chapter 7 summarizes all the research results and discussions presented in this Thesis and the overall conclusions drawn from it. Additionally, future directions for optimization of thin film Si:H solar cells from different perspectives are discussed in detail in this final Chapter.

Chapter 2

Ellipsometry and Experimental Apparatus

2.1 Introduction

Ellipsometry is an optical measurement in which plane waves of light having known wavelength and polarization are directed onto a sample surface, and the change in polarization state of the wave upon specular reflection is analyzed to obtain the structural and the optical properties of the sample. Layer thicknesses on the reflecting sample surface can be obtained with atomic layer sensitivity when the polarization state of the light wave reflected from the sample can be obtained accurately i.e. to within ± 0.1o in the azimuth and ellipticity angle. In the 1970’s, automatic ellipsometers of different designs have been developed to collect spectroscopic data from the near infrared (NIR) to the ultraviolet (UV) range. In the 1990’s, multichannel detection systems were integrated into spectroscopic ellipsometry instrumentation so that the data acquisition time for full spectra can be very short. As a result sub-monolayer sensitivity can be achieved in-situ and in real time during dynamic processes. Dynamic processes of interest may include thin film nucleation and growth during deposition or thin film removal during etching.

Spectroscopic ellipsometry data collection in-situ during dynamic processes is often referred to as the real time spectroscopic ellipsometry (RTSE). Since spectroscopic

11 ellipsometry uses a low irradiance light source, usually a Xe lamp, it is a non-destructive probe for thin films as well as bulk materials. Because of its real time spectroscopic capabilities and non-invasive character, RTSE has become a powerful optical tool to monitor a wide variety of surface and thin film processes in-situ in various environments

(Collins, 1990; Collins et al., 2001). In the field of amorphous and nanocrystalline

(previously known as microcrystalline) semiconductor materials, most notably silicon, silicon-carbon alloys, and silicon-germanium alloys, RTSE has been applied to analyze nucleation, coalescence, and microstructural evolution (An et al., 1990; Koh et al., 1999;

Ferlauto et al., 2004, Stoke et al., 2008), optical band gap (An et al., 1991; Koh et al.,

1995; Kim et al., 1996), void volume fraction (Kim et al., 1996), and alloy composition

(Fujiwara et al., 1998; Podraza et al., 2006) among other thin film structural and compositional properties. It has also been successfully applied to study hydrogenated amorphous and nanocrystalline silicon film growth from Si2H6 and H2 at various deposition conditions (Stoke et al., 2008).

The first section of this chapter describes the cluster tool deposition system used to deposit the component layers of thin film a-Si:H solar cells. Both sputtering

(metal/TCO deposition) and PECVD (n-, i-, p-layer deposition) chambers are described in detail in this section. The second section of this chapter introduces the theoretical formalism of polarized light and ellipsometry that describes the interaction of light waves with matter. The first part of this section starts with the fundamental concepts of electromagnetic wave propagation as described from Maxwell equations and proceeds to the optics of the multilayer thin film stack. The fundamental concepts discussed in this part form the basis of the optical modeling and data analysis described in the later parts of

12 this section. The experimental equipment used for the data acquisition by RTSE and by ex-situ mapping spectroscopic ellipsometry (SE) are described in the second part of this section. The third part of the section on ellipsometry addresses the analysis of the ellipsometric data so that the layer thicknesses, optical properties, chemical composition, etc., of the component layers of the multilayer stack can be extracted. Multi-sample and global -minimization analysis routines as applied to RTSE data are discussed in great detail, and the virtual interface (VI) analysis for thin films of mixed-phase and nanocrystalline silicon are presented. In the final part of the second section, effective medium approximations that represent the dielectric functions of homogeneous mixtures will be discussed and, as an example, the surface roughness of Ag films will be modeled using various effective medium approximations. At the end of the chapter, a brief description of the solar simulator and the measurement of the fundamental solar cell parameters are presented.

2.2 Experimental Methods in Thin Film Deposition

This section provides a brief description of the experimental methods that have been applied to fabricate the various layers of the thin film Si:H solar cell in the n-i-p configuration. The description starts with the cluster tool deposition system for sputtering as well as for plasma enhanced chemical vapor deposition (PECVD). In Section 2.3, instrumentation for real time spectroscopic ellipsometry (RTSE) and ex-situ mapping spectroscopic ellipsometry are discussed. These tools enable characterization of the film growth process within the deposition chambers and the uniformity of different thin film parameters over large area samples, respectively. In Section 2.4, the solar simulator is

13 described for measurement of the solar cell parameters through the J-V characteristics performed on the multilayer devices fabricated in the cluster tool deposition system.

2.2.1 Cluster Tool Deposition System

The cluster tool deposition system at University of Toledo has a load lock; two sputtering chambers, one for metal and the other for transparent conducting oxides

(TCOs); three plasma enhanced chemical vapor deposition (PECVD) chambers for standard Si:H n-, i-, and p- layer depositions; and one chamber specifically for nanocrystalline Si:H deposition at high temperature. These chambers are connected through a central transfer zone, called the isolation and transfer zone (ITZ) so that the thin film Si:H solar cell layers Cr/Ag/ZnO/n/i/p can be deposited in succession without a vacuum break. Each chamber is equipped with ellipsometry ports for real time spectroscopic ellipsometry (RTSE) measurement. Figure 2-1shows a photograph of the cluster tool deposition system with a spectroscopic ellipsometer connected to the i- layer deposition chamber. The RTSE study of Ag/ZnO and Al/ZnO back-reflectors, which will be discussed in Chapter 4, however, has been performed in a separate sputtering chamber as this study was undertaken well before the cluster tool deposition system was installed.

2.2.2 Sputtering Chamber Two sputtering chambers exist as components of the cluster tool system, one for metal layer deposition and the other for TCO deposition. Each chamber has two sputtering targets each. The metal chamber holds Cr and Ag targets whereas the TCO chamber holds ZnO and ITO targets. Each of these sputtering targets is 11.25" x 2.25" in size. The separate sputtering chamber which is used for the Ag/ZnO and Al/ZnO back- reflector deposition but is not part of the cluster tool system, accepts three circular targets

Figure 2-1 Six chamber cluster tool deposition system with the capabilities for magnetron sputtering of metals and TCOs in two separate chambers; rf PECVD of Si:H n-, i-, and p- layers in three separate chambers; and vhf PECVD of nanocrystalline Si:H i-layer deposition in a single chamber. With the exception of the latter chamber, each is designed for (i) rigid glass substrates and (ii) flexible substrates using a roll-to-roll cassette configuration. Also shown is a spectroscopic ellipsometer connected to the i-layer chamber for RTSE data acquisition. In fact, all chambers are fitted with ellipsometry ports and possess this RTSE capability. This chamber was built by MV Systems Golden Colorado.

with 3" diameters. The deposition conditions of the various layers deposited by sputtering are provided in the relevant chapters.

Sputtering is a physical vapor deposition (PVD) process, one example being depicted in Figure 2-2, in which the atoms of a solid target material are ejected into the

15 gas phase as a result of the bombardment of this material by energetic ions. It is a vacuum process designed to deposit thin films onto substrates for the purposes of scientific research as well as for commercial production coating. The sputtering process is analogous to the so-called opening break in the game of billiards in which the cue ball

(the bombarding ion) strikes the neatly arranged pyramid (the atomic array of the crystalline target) thereby scattering the balls of the pyramid in all directions (Chapman,

1980). There are many different types of plasma processes that can be used to sputter thin films, one of the most popular being magnetron sputtering, which is the process applied in the present work and shown in Figure 2-2. In magnetron sputtering, the

Figure 2-2 Schematic of the rf magnetron sputtering process for metal and TCO depositions on planar substrates mounted above the rectangular target. The rf power leads to dc self biasing of the target relative to the substrate, and hence this process can be used to deposit films of non-conducting materials as well.

16 density of the plasma used in the process is enhanced by a magnetic field oriented parallel to the surface of the target (or cathode), trapping energetic electrons in this region

(Rossnagel, et al., 1990). For both metal and TCO sputtering in this work, alternating radio frequency (rf) power at 13.56 MHz is applied to the cathode with the chamber walls grounded. An rf frequency is preferred since the rf voltage can be coupled through any kind of impedance, and hence the electrodes (target and substrate plane) need not be conductors. In other words, rf magnetron sputtering is required for TCO deposition, although either rf or dc sputtering is possible for the metal layer depositions. In rf magnetron sputtering, the target becomes self-biased to a negative potential relative to ground such that it behaves as in dc sputtering whereby positive ion bombardment removes target atoms for subsequent deposition. The difference in electron and ion mobilities implies that the positively charged electrode draws more electron current than the negatively charged electrode draws positive ion current. Thus, a large initial electron current flows during the positive half cycle of the rf power supply whereas a small positive ion current flows during the negative half cycle. This implies that there is a net current averaged over each cycle of the rf supply thereby charging the capacitive plasma through which the rf power is dissipated via connections to target and substrate holder

(normally grounded). As a result, the operating point shifts to an average negative

Before the self-bias is established the high voltage applied across the electrodes creates a plasma which consists of high energy electrons and ions (Chapman, 1980). If the film to be fabricated is to be composed of the target material alone, then an inert gas

(most often argon) is used in the sputtering process. In contrast if the film to be deposited is a compound consisting of the target material and a sputtering gas component such as

17 nitrogen or oxygen, then the process is called “reactive sputtering” and uses an adjustable mixture of an inert gas and a reactive gas. The plasma emits radiation with a spectral distribution that depends on the nature of the gas used for the sputtering; as a result the plasma is sometimes called a “glow discharge”. The substrate is generally placed on a conducting holder so that the desired rf power can be supplied to the plasma between the magnetron electrode and the substrate holder.

In the current work, Ar is used in the metal layer sputtering process for both Cr and Ag deposited in the metal sputter chamber. Ar with a very small flow ratio of O2 is used as the sputtering gas for TCO deposition. The role of O2 in this reactive sputtering process is to provide sufficient oxygen for a nearly stoichiometric TCO layer. Otherwise the layer has high concentration of metal interstitials so that it becomes more conducting, but less transmitting, thus unsuitable as a transparent conductor.

2.2.3 Plasma Enhanced Chemical Vapor Deposition (PECVD) Chamber The thin film hydrogenated silicon layers for photovoltaic applications (n-, i-, and p- layers) are fabricated using rf plasma enhanced chemical vapor deposition (PECVD).

In the deposition chambers used for these processes, carefully controlled source gas flows including dopants are introduced and decomposed in a rf plasma between two electrodes.

As a result, the reactive radical species accumulate on the substrate surface to form the film. This deposition process is more localized than sputtering because of the uniform electric field which is established between two parallel plates, one being the cathode plate and the other being the grounded substrate holder. Thus, the reactive species from the plasma are deposited predominantly on the inner surfaces of the electrodes with very little deposited on the walls of the deposition chamber. A schematic of the PECVD apparatus including the windows for RTSE is shown in Figure 2-3.

Figure 2-3 Schematic of the PECVD chamber used in the deposition of intrinsic and doped hydrogenated silicon (Si:H) thin films for incorporation into Si:H based solar cells. The graphite heater is attached to the cathode under vacuum whereas the heater well is mounted outside the chamber at atmospheric pressure. The heater well operates radiatively and heats the chamber as well as the substrate and substrate holder.

The parameters that can be adjusted from deposition to deposition in the rf

PECVD process are the cathode configuration, rf plasma power, substrate temperature, total chamber pressure, the gas flows, and even more importantly, the gas flow ratios.

The spacing between the cathode and the substrate is 1.5 cm whereas the dimensions of the cathode are is 7" x 7", yielding a surface area of 49 inch2 or 316.13 cm2. The cathode configuration is kept fixed in all PECVD processes whereas the other parameters are varied from one deposition to another. The specific parameters for the different series of

19 depositions are given in Chambers 3 and 5 including processes using rigid as well as flexible substrates.

In the cluster tool deposition system, all parameters other than the heater temperature are controlled by computer through a programmable logic controller (PLC).

Both heaters are controlled by proportional-integral-derivative (PID) loops. The graphite heaters attached to the cathode inside each PECVD chamber are under phase angle control such that a constant current flows through it continuously in order to maintain constant temperature. A constant current through the graphite heater is very important in order to maintain a stable plasma during the deposition. The heater-well is mounted immediately above the substrate holder, but outside the chamber at atmospheric pressure.

The heater well operates radiatively and is controlled by a solid state controller. It turns on/off when the actual temperature is below/above the set point, respectively.

At lower hydrogen dilution the rf plasma in the PECVD process generally ignites spontaneously once the operating pressure and the rf power is reached. At higher hydrogen dilution, however, plasma ignition must be stimulated by a hot wire mounted at the corner of the cathode which injects electrons into the plasma region. Almost all i- layer depositions and most p-layer depositions required hot wire ignition of the plasma.

For the n-layer deposition, however, the rf power and pressure are ramped up for a short time interval to ignite the plasma and then are returned immediately to the set point values. This transient for such a short time interval in the n-layer deposition was believed to have a negligible effect on the solar cell performance, as most of the light is absorbed in the overlying p- and i- layers, before reaching into the n-layer. Recent work on p-i-n thin Si:H solar cells in superstrate configuration, however, has shown a strong

20 dependence of fill factor on the nature of the n-layer. Investigation of a similar dependence for n-i-p thin film Si:H solar cells in the substrate configuration can be a suitable future project for optimization of these single junction cells.

The strong oscillating electric field between the cathode and substrate generated by the rf power supply causes the precursor gas molecules to dissociate forming radicals.

These radicals diffuse and chemisorb first onto the substrate and then onto the growing film surface. Because the electric field is confined between the cathode and the flat substrate holder and the gas pressure is high, most radicals either reacts in the gas phase or at the surfaces of the cathode or substrate. It has been reported that in case of Si:H films from SiH4, the primary radical that contributes to film growth is SiH3, due to its weak reactivity with SiH4 and H2, the highest concentration species in the plasma

(Matsuda and Tanaka, 1986). Figure 2-3 shows the components of the PECVD system as described in this sub-section.

2.3 Theory and Experimental Methods in Spectroscopic Ellipsometry

2.3.1 Theoretical Formalism in Spectroscopic Ellipsometry

2.3.1.1 Propagation of Light in Thin Films

The propagation of electromagnetic radiation in free space and its interaction with a medium can be described by Maxwell’s Equations. The free space versions of

Maxwell’s Equations are given (in SI units) by:

E  /, 0 (2.1)

B E   , (2.2) t

B  0, (2.3)

21 E BJ  00   , (2.4) t

where E, B, J, and  are the macroscopic quantities, namely the electric field vector,

magnetic induction vector, current density vector, and charge density, respectively. In

Eqs. (2.1) and (2.4), 0 and 0 are the permittivity and permeability of free space,

respectively (Born and Wolf, 1997; Jackson, 1998).

Maxwell Equations (2.1 - 2.4) above require modifications in order to describe the

propagation of electromagnetic radiation in matter. In fact, such a description is best

formulated by introducing two additional field vectors, namely the displacement vector D

and the magnetic field intensity vector H (Collins and Vedam, 1995) as:

D = 0ˆ E, (2.5)

B = 0ˆ H, (2.6)

where ˆ and ˆ are general tensor functions called the relative dielectric permittivity and

the magnetic permeability of the material, respectively. These tensors describe the  response of the material to propagating electromagnetic radiations and are functions of

the frequency of the radiation. Thus and are called "optical functions" of the

material (Wooten, 1972).

In the case of an isotropic medium, the tensor functions of frequency and

reduce to the scalar functions  and  respectively. Furthermore, in the case of a

homogeneous and non-magnetic medium further simplification results, namely no spatial

dependence of  and and =1, respectively. Finally, if one assumes that no external

charges and currents are present in the material i.e. that the material is electrically neutral,

then the solution of Maxwell’s Equations gives a polarized transverse electromagnetic

22 wave propagating at phase speed v = c/[Re(N)] in the medium, where N = ε1/2 is the complex index of refraction of the material, and decaying in accordance with an absorption coefficient  given by  = (2/c)[Im(N)]. If the propagation direction of the electromagnetic wave is chosen to be the z-axis of a Cartesian coordinate system, then the electric field of the electromagnetic plane wave can be represented by:

E(z,t) = E0exp[i(Nz/ct)], (2.7)

Here E0 is a complex vector in the x-y plane, whose components in general have amplitude and phase terms to represent a polarized electromagnetic plane wave of angular frequency The complex refractive index N can be written as N = n + ik, where the real part n is the real index of refraction and the imaginary part k is the extinction coefficient of the material. The complex refractive index N is related to the dielectric function of the material  according to

2   12 iN   . (2.8)

Expanding N2 and equating the real parts on both sides and then the imaginary parts similarly gives:

22 1 n  k , (2.9a)

2 2nk. (2.9b)

In a Cartesian coordinate system with orthogonal unit vectors xˆ and ŷ , the complex vector E0 in Equation 2.7, that determines the polarization state of the wave in the x-y plane, can be written as:

E0E 0x exp i  x x  E 0y exp i  y  y , (2.10)

23 where x and y represent the absolute phases of the electric field components Ex and Ey, respectively, at z = 0 and t = 0.

2.3.1.2 Ellipsometry and Reflectance

In its most general progression, the electric field of a plane wave of light propagating along the z-direction, as given by Eqs. (2.9) and (2.10), traces out an ellipse in the x-y plane as a function of time t, at a fixed point in space, z = zo as shown in Figure

2-4. The two special cases of the light wave polarization are: (i) linear polarization with

Figure 2-4 Schematic representation of the electric field vector trajectory E(z0, t) for an elliptically polarized light wave. For a given z = z0, E traces out an ellipse over time. The sense of rotation determines whether the light wave exhibits left or right handed polarization. Q is the tilt angle between the ellipse major axis a and the x-axis, measured in counterclockwise-positive sense when facing the light beam source.  is the ellipticity angle given by tan–1 (b/a), where  > 0 corresponds to right-handed polarization and  < 0 corresponds to left-handed polarization (Ferlauto, 2001).

24 x = y, and (ii) circular polarization with x = y ± /2 and E0x = E0y. For the most general polarization state, the polarization can be described by an ellipse having the tilt angle Q (–90o < Q < 90o) between its major axis and the x-axis, and the ellipticity angle  determined by the ratio of the minor axis (b) to the major axis (a) given by,  = tan–1 (b/a)

(–45o <  < 45o) (Azzam and Bashara, 1977).

In ellipsometry, it is conventional to redefine the arbitrary orthogonal coordinates x-y to those based on the plane of incidence in a reflection experiment. By convention, the electric field in such an experiment is resolved into a p-component parallel to the plane of incidence and an s-component perpendicular to the plane of incidence, as shown in Figure 2-5. Hence, in this p-s coordinate system, the effect of a specularly reflecting

Figure 2-5 Schematic of the plane of incidence along with the propagation vectors ki (incident), kt (transmitted), and kr (reflected). This schematic demonstrates the definition of p-polarized and s-polarized waves (Ferreira, 2004).

25 surface on an incident plane electromagnetic wave can be described by the complex amplitude reflection coefficients defined as:

r Ep rp r p exp i  p   i , (2.11) Ep

r Es rs r s exp i  s   i . (2.12) Es where E and represent the complex electric field components and the phase shifts due to reflection, respectively. The superscripts “ i ” and “ r ” represent the incident and reflected fields of the corresponding waves, respectively.

In reflection ellipsometry, the ratio of the p and s reflection coefficients are of interest, rather than their individual values. Thus, the complex amplitude reflection ratio

r is defined as:

r r  p p exp i    . (2.13) r p s  rrss

The complex quantity r can be described in terms of the well-known ellipsometric angles (, ) which define the relative (p-to-s) field amplitude ratio (tan ) and the phase shift difference () between the p and s waves:

r tan  exp i  , (2.14) where

r tan p , (2.15) rs

  ps  . (2.16)

26 In the case of multilayer structures such as thin film solar cells, each individual layer, the substrate, and the ambient medium exhibit optical properties that differ from one another. Moreover, the substrate and the ambient medium are considered to possess an infinite thickness whereas all other layers in the structure possess a finite thickness.

As a result, there is only one incoming wave from the ambient medium and no incoming wave from the substrate medium. The reflection and transmission behavior of light passing through this multilayer structure can be calculated using the S-matrix formalism

(Azzam and Bashara, 1977). In this formalism, the optical spectra in the reflectance, transmittance and the ellipsometric angles of the multilayer structure are simulated based on the frequency or wavelength dependent refractive indices and extinction coefficients of the component layers, including the ambient as well as the substrate. In addition, the individual layer thicknesses excluding those of the ambient and the substrate, as well as the angle of incidence of the incoming beam are needed as known frequency-independent parameters in the simulation. Since these simulated optical spectra can also be measured directly, the frequency-independent model parameters can be adjusted in such a way to force the simulated spectra to agree more closely with the corresponding measured spectra. From a least squares fitting procedure, the direct physical quantities of interest such as the layer thicknesses in the multilayer structure and potentially the indices of refraction and extinction coefficients of the individual layers can be obtained. In order to obtain information on the indices of refraction and extinction coefficients using such a fitting procedure, these frequency dependent functions must be described in terms of frequency-independent adjustable parameters.

27 Figure 2-6 shows the configuration described in the previous paragraph, namely, a plane wave incident on a multilayer stack with m layers between a transparent semi- infinite ambient medium and a semi-infinite substrate. The angle of incidence of the

Figure 2-6 Schematic representation of plane wave reflection from a multilayer structure at non-normal incidence. The structure consists of m layers plus the substrate (m+1) and the ambient medium (0). 0 is the angle of incidence at the interface between the ambient medium 0 and layer 1, and j is the angle of incidence at the interface between layer j and j+1. The wave vectors k within the ambient and at the (j, j+1) interface are shown as arrows (Ferreira, 2004).

28 wave is o. The optical properties of each layer are represented by the complex refractive index Nj and the corresponding layer thickness dj. The incident plane wave at any given interface undergoes reflection and refraction. After reflection and refraction, the waves propagate through the upper and lower layers, respectively, before reaching the next interface along their paths. Accounting for all multiple reflections, a 2 x 2 scattering matrix S is formulated according to the procedure described by Azzam and Bashara

(Azzam and Bashara, 1977), which contains information on the thickness and optical properties of the component layers of the stack. The component layers and the interfaces that constitute the multilayer structure are represented by 2 x 2 matrices L and I, respectively, and the scattering matrix S is the product of these matrices. Assuming that the ambient medium is indicated by the numeral ‘0’ and the substrate is indicated by

‘m+1’, the scattering matrix S for the entire structure is a product of 2 x 2 matrices given by:

m SILI . (2.17) 01 j j( j 1) j1

The interface matrix between the jth layer and (j+1)st layer can be written as:

1 1rj( j 1) I  , (2.18) j( j 1) r1 t j( j 1) j( j 1) where r and t represent the complex amplitude (or Fresnel) reflection and transmission coefficients which can be calculated from the Fresnel equations for the j/(j+1) interface.

The complex Fresnel coefficients at the j/(j+1) interface are given by:

qqj j 1 r,j, j 1  (2.19a) qqj j 1

29 2q j t,j, j 1  (2.19b) qqj j 1 for the s-polarized wave, and by:

Nj 1 cos j  N j cos  j 1  r,j, j 1  (2.20a) Nj 1 cos j  N j cos  j 1 

2Njj cos  t,j, j 1  (2.20b) Nj 1 cos j  N j cos  j 1  for the p-polarized wave.

In these equations,

1/2 q N cos   N2  N 2 sin 2  and (2.21) j j j  j 0 j 

N0 and  are the complex refractive index of the ambient medium and the angle of incidence of the wave in the ambient medium, respectively.

The layer matrix Lj, also known as the phase matrix, characterizes the propagation of the light wave through the layer j and can be written as:

e0idjj L  , (2.22) j id 0ejj

2q where,  j (2.23) j  and  is the wavelength of the wave in the free space.

The product jdj is the phase shift of the wave as it propagates through the layer of thickness dj. This layer is characterized by the complex refractive index Nj.

30 After determining the interface and layer matrices according to Eqs. 2.18 – 2.23, the scattering matrix components can be obtained according to Eq. 2.17. By the definition of the scattering matrix, the complex amplitudes of the electric fields E0 at the top of the structure in the ambient and at the bottom of the structure within the substrate [ or the (m+1)st layer] are related through the matrix S by:

E EEE SS   m    ESILI0 m 1 11 12 m  1  m  1 , (2.24) 0      01 j ( j 1)    E0 EEEm 1 SS21 22  m  1 j1  m  1  where the “+” sign refers to the wave that propagates through the multilayer structure in the forward or + z-direction from ambient medium, whereas the “-” sign refers to the wave propagating in the reverse direction from the substrate toward the ambient. Eq.

2.24 is the most general form that describes the wave propagation in the multilayer structure and hence it is valid for either s or p-polarized waves. However, in this case, the electric field component  vanishes, as no component reflects back once it reaches the Em1 semi-infinite substrate. Therefore, from Eq. 2.24, the complex Fresnel reflection coefficients of the entire structure can be written in terms of the S matrix components as:

Sp s 21 r.ps   (2.25) Sp s 11

Thus, the ellipsometry angles (, ) are determined from the ratio of the reflection coefficients according to

i rSp p21 Ss11 r tan  e   . (2.26) rs S p11 S s21

The unpolarized reflectance, i.e. the ratio of the total reflected irradiance to the total incident irradiance on the stack, is the average of the p-polarized reflectance and the s- polarized reflectance. Hence the reflectance is given by:

31 11SS* SS* R r** r  r r p21 p21  s21 s21  p p s s  ** (2.27) 2 2 Sp11 S p11 S s11 S s11

Finally, the scattering matrix can be applied at any depth within the structure to determine the power flux passing through a planar interface (Leblanc et al., 1994). This result forms the basis for determining the absorbance of a given layer.

2.3.2 Instrumentation for Spectroscopic Ellipsometry

2.3.2.1 Real Time Spectroscopic Ellipsometry (RTSE)

RTSE is a non-invasive analysis method for thin films, in which case the spectra are collected at regular intervals in real time during the film growth process. In an ellipsometry experiment, a weak polarized light beam is directed at an oblique angle onto the surface of a sample under analysis, and the reflected light beam is collected. The reflected light beam has a different polarization state than the incident beam, and contains information about the optical and structural properties of the sample. These sample properties are obtained by analyzing the change in the polarization state of the light wave induced by the reflection.

The overall reflection spectroscopic ellipsometry procedure from data collection to sample property analysis can be broken down into five sequential steps: (i) polarization generation by passing the incident light beam through polarizer and optionally through a compensator, (ii) reflection of the polarized light beam from the sample surface, resulting in a change in polarization state, (iii) collection of the reflected beam and analysis of its polarization state either wavelength by wavelength through interaction of the first three steps or in parallel with a spectrometric multichannel detector, (iv) calculation of the

32 spectra in the ellipsometry angles from the change in polarization induced by reflection and from the ellipsometer calibration parameters, and finally (v) construction of a realistic model for the sample such that model parameters can be adjusted to obtain agreement between the simulated ellipsometry spectra in ( ) and the measured spectra. Model parameters such as bulk and surface roughness layer thicknesses, effective medium compositions, and the parameters in analytical expressions for the unknown dielectric functions can all be varied using mathematical tools built into the computational programs. The goal is to match the experimental spectra in the ellipsometry angles (  by the simulated spectra through least square regression analysis (Azzam and Bashara, 1977; Collins 1990; Tompkins, 1992).

Figure 2-7 is a detailed schematic of the optical components and hardware that constitute the rotating-compensator multichannel ellipsometry system used to study the sputter deposition of Ag/ZnO and Al/ZnO back-reflectors. Figure 2-3 represents the corresponding equipment to study the PECVD process for Si:H layers, but with less schematic detail. The polarization generation arm in both Figures 2.3 and 2.7 consist of a light source, a polarizer, and a single rotating compensator. The polarization detection arm in both cases is an analyzer (another polarizer), a detector assembly, and a computer.

The ellipsometry instrumentation used in both studies was manufactured by J. A.

Woollam Company. Ellipsometer model M-2000 XI was used for real time data collection in the back-reflector studies whereas ellipsometer model M-2000 XI-210 was used for real time data collection in the PECVD studies. Both of these ellipsometers are single rotating compensator multichannel system with the detail given in the schematic of

Fig. 2-7. The calibration, operation, and data reduction procedures for these instruments

33 r p tan eiΔ rs

 i ~ 65 ZnO Ag/Al source source

Xe Light Source

Figure 2-7 Schematic of the real time spectroscopic ellipsometry (RTSE) instrumentation used to study the sputter deposition of Ag/ZnO and Al/ZnO back-reflectors. The figure shows the components of the single rotating-compensator-type ellipsometer from the light source to the detector. The reflecting sample is shown within the sputter deposition system.

are described in the references (Woollam et al., 1999; Johs et. al., 1999; Johs et. al.,

2001). The data analysis was performed using CompleteEASE and WVASE software, also from J. A. Woollam Company.

As described earlier, spectroscopic ellipsometry data collection starts with the generation of polarized light from an unpolarized broadband light beam with wavelengths that span the desired spectral range. The spectral range (in terms of photon energy) for

34 the ellipsometer used in the back-reflector studies (M-2000 XI) is 0.75 -5.0 eV whereas the spectral range of the ellipsometer (M-2000 XI-210) used in PECVD is 0.75 - 5.8 eV.

In both cases, a xenon lamp is used as the broadband light source. In these ellipsometers, the light beam is collimated and then linearly polarized by a stationary polarizer with its transmission axis set at 45o with respect to the plane of incidence. This linearly polarized light beam is then passed through a rotating-compensator element. In general, a standard compensator imposes a relative phase shift onto the two orthogonal electric field vector components resolved along the fast and the slow axes of the compensator. This phase shift or retardance depends on the wavelength of the light beam and is 90o at the device quarter wave point. Consequently, the compensator generates a phase shift between the p- and s- components of the electric field vector incident on the compensator and in general generates different amplitudes of the two field components. This phase shift and amplitude ratio depend on the angle between the fast axis of the compensator and the plane of incidence as well as the compensator retardance. Hence, the compensator creates a time dependent or modulated polarization state at its exit, varying from linearly polarized to elliptically polarized. In fact, when the retardance is quarterwave, the polarization state varies from linear, when the compensator fast axis is aligned with the polarizer, to circular, when this fast axis is at 45o with respect to the polarizer. Thus, in this case, as the compensator rotates at angular frequency c, the polarization state of the light wave incident on the sample oscillates between linear and circular with a period of

[1/4 (2/c)]. This beam with oscillating polarization state then reflects from the sample which induces the change in Fourier coefficients that describe the polarization state modulation.

35 The reflected beam having modified polarization modulation characteristics relative to the known characteristics of the incident beam then passes through another polarizer called analyzer, before being focused onto the input slit of the spectrograph. A beam splitter within the spectrograph directs the long wavelengths of the broadband light onto a grating followed by an InGaAs photodiode array. The short wavelength are directed onto a second grating followed by the silicon CCD detector array. It should be emphasized that both gratings and detectors are mounted within the spectrograph for fully parallel spectroscopic ellipsometry. At each detector, the irradiance associated with the dispersed wave is accurately determined as a function of the pixel number or wavelength at several equally spaced compensator orientations. Based on the resulting Fourier coefficient spectra, the J.A. Woollam Company software CompleteEASE performs data reduction by calculating spectra in the experimental ellipsometry angles,  and .

Finally, a model is constructed assuming a semi-infinite substrate and an ambient medium having known dielectric functions. The model consists of one or more intervening layers with user-defined variables, such as layer thicknesses, EMA volume fractions, or parameters describing the dielectric function. These parameters are adjusted to generate agreement between the simulated  and  spectra and the experimental spectra.

The description of spectroscopic ellipsometry presented here holds for any ellipsometry measurement in the single rotating compensator configuration whereby the compensator is placed before the sample. In an RTSE measurement in particular, the angle of incidence is fixed and the spectral data ( ) are collected as a function of time.

The time interval between two full spectral acquisitions in (, ) is chosen such that no

36 more than a few monolayers of the film are deposited on the substrate during the interval.

This ensures that important events such as coalescence of initial nuclei that occur during initial stages of film growth are not missed by the measurement. The analysis of the

RTSE data will be discussed in Section 2.3.3.

2.3.2.2 Ex-Situ Mapping Ellipsometry

In ex-situ mapping ellipsometry, the ellipsometer assembly including the polarization generation and detection arms is translated in a plane defined by the surface of the large area sample. A pre-defined grid pattern is established so that a map of the surface can be generated in the ellipsometry spectra with millimeter resolution. Both the mechanical translation system and the spectroscopic ellipsometer used in the mapping system have been developed by J. A. Woollam Company. Spectroscopic ellipsometer model M-2000 DI with the spectral range of 0.75 – 6.5 eV is used for the mapping system. The combination of a deuterium lamp and a quartz-tungsten-halogen lamp distinguishes the DI version (J. A. Woollam Co. Inc., AccuMap-SE) from the above mentioned XI version. Figure 2-8 shows a photograph of the ex-situ mapping ellipsometer with a flexible substrate mounted on the sample platform. This instrument is capable of mapping up to 1.5 m x 1.0 m sample plates in various spatial patterns, for example rectangular, circular, hexagonal etc. The angle of incidence is fixed at 65o. The operating principle of the single rotating-compensator multichannel ellipsometer (model

M-2000 DI) used in the mapping system is same as that used for RTSE, explained in

Section 2.3.2.1. The mapping spectroscopic ellipsometry data set can also be considered analogous in structure to the RTSE data set in the sense that both measurements are performed at a fixed angle of incidence, and represent a multilayer sample in different

Figure 2-8 A single rotating compensator multichannel ellipsometer used for large area mapping (J. A. Woollam Co. Inc., AccuMap-SE). This instrument is capable of scanning samples up to 1.5 m x 1.0 m size with a spatial resolution of ~ 1 millimeter in both directions.

states associated with temporal and spatial variations of structural properties. For a large area deposition on a flexible substrate prepared in the start up period of the roll-to-roll process, the layer thickness in general increases from one end of the substrate to the other, similar to the thickness increase with time during an RTSE measurement. Hence, in both cases the dielectric functions and thicknesses (bulk, surface roughness) of the deposited layer and the thicknesses of the various substrate layers can be determined simultaneously, based on the multi-time or the multi-space data set.

38 The purpose of the mapping spectroscopic ellipsometry in the current research is to evaluate the spatial uniformity of the component layers on large area substrates.

Currently, in photovoltaics research and production, there is a large difference between the performance of small area dot cells fabricated in the laboratory and large area module from the production line. Typically production modules exhibit 25 – 50 % lower performance than champion research cells. Such a difference can be addressed by understanding the reasons for the spatial non-uniformities in the film thickness, film structure, and properties through mapping spectroscopic ellipsometry. At present, this capability is available for ex-situ mapping in off line applications only, in which case measurement time is not a critical parameter. In the future, however, the mapping capability will be implemented for in-situ analysis of thin film deposition processes so that the film properties can be evaluated without exposing the sample to atmosphere between depositions of successive layers. Such an in-situ tool can serve as an excellent layer-by-layer process monitor with the potential for real time control designed to maintain optimum performance of large area PV modules.

2.3.3 Data Analysis Strategies in Spectroscopic Ellipsometry

As described in Sec. 2.2, reflection spectroscopic ellipsometry data collected over a desired range of photon energies, E, are analyzed through a series of mathematical computations in order to extract physical information from the data such as the complex dielectric functions and component layer thicknesses. In fact, spectroscopic ellipsometry is an indirect method, in which the measured ellipsometry spectra [(E), (E)] describe the changes in the polarization state of the light beam upon reflection, rather than the physical and optical properties of the sample directly. Several data analysis methods

39 have been developed that can be employed to determine sample parameters such as layer thicknesses and phase compositions, as well as to extract dielectric functions of single- phase bulk materials and thin films. The most common mathematical methods for spectroscopic data analysis, such as least square regression (LSR) and the mathematical inversion, have been discussed in detail previously (Collins and Ferlauto, 2005; Jellison,

2005; Stoke, 2008; Podraza, 2008; Li, 2010). This work focuses on analysis of RTSE data collected on multilayer stacks in order to obtain dielectric functions and component layer thicknesses from the data at various time points. The version of multi-time analysis used in this research applies the J. A. Woollam Company CompleteEASE software. The same software is also applied for ex-situ mapping data analysis replacing the data in the temporal domain by data in the spatial domain. In addition, virtual interface (VI) analysis is used for materials whose optical properties change continuously and significantly with thickness as they grow, an example being the amorphous-to-(single-phase nanocrystalline) evolution in which case a Si:H film transitions through a mixed-phase having increasing nanocrystalline Si:H volume fraction versus thickness. In VI analysis, only the top few monolayers are considered semi-transparent and the material beneath those layers is assumed to serve as a pseudo substrate. These two methods of multi- time/multi-space analysis and VI analysis are discussed in detail in the following sub- sections.

2.3.3.1. Multilayer Analysis of RTSE and Ex-Situ Mapping Data

In order to address the general data analysis problem, one considers the multilayer stack with m number of layers shown earlier in Figure 2-6. The thicknesses of the layers are represented by the variables d1, d2, d3, ..., dm with the corresponding dielectric

40 functions (1, 2)1, (1, 2)2, (1, 2)3, …, (1, 2)m. The ambient medium is represented by the subscript 0 and the substrate is represented by the subscript (m+1) with corresponding dielectric functions (1, 2)0 and (1, 2)m+1, respectively. Here, if all the layer thicknesses

(d1, d2, …, dm); the dielectric functions (1, 2)0, (1, 2)1, (1, 2)2, …, (1, 2)m, (1, 2)m+1; and the angle of incidence 0 are all known, then the (, ) spectra of the sample can be uniquely determined from the scattering matrix formalism of Eqs. (2.25) and (2.26) as explained in detail in Sec. 2.3.1. (Azzam and Bashara, 1977). If all the above mentioned quantities are known with the exception of the thickness and dielectric function of the jth layer (1≤ j ≤ m), which are to be determined in the analysis, then a single measured pair of ( from spectroscopic ellipsometry seems insufficient because the number of measured knowns, 2n, is less than the number of unknowns to be determined, 2n+1. The unknowns include 2n dielectric function values (1, 2)j and one thickness, dj. Several methods have been applied in spectroscopic ellipsometry to address and overcome this problem.

One important method, often called artifact minimization, is an analysis procedure in which the thickness of the unknown layer, dj, is fixed at an estimated value so that the number of unknown parameters is then equal to the number of known parameters. Under this condition, it becomes possible to invert numerically the n pairs of (, ) to obtain the n pairs of (1, 2), by solving the corresponding non-linear equations through successive approximations. This method is called inversion because it describes the transformation of n pairs of measured quantities (, ) to the n pairs of dielectric function values (1, 2)j through the scattering matrix expressions given in Eqs. (2.25) and

(2.26). The inverted n pairs of dielectric function values will be incorrect if the

41 estimated value of thickness dj does not match the true thickness of the layer. In such a case, artifacts may be observed in the inverted dielectric function of the unknown layer.

These artifacts may arise from different sources including: (i) substrate artifacts, which arise when features of the substrate or any other optically specified layer in the stack appear erroneously in the inverted dielectric function of the unknown layer; (ii) interference artifacts, which arise due to the erroneous coupling of interference oscillations versus wavelength to the inverted dielectric function of the jth layer, and (iii) semiconductor artifacts, which arise when 2 from the inversion is non-zero below a known band gap of the material of layer j. Details of the artifact minimization procedure and examples showing identification of the correct thickness dj of the unknown layer are given in a previous review (Collins and Ferlauto, 2005). The thickness dj and associated dielectric function (1, 2)j from an inversion obtained with minimum artifacts can be considered as the correct parameters of the unknown layer.

In the case of the materials whose dielectric functions are well understood, these spectra can be constrained to follow analytical forms as a function of wavelength or photon energy. For example, if the jth layer under consideration is a transparent material with a band gap higher than the upper limit of the spectroscopic ellipsometer, then one can assume that the real part of the dielectric function of the material follows the

Sellmeier function versus photon energy and that the imaginary part of the dielectric function is zero. In such a case, the Sellmeier function requires only a few photon energy independent parameters to describe the dispersion of the real part of the dielectric function. By fitting the measured (, ) spectra with the simulated spectra, the photon energy independent parameters along with unknown thicknesses, for example, can be

42 determined. Since the number of unknown fitting parameters in this case is much smaller than the number of known values of (, ), not only the layer thicknesses but also EMA volume fractions can be fitted together with the dielectric function parameters. The analysis approach in this case is not based on exact inversion, but rather on least square regression as there is no one-to-one correspondence between the generated dielectric function values and the measured (, ) values. The quality of the fit is evaluated on the basis of the mean square error (MSE). A commonly used form of MSE from the software used here is given by:

n 1 gen exp2 gen exp 2 gen exp 2 MSE Ni  N i  C i  C i  S i  S i   1000 3n -k  i1

(2.28) where k is the number of fitting parameters and N, C and S are defined according to N = cos(2), C = sin(2) cos( and S = sin(2) sin(The superscript “gen” denotes the generated value and “exp” denotes the experimental value of the identified parameters.

The procedure to minimize this MSE is least square regression which is used extensively in SE and RTSE data analysis.

So far, analysis has been discussed for ellipsometry data taken at one angle of incidence and at a single point on the sample. In general, however, multiple sets of ellipsometry data can be collected at different angles of incidence in ex-situ experiments so that the number of known parameters are multiplied whereas the number of unknown parameters, including the dielectric function values and thickness of one of the layers in the stack, remains the same. Hence, it becomes possible to find the dielectric function

(1, 2)j and the layer thickness dj of the unknown layer simultaneously through least

43 squares regression. This method is classified as least square regression as there is no one- to-one correspondence between the measured (, ) values and the deduced dielectric function values. Instead, the resulting dielectric function is obtained as a best fit result through MSE minimization.

In the case of real time spectroscopic ellipsometry (RTSE), the angle of incidence cannot be varied. In this case, however, the topmost layer thickness increases with time assuming that the surface roughness layer thickness can be neglected or is constant. The ellipsometry data are collected at regular interval of time t1, t2, t3, …, tK and hence a set of

(, ) spectra at increasing film thickness is obtained. Since the ellipsometry spectra (,

) are a function of film thickness also, once again the problem becomes mathematically solvable through least square regression. The number of known data values becomes much greater than the number of unknowns which include a single dielectric function relevant for all the time points and a film thickness value at each time point

In order to solve for dielectric functions and thicknesses in RTSE data analysis, a specific time point ti (1≤ i ≤ K) is selected and the bulk layer thickness at this time point is chosen as dj(ti), so that the dielectric function (1, 2) can be obtained by inversion from the measured (, ) data. The inverted dielectric function (1, 2) is then applied in a least square regression fit of the ellipsometry spectra taken at neighboring time points.

This fit provides the thickness versus time and the MSE summed over all photon energies as in Eq. (2.28) and then averaged over time. This time-averaged MSE serves as a measure of the fit quality and can be minimized by adjusting the thickness dj(ti) iteratively to the correct value. A proper choice of the grid is required to increase/decrease the thickness from its initial estimated value. The inverted dielectric

44 function (1, 2) obtained with the minimum time-averaged MSE can be treated as the correct dielectric function of the top layer material. Many early studies (Cong et al.,

1991; An et al., 1991a) have applied this procedure to analyze RTSE data.

An alternative procedure that has been implemented recently in J. A. Woollam

Company CompleteEASE software in order to fit RTSE data assuming that the same dielectric functions is valid for all time points. Initial estimates are made for the layer thicknesses at several time points. The dielectric function at each time point is obtained by inversion. The dielectric functions are then averaged and the average MSE from the chosen time points is calculated. The average MSE is then minimized through the choice of the thicknesses. The averaged dielectric function that corresponds to the minimum

MSE can be taken as the correct dielectric function of the growing top layer material.

The main difference between these two methods is that the first method gives more weight to the data at time point ti since the dielectric function is obtained by inversion from that time point. In contrast, in the CompleteEASE method, dielectric functions are obtained by inversion at all time points under consideration, and the average is taken as the dielectric function of the top layer material.

In almost all real time data analyses in this research, however, both the bulk layer thickness and the surface roughness layer thickness are taken as variable thicknesses, the latter modeled by the Bruggeman EMA assuming a mixture of the underlying material and void (50 vol.% each). Thus, instead of a single variable bulk layer thickness in the analysis of the dielectric function of the top layer material, the two layer thicknesses are used in the MSE minimization. Once the dielectric function is identified by MSE minimization, the bulk layer and the surface roughness layer thickness evolution

45 throughout the time interval can be obtained by least squares fitting provided that there is no appreciable change in the dielectric function of the material over the time interval.

Finally, the ex-situ mapping spectroscopic ellipsometry data can be analyzed using the same methods as the RTSE data, since the layer thicknesses are the primary variables in analyses over the area of a given map. In other words, the mapping data in the spatial domain can replace the RTSE data in the temporal domain. Hence, the dielectric function of the mapped layer can be obtained from MSE minimization through least square regression, and then the thickness variation over the area can be obtained by fixing the dielectric function and letting the bulk layer as well as the surface roughness thickness vary as fitting parameters in the least square regression method.

2.3.3.2 Virtual Interface (VI) Analysis

Thin films that grow uniformly and yield a homogeneous dielectric function versus the thickness of the film depth can be analyzed with the MSE minimization procedure described in the previous sub-section. If the material has dielectric function inhomogeneities in the growth direction, however, attributed to an evolution of the structure or composition (or both) within the film as the thickness increases, then the dielectric functions obtained, for example, at ~200 Å thickness will no longer represent the optical response of the film material that accumulates after this thickness is deposited upon continued growth. For such films in which there is a profile in the structural or compositional parameters with thickness on that depth that leads to a profile in the dielectric function of the layer material, a virtual interface (VI) approach is applied to extract the optical response of the top few monolayers. The overall effect of the underlying layers in the VI approach is represented by a semi-infinite pseudo-substrate.

46 Virtual interface analysis of RTSE data was first introduced by Aspnes based on a three-medium model (Aspnes, 1993). Instead of using a multilayer stack of numerous discrete underlying layers to simulate a profile in film optical properties, Aspnes developed a new concept of the virtual interface between an outerlayer film and a semi- infinite pseudo-substrate. In other words, the optical model in the virtual interface analysis of RTSE data consists of an actual ambient/outerlayer interface and a virtual outerlayer/pseudo-substrate interface with an intervening outerlayer whose properties are to be determined. Hence, the virtual interface approach facilitates the handling of a complicated graded layer by converting all the information of the underlying variations into a single pseudo-substrate and focusing only on the top-most outerlayer. This analysis procedure was later modified to include the possibility of a surface roughness layer, which is located on top of the outerlayer in the model (Kim and Collins, 1995).

Hence, this modified virtual interface model incorporates four media: (i) ambient, (ii) a surface roughness layer that consists of the outerlayer and void typically 50 vol.% for each, (iii) the outerlayer, and (iv) the pseudo-substrate.

This four medium approach for analysis of continuously varying material properties has been applied to the RTSE study of the evolution of the nanocrystalline volume fraction in Si:H thin film deposition (Ferlauto et al., 2004) and the Ge content in a-Si1-xGex:H films (Podraza, 2008). In this Thesis also, quantification of the nanocrystalline Si:H volume fraction at the top of the growing Si:H layer is of most interest to perform through virtual interface analysis of RTSE data. The software used in this analysis is CompleteEASE (J. A. Woollam Company) which applies similar underlying principles as those used by Ferlauto et al. and Podraza. The details of the

47 virtual interface analysis procedure that applies an earlier version of the J. A. Woollam

Company software, given the acronym EASE, is described by Stoke (Stoke, 2008). As a specific example, the description in the following paragraph focuses on virtual interface analysis of the RTSE data from a Si:H layer deposited at relatively high hydrogen dilution that leads to nucleation and coalescence of an initial amorphous phase and then evolution of the film to the nanocrystalline phase which exhibits a distinctly different optical response.

The virtual interface analysis begins with the determination of the dielectric functions of the pure amorphous and nanocrystalline phases of the material under investigation, which in this case is hydrogenated amorphous and nanocrystalline silicon.

Based on these results, the time evolution of the nanocrystalline volume fraction is obtained in the mixed phase growth regime using the virtual interface analysis. A schematic of the evolution from the amorphous to the nanocrystalline phase and the resulting four medium optical model used as the basis of virtual interface analysis is shown in Figure 2-9.

The amorphous Si:H dielectric function is obtained from the MSE minimization procedure at ~ 200 Å thickness before the formation of nanocrystals from the amorphous phase. The resulting amorphous Si:H dielectric function is smoothed using an analytical formula consisting of a Lorentz oscillator modified by a band gap and an absorption onset based on the assumption of a constant- dipole matrix element (CD-ME). This oscillator is referred to as the Cody-Lorentz oscillator (Ferlauto et al., 2002). The expression for the imaginary part of the dielectric function of this oscillator is given in the Appendix

[Eq. (A.14)]. The bulk layer thickness and the surface roughness layer thickness

Figure 2-9 a) Schematic of a four-medium optical model used in virtual interface analysis; the model consists of (i) the ambient, (ii) a surface roughness layer, (iii) an outerlayer with dielectric function o, and (iv) a pseudo- substrate with dielectric function <>. b) Schematic of a typical film with non-uniform optical response in the growth direction, whereby the non- uniformity is due to microstructural evolution from the pure amorphous phase through a mixed-phase regime to the pure nanocrystalline phase, (Stoke, 2008).

49 evolutions are then determined by the least squares regression applying the analytical form of the dielectric function. After amorphous Si:H nucleation which is a roughening effect, the surface roughness decreases due to amorphous cluster coalescence and then increases again with increasing bulk layer thickness, as the film enters into the mixed- phase regime. This second roughening regime is due to the nucleation of the nanocrystalline phase followed by its continued growth, as shown in Figure 2-9. Once the nanocrystalline nuclei make contact and start to coalesce, forming single phase nanocrystalline Si:H, the surface roughness saturates and starts to decrease with the increase in bulk layer thickness.

After nanocrystals contact and coalesce, the spectral range of SE analysis is confined to

3.5 eV and above so that the probe beam does not penetrate deeply into the layer. The nanocrystalline dielectric function is then extracted at a bulk layer thickness ~ 200 Å after the coalescence thickness. In order to extract the nanocrystalline dielectric function, the ellipsometry data at the corresponding time point are inverted assuming different surface roughness values by applying a two layer model. This model consists of a bulk nanocrystalline layer with a surface roughness layer on top.

The resulting inverted nanocrystalline Si:H dielectric function along with the amorphous Si:H dielectric function obtained previously are then used in the Bruggeman

EMA to represent the mixed-phase dielectric function in the virtual interface analysis of the mixed-phase growth regime. In this analysis, the nanocrystalline volume fraction and the surface roughness layer thickness are taken as the fitting parameters in least squares regression in order to minimize the MSE. The number of time points in the virtual interface analysis is chosen such that the mixed-phase outerlayer from which the

50 nanocrystalline volume fraction is determined is at most 15 Å thick. The underlying material is treated as the semi-infinite pseudo-substrate. Hence, the correct nanocrystalline Si:H dielectric function is the one obtained by inversion assuming the surface roughness thickness value ds0 at which the MSE from the virtual interface analysis is minimized. In this MSE minimization, the grid describing the surface roughness estimation is taken at 10 Å and is then reduced to 1 Å. Thus, the correct ds0 value typically can be obtained to within ± 0.5 Å, which is necessary for an accurate nanocrystalline Si:H dielectric function. The resulting nanocrystalline Si:H dielectric function can be smoothed by using an analytical formula consisting of two Lorentz oscillators with a common Tauc gap, similar to that approach used in previous research

(Collins and Ferlauto, 2005a). The mathematical form of Tauc Lorentz oscillator is given in Eqs. (A.12) - (A.13) in Appendix section. This step completes the virtual interface analysis of RTSE data acquired during the thin film Si:H deposition at higher hydrogen dilution levels that lead to amorphous-to-(mixed-phase) and (mixed-phase)-to-(single phase) transitions.

2.3.4 Applications of Spectroscopic Ellipsometry in Thin Film Growth

2.3.4.1 Effective Medium Theory

Bulk materials with homogeneous structure from the atomic scale to the probe beam size have well-defined optical responses in reflection from and transmission through specular interfaces. For a composite medium consisting of two or more homogeneous component materials, however, the optical functions of the structure can be estimated from the optical functions of the homogeneous component materials and the component material volume fractions using an effective medium theory (EMT). The

51 scale of the inhomogeneities that characterize the composite structure to which effective medium approximation methods are applicable must be sufficiently large so that the optical response is independent of the structure scale, but must be much smaller than the wavelength of the probe beam. Typical composite structure include materials with porosity or void, grain boundaries, and mixed phases as examples. Surface roughness between the material and the ambient on top of a thin film is another example of a composite. In this case, a 50 vol.%/50 vol.% mixture of underlying material and free space is used. A final example of a composite occurs at the interface between two films.

When an overlying film is prepared on top of a previously deposited film, the voids in the roughness layer of the first film are filled by the second material, thereby forming an interface roughness layer. In some cases, when the void volume in the surface roughness of the first material is not completely filled by the second material to form the interface, a three component EMT, including the two materials and void, is applied to obtain the interface layer optical functions.

A general expression for the EMT appropriate for an inclusion embedded in a host material can be written as (Aspnes, 1982):

eff   h ih     f,i (2.29) eff   hi  i   h where eff, h, i, and fi are the effective medium dielectric function, the host dielectric function, and the dielectric function and volume fraction of the ith component, respectively. The quantity = (1/q)1 and q (0 ≤ q ≤ 1) is the screening parameter incorporated so that various optical functions can be obtained, which depend not only on the volume percent inclusions through fi, but also on their space through q. Depending upon the shape of the inclusions and the choice of the host material, Equation (2.29) can

52 be simplified in different ways, resulting in several different EMAs. In most cases, however, the inclusions are assumed to be spherical in shape in which case q = 1/3 and hence the screening parameter is given by =2. Spherical inclusions lead to an isotropic dielectric function and in this case there are three effective medium theories, depending upon the choice of the host material, as follows.

(i) Lorentz-Lorentz effective medium theory with air as the host (h = 1);

(ii) Maxwell Garnet effective medium theory with the dominant component as the

host (h = k where index k is selected such that fi < fk for all i ); and

(iii) Bruggeman approximation (EMA) with the mixture itself as the host (h = eff)

Moreover, there are two extreme cases (Fujiwara et al., 2002) with non-spherical inclusions, including

(iv) no screening (q = 0); and

(v) maximum screening (q = 1).

No screening occurs when the optical electric fields are parallel to the component boundaries. This is possible if the inclusions are needle-like structures lying in the plane of the film. Then the effective dielectric function of Eq. (2.29) becomes eff = f11 + f22, assuming two components within the structure. On the other hand, maximum screening occurs when the optical electric fields are perpendicular to the phase boundaries. This situation arises if the inclusions are needle-like structures and standing on end within the film. Then again, assuming two components within the structure, the effective dielectric

-1 -1 -1 function of Eq. (2.29) becomes, eff = f11 + f22 .

As described said earlier, the effective medium approximation is a theory used to predict the optical response of composite materials, and the modeling of roughness on the

53 surface of a thin film is one of the most common examples that can be described using an effective medium approximation. According to Fujiwara et al. (Fujiwara et. al., 2000), the Bruggeman EMA offers the best fit to experimental real time spectroscopic ellipsometry data collected during PECVD a-Si:H film growth using a model that incorporates a surface roughness layer. As an illustration, presented in this Thesis, five different EMAs are applied to model the optical functions of a surface roughness layer on a Ag film as it evolves during growth on a smooth c-Si substrate. The results of film growth analyses are compared to evaluate which EMA provides the best fit to the data.

2.3.4.2 Ag Bulk Film Modeling

For the EMT modeling of the evolution of surface roughness on Ag films, three different films with increasing average roughness layer thickness were sputter deposited onto smooth ~ 400 Å thermal oxide covered c-Si substrates. The average roughness thickness values for these Ag films, obtained by modeling RTSE data using the

Bruggeman EMA with 50 vol.% bulk layer and 50 vol.% void, were determined as 8 Å,

27 Å and 71 Å. This roughness thickness variation was achieved by increasing the deposition temperature, from room temperature first to 50oC and then to 105oC. Both elevated temperature values were deduced from a calibration based on the energy shift of the E1 and E2 critical points of crystalline silicon (Lautenschlager et al., 1987). In this calibration, a native oxide covered silicon wafer was used as the calibration substrate.

The deposition pressure, rf plasma power density, and the Ar gas flow for all three depositions were 5 mTorr, 1.1 W/cm2, and 10 sccm, respectively.

Real time spectroscopic ellipsometry (RTSE) was performed using a rotating- compensator multichannel instrument that can provide spectra (0.75 to 5.0 eV) in (, Δ)

54 with a minimum acquisition time of 32 ms, as an average over a single pair of optical cycles. To improve precision, pairs of (, Δ) spectra were collected within a time of ~ 1 second, as averages over ~ 30 optical cycle pairs. During the acquisition time for one set of (, Δ) spectra, a bulk layer thickness of ~ 6 Å accumulates at the maximum deposition rate used here. The angle of incidence was 65.08±0.1, where 0.1o indicates the range for all depositions. Analyses of all spectra involve numerical inversion and least-squares regression algorithms, as described previously in Sec. 2.3.2.

Figure 2-10 shows the evolution of the mean square error (MSE) and the surface roughness thickness for the smoothest (ds ~ 8 Å) Ag layer on thermal oxide coated c-Si, modeled applying in turn five different effective medium theories (EMT's) to describe the dielectric function of the surface roughness. The Ag dielectric functions used in each analysis is obtained in turn from multi-time analysis when the Ag film reaches ~ 1000 Å bulk layer thickness. Initially, the void fraction in each EMT expression was allowed to vary, but in each case it was found to be within 3 vol.% of 50 vol.% and as a result the void content was fixed at 50 vol.%. From Figure 2-10, a minimum MSE is observed at

1000 Å because this thickness is the focus of the multi-time analysis. The Lorentz-

Lorentz EMT is observed to be the poorest in representing the Ag surface roughness.

The maximum screening EMT is also poor. The other three EMT's including the

Maxwell-Garnett EMT with Ag as the host, the minimum screening EMT, and the

Bruggeman effective medium approximation (EMA) are relatively better. Among the five EMT's, the minimum MSE is obtained by using the Bruggeman EMA. As a result, it can be concluded that the Bruggeman EMA, calculated applying the dielectric functions

Figure 2-10 Surface roughness evolution (top) and the MSE evolution (bottom) for the smoothest Ag film deposited on thermal oxide covered c-Si. The Bruggeman EMA results in the minimum average MSE. Moreover, the average surface roughness thickness is ~ 8Å, modeled using 50 vol.% void in the Bruggeman EMA.

56 of the underlying bulk film Ag and void (~ 50 vol.% each) best represents the roughness on the surface of the smoothest Ag studied in this analysis. The roughness evolution obtained using the Bruggeman EMA from Figure 2-10 (top) gives an average roughness layer thickness of ~ 8Å. The corresponding Ag dielectric function obtained by modeling the surface roughness using the Bruggeman EMA with 50 vol.% void in the surface roughness layer is presented in Figure 2-11.

Apparently similar results were obtained for the moderately rough (ds ~ 27Å) and rough Ag films (ds ~ 71Å), as shown in Figures 2-12 2-15. For all three films, the

Bruggeman EMA appears to best represent the surface roughness considering the five

EMT's explored in this study. The dielectric functions of the moderately rough (ds ~

27Å) and the rough (ds ~ 71Å) Ag layers are given in Figures 2-13 and 2-15, respectively. The real parts of the three dielectric functions cannot be distinguished as a result of the large scale of the data. Although, the interband absorption in Ag due to d- band electron at ~ 3.8 eV is nearly identical in all three cases, the imaginary parts show clear differences near 3 eV due to plasmonic absorption, evident for the two elevated temperature depositions. The presence of the plasmon-resonance related feature in the bulk dielectric function, a feature which is generally associated with the free electron resonances in the surface roughness protrusions, is an indication that, although the

Bruggeman approximation provides the overall best fit, it is not accurately addressing the shape of the roughness layer dielectric function in the energy range of the plasmon feature. Apparently the improved fitting for the Bruggeman EMA as compared to the

Maxwell-Garnett EMT with free space as the host (or Lorentz-Lorentz EMT), the latter generally understood to fit localized plasmon resonances associated with metallic

Figure 2-11 The dielectric function of the smoothest Ag deposited on a thermal oxide coated c-Si substrate. The modeling to obtain the dielectric function was performed using the Bruggeman EMA with 50 vol.% void in a simulation of the surface roughness layer.

Figure 2-12 Surface roughness evolution (top) and the MSE evolution (bottom) for the moderately rough Ag film deposited on thermal oxide covered c-Si. In this case also, the Bruggeman EMA resulted in the minimum average MSE. The average surface roughness is ~ 27Å, modeled with 50 vol.% void using the Bruggeman EMA.

Figure 2-13 The dielectric function of the moderately rough Ag deposited on a thermal oxide coated c-Si substrate. As in the case of smoothest Ag layer, the modeling to obtain the dielectric function was performed using the Bruggeman EMA with 50 vol.% void in a simulation of the surface roughness layer.

Figure 2-14 Surface roughness evolution (top) and the MSE evolution (bottom) for the rough Ag film deposited on thermal oxide covered c-Si. Once again, the Bruggeman EMA results in the minimum average MSE. The average surface roughness is ~ 71Å, modeled using 50 vol.% void in the Bruggeman EMA.

Figure 2-15 The dielectric function of the rough Ag deposited on thermal oxide coated c-Si substrate. As in the cases of the smooth and moderately rough surfaces, the modeling to obtain the dielectric function was performed using the Bruggeman EMA with 50 vol.% void in a simulation of the surface roughness layer.

62 particles and protrusions, is due to photon energy regions away from the plasmon resonance. This suggests that an improved EMT would exhibit features of both the

Bruggeman and Maxwell-Garnett EMT's with free space as the host. An alternative analysis approach in this case is to assume that this sample has the same underlying dielectric function as the sample with thinnest roughness layer (obtained at the relevant measurement temperature) and to extract the thickness and the dielectric function of the surface layer using multi-time analysis.

In fact, the most common approach for handling the optical functions of metallic particles and protrusions is to substitute the Drude expression for  into the Maxwell-

Garnett effective medium theory with the host being free space (or Lorentz-Lorentz

EMT). The result is a Lorentz oscillator with a resonance energy given by E0 ~

-1/2 Ep{∞+[(2+f)/(1f)]} where f is the volume fraction of Ag particles or protrusions, Ep is the bulk plasmon energy of Ag, and ∞ is the constant contribution in the Drude expression. Substitution of values appropriate for the roughness layer of Ag including f =

0.5, Ep = 8.8 eV, and ∞ = 1.3 yields E0 = 3.5 eV. A higher volume fraction of f = 0.63 yields E0 = 3.0 eV. Further discussion of these plasmon resonances will appear in

Chapter 4.

2.4 Experimental Methods in Solar Cell Characterization

A photovoltaic device or solar cell is a semiconductor junction that converts the energy of sunlight into electrical energy. Conventional solar cells are p-n junctions in which a light beam photon absorbed near the junction region produces an electron hole pair. The minority carries diffuse to the junction region due to their concentration

63 gradient and then across the junction by drift due to a strong electric field created by the immobile ions at the junction. This sets up a current with the opposite charge majority carriers diffusing to their nearest contact. The details of the solar cell operation can be found elsewhere (Green, 1992; Gray, 2003).

The thin film Si:H solar cell design adopted in this Thesis research is different than the conventional p-n junction solar cell in that a thick intrinsic layer is sandwiched between a thin p-doped layer on the sun side and an n-doped layer on the opposite side.

The resulting thin Si:H solar cell deposited on an opaque substrate is often called the n-i-p or substrate configuration according to the order in which it is deposited. This design should be distinguished from the p-i-n or superstrate configuration fabricated on a transparent substrate. In any solar cell, however, the performance is measured from the current-voltage (J-V) characteristic of the device in the presence of photon flux that simulates the solar radiation spectrum and its total irradiance. The device is connected to a variable voltage source, a voltmeter, and a current meter so that the applied voltage and the induced current can be measured. The solar simulator system exposes the solar cell to a standard 1000 W/m2 spectrum, and the electronic response to light is measured as the induced current at a given voltage step. The dark J-V characteristic, providing a measure of the diode behavior of the solar cell without illumination is obtained by the same procedure.

The measurement starts with zero voltage applied across the cell under illumination as indicated by the source meter, and the induced current is recorded. The measured current density at zero applied voltage is the short circuit current density (Jsc) of the device. Then the induced current from the device is measured at increasing steps of

64 the applied voltage in forward bias until the current vanishes. The voltage at which the total current in the circuit, consisting of photocurrent and forward bias diode current, vanishes is the open circuit voltage (Voc). In addition to short circuit current (Jsc) and open circuit voltage (Voc), the fill factor (FF) and efficiency () are critical parameters used to evaluate the solar cell performance. The fill factor (FF) is determined by the ratio of the maximum output power from the device to the product of Jsc and Voc. The maximum output power point on the J-V characteristic is the point at which the product of the current and the voltage (or equivalently the output power) is a maximum. The solar cell efficiency () is obtained from the following relation:

J V FF η= sc oc (2.30) Pin where Pin is the power flux in the incident beam.

Chapter 3

Si:H Layer Optimization for Solar Cell Application

3.1 Introduction and Motivation

Hydrogenated silicon (Si:H) thin films have been studied in great detail starting with the first films deposited using plasma enhanced chemical vapor deposition

(PECVD) by Chittick et al. in 1969. After Spear and Lecomber showed in 1975 that the amorphous form of these films could be doped n- and p-type, an effect which shifts the

Fermi level from the middle of the band gap toward the band edges (Spear and

LeComber, 1975), this material has generated significant interest for electronic applications, in particular thin film transistor and photovoltaic technologies. Although hydrogenated amorphous silicon (a-Si:H) is considered inferior to its crystalline silicon

(c-Si) counterpart in terms of electronic properties, due to a continuous distribution of localized states in the band gap region and a light induced degradation effect over time

(Staebler and Wronski, 1977), its distinct optical properties relative to those of c-Si make it suitable for a wide variety of optoelectronic applications.

In photovoltaics, a-Si:H has an advantage over c-Si due to the enhanced absorption across much of the solar spectrum. Much less silicon material is required in an a-Si:H solar cell to produce the same number of electron-hole pairs as compared to a

66 c-Si solar cell. The first a-Si:H solar cell was reported by David Carlson and Christopher

Wronski (Carlson and Wronski, 1976) in 1976. At present, such a-Si:H films are used in single, tandem and triple junction solar cell applications in both substrate and superstrate configurations. In this Thesis research, the solar cells are fabricated in the n-i-p substrate configuration, which describes the deposition sequence from the substrate to the surface.

The main focus of this work is on the intrinsic absorber layer (i-layer) and the top p-layer of the single junction n-i-p solar cell device. The bulk i-layer, p-layer and the i/p interface are most critical for optimization of the solar cell parameters, i.e. short circuit current (Jsc), open circuit voltage (Voc), fill factor (FF) and ultimately the solar cell efficiency (). Real time spectroscopic ellipsometry (RTSE) serves as an ideal tool for non-invasive, in-situ studies of the component layers of these solar cells.

In this chapter, a detailed description is provided for the amorphous-to- nanocrystalline phase transitions and the nanocrystalline volume fraction evolution of i- layer as measured by RTSE. These results are used to construct i-layer deposition phase diagrams, which include a series of contour lines that represent fixed nanocrystalline volume fractions observed at different pairs of values for the process variables and the i- layer thicknesses. Because the p-layer is very thin, however, its phase diagram is drawn without contour lines. Instead of contour lines, the p-layer phase diagram incorporates two transition lines separating amorphous, mixed-phase, and single-phase nanocrystalline film growth regimes. The primary goal of developing a deposition phase diagram is to ensure deposition of the most ordered amorphous, called “protocrystalline”, i- and p- layers for optimized solar cell performance (Wronski and Collins, 2004; Koval et al.,

2002). These phase diagrams, which describe how the films evolve structurally under

67 different conditions of hydrogen dilution ratio and other deposition parameters, will be applied in Chapter 6 to understand correlations between device structure and performance and to determine whether the protocrystalline i- and p-layers result in the optimized solar cell performance for the deposition processes studied in this Thesis research. Moreover, the ex-situ mapping spectroscopic ellipsometry techniques, in conjunction with RTSE, have been applied to construct spatially resolved phase diagrams of p-layers on a flexible polymer substrate, across its entire area. The goal of the spatial phase diagram is to ensure spatial uniformity of the component layers in terms of their thicknesses and optical properties across the entire area of the flexible substrate. Thus, solar cell optimization simultaneously over the entire substrate area can be ensured.

3.2 Deposition Processes and Phase Diagram Development

A phase diagram is a plot that displays the dependence of the structural evolution of a thin film on a specific process parameter. More specifically, for each film grown under a fixed set of process variables, microstructural events occur near the film surface at well-defined bulk layer thicknesses. These events include nucleation or coalescence of a new phase, or a specific near-surface value for the volume fraction of the new phase, and are plotted according to the thickness at which they occur versus the process variable that identifies the particular deposition. These process variables can be the deposition pressure, deposition temperature, rf power or the flow ratios of the gases in the PECVD process. Thus, on the deposition phase diagram the ordinate is the bulk layer thickness at which the event of interest takes place and the abscissa is the process variable under investigation. Moreover, the same event such as nucleation of a new phase, a fixed

68 fraction of the new phase etc. are connected by contour lines for all experiments, thereby giving the plot a sense of a third dimension of phase composition.

In the development of the phase diagram of the intrinsic i-layer and the top p- layer, solar cells deposited on 2" x 2" borosilicate glass substrate were fabricated. Two major types of events are identified from the RTSE data analysis. These events include the amorphous-to-(mixed-phase) and (mixed-phase)-to-(single-phase nanocrystalline) transitions, which in short hand are represented as [a  (a+nc)] for the amorphous-to-

(mixed-phase) transition and [(a+nc)  nc] for the (mixed-phase)-to-(single-phase nanocrystalline) transition. The bulk layer thicknesses at which these two events [a 

(a+nc) and (a+nc)  nc] are observed exhibit the strongest dependence on the hydrogen dilution ratio, i.e. the ratio of the hydrogen gas flow rate [H2] to the source gas silane flow rate [SiH4], often referred to using the variable R (R = [H2]/[SiH4]). Thus, this parameter is the primary process variable used in the development of the phase diagrams of both i- and p-layers. Moreover, for the n- and p-layers, the dopant gas ratio D (D =

[PH3]/[SiH4] and D = [B2H6]/{[SiH4] + [CH4]}, respectively) is also a critical parameter of interest having a significant influence on the structural as well as the electronic properties of these layers.

The i-layer of the solar cell was deposited onto a Cr/Ag/ZnO/n-layer coated borosilicate glass substrate. The deposition conditions of all the layers deposited for the i-layer phase diagram study are given in Table 3.1. Here, Cr was used as an adhesion interlayer to avoid delamination of Ag from the borosilicate glass surface when the interlayer is absent. The Ag layer was used as a back-reflector, although the smooth Ag used in this study is not yet optimized for this application. During sputtering, the

69 Table 3.1 Deposition conditions of the component layers used for the i-layer phase diagram study relevant for applications in thin film Si:H n-i-p solar cells on 2" x 2" glass substrates. The ZnO, n-layer and p-layer thicknesses and deposition rates are given for representative depositions.

Layer Dep. RF Substrate Time Gas flows (sccm) Intended Nom. type pressure plasma Tempt. (min) thick- dep. (mTorr) power (oC) ness rate (W/cm2) (Å) (Å/s) Cr 5 0.92 RT 20.0 [Ar] = 10 1000 0.84 Ag 5 0.92 RT 30.0 [Ar] = 10 5000 2.78 ZnO 5 0.92 RT 37.0 [Ar] = 10 3000 1.35 R = 0.1, D = 0.005

n-layer 350 0.01 200 2.5 [SiH4] =10, 250 1.67

5% [PH3] in [H2]= 1 R = 5 800 0.033 200 26.1 3000 1.92 [H2] = 25, [SiH4] = 5 R = 10 800 0.033 200 45.2 3000 1.11 [H2] = 50, [SiH4] = 5 R = 15 800 0.033 200 57.3 3000 0.87 [H2] = 75, [SiH4] = 5 R = 20 i-layer 800 0.033 200 66.1 3000 0.76 [H ] = 100, [SiH ] = 5 (diff. R 2 4 R = 25 values) 800 0.033 200 87.1 3000 0.57 [H2] = 125, [SiH4] = 5 R = 30 800 0.033 200 93.0 3000 0.54 [H2] = 150, [SiH4] = 5 R = 35 800 0.033 200 111.2 3000 0.45 [H2] = 175, [SiH4] = 5 R = 40 800 0.033 200 120.5 3000 0.41 [H2] = 200, [SiH4] = 5 R = 135, D = 0.01

p-layer 1500 0.033 100 10.0 [H2] = 270, [SiH4] = 2 120 0.20

5% [B2H6] in H2 = 0.4 [Ar] = 10 ITO 5 0.58 150 8.0 570 1.19 5% [O2] in Ar = 3

Note: The 5% dopant gas in H2 and O2 in Ar both are by volume.

70 deposition conditions were set such that the Cr adhesion layer was deposited to a thickness of ~ 1000 Å, the Ag back-reflector layer was deposited to a thickness of ~ 5000

Å, and the intrinsic ZnO diffusion barrier and dielectric spacer layer was deposited to a thickness of ~ 3000 Å, all in succession without intentional substrate heating. After ZnO deposition, the sample was moved into the n-layer chamber, which was operated at nominal substrate temperature of 290oC, which corresponds to a true temperature of the substrate surface of 200oC. For solar cell deposition on the borosilicate glass substrates, all the PECVD chambers, including the n-, i- and p-chambers, were calibrated to the true substrate temperature on the basis of the amorphous silicon band gap shift as characterized by spectroscopic ellipsometry (SE) (Podraza et.al., 2006). The calibration begins by depositing ~ 2000 Å a-Si:H on a borosilicate glass substrate. The SE data were taken by stabilizing the temperature at increasing set points of interest starting from room temperature and then extracting the true temperature at the set point based on the known temperature shift of the a-Si:H band gap (Podraza et.al., 2006). This calibration is performed for all three chambers separately. In these studies, the temperature calibration performed on the basis of the temperature shift of the a-Si:H band gap was preferred over that performed on the basis of the shifts of the E1 and E2 critical points c-Si with temperature (Lautenschlager et al., 1987). The reason for this choice is that the former gives the temperature calibration relevant for the borosilicate glass, which is the substrate used for the solar cell deposition.

The Cr/Ag/ZnO coated borosilicate glass was pre-heated in the n-layer chamber at a true temperature of 200oC for 3 hours. After that, a ~ 250 Å thick n-layer was deposited in the PECVD process using the conditions of Table 3.1. On top of the n-layer,

71 a different i-layer was deposited in the i-chamber for each individual solar cell deposition. The i-layer substrate temperature was the same as that of the n-layer, and i- layer R values of 5, 10, 15, 20, 25, 30, 35, and 40 were used. These cells were then completed by depositing a ~ 120 Å p-layer in the p-chamber at a reduced substrate temperature of ~ 100oC. Again, the deposition conditions of all these PECVD deposited layers, including the several hydrogen diluted i-layers, are given in Table 3.1. Finally, these cells were removed from the chamber after cooling to room temperature and then returned to the In2O3:Sn (ITO) chamber with stainless steel masks having twenty-four 5 mm square openings. The ITO square dots were sputtered deposited after pre-heating the cells for 3 hours in the ITO chamber, which was kept at a calibrated substrate temperature of 150oC. The other ITO deposition conditions are given in Table 3.1. The intended thickness of each ITO contact dot was ~ 570 Å, optimized for antireflection in the single junction n-i-p solar cell (Fan et al., 2010). All the sputtering targets used in this study,

Cr, Ag, ZnO, and ITO were 99.99% pure as supplied by Plasmaterials Inc. Livermore,

California. The targets were rectangular with dimensions of 2.25" x 11.25" x 0.25". The

ITO target was composed of 90 weight % of In2O3 doped with 10 weight % of SnO2. The detailed performance parameters of these solar cells at different R values will be presented in Chapter 6.

Real time spectroscopic ellipsometry (RTSE) was performed during i-layer deposition using a rotating-compensator multichannel instrument that can provide (, Δ) spectra from 0.75 to 5.8 eV. The RTSE measurement setup was that shown in Chapter

2, Figure 2-3. To improve precision, pairs of (, Δ) spectra were collected within a time of ~ 1 s, as averages over ~ 31 optical cycle pairs. During the acquisition time for one

72 pair of (, Δ) spectra, ~ 1-2 Å effective thickness of material accumulates on the multilayer stack for the deposition rates used in this study. The angle of incidence for all depositions was fixed at a value within the range of 70.0 ± 0.6. Moreover, before acquiring RTSE data during the i-layer deposition, single scan data were taken after Ag,

ZnO and n-layers, respectively, so that their optical properties could be extracted.

In order to study the phase diagram for the i-layer deposited on top of the

Cr/Ag/ZnO/n-layer coated borosilicate glass, the i-layer optical properties at a bulk i- layer thickness of ~ 200 Å thickness were extracted by multi-time analysis. In this analysis, a known set of a-Si:H optical properties were taken as the first guess values.

Here, the optical properties of the underlying materials were known from the single scan data and analysis through an iterative least-squares regression algorithm. This enabled use of the the global referred to as MSE earlier)-minimization routine for identification of the phase transition of the i-layer. The global -minimization routine has been used to investigate films grown on native-oxide-covered crystal silicon substrates that develop a nanocrystalline Si:H phase and thus, clearly show signs of structural evolution (Ferlauto, 2001; Fujiwara et al., 2001; Stoke et al., 2008).

In these previous studies, it was shown that when crystalline nuclei develop on an a-Si:H thin film surface, they protrude outward. This gives rise to a rapid increase in surface roughness with the increase in bulk layer thickness due to the preferential growth of the nanocrystalline phase over the amorphous phase. Thus, a sharp increase in surface roughness on a plot of the surface roughness layer thickness, ds, as a function of the bulk layer thickness, db, represents the transition from amorphous material to mixed-phase material consisting of amorphous and nanocrystalline hydrogenated silicon. This feature

Figure 3-1 Surface roughness thickness versus bulk layer thickness for a Si:H i-layer film deposited on an a-Si:H n-layer which in turn covers a glass/Cr/Ag/ZnO substrate structure. The hydrogen dilution ratio for the i- layer was R = 30. Nucleation of amorphous material occurs early in the deposition, followed by nucleation of nanocrystallites from the amorphous phase. Subsequently, the film grows as a mixture of amorphous and nanocrystalline Si:H, which continues until the isolated crystallites coalesce to form a purely nanocrystalline phase. The graphic above the plot is a schematic representation of the phase evolution of the film, which depicts the number of nanocrystallite nucleation sites per area of film surface, known as the “areal nucleation density” or simply “nucleation density” (Nd).

74 is extremely important in the global -minimization results shown in Figure 3-1, whereby the transition occurs at a bulk i-layer thickness of 190 Å. An increase in surface roughness with bulk layer thickness, however, does not necessarily represent an amorphous-to-(mixed-phase) transition (Podraza, 2008). Rather it can simply represent an amorphous roughening transition. The clearest indication of the amorphous-to-

(mixed-phase) transition (as opposed to an amorphous roughening transition) is a subsequent maximum in the roughness in the former case followed by smoothening due to nanocrystallite coalescence. In fact after nucleation of the nanocrystallites with the film becoming mixed-phase, the crystalline inclusions increase in size with increasing bulk layer thickness, forming inverted conical structures. These structures eventually come in contact with one another resulting in nanocrystalline film coalescence, at which time the (mixed-phase)-to-(single-phase) nanocrystalline transition event occurs. This transition is characterized by the onset of a reduction in surface roughness thickness versus bulk layer thickness, i.e. a smoothening effect. This phase evolution is also shown in Figure 3-1 at 1900 Å bulk i-layer thickness. The phase behavior in Figure 3-1 observed for the a-Si:H i-layer on the n-layer coated borosilicate glass substrate is similar to the top and middle cell phase transitions observed by Stoke (Stoke, 2008) on a substrate consisting of c-Si/ native-oxide/n-layer. Stoke et al. used Si2H6 as the source gas, instead of the SiH4 gas used here and elsewhere (Collins et al., 2003; Fujiwara et al.,

2001). The details of the i-layer phase transitions at the various R values, which ultimately generate the i-layer deposition phase diagram, will be presented in Section 3.3.

Similar to the approach for i-layer phase diagram development, the p-layer phase diagram was obtained by depositing various p-layers of ~ 150 Å thickness at R values of

75 50, 75, 100, 125, 150, 200 and 250 on Cr/Ag/ZnO/n/i-layer coated borosilicate glass.

The deposition conditions for the layers used in the p-layer phase diagram study are given in Table 3.2. The Cr, Ag, ZnO and n-layers were all deposited under the same conditions as were used for the i-layer phase diagram study, whereas the i-layer in each case was deposited to ~ 3000 Å thickness at R = 15. The dopant gas for the p-layer was B2H6, with a doping flow ratio D = [B2H6]/[SiH4]= 0.01. This ratio corresponds to a 0.4 sccm flow of 5% B2H6 in H2. The RTSE data were acquired during the p-layer deposition, whereas single scan SE data were acquired after depositing the Ag, ZnO, and n- and i-layers separately. Thus, the optical model of the stack was constructed and thickness and optical properties of the underlying materials were obtained before depositing each p- layer. During the acquisition time for one pair of (, Δ) spectra, ~ 1-2 Å p-layer material accumulates on top of the underlying multilayer stack. As in the case of the i-layer phase diagram study, each of these solar cells was completed by depositing ITO dots as top contacts with the same deposition condition as in the i-layer study. The results demonstrating the performance of the solar cells of this series will be presented in

Chapter 6.

Finally, a spatially resolved deposition phase diagram was developed for roll-to- roll cassette deposition of p-layers on Cr/Ag/ZnO/n/i-layer coated polyethylene naphthalate (PEN) polymer (Dahal et al., 2011a). The detailed procedure for roll-to-roll sputtering, as well as the roll-to-roll PECVD of the solar cell component layers will be discussed in Chapter 5. The deposition conditions of the individual layers used for the spatially resolved p-layer phase diagram study are given in Table 3.3. First, the polyethylene naphthalate (PEN) plastic was fully coated with Cr metal, which acts as an

76 Table 3.2 Deposition conditions of the underlying layers in the phase diagram study of the p-layer relevant for thin film Si:H n-i-p solar cells deposited on 2" x 2" glass substrates. The ZnO, n-layer and i-layer thicknesses and deposition rates are for representative depositions.

Layer Dep. RF Substrate Time Gas flows (sccm) Int. Nom. type pressure plasma temp. (min) thick- dep. (mTorr) power (oC) ness rate (W/cm2) (Å) (Å/s) Cr 5 0.92 RT 20.0 [Ar] = 10 1000 0.84 Ag 5 0.92 RT 30.0 [Ar] = 10 5000 2.78 ZnO 5 0.92 RT 37.0 [Ar] = 10 3000 1.35 R = 0.1, D = 0.005

n-layer 350 0.01 200 2.5 [SiH4] =10, 250 1.67

5% [PH3] in [H2]= 1 R = 15 i-layer 800 0.033 200 58.2 3000 0.86 [H2] = 75, [SiH4] = 5 R = 50, D = 0.01 1500 0.066 100 3.1 [H2] = 100, [SiH4] = 2 120 0.65 5% [B2H6] in H2 = 0.4 R = 75, D = 0.01 1500 0.066 100 4.5 [H2] = 150, [SiH4] = 2 120 0.44 5% [B2H6] in H2 = 0.4 R = 100, D = 0.01 1500 0.066 100 5.7 [H2] = 200, [SiH4] = 2 120 0.35 5% [B2H6] in H2 = 0.4 p-layer R = 125, D = 0.01 (diff. R 1500 0.066 100 8.8 [H2] = 250, [SiH4] = 2 120 0.23 values) 5% [B2H6] in H2 = 0.4 R = 150, D = 0.01 1500 0.066 100 10.7 [H2] = 300, [SiH4] = 2 120 0.19 5% [B2H6] in H2 = 0.4 R = 200, D = 0.01 1500 0.066 100 12.3 [H2] = 400, [SiH4] = 2 120 0.16 5% [B2H6] in H2 = 0.4 R = 250, D = 0.01 1500 0.066 100 14.3 [H2] = 500, [SiH4] = 2 120 0.14 5% [B2H6] in H2 = 0.4 ITO 5 0.58 150 8.0 [Ar] = 10 570 1.19 5% [O2] in Ar = 3 Note: As before, the 5% dopant gas in H2 and O2 in Ar both are by volume.

77 Table 3.3 Deposition conditions of the underlying layers for the spatially resolved phase diagram study of the p-layer used for roll-to-roll cassette deposition of a-Si:H solar cells on PEN polymer substrates.

Layer Dep. RF Substrate Web Gas flows Intended Nominal type pressure plasma temp. speed (sccm) thickness dep. rate (mTorr) power (oC) (cm/s) (Å) (Å/s) (W/cm2) Cr 5 0.92 RT 0.025 [Ar] = 10 1000 1.56 Ag 5 0.92 RT 0.020 [Ar] = 10 3000 3.75 ZnO 5 0.92 RT 0.015 [Ar] = 10 3000 2.81 R = 0.1, D = 0.005

n-layer 350 0.013 110 0.13 [SiH4] =10, 250 1.81

5% [PH3]

in [H2] = 1 R = 1

i-layer 400 0.025 110 0.012 [H2] = 25, 3000 2.00

[SiH4] = 25 R = 150 D = 0.01 1500 0.13 110 0.015 [H2] = 300 750 0.63 [SiH4] = 2 5% [B2H6] p-layer in H2 = 0.4 R = 150 D = 0.01 1500 0.13 110 0.020 [H2] = 300 500 0.63 [SiH4] = 2 5% [B2H6] in H2 = 0.4 Note: Once again, the 5% dopant gas in H2 is by volume.

adhesion layer. On top of the Cr, an opaque Ag metal layer was deposited, followed by a ZnO:Al layer to form the back-reflector. The Cr, Ag, and ZnO:Al depositions were performed by magnetron sputtering at room temperature under the deposition conditions given in Table 3.3. The web speeds for Cr, Ag and ZnO depositions were chosen such

78 that the final Cr, Ag and ZnO thicknesses reached ~ 1000 Å, 5000 Å and 3000 Å, respectively, at the end of the deposition zone. Here, ZnO:Al instead of intrinsic ZnO was used for the solar cell deposition on roll-to-roll polymer. Next, the coated PEN was loaded into the n-layer chamber and preheated for 3 hours such that the PEN polymer reached ~ 110oC substrate temperature. After that, the n- and i-layers were deposited in their respective chambers in succession.

As the last PECVD Si:H step in roll-to-roll deposition, two different p-layers were deposited at 0.015 cm/s and 0.020 cm/s web speeds such that the former p-layer remains in the deposition zone for a longer period of time and thus, accumulates a larger thickness. All deposition conditions of the p-layers as well as the underlying layers are given in Table 3.3. Similar to the case of the p-layer phase diagram study on rigid glass substrates, RTSE studies were also performed during the roll-to-roll p-layer deposition, whereas single scan SE was performed after depositing the Ag, ZnO, n-layer and i-layer separately. Thus, the optical model of the stack could be constructed before the deposition of the p-layer. For the two p-layer depositions performed along different lengths of the web, one at a web speed of 0.015 cm/s and the other at 0.020 cm/s, the final effective p-layer thicknesses reached ~ 800 Å and ~500 Å, respectively. These thicknesses were obtained after the web passed through the full 18 cm deposition zone, as determined by mapping SE. A detailed description of the mapping spectroscopic ellipsometry is given along with Figure 2-8 in Chapter 2. Using RTSE, one can observe at most only a fraction of ~ 0.7 (13 cm/18 cm) or ~ 580 Å and 380 Å of the total effective thickness evolution. The deficits of these values from 800Å and 500Å, respectively, are due to the deposition that occurs over the 5 cm length from the monitoring point, to the

79 end of the deposition zone. This situation will be discussed in detail in Chapter 5 with figures to show the monitoring point relative to the total length of the deposition zone in the sputtering as well as in the PECVD processes. Unlike the depositions on the rigid borosilicate glass, the solar cell structure was not completed after determination of the p- layer spatial phase diagram on the PEN polymer substrate. Instead, completed flexible solar cells were fabricated on a high temperature tolerant Kapton polymer substrate. The performance of these flexible solar cell will be discussed in Chapter 6.

3.3 i-layer Phase Diagram on 2" x 2" Glass Substrate

The i-layer serves as the absorber of the thin film a-Si:H solar cell in both n-i-p substrate and the p-i-n superstrate configurations. In the substrate design, sunlight enters the solar cell first and, if absorbed in the i-layer, does not encounter the substrate, e.g. stainless steel plastic etc. on its path. In the superstrate design, however, sunlight enters through the transparent substrate first, usually glass, plastic etc. In both configurations, the sunlight encounters the p-layer which acts as the window before reaching the i-layer, which acts as the absorber.

The use of an n-i-p structure for a thin film a-Si:H based solar cell is a departure from the conventional solar cell designs used in other material technologies, which are more often based on the p-n structure. For doped a-Si:H, however, the diffusion lengths of the minority photocarriers (holes in n-type a-Si:H and electrons in p-type a-Si:H) are exceedingly small and so a p-n structure only collects the electrons and holes generated by photons absorbed in the very thin regions of a doped a-Si:H closest to the junction

(Deng and Schiff, 2003). Essentially, any photons absorbed in the doped layers of an a-

80 Si:H n-i-p solar cell represent quantum efficiency losses. Hence, a relatively thick ( ~ 0.3

m) high electronic quality intrinsic absorber layer is sandwiched between very thin doped layers to generate a built-in electric filed. This structure enables absorption of most photons of the incident sunlight within the i-layer. The built-in field separates the photogenerated electrons and holes which are transported to the contacts. As a result, the i-layer is the most critical layer for optimization of the performance of the thin film a-

Si:H solar cell. A high quality i-layer yields a better fill factor (FF), whereas its thickness should be sufficient to absorb nearly all photons of energy above the band gap in order to optimize the short circuit current (Jsc). The open circuit voltage (Voc), however, is determined by the i/p and n/i junctions and both the i-layer and p-layer are most responsible for Voc optimization. A phase diagram study of the absorber i-layer assists in optimization for the best a-Si:H n-i-p solar cell performance.

As described in Section 3.2, i-layers were deposited by PECVD at different R values on Cr/Ag/ZnO/n-layer coated borosilicate glass substrates. The optical properties of the Ag, ZnO, and n-layer were obtained from the single scan SE data acquired after each layer deposition. The Ag layer optical properties are generated by fitting the single scan ) spectra using Drude behavior for the free electrons in the low photon energy, near-IR region and a pair of critical point (CP) resonances for the bound electrons in the high photon energy, UV region. The CP resonances for Ag are derived assuming parabolic bands in k-space in the neighborhood of (d-band)-to-(Fermi-level) absorption.

The intrinsic ZnO layer was modeled with two CP oscillators assuming parabolic bands in k-space in the neighborhood of the fundamental band gap. The a-Si:H n-layer was modeled assuming square root densities of states versus the hole and electron energies in

81 the valence and conduction band states as well as a constant dipole matrix element (CD-

ME) for transitions near the band edge (Cody, 1984). By incorporating a Lorentz oscillator to simulate the behavior at higher energies, one arrives at the full Cody-Lorentz oscillator function (Ferlauto et al., 2002). The mathematical form of the Drude free electron expression, as well as the Lorentz, CPPB, Tauc-Lorentz and Cody-Lorentz oscillators are given in the Appendix, Eqs. (A.1)-(A.14). Once the underlying layer optical properties are known, the stack was modeled with the Ag/ZnO/n/i layers in succession. Here, the i-layer optical properties were obtained at ~ 200 Å bulk thickness, by multi-time SE analysis. These optical properties are obtained as inverted results for a given pair of db and ds such that the mean square error (MSE) is a minimum over the given time range, corresponding to a thickness variation of ~ 50 Å. These inverted optical properties obtained from multi-time analysis for each deposition at a given R value are then smoothened using the Cody-Lorentz oscillator function. The oscillator parameters of all the layers and the corresponding layer thicknesses are presented in

Table 3.4. Once all the optical properties for a given a-Si:H i-layer deposition are known, the RTSE data can be analyzed as a function of time using the global -minimization routine for that deposition. In this analysis, bulk i-layer thickness (db) and the surface roughness thickness (ds) are the fitting variables.

To construct a deposition phase diagram of an i-layer, specific events of significance and the thicknesses at which the events occur, must be identified. As explained in Section 3.2, the global -minimization routine for analysis of the RTSE data identifies the phase transitions (if they exist) as well as times and associated thicknesses at which these transitions occur. Even though the optical functions obtained in the initial

82 Table 3.4 Oscillator parameters used to represent the underlying layers for the i- layer phase diagram study. These results are appropriate for a measurement temperature of 200oC. The i-layer Cody-Lorentz oscillator parameters were obtained by smoothening the multi-time results obtained at ~ 200 Å bulk i-layer thickness, whereas other parameters are obtained from least square regression fit of the single scan SE data taken after each layer deposition at the corresponding deposition temperatures.

inf db ds Layer Oscillator parameters (Å) (Å)

Drude parameters CPPB parameters (= 0.5 fixed)  (-cm)  (fs) A (eV)  (eV) E (eV) Phase (o) 1.12± o Ag 3.87± 0.45± 3.99± -60.83 ± 5000 10 0.05 2.07x10-6 30.12 0.03 0.01 0.03 0.64 ±7.9 x 10-8 ±1.17 3.19± 2.35± 4.27± 18.77± 0.04 0.05 0.04 2.09 Drude parameters Lorentz/ Tauc-Lorentz parameters  (-cm)  (fs) A (eV)  (eV) E (eV) E (eV) Intf. o g 1.58 ± 7.82± 0.46± 2.58± Ag/ - 25 - 0.02 -5 0.65 0.03 0.01 ZnO 1.58x10 15.72 ±8.2 x 10-7 ±0.44 592.17 1.13± 3.49± 3.48 ± 0.12 ± 10.05 0.63 0.05 CPPB parameters (= 0.5 fixed) o A (eV)  (eV) Eo (eV) Phase ( ) 1.71± ZnO - - 2.33± 0.23± 3.30± -22.79 ± 3030 52 0.23 0.04 0.01 0.01 0.92 1.30 3.86± 4.53± 0.23± ±0.03 0..31 0.05 0.15

Cody-Lorentz parameters (Ep = 1 eV, fixed) inf R A (eV) Eo (eV) (eV) Eg (eV) n-layer 1.07± 0.03 73.22±0.34 3.96±0.01 2.83±0.02 1.58±0.01 0.1 245 32 1.11±0.11 72.72±1.10 4.07±0.01 2.54±0.04 1.56±0.02 5 3035 21 1.13±0.21 75.51±1.65 3.92±0.02 2.55±0.06 1.64±0.04 10 3040 25 1.06±0.13 73.14±1.51 3.90±0.10 2.71±0.06 1.69±0.02 15 3048 26 1.12±0.21 72.10±1.72 4.02±0.02 2.99±0.08 1.69±0.05 20 3085 37 i-layer 1.09±0.23 70.86±2.27 4.00±0.03 2.62±0.10 1.68±0.06 25 3053 68 1.09±0.27 74.68±1.66 4.08±0.02 2.51±0.06 1.81±0.03 30 3092 70 1.07±0.25 60.13±2.16 4.03±0.12 2.51±0.11 1.80±0.09 35 3082 71 1.11±0.32 63.07±2.35 3.98±0.21 2.51±0.17 1.82±0.12 40 3020 44 p-layer 1.03±0.24 75.36±1.28 3.96±0.20 2.93±0.19 1.92±0.05 135 122 18

83 stage of the deposition are not accurate due to phase evolution that may occur during growth, the bulk layer thickness db is quite robust, and from the slope of db versus time, the growth rate can be determined. This growth rate then allows estimates of the thicknesses at which transitions occur, by evaluating the product of the growth rate and the time intervals from the beginning of the deposition to the times of the transitions. A plot of the growth rates for the various i-layer depositions is shown in Figure 3-2.

Figure 3-2 Deposition rates of the i-layer as a function of the hydrogen dilution ratio. This series of i-layers was deposited on Cr/Ag/ZnO/n-layer coated borosilicate glass for phase diagram studies.

84 The amorphous-to-(mixed-phase) and the (mixed-phase)-to-(single-phase) nanocrystalline transitions were identified using the method described in Section 3.2.

The surface roughness evolution of i-layers deposited at R = 10 and R = 30 as functions of the bulk i-layer thickness for each deposition are shown on semi-logarithmic plots in

Figure 3-3. Clearly, at R = 10, the film grows initially in the amorphous phase and

Figure 3-3 Surface roughness thickness versus the bulk i-layer thickness for Si:H films deposited with hydrogen dilution ratios of R = 10 and 30. The deposition at R = 30 clearly shows the characteristics of nanocrystalline Si:H phase transitions including nucleation and coalescence events. In contrast, the deposition at R =10 does not show such transition, indicating that the R = 10 film remains amorphous throughout the process.

85 remains amorphous throughout the deposition, as evidenced by the constant ds as a function of db. On the other hand, at R = 30, the i-layer initially grows in the amorphous phase and nucleates nanocrystals, becoming mixed-phase at db ~ 180 Å when ds starts to increase. Finally, the growing R = 30 film transitions to single-phase nanocrystalline silicon at db ~ 1800 Å, when ds peaks and starts to decrease with a further increase in db.

The volume fraction evolution of the nanocrystalline phase is characterized by plots of fnc versus db obtained from virtual interface analysis, as explained in detail in Section

2.3.3.2. The virtual interface analysis in this case was performed over the 3.0 - 5.0 eV range for the top ~10 Å of the film. For the R = 30 deposition, the nanocrystalline optical properties over the spectral range of 3.0 - 5.0 eV are obtained by inversion at a thickness of ~ 2000 Å or at ~ 200 Å beyond the coalescence thickness (~1800 Å). Global - minimization is applied to obtain the correct surface roughness thickness, ds , which then leads to the dielectric function via inversion as noted. The dielectric function is then incorporated into virtual interface analysis in order to generate (t), which provides a criterion for identifying the correct ds value iteratively. The details of this procedure are provided in Section 2.3.3.2. Similar procedures are applied to obtain the nanocrystalline optical properties of all higher hydrogen dilution ratio i-layer depositions that exhibit nanocrystallite coalesce before the end of the process, which in this case are the R = 35 and R = 40 films. The individual nanocrystalline Si:H optical properties for R = 35 and R

= 40, along with the corresponding amorphous silicon optical properties are used for the virtual interface analysis of the respective depositions. In this study, R = 30 is the lowest hydrogen dilution ratio that gives rise to coalescence within the first ~ 3000Å of bulk i-

86 layer thickness. Hence the nanocrystalline optical properties obtained at R = 30 are used for the virtual interface analysis for all depositions with R values less than R = 30.

The three sets of nanocrystalline Si:H optical properties spanning the spectral range of 3.0 - 5.0 eV for depositions with R = 30, 35 and 40 were smoothened by using a sum of two Lorentz oscillators, modified by a common Tauc band gap. The mathematical form of this oscillator is given in Appendix section in Eq. (A.12) and the values of the associated oscillator parameters are presented in Table 3.5. These Tauc-

Lorentz oscillator parameters are comparable to those for the nanocrystalline Si:H optical properties also obtained at 200oC from a previous study (Ferlauto et al., 2001). The virtual interface analysis has been effective for quantifying the nanocrystalline volume fraction in Si:H (Stoke, 2008) as well as in Si1-xGex:H (Podraza, 2008) thin films. An example of one such plot for a film deposited at a hydrogen dilution ratio of R = 30 is shown in Figure 3-4. The culmination of all the virtual interface analysis results is the deposition phase diagram, drawn as a function of the hydrogen dilution ratio R, as shown in Figure 3-5. It is interesting to note that the depositions with hydrogen dilution ratio given by R ≥ 25 eventually nucleate nanocrystalline Si:H. The amorphous material at the beginning of these depositions, i.e. before the a(a+nc) transition, is believed to be the most ordered amorphous phase with the most effective passivation of dangling bonds by

H-atoms. Such material is referred to as protocrystalline a-Si:H (Collins et al., 2003).

The films deposited with hydrogen dilution ratios of R < 25 do not nucleate nanocrystalline Si:H, at least not within the first 3000 Å, which is the typical thickness of the i-layer used for single junction a-Si:H solar cell devices. Hence, the best hydrogen

87 Table 3.5 Parameters used in an expression that represents the nanocrystalline Si:H dielectric function, as described by two Lorentz oscillators modified by a common Tauc band gap. These results for i-layers were obtained at a measurement temperature of 200oC and at higher hydrogen dilution such that the film coalesces to form single phase nanocrystalline Si:H within the deposited thickness of 3000 Å. Also included are the Tauc-Lorentz parameters for a nanocrystalline i-layer at 200oC from earlier similar work.

Layer R inf Tauc-Lorentz parameters type

(eV)  (eV) Eo (eV) Common Eg (eV)

3.441± 0.361± 3.451± 1.312 0.101 0.125 30 1.573 1.495 ± 0.231 98.138± 1.656± 4.149± 2.041 0.028 0.011 4.135± 0.370± 3.531± i-layer 1.681± 1.321 0.081 0.022 35 1.511 ± 0.151 0.071 81.151± 1.493± 4.087±

1.190 0.042 0.012 5.051± 0.382± 3.496± 1.815± 1.531 0.044 0.076 40 1.483 ± 0.065 0.356 91.351± 1.361± 4.048± 5.486 0.017 0.011

Results from earlier work by Ferlauto (Collins and Ferlauto, 2005a)

13.094 0.696 3.512 i-layer 1.175 1.345 87.178 1.466 4.137

Figure 3-4 Nanocrystalline volume fraction as a function of the bulk i-layer thickness for a Si:H film deposited at R = 30. The plot clearly shows the specific phase evolution regimes of amorphous, mixed-phase, and single-phase nanocrystalline Si:H.

dilution ratio for optimized a-Si:H solar cells with a protocrystalline i-layer is in the neighborhood of R = 20, but surely less than R = 25.

Each of the Cr/Ag/ZnO/n/i-layer coated glass substrates was loaded into the p- chamber for completion of the solar cell active layer structure by deposition of a protocrystalline Si:H p-layer. RTSE was also performed during each p-layer deposition in order to control the final p-layer thickness at ~ 120 Å. The resulting n-i-p solar cell

Figure 3-5 A deposition phase diagram for rf PECVD of Si:H i-layers fabricated on borosilicate glass coated with a Cr/Ag/ZnO/n-layer structure. The n-layer is fabricated under conditions leading to single-phase a-Si:H:P. The i- layer amorphous-to-(mixed-phase) transition thickness is represented by the lowermost solid line with open circles, and the (mixed-phase)-to- (single-phase) nanocrystalline transition thickness is represented by the uppermost solid line with solid squares. The upward arrow indicates that the transition may occur at thicknesses above the indicated value. Contour lines representing specific nanocrystalline volume fractions fnc are also plotted. The dashed lines represent extrapolations of the transitions to lower R values. The extrapolations also include the contours for different volume fractions of nanocrystalline Si:H.

90 structure was cooled to room temperature, removed from the p-layer chamber, and then completed by depositing an ITO layer on top of the p-layer, through a stainless steel mask, using the chamber designed for sputtering of transparent conducting oxides. The solar cell parameters for cells with i-layers prepared at various R values will be presented and compared with the i-layer phase diagram in Chapter 6.

3.4 p-layer Phase Diagram on 2" x 2" Glass Substrate

The thin Si:H p-layer is deposited on top of the i-layer in the n-i-p substrate-type a-Si:H solar cell and, like the i-layer, is critically important in the optimization of the thin film n-i-p solar cell. a-Si:H solar cell. The p-layer has the greatest impact on the open circuit voltage (Voc) and the short circuit current (Jsc). Since the carriers generated in the doped layers of the thin film a-Si:H solar cell recombine very quickly, they do not contribute to the total current generated in the device. Hence, any photons absorbed within the doped layer are considered as quantum efficiency loses (Deng and Schiff,

2003). As a result, the so called “window” p-layer used in the thin film a-Si:H solar cell should be very thin (~100 Å), just sufficient to establish a built-in electric field within the absorber i-layer, acting in conjunction with a thin n-layer on the opposite side of the i- layer. Also, the band gap of the p-layer should be as large as possible so that most of the photons of sunlight pass through it without absorption. The band gap of the p-layer can be increased by increasing the hydrogen dilution ratio R during deposition, but not exceeding the R value at which the amorphous phase transitions to mixed-phase during the deposition. The open circuit voltage (Voc), on the other hand, depends critically on the i/p interface, which can be optimized by using a protocrystalline p-layer (Koval et al,

91 2002) on top of the optimized i-layer. Such p-layer optimization, as in the case of i-layer optimization discussed in Section 3.3, can be undertaken based on the p-layer phase diagram, which is plotted as a function of the hydrogen dilution ratio R. This is the most critical parameter that controls the thickness at which the phase transitions occur.

As described in Section 3.2, a series of p-layers was deposited on Cr/Ag/ZnO/n/i- layer coated borosilicate glass at different R values, whereas the other deposition parameters, i.e. the pressure, rf power, and temperature, were the same for all depositions.

The optical properties of the underlying layers from the Ag through to the n-layer were obtained in the same way as was done for the i-layer phase diagram study explained in

Section 3.3. The optical properties of the i-layer was modeled using the Cody-Lorentz oscillator function by fitting single scan data acquired at the end of the deposition. The oscillator parameters used to represent the underlying Ag, Ag/ZnO interface, and ZnO layers are the same as those applied in the i-layer phase diagram study, given in Table-

3.4. The Cody-Lorenz parameters representing the n-layer and i-layer were obtained by fitting single scan data, and the corresponding thicknesses are given in Table 3.6.

After determination of the optical properties and the thicknesses of the underlying layers, the final optical model was generated. The p-layer, whose optical properties and thickness are to be determined, was then placed at the top of the model structure. Each p- layer was deposited to a final bulk layer thickness of at most ~ 120 Å, and the hydrogen dilution for the depositions at higher R values was sufficiently large to result in coalesce of the film to single-phase nanocrystalline Si:H. As a result, the optical properties of the amorphous phase were extracted from the lower R depositions that remain amorphous throughout the deposition process. These optical properties were obtained near the end of

92 Table 3.6 Oscillator parameters used to represent the thin film Si:H layers for p- layers in phase diagram studies. The p-layer optical properties at the deposition temperature were obtained for film that remain amorphous throughout the deposition of ~120 Å bulk p-layer thickness (R ≤ 125). The R = 125 optical properties were used for all p-layers deposited at hydrogen dilution ratios R > 125. The Ag, Ag/ZnO, and ZnO oscillator parameters were fixed to the values used in the i-layer phase diagram study as presented in Table 3.5.

Layer Cody-Lorentz parameters (Ep =1 eV, fixed) inf R db (Å) ds (Å) type A (eV) E (eV)  (eV) Eg (eV) 1.12 ± 72.76 ± 4.03 ± 2.82 ± 1.56 ± n-layer 0.1 235 34 0.12 0.38 0.01 0.02 0.01 1.07 ± 76.72 ± 3.97 ± 2.58 ± 1.66 ± i-layer 15 3034 19 0.15 0.31 0.02 0.01 0.01 1.11 ± 67.03 ± 4.09 ± 2.74 ± 1.73 ± 50 125 17 0.12 1.10 0.01 0.05 0.02 1.09 ± 67.68 ± 4.06 ± 2.62 ± 1.89 ± 75 118 23 0.19 1.37 0.05 0.11 0.04 1.13 ± 80.22 ± 4.11 ± 2.84 ± 1.95± 100 124 22 p-layer 0.16 1.53 0.02 0.06 0.03 1.13 ± 74.98 ± 4.12 ± 2.58 ± 1.99± 125 112 24 0.15 1.56 0.01 0.06 0.02 150 108 59 200 102 96 250 94 86

the lower R depositions, by using multi-time analysis, as explained earlier. Next, the

RTSE data obtained as a function of time for each deposition were analyzed using the global -minimization routine, with the bulk p-layer thickness (db) and the surface roughness thickness (ds) as the fitting variables in order to identify the possible presence

93 of a phase transition and, if it exists, the thickness at which the transition occurs. The deduced optical properties obtained for the p-layer deposited at the maximum R value for which the film remains amorphous throughout the deposition, was used in all analyses of higher R p-layers in order to identify the presence of phase transitions. This approach is different than that of the i-layer phase evolution study in which the optical properties of the pure amorphous Si:H phase were extracted from each deposition separately. This could be done because each deposition exhibited al least a ~ 200 Å thick amorphous deposition region. As one similarity in the development of the p- and i-layer phase diagrams, however, the relatively low R i-layer films that develop a mixed-phase structure, but do not coalesce to the pure nanocrystalline phase, were analyzed by using the nanocrystalline Si:H optical properties from the nearest higher R value that does exhibit coalescence. The inverted a-S:H p-layer optical properties obtained from multi- time analysis were smoothed using a Cody-Lorentz oscillator expression. The resulting oscillator parameters along with the corresponding layer thicknesses db and ds are presented in Table 3.6 for the R values for which the films are amorphous throughout the thickness.

The hydrogen dilution flow ratio of R = 150 is the lowest R value at which the amorphous-to-mixed-phase transition was observed in these sets of p-layer depositions.

Hence, the p-layer optical properties obtained at R = 125, which is the highest dilution ratio for which the film remains amorphous throughout the deposition, is used in the analysis of the phase evolution of all higher hydrogen dilution p-layer depositions including R =150, 200, and 250. Once again, even though the R = 125 optical properties do not accurately represent the R > 125 materials throughout their deposition processes,

94 the bulk layer thickness (db) is quite robust and the deposition rate obtained from the slope of db versus time is deemed accurate. This growth rate allows calculation of the bulk p-layer thickness at which the phase transitions occur including the amorphous-to-

(mixed-phase) and (mixed-phase)-to-(single-phase) nanocrystalline Si:H transitions. A graph showing the growth rates of different p-layers is presented in Figure 3-6.

Figure 3-6 Deposition rates of the p-layer as a function of the hydrogen dilution ratio R. This series of p-layers was deposited on Cr/Ag/ZnO/n/i-layer coated borosilicate glass for phase diagram development.

95 Although the amorphous-to-(mixed-phase) and the (mixed-phase)-to-(single-phase) nanocrystalline transitions in different Si:H p-layers are identified in the same way as was done for the i-layer, the quantification of the nanocrystalline volume fraction in such thin p-layers is extremely difficult. As a result, there are insufficient data to apply virtual interface (VI) analysis to quantify the nanocrystalline volume fraction in the mixed-phase regions of the p-layer depositions. Thus, the p-layer phase diagram only includes the amorphous-to-(mixed-phase) and the (mixed-phase)-to-(single-phase) transitions, determined on the basis of the surface roughness evolution as shown in Figure 3-1. In other words, no contour lines can be drawn on the p-layer phase diagram to show the different volume fractions of the nanocrystalline phase, in contrast to the i-layer phase diagram discussed in Section 3.3. Figure 3-7 shows the surface roughness evolution of two p-layers deposited at R = 75 and R = 250 on a semi-logarithmic plot as functions of the bulk p-layer thicknesses. Clearly, for R = 75, the p-layer remains amorphous throughout the deposition. At R = 250, however, the p-layer transitions from amorphous to mixed-phase at ~12 Å bulk p-layer thickness when ds starts to increase, and from mixed-phase to single-phase nanocrystalline Si:H at ~ 90 Å bulk p-layer thickness, when ds peaks and starts to decrease with a further increase in bulk p-layer thickness.

On the basis of similar observations, bulk layer thicknesses can be obtained at which the transitions from amorphous to mixed-phase and from mixed-phase to single-phase nanocrystalline Si:H occur for p-layer depositions at various R values, and the resulting deposition phase diagram is established as shown in Figure 3-8. From the deposition phase diagram, it can be observed that the p-layer depositions with R ≥ 150 transition to mixed-phase, whereas only the depositions with R ≥ 200 transition to single-

Figure 3-7 Surface roughness thickness versus the bulk p-layer thickness for Si:H films deposited with hydrogen dilution ratios of R = 75 and 250. The deposition at R = 250 clearly shows the characteristics of nanocrystalline nucleation and coalescence events, whereas the deposition at R = 75 does not. These results indicate that the R = 75 film remains amorphous throughout the deposition.

phase nanocrystalline Si:H. All p-layers deposited with R ≤ 125 remain amorphous throughout their ~ 120 Å bulk thicknesses. As noted earlier, the p-layer optical properties obtained at R = 125 were used to deduce the amorphous-to-(mixed-phase) and (mixed- phase)-to-(single-phase) nanocrystalline Si:H transitions for p-layer depositions with R ≥

Figure 3-8 A phase diagram for rf PECVD of Si:H p-layers deposited on borosilicate glass coated with a Cr/Ag/ZnO/n/i-layer structure having amorphous n- and i-layers. The amorphous-to-(mixed-phase) transition thickness is represented by the lower line with solid squares and the (mixed-phase)-to- (single-phase) nanocrystalline transition thickness is represented by the upper solid line with solid diamonds. Unlike the situation for the i-layer phase diagram study, in this study the p-layer thickness (~120 Å) used in the solar cell is not sufficient to determine the contour lines for various nanocrystalline fractions.

150. Because the R = 125 p-layer remains amorphous throughout the deposition but the

R = 150 p-layer undergoes a mixed- phase transition during the deposition, the hydrogen dilution ratio for optimization of the a-Si:H solar cell performance with a protocrystalline p-layer is expected to be in the neighborhood of R = 125. This p-layer deposition phase

98 diagram result is comparable to an earlier such diagram obtained for n-i-p Si:H solar cells with 1200 Å thick p-layers (Koval et al., 2002a; Wronski and Collins, 2004). It is also comparable to that for 1800 Å p-layer deposited in the p-i-n configuration on ZnO coated glass (Rovira et al., 2002). One difference, however, is that the p-layers in this Thesis study are deposited to the same thickness as is used in the n-i-p solar cell (~ 120Å). As was done in the i-layer phase diagram study, after each p-layer deposition the solar cells are completed by depositing ITO dots onto the p-layer. Because the ITO deposition requires a stainless steel mask, the solar cell structure must be removed from the p-layer chamber and exposed to laboratory atmosphere after the p-layer is cooled to room temperature. The correlation of the p-layer phase diagram with the solar cell results will be presented in Chapter 6.

3.5 Spatial Phase Diagram of p-layer on Polymer Substrate

The phase diagram studies of the p-layers deposited on 2" x 2" rigid glass substrates, as discussed in Section 3.4, are further extended to include the spatial dependence of the p-layer phase boundaries for large area solar cell structures deposited on flexible substrates. The concept is to extend the scope of spectroscopic ellipsometry from phase diagram studies of small dot cells to studies of large area solar modules. In this manner, the losses of solar cell performance in scaling optimized deposition conditions from the laboratory to the factory can be understood and potentially minimized. The large area flexible roll-to-roll substrates used in this research simulate the industrial scale fabrication of a-Si:H solar modules in the n-i-p substrate configuration. This research focuses on the top-most p-layer of the n-i-p solar cell structure, with the goal being to develop a thin protocrystalline p-type Si:H film growth

99 process uniformly across the 15 cm. wide moving web, thus contributing to optimum performance of the resulting a-Si:H solar modules over large areas. The first step toward this goal is the determination of a spatially-resolved deposition phase diagram, which shows Si:H phase transitions superimposed onto a bulk thickness map of the p-layer.

As discussed in Section 3.2, two different p-layers were deposited on

Cr/Ag/ZnO:Al/n/i-layer coated PEN at web speeds of 0.015 cm/s and 0.020 cm/s. Single scan data were collected after each underlying film deposition including Ag, ZnO:Al, the a-Si:H n-layer, and the a-Si:H i-layer in succession. Real time spectroscopic ellipsometry

(RTSE) data were collected during both p-layer depositions. The optical properties of Ag were obtained by fitting the single scan data using a Drude oscillator to describe free electron transitions in the visible and NIR spectral regions and a pair of critical point resonances to describe bound electron transitions in the high photon energy UV region, as discussed in Sections 3.3 and 3.4. The CP components are derived assuming parabolic bands in k-space in the neighborhood of (d-band)-to-(Fermi-level) absorption in Ag. The

ZnO:Al was modeled using a Drude oscillator in the NIR region to describe free electrons arising from Al doping of the ZnO and a CP oscillator with parabolic bands in k-space in the neighborhood of the fundamental band gap of ZnO. The a-Si:H n-layer and i-layer optical properties were obtained by fitting the corresponding single scan data acquired at the end of each deposition, using a different Cody-Lorentz oscillator function for each layer. As indicated earlier, the mathematical forms of all the oscillators are presented in the Appendix. The collections of oscillator parameters, used to represent the individual layers underneath the p-layer on the PEN polymer substrate, are given in Table 3.7. The

RTSE data for each p-layer was then fitted by generating its optical properties at ~ 200 Å

100 Table 3.7 Oscillator parameters that represent the underlying layers in the development of the phase diagram for the p-type Si:H layer of an n-i-p solar cell structure on PEN polymer substrate in order to fit the mapping SE data. The Ag/ZnO interface parameters are fixed, as are the Cody- Lorentz parameters Ep for both the n- and i-layers. The p-layer parameters are coupled to the associated optical band gap Eg through Eqs. (A.24) A.31).

db ds Layer inf Oscillator parameters (Å) (Å) Drude parameters CPPB parameters (= 0.5, fixed)

o  (-cm)  (fs) A (eV) (eV) Eo (eV) Phase ( ) 1.39± Ag 4.57 ± 0.54 ± 3.99± -50.55± 5000 42 0.13 1.08 x10-5 6.71± 0.53 0.09 0.12 1.23 ±1.1 x10-6 0.58 2.15 ± 5.41 ± 4.60 ± 1.05 ±

0.14 0.10 0.15 0.32 Drude parameters Lorentz/ Tauc-Lorentz parameters Intf.  (-cm)  (fs) A (eV)  (eV) Eo (eV) Eg (eV) Ag/ 1.58 82 - 7.82 0.46 2.58 - ZnO 1.58 x10-5 15.72 592.17 1.13 3.49 3.48 CPPB parameters (= 0.5, fixed) -4 6.15 x10 4.16± o ZnO 1.61± A (eV)  (eV) Eo (eV) Phase ( ) 3140 92 0.02 ± 7.8x10-6 0.03 6.67± 0.43± 4.16± 0.71 ± 0.04 0.01 0.01 0.12 Cody-Lorentz parameters inf R A (eV) Eo (eV) (eV) Ep (eV) Eg (eV) 1.10± 71.33 ± 3.95 ± 2.72 ± 1.581± n-layer 1.00 0.1 185 65 0.13 1.32 0.16 0.18 0.190 1.05± 68.59 ± 3.88 ± 2.61 ± 1.629± i-layer 1.00 1 2982 28 0.09 1.08 0.17 0.43 0.083 1.21± 1.816± 117.69 3.69 2.65 2.17 150 506 54 0.11 0.132 p-layer 1.19± 1.820± 119.53 3.68 2.68 2.22 150 318 70 0.23 0.143

101 bulk layer thickness. These optical properties were described by a Cody-Lorentz oscillator function with all parameters coupled to the band gap Eg, through the relations given in Appendix section from Eqs. (A.24) (A.31) (Collins and Ferlauto, 2005a). Due to parameter coupling, the only free parameter is the p-layer band gap, which was found to be 1.82 eV for each of the two depositions.

Figure 3-9 (left) shows the evolution of the p-layer effective thickness, which consists of a sum of individual interface roughness, bulk, and surface roughness components, respectively, according to the equation deff = 0.5di + db + 0.5ds. Also shown in Figure 3-9 (left) is a prediction based on assumptions of (i) a time independent deposition rate starting from plasma ignition, and also (ii) a position independent rate along the center line in the first 13 cm of the deposition zone. Deviations from the prediction can be understood by considering the time evolution of the three effective thickness components also shown in Figure 3-9 (right).

Before p-layer deposition, a 28 Å thick microscopic roughness layer exists on the i-layer surface, as a 50%/50% mixture by volume of i-layer/void. The initial p-layer deposition is modeled by considering a transition from i/p interface filling to bulk p-layer growth, the later on top of the resulting i/p interface roughness layer (Koh et al., 1995).

At the onset of p-layer deposition, the void volume in the i-layer surface roughness is filled in by the p-layer material in a time of ~ 1 min. During this time, the surface roughness on the p-layer increases to ~ 28 Å, the same thickness as the i-layer surface roughness, indicating conformal coverage of the i-layer surface by the p-layer material. The surface roughness and bulk layer thickness evolution for the p-layer, as shown in the top two panels of Figure 3-9 (right), suggests that the p-layer grows initially

102 time (min)

Figure 3-9 (left) Evolution of the effective thickness as measured by SE during roll- to-roll deposition of a thin film Si:H p-layer at a web speed of v = 0.015 cm/s on an underlying a-Si:H i-layer; also shown is a prediction assuming a time and position independent deposition rate Ro within the plasma zone. The assumed rate of Ro = 0.51 Å/s is that associated with an amorphous phase as measured in the early stages of growth. (right) Evolution of (top) bulk layer thickness, (center) surface roughness layer thickness, and (bottom) interface filling percentage during roll-to- roll PECVD of the same thin film Si:H p-layer at v = 0.015 cm/s web speed on its underlying a-Si:H i-layer. In the bottom panel, a transition from i-layer surface roughness to i/p interface roughness occurs when the p-layer filling percentage reaches 50.

Si:H] transition at ~ 8 min, after ~ 155 Å of bulk p-layer deposition when the surface roughness abruptly increases. Thus, the acceleration of the p-layer effective layer thickness (left) can be attributed to a higher growth rate for the nc-Si:H phase relative to

103 the protocrystalline Si:H phase, (Stoke et al., 2008). This effect appears in the bulk layer thickness evolution in the top panel of Figure 3-9 (right), as well.

After the mixed-phase growth regime for the v = 0.015 cm/s deposition of Figure

3-9, the p-layer undergoes a (mixed-phase)-to-(single-phase) nc-Si:H transition at ~ 13 min. when the surface roughness reaches its maximum and begins to decrease. This transition occurs after ~ 320 Å bulk p-layer thickness. The decrease in surface roughness is attributed to the coalescence of inverted conical crystallites that protrude above the surface; the result is single-phase nc-Si:H (Stoke et al., 2008). The bulk layer thickness saturates at 17 min, at which time the web has fully crossed the deposition zone. For later times, all film characteristics should stabilize at the values obtained at 17 min; however, the continued decrease in surface roughness suggests a temporal non- uniformity such that crystallite nucleation and coalescence are favored with increasing time after plasma ignition.

The transitions from amorphous Si:H to mixed-phase (a+nc)-Si:H and then to single-phase nc-Si:H can be seen more clearly in the surface roughness evolution as a function of bulk p-layer thickness on a logarithmic scale, as shown in Figure 3-10. Here the top panel corresponds to the results for a p-layer web speed of 0.015 cm/s as in the center panel of Figure 3-9 (right), whereas the bottom panel depicts corresponding results for a web speed of 0.020 cm/s. From Figure 3-10 (bottom), it is clear that the p-layer deposited at 0.020 cm/s undergoes an amorphous-to-(mixed-phase) transition at ~ 130 Å bulk p-layer thickness, but there is no clear transition to single-phase nc-Si:H up to a bulk p-layer thickness of 380 Å. At 380 Å, the bulk p-layer thickness saturates, indicating that the leading end of the roll has been fully coated. This saturation thickness is greater than

104

Figure 3-10 Surface roughness evolution of the p-layers deposited at web speeds of 0.015 cm/s (top) and 0.020 cm/s (bottom) as measured by RTSE. The p- layer deposited at 0.015 cm/sec web speed shows an amorphous-to- (mixed-phase) transition at db ~ 155 Å where the surface roughness increases rapidly and a (mixed-phase)-to-(single-phase) nanocrystalline transition at db ~ 320 Å where the surface roughness reaches a maximum. The p-layer deposited at 0.020 cm/s exhibits only the amorphous-to-(mixed-phase) transition at db ~ 160 Å.

105 the single-phase transition thickness of 300 Å for the 0.015 cm/s deposition. This comparison suggests that, even though the deposition processes are identical with the exception of the web speed, the conditions across the deposition zone may vary from point to point. By performing similar depositions with a fixed substrate, regions where crystallite growth is preferred are more readily identified, which may then motivate modifications of the electrode design and gas flow pattern for uniformity of the near- surface nanocrystalline volume fraction.

The ex-situ mapping results are shown in Figure 3-11 for the p-layer deposited at

0.015 cm/s, which in fact generates the p-layer spatial phase diagram. These results were obtained by fitting the ex-situ mapping data with the bulk i-layer thickness, the bulk p- layer thickness and the p-layer surface roughness thickness as the free parameters. The same model used in real time SE analysis was also used for this mapping analysis. In

Figure 3-11, the surface roughness variation along the center line (top) is in good agreement with the time evolution from real time SE shown in Figure 3-9. This would be expected due to the relationship between the location relative to the edge of the deposition zone x and the elapsed time t, according to x = vt, where v is the web speed. Both real time SE and the mapping data sets show the initial growth of the a-Si:H

(or protocrystalline) phase as well as transitions to mixed-phase (a+nc)-Si:H and finally coalescence to single-phase nc-Si:H. On the map of Figure 3-11, the mixed-phase transition occurs when the surface roughness layer is ~30 Å. Above that transition, there is a continuous increase in the roughness layer thickness to ~100 Å, as also indicated by the real time SE result in the center panel of Figure 3-9 (right). Thus, the (amorphous phase)-to-(mixed-phase) transition line is drawn on the surface roughness thickness map

106 (a)

surface roughness thickness

(b) bulk layer thickness

Figure 3-11 Maps of the p-layer (a) surface roughness (top) and (b) p-layer bulk (bottom) thicknesses deposited on Cr/Ag/ZnO/n/i-layer coated PEN polymer at a web speed of v = 0.015 cm/s. The left side broken line indicates the locations at which the (amorphous-Si:H)-to-[mixed-phase (a+nc)-Si:H] transition occur at the top of the deposited p-layer. The right side broken line indicates the locations at which the (mixed-phase)-to- (single-phase) nc-Si:H transition occurs at the top of the p-layer.

107 of Figure 3-11 (top) where this abrupt increase is observed (left broken line). Along the center line, this transition occurs at a point of ~ - 5 cm. By superimposing this transition line onto the bulk layer thickness map, the amorphous-to-(mixed-phase) transition is observed to occur at bulk layer thicknesses ranging from 30 Å to 200 Å, depending on the location on the substrate. Similarly, the transition from the mixed-phase (a+nc)-Si:H to single-phase nc-Si:H occurs at the positions where the surface roughness thickness reaches a maximum in the top panel of Figure 3-11 (right broken line). Along the center line, this transition occurs at a point of ~ + 3 cm. By superimposing this transition line onto the bulk layer thickness map, the transition is observed to occur at bulk layer thicknesses over the range of 300 to 600 Å.

The thickness maps in Figure 3-11 enable one to evaluate the uniformity across the width of the flexible substrate. From the contours in the lower panel of Figure 3-11, it is clear that the bulk p-layer thickness is greater in the central region than at the edges.

The effect appears to be enhanced in the nc-Si:H growth regime, in part due to the higher growth rate of the nc-Si:H phase coupled with the apparent lower nanocrystal nucleation density near the substrate edges. A thicker layer at the center may also occur if the plastic is slightly warped such that the central portion of the substrate is closer to the cathode plate than the edges. A third possible reason may be that the plasma is more intense in the central region of the substrate than at the edges. At positions to the left of the transition to single-phase nc-Si:H in Figure 3-11 (top), the surface roughness layer tends to be larger near the center of the substrate; however, near and above this transition, the situation is reversed. The net effect of the observed behavior is that near the edge of the substrate, nucleation occurs at a lower thickness and the density of these nuclei

108 appears to be lower since the coalescence occurs at a somewhat greater bulk layer thickness.

The roughness evolution of the p-layer deposited at 0.020 cm/s web speed along the center line in Figure 3-12 (top) shows the amorphous-to-(mixed-phase) transition at ~

100 Å. Along the center line, this transition occurs at a position of ~ -5 cm. However, there is no clear (mixed-phase)-to-(single-phase) nc-Si:H transition along this line, in consistency with real time SE observations. Once again, the surface roughness evolution along the center line given by ex-situ mapping is in good agreement with real time SE results; however, the bulk p-layer saturation thickness from the RTSE is smaller than that of the ex-situ mapping ellipsometry.

In order to understand the uniformity in this case, the (amorphous-Si:H)-to-

[mixed-phase (a+nc)-Si:H] transition line is first drawn on the surface roughness map of

Figure 3-12 (top), where the abrupt increase in roughness thickness is observed. This same line is then superimposed onto the bulk p-layer thickness map of Figure 3-12

(bottom) so that the spatial dependence of the bulk p-layer thickness at the transition can be estimated. Figure 3-12 shows that crystallite nucleation leading to the (amorphous

Si:H)-to-[mixed-phase (a+nc)-Si:H] transition thickness occurs over a bulk p-layer thickness range from 70 to 140 Å. Lower transition thicknesses occur near the top edge of the substrate. As described earlier, the deposition clearly saturates at the top and center of the substrate before the p-layer undergoes the (mixed-phase)-to-(single-phase) nc-Si:H transition. The hint of such a transition may be observed in the lower right edge of the map where the bulk layer thickness is largest. Across the width, once again, the

109 (a)

surface roughness thickness

(b)

bulk layer thickness

Figure 3-12 Maps of the p-layer (a) surface roughness and (b) bulk thicknesses deposited on Cr/Ag/ZnO/n/i-layer coated PEN polymer at a web speed of v = 0.020 cm/s. The broken line indicates the locations at which the (amorphous-Si:H)-to-[mixed-phase (a+nc)-Si:H] transition occurs at the surface of the deposited p-layer.

110 bulk p-layer thickness within the central region is larger than that at the edges, indicating that the deposition rate peaks in the center and decreases towards the edges.

Since the web speed determines the time during which the substrate resides within the deposition zone, the desired final thickness can be obtained by choosing the web speed proportionately. By optimizing the deposition parameters, in particular the gas flows, their ratios, and patterns, and ensuring that the web is uniformly flat by maintaining constant tension across the width, a uniform p-layer can be obtained with the desired final thickness after saturation. A similar process can also be used for studies of the i-layer used in the thin film a-Si:H solar cells, evaluating and ultimately improving the uniformity of thickness, phase, and optical properties. Since this is an intermediate

PECVD step, however, an in-situ mapping tool would be most beneficial. Such an in-situ mapping instrument has been recently installed within one of the vacuum chambers of the multichamber cluster tool. It can be used in successive a-Si:H based depositions to obtain thickness maps and spatial phase diagrams of the multiple layer components of solar cells.

3.6 Summary

Real time spectroscopic ellipsometry (RTSE) has been applied successfully to study the evolution of the intrinsic absorber layer (i-layer) and the topmost p-layer, the most critical layers for optimization of the performance of thin film Si:H photovoltaic devices in the n-i-p substrate configuration. The thickness evolution of the phases of both i- and p-layer at different hydrogen dilution ratios, R = [H2]/[SiH4] is described by deposition phase diagrams. Phase transitions from amorphous to mixed-phase and from

111 mixed-phase to single-phase nc-Si:H are identified on these diagrams. From a plot of the surface roughness thickness ds versus the bulk layer thickness db, the amorphous-to-

(mixed-phase) transition is identified as the point at which ds starts to increase rapidly with db. The (mixed-phase)-to-(single-phase) nc-Si:H transition is identified as the point at which ds reaches a maximum and starts to decrease. Phase diagrams have been drawn to identify the amorphous, mixed-phase and single-phase nanocryatalline regions of both i- and p-layers as functions of the hydrogen dilution ratio and the bulk i- and p-layer thicknesses. This phase diagram allows one to choose the proper conditions for the most ordered protocrystalline i- and p- layers, which have been reported as the best such layers for the optimum stabilized thin film Si:H solar cell performance. In this research, at

200oC substrate temperature, 0.8 Torr pressure, and 0.033 W/cm2 rf plasma power, the hydrogen dilution ration R = 15 is the optimum for a protocrystalline i-layer at ~ 3000 Å bulk i-layer thickness. For the p-layer at ~ 120 Å thickness, ~ 100oC substrate temperature, 1.5 Torr deposition pressure, and 0.066 W/cm2 rf plasma power, the hydrogen dilution ration R = 125 yields the best protocrystalline p-layer. The correlations between the phase diagrams and the device performance for all these depositions will be shown later in Chapter 6.

In addition to i-layer and p-layer phase diagrams obtained for a rigid substrate at a single location, real time SE and ex-situ mapping SE have been applied successfully to study the evolution of the topmost thin film Si:H p-layers of substrate-type a-Si:H n-i-p solar cells in cassette roll-to-roll deposition. Two p-layers have been deposited at web speeds of 0.015 and 0.020 cm/s with all other process parameters unchanged. Both the real time SE and the ex-situ mapping SE results for the p-layer deposited at 0.015 cm/s

112 show clear transitions from amorphous (protocrystalline) Si:H to mixed-phase (a+nc)-

Si:H and then finally to single-phase nc-Si:H with increasing bulk p-layer thickness to

800 Å. A spatially-resolved deposition phase diagram that maps the amorphous Si:H, mixed-phase (a+nc)-Si:H, and single-phase nc-Si:H regions at the top surface of the film has been identified on the basis of the surface roughness evolution. The transition boundaries are superimposed onto the bulk p-layer thickness map in order to generate the spatially-resolved deposition phase diagrams. In contrast, the RTSE results for the p- layer deposited at 0.020 cm/s show only the transition from amorphous Si:H to mixed- phase (a+nc)-Si:H. In this case, the deposition saturates before reaching the nanocrystallite coalescence thickness. Thus, the spatial phase diagram for the 0.020 cm/s speed exhibits only an (amorphous Si:H)-to-[mixed-phase (a+nc)-Si:H] transition boundary. In general, such spatial phase diagrams can be developed under different deposition conditions to provide insights into p-layer process optimization that yields high performance for large area thin film Si:H solar modules. Similarly, optical monitoring can be performed for other layers of the thin film Si:H solar cells so that the uniformity of each component layer can be ensured with the goal being to reduce the difference between small area solar cell and large area module performance. An in-situ

SE mapping tool is under development to expedite mapping of successive component layers of a solar module structure without exposure to laboratory air between layers.

113

Chapter 4

Back-Reflectors in Thin Film Si:H Solar Cell

4.1 Introduction and Motivation

Thin film Si:H-based solar cell performance can be limited by many factors. One such factor is the optical loss that occurs within the back-reflector (BR) structure. The back-reflector is the rough thin-film-metal/transparent-conducting-oxide bi-layer at the back side of the solar cell. This bi-layer not only serves as one of the electrodes of the solar cell, but also reflects photons of the red and the near-infrared region back into the active layer of the thin film a-Si:H solar cell structure; hence the name "back-reflector".

Because the absorption onset of the absorber i-layer of a-Si:H is not very sharp relative to that of a direct band gap semiconductor, the penetration depth is high in that region relative to the i-layer ambipolar diffusion length. This can be observed from the optical properties of the a-Si:H layers presented in the previous chapter. Thus, in the absence of a back-reflector, the photons in the red and NIR regions traverse the i-layer all the way to the back contact for the electronically optimum i-layer thickness and may not contribute to the current in the first pass. In the presence of an effective back-reflector, however, a large fraction of these photons can be reflected back into the absorber layer, in this case the a-Si:H solar cell i-layer, and hence the optical path length for possible

114 absorption of the photons is increased at least by a factor of two. In this way, the probability of absorption of optical photons in the active i-layer in the absorption onset region is increased, thereby producing a larger concentration of electron-hole pairs to enhance the short circuit current (Jsc) of the thin film a-Si:H solar cell. The back-reflector becomes more effective if the metal layer is rough (assuming no losses due to the introduction of the roughness) so that the photons are scattered into oblique angles, i.e. through diffuse reflection, or scattering. It has been shown that the short circuit current,

Jsc, can increase by up to 30% with a Ag/ZnO back reflector in the a-Si1-xGex:H solar cell on a flexible stainless steel substrate (Yang et al., 2003).

The most common back reflector (BR) for thin film Si:H solar cells in the substrate/BR/n/i/p configuration consists of opaque Ag or Al, followed by a ~ 3000 Å thick layer of ZnO, both films sputtered onto the substrate. The ZnO layer is used as a diffusion barrier layer to block metal diffusion into the active Si:H layers. Other reasons for using ZnO have become clear through this research.

In this chapter, a comparative study of the optical properties of Ag/ZnO and

Al/ZnO interfaces is reported using real time spectroscopic ellipsometry (RTSE). As a component of this study, the dielectric functions of the metal and ZnO thin films are presented. In addition, the RTSE deduced surface roughness on the metal films is correlated with the directly measured rms roughness from AFM for both the Ag and Al components of the back reflectors. The primary focus of this research, however, is to describe the plasmonic behavior of the Ag/ZnO interface (Dahal et al., 2008, Dahal et al.,

2011), compare it with the Al/ZnO interface optical properties -- in terms of plasmonic absorption (Dahal et al., 2009) in the spectral region of the back-reflector operation, and

115 then determine if Al/ZnO can be used as a back-reflector in a-Si:H based solar cells as effectively as the Ag/ZnO back-reflector has been used.

A detailed study of Ag/ZnO back-reflector work will be presented by Sainju in a

Ph.D. Thesis (Sainju, 2013). In fact, the effectiveness of each of the Ag/ZnO and Al/ZnO back-reflectors is studied here on the basis of the total reflectance (specular + scattering) from each of the back-reflectors at normal incidence. The normal incidence specular reflectance Re,sp is measured using a commercial reflectance spectrophotometer and the scattering or the diffuse reflectance Re,sc is measured using the same instrument, but with an integrating sphere option. Thus the measured total reflectance including both specular and scattered components can be given as Re,tot = Re,sp + Re,sc. The measured absorption

Ae = 1 – Re,tot is based on the assumption that all light emitted from the film is collected and no light is transmitted through the stack. Also from spectroscopic ellipsometry modeling, the normal incidence specular reflectance Rth from each stack is calculated and compared with the measured normal incidence specular reflectance as well as the total reflectance.

The difference Rsp = Rth  Re,sp can have different components arising from non- specular reflection and emission, which is lost from the specular experiment. This includes positive terms of direct scattering from the surface, surface plasmon coupling followed by dissipation or non-specular emission, and waveguiding in the films that yields emission from the film edges or outside the collection cone. A negative term can result from localized plasmon re-emission in the specular direction. By forming the difference Rtot = Rth – Re,tot, positive components to Rtot now include surface plasmon coupling or waveguiding that leads to dissipation not accounted for in the Fresnel’s

116 Equations. Localized plasmon re-emission, both specular and diffuse, generates a negative term in this Rtot.

Finally, the calculated absorbance Ath assuming no transmission through the back- reflector is given by Ath = 1  Rth with Rth being the predicted normal incidence specular reflectance from spectroscopic ellipsometry. Ath is determined and then is compared with the experimental absorbance Ae for different roughness thicknesses of the metal layers.

In this way, the plasmonic re-radiation of any absorbed photon flux in the form of scattering is determined. In particular, the absorbance difference A = Ath – Ae reveals positive terms due to surface plasmon coupling and dissipation since this effect is not included in the ellipsometric theory. A reveals negative terms due to localized or particle plasmon re-radiation since this effect would be observed in Ae but not modeled in

Ath. The relationships among the measured and the calculated parameters in this chapter are given in Table 4.1.

4.2 Deposition Processes for the Ag/ZnO and Al/ZnO Back Reflectors

The Ag films were deposited by magnetron sputtering onto c-Si wafer substrates covered with native or thermal oxides (dox ~ 15 120 Å). Ultra-smooth Ag deposition is achievable on atomically smooth c-Si/SiO2 substrates under specific conditions. The smoothest Ag film exhibits a microscopic roughness thickness ds = 4 Å, as deduced by

RTSE. Such a film is obtained at room temperature using a low Ar gas pressure of ~ 4 mTorr, an Ar gas flow of 10 sccm, and an intermediate target power level of 50 W.

Increasing the substrate temperature step-wise to a nominal value of ~ 190C, results in a larger microscopic surface roughness thickness of ds = 105 Å. In Chapter 2, the dielectric

117 Table 4.1 List of measured and deduced quantities and their comparisons useful in studies of the plasmonic behavior in Ag/ZnO and Al/ZnO back-reflectors.

Measured Quantities Deduced Quantities Comparisons: Differences

Symbol Definition Symbol Definition Deficits Contributions

Re,sp  Normal Reflectance + Direct scattering incidence deficit, specular: from surface specular + Surface plasmon reflectance Re,tot  Total Rsp =Rth  Re,sp coupling leading to from spectro- = Re,sp+ Re,sc normal dissipation or non- photometer incidence specular emission reflectance + Waveguiding losses – Particle plasmon emission in specular direction

Re,sc  Scattered Ae = 1  Re,tot  Absorbance Reflectance + Surface plasmon reflectance loss deficit, total: coupling leading to from dissipation integrating Rtot =Rth  Re,tot + Waveguiding losses sphere – Particle plasmon component of emission (total) spectrophotometer

(t) e ,  Ellipsometry (1s, 2s),  substrate Absorbance – Surface plasmon (t) angles from and ambient deficit, total: coupling e ) in-situ and (1a, 2a), dielectric  Waveguiding losses real time functions A =Ath – Ae + Particle plasmon spectroscopic (1j, 2j);  layer = Rtot emission (total) ellipsometry j = 1,…, M dielectric functions dj ; j =1,…,M  layer thicknesses  theoretical Rth specular reflectance Ath = 1  Rth and absorbance at normal incidence

118 functions of three different Ag layers having different surface roughness levels have been presented, with the surface roughness being modeled using the Bruggeman effective medium approximation assuming 50 vol. % underlying bulk material and 50 vol. % void.

ZnO is deposited at room temperature on these Ag surfaces having 4 ≤ ds ≤ 105 Å using same sputtering conditions as for the Ag.

Additional Ag dielectric functions for comparison with the present study will be given by Sainju in a Ph.D. Thesis (Sainju, 2013). These latter dielectric functions were obtained for thin films having a range of roughness levels obtained at different substrate temperatures under otherwise identical deposition conditions.

In studies of the Al/ZnO back-reflectors in this Thesis research, the approach was similar to that of the Ag/ZnO back-reflector studies. As in the Ag/ZnO studies, the Al films were deposited on thermal oxide coated crystalline silicon substrates by magnetron sputtering at various temperatures to obtain different levels of roughness on the Al surface. The smoothest Al films obtained in in this deposition process exhibit a final microscopic roughness thickness of ds = 15 Å, as deduced by RTSE. Such films were obtained at room temperatures using a low Ar sputtering gas pressure of ~ 4 mTorr, an Ar gas flow of 10 sccm, and a target power of 50 W. By increasing the substrate temperature to 85C, the final microscopic surface roughness thickness on Al is observed to increase to ds = 122 Å.

Figure 4-1 shows the dielectric function of the smoothest Al film obtained by multi-time analysis at ~ 200 Å bulk layer thickness along with the best fit to this dielectric function using an analytical model consisting of a Drude free electron component and a Lorentz oscillator component. The Drude free electron and Lorentz

119

Figure 4-1 Dielectric functions of the smoothest Al film (ds = 15 Å) deposited on a thermal oxide covered c-Si substrate. The open circles are the inverted results from multi-time analysis at ~ 200 Å bulk Al layer thickness whereas the solid line is the fit of the dielectric function using a Drude free electron component and a Lorentz oscillator component.

120 oscillator parameters used to represent the dielectric functions of all the other Al films of this study are collected in Table 4.2. ZnO was deposited on the Al surfaces at room temperature without a vacuum break using the same conditions as for the Al layer prepared under the smoothest surface conditions. The dielectric functions of the ZnO layers used in Ag/ZnO and Al/ZnO analysis are given in Figure 4-2.

Real time spectroscopic ellipsometry (RTSE) was performed using a rotating- compensator multichannel instrument that can provide spectra in (, Δ) with a minimum acquisition time of 32 ms, as an average over a single pair of optical cycles. The instruments used for RTSE are multichannel ellipsometers with spectral ranges of 0.75

6.5 eV and 0.75  5.0 eV (models M2000DI and M2000XI, respectively, from J.A.

Woollam Company). The ellipsometer and a schematic of the interior of the sputtering chamber for the Ag, Al, and ZnO depositions are as shown in Figure 2-7 of Chapter 2.

Pairs of (, Δ) spectra were collected within a time of ~ 1 s, as averages over ~ 30 optical cycle pairs, in order to improve the precision of the ellipsometry data. During this acquisition time for one set of (, Δ) spectra, a bulk layer thickness of ~ 6 Å accumulates at the maximum deposition rate of 6 Å/s used here. The angle of incidence was 65.0 ±

0.3, where 0.3o indicates the range for all depositions. Analyses of all spectra involve numerical inversion and least-square regression algorithms.

In addition to real time spectroscopic ellipsometry (RTSE), ex-situ normal incidence specular reflectance and non-specular reflectance (or diffuse scattering) spectroscopies have been applied to quantify the specular and the diffuse reflections from

Ag/ZnO and Al/ZnO back-reflector (BR) structures used in thin film Si:H photovoltaics.

Figure 4-3 shows the schematics of the instruments used for the normal incidence

121 Table 4.2 Oscillator parameters that represent the Al dielectric functions for thin films deposited at various substrate temperatures on thermal oxide coated c-Si substrates. The intended Al bulk layer thickness in each case was 1000 Å. In this analysis, the surface roughness is modeled using the Bruggeman effective medium approximation as a 50-50 vol.% mixture of underlying bulk material and void.

Surface Substrate Drude parameters Lorentz parameters  roughness temp. inf  (-cm)  (fs) A (eV)  (eV) Eo (eV) thickness (oC) ds (Å) 1.215± 9.011x10-6 3.586± 28.205± 0.726± 1.661± 20 (RT) 15 0.137 ± 5.8x 10-8 0.022 0.177 0.009 0.003 1.774± 2.071x10-5 2.055± 14.874± 1.265± 2.055± 35 33 0.071 ± 7.6 x 10-8 0.008 0.081 0.013 0.008 2.054± 5.822x10-6 4.998± 22.136± 0.684± 1.666± 42 54 0.137 ± 4.1 x 10-8 0.323 0.176 0.011 0.003 1.386± 8.445x10-6 2.962± 27.425± 0.993± 1.722± 48 65 0.146 ± 4.1 x 10-8 0.014 0.168 0.012 0.004 2.743± 9.388x10-6 4.514± 19.257± 0.851± 1.660± 54 42 0.144 ±1.04x 10-7 0.047 0.176 0.015 0.004 3.511± 9.531x10-6 4.045± 16.439± 0.869± 1.699± 65 98 0.141 ± 8.5 x 10-8 0.034 0.174 0.082 0.005 1.599± 6.525x10-6 2.829± 38.249± 1.028± 1.715± 72 122 0.238 ± 3.9 x 10-8 0.016 0.281 0.015 0.004

specular reflectance measurement (top) and the non-specular reflectance, or diffuse scattering, measurement (bottom). Two different spectrophotometers have been used for the reflectance measurement, one for the Ag/ZnO back-reflectors, and the other for the

Al/ZnO back-reflectors. The Al/ZnO back-reflectors were measured later in this Thesis research when a new spectrophotometer becamse available. Both instruments use similar configurations as shown but provide different spectral ranges. The spectrophotometer used for the Ag/ZnO specular/scattering measurement provided a spectral range of 1.40 -

4.25 eV (Shimadzu, model UV-2450), whereas the other used for Al/ZnO back-reflectors provided a wider spectral range of 0.6 - 5.2 eV (Perkin-Elmer, model Lambda-1050). For

122

Figure 4-2 Real (top) and imaginary (bottom) parts of the dielectric functions of ZnO used in the Ag/ZnO and Al/ZnO RTSE data analyses. Each complex dielectric function was deduced as an analytical expression by fitting inverted results obtained by RTSE during ZnO deposition on c-Si substrates. The analytical expression includes two critical point oscillators that describe transitions between parabolic bands.

123

Figure 4-3 Schematic of the specular reflectance measurement (top) and the diffuse reflectance, or scattering, measurement (bottom) used together to quantify the total reflectance from Ag/ZnO and Al/ZnO back-reflectors. In the diffuse reflectance measurement, an optical port is removed so that the specular beam entering the integrating sphere at an ~ 8o angle of incidence, can leave the sphere without being collected.

124 studies of Ag/ZnO back-reflectors by spectrophotometry, a single crystal silicon wafer and a substrate coated with BaSO4 powder served as the references for the normal incidence specular reflectance and the scattering measurements, respectively. For corresponding studies of Al/ZnO back-reflectors, an Al coated glass mirror and a substrate coated with Teflon powder were used as the specular reflectance and scattering references. The spectral resolution of the measurement in terms of wavelength for the spectrophotometers used in Ag/ZnO and Al/ZnO studies were 1 nm and 2 nm, respectively, with a 0.2 s acquisition time at each wavelength for the two instruments.

4.3 Comparative Study of Al/ZnO and Ag/ZnO Interfaces

A widely-used back-reflector (BR) for thin film Si:H solar cells in the substrate/BR/n/i/p configuration, as well as for tandem or triple junction solar cells, consists of opaque Ag followed by a ~3000 Å thick layer of ZnO, both sputtered onto a low-cost substrate such as stainless steel (Deng et al., 2003). The Ag/ZnO interface is designed to be macroscopically rough so that the light rays are non-specularly scattered upon back-reflection and as a result exhibit increased optical path lengths relative to the case of normal-incidence specular reflection. The Ag/ZnO interfaces are characterized using RTSE for starting Ag surfaces of different roughness thicknesses. When ZnO is deposited on top of the Ag layer, an interface layer is formed between the underlying Ag and the overlying ZnO bulk layer. RTSE analysis shows that the dielectric function  =

1 + i2 of the Ag/ZnO interface exhibits a clear localized or particle plasmon absorption feature that shifts to lower energy – toward the near-infrared – with increasing surface roughness on the starting Ag film.

125 The details of the RTSE results for Ag/ZnO back-reflectors prepared with different Ag roughness levels will be presented by Sainju in a Ph.D. Thesis (Sainju,

2013). The evolution of each ZnO film, in this case, was modeled using a layer with the optical properties of bulk ZnO and a Ag/ZnO interface layer with optical properties determined by inversion without assuming a specific analytical form. In fact, inclusion of such a layer has been shown to significantly improve the quality of the fit to the RTSE data (Sainju et al., 2006). Also, during ZnO growth, the interface layer thickness di has been shown to increase approximately linearly with time until it reaches a saturation thickness. The interface thickness of the final structure is obtained by averaging di from the saturation point until the end of the deposition.

Improvements can be made to the work of Sainju (2013). The starting condition of the Ag surface consists of a roughness layer of thickness ds whose dielectric functions can be described as a 50 vol.%  50 vol.% mixture of Ag  void, using an effective medium theory. Because the Ag/ZnO interface layer thickness di is larger than the roughness thickness ds on the Ag, then an interface filling process can be developed whereby the 50 vol.%  50 vol.% Ag  void, as an effective medium composite, decreases to 0 vol.% while the interface component, with its dielectric function, determined from a single time analysis as soon as the interface is completely filled, increases to 100 vol.%.

The current work focuses on a study of the Al/ZnO back reflector for comparison with previous studies of the Ag/ZnO back reflector. By varying the substrate temperature for Al sputter deposition over the range 20 < T < 85oC, Al films ~ 2000 Å thick with final microscopic surface roughness thicknesses over the range 15 < ds < 122 Å were

126 obtained. The RTSE data for ZnO growth on these Al surfaces were analyzed in a similar manner as those obtained previously for ZnO growth on Ag surfaces. A two- layer model of Al/ZnO was used consisting of an opaque semi-infinite Al layer with optical properties determined before ZnO deposition and an interface layer of thickness di with optical properties determined in the RTSE analysis. This model for the Al substrate and its interface is based on the assumption that the Al surface roughness is subsumed into the interface layer. The reason for this will become clear when the results are discussed. On top of the interface layer, a ZnO layer of thickness db is used with optical properties determined in studies of growth under the same conditions on a smooth c-Si surface.

Figure 4-4 shows such an example with an Al layer having a 15 Å RTSE-deduced surface roughness and with an interface layer thickness di of 35 Å. This value of 35 Å is an average of di from the time at which saturation occurs until the end of the deposition.

The figure clearly shows an improvement in the fit quality as indicated by the decrease in mean square error with the incorporation of an interface layer between the Al and ZnO layers. These results reveal the same overall behavior as is observed in the case of ZnO growth on Ag and consequent Ag/ZnO interface formation (Sainju, 2013). Once again, as in the case of the Ag/ZnO interface layer, the Al/ZnO interface layer dielectric function is obtained by mathematical inversion without assuming any analytical form.

As another example, Figure 4-5 shows the real and imaginary parts of the dielectric function for an Al/ZnO interface layer that is thicker than the layer of Figure

4-4. This interface layer, 83 Å thick, is obtained for an Al film with a final surface roughness layer thickness 33 Å. When the interface layer is thicker, confidence in the

127

Figure 4-4 RTSE analysis of Al/ZnO interface layer formation during deposition of a ZnO layer on an Al film with starting 15 Å thick surface roughness layer. Shown here (from top to bottom) are the roughness layer thickness on the ZnO surface, the ZnO bulk layer thickness, the Al/ZnO interface thickness, and the mean square error. The interface layer thickness saturates after the bulk layer reaches 600 Å. In fact, the incorporation of the interface layer significantly improves the fit quality, as well as the linearity in the bulk layer thickness.

128

Figure 4-5 Real (upper) and imaginary (lower) parts of the dielectric function of the Al/ZnO interface layer for a structure with a starting Al surface roughness thickness of ds = 33 Å before ZnO deposition, and a final interface thickness of 83 Å after ZnO deposition (circles). These results were obtained by inversion of RTSE spectra at a ZnO bulk layer thickness of 300 Å and a ZnO surface roughness thickness of 56 Å. A fit to the inverted spectra using a Kramers-Kronig consistent model is also shown (lines).

129 inverted dielectric function is greater. For comparison, corresponding results from a previous study (Sainju, 2013) are given in Figure 4-6 -- in this case for a 78 Å thick

Ag/ZnO interface layer obtained for ZnO growth on a Ag film with a final surface roughness layer thickness of 28 Å. In both cases, the interface layer optical properties obtained from numerical inversion (circles) are fitted by using Kramers-Kronig consistent models (lines).

For Ag/ZnO, the interface layer model includes (i) a free electron component modeled using the Drude expression, (ii) a plasmon band at 2.75 eV with a width of ~ 1 eV modeled using a Lorentz oscillator, and (iii) a bound electron critical point feature to the interband transitions for both Ag and ZnO above 3.5 eV, modeled assuming transitions between parabolic bands near a single band gap critical point, (Collins and

Ferlauto, 2005). The rapid decrease in 1 to negative values as the energy decreases in

Figures 4-5 and 4-6 is indicative of a Drude component. The absorption bands with positive values of 2 and a derivative structure in 1 are indicative of an oscillator, and a step in 2 and a peak in 1 is indicative of a band gap critical point. In Al/ZnO the plasmon peak is better represented by a more general oscillator, a critical point oscillator at ~ 3.3 eV with an adjustable phase and exponent that can describe the asymmetric line shape, (Collins and Ferlauto, 2005). Also an additional weak Lorentz oscillator must be incorporated into the Al/ZnO interface dielectric function. This oscillator represents the parallel band transition in Al peaked near 2|U200| = 1.5 eV, (Nguyen et al., 1993), which is the strongest Al interband absorption in bulk Al film, (Nguyen and Collins, 1993).

Here, |U200| is the Fourier coefficient of the crystal potential for the reciprocal lattice vector perpendicular to the (200) planes in the Brillouin zone.

130

Figure 4-6 Real (upper) and imaginary (lower) parts of the dielectric function of the Ag/ZnO interface layer for a starting structure with an Ag surface roughness thickness of ds = 28 Å, and a final interface thickness of 78 Å (circles). These results were obtained by inversion of RTSE spectra at a ZnO bulk layer thickness of 300 Å, without taking into account the ZnO surface roughness thickness. A fit to the inverted data using a Kramers- Kronig consistent model is also shown (lines) (Sainju, 2013).

131 The bulk free electron plasmon energy of Al is larger than Ag (12.5 eV versus 8.8 eV), which gives rise to higher energy localized and propagating plasmon modes and hence the plasmon band in Al/ZnO is expected to be centered at a shorter wavelength or higher energy than that in Ag/ZnO. Thus, for isolated protrusions with weak dipole- dipole interactions, the localized plasmon in Al/ZnO may actually overlap with the interband transitions in the overlying ZnO, whose onset is ~ 3.4 eV.

In order to understand the plasmon band in the Al/ZnO and Ag/ZnO interface

1/2 layers, the simple expression Eo ~ Ep{∞+ [(2+Q)/(1Q)]a} for the confined plasmon resonance is applied, where ∞ is the wavelength-independent dielectric constant contribution to 1, Ep is the bulk plasmon energy, a is the real part of the dielectric function of the ambient ZnO at the plasmon energy (a ~ 3.6) and Q is the volume fraction of metal protrusions in the surface layer (Collins and Ferlauto, 2005). In the limit of a very small fraction of metal protrusions on the surface layer (Q~0), one obtains

E0 = 4.31 eV for the Al/ZnO localized plasmon modes, applying the value of ∞ = 1.2, obtained from a fit of the Al dielectric functions over the range of 0.75 5.0 eV. For the

Ag/ZnO localized plasmon modes, one obtains either 2.98 eV or 2.63 eV depending on whether the value of ∞ from this work of 1.5 is used or the value of ∞ of 4.0 from the literature is used. The former value is derived from a fit of the Ag dielectric function over the full spectral range of 0.75 5.0 eV, whereas the literature value is believed to result from a fit over a narrower spectral range. The observed value for Ag/ZnO of 2.75 eV in Figure 4-6 is near the prediction consistent with a small fraction of Ag, whereas the observed value for Al/ZnO (Figure 4-5) is much lower than the prediction, in fact lower by ~ 1.2 eV. The discrepancy for the Al/ZnO structure may arise since the predicted

132 energy lies within the interband region of the ZnO ambient. As a result only lower energy modes are allowable, i.e., below the band gap of the ZnO where there is weak absorption. In the case of larger metal protrusions (Q > 0), the plasmon energies of both interface layers, Al/ZnO and Ag/ZnO, are predicted to be red-shifted from the Q = 0 values of 4.31 eV and 2.98 eV, respectively, selecting the higher energy result for

Ag/ZnO as being most accurate.

For the results in Figures 4-5 and 4-6, the dielectric functions of Al/ZnO and

Ag/ZnO interface layers are compared for a starting surface roughness layer thickness on the metal surface in the range ds ~ 28  33 Å before ZnO deposition. It is of interest to vary the roughness on the Al -- in particular to increase it -- and determine how the interface optical properties change, as has been done previously in the case of the

Ag/ZnO interfaces, (Sainju, 2013). Before doing so, however, it is important to gain greater confidence in the ability of RTSE to measure accurately the surface roughness layer thickness ds on the surface of a metal film.

Thus, in Figure 4-7, the roughness layer thicknesses on both Al and Ag films, as determined by RTSE at the end of the metal deposition, have been correlated with the root mean square (rms) roughness measured by AFM. These results were obtained using

5 m x 5 m scanning area for the AFM measurement. From the figure for Ag films, the near unity slope and small intercept indicate that RTSE is measuring a roughness value very close to the AFM rms value. In contrast for Al, the > 1 slope indicates that RTSE returns a value of roughness somewhat larger than rms, and the negative intercept indicates that AFM detects a component of roughness that RTSE does not -- possibly roughness of large in-plane scale. Most importantly, the relationships in Figure 4-7 are

133

Figure 4-7 Correlation of surface roughness thickness from real time spectroscopic ellipsometry (RTSE) with rms roughness from 5 m x 5 m atomic force microscopy (AFM) images Results are shown for Al (top) and Ag (bottom) films. For the RTSE results, a model for the surface roughness layer using a 50-50 volume percent mixture of metal-void is applied. The Bruggeman effective medium approximation is used to calculate the dielectric function of the roughness layer.

134 precisely linear so that confidence in RTSE as a probe of surface roughness on metal films on a relative scale is clearly demonstrated.

With the ability to determine and control the roughness thickness on Al, Figure 4-

8 shows that the thickness di of the Al/ZnO interface layer increases monotonically with the final roughness on the uncoated Al film; however, the slope is almost a factor of two.

This indicates that the influence of the plasmonic characteristics of the interface extends beyond the roughness region into the ZnO. This is understandable since the nature of the dielectric function of the Al/ZnO interface depends on the ability of the overlying ZnO to screen the plasmon oscillations.

A very similar trend has been observed for Ag/ZnO interface formation as shown in Figure 4-9, and this supports the role of screening by ZnO as a general interpretation.

Moreover, the larger interface layer thickness compared to the corresponding metal surface roughness thicknesses may be attributed in part to the additional damage caused by the ZnO species during ZnO layer deposition so that the metal roughness itself is increased after ZnO deposition. This may explain the 18 Å intercepts in both Figures 4-8 and 4-9. This is the interface thickness that would be generated for an atomically smooth metal surface. Such an interface may result from bombardment damage of the metal by depositing ZnO species that leads to an intermixed component layer of the interface.

This interface component may be a significant fraction of the interface layer for the smoothest metal films, but becomes less important as the metal roughness thickness increases. This interface mixing effect, however, can be evaluated after deposition of the metal/ZnO structure by chemically etching away the ZnO layer in an ex-situ experiment and measuring the surface characteristics of the individual metal layers through ex-situ

135

Figure 4-8 (top) Resonance energy (E0) of the plasmon band at the Al/ZnO interface obtained by fitting this band to a generalized oscillator; (bottom) Al/ZnO interface layer thickness (di) obtained as an average versus time during ZnO deposition on Al (after the saturation thickness). The results in both panels are plotted as functions of the Al surface roughness thickness (ds) measured at the end of each Al deposition.

136

Figure 4-9 (top) Resonance energy (E0) of the plasmon band at the Ag/ZnO interface obtained by fitting this plasmon band to a Lorentz oscillator; (bottom) Ag/ZnO interface layer thickness (di) obtained as an average versus time during ZnO deposition (after the saturation thickness). The results in both panels are plotted as functions of the Ag surface roughness thickness (ds) measured at the end of Ag deposition.

137 spectroscopic ellipsometry (SE) again. Such a study has been described elsewhere

(Sainju, 2013).

Returning to the results for the Al/ZnO interface in Figure 4-8, the peak energy of the localized plasmon band as observed in the interface dielectric function appears to increase weakly by ~ 0.1 eV as the roughness on the Al surface increases from 15 Å to

122 Å. This behavior is in contrast to the Ag/ZnO interfaces shown in Figure 4-9, in which case the localized plasmon band energy decreases by ~0.5 eV over the same range of metal roughness thickness. In the case of Ag/ZnO interface, the effect can be understood in terms of dipole-dipole interactions among resonances in nearby protrusions. It is expected that the density of plasmon sustaining protrusions increases as the surface roughness thickness increases. The effect can be quantified though the

1/2 simplified expression E0 ~ Ep {∞ + [(2+Q)/(1Q)]a} presented previously, where Q is the volume fraction of metal protrusions in the surface layer. For Ag, E0 decreases from 2.98 to 2.45 eV when Q increases from 0 to ~ 0.25 0.30.

In view of this explanation, the different behavior for the plasmon feature of the

Al/ZnO interface as the Al roughness increases may be attributed to the previously emphasized fact that the Q = 0 prediction for E0 lies at the same energy as the interband transitions, and in such circumstances, the plasmon cannot be sustained. The slight shift to higher energy may be attributed to the fact that sustainable plasmon modes can only occur where there is weak absorption in the ZnO, and the ZnO absorption onset may shift to higher energies due to the Moss-Burstein effect. If so, the effect implies a trend toward increasing Fermi level position with increasing interface thickness for the ZnO near the interface.

138 4.4 Scattering Behavior of Ag/ZnO Back Reflector

Scattering or non-specular reflectance plays a significant role in the operation of the back-reflector. Since the angle of reflection is not necessarily equal to the angle of incidence in the scattering process, the scattered light is characterized by a propagation vector that can take any direction on the reflection hemisphere of 2 steradians. Such light scattering can be measured collectively with the help of an integrating sphere. The integrating sphere is an optical component consisting of a hollow cavity with its interior

® coated with BaSO4 or Teflon designed for highly diffuse reflectivity. Thus, the interior of the sphere is fabricated to behave as a Lambertian surface, and hence the light falling on it is scattered such that the apparent brightness of the surface to an observer is the same regardless of the observer’s viewing angle. Simply stated, the surface luminance is isotropic.

The primary goal of the Ag/ZnO interface studies for different Ag roughness layer thicknesses and in-plane scales, as explained in the previous section, is to evaluate the specular reflectance, dissipative losses, direct scattering and re-emission by plasmons, the latter two integrated over the hemisphere. The roughness scales of interest range from the microscopic roughness regime (in which case the scales of the roughness are much smaller than the wavelength) into the macroscopic regime (in which case the scales of the roughness approach within an order of the wavelength). Such studies may reveal direct processes (i.e. no interaction with plasmons), including (1) specular reflection, (2) non- specular scattering, and (3) absorption as indicated in Figure 4-10. In addition, such studies may enable separation of two different plasmonic coupling mechanisms at the

Ag/ZnO interface. (4) Localized or confined electron resonances in Ag protrusions may

139

Figure 4-10 Optical processes at the Ag/ZnO interface including (1) specular reflectance, (2) direct scattering, (3) dissipation by interband and intraband electron excitations, (4) confined plasmon excitation followed by either (5) dissipation or (6) re-emission, (7) surface plasmon excitation, followed by either (8) dissipation or (9) re-emission.

appear in the interface layer dielectric function, and the resulting excitations may (5) dissipate or (6) re-radiate. (7) Propagating surface plasmons can only be observed in the deficit between the RTSE-predicted and ex-situ measured reflectances and these may also

(8) dissipate and (9) re-radiate as shown in Fig. 4-10. As a summary of Fig. 4-10, the direct processes are labeled (1) – (3) and the plasmon mediated processes are labeled (4)

– (9). Thus, both plasmon excitation processes may serve as coupling mechanism that can promote re-radiation, i.e., scattering, or result in dissipation. Quantitative comparisons among the three contributions to the non-specular scattering shown in Fig.

4-10 [(2), (6), and (9)] are of interest. Moreover, for the studies of optimized back- reflector structures, the contribution from the localized plasmon mode is of critical importance as a large fraction of the light coupled into plasmon modes can be re-radiated as scattered light, and the actual losses as dissipation to heat may not be as large as the

140 interface dielectric function would indicate. In fact, the interface structure of the BR may be tunable in such a way that the actual loss in terms of dissipation can be minimized over the desired spectral range. Considering that plasmons provide a means for absorption followed by re-radiation or dissipation, it is important to identify the factors that control the branching and the resulting contributions. These factors include the grain structure and morphology of the interface Ag; the nature of the plasmon resonances, their dipolar interactions, and damping of plasmons; as well as the optical properties, including absorptive and screening effects of the interface and overlying ZnO.

The scattering from different c-Si covered Ag/ZnO back-reflector structures having different Ag/ZnO interface roughness thicknesses including one highly textured back-reflector i.e. having macroscopic roughness, was measured using the integrating sphere apparatus setup as shown in Figure 4-3. Since the light rays are incident on the sample normally, all specularly reflected rays leave the sphere through the entrance aperture and so only the scattered light rays are collected using this apparatus. The measured scattering spectra Re,sc for different interface roughness thicknesses of the

Ag/ZnO back-reflector have been compared with the (i) specular reflectance deficit Rsp

= Rth – Re,sp, which is the difference between the calculated and measured specular reflectance, and (ii) the calculated absorbance Ath = 1 – Rth, both obtained for normal incidence. Table 4.1 provides a summary of the measured optical quantities, the calculated quantities, and the differences of interest between the measured and the calculated quantities. As described earlier, the calculated specular reflectance, Rth is obtained on the basis of an optical model that represents the back-reflector stack and best fits the ellipsometric spectra, whereas the calculated normal incidence absorbance is for

141 the final film stack given simply by Ath = 1 – Rth, when no transmission occurs through the stack. The correlations with experimental scattering spectra are a challenge to interpret, however, since the calculated reflectance and absorbance Rth and Ath are indirectly determined quantities based on an analysis of RTSE data collected at the end of the deposition, and furthermore the measured reflectance Re,sp is difficult to obtain with high accuracy. As a result, the uncertainties associated with these correlations are high.

In the top panels of Figures 4-11, 4-12, and 4-13, the spectra in the measured scattering integrated over all solid angles Re,sc is compared with spectra in the difference between the predicted and measured normal incidence specular reflectance Rsp = Rth –

Re,sp for Ag/ZnO interface thicknesses of 18 Å (smoothest specular), 78 Å (rough specular), and 250 Å (fully textured), respectively. Because this RTSE measurement and analysis is essentially blind to macroscopic roughness, the predicted reflectance includes only the specular component derived according to the Fresnel equations. As a result, the reflectance deficit exhibits positive contributions due to optical mechanisms such as direct scattering by macroscopic roughness, or the coupling of the incident light to surface plasmons -- another effect made possible by the macroscopic roughness. A third possible positive contribution is due to waveguiding losses which result when scattered waves propagate within the plane of the film and exit from its sides. Such light is not collected and leads to reduction in Re,sp. Finally, if plasmons confined to surface protrusions absorb light, but then emit in the specular direction, this would enhance Re,sp, generating a negative contribution to Rsp. These possible mechanisms, four in all, that account for the difference between Rth and Re,sp are summarized in Table 4.1. In the lower panels of the Figures 4-11, 4-12, and 4-13, the integrated scattering Re,sc is

142

Figure 4-11 (top) Comparison of the difference between the predicted and measured specular reflectance Rsp = Rth – Re,sp with the measured scattering Re,sc, all three spectra at normal incidence, for a Ag/ZnO back-reflector with a starting Ag roughness layer thickness of 4 Å and a final Ag/ZnO interface layer thickness of 18 Å; (bottom) comparison between the predicted absorbance Ath = 1 – Rth and the measured scattering Re,sc.

143

Figure 4-12 (top) Comparison between the specular reflectance deficit Rsp = Rth – Re,sp and the measured scattering Re,sc, all spectra at normal incidence, for a Ag/ZnO back-reflector with a starting Ag roughness layer thickness of 28 Å and a final Ag/ZnO interface layer thickness of 78 Å; (bottom) comparison between the predicted absorbance Ath = 1 – Rth and the measured scattering Re,sc.

144

Figure 4-13 (top) Comparison between the specular reflectance deficit Rsp = Rth – Re,sp and the measured scattering Re,sc, all spectra at normal incidence, for a Ag/ZnO back-reflector with a final Ag/ZnO interface layer thickness of 250 Å; (bottom) comparison between the predicted absorbance Ath = 1 – Rth and the measured scattering Re,sc.

145 compared with the predicted absorbance Ath = 1 – Rth. For these latter comparisons, the scattering can provide information on elastic re-radiation by localized (or confined) plasmons whose existence is identified through the absorption spectra.

In the following, various features and commonalities of the results will be discussed that appear to be outside the experimental errors for the determined quantities.

(1) The primary mechanism that controls dissipation in the minimum 2 range of

1.5 -3.0 eV in these materials [below the bound electron (or interband) transition

onsets for ZnO and Ag, and above the free electron (or intraband) 2 rise with

decreasing energy] is interference-enhanced plasmon absorption. When the

optical path difference 2d, where d is the physical or effective thickness of the

ZnO, matches an integer number of wavelengths within the ZnO mo/n, then the

wave resonates within the ZnO. If the resonance photon energy of the light Eo =

hc/ matches the energy of confined plasmon modes, then strong coupling of the

wave to the plasmon modes occurs, which appears as an absorption process. This

accounts for the strong absorption band at 2.6 eV in Fig. 4-12 and the multiple

bands in Fig. 4-13. The approximate energy spacing of these resonances is given

by E ~ hc/ 2nav d, where nav is the average index of refraction for the photon

energy range of the neighboring resonances. A single such band is observed for

the thin ZnO (0.154 m) with E ~ 1.9 eV, and the three bands are observed for

the thick ZnO (0.316 m) with E ~ 0.9 eV. Thus, such resonances require not

only constructive interference in the ZnO, but also confined plasmon modes at

the interference maxima.

146 (2) For all Ag/ZnO interface structures, the peaks in the scattering spectra as

indicated by the vertical lines are correlated with the peaks in the absorbance

spectra, but shifted to the low energy side. The shifts tends to decrease with

increasing interface roughness ranging from 0.2 eV for the rough but specular

interference in Fig. 4-12 to 0.05 eV for the textured interface in Fig. 4-13. This

alignment may indicate that scattering derives predominantly from damped,

driven oscillations of localized plasmons that are in phase with the incident

optical field. Another simpler possible explanation is that scattering is direct,

being enhanced at the energies that result in constructive interference within the

film. The downward shift in energy may then be attributed to the plasmon

absorption which suppresses the multiple reflections.

(3) The absorbance features in the highest roughness back-reflector tend to occur

where the reflectance deficit shows minima. The most common positive

contribution to the reflectance deficit is direct scattering. If the scattering

mechanism transitions from direct to confined-plasmon-mediated and then back

to direct as function of photon energy, then the reflectance deficit must pass

through a minimum at the plasmon absorption band maximum. Thus, the

observed behavior suggests that plasmon-mediated scattering predominates for

the back-reflector with the largest interface roughness. The inverse correlation

between the reflectance deficit and the scattering may also suggest that surface

plasmons do not significantly account for scattering through re-radiation.

(4) In fact, the correlation between the minima in the reflectance deficit and the

maxima in the absorbance seems to reflect the fact that the electromagnetic wave

147 does not in general strongly couple to the surface plasmon modes whose energies

match the resonance energies of localized plasmons at the interface. Otherwise

the reflectance deficit would be strong at these photon energies.

(5) Similarly, the electromagnetic wave cannot strongly couple to surface plasmons

-- and thus the positive contribution to the reflectance deficit due to this effect is

low -- under two additional photon energy criteria. First, if the photon energy is

low for the specular structures, there are no significant surface spatial frequency

components that provide the momentum contribution necessary for this coupling

to occur. Second at high energies, the electromagnetic wave stimulates one-

electron absorption either within the ZnO, or in the Ag. This also suppresses

propagating surface plasmon generation from the electromagnetic wave.

These energy constraints would force the propagating surface plasmons to exist

within a well-defined range leading to a band in the reflectance deficit that falls

off at low and high energies and exhibits a central maximum. This behavior is

not observed for the roughest (or textured sample) of greatest interest as a back-

reflector.

The scattering behavior of the back-reflectors with different Ag/ZnO roughness levels as discussed so far has several implications for solar cell performance. Even though the spectral range of the scattering processes > 2 eV for the specular, smooth and rough films of Figures 4-11 and 4-12 have limited direct interest for thin film Si solar cells, these results provide information on the nature of the limiting structures and allow assessment of energy partitioning in the normal incidence reflection and absorption processes as discussed next and summarized in Table 4.3.

148 Table 4.3 The photon energy of the lowest energy scattering maximum for Ag/ZnO back-reflectors, the experimental specular reflectance and the predicted absorbance at this scattering maximum, measured scattering, the estimated percentage of absorbed light that is subsequently re-radiated by localized plasmons, and the dissipation given as De = 1 (Re,sp + Re,sc).

Sample Photon Experimental Predicted Experimental Re- Dissipation,

Energy Specular Absorbance, Scattering, radiation, 1(Re,sp+ Re,sc) (eV) Reflectance, Ath Re,sc Re,sc /Ath Re,sp specular 2.6 0.86 0.14 0.012 ~ 10% 13% smooth specular 2.4 0.50 0.40 0.12 ~ 30% 38% rough textured 1.5 0.39 0.50 0.44 ~ 90% 17%

Considering first the sample with the smoothest Ag/ZnO interface (18 Å interface layer thickness) and the photon energy of maximum scattering at 2.6 eV, it is predicted that 14% of the incident light is absorbed by the localized plasmons associated with the interface microstructure and only ~1.2% is observed as scattered light. Because the reflectance deficit vanishes at 2.6 eV, much of this scattering apparently occurs through localized plasmon modes as the scattering maximum coincides with the broad confined plasmon band below the ZnO and Ag interband absorption onsets. Thus, the efficiency of re-radiation at 2.6 eV, i.e., the percentage of light re-radiated to that absorbed is estimated as (1.2/14)% ~ 10% as shown in Table 4.3.

Considering next the Ag/ZnO sample with the 78 Å interface layer and the photon energy of maximum scattering of 2.4 eV, it is found that ~40% of incident light is predicted as absorbed by the localized plasmons associated with the interface microstructure. In fact, the peak absorbance is very strong, ~ 73%, occurring at 2.6 eV, enhanced by interference in the ZnO layer as described previously. About 12% of the

149 incident light is scattered at 2.4 eV; however in this case, because the reflectance deficit is comparable, the origin of this scattering is unclear. It could be either direct, or due to re-radiation by excited localized or surface plasmons. Because of the similarity of the scattering spectra for both samples of Figures 4-11 and 4-12, localized plasmons appear to be the more likely interpretation. If this interpretation is correct, the reflectance deficit due to surface plasmons would be dissipated as heat, and the efficiency of re-radiation by localized plasmons would be (0.12/0.40)% ~ 30%.

Finally, considering the fully textured Ag/ZnO sample with the 250 Å interface layer and the photon energy of 1.5 eV near a maximum in the scattering spectrum,

Figure 4-13 shows that ~50% of the incident light is predicted as absorbed by the localized plasmons associated with the interface microstructure, again enhanced by interference. About ~44% of the incident light is scattered at 1.5 eV, however, in this case, because the reflectance deficit is 11%, some of the scattering may be direct or due to re-radiation by surface plasmons. Neglecting these possibilities, the efficiency of re- radiation of 1.5 eV light absorbed through localized plasmons is (0.44/0.50)% ~90%.

Considering that 39% of the incident light at 1.5 eV is specularly reflected [1 Ath –

(RthRe,sp) = Re,sp] and 44% is scattered, then the dissipative losses to heat amount to 17%.

These losses are attributed to scattering processes of free electrons in the Ag excited directly by the electromagnetic wave or through excited plasmonic oscillations. Such scattering processes are likely to be due to defects and grain boundaries.

Table 4.3 summarizes all results for the experimental specular reflectance, the predicted absorbance, the measured scattering, the estimated re-radiation, and the

150 dissipation to heat all evaluated at the lowest energy scattering maximum for the three back-reflectors of Figures 4-11, 4-12, and 4-13.

4.5 Scattering Behavior of the Al/ZnO Back-Reflector

In order to assess further the possible origins of diffuse reflection in terms of direct scattering by macroscopic surface structure or re-radiation mediated by plasmons, a back-reflector incorporating Al was studied in detail. For this back-reflector also, the calculated specular reflectance deficit and absorbance spectra at normal incidence have been correlated with measured scattering spectra for the case of a moderately rough

Al/ZnO interface with di = 181 Å, (Figure 4-14). Here, the moderately rough

Al/ZnO was chosen because the smooth Al/ZnO did not exhibit measurable scattering whereas optical modeling of the RTSE data for very rough Al/ZnO was not successful, as it required a more rigorous optical modeling approach beyond the effective medium approximation due to the large in-plane scales of roughness. Moreover, the results for the

Al/ZnO back-reflector have been compared with those of a Ag/ZnO back-reflector having similar final metal roughness and interface layer thicknesses, as shown in Figure

4-15. The normal incidence specular reflectance deficit Rsp is calculated as before by subtracting the measured reflectance Re,sp from the reflectance Rth predicted based on the

RTSE analysis of the full structure. As before, the predicted normal incidence absorbance is given simply by Ath = 1  Rth, where Rth is the calculated reflectance, and it is assumed that no transmission occurs through the stack.

In Figures 4-14 and 4-15, the measured spectra in the scattering integrated over all solid angles is compared with the reflectance deficit for structures with an Al/ZnO

151

Figure 4-14 (top) Comparison between reflectance deficit and measured scattering spectra at normal incidence for an Al/ZnO back-reflector with an Al roughness layer thickness of 98 Å and a final Al/ZnO interface layer thickness of 181 Å; (bottom) comparison between predicted absorbance and measured scattering. spectra.

152

Figure 4-15 (top) Comparison between reflectance deficit and measured scattering spectra at normal incidence for a Ag/ZnO back-reflector with a Ag roughness layer thickness of 100 Å and a final Ag/ZnO interface layer thickness of 170 Å; (bottom) comparison between predicted absorbance and measured scattering spectra.

153 interface thickness of 181 Å and with a Ag/ZnO interface thickness of 170 Å, respectively. Once again, the predicted reflectance is that based on the assumption of a fully specularly reflecting structure in accordance with the Fresnel Equations, as the

RTSE measurement and analysis is essentially blind to macroscopic roughness and scattering. Thus, the reflectance deficit depicts branching mechanisms that deplete the specularly reflected beam due to macroscopic roughness. As summarized in Figure 4-10 and Table 4.1, these include (i) direct scattering by macroscopic roughness on the surface and (ii) coupling of the incident light to propagating surface plasmons as facilitated by macroscopic roughness via the grating effect (Collins and Ferlauto, 2005). Another branching mechanism not taken into account is the determination of Rth is waveguiding losses which also rely on direct scattering or re-radiation leading to light trapping within the ZnO layer. Re-radiation by localized plasmons in the specular direction is not included in the reflectance and adds to the specularly reflected beam since this is a branching mechanism arising from an absorption which is included in Ath. The measured scattering spectra for comparison with the reflectance deficit spectra in the upper panels of Figures 4-14 and 4-15 include (i) the direct scattering, along with re-radiation by (ii) propagating surface plasmons and (iii) confined plasmons. In the lower panel of the

Figures 4-14 and 4-15, the integrated scattering is compared with the predicted absorbance.

By comparing the scattering first with the reflectance deficit and then with the absorbance -- considering both the position of the peaks and their amplitudes, one can obtain approximate quantitative information on the physical mechanisms of scattering and dissipative losses as has been performed in the previous sub-section for three

154 different Ag/ZnO structures. Starting with the Al/ZnO structure having a moderate interface thickness of di ~ 181 Å (Figure 4-14), the scattering peaks appear to coincide best with the reflectance deficit peaks and not with the predicted absorbance peaks. This suggests that the origins of scattering include direct diffuse reflectance from macroscopic roughness or scattering mediated through propagating surface plasmons. Near 1.5 eV, the key region for back-reflector operation in triple junction amorphous Si:H-based solar cells, the difference between the reflectance deficit and the measured scattering of ~7% can be interpreted as the maximum possible dissipative losses from propagating surface plasmon modes. Thus, most of the predicted ~ 60% absorbance arises from dissipation that can be described by the Fresnel equations, i.e., through interband and intraband transitions and through localized plasmons.

In contrast, for Ag/ZnO structures with di ~ 170 Å, the scattering peaks coincide with both the reflectance deficit and the absorbance peaks. This implies that the scattering in this case can occur directly from macroscopic interface structure as well as from re-radiation through both confined and propagating plasmons. Moreover, the maximum possible dissipative losses through propagating surface plasmons is ~ 2% at

1.5 eV, and hence the predicted absorbance (~ 38%) again arises mostly from dissipation that can be described via the Fresnel equations.

The above comparison of Al/ZnO and Ag/ZnO back-reflectors clearly shows that at ~ 100Å metal layer roughness level (Al or Ag), the back-reflectors from Ag/ZnO are preferred over those from Al/ZnO, as the former provide a higher better total reflectance

(specular + scattering) at the photon energy of operation (~1.5 eV). Quantitatively, at 1.5 eV, the total reflectance of the Al/ZnO back-reflector is given from the data in Table 4.4

155 Table 4.4 A comparison of the parameters for Al/ZnO and Ag/ZnO back-reflectors, including the photon energy of the lowest scattering maximum, the experimental specular reflectance at the photon energy, as well as the predicted absorbance, measured scattering and approximate efficiency of re-radiation, and finally, the experimental dissipation, given as De = 1 (Re,sp + Re,sc).

Sample Photon Experimental Predicted Experimental Re- Dissipation,

Energy Specular Absorbance, Scattering, radiation, 1(Re,sp+ Re,sc) (eV) Reflectance, Ath Re,sc Re,sc /Ath Re,sp

Al/ZnO 1.5 0.32 0.60 0.02 ~ 3% 66%

Ag/ZnO 1.5 0.21 0.38 0.36 ~ 95% 43%

by Rtot = 1 – Ath – Rsp + Re,sc ~ 34% , whereas the total reflectance of the Ag/ZnO back- reflector is ~ 57%. In fact, the back-reflector of Ag/ZnO exhibits much greater scattering compared to that of Al/ZnO. This may occur because any scattering mediated through propagating surface plasmons as well as through confined particle plasmons is strongly suppressed by the interband absorption of Al at ~ 1.5 eV. Since there is no such absorption in Ag, the re-radiation in terms of scattering is significantly higher in the

Ag/ZnO back-reflector. The following section includes a discussion of the possible remedies for the dissipation in both Al/ZnO and Ag/ZnO back-reflectors.

Table 4.5 incorporates results from Table 4.3 and Table 4.4 with all data selected from the spectra at a photon energy of 1.5 eV. This summary of results shows that an interface roughness thickness of at least > 80 Å is needed to generate significant scattered light, which increases monotonically with increasing interface thickness. Dissipation accompanies the scattering, but this can be reduced by the appropriate interface

156 Table 4.5 A comparison of the optical properties at 1.5 eV for four Ag/ZnO back- reflector structures tabulated in order of interface layer thickness. di (Å) Photon Experimental Predicted Experimental Re- Dissipation, Energy Specular Absorbance, Scattering, radiation, 1(Re,sp+ Re,sc) (eV) Reflectance, Ath Re,sc Re,sc /Ath Re,sp

18 1.5 0.98 0.02 0.005 ~ 40% 1%

78 1.5 0.96 0.03 0.03 ~ 100% 1%

170 1.5 0.21 0.38 0.36 ~ 95% 43%

250 1.5 0.39 0.50 0.44 ~ 90% 17%

microstructural scale, in which case not only is scattering significant, but also re-radiation efficiency is high.

4.6 Improvement of the Back-Reflectors

It should be emphasized that for both Al/ZnO and Ag/ZnO back-reflector structures, various mechanisms cause absorption. Not all such mechanisms lead directly to dissipation, however, since plasmons can decay radiatively, generating scattered light.

In the bulk and interface components of Al/ZnO structures, the Al (200) parallel band electronic transitions with band gap 2|U200| = 1.5 eV cause the most significant absorption in the near-infrared region at 1.5 eV. The absorption in Al/ZnO at 1.5 eV is also enhanced by the Drude free electron tail as seen in the imaginary part of the dielectric function (2) of the interface layer (Nguyen and Collins, 1993). On the other hand, the

157 Ag/ZnO interface behaves quite differently as there is no interband absorption in Ag in the near infrared region and the intraband 2 is weaker in Ag than in Al. As a result, the primary source of absorption in Ag/ZnO is the confined plasmon that appears in the imaginary part of the dielectric function of the interface layer. The undesirable dissipation in the region of operation (1.4 – 1.8 eV) of the Al/ZnO and Ag/ZnO back- reflectors can be remedied by applying different methods as described next.

In Al/ZnO, the interband absorption of Al near 1.5 eV can be narrowed by increasing the interband electron mean free time so that there is weak absorption except in a relatively narrow region about 1.5 eV (Nguyen et.al., 1993). This is achievable in a polycrystalline Al film composed of large crystalline grains having a high quality i.e. a low defect density. Increasing the grain size and reducing the intragrain defect density would also be expected to lead to a longer electron mean free time for intraband excitations (Kasap, 2005), and this in turn is expected to reduce the intraband absorption near 1.5 eV, as well. Even higher back-reflector performance may be obtained with this approach in the case of nanocrystalline Si:H bottom cells. In this case, the energy of interest red-shifts, thus avoiding the 1.5 eV interband absorption onset, but at the same time increasing the potential for intraband absorption unless the grain size is very large.

A demonstration of the ability to increase the intraband or free electron mean free time in metal films has been presented in this study for Ag, as shown in Figure 4-16.

This figure shows the imaginary parts of the dielectric functions of two opaque Ag films prepared with equal thicknesses of surface roughness. In one case, Ag deposited on rough Al at room temperature yields substrate-induced roughness and, in the other case,

Ag deposited directly on smooth oxide-covered Si wafers at an elevated temperature

158

Figure 4-16 Imaginary part of the dielectric function for Ag deposited on c-Si at an elevated temperature yielding a roughness thickness of ~ 71 Å (solid line); also shown is the result for Ag deposited at room temperature on rough Al yielding ~ 68 Å thick substrate-induced roughness. The Ag layer in each case was deposited to ~ 1000 Å thickness.

yields deposition-induced roughness. The high temperature in the second case induces the growth of larger crystalline grains, possibly with a lower density of defects, resulting in a longer intraband mean free time. This leads to a decrease in 2 and thus less dissipative absorption, which is an advantage for back-reflector operation.

159 For the high quality Al/ZnO and Ag/ZnO back-reflector structures, the mechanisms for dissipation are different and therefore the mitigating approaches are also different. In the case of high quality Ag/ZnO back-reflectors, plasmonic excitation dominates over the intraband excitation, and as a result, mechanisms that lead to dissipation through plasmons must be understood. First, one may attempt to tune the size of the protrusions so as to increase the radiative rate. One may also ensure that the protrusions consist of single grains each having a low defect density. Such optimization can be performed through adjustment of the process parameters including substrate temperature, deposition pressure, rf power and Ar gas flow. With such optimization, the plasmon non-radiative rate is reduced relative to its radiative rate. The second method for mitigating dissipation in Ag/ZnO back-reflectors is to blue-shift the plasmon mode.

This can be done by reducing the screening effect through a. In the expression for the

-1/2 plasmon energy position presented earlier, E0 ~ Ep{∞+[(2+Q)/(1Q)]a} , if one measures that ∞ = 1.5, one obtains a localized plasmon energy of E0 ~ 1.5 eV for Q ~

0.67. For this value of Q, however, the plasmon energy shifts to E0 ~ 2 eV with a reduction in the index of refraction of the ZnO layer from n = 2 to n = 1.5. The index of refraction of the ZnO film can be lowered by introducing voids during deposition so that the film becomes porous. The simplest approach for the deposition of a porous film in the sputtering process is via a high Ar pressure so that the deposited species are thermalized by sputtering gas atoms before reaching the substrate, and hence they carry little momentum for densifying the film structure. In fact Sainju has demonstrated that, by increasing the substrate temperature (25oC to 300oC) and Ar pressure (4 mTorr to 40 mTorr), n (1.5 eV) for ZnO was found to decrease from 1.95 to 1.52 in a layer 500Å thick

160 (Sainju, unpublished, 2011). This high void fraction layer could be used as the first step of a two-step ZnO deposition. An alternative to this approach is grazing angle sputter deposition in which case each protrusion on the film surface shadows the area behind it.

As a result, film growth is columnar in nature and a large volume fraction of void is trapped between the columns within the ZnO layers.

4.7 Summary

RTSE and ex-situ optical spectroscopies have been applied to investigate the optical properties of Al/ZnO and Ag/ZnO interfaces in back-reflectors in the configuration used for n-i-p thin film Si:H solar cells. The coupling of electromagnetic waves to localized plasmons associated with metal nano/microstructure that generates absorption bands in the imaginary parts of the dielectric functions of the Al/ZnO and

Ag/ZnO interface layers, can lead to both dissipation and re-radiation. The coupling of the electromagnetic waves to surface plasmons associated with plane metal surfaces appears in the reflectance deficit, i.e., the difference between the normal incidence specular reflectance predicted from RTSE analysis and that measured directly. Coupling to surface plasmons requires macroscopic roughness, but is suppressed when localized plasmonic absorption or other absorption processes occur at the same energy. In

Ag/ZnO, one mechanism for back-reflector optimization appears to be interference enhanced localized plasmon coupling, which can lead to efficient re-radiation when the microstructure is properly tuned. This optimization is wavelength dependent and for a multijunction solar cell incorporating the a-Si1-xGex:H, photon energy for optimization is

~ 1.4 eV, which is near the band gap of the bottom cell. An alternative approach is to

161 shift the plasmon bands out of the range of interest as described above by tailoring the

ZnO index of refraction. This approach relies on direct scattering which may not be as efficient as plasmon-mediated scattering. In contrast to Ag/ZnO, no significant role of plasmons in dissipation and/or re-radiation is observed at 1.5 eV for Al/ZnO interfaces of moderate roughness. This behavior is due to the higher bulk plasma energy in Al and to the presence of Al interband transitions near 1.5 eV. The presence of the Al and ZnO interband transitions at low and high energies, respectively, tends to place the allowable plasmon modes in the minimum absorption region of ~ 3.3 eV. Thus, the dissipation in

Al/ZnO at 1.5 eV is large not due to confined plasmons, but rather due to the combination of the interband and intraband transitions. The behavior for Al/ZnO contrasts to that of

Ag/ZnO in which case the primary dissipation at 1.5 eV is through confined plasmons.

This fact provides more options for mitigating losses in the Ag/ZnO structures, either by exploiting the plasmons, or by shifting the plasmons and avoiding them depending on which approach minimizes the dissipation. Minimization of dissipation in conjunction with efficient scattering that leads to light trapping are the key features that serve to optimize Ag/ZnO back-reflectors for thin film silicon solar cell application, in single, tandem, as well as triple junction configurations.

162

Chapter 5

Roll-to-Roll Deposition of Thin Film a-Si:H Solar Cell Structures on Polymer Substrates

5.1 Introduction and Motivation

Improving the performance of thin film solar cells on inexpensive flexible substrates such as thin polymer sheet in the roll-to-roll configuration is of great interest in photovoltaics technology. This chapter focuses on the deposition of thin film hydrogenated amorphous silicon (a-Si:H) multilayer solar cell device structures in the substrate/Ag/ZnO/n-i-p configuration on a 15 cm wide flexible polymer in a roll-to-roll cassette deposition system. The polymer used here is poly-ethylene naphthalate (PEN), which can be subjected to deposition temperatures up to ~ 160C, (Madan, 2004; Dahal et al., 2010). The Ag/ZnO back-reflector (BR) deposition forms the first steps in the fabrication of a complete thin film Si:H solar cell structure on the flexible polymer substrate. Deposition of the BR is then followed by a-Si:H n, i, and p layers in succession. Solar cells are completed with the deposition of an In2O3:Sn (ITO) top transparent conducting oxide contact. The emphasis of this work involves real time spectroscopic ellipsometry (SE) analyses of the magnetron sputter deposition of ZnO and the plasma-enhanced chemical vapor deposition (PECVD) of the a-Si:H i and p-layers

163 during cassette roll-to-roll deposition of the films on the PEN substrate. Another emphasis of this work is to evaluate the uniformity of the layers across the width of the roll-to-roll substrate by ex-situ mapping SE.

The methodology developed in this thesis research is first demonstrated in growth studies from nucleation to the final thickness for a magnetron sputtered aluminum doped zinc oxide (ZnO:Al) layer on top of opaque Ag in the BR structure. The methodology is then extended to plasma-enhanced chemical vapor deposition (PECVD) of the a-Si:H i and p-layers in succession on the BR/n-layer stack. Real time SE (RTSE) data collection is initiated while the substrate is moving, but before the plasma is ignited, so that the nucleation of the layers can be observed. As the substrate moves by, the film thickness increases with time until a steady state is reached, after which the bulk layer thickness at the monitoring point is constant with time. This steady state begins when the elapsed deposition time equals the time required for the moving substrate to travel from the leading edge of the deposition zone to the monitoring point. A constant substrate speed, so called “normal speed”, is ultimately set such that the desired final film thickness is achieved in the time required for a substrate point to move through the entire deposition zone. This normal speed, however, does not permit study of film growth that occurs after the substrate passes the monitoring point. To address this deficiency, the substrate speed is reduced only over an initial length of the roll such that the final film thickness of interest is reached at the monitoring point and the corresponding speed is described as

“reduced speed”.

Figure 5-1 shows graphical representations of the normal speed and the reduced speed depositions for ZnO:Al on Ag coated PEN during sputtering, and the

164

“ Normal speed ” = 0.0077 cm/s “ Reduced speed ” = 0.0039 cm/s

7.5 cm 7 cm 7.5 cm 7 cm ellipsometry monitoring point

0 1400 Å 2400 Å 0 2400 Å 4110 Å start end start end of of of of dep. dep. dep. dep. zone zone zone zone

Ag/ZnO coated web during sputter deposition at 1.65 Å/s deposition rate

“ Normal speed ” = 0.0120 cm/s “ Reduced speed ” = 0.0086 cm/s

13 cm 5 cm 13 cm 5 cm ellipsometry monitoring point

0 2080 Å 2800 Å 0 2800 Å 3770 Å

start end start end of of of of dep. dep. dep. dep. zone zone zone zone

Ag/ZnO/n/i-layer coated web during PECVD deposition at 1.88 Å/s deposition rate

Figure 5-1 Schematics of normal speed and reduced speed roll-to-roll cassette depositions of (i) ZnO:Al during sputtering (top) and (ii) a-Si:H i-layer during PECVD (bottom) as monitored by real time spectroscopic ellipsometry.

165 corresponding representations for the a-Si:H i-layer on Ag/ZnO/n-layer coated PEN during PECVD. Similar representations also apply, but with much smaller thicknesses, for the normal and the reduced speed depositions of the p-layer on Ag/ZnO/n/i-layer coated PEN during the PECVD process. At the reduced speed, RTSE can be used to analyze the entire layer on an initial length of the roll before its full length is coated. The coated web is then mapped ex-situ to evaluate the uniformity of ZnO:Al and the i- and p- layers across their width. The goal of this work is to develop and verify optimum deposition procedures based on optical monitoring of thin film Si:H solar cell structures in roll-to-roll multi-chamber deposition.

In this chapter, the RTSE analysis of the sputter deposition of ZnO:Al and the

PECVD of a-Si:H i-layers and p-layers, both at normal speed and reduced speed are presented. These results are then compared with the corresponding theoretical predictions for an ideal deposition model and for various complexities introduced into the model. Possible reasons for the deviations from the predictions are discussed.

5.2 Deposition Processes

5.2.1 ZnO:Al Layer

In order to study the growth evolution of sputtered ZnO:Al in roll-to-roll cassette deposition, a Ag film was deposited first by magnetron sputtering onto PEN polymer in the multi-chamber deposition system. This film was deposited at room temperature using an Ar sputtering gas pressure of 5 mTorr, an Ar gas flow of 10 sccm, and an rf plasma power of 120 W over a target area of 163 cm2, yielding a power density of 0.73 W/cm2.

The Ag film described here exhibits a final microscopic surface roughness layer thickness

166 of ds ~ 20 Å as deduced by in situ (but not real time) spectroscopic ellipsometry analysis.

The ZnO:Al film was magnetron sputtered onto the Ag surface using the same conditions as for the Ag deposition.

During real time monitoring of the ZnO deposition, the substrate travelled at a constant linear speed as shown in Figure 5-2. The film properties were measured by

RTSE at a location at the center of the substrate width and vertically above the center of the ZnO:Al target. The start of the deposition zone is assumed to occur as the longest line-of-sight from the target to the substrate at a distance of x = xmax ~ 7.5 cm along the substrate from the monitoring point. This line-of-sight limit is established by a shutter in the position shown in Figure 5-2.

The thickness evolution was modeled theoretically as a two-dimensional problem within the plane oriented normal to the substrate and containing the center line of the substrate roll. Thus, uniformity across the width of the substrate roll is assumed. In this simple deposition model, a flux f (x', w' ) arrives line-of-sight at a fixed point x' on the moving substrate from point w' on the target. Thus, the target width 2w is taken into account such that the deposition rate at any point on the substrate is ultimately determined as an integration of line-of-sight fluxes from an array of sputter point sources

2 2 1/2 across the target width, each source at a distance given by r' = [ro + (x'  w' ) ] from the substrate point (where w < w' < w). The ZnO layer thickness monitored at point O in Figure 5-2, just above the target at time t is then the integration over prior times t' of deposition occurring at that fixed point on the substrate as it traversed to the left within the deposition zone. Assuming point P lies at distance x' from O at t' as shown in

Figure 5-2, the integration over time t' is converted to an integration over x'

167

Figure 5-2 Schematic of the monitoring configuration used for real time spectroscopic ellipsometry of thin film ZnO:Al deposited by magnetron sputtering in a cluster tool with a roll-to-roll cassette substrate. The plasma is ignited (at t0) while the substrate is moving to the left at a constant rate vp.

168 through the relationship t' = (xmaxx' )/vp < xmax/vp so that dt' = vp dx', where vp is the constant linear speed of substrate motion. This relationship between t' and x' assumes that the fixed point entered the deposition zone at x' = xmax at t' = 0, and reached the observation point at x' = 0 at t' = xmax/vp. This simple two-dimensional line-of-sight model leads to a final expression of the form:

w x w' x + w'

Ro 0 { 0 f (x', w' ) dx' + 0 f (x', w' ) dx' } dw' ______deff (x) = , (5.1) w

2vp 0 f (ro, w') dw'

where the integral over x' tracks the accumulated deposition on the moving substrate, and the integral over w' accounts for the target as an array of point sources. Assuming that the plasma is started at t = t0 = 0, and x = 0 defines the substrate location directly above the target at t = 0, then x in this expression is simply given by x = vp t for t < xmax/vp = (7.5 cm)/vp and then is fixed at xmax = 7.5 cm thereafter. In Equation (5.1), assuming the function f is known, Ro is the only variable; it is the assumed constant deposition rate at

O due to the integrated flux from all points of the target. In addition, parameters fixed by the geometry include w = 2.54 cm, which is the half width of the target, and ro = 7 cm, which is the target-to-substrate distance at its closest point.

If one assumes Lambertian emission of deposition flux from the target point, similar to that observed for -Ta (Chouan and Collobert, 1977) and an inverse square variation of deposition flux with target-substrate distance, then

4 2 2 2 f (x', w') = ro [(x' w') + ro ] , (5.2)

169 which is normalized to unity at x' = w' = 0. Also taken into account in this expression is the angular orientation of the normal at the substrate surface relative to the line-of-sight to the target.

The final expression for the ZnO thickness monitored at point O versus time is given by substitution of Equation (5.2) into Equation (5.1). This yields the expression:

r22 w R  oo    11  x  w   x w  . (5.3) de f f  x  x  w ta n   x  w  ta n   rr 2 2 1 w oo    2vp r o w r o w  ta n  ro

In the first approach for a simulation based on this equation, Ro can be determined such that simulation of Equation (5.3) yields the measured effective thickness [deff(xmax)] of

ZnO:Al after a time of t = xmax/vp = (7.5 cm)/vp. This approach assumes that the deposition on the moving substrate starts only when the web is within line-of-sight of the target as shown in Figure 5-2. A second approach is to choose Ro such that the simulation of Equation (5.3) matches the measured saturation thickness of deff, irrespective of when that occurs. When deposition occurs beyond the maximum line-of- sight position xmax, e.g., due to scattered, reflected, or re-emitted flux, then these two different approaches yield different results for the rate and for the fit to the data. This non-ideality due to non-line-of-sight flux is addressed in greater detail in the next paragraphs. A third approach chooses Ro as that from the second approach and in addition ignores the shadowing by the shutter altogether, placing xmax in Eq. (5.3) at the saturation in thickness.

170 From Equations (5.1) (5.3), which assume all line-of sight-flux, it is predicted that the thickness abruptly saturates for t ≥ xmax/vp = (7.5 cm)/vp, in other words, after the length of substrate equal to xmax passes the observation point. Experimentally, however, no abrupt saturation is observed. This observation is attributed to non-line-of-sight deposition flux that coats the substrate surface beyond xmax, for example due to scattering.

Two features can be added to the deposition model in an attempt to simulate the effects of gas phase scattering of the depositing species.

First, the flux function of Equation (5.2) can be modified to include an exponentially decaying factor according to:

4 4 f (x', w') = (ro /r' ) exp(r' /) (5.4a)

4 4  (ro /r' ) [1  (r' /)] ; when  >> r' , (5.4b)

2 2 1/2 where r' = [ro + (x'  w' ) ] . This expression is based on the concept that after a distance equal to a mean free path , the flux available for deposition has decreased by e1 due to gas phase scattering. At the same time, however, the arrival of additional flux at point x' due to such scattering is neglected.

The second effect is the simulation of the deposition flux that reaches substrate points beyond xmax due to scattering. This effect can be simulated by assuming that the opening between the shutter and the substrate serves as a source of deposition flux given by f (x', w' ). The relevant expression for this case is:

171 2D x

Ro 0  x f (x', w') dx' dw' s ______s ______d eff (x) = , (5.5) 2D

vp 0 f(D, w') dw'

where D is the half-width of the opening. In addition, the deposition rate contribution Ro is normalized to that at x = xs + D, (xs= 5.3 cm and D = 1 cm). This equation is applicable for xs < x < xmax + xadd, where xs is the distance between the point on the substrate vertically above the shutter and that vertically above the center of the target

(which defines x = 0), xadd is the additional length of substrate beyond xmax that can be coated by this flux. As a result, the total length of substrate that accumulates material is no longer given by xmax, but instead by xtot = xmax + xadd. In this case, the assumption of a

Lambertian point source of flux at a location w' of the shutter opening, as measured from the substrate, yields a flux function of the form:

f (x',w' ) = 4w' 3x' (x' 2 + w' 2 )2, (5.6)

where x' is measured from xs, the point on the substrate vertically above the shutter. This flux is normalized to that at x' = w'. Substitution of Equation 5.6 into Equation 5.5 yields the expression:

R s  x  x  22   x  x   4 D 2 dxs    o sln  s eff 4 2 xx s  2 Dv p  ln 5   5

for xs < x ≤ xtot ----- (5.7) which can be applied to model the component of the deposition that occurs starting from xs and then proceeding beyond xmax to xmax + xadd.

172 Based on the ideal deposition model without gas phase scattering, the final ZnO thickness on the substrate before it exits the deposition zone at F is the sum of the ZnO thicknesses acquired in the portions EO and OF. Equation 5.3 for the effective thickness also holds to describe (under ideal conditions) the ZnO:Al thickness component at the end of the deposition zone that accumulates in the portion OF, with the difference being that over the portion OF, x = xmax = 7 cm.

In this work, the final ZnO:Al thickness was intended to be ~ 2000 Å, and as a result the required speed of substrate motion was estimated as 0.0077 cm/s for the first, normal speed monitoring experiment, assuming ideal deposition at a rate of 1.6 Å/s vertically above the center of the target. At this speed, observations of the nucleation along with (7.5/14.5) x 100% = 52% of bulk layer growth were anticipated. A second experiment was performed with the reduced speed of 0.0039 cm/s so that the steady state

ZnO:Al thickness would reach ~ 2000 Å at the monitoring point O. The purpose of this reduced speed run was to study the entire ZnO:Al growth profile to its final desired thickness. Once the steady state was reached, the speed was returned to 0.0077 cm/s.

Since the plasma was started and stopped for the two different substrate speed depositions, it is possible that two different values of Ro may occur, depending on the reproducibility of the deposition.

5.2.2 a-Si:H i- and p-layers

The a-Si:H i-layer evolution was studied in a deposition on 15 cm wide PEN coated with layers of Ag/ZnO/n-layer. The deposition conditions of the component layers used in this structure are given in Table 5.1. Both the i-layer and p-layer films

173 Table 5.1 Deposition conditions used for the n-i-p solar cell component layers in studies of i- and p-layer growth on Ag/ZnO/n-layer coated PEN polymer substrates using a roll-to-roll cassette capability at both normal and reduced speeds.

Layer type Deposition RF plasma Substrate Gas flows (sccm) pressure power temperature (oC) (mTorr) (W/cm2)

Ag 5 0.73 RT [Ar] = 10

ZnO 5 0.73 RT [Ar] = 10

R = 0.1, D = 0.005

n-layer 350 0.0131 110 [SiH4] =10, 5% [PH3]

in H2 = 1 (by volume) R = 1 i-layer 400 0.0192 110 [H2] = 25, [SiH4] = 25 R = 0.07, D = 0.004

[SiH4] = 13, [CH4] = 6 p-layer 400 0.0095 110 5% [B2H6] in H2 = 1 (by volume)

were deposited at a calibrated substrate temperature of Tm ~ 110C. The calibration that provides the true Tm value from a thermocouple reading is performed by using a c-Si wafer and applying SE to deduce the critical point energies both at the substrate temperature and after cooling the wafer to room temperature. The critical points energies are known functions of Tm (Lautenschlager et al., 1987). Higher accuracy is achieved, however, by relying on critical point energy differences between unknown and known temperatures in order to extract the unknown temperature.

174 The source gases for the i-layer deposition were SiH4 and H2 and those for the p- layer deposition were SiH4, CH4, H2, and B2H6. The gas flows and pressures and the plasma power densities are provided in the Table 5.1. The hydrogen dilution ratio R

(R=[H2]/[SiH4]) and dopant gas ratio D (D = [PH3]/[SiH4] for the n-layer and D =

[B2H6]/{[SiH4]+[CH4]} for the p-layer) are also included in the table.

The i-layer and p-layer films were monitored by RTSE at a location 13 cm from the start of the plasma deposition zone. As in sputtering of ZnO, the substrate travelled at a constant linear speed during the deposition as shown in Figure 5-3. The thickness profile was modeled assuming a constant deposition rate throughout the PECVD zone.

Under ideal conditions, the i or p-layer effective thickness observed at any time t

= x/vp < xmax/vp is simply given as:

deff (x) = Rox/vp (5.7)

where Ro is the assumed constant deposition rate in the deposition zone and the plasma is assumed to start at t = 0. The parameter Ro is selected in this case such that the predicted saturation thickness for t > xmax/vp matches the measured stable thickness. The PECVD process at relatively high pressure differs from the sputtering process in that the transition to stable growth occurs more abruptly because the edge of the plasma and the fall-off in the reactive gas distribution is relatively well defined. Thus in this case, a single approach is used to obtain Ro. As in the case of sputtering, the Ro value, however, may be different for the different substrate speeds because the PECVD process is stopped and restarted for both the PECVD i-layer and p-layer.

175

Figure 5-3 Schematic of the monitoring configuration used for real time spectroscopic ellipsometry (SE) studies of a-Si:H n-i-p solar cells fabricated by plasma enhanced chemical vapor deposition (PECVD) in a cassette roll-to-roll cluster tool. For deposition of the i or p-layers, the plasma is ignited (at t0 = 0) while the substrate is moving at a constant rate vp. Under ideal growth conditions, the thickness at the monitoring point

increases from 0 linearly according to deff = (Ro/vp) x ; 0 ≤ x ≤ xmax, where Ro is the constant deposition rate and x is the distance that a fixed point on the substrate travels in a time t, as, defined so that x(t0) = 0. Under ideal conditions, after a time t = xmax/vp, the thickness is predicted to abruptly saturate at deff = (Ro/vp)xmax, where xmax = 13 cm, the distance between the monitoring point and the edge of the plasma zone where the substrate first enters.

176 In spite of the rapid fall-off in the plasma at the edge of the cathode plate, reactive gas species do exist beyond this edge, and so the effective deposition zone is somewhat longer than the cathode plate length. This effect is modeled assuming n reactive species having exponential decays with distance characterized by mean free paths n due to reaction within the gas phase. As a result of this effect, in both normal speed and reduced speed depositions, the thickness does not saturate with a discontinuous rate in reaching the steady state. The contributions to the deposition outside the plasma zone are given by expressions analogous to Equation (5.5) and (5.6), but with an exponentially decaying flux in the latter given by:

3 2 2 2 2 2 1/2 fn (x',w' ) = 4w' x' (x' + w' ) exp[(x' + w' ) /n] , (5.8)

where w' is the distance from the substrate to the plasma region from which the flux originates, as measured normal to the electrodes. If it is assumed that the reactive flux arrives from the edge of the plasma region close to the substrate so that w' << n and w'

<< x, then:

2 ______deff (x) = nRn {1  exp[xxmax)/n]} . (5.9) n vp

In deriving this formula, the rate Rn for each reactive component in this case is normalized to that occurring at x = w, where w is the half-width of the electrode spacing.

177 5.3 Experimental Details for Real Time Spectroscopic Ellipsometry

Real time spectroscopic ellipsometry (RTSE) was performed using a rotating- compensator multichannel instrument that can provide (, Δ) spectra from 0.75 to 5.04 eV. To improve precision, pairs of (, Δ) spectra were collected within a time of ~ 1 s, as averages over ~ 30 optical cycles, since the rotation frequency of the compensator is ~

31 Hz. During the acquisition time for one pair of (, Δ) spectra, ~ 1-2 Å effective thickness of ZnO or a-Si:H material accumulates on the underlying stack. Analyses of all spectra involve numerical inversion (Cong et al., 1991) and least-squares regression analysis algorithms (Jellison et al., 2005). The angle of incidence for all SE measurements during depositions was fixed at a value within the range of 70.0 ± 0.6.

The thickness uniformity of the layers across the width of the web was evaluated by mapping with ex-situ SE, as described in Chapter 3. The (, ) spectra for ex-situ mapping were collected from 0.75 to 6.5 eV. In order to improve the signal-to-noise ratio in mapping, data acquisition in those experiments was performed with a ~10 s optical cycle averaging time in a high accuracy mode, yielding an acquisition time of ~ 2 x the averaging time. The grid size in mapping was chosen to be 1 cm2. Analyses of the mapping spectra involve least-squares regression algorithms parameterized with a small number of wavelength-independent parameters; the details of these analyses are provided in Chapter 2. The angle of incidence for all mapping SE measurements was fixed at

65.0.

178 5.4 RTSE of ZnO:Al Evolution on Ag Coated PEN

The growth of ZnO:Al films on Ag coated polymer substrates was analyzed using a ZnO:Al dielectric function determined from the real time data collected at ~ 1000 Å bulk layer thickness. Both a Drude expression and a critical point (CP) oscillator expression were combined to simulate the ZnO:Al dielectric function. The Drude component represents the behavior of the free electrons, and the CP component is derived assuming parabolic bands in k-space in the neighborhood of a fundamental band gap.

The multilayer model to obtain the ZnO:Al dielectric function includes the Ag layer, a

Ag/ZnO interface layer, the ZnO:Al bulk layer, and ZnO:Al surface roughness in succession. The Ag dielectric function was obtained by fitting single scan ellipsometry spectra of the Ag layer on the PEN polymer substrate with ~ 20 Å Ag surface roughness.

A Drude free electron component and two critical point (CP) oscillators were used to represent the Ag dielectric function. As indicated in previous chapters, the mathematical forms of these oscillators are given in the Appendix, in Eqs. (A.8), (A.9), and (A.11).

The dielectric function of the interface layer between the bulk Ag and ZnO:Al layers was modeled as in the studies of back-reflector structures on c-Si substrates presented in

Chapter 4. This dielectric function was represented by a Drude free electron component as well as Lorentz and Tauc-Lorentz oscillators (Sainju et al., 2006; Dahal et al., 2011).

The mathematical form of the Lorentz and Tauc-Lorentz oscillators are given in Eqs.

(A.1), (A.2), (A.12), and (A.13) of the Appendix.

In order to obtain the dielectric functions of the Ag/ZnO interface layer and the bulk ZnO:Al layer, the oscillator parameters and the corresponding bulk and roughness layer thicknesses were fitted by least squares regression at a time-point at which bulk

179 ZnO:Al thickness was ~ 1000 Å. Figure 5-4 shows the final results for the best fit analytical dielectric function along with the corresponding exact inversion result for the normal speed deposition. The inversion was performed by fixing the best fit thicknesses as follows: Al/ZnO interface layer at 31 Å, ZnO:Al layer at 1003 Å, and the ZnO:Al roughness layer at 96 Å. These thicknesses were the best-fit values obtained from the least squares regression at the same time-point. The appearance of the Drude free electron component in the infrared region is the result of Al doping of the ZnO. The optically-determined resistivity of the ZnO:Al is 8.53 x 104  cm, as obtained from the fit when using a Drude component expressed in terms of the resistivity and relaxation time, rather than the amplitude and broadening parameter. The deduced resistivity gives a sheet resistance of 43 /sq for the final 2000 Å ZnO thickness expected to be obtained at the end of the normal speed deposition

Figure 5-5 shows the dielectric functions of the Ag/ZnO interface layer obtained together with the dielectric functions of the bulk ZnO:Al layer. The oscillator parameters representing the Ag layer, Ag/ZnO interface layer, and ZnO:Al layer for the normal speed deposition are given in Table 5.2. The stable interface thickness at the observation point for this depostion is ~ 31 Å. The evolution of the interface layer between the bulk

Ag and ZnO layers is shown in Figure 5-6 for the normal speed deposition. Inclusion of such an interface layer has been shown to significantly improve the fit to the full RTSE data set (Sainju et al., 2006). In this case, after ZnO nucleation in the normal speed deposition, the stable MSE value expressed in terms of the N, C, and S parameters, as given in the Eq. 2.28 in Chapter-2, decreases by ~ 27% (from 0.049 to 0.036) upon

180

Figure 5-4 Real (upper) and imaginary (lower) parts of the ZnO:Al dielectric function as obtained in normal speed deposition assuming an analytical model (lines); the results of an exact inversion of experimental data are also shown (circles).

181

Figure 5-5 Real (upper) and imaginary (lower) parts of the Ag/ZnO interface dielectric function for normal speed ZnO:Al roll-to-roll deposition on a Ag coated polymer substrate; these results were obtained by fitting RTSE data using as free parameters those in an analytical expression having Drude (intraband electron), Lorentz (plasmon), and Tauc-Lorentz (interband) components.

182 Table 5.2 Oscillator parameters used to represent the Ag layer, Ag/ZnO interface layer, and the ZnO:Al layer obtained in studies of normal speed cassette roll-to-roll deposition of ZnO:Al on PEN/Ag at room temperature. All oscillator parameters are obtained from least squares regression analysis by fitting the corresponding ( data. The Ag and the Ag/ZnO interface layer thicknesses are the final thicknesses whereas the ZnO:Al thickness is the deduced saturated thickness at the monitoring point during the normal speed deposition, which is only about half-way through the deposition zone.

Layer inf Oscillator parameters db(Å) ds(Å) type Drude parameters CPPB parameters (= 0.5 fixed) Phase  (-cm)  (fs) A (eV)  (eV) E (eV) o 1.43± o ( ) Ag 3000 20 0.02 6.04± 0.57± 4.09± -38.72 3.64x10-6 15.75 0.04 0.01 0.02 ± 0.11 ±2.86 x 10-7 ±0.11 1.85± 1.27± 3.32± 32.40± 0.01 0.02 0.03 0.16 Drude parameters Lorentz/ Tauc-Lorentz parameters  (-cm)  (fs) A (eV)  (eV) E (eV) E (eV) Intf. o g 1.13± 7.26± 0.71± 2.78± Ag/ - 31 - 0.15 -6 0.53 0.21 0.58 ZnO 4.43x10 37.07 ±1.15 x 10-6 ±5.24 488.78 2.08± 3.5 3.48 ± 55.32 0.34 (fixed) (fixed) CPPB parameters (= 0.241± 0.001) Phase -4 A (eV)  (eV) E (eV) o 1.36± 8.43x10 3.82± o ( ) ZnO:Al 1210* 92 0.07 ±1.57x 10-5 0.07 4.21± 0.34± 3.77± -1.95 ± 0.07 0.01 0.01 0.14

incorporation of the interface layer between the bulk Ag and ZnO layers in the optical model.

Figure 5-7 shows the evolution of the ZnO effective thickness at the monitoring point during normal speed roll-to-roll deposition along with two of the three different simulation approaches as described in Section 5.2.1. The first simulation approach described in Section 5.2.1 is not shown in Figure 5-7. The second simulation approach

(broken line in Figure 5-7) is based on the ideal assumption that saturation must occur

183

Figure 5-6 Ag/ZnO interface layer thickness evolution during normal speed (0.0077 cm/s) roll-to-roll deposition of ZnO:Al layer on top of Ag coated polymer substrate based on RTSE data taken during ZnO:Al coating.

after web motion of x = xmax, or after an elapsed time of t = xmax/vp, since no deposition flux should reach beyond the line-of-sight between the target and the substrate. Unlike the first approach, however, the rate Ro is determined to achieve the experimentally observed saturation thickness, irrespective of when that thickness is reached. A saturation time longer than t = xmax/vp can result only under non-ideal conditions with deposition occurring beyond the line-of-sight limit. The third simulation approach (solid

184

Figure 5-7 Measured (points) and simulated (line) effective thickness evolution of the ZnO:Al layer during normal speed roll-to-roll deposition at 0.0077 cm/s on a Ag coated polymer substrate; the inset shows the thickness stability (in Å). The broken line simulation assumes saturation after a thickness of t = xmax/vp, but uses a deposition rate Ro consistent with the measured saturation thickness. The solid line assumes that saturation is possible at a time later than t = xmax/vp, which can occur only under non-ideal conditions with film deposition beyond the line-of-sight limit.

line) relaxes the line-of-sight condition, in essence neglecting the presence of the shutter altogether.

The observation of thickness stabilization in Figure 5-7 at a web position of 14 cm, or at a time of 1800 s (30 min), much longer than the line-of-sight prediction, implies that the deposition zone extends well beyond xmax (i.e., beyond point E in Fig. 5-2).

185 consistent with gas phase scattering, reflection, or re-emission of the deposition species.

Once the experimentally observed saturation point is reached, the deposition process is quite stable with a variation in the ZnO effective thickness (inset) of no more than 9 Å over a 2.5 cm span of the substrate from 15 to 17.5 cm. The high quality fit obtained using the third simulation method described in Section 5.2.1 suggests that, although the line-of-sight extends only to 7.5 cm due to the presence of the shutter, the flux accumulation on the substrate surface up to 14 cm is close to that predicted by ignoring the presence of the shutter altogether. This result is only possible as a result of non-line- of-sight effects in the deposition model such as gas phase scattering of the deposition species and possible reflection or re-emission of the species from the substrate, the shutter, and other internal components of the system. Such non-ideal effects will be discussed in greater detail in the later part of this section.

Observations similar to those of Figure 5-7 also hold for the reduced speed ZnO effective thickness evolution in Figure 5-8. In this case as well, the deposition stabilizes only after the web has travelled a length of ~ 14 cm, rather than the ideal deposition zone length of xmax = 7.5 cm, defined by maximum line-of-sight. In this case, only the third approach, as described in Section 5.2.1, is shown for the simulations. Once the web speed is increased to normal, the thickness is observed to fall off as would be expected based on the predicted evolution, and the final thickness matches the previous result of

~1200 Å as in Figure 5-7. This indicates that the deposition rate is quite reproducible upon stopping and restarting the sputtering plasma.

In order to account for the gas phase scattering, reflection, or re-emission of the depositing species, for both normal speed and reduced speed ZnO depositions, two

186

Figure 5-8 Measured (points) and simulated (line) effective thickness evolution for ZnO:Al during roll-to-roll coating of a Ag coated polymer substrate for reduced speed deposition at 0.0040 cm/s, followed by normal speed deposition at 0.0077 cm/s. The simulation assumes that a Lambertian deposition flux that falls off as the inverse-square with the distance from target to the flexible substrate, and neglects the presence of the shutter which would otherwise define a line-of-sight limit.

different simulation methods as described by the equations of Section 5.2 have been applied. Using these two methods, modifications to the line-of-sight, inverse-square variation are applied to in an attempt to understand the observations.

The first simulation method involves multiplying the deposition rate expression by a simple scattering term given by exp(r'/) according to Equation (5.4a). Here,  is a

187 mean free path of the deposition species and r' is the distance travelled by the species from the target to the flexible substrate. This approach required a value of  > 100 cm, however, for a reasonable fit of the thickness evolution data. Because this distance is larger than the size of the deposition chamber, this approach based on the simple exponential decay of the deposition species does not explain the gas phase scattering necessary to generate deposition beyond line of sight, i.e., for x > xmax.

The second simulation approach to describe the gas phase scattering of Section

5.2.1 is to consider the opening between the shutter and the substrate as the virtual source of the deposition flux for the substrate beyond the maximum line-of-sight position.

Equation 5.7 is the expression used to describe the flux due to this virtual source beyond x = xs = 5.3 cm. Figure 5-9 shows the ZnO:Al thickness evolution data for two depositions, a normal speed deposition and a normal speed followed by reduced speed deposition. The solid line simulation in Figure 5-9 assumes saturation at the line-of-sight between the ZnO:Al target and the substrate (at x = xmax = 7.5 cm), but also includes deposition beyond line-of-sight from the virtual source at the shutter position, x = xs = 5.3 cm. The Ro parameters for the real sources in each deposition are chosen such that the simulation fits the early film growth regime. In contrast, the parameters for the virtual source are chosen such that the simulation fits the later stage of the deposition.

The deviation of the prediction from the ellipsometry determined ZnO:Al layer thickness implies that the virtual source method developed here does not well simulate the gas phase scattering of the deposition species. This may result because other, more random, non-line-of-sight effects such as the reflection of deposition species from the internal chamber components are dominant over the contribution due to the localized

188

Figure 5-9 Measured (points) and simulated (line) effective thickness evolution for ZnO:Al during roll-to-roll coating of a Ag coated polymer substrate during normal speed deposition at 0.0077 cm/s and during reduced speed deposition at 0.0040 cm/s, followed by normal speed at 0.0077 cm/s. The simulation takes into account scattering of the incoming flux from the line-of-sight source to positions beyond the maximum at xmax = 7.5 cm. This scattering is simulated by considering additional deposition beyond xmax from a virtual source located at the shutter position (5.3 cm from the point on the substrate vertically above the ZnO:Al target).

virtual source. In fact, in this simulation there are two discontinuities in both normal speed and reduced speed simulations. These occur (i) at the position of the virtual source

(x = xs = 5.3 cm) and (ii) at the line-of-sight position (x = xmax = 7.5 cm). No such discontinuities are present in the data, indicating that the concept of the virtual source is too simple to explain the non-line-of-sight behavior of the deposition species.

189 The leading edge of the roll-to-roll deposited ZnO:Al film on the Ag coated PEN substrate at normal speed was analyzed ex-situ by mapping ellipsometry, and the results are presented in Figure 5-10. The horizontal axis is the direction along which the web was advanced during deposition. In the figure, the non-linear dependence of ZnO:Al effective thickness with distance is due to the variation in the deposition rate along the deposition zone within the chamber. The web with thinner ZnO:Al (at the left in Figure

5-10) not only remained within the deposition zone for a shorter time period, but was also located further away from the target, where the deposition rate was lower due to (i) the inverse square dependence, (ii) the Lambertian flux emission from the target, (iii) the increasing angle between the substrate normal and the line-of-sight to the target, and (iv) possible deposition species scattering at long target-to-substrate distances. On the other hand, the web toward the right with thicker ZnO:Al, spent increasing time closer to the target where the deposition rate is relatively higher. The flattening of the effective thickness towards the end (at the right in Figure 5-10), shows that the deposition is about to saturate since its position is > 16 cm from the leading end, which is greater in length than the line-of-sight deposition zone of 14.5 cm. The vertical axis is the width of the substrate, from which the edge-to-edge uniformity of the deposition can be evaluated. In this case, the bending of the contour lines across the vertical width of the substrateconfirms that its central portion is thicker compared to both edges, and this may be due to a slight sagging of the web, when it moves through the deposition zone.

190

Figure 5-10 Map of the effective thickness of ZnO:Al deposited at the normal speed of 0.0077 cm/s on Ag coated PEN starting from its leading edge at the left. The horizontal axis is the direction of web advancement in the deposition zone within the chamber, whereas the vertical axis is the width of the web from which the edge-to-edge uniformity of the deposition can be evaluated.

5.5 RTSE of i-layer Evolution on Ag/ZnO/n-layer Coated PEN

The growth of the i-layer film on Ag/ZnO/n-layer coated PEN polymer was analyzed using an i-layer dielectric function determined from the real time SE data at a thickness of ~200 Å. The i-layer dielectric function was obtained by multi-time analysis over a range of time points within which the i-layer thickness varies by 50 Å.

191 Also, the resulting dielectric function was smoothened by a Cody-Lorentz oscillator fit, in the same way as described in Chapter 3. The mathematical form of these oscillators are given in the Appendix. The dielectric functions from multi-time analysis and the corresponding Cody-Lorentz oscillator fit are shown in Figure 5-11. The resulting Cody-

Lorentz oscillator parameters are given in Table 5.3.

The band gap of the i-layer obtained in this analysis is 1.590 eV, which is a characteristic of the elevated substrate temperature. After deposition, the cell structure was measured at room temperature (20C) by SE. These ex-situ data were then fitted to determine the i-layer band gap, yielding 1.627 eV. This value is close to Cody's original determination of the band gap of 1.64 eV for PECVD a-Si:H prepared under a standard set of conditions (Cody, 1984). Using 4.2 x 104 eV/C as the band-gap temperature coefficient (Podraza et al., 2006), the true substrate temperature can then be calibrated as

(1.627  1.590)/(4.2 x 104 ) + 20C = 108oC, which closely matches the calibrated substrate temperature of 110oC, obtained from the shift in critical point energies of the c-Si wafer. Figure 5-12 shows the evolution of i-layer effective thickness at the monitoring point during normal speed roll-to-roll cassette deposition at 0.012 cm/s. The initial i-layer growth is modeled by considering an interface filling mechanism, in other words, a transition from n-layer surface roughness to n/i interface roughness (Koh et al.,

1995). One might expect that the interface filling mechanism can be applied generally to model film growth on any rough underlying surface. In the case of Ag/ZnO:Al interface formation, however, the situation is more complicated in that a new plasmon feature develops due to the change in screening that occurs when the interface forms. In the case

192

Figure 5-11 Real (upper) and imaginary (lower) parts of the i-layer dielectric function obtained by inversion (circles); also shown are the results of a model obtained by applying the Kramers-Kronig consistent Cody- Lorentz oscillator (lines).

193 Table 5.3 Oscillator parameters used to represent the underlying layers for the cassette roll-to-roll deposition of the i-layer on Ag/ZnO:Al/n-layer coated PEN polymer substrate appropriate for both normal and reduced speed depositions. The i-layer Cody-Lorentz oscillator parameters were obtained by smoothing the multi-time results obtained at ~ 200 Å bulk i-layer thickness whereas all other oscillator parameters are obtained from least square regression fits to single scan SE () data after each layer deposition at the corresponding deposition temperatures. The Ag/ZnO parameters, being least sensitive, are fixed to those obtained during ZnO:Al evolution from Table 5.2. The layer thicknesses other than i-layer are the final thicknesses whereas the i-layer thickness is the deduced saturated thickness at the monitoring point during the normal speed deposition, which is only about two-thirds through the deposition zone.

Layer  db ds inf Oscillator parameters material (Å) (Å)

Drude parameters CPPB parameters (= 0.5 fixed)

o  (-cm)  (fs) A (eV)  (eV) Eo (eV) Phase ( ) 1.06± Ag 3000 22 0.11 4.42± 0.39± 3.92± -82.77 ± 5.68x10-6 10.07 0.68 0.06 0.05 6.92 -7 ±2.23 x 10 ±0.04 3.19± 2.35± 4.27± 18.77± 0.04 0.05 0.04 2.09 Drude parameters Lorentz/ Tauc-Lorentz parameters *Intf.  (-cm)  (fs) A (eV)  (eV) E (eV) E (eV) Ag/ 1.13 o g 52 - ZnO 7.26 0.71 2.78 - 4.43x10-6 37.07 488.78 2.08 3.50 3.48

CPPB parameters (= 0.298 ± 0.039) 1.38± 5.41x10-4 4.35± o ZnO A (eV)  (eV) Eo (eV) Phase ( ) 3648 104 0.24 ±1.03 x 10-5 0.05 3.57± 0.45± 3.55± -0.463 ± 0.15 0.02 0.04 0.11

Cody-Lorentz oscillator parameters (Ep =1 eV, fixed) inf R A (eV) E (eV) (eV) E (eV) o g 1.12 70.13 3.93 2.82 1.565 n-layer 0.1 175 45 ± 0.15 ± 1.52 ± 0.26 ± 0.19 ± 0.137

1.42 69.17 3.89 2.57 1.590 i-layer 1 1962 22 ± 0.04 ± 0.45 ± 0.01 ± 0.03 ± 0.004

194

Figure 5-12 Evolution of the effective, bulk, and surface roughness layer thicknesses for the i-layer during normal speed roll-to-roll deposition at 0.012 cm/s on a Ag/ZnO:Al/n-layer coated polymer substrate. The filling volume fraction of the i-layer within the surface roughness of the n-layer is also shown (lower right); the volume fraction reaches 0.5 as the surface roughness on the n-layer transitions to n/i interface roughness.

of n/i interface formation, the 38 Å thick surface roughness on the n-layer before i-layer deposition consists of 0.5/0.5 n-layer/void. After the onset of deposition, the void is filled in by the i-layer material in about 30 s. During this time, the i-layer surface roughness increases to ~ 50 Å, indicating nearly conformal coverage of the n-layer by the i-layer. During bulk i-layer growth, the surface roughness on the i-layer decreases and stabilizes at ~25 Å, which is thinner than the starting roughness on the n-layer. Thus, i-

195 layer deposition has the capability of smoothening the surface of the stack, presumably as a result of the longer surface diffusion length associated with the film precursors in the deposition of a high quality i-layer. A longer surface diffusion length implies that roughness having spatial frequencies less than the diffusion length are suppressed, and it is this suppression that accounts for the smoothening effect, (Collins and Yang, 1989;

Podraza et al., 2006a; Kryukov et al., 2009).

In Figure 5-12, good agreement is observed between the measured and simulated thickness assuming a constant deposition rate. The measured effective thickness is slightly higher at the linear increase region due to the higher deposition rate during plasma ignition, which is performed at higher rf power and pressure than the steady-state values. Once the substrate length exposed to plasma ignition has passed the monitoring point, then the effective thickness has stabilized, and thus the simulation better matches the experimental result. The inset focuses on the stability of the steady state thickness value, which varies by no more than ~ 20 Å as 10 cm of the polymer substrate passes after the stabilization of thickness. Thus, the stability of PECVD per unit substrate travel for the i-layer (~ 2 Å/cm) is on the same order as that of magnetron sputter deposition for the ZnO:Al (~ 4 Å/cm; see inset of Fig. 5-6).

Similar behavior is observed for i-layer deposition at the reduced speed of 0.0086 cm/s. A reduced speed deposition has been performed to access the later part of the growth process at the monitoring point, as shown in Figure 5-13. The normal speed deposition that follows the reduced speed one, however, deviates substantially from the simulated result which assumes a constant deposition rate -- possibly different from that during reduced speed deposition due to the necessity of stopping and restarting the

196

Figure 5-13 Evolution of the effective, bulk, and surface roughness layer thicknesses for the i-layer during roll-to-roll deposition on a Ag/ZnO:Al/n-layer coated polymer substrate at a reduced speed of 0.0086 cm/s, followed by normal speed deposition at 0.0120 cm/s. The filling volume fraction of the i-layer within the surface roughness of the n-layer, starting from the onset of normal speed deposition, is also shown (lower right); the volume fraction reaches 0.5 as the surface roughness on the n-layer transitions to n/i interface roughness.

plasma. Initially, the substrate begins to move before the plasma is ignited so that the observed thickness drops below the steady state value. Once the plasma is restarted, however, the measured thickness ramps up due to the higher rate at plasma ignition, generated by the higher initial rf power and pressure settings. The plasma transient behavior in this region only disappears when the length of the substrate exposed to

197 plasma ignition crosses the monitoring point. The saturation thickness is then reached, which is 6.5% less (1940 Å) than the final thickness observed at the end of the normal speed deposition (2076 Å). The comparative plot of these two cases is shown in Figure

5-14.

The predictions of i-layer effective thickness evolution in both the normal speed and reduced speed depositions are based on the assumption of a uniform distribution of deposition species in the plasma across the area of the cathode plate. The predictions are also based on the assumption that no deposition occurs beyond the edge of the cathode plate. In other words, this model proposes that the deposition rate is constant across the length of the cathode and immediately drops to zero beyond its edges. In practice, however, reactive species do exist beyond the edges of the cathode and so the deposition zone is larger than the length of the cathode plate alone. In both normal speed and reduced speed depositions, the effective thickness rate is observed to saturate exponentially, rather than discontinuously, in reaching the steady state. This effect is modeled using Equation (5.9) for the exponential decay of the reactive deposition species in the plasma due to gas phase reactions, possible examples being SiH3 + H → SiH4, and

SiH2 + SiH4 → Si2H6. Assuming two different species whose fluxes decay at different rates, the equation used to fit the data is given by:

A x-- x   R A   x x    d Å 1963  1  exp o  o 1  exp  o b           ------(5.10) pp         

with best fit values of A = 0.53 Å/s, = 0.144 cm, Ro  A = 1.35 Å/s, and  = 0.91 cm, where vp = 0.012 cm/s is the speed of the web. The offset of 1963 Å is the i-layer

198

Figure 5-14 Effective i-layer thickness evolution during normal speed roll-to-roll deposition and during reduced speed followed by normal speed deposition; the substrate is Ag/ZnO:Al/n-layer coated PEN polymer. The final effective thickness for normal speed followed by reduced speed deposition is 6.5% less than the final thickness at the end of the normal speed deposition (1940 Å vs. 2076 Å).

thickness at x = 0 and the total deposition rate at x = 0 is Ro. The improved fit to the measured film thickness evolution of the i-layer is shown in Figure 5-15. The figure also includes the best fit assuming a model in which a single species decays outside the plasma zone (broken line). In this case the best fit offset is 1958 Å and the decay length

199

Figure 5-15 Measured and predicted thickness evolution for the i-layer in the neighborhood of the saturation region for the normal speed (0.012 cm/s) roll-to-roll deposition; the predictions are based on the exponential decay of one and two types of reactive species outside the cathode width.

is 0.69 cm. The improved fit using a model with two species may reflect the different hydride radicals of Si that are known to actively take part in the deposition and decay at different rates at the end of the deposition zone.

The decay of the reactive species beyond the cathode may be due to 1/x' 3 fall of rf electric field outside the cathode, as the cathode plate and the flexible substrate behave as

200 a parallel plate capacitor. Reactive species may be present if there is sufficient field to ionize the source gas in the regions beyond the width of the cathode plate. Alternatively, the species may arrive via gas phase transport as described by Equations (5.9) and (5.10).

The two species, whose fluxes decay at different rates, may be the different silicon hydride radicals, SiH2 and SiH3. Further work needs to be done as a function of gas flow ratio R = [H2]/[SiH4] and as a function of pressure, in order to understand the nature of the reactive species and their decay beyond the cathode width in the PECVD process.

The leading edge of the normal speed deposition of the i-layer on Ag/ZnO:Al/n- layer coated PEN was mapped ex-situ by spectroscopic ellipsometry, in the same way as was the ZnO:Al normal speed deposition on Ag coated PEN. These results for the i-layer are shown in Figure 5-16. The i-layer thickness on the map does not start from zero at the left because the web was mapped on its leading edge only within 13 cm of the saturation thickness (on the right). Because of the ex-situ nature of the experiment, complete oxidation of very thin layers may occur, and to avoid this complication, the very thin layer regime was not studied. The thickness variation with distance along the horizontal center line, i.e., along which the web advanced during deposition within the chamber, is linear and is similar to the real time SE result. This observation supports the assumption of a constant deposition rate within the deposition zone. In addition, the larger i-layer final thickness (~ 2650 Å) in Figure 5-16 compared to the saturation thickness observed in real time (~ 2075 Å in Figure 5-12) is due to additional deposition occurring after the monitoring point up to the end of the deposition zone in the chamber;

(see Figure 5-3). Similar results were observed for ex-situ mapping of normal speed deposition of the ZnO:Al on Ag coated PEN (see Figures 5-7 and 5-10).

201

Figure 5-16 Map of the effective i-layer thickness deposited at the normal speed of 0.012 cm/s onto Ag/ZnO:Al/n-layer coated PEN from its leading edge (left side) toward the saturation thickness (right side). The horizontal axis is the direction of web advance along the deposition zone within the chamber, whereas the vertical axis is the width of the web from which the edge-to-edge uniformity of the deposition can be evaluated.

In further consideration of the i-layer map in Figure 5-16, the vertical axis is the width of the web, from which the edge-to-edge uniformity of deposition can be evaluated. Similar to the ZnO:Al map, the central portion of the web is thicker compared with the edges, which may be due to a slight sagging of the web as it moves through the

202 deposition zone. In this case, sagging is more likely due to the higher temperature i-layer deposition (110oC) compared to the room temperature ZnO:Al deposition. The bending of the contour lines show the distribution of i-layer thickness non-uniformity across the width of the web. The features in Figure 5-16 leading to minima in the thickness across the width at web positions of  5.5 cm are attributed to holes in the cathode plate that enable the light beam to pass through for the real time SE measurements.

The surface roughness map given in Figure 5-17 shows that the i-layer is still smoothening until the center of the substrate is reached, where deff ~ 1800 Å, as measured from the left along its length. The optical band gap stabilization takes place beyond the center at a somewhat greater thickness (toward the right), as shown in Figure 5-18. In

Figure 5-18, the optical band gap distribution across the width of the web (vertical axis) shows that the band-gap is larger near the edges than in the central region. This effect can be attributed to the ellipsometry holes in the cathode plate in consistency with earlier results for the i-layer optical band gap distribution on rigid glass substrates (Huang et al.,

2010).

5.6 RTSE of p-layer Evolution on Ag/ZnO/n/i-layer Coated PEN

The growth of the p-layer film on Ag/ZnO/n/i-layer coated PEN polymer was analyzed using a p-layer dielectric function determined analytically from real time SE data at ~ 100 Å thickness. A Cody-Lorentz oscillator was used as the analytical expression for the dielectric function with the parameters of amplitude A, resonance energy E0, broadening , and transition energy Ep, all coupled to the band gap Eg, through relations similar to those given in the Appendix [Eqs. (A.24) - (A.31)]. In fact,

203

Figure 5-17 Map of the roughness thickness on the surface of the i-layer which was deposited at the normal speed of 0.012 cm/s onto Ag/ZnO:Al/n-layer coated PEN. The measurements were performed by ex-situ SE from the leading edge of the substrate. These results have been obtained from SE data analysis, together with the effective i-layer thickness map presented in Figure 5-16 and the optical band gap map presented in Figure 5-18.

the coupling relations applied in this case are slightly modified using the oscillator parameter temperature coefficients given elsewhere (Podraza et al., 2006). This modification accounts for the elevated deposition temperature of 108oC, a calibrated value deduced from the i-layer band-gap shift. Figure 5-19 shows the resulting dielectric function of the p-layer at the deposition temperature obtained from this Cody-Lorentz

204

Figure 5-18 Map of the optical band gap of the i-layer which was deposited at the normal speed of 0.012 cm/s onto Ag/ZnO:Al/n-layer coated PEN. The measurements were performed by ex-situ SE from the leading edge of the substrate. These results have been obtained from SE data analysis, together with the effective i-layer thickness map presented in Figure 5- 16 and the surface roughness map presented in Figure 5-17.

modeling procedure. The best fit band gap obtained in this analysis is 1.82 eV. Using

108oC as the true deposition temperature deduced from the band-gap shift of the i-layer, as described in the previous section, the p-layer band-gap at room temperature (20oC) is predicted to be 1.86 eV. This estimate is based on an assumed band gap shift with

205

Figure 5-19 Real (upper) and imaginary (lower) parts of the p-layer dielectric function as modeled by a Kramers-Kronig consistent Cody-Lorentz oscillator. The dielectric function is obtained at ~100 Å p-layer thickness at the normal web speed of 0.20 cm/s.

206 temperature of 4.2 x 104 eV/C. The oscillator parameters of all individual layers used in the analysis to obtain the thickness evolution of normal speed and reduced speed p- layer deposition are given in Table 5.4.

As in the case of data acquisition and analysis for the ZnO:Al and i-layer depositions, the evolution of a thin p-layer on Ag/ZnO:Al/n/i-layer coated PEN polymer has been studied at a normal speed of 0.20 cm/s, and at a reduced speed of 0.14 cm/s followed by a return to normal speed. The normal speed deposition produces a final p- layer thickness of ~ 130 Å at the end of the deposition zone whereas, at reduced speed, the same final thickness is reached instead at the monitoring point.

Table 5.4 Oscillator parameters used to represent the underlying layers for the cassette roll-to-roll deposition of p-layers on Ag/ZnO:Al/n/i-layer coated PEN polymer substrates, relevant for both normal and reduced speed p-layer depositions. The oscillator parameters for the underlying layers of the Ag, Ag/ZnO interface, and ZnO:Al layers are fixed as those given in Table 5.3. The Cody-Lorentz expression for the p-layer is obtained by coupling its parameters to the band gap parameter Eg for the calibrated substrate temperature of 108oC. The layer thicknesses other than the p- layer are the final thicknesses, whereas the p-layer thickness is the deduced saturated thickness at the monitoring point during the normal speed deposition, which is only about two-thirds of the distance through the deposition zone.

Layer Cody-Lorentz oscillator parameters db(Å) ds(Å) material inf R

A (eV) Eo (eV) (eV) Eg (eV) Ep (eV)

1.12 72.46 3.97 2.73 1.563 1.00 n-layer 0.1 188 38 ± 0.15 ± 1.34 ± 0.21 ± 0.17 ± 0.094 (fixed)

1.34 63.97 3.86 2.21 1.593 1.00 i-layer 1 2537 14 ± 0.09 ± 0.66 ± 0.02 ± 0.04 ± 0.003 (fixed)

1.12 1.820 ± p-layer 117.92 3.68 2.74 2.22 0.07 89 26 ± 0.23 0.023

207 Figure 5-20 shows the evolution of the effective p-layer thickness on

Ag/ZnO:Al/n/i-layer coated PEN polymer at the normal speed of 0.20 cm/s in roll-to-roll deposition. The i-layer thickness was fixed to the end value obtained from i-layer evolution. This result demonstrates the impressive capability of real-time spectroscopic ellipsometry in detecting such a thin p-layer and in determining its thickness evolution on top of an optically similar i-layer. The thickness evolution of the p-layer at the normal web speed is similar to that of the i-layer at normal speed with the difference being that

Figure 5-20 Evolution of the effective, bulk, and surface roughness layer thicknesses for the p-layer during normal speed roll-to-roll deposition at 0.20 cm/s on a Ag/ZnO:Al/n/i-layer coated polymer substrate. The filling volume fraction of the p-layer within the surface roughness of the i-layer is also shown (lower right); the volume fraction reaches 0.5 as the surface roughness on the i-layer transitions to i/p interface roughness.

208 the plasma transient is much more pronounced due to the significantly reduced p-layer thickness. The interface filling mechanism between the i-layer and the p-layer is also shown in Figure 5-20. In this case, the deposition begins with a surface roughness layer on the i-layer, consisting of 0.5/0.5 i-layer/void, and the void space is quickly filled in by p-layer material soon after the onset of p-layer deposition.

The p-layer deposition at reduced substrate speed followed by normal speed is shown in Figure 5-21. In all these p-layer depositions, the parameter Ro is selected so that the predicted thickness matches the final saturation thickness for each deposition.

The effective thickness in the second stage of deposition at normal speed in Figure 5-21 does not closely follow the simulation. In this case also, the deposition is ignited with a higher rf power and gas pressure. The initial movement of web before plasma ignition generates the first drop in effective thickness in the second stage of the deposition, and plasma ignition under conditions leading to an elevated deposition rate gives rise to the subsequent transient behavior. After the initial length of the substrate that is exposed to the plasma transient passes the monitoring point, the effective thickness stabilizes at the predicted value. Again, the final thickness after saturation (~100 Å) at the end of the normal speed stage is close to that obtained in the normal speed p-layer deposition of

Figure 5-20, indicating that the depositions are quite reproducible, even in the case of such a thin p-layer. For ease of comparison, the p-layer deposition at normal substrate speed and that at reduced speed followed by normal speed are shown together on the same plot in Figure 5-22.

It has been verified that there is no transient behavior if the plasma is ignited with the help of a hot filament at the operating pressure and rf power. Under these conditions,

209

Figure 5-21 Evolution of the effective, bulk, and surface roughness layer thicknesses for the p-layer on a Ag/ZnO:Al/n/i-layer coated polymer substrate during reduced speed roll-to-roll deposition at 0.14 cm/s followed by normal speed deposition at 0.20 cm/s. The filling volume fraction of the p-layer within the surface roughness of the i-layer is also shown, starting from the onset of reduced speed deposition (lower right); the volume fraction reaches 0.5 as the surface roughness on the i-layer transitions to i/p interface roughness.

the predicted thickness closely matches the measured thickness as shown in Figure 5-23.

The deviation from the predicted linear behavior in the later stages of the growth is due to the change in phase from an amorphous p-layer to a nanocrystalline p-layer. Although the dielectric functions of the amorphous phase does not well represent the nanocrystalline phase, the observed increase in rate is expected with such a transition.

210

Figure 5-22 Effective p-layer thickness evolution during normal speed roll-to-roll deposition and during the reduced speed deposition followed by normal speed deposition. The substrate is Ag/ZnO:Al/n-layer coated PEN. The final effective thickness of the deposition performed at reduced speed followed by normal speed is within 5 Å of the saturation thickness of the single normal speed deposition.

211

Figure 5-23 Evolution of the effective p-layer thickness on a Cr/Ag/ZnO:Al/n/i-layer coated polymer substrate during roll-to-roll deposition at 0.015 cm/s web speed, 110oC calibrated substrate temperature, 0.13 W/cm2 rf power with 2 sccm SiH4, 300 sccm H2 and 0.5 sccm B2H6 at 1.5 Torr chamber pressure. The plasma was ignited by a hot wire filament and, hence, unlike previous p-layer depositions, there is no initial transient. The deviation from the predicted thickness is due to phase changes from amorphous-to-(mixed-phase) and then to single-phase nanocrystalline Si:H.

5.7 Summary

Real time spectroscopic ellipsometry (RTSE) has been applied successfully to study the different layers of the thin film a-Si:H solar cell in roll-to-roll deposition. A normal speed deposition enables study of the nucleation and interface filling processes in

212 the deposition of interest, whereas the reduced speed enables study of the later deposition process that occurs beyond the monitoring point. Deviations of the thickness evolution of

ZnO:Al sputter deposition from predicted ideal, line-of-sight behavior are attributed primarily to gas phase scattering of sputtered species whereas deviations for both the i-layer and the p-layer depositions are attributed to plasma extension, or reactive species diffusion, beyond the cathode plate. Significant transients are also observed upon

PECVD plasma ignition, in particular for the thin p-layer. The latter are no longer observed when the full length of the polymer substrate exposed to plasma ignition crosses the monitoring point. These results suggest that real time analysis of the roll-to-roll deposition can assist in understanding the details of thin film growth and plasma processes and in optimizing these processes.

In this study as well, the uniformity of the normal speed deposition of the ZnO:Al layer and the i-layer have been characterized ex-situ using a mapping spectroscopic ellipsometer. Of particular interest is the uniformity of the film growth across the width of the polymer substrate. Both the ZnO:Al and the i-layer are observed to be slightly thicker in the central region, compared to the edges. In PECVD, deviations characterized by two minima in thickness as a function of web width are also observed due to the holes in the cathode plate. These holes are designed to enable the incident beam to reach the substrate and the reflected beam to reach the detector in the real time SE measurement.

213

Chapter 6

Correlations Between a-Si:H Solar Cell Performance and Structural/Optical

Properties

6.1 Introduction

Chapters 2 through 5 included a detailed discussion of the real time, in-situ, and ex-situ spectroscopic ellipsometry data collection and analysis techniques. Also discussed was the application of these techniques toward an understanding of thin film structure and optical properties for rigid as well as flexible substrates. In this Chapter, parameters deduced from the optical properties and microstructural evolution obtained from spectroscopic ellipsometry analysis are correlated with parameters that describe solar cell performance, also obtained for both rigid and flexible substrates. This effort is devoted to solar cells in the single junction n-i-p substrate configuration. All four solar cell performance parameters of short circuit current density (Jsc), open circuit voltage

(Voc), fill factor (FF), and power conversion efficiency () are considered in these correlations. Among these parameters, Voc depends most sensitively on the component layer phases at the top of the i-layer. Such correlations will serve as a guide for the fabrication of more efficient thin film Si:H based solar cells in multiple configurations.

214 In the scale-up of thin film photovoltaic (PV) technologies, however, it is critical to be able to reproduce the optimum device performance achieved on the laboratory scale when transitioning to larger area configurations on the industrial scale. In thin film PV technologies -- in particular for hydrogenated amorphous and nanocrystalline silicon

(a-Si:H and nc-Si:H), and Cu(In,Ga)Se2 (CIGS) -- significant differences exist between champion cells and modules (Green et al., 2012). One component of this difference relates to large area deposition uniformity. In the research laboratory, optimum a-Si:H and nc-Si:H i-layers of solar cells are prepared within narrow regions of deposition parameter space (Collins et al., 2003; Guha et al., 2003; Vetterl et al., 2000). First, the a-Si:H i-layer (Collins et al., 2003; Guha et al., 2003 ) and the p-layer (Koval et al.,

2002, Pearce et al., 2007) for a-Si:H solar cells are prepared under maximum H2 dilution conditions while avoiding nanocrystallite nucleation and coalescence, respectively, based on established concepts of protocrystallinity. Second, steady-state growth of nc-Si:H, in contrast, requires minimal H2 dilution while avoiding conversion to the amorphous phase

(Vetterl et al., 2000; Shah et al., 2003). It is a challenge to maintain such conditions over large areas, and this can account in part for the performance difference between laboratory cells and production modules. Thus, methods that map fundamental properties of PV materials over large areas and enable local correlations between these properties and device performance can be useful for understanding the uniformity issues that limit the device performance.

In the first studies, the structural parameters from RTSE generated phase diagrams for the i- and p-layers of solar cells fabricated on small area 2" x 2" borosilicate glass substrates were correlated with the solar cell performance parameters. In this case,

215 24 dot cells, each 5 mm square, were fabricated in 4 rows. The deposition conditions for these cells are given in Table 3.2 of Chapter 3. A statistical box and whisker plot was generated for all four solar cell parameters each as a function of the hydrogen dilution ratio R (R = [H2]/[SiH4]). These results will be presented in Section 6.2. In addition, solar cells were fabricated on larger area 6" x 6" borosilicate glass substrates as a closer simulation of the production scale. In this case, a total of 256 dot cells, 5 mm square, were fabricated in a 16 x 16 format. The details of the deposition conditions for these larger size substrate plates are provided in Section 6.5. Finally, 5 mm x 5 mm square dot cells were also fabricated on flexible Kapton® substrate and the corresponding status of these solar cells is presented.

After solar cell fabrication, the 6" x 6" substrate plate was mapped using an ex- situ spectroscopic ellipsometer based on multichannel detection (Huang et al., 2010). A description of mapping spectroscopic ellipsometry is given in Chapter 2. The individual measurements of the map have been performed adjacent to each dot cell, and the solar cell performance parameters have been correlated with the corresponding ellipsometry analysis parameters, including i-layer thickness, i-layer band gap, p-layer thickness, p- layer band gap, and p-layer surface roughness thickness. This capability is possible because SE data analysis has become increasingly advanced through the use of analytical expressions that reduce the number of free parameters required in the analysis (Ferlauto et al., 2002; Rovira et al., 1999) so that even very rough surfaces, such as those in actual

PV devices, can be probed (Rovira et al., 1999). It is the first time that this property- performance correlation methodology has been applied to a-Si:H solar cells. This first

216 demonstration of the methodology results in expected and unexpected relationships between local material properties and solar cell performance.

6.2 Optical Properties of i-layer and p-layer Materials

An important goal in Si:H photovoltaics technology is to develop new deposition methods or approaches that can be applied to fabricate Si:H materials with improved electronic properties. The optimized electronic properties of the absorber i-layer are those that maximize the performance parameters of the solar cell device, typically the product of fill factor and Voc in the stabilized state. The i-layer of the Si:H based n-i-p solar cell, acting as the photon absorber layer, is the only source of photocurrent in the solar cell.

Thus, with a knowledge of the optical properties of the optimized Si:H i-layer and its optimum thickness, along with the corresponding information for all other layer components of the stack, the quantum efficiency and Jsc can be predicted based on the assumption that, for optimized electronic properties and thickness, all electrons and holes photogenerated in the i-layer are collected. Generally, the electronic property and thickness optimization in terms of fill-factor and Voc is done first, and then approaches, for example a thickness increase trade-off, light trapping, or multijunctions are developed to enhance the collection and Jsc, since the best materials electronically are inevitably not the best materials optically.

The structural evolution and optical properties of the Si:H i-layer in the PECVD process are closely related to the electronic properties and defect density, with the latter two being optimized by varying the critical deposition parameters. Thus the structural

217 evolution and optical properties can be used as fingerprints of high solar cell performance, as will be described in the succeeding sections.

The top p-layer, which acts as the window layer in thin film Si:H solar cell, is equally important for the optimization of solar cell performance. In this case the doping, which induces a Fermi level shift, and the optical properties are critical. The p-layer doping should induce a large shift of the Fermi level from the center of the band gap toward the valence band in order to optimize the open circuit voltage (Voc). The p-layer should form a good i/p interface in order to maintain the field within the i-layer, and should be thin with a large band gap in order to allow the solar irradiance to pass through it for maximum absorption in the i-layer.

It has been reported that the best solar cell performance is obtained with protocrystalline i-layers (Collins et al., 2003; Wronski and Collins, 2004). The proposed reason is that these are the most ordered amorphous layers with essentially complete passivation of dangling bonds. Thus, there are low recombination losses and also low degradation due to light induced defect generation (Staebler and Wronski, 1977).

Minimization of recombination losses has a significant impact on cell performance by increasing the fill factor (FF) as a result of reduced voltage-dependent collection, meaning that the generated holes, the lowest mobility carrier, can drift to the top electrode irrespective of the forward bias below Voc. As a result, the short circuit current

(Jsc) is also increased due primarily to the increase in quantum efficiency in the red side of the spectrum, where the light can be most deeply absorbed.

Initially protocrystalline p-layers (Koval et al., 2002; Rovira et al., 2000) were also reported as optimum. More careful studies (Pearce et al., 2007), however, revealed

218 the presence of a small fraction of isolated crystallites in the upper part of the optimum p-layers that appeared incidental to the high performance. It can be concluded that protocrystallinity of the i-layer and p-layer near the i/p interface leads to the optimized solar cell performance.

The optical properties of the amorphous i- and p-layers obtained by fitting the

RTSE data were described in Chapter 3. The i-layer optical properties were measured at a true deposition temperature of 200oC. The RTSE data were fitted by multi-time analysis, centered at a bulk i-layer thickness of 200 Å. The inverted amorphous i-layer optical properties from multi-time analysis for a given hydrogen dilution R were smoothed by using the Cody-Lorentz oscillator expression. Figure 6-1 gives an example for an amorphous silicon i-layer deposited with R =10. In fact all the Cody-Lorentz oscillator parameters have been presented previously in Table 3.4 of Chapter 3. The band gaps of all the i-layers, often referred to as the Cody gaps, are plotted in Figure 6-2 as a function of the hydrogen dilution ratio R used in the i-layer deposition. In this figure, the band gaps of the i-layers deposited at R= 5, 10, and 15 show a linearly increasing trend with R. The trend appears to saturate, however, in the range of R =15 - 25. Above R =

25, an abrupt step to increasing band gap is observed; the gap then remains constant for R

= 30 - 40.

The increase in a-Si:H band gap with the increase of R is due to the alloying effect of the amorphous Si matrix by hydrogen atoms. Higher R suggests that more hydrogen atoms are incorporated that relax the strain in the network. The flattening of the band gap at R = 15 may be due to the first appearance of nanocrystals which could result in stronger absorption near the band edge of a-Si:H. Smaller nanocrystals, although subject

219

Figure 6-1 Real (upper) and imaginary (lower) parts of the dielectric function for an amorphous Si:H i-layer at 200C deposited at R =10. These results were obtained by multi-time analysis at ~ 200 Å bulk i-layer thickness (circles). The fit result using the Cody-Lorentz oscillator expression (lines) is also shown.

220

Figure 6-2 Band gap energy (Cody gap) with confidence limits plotted versus the hydrogen dilution ratio R for i-layers deposited on Cr/Ag/ZnO/n-layer coated glass substrates. Band gap information was extracted from the first ~ 200 Å of bulk layer deposition with a true substrate temperature of 200°C.

to quantum size effects, may exhibit this behavior due to a higher oscillator strength for indirect transitions. The abrupt increase in band gap beyond R = 25 may be due to the development of a nanocrystalline phase of larger grain size in the first 200 Å of the bulk i-layer relative to that at R = 25. With the increase in grain size, indirect absorption weakens significantly, leading to an apparent increase in the band gap. This latter

221 explanation is supported by the decrease in the broadening parameter from the i-layer optical properties (to ~ 2.5 eV) beyond R = 30 observed in Table 3.4, an effect which could also indicate an increase in grain size of the nanocrystalline component. It should be noted that the band gaps, or more precisely the Cody gaps, of the i-layers given in

Table 3.4 were obtained at a calibrated deposition temperature of 200oC, and so all those band gap values should be increased by (0.00042 eV/C)(200C20C) = 0.076 eV

(Podraza et al. 2006) in order to obtain the corresponding room temperature values.

The variation in the p-layer band gap (or Cody gap) as a function of the hydrogen dilution ratio R at a true deposition temperature of 100C has been obtained in a similar manner as the variation of the i-layer band gap with R at 200C. The p-layer values are plotted in Figure 6-3 and also given in Table 3.6 in Chapter 3. Since the p-layers were deposited to only ~ 120 Å, the optical properties of all p-layers that remain amorphous throughout the deposition process were extracted toward the end of the process by multi- time analysis. For the the p-layers above R = 125, a mixed phase transition is observed at a very early stage of the deposition. Hence the amorphous film optical properties required to develop the p-layer phase diagram for all higher hydrogen dilution depositions (R >125) assume the same amorphous Si:H optical properties as those obtained at R = 125. As before, these optical properties are smoothed by using the Cody-

Lorentz oscillator expression.

From Figure 6-3, it is clear that the p-layer band gap (or Cody gap), similar to that of the i-layer, increases with the increase in R and reaches its maximum value when it is in the dominantly protocrystalline phase. A larger band gap of the p-layer, being a window layer, is desirable for improved solar cell performance, assuming the desirable

222

Figure 6-3 The band gap energy (or Cody gap) with its confidence limits plotted as a function of the hydrogen dilution ratio R for amorphous p-layers deposited on Cr/Ag/ZnO/n/i-layer coated glass substrates at a true substrate temperature of 100oC. Band gap information for each amorphous p-layer deposited at R values up to R = 125 was extracted by determining the Cody-Lorentz parameters towards the end of the ~ 120 Å p-layer deposition. At higher hydrogen dilution ratios (R > 125), the p-layer transitions to mixed-phase Si:H at a very early stage of the deposition. For this series, the amorphous Si:H dielectric function obtained at R = 125 was used to study the phase transitions of all higher R depositions.

223 electrical properties are maintained. The reason is that photons with energy less than the p-layer band gap are transmitted through it without absorption, and thus with an increase in this band gap, a larger fraction of the solar photons are absorbed in the i-layer. As a result, the short circuit current (Jsc) of the solar cell is higher compared to that of a cell with a lower band gap p-layer. Moreover, the wide band gap protocrystalline p-layer forms a better p/i interface with the i-layer below it, which then significantly reduces the concentration of recombination centers in the junction region, and hence, increases the open circuit voltage (Voc). Correlations of the solar cell performance parameters with the deposition phase diagrams of the i-layer and p-layer will be presented in Sections 6.3 and

6.4, respectively.

6.3 Correlation of the Parameters of Solar Cells Deposited on 2" x 2"

Borosilicate Glass Substrates with the i-layer Phase Diagram

The parameters of solar cells in the Cr/Ag/ZnO/n/i/p/[In2O3:Sn (ITO)] configuration incorporating i-layers deposited with increasing R values are compared to the i-layer phase diagram obtained in Chapter 3. Figure 6-4 displays the variations of open circuit voltage (Voc), short circuit current (Jsc), fill factor (FF), and efficiency () as functions of the i-layer hydrogen dilution ratio R. Figure 6-5 (top) is the i-layer phase diagram that has been developed on the basis of real time spectroscopic ellipsometry

(RTSE) analysis as described in Chapter 3.

From the device performance shown in Figure 6-4, the highest Voc and efficiency

() correspond to the deposition with a hydrogen dilution ratio of R = 15. At this R value, the film appears to be amorphous throughout the entire ~3000 Å film thickness, as

224 shown in Figure 6-5 (top). The rapid decrease in Voc and efficiency at hydrogen dilution ratios  15 is attributed to the development of a nanocrystalline component of low volume fraction within the topmost region of the i-layer film. This component is not detected by RTSE studies of i-layer growth on Cr/Ag/ZnO/n-layer, but only appears through its effect on Voc. Hence, the single-step deposition process for the best single- junction amorphous silicon solar cell is that with R = 15. In fact for this series, the optimum efficiency cannot be identified on the basis of the phase diagram developed by

RTSE analysis of i-layer growth on the Cr/Ag/ZnO/n-layer structure; only the solar cell itself displays the required sensitivity to identify the optimum. The reason for this loss of sensitivity of the RTSE generated phase diagram will be discussed later in this subsection.

Figure 6-4 shows that the fill factor (FF) at the R value that leads to an optimum efficiency single junction solar cell (R = 15) is about 13% less than the maximum value at

R = 25, whereas the fill factor at R = 20 is intermediate between those at R = 15 and R =

25. This result implies that, even though the i-layer deposited at R = 15 is the most ordered protocrystalline Si:H at the i/p interface, leading to a maximum Voc of 0.91 V, the bulk component of the i-layer is not optimized and leads to a lower FF. If one attempts to increase R to 20, and even to 25, for improved FF as a bulk (sub-surface) i-layer effect, the improvements sought are overcome by losses in Voc. The reduction in

Voc to 0.5 V at R = 25 is consistent with the almost complete coalescence of nanocrystals with fnc ~ 0.8 at the top of the i-layer adjacent to the i/p interface, as indicated by the phase diagram of Fig. 6-5 (top).

225

Figure 6-4 Open circuit voltage (Voc, upper left panel), short circuit current (Jsc, upper right panel), fill factor (FF, lower right panel), and the efficiency (, lower left panel) versus the i-layer hydrogen dilution ratio R for rf PECVD single junction solar cells deposited on Cr/Ag/ZnO coated borosilicate glass.

Returning to the phase diagram shown in Figure 6-5 (top), it is interesting that this diagram cannot explain the drop in the open circuit voltage Voc at R = 20, since there is no indication of an amorphous-to-(mixed-phase) transition within the first 3000 Å of the

R=20 i-layer deposition. A low volume fraction of nanocrystals may have formed at the i/p interface at R = 20, however, but not observed due to the reduced sensitivity to the roughening transition, which is given the designation a → (a+nc) in Figure 6-5 (open

226 circles). A reduced sensitivity may result when deposition occurs on the relatively rough n-layer on Cr/Ag/ZnO coated glass. In fact, the roughness on the n-layer surface, ~ 32 Å in thickness, induces a similar amount of roughness on i-layer. If the additional roughness thickness induced by the surface nanocrystals at R = 20 is less than 32 Å by the end of deposition, then the a → (a+nc) roughening transition may not be detected.

In order to evaluate this hypothesis, two different i-layers were deposited on smooth native oxide coated crystalline silicon (c-Si) substrates. One was deposited with

R = 20 directly on the c-Si substrate, and the other was deposited with R = 20 on an n-layer coated c-Si substrate. Figure 6-6 shows the surface roughness evolution for these two i-layers on the c-Si substrate, with and without the intervening n-layer. Both data sets clearly show the roughening transition as an indication of the amorphous-to-(mixed- phase) [a → (a+nc)] transition at thicknesses below 3000 Å. For the deposition directly on the c-Si wafer, the a → (a+nc) transition occurs at ~ 1000 Å, and 32 Å roughness thickness is reached after ~ 2000 Å. For the deposition on the c-Si/n-layer structure, which is more relevant for the full solar cell stack, the a → (a+nc) transition occurs at

~2000 Å, and 32 Å of roughness is reached after 7500 Å, thus demonstrating the clear substrate dependence. It is evident that for the R = 20 deposition performed directly on c-Si, the nucleation density is much higher than for the deposition performed on the c-Si/n-layer, and for the latter, no significant roughening occurs in the 1000 Å after the transition. Thus, the results for the c-Si/n-layer substrate structure using the same deposition conditions and substrate layer as the phase diagram of Fig. 6-5 (top) provide much higher sensitivity to the a → (a+nc) transition. The results of Fig. 6-6 (lower panel) indicate that the top portion of the Si:H i-layer at R = 20 on Cr/Ag/ZnO/n-layer coated

227

Figure 6-5 (Top) Phase diagram for rf PECVD of single-junction thin film Si:H i-layers deposited on Cr/Ag/ZnO/n-layer coated borosilicate glass. These results deduced by RTSE suggest that the optimal one-step deposition process that assures the protocrystalline i-layer throughout the deposition occurs near the hydrogen dilution ratio R = 20.

228 (Bottom) Phase diagram as in the top panel, but including a data point at R = 20 obtained using a smoother c-Si/n-layer substrate for higher sensitivity to the a → (a+nc) transition. These results suggest that a small volume fraction of crystallites are likely to be present at the top i-layer surface for R = 20 in the case of the Cr/Ag/ZnO/n-layer coated borosilicate glass substrate structure, although not detected by RTSE due to the thicker starting roughness on the over-deposited i-layer. The fact that the highest performance solar cell is obtained at R = 15, however, supports this suggestion.

glass has undergone the a → (a+nc) transition, and the drop in Voc in Fig. 6-4 is now explained. Hence, it can be concluded that R = 15 is the maximum hydrogen dilution that results in the protocrystalline i-layer throughout the first 3000 Å of i-layer thickness on the Cr/Ag/ZnO/n-layer coated borosilicate glass at 800 mTorr pressure, 0.033 W/cm2 power, and 200oC substrate temperature. A revision to the phase diagram is shown in

Figure 6-5 (bottom panel) that includes the new information from Figure 6-6 (bottom panel).

It is possible that a three-step deposition procedure can be implemented, using the phase diagram and the solar cell results given in Figures 6-4 and 6-5 in order to improve device performance above the current optimum by avoiding the deterioration caused by the nanocrystalline phase at the i/p interface. For example, the peak in the fill factor (FF) at R = 25 suggests that a majority of the intrinsic layer bulk material can be deposited at this dilution level to obtain a favorable fill factor. After this first step, the fill factor optimizing layer can then be overdeposited with a second-step “memory-erasing” layer that would suppress the development of nanocrystallite nucleation sites. Finally in a third step, the top-most i-layer component could be deposited with an even higher hydrogen dilution level, but with a thickness small enough to avoid the transition from

229

Figure 6-6 Surface roughness evolution of i-layers deposited on a c-Si wafer (top) and on an amorphous n-layer coated c-Si wafer (bottom) at a hydrogen dilution ratio of R = 20. Both figures show the amorphous-to-(mixed- phase) transition in the 1000-2000 Å bulk i-layer thickness range.

230 amorphous to mixed-phase. Utilization of such a three-step deposition routine could provide a better single-junction thin film silicon solar cell with (i) quality bulk material as reflected through the optimization of the fill factor and (ii) a superior i/p interface as reflected through the optimization of Voc. Additional details of this proposal for a three- step i-layer are provided later in this subsection.

In fact, rather than addressing this three-step process, a simpler two-step process was attempted. First a bulk i-layer with thickness ~ 2000 Å was deposited on an amorphous n-layer at R = 25, followed by an additional 1000 Å at R =15. The efficiency of such a solar cell fabricated with a two-step i-layer was improved relative to the cell with the single-step cell i-layer deposited at R = 25 (4.5% vs. 4.0%). For the two-step i- layer, Voc increased to 0.59 V from 0.52 V; however, the fill factor decreased to 72%

2 from 74%, whereas Jsc remained essentially unchanged at 10.5 mA/cm . This result suggests that the R = 15 layer grows differently on an R = 25 layer as compared to an n- layer. The key effect is a significant fraction of nanocrystalline component on top of the

1000 Å layer deposited at R = 15. Based on this result, improved cell performance may be expected by varying the two component layer thicknesses in an optimization procedure to ensure that no crystallites are present at the top surface of the i-layer.

Alternatively, as described previously the three step process can be explored. In this process, the R = 15 layer can be replaced by a thin lower hydrogen dilution layer (at

R = 1 or R = 5) to rapidly suppress nanocrystalline growth on top of the bulk i-layer at R

= 25. Another i-layer can then be deposited on top of the lower dilution layer to the desired final thickness, but at even higher dilution, ensuring that the amorphous phase is obtained at the top of the i-layer. The over-deposition at higher dilution would be

231 designed to optimize Voc without significantly decreasing fill factor. With the short circuit current Jsc remaining essentially unchanged, the overall efficiency is expected to improve with this three-step approach.

6.4 Correlation of the Parameters of Solar Cells Deposited on 2" x 2"

Borosilicate Glass Substrates with the p-layer Phase Diagram

In this subsection, the p-layer phase diagram reported in Chaper 3 is correlated with the performance of solar cells fabricated with a fixed p-layer thickness of 120 Å and a range of p-layer hydrogen dilution ratios. Figure 6-7 displays the open circuit voltage

(Voc), short circuit current (Jsc), fill factor (FF), and efficiency () as functions of the hydrogen dilution ratio, R. Figure 6-8 is the phase diagram of the p-layer deposited on

Cr/Ag/ZnO/n/i-layer coated borosilicate glass, obtained from RTSE data analysis as described in Chapter 3. Since the p-layer is very thin compared to the i-layer, the effect of p-layer thickness on solar cell performance is more critical than that of the i-layer thickness, and in this study the p-layer was controlled by RTSE to a thickness of 120 Å.

The open circuit voltage (Voc) shows a clear peak at R = 150, whereas the cell efficiency increases and flattens at R = 125 and above. The drop in Voc and fill factor above R =

150 is due to the formation of nanocrystals within the bulk of the p-layer and near the i/p interface. The accompanying increase in Jsc, however, leads to a rather flat efficiency with increasing R above R = 150. The increase in Jsc is due to the higher transmittance of the predominantly nanocrystalline p-layer. This increase can ensure a relatively flat efficiency as a function of R because the decreases in Voc and fill factor due to nanocrystallite development near the i/p interface are not large. In contrast, when

232

Figure 6-7 Open circuit voltage (Voc, upper left panel), short circuit current (Jsc, upper right panel), fill factor (FF, lower right panel), and efficiency (, lower left panel), each plotted versus the p-layer R value for rf PECVD single- junction n-i-p solar cells deposited on Cr/Ag/ZnO coated borosilicate glass.

nanocrystals develop at the i-layer side of the i/p interface, the loss in efficiency due to large drop in Voc cannot be overcome by an accompanying increase in Jsc. In conclusion, the 120 Å p-layer deposited at 100oC substrate temperature, 1.5 Torr pressure, and 0.066

W/cm2 rf plasma power gives the best solar cell performance at R = 150. At this dilution level, the product of Voc and fill factor are optimized, whereas Jsc should be increased

233

Figure 6-8 Phase diagram for rf PECVD of thin film Si:H p-layers deposited on Cr/Ag/ZnO/n/i-layer coated borosilicate glass substrates. From the figure, it is clear that the p-layer deposited at R = 150 is protocrystalline in the first 80 Å.

further through possible reduction of the p-layer thickness under these conditions and development of a back-reflector. Thus, as was concluded for the solar cell i-layer, the most ordered protocrystalline p-layer at the i/p interface yields the best solar cell performance. In the case of the p-layer, a small volume fraction of crystallites at the contact to the ITO is evident, but it is not clear if these are incidental or critical to the performance. Overall, the results of this thesis research are consistent with the earlier

234 findings that the best solar cell performance derives from a protocrystalline p-layer, paired with an adjacent protocrystalline i-layer (Koval et al., 2002).

6.5 a-Si:H Solar Cell on 6" x 6" Borosilicate Glass Substrate

A thin film single junction a-Si:H n-i-p solar cell stack has been fabricated onto

6" x 6" borosilicate glass in the Cr/Ag/ZnO/n/i/p/[In2O3:Sn (ITO)] configuration using standard plasma-enhanced chemical vapor deposition (PECVD) for the Si:H layers and magnetron sputtering for the metal and transparent conducting oxide (TCO) contact layers. The cell configuration is the same as that of the 2" x 2" glass substrates. The deposition parameters of all layers are given in Table 6.1. For the i-layer, the nominal substrate temperature and H2 dilution ratio were 200C and R = [H2]/[SiH4] = 15, respectively, whereas for the p-layer, the corresponding values were 100C and R ~ 250.

As in the case of the 2" x 2" glass substrate, all layers were deposited without vacuum breaks, with the exception of the final ITO deposition. The ITO top contact was deposited by inserting a stainless steel shadow mask incorporating a 16 x 16 array of 5 mm square openings to finalize the small-area PV devices. As described earlier, the Cr in this stack serves as an adhesion promoting layer for the back-reflector on glass. The Ag layer was deposited under smooth surface roughness conditions in this initial study in order to correlate mapping SE results and device performance with minimal additional complications. As a result, the device performance and structural parameters in this first study are relevant for specular devices not optimized for light trapping and optical enhancement.

235 Table 6.1 Deposition conditions of the individual layers of the hydrogenated amorphous silicon (a-Si:H) based solar cell structure consisting of Cr/Ag/ZnO/n/i/p layers on a 6" x 6" borosilicate glass substrate.

Gas flow (sccm) Plasma Intended Layer T P o power Thickness Ar 5% SiH4 5% 5% H2 material ( C) (mT) 2 (W/cm ) (Å) O2 B2H6 PH3 in Ar in H2 in H2

Cr RT 5 0.92 2000 10 x x x x x

Ag RT 5 0.92 5000 10 x x x x x

ZnO RT 5 0.92 3000 10 x x x x x

n 200 350 0.0095 200 x x 10 x 1 x

i 200 800 0.032 3000 x x 5 x x 75

p 100 1500 0.064 100 x x 2 0.5 x 500

ITO 150 4 0.58 600 10 3 x x x x T: substrate temperature (oC); RT: room temperature; P: deposition pressure (mTorr)

The ex-situ mapping spectroscopic ellipsometry (SE) measurements were performed over a grid pattern covering the deposition area. The experimental details of mapping SE have been presented in Chapter 2. For simplicity, mapping points avoided the ITO dot cells so that the top layer in the measurement and analysis was the Si:H p-layer surface roughness component. The mapping ellipsometry data were analyzed by using the earlier Ag, Ag/ZnO interface, and ZnO parameterized optical properties from

Table 3.4, obtained in depositions on 2" x 2" substrates. These optical properties also work well for the larger 6" x 6" substrate, the reason being that the deposition parameters for the sputter depositions were the same for the two substrate sizes. The ZnO thickness,

236 however, is allowed to vary while fitting the mapping SE data for the 6" x 6" substrate.

In the optical model, the thin n-layer is considered as the part of the thick i-layer, i.e., is assigned the same optical properties since the light beam, having transmitted through the p- and i-layers, cannot provide the ability to detect the weak optical contrast between the i-layer and the n-layer.

Figures 6-9(a-d) show maps of solar cell performance over the center ~ 5" x 5" area of the 6" x 6" glass plate coated by the Cr/Ag/a-Si:H-(n-i-p) structure. The clearest spatial patterns are observed in the open circuit voltage (Voc) and short circuit current

(Jsc). The fill factor (FF) and overall device efficiency () show more complexity and variability over the mapped area. Figures 6-10(a-b) show maps of the i- and p-layer thicknesses over the same 5" x 5" area of the solar cell stack, whereas Figure 6-10(c) shows the corresponding results for the p-layer surface roughness thickness, which provides information pertaining to the relative crystallite content. In fact, the nucleation, growth, and coalescence of nanocrystals under these high H2 dilution conditions (R ~

250) lead to crystallites protruding from the surface that contribute to the p-layer surface roughness variations. The optical band gap maps for the a-Si:H i-layer and the Si:H p- layer are shown in Figures 6-11(a-b), as obtained by a Cody-Lorentz oscillator parameterization (Ferlauto et al., 2002).

Different non-uniformity patterns are seen in the basic property maps of Figures

6-10 and 6-11. The a-Si:H i-layer thickness pattern reflects the power coupling into the plasma and associated effects due to field fringing at the electrode edges. The Si:H p-layer thickness effect is apparently due at least in part to the gas flow pattern in the chamber. A thicker p-layer on the right side of the substrate appears correlated with a

237 (a) Voc (b) Jsc

Figure 6-9 Maps of n-i-p a-Si:H solar cell performance parameters of (a) open circuit voltage, Voc; (b) short circuit current, Jsc; (c) fill factor, FF; and (d) power conversion efficiency, measured from a total of 246 operating dot cells 0.25 cm2 in size over an area of 5 x 5 inch2. The substrate of the n-i-p solar cell consists of borosilicate glass coated with a specular Cr/Ag/ZnO back-reflector/electrical-contact multilayer structure.

238 (a)

(b)

(c)

Figure 6-10 Maps of thicknesses of the (a) a-Si:H bulk i-layer, (b) Si:H bulk p-layer, and (c) Si:H p-layer surface roughness over a 5 x 5 inch2 area of an n-i-p solar cell structure on a Cr/Ag/ZnO back-reflector/electrical-contact layer stack.

239 (a)

(b)

Figure 6-11 Optical band gaps of the (a) a-Si:H i-layer and (b) Si:H p-layer over the 5 x 5 inch2 area of an n-i-p solar cell structure on a Cr/Ag/ZnO back- reflector/electrical-contact layer stack.

smaller surface roughness thickness, indicative of a more compact film on the right side as compared to the left. Because the gas flow is from left to right, we interpret this compact material as more highly coalesced (i.e., smoother) nanocrystalline Si:H since

SiH4 depletion is likely to occur as the gas flows from left to right, in effect leading to a

240 locally increasing R value. In contrast, on the left, contacted but not fully coalesced crystallites exist with a rougher surface and a larger volume fraction of a-Si:H. The p-layer behavior in Figures 6-9(b-c) may also result from the possibility that a thicker i-layer on the right side may itself exhibit near-surface nuclei that promote p-layer nanocrystal nucleation preferentially on that side. The larger optical band gap of the p- layer material may arise from the shift in near band edge (~2.0 3.0 eV) absorption when the material transitions from the amorphous phase to a larger grain nanocrystalline phase

(Collins and Ferlauto, 2005a). Finally, the smaller circular patterns in Figures 6-10(a-c) are generated by holes in the cathode plate that enable a light beam to pass through for

RTSE monitoring. These openings can be closed for device studies, but in this case they lead to greater basic property non-uniformity, useful for this demonstration.

Figures 6-12 – 6-15 show correlations of the performance parameters for the 246 operating dot cells given in Figures 6-8(a-d) with the material property parameters for the i- and p-layers, as determined by ex-situ SE and given in Figures 6-10 and 6-11. Figure

6-12 shows correlations of the i-layer thickness with Voc, Jsc, FF, and efficiency; Figure

6-13 provides correlations of Voc and efficiency with bulk p-layer thickness and surface roughness layer thickness; and Figures 6-14 and 6-15 illustrate correlations between device properties and the i- and p-layer optical band gaps. The broad distribution in the device performance parameters for a fixed material property value originates from the fact that other properties are varying. Thus, the approach is combinatorial over relatively narrow ranges of the material property values. Of interest are the upper limit envelopes shown as solid lines and describe the maximum performance parameter for a given basic property value.

241

Figure 6-12 Solar cell performance parameters (Voc, Jsc, FF, efficiency) correlated with i-layer thickness for the 5 x 5 inch2 area of an n-i-p solar cell structure on a Cr/Ag/ZnO back-reflector/electrical-contact layer stack.

242

Figure 6-13 Solar cell parameters (Voc, efficiency) correlated with the p-layer bulk thickness (top) and surface roughness layer thickness (bottom) for the 5 x 5 inch2 area of an n-i-p solar cell structure on a Cr/Ag/ZnO back- reflector/electrical-contact layer stack.

243

Figure 6-14 Solar cell performance parameters (Voc, Jsc, FF, efficiency) correlated with i-layer optical gap for the 5 x 5 inch2 area of an n-i-p solar cell structure on a Cr/Ag/ZnO back-reflector/electrical-contact layer stack.

244

Figure 6-15 Solar cell parameters (Voc, efficiency) correlated with the p-layer optical band gap for the 5 x 5 inch2 area of an n-i-p solar cell structure on a Cr/Ag/ZnO back-reflector/electrical-contact layer stack.

In Figure 6-12, an optimum efficiency is observed at a thickness of 2800 Å. This optimum results from a rapid rise in Jsc with thickness on the low thickness side followed by a saturation in conjunction with a decrease in fill factor on the high thickness side - both of which are generally expected trends. Unexpected behavior contributing to the well-defined optimum position, as well, is the decrease in Voc with increasing thickness above 2800 Å. This effect may be due to the fact that at larger i-layer thicknesses at R =

245 15, there may be improved ordering or small crystallites near the surface that enhance crystallite nucleation in the overlying p-layer, thus leading to a reduced Voc. This may also lead to a premature reduction in fill factor, greater than expectations based on an increase in thickness alone.

Figure 6-13 suggests that the cell performance is strongly affected by p-layer crystallinity, as may be expected given the high H2 dilution ratio of R ~ 250. The decrease in Voc with p-layer bulk thickness and its associated increase with p-layer roughness thickness suggests that the p-layer in nanocrystalline phase, is evolving beyond the crystallite contact point where maximum roughness occurs, and is undergoing smoothening with increasing thickness. This conclusion is verified by RTSE measurements at a single point during p-layer deposition. Figure 6-16 shows the roughness evolution of the p-layer, which reveals an onset of roughening consistent with the a → (a+nc) transition at a bulk layer thickness of 50 Å, and an apparent onset of surface smoothening consistent with the (a+nc) → nc transition close to the end of the deposition. The optimum cell performance is obtained with a bulk p-layer thickness of ~

105 Å and a roughness thickness of ~ 110 Å. This behavior may suggest that the optimum p-layer starts as protocrystalline Si:H at the i/p interface but evolves crystallites that may yield improved contact to the ITO. The highest Voc in Figure 6-8(a) occurs in the upper left where the surface roughness in Figure 6-9(c) is a maximum, implying the lowest volume fraction of crystallinity. In this situation, some small amount of crystallites may still be providing improved contact with the ITO, while protocrystalline

Si:H produces the best i/p interface. These results are consistent with those comparing

Voc with nanocrystallite fraction (Pearce et al., 2007). In this study, however, it is

246

Figure 6-16 Surface roughness thickness as a function of bulk layer thickness for the Si:H p-layer deposited at R = 250, showing an onset of roughening consistent with the a → (a+nc) transition, and an apparent onset of smoothening consistent with the (a+nc) → nc transition. These results were obtained at a single spot for the 6" x 6" deposition on the Cr/Ag/ZnO/n/i structure.

suggested that the nanocrystals at the top surface of the p-layer are providing an improved contact to the ITO.

Figure 6-14 shows an optimum in the solar cell performance at an i-layer optical gap of 1.69 eV. As described earlier, it should be noted that this optical gap derives from the Cody-Lorentz description of the dielectric function, often referred to as the Cody gap,

247 based on the assumption of a constant dipole matrix element (Ferlauto et al., 2002). This maximum in efficiency is defined by an expected increase in Voc with increasing band gap at low gap values and a decrease in Jsc with increasing band gap at high gap values.

It should also be noted that the highest optical band gaps derive from the edges of the plate where there exist a lower density of points on the correlation, and these high gaps are also correlated with low fill factor values, suggesting lower quality material. Figure

6-15 shows an optimum in the cell performance at a p-layer optical band gap of 1.84 eV.

This maximum is defined as expected by an increase in Jsc with increasing band gap at low gap values and a decrease in Voc with increasing band gap at high gap values due to the increase in crystallite content. A higher crystallite content in very thin films leads to an apparent higher energy absorption onset and optical gap.

The effects of the structural and optical properties of the i- and p-layers on the solar cell performance studied over a large area 5" x 5" solar cell stack, as discussed so far, have been observed from a single fabrication process under the conditions given in

Table 6.1. Due to the non-uniformity in each component layer deposition across the full

5" x 5" area of the glass surface, various solar cells with different i- and p-layer thicknesses and band gaps can be obtained from a single run. Hence, the solar cell performance can be optimized from a fewer number of depositions, compared to optimization of solar cell depositions on a small area (2" x 2") substrate. The optimized deposition parameters for the 0.25 cm2 dot cells on 2" x 2" solar cell structures, as discussed in Sections 6.3 and 6.4, are different than those for the cells on 6" x 6" large area glass due to differences in the designs of the two substrate holders. Because of the large number of solar cells and improved statistics, the correlations of the basic properties

248 with solar cell performance parameters, as obtained from ex-situ mapping spectroscopic ellipsometry for the 6" x 6" substrate, provides faster and more definitive pathways toward solar cell optimization. In the first next step, variations of the deposition conditions in terms of gas flows, pressure, power, hydrogen dilution, etc., in a relatively small number of runs is expected to generate overall optimization of thin film amorphous silicon solar cells on smooth borosilicate glass substrates. In a second next step, the smooth back-contact Ag must be roughened appropriately so that it serves as a high quality back-reflector. Scattering of the light ray photons of energy just above the optical band gap by the roughness at the Ag/ZnO interface enhances the optical path length and thus the short circuit current (Jsc), through absorption of the scattered photons in the i- layer. Details of the back-reflector operation have been discussed in Chapter 4. With the above two steps, the solar cell performance on 6" x 6" borosilicate glass is expected to be further optimized to better performance levels than the single 6" x 6" deposition reported in this chapter.

6.6 a-Si:H Solar Cells on Kapton® Polymer Substrate

In addition to efforts toward optimization of single junction thin film a-Si:H solar cell on rigid glass substrates, single junction a-Si:H n-i-p solar cell stacks have also been fabricated onto 5" wide flexible Kapton® (DuPont polyimide) polymer substrates.

Kapton® is chosen over the polyethylene naphthalate (PEN) polymer substrate used earlier as Kapton® has higher tolerance to temperature than the PEN polymer. The solar cell structure was identical to those on 2" x 2" or 6" x 6" rigid glass substrates. The layers of Cr/Ag/ZnO/n/i/p were deposited in succession using the cassette roll-to-roll

249 configuration, whereas the topmost ITO dots were deposited in 16 x 14 patterns with the help of a stainless steel mask. The roll-to-roll deposition process of the individual layers on a flexible substrate such as Kapton® has been discussed in detail in Chapter 5. The

ITO top layer deposition process, which was performed on the rigid substrate holder, was similar to that on the 6" x 6" glass substrate as described in the previous section. Once again, the dimension of each ITO dot defining the solar cell area was 5 mm x 5 mm. The deposition conditions of the solar cell layers used in this study are given in Table 6.2.

The deposition parameters in Table 6.2 are equivalent to the optimized parameters used for the thin film n-i-p a-Si:H solar cell on the glass substrates. The roll-to-roll speeds were chosen such that the final thicknesses of the individual layers at the end of

Table 6.2 Deposition conditions for the individual layers of the hydrogenated amorphous silicon (a-Si:H) based n-i-p solar cell on flexible Kapton® substrate.

Roll- Intended Gas flow (sccm) Plasma to-Roll Thick- Layer T P o power speed ness Ar 5% SiH4 5% 5% H2 type ( C) (mT) 2 (W/cm ) (cm/s) (Å) O2 B2H6 PH3 in Ar in H2 in H2 0.01 2000 Cr RT 5 0.92 10 x x x x x 0.015 3000 Ag RT 5 0.92 10 x x x x x 0.01 3000 ZnO RT 5 0.92 10 x x x x x 0.12 200 n 200 350 0.0095 x x 10 x 1 x 0.005 3000 i 200 800 0.032 x x 2 x x 20 0.03 100 p 100 1500 0.064 x x 2 0.5 x 280

ITO 150 4 0.58 N/A 600 10 3 x x x x T: substrate temperature (oC); RT: room temperature; P: deposition pressure (mTorr)

250 the deposition zone reach the corresponding desired values, given in Table 6.2. The roll- to-roll cassette loaded with Cr/Ag/ZnO coated Kapton® was pre-heated in the n-layer chamber at T = 200C for 3 hours before n-layer deposition. After the n-layer, the i-layer was immediately deposited in the designated chamber, since both the n-layer and i-layer were each deposited at 200oC. In contrast, the roll-to-roll cassette was left in the p-layer chamber for 3 hours after i-layer deposition in order to equilibrate the cassette at the lower deposition temperature of 100oC used for the p-layer. Finally, the Kapton® solar cell structure together with the stainless steel mask were pre-heated for 3 hours on the rigid substrate holder before ITO deposition in the TCO chamber. This pre-heating step was needed in order to equilibrate the substrate temperature at 150oC.

Figure 6-17 shows a photograph of the solar cell structure on the Kapton® polymer substrate with 16 x 14 dot cells. Although 224 dot cells were fabricated, only a few were successfully operating cells, as shown in Figure 6-18. In the figure, the black square dots indicate failed cells due to shunting, whereas the white dots are the operating cells with the corresponding solar cell performance given in tabulated form in order of

(row, column). The poor yield may be due to lack of proper substrate cleaning, as the

Kapton® substrate was simply blown with nitrogen gas in order to remove dust particles before degassing it the load lock at ~ 150oC. In the future, a more rigorous cleaning procedure must be applied to improve the yield. This will involve the acquisition of equipment for a multistep roll-to-roll washing and drying process.

In addition to the poor yield, the performance of the operating cells is relatively poor as well. Apparently, the optimized deposition parameters for rigid glass substrates are different from those of the moving flexible substrate at the given web speeds. In the

251

Figure 6-17 Large area (6.2" x 5") thin film a-Si:H n-i-p solar cell structure fabricated on a flexible Kapton® substrate coated with Cr/Ag/ZnO. All layers with the exception of the topmost ITO dots were deposited in a roll-to-roll cassette configuration. The ITO dots were deposited on a rigid substrate holder.

future, the cell performance should be optimized through the development of deposition phase diagrams, multistep i-layers guided by the phase diagrams, and rough Ag/ZnO interfaces for light trapping. In this way, all solar cell parameters, i.e. short circuit current (Jsc), fill factor (FF) and open circuit voltage (Voc) will be maximized for the

252 Length = 6.2 ” Jsc Voc (V) FF Eff. (mA/cm2) (%) (%) 10.99 0.801 54.7 4.81 10.91 0.795 54.1 4.69 10.69 0.798 52.4 4.47 10.45 0.793 50.1 4.15 11.81 0.786 49.6 4.61

11.96 0.791 53.6 5.07 ” ” 11.99 0.408 25.4 1.24 11.52 0.789 52.7 4.78

13.09 0.808 54.2 5.73 Width= 5.0 Width= 5.0 11.52 0.798 37.9 3.48 12.97 0.83 54.8 5.90 11.14 0.82 50.9 4.64

Figure 6-18 Spatial distribution of solar cells fabricated on a large area (6.2" x 5") flexible Kapton® polymer substrate. The black square dots represent the shunted cells whereas the white dots represent the operating cells, twelve in all, with the solar cell performance parameters given in the table at right in (row, column) order.

highest efficiency. More details on the required improvements are provided in the next paragraph.

From quantum efficiency measurements of the operating solar cells on flexible

Kapton® substrates, low carrier collection was observed in the long wavelength regime of the spectrum, which consequently reduces the short circuit current (Jsc). The current is improved simply by increasing the thickness of the absorber i-layer. This inevitably involves a trade-off, however, because the increase in i-layer thickness reduces the fill factor (FF) as the thickness exceeds the hole diffusion length. Thus, in order to improve the current it is preferable to develop a back reflector using rough Ag coated with ZnO,

253 rather than increasing the thickness of the i-layer. The details of the back-reflector design, analysis, and operation have been discussed in Chapter 4. Since the back- reflector has yet to be developed for solar cells on rigid glass substrates, this should be undertaken first before the more challenging flexible Kapton® substrates are addressed.

Then the optimized deposition conditions for the back-reflector on flexible Kapton® should be obtained by starting from the optimized conditions for the back-reflector on the rigid glass substrates.

6.7 Summary

Presented first in Chapter 3 as developed from RTSE data, the phase diagrams of i- and p-layers deposited in succession over 2" x 2" Cr/Ag/ZnO/n-layer coated borosilicate glass substrates have been correlated with performance parameters of a-Si:H solar cells in the n-i-p substrate configuration. Each 2" x 2" multilayer structure incorporated 24 small-area (0.25 cm2) n-i-p dot cells along four rows. Correlations for both the i-layers and p-layers reveal that the solar cell performance is optimized when these layers are in the protocrystalline state. This result is consistent with earlier findings of thin film a-Si:H solar cell optimization by adjustment of the deposition conditions of the i- and p-layers.

The understanding established from the correlation between the structural parameters and the n-i-p solar cell results on 2" x 2" borosilicate glass in the substrate configuration is further applied to cells deposited over a larger area, on 6" x 6" borosilicate glass. In this case, statistics are improved by fabricating identical 16 x 16 =

256 dot cells 0.25 cm2 in size. Ex-situ mapping spectroscopic ellipsometry (SE) has been

254 performed at the upper right corner of each dot cell. The basic film properties of i- and p- layers obtained from analysis of mapping SE data, namely the bulk layer thicknesses and optical band gaps, and the p-layer surface roughness thickness have been correlated with a-Si:H thin film solar cell performance parameters. Based on this correlation, structural and optical parameters of i- and p-layers that optimize solar cell performance have been identified. The goal of this research on larger scale substrates is to understand the origin and effects of deposition non-uniformity on cells and modules from both basic property and device standpoints, and ultimately to apply this knowledge to reduce the large difference between the small area cell and full-scale module performance. Although this methodology has been applied here for the first time to single junction a-Si:H solar cells with a specular back-reflector configuration, it will be more powerful when applied to multijunctions as well as to other thin film PV technologies, assuming the appropriate optical databases exist or are developed to enable the analysis of the mapping SE data.

An understanding of the fabrication of optimized solar cells on rigid borosilicate glass in the n-i-p substrate configuration has been applied as a starting point for optimized cells on flexible Kapton® substrates. The depositions other than the topmost

ITO layer were performed in the roll-to-roll cassette configuration, whereas the ITO layer was deposited using the rigid substrate holder. Although the coatings of the individual layers were uniform and free of visible defects such as pinholes and delaminated regions, only a few dot cells were operable and all others were shunted. The poor yield has been attributed to the lack of appropriate substrate cleaning equipment, which must be developed in continuing research. In spite of the poor yield, the solar cell performance parameters could be determined for the few operating cells fabricated on flexible

255 Kapton® substrates. The results are encouraging when using the optimized deposition conditions developed for rigid glass substrates. It is expected that further improvement will be possible by adjustments of the starting point deposition conditions in order to optimize solar cells on a flexible roll-to-roll substrate such as Kapton®. Once the single junction cells are optimized on both rigid and flexible substrates, the Si:H process development and optimization effort will be extended to multijunction solar cells on both rigid and flexible substrates.

256

Chapter 7

Summary and Future Research

7.1 Summary

The component layers of the thin film hydrogenated silicon (Si:H) solar cell in the n-i-p substrate configuration have been studied in detail with the goal of optimizing the amorphous Si:H (a-Si:H) cell performance. The primary tools in this optimization process were non-invasive, non-destructive real time spectroscopic ellipsometry (RTSE) and ex-situ mapping spectroscopic ellipsometry (SE). Using rigid silicon wafer and glass substrates in the deposition processes, RTSE was applied to generate deposition phase diagrams of the i-layer and p-layer so that the most ordered protocrystalline phases of both layers could be ensured. Also for these substrates, RTSE was used to study the metal/TCO interface in efforts to understand the performance of back-reflectors in thin film Si:H solar cells. On the other hand, for flexible polymer substrates, RTSE has been applied in the roll-to-roll substrate configuration as an online monitoring tool for analysis of the thin film nucleation and growth both in sputter deposition of the TCO layer and in

PECVD of the semiconductor layers. Once the thickness on the moving substrate stabilizes, RTSE can be an effective monitoring and control tool to ensure thickness uniformity of the depositing layer along the length of the substrate roll.

257 Ex-situ mapping spectroscopic ellipsometry was used to evaluate the spatial uniformity of the component layers such that, in the scale-up from small area dot cells to large area solar modules, origins of losses in device performance can be understood and methods can be developed to minimize these losses. In addition, ex-situ mapping ellipsometry has been applied to study the spatial dependence of the p-layer phase diagram. The p-layer deposition process is critical as it controls key device performance parameters, but its optimized thickness is only ~100 Å. This implies a considerable optimization challenge, one that can be uniquely met by SE methods. Another important application of ex-situ spectroscopic ellipsometry has been established that involves mapping the spatial distribution of the structural and optical parameters of the thin film

Si:H n-i-p solar cell for correlation with the solar cell performance parameters. Non- uniformity in the deposition process provides a range of structural parameters of the i- and p-layers in a single deposition. Hence, this process exploits non-uniformities to provide a pathway to optimize thin film Si:H solar cells keying on correlations with fundamental parameters and using far fewer depositions.

The evolution of the properties of the Si:H i-layer on Cr/Ag/ZnO/n-layer coated borosilicate glass, as determined by RTSE, has provided a phase diagram of the i-layer as a function of hydrogen dilution ratio R (R = [H2]/[SiH4]). A similar phase diagram for the Si:H p-layer deposited on Cr/Ag/ZnO/n/i-layer coated borosilicate glass has also been developed as a function of the hydrogen dilution ratio R. For the p-layer, B2H6 was used as the p-type dopant gas with a flow ratio D fixed at D = [B2H6]/[SiH4] = 0.01. Such phase diagrams incorporate information on the phase transitions from amorphous to mixed-phase and from mixed-phase to single-phase nc-Si:H as a function of accumulated

258 thickness, which is plotted on the ordinate, and a deposition parameter (R in this case), which is plotted along the abscissa. A separate plot of the surface roughness layer thickness ds as a function of the bulk layer thickness db provides the amorphous-to-

(mixed-phase) transition as the point at which ds begins to increase rapidly with db. The

(mixed-phase)-to-(single-phase) nc-Si:H transition is defined to occur when ds reaches a maximum and begins to decrease with the further increase of db. The primary objective in establishing the phase diagrams for the i- and p-layers is to identify the deposition conditions yielding the most ordered amorphous material, often referred to as protocrystalline. In the protocrystalline state, the film is amorphous but ultimately evolves to the crystalline phase with increasing thickness. The most ordered films for a given thickness are obtained at the maximum H2 dilution ratio possible while avoiding nucleation of nanocrystals at the top of the film as it evolves. The protocrystalline i- and p-layers prepared with maximum H2 dilution have been recognized as the best such layers for optimum stabilized thin film Si:H solar cell performance.

Based on RTSE analysis and in consideration of these optimization guidelines, the phase diagram of the Si:H i-layer, deposited at 200oC substrate temperature, 0.8 Torr pressure, and 0.033 W/cm2 rf plasma power, exhibits protocrystalline behavior at a hydrogen dilution ratio of R = 15 for the target ~ 3000 Å bulk thickness. Similarly, for the phase diagram of the p-layer at 100oC temperature, 1.5 Torr pressure, and 0.066

W/cm2 rf plasma power, R = 125 yields the optimum protocrystalline p-layer for a target

~ 120 Å thickness. For the i-layer phase diagram, several contour lines have been drawn in the R-db plane at different volume fractions of nanocrystalline Si:H in the film, providing improved quantification of the i-layer transition from the amorphous phase to

259 the nanocrystalline phase. For the very thin p-layer, however, only the amorphous-to-

(mixed-phase) and (mixed-phase)–to-nanocrystalline phase transitions are included on the phase diagram.

In addition to the development of deposition phase diagrams for i- and p-layers on rigid glass substrates at a single location, real time SE and ex-situ mapping SE have been successfully applied to analyze similarly cassette roll-to-roll deposition of thin film Si:H p-layers. Two p-layers have been deposited at web speeds of 0.015 and 0.020 cm/s, both at 100oC substrate temperature, 1.5 Torr pressure, and 0.13 W/cm2 rf plasma power.

Based on RTSE along the substrate center line, the p-layer deposited at the slower web speed of 0.015 cm/s shows amorphous (protocrystalline) Si:H-to-[mixed-phase

(a+nc)-Si:H] and then (mixed-phase)-to-(single-phase) nanocrystalline transitions with increasing bulk p-layer thickness to 800 Å. The final thickness deduced by RTSE was corroborated by ex-situ mapping SE. Based on the mapping SE, boundaries defining the amorphous Si:H, mixed-phase (a+nc)-Si:H, and coalsced nc-Si:H at the top surface of the p-layer have been drawn on the basis of the surface roughness characteristics. The transition boundaries drawn on the surface roughness map are then superimposed onto the bulk p-layer thickness map to generate the spatially resolved deposition phase diagram.

In contrast to RTSE results for the slower substrate speed deposition, those of the faster speed of 0.020 cm/s show only the transition from amorphous Si:H to mixed-phase

(a+nc)-Si:H along the substrate center line. In this case, the deposition process saturates to its final thickness, i.e., the substrate has passed completely through the deposition zone, before reaching the nanocrystallite coalescence thickness. Thus, for the above p-

260 layer deposition parameters and the 0.020 cm/s substrate speed, the spatial phase diagram exhibits only a single (amorphous Si:H)-to-[mixed-phase (a+nc)-Si:H] transition boundary. Spatial phase diagrams of interest can be developed by varying the critical deposition parameters, e.g, H2 dilution, substrate temperature, total gas pressure, rf plasma power density, etc., in order to optimize the p-layer process for high performance in large-area thin-film Si:H solar module applications.

RTSE has also been applied in this Thesis research to study metal/TCO back- reflectors. A detailed comparative study of two different back-reflectors, Ag/ZnO and

Al/ZnO, has been performed. In both cases, the coupling of the electromagnetic waves to localized plasmons associated with metal nano/microstructure appears in the optical properties of metal/ZnO interfaces, and this coupling can lead to both dissipation and re- radiation. The coupling of the electromagnetic waves to propagating surface plasmons is expected to appear in the reflectance deficit, which is the difference between the normal incidence specular reflectance predicted from RTSE and that measured directly.

Suppression of the coupling of waves to propagating surface plasmons through macroscopic roughness is expected when the localized plasmonic or other absorption processes occur at the same wavelength.

In Ag/ZnO, the mechanism that can be exploited for back-reflector optimization appears to be interference enhanced localized plasmon coupling, as it can lead to efficient re-radiation for properly tuned microstructures. This optimization is wavelength dependent, and for multijunction solar cells incorporating a-Si1-xGex:H, the optimum photon energy is 1.4-1.5 eV which is just above the band gap of the bottom cell. Another approach for optimization of Ag/ZnO back-reflectors is to shift the plasmon band to

261 higher photon energies by tailoring the refractive index of interfacial ZnO. This approach may not be as effective as plasmon-mediated scattering, since it relies on direct scattering via non-specular reflection from the surface structure. In contrast to the findings for

Ag/ZnO, no significant role of plasmons in dissipation and/or re-radiation is observed at

1.5 eV for Al/ZnO interfaces of moderate roughness due to the higher bulk plasma energy of Al. In addition, as the interface roughness increases, the presence of Al interband transitions at low energy and ZnO interband transitions at high energy tends to force the sustainable plasmon modes to locate in the minimum absorption region of ~ 3 eV. As a result, the dissipation in Al/ZnO at 1.5 eV is large due to the combination of the interband and intraband transitions rather than to confined plasmons. The plasmon- mediated scattering in Ag/ZnO, by mitigating losses due to dissipation, provides more options for efficient light scattering leading to light trapping. Eliminating dissipation is the key to optimizing Ag/ZnO back-reflectors for thin film silicon solar cell applications in single, tandem, as well as the triple junction solar cell configurations.

This Thesis research has demonstrated the application of RTSE for monitoring roll-to-roll deposition of thin film Si:H solar cell structures on a low-cost PEN polymer substrate as it transits through the deposition zone. The moving substrate, or web, enables simulation of the processes applied for the fabrication of large area multilayer stacks used in solar cells. Magnetron sputter deposition of the ZnO:Al layer and PECVD of the a-Si:H i-layer and the p-layer were investigated. Since the RTSE monitoring point was inside the deposition zone, two different substrate speeds were selected in all cases. The so-called "normal speed" ensures that the intended final thickness is reached after the substrate exits the deposition zone, and the "reduced speed" ensures that the desired final

262 thickness is reached when the web reaches the monitoring point. At normal speed, the nucleation and the early stage processes of the film growth are studied, as well as the interface filling on top of the previously-deposited film. At reduced speed, the evolution of the film structure is studied in the later stages of the growth process until the end of deposition of the desired thickness.

The thickness evolution of ZnO:Al during sputtering was modeled assuming an inverse square variation of sputtered flux from the target to the substrate, assuming

Lambertian emission of deposition species from the target. The i- and p-layer film growth processes in PECVD were modeled by assuming a constant flux of reactive Si- based species throughout the deposition zone. The deviation of the ZnO:Al sputter deposition process from predicted ideal line-of-sight behavior is attributed to gas phase scattering of sputtered species. On the other hand, the deviations for both the i- layer and p-layer depositions from the ideal predicted linear behavior are attributed to extension of the plasma or diffusion of reactive species beyond the deposition zone defined by the cathode plate. Significant plasma transient behaviors are also observed upon PECVD plasma ignition, which may require an elevated pressure and rf plasma power under some plasma conditions. Such transient effects dominate the thickness evolution for the thin p- layer, but are avoided by igniting the p-layer plasma at the operating pressure and rf power with the help of hot filament which injects electrons into the plasma zone.

In the case of static rigid substrates, such a transient effect influences the material deposited at the interface to the underlying film. In roll-to-roll deposition, however, the transient effects influence the interface material only in the initial start-up stretch of the roll. Thus, such effects play no role in the film structure or properties once the full length

263 of the polymer substrate exposed to plasma ignition crosses the end of the deposition zone. These results suggest that real time analyses of both rigid substrate and roll-to-roll deposition can assist not only in understanding the details of the differences between the thin film growth and plasma processes in the two cases, but also in optimizing these processes.

The uniformity of normal speed deposition of the ZnO:Al back-reflector layer and the a-Si:H i-layer was characterized ex-situ using a mapping spectroscopic ellipsometer.

The main goal of mapping ellipsometry is to evaluate the uniformity across the width of the polymer substrate. Both the ZnO:Al layer and the i-layer were observed to be slightly thicker along the center of the polymer substrate than at the edges. This may be due to a slight sagging of the polymer at the process temperature, as the PEN polymer has a relatively low glass transition temperature of 150oC. In PECVD, deviations characterized by two minima in the thickness along the width of the web were also observed due to the symmetric holes in the cathode plate toward the end of the deposition zone. These holes are designed for real time SE measurement during the PECVD process so that the incident beam can enter and the reflected beam from the substrate can exit and travel through windows to the detector. These holes can be closed when performing depositions for devices in which case uniformity of layer thickness and properties is sought.

In this Thesis research, the i- and p-layer phase diagrams were correlated with the corresponding performance parameters of the solar cells fabricated first on 2" x 2" size

Cr/Ag/ZnO/n-layer coated borosilicate glass substrates. Each 2" x 2" multilayer structure incorporated 24 small area n-i-p dot cells having dimensions of 5 mm x 5 mm.

264 Correlations for both the i- and p-layers reveal that the optimized solar cell performance results when these layers are in the protocrystalline state. These results are consistent with earlier findings of thin film a-Si:H solar cell optimization performed by adjusting the deposition conditions of the i- and p-layers.

The initial correlations between the structural and solar cell performance parameters for the n-i-p cells on 2" x 2" borosilicate glass substrates have been further extended to similar structures deposited on larger size 6" x 6" borosilicate glass. In this case, improved statistics result by fabricating 256 identical dot cells 5 mm x 5mm in size in a 16 x 16 square array. The solar cell performance parameters were correlated with structural and optical parameters deduced by ex-situ mapping spectroscopic ellipsometry

(SE) performed at the upper right corner of each dot cell. The parameters obtained from spectroscopic ellipsometry analysis that have been correlated with the solar cell performance parameters include the i- and p-layer bulk thicknesses, the i- and p-layer optical band gaps, and the p-layer surface roughness thickness. This correlation provided the specific structural and optical parameters of the i- and p-layers that yield optimum solar cell performance. The goals of this research are to understand the origin and effects of deposition non-uniformity, first on small area solar cells, then on large area solar cell structures, and ultimately to apply this knowledge toward reducing the large difference between the small area solar cell and the full-scale module performance. Furthermore, this methodology is of particular interest for the optimization of multijunction thin film

Si:H solar cells as well as other multilayer thin film PV technologies, provided the appropriate optical databases exist or can be developed.

265 Finally, an understanding of the deposition of individual layers of the a-Si:H thin film solar cell in the n-i-p substrate configuration has been applied to the fabrication of complete solar cell structures on flexible polyimide (DuPont Kapton®) substrates.

Although the cells were free of visible defects such as pinholes and delaminated regions, only a few dot cells were operable whereas all others were shunted. The poor yield has been attributed to the lack of proper cleaning of the flexible substrate, which must be rectified in order to continue this research. In spite of the poor yield, encouraging performance is obtained for operable solar cells on the flexible polyimide substrates fabricated under the conditions optimized for rigid glass substrates. Further improvement is expected by adjusting the deposition conditions for optimization specific to the polyimide substrate. Once the single junction Si:H solar cells have been optimized on both rigid and flexible substrates, the process development and optimization effort can then be extended to multijunction solar cells on both substrates.

7.2 Future works

This Thesis work describes comprehensive real time and ex-situ mapping spectroscopic ellipsometry analyses of the component layers of thin film Si:H solar cells in the substrate configuration on both rigid and the flexible substrates. Toward the goal of solar cell performance optimization, there are still several steps that can be implemented for further progress beyond this Thesis research. The following paragraphs enumerate possible future efforts that can be undertaken for higher performance and higher yield thin film Si:H-based solar cells.

266 (1) Phase diagrams for the i-layer and the p-layer on rigid glass substrates should be developed for the different deposition parameters of rf power density and total gas pressure. In addition to the H2 dilution ratio R, these additional parameter values should be selected so as to obtain the highest performance for the desired protocrystalline layers in solar cells. It is expected that the rf power density yielding highest performance devices is the lowest value possible for a stable plasma, also resulting in the lowest a-Si:H i-layer deposition rate. For the total gas pressure, a trade-off is expected to lead to optimum devices. At lowest pressure, short-lived radicals generated in the plasma such as SiH2 may reach the film surface due to the lack of gas phase reactions and result in a lower quality material. At high pressures polysilane radicals may be generated that are also detrimental to the film properties. One indication of an improvement in the protocrystalline regime is an amorphous-to-(mixed-phase) boundary that has a shallower slope, yielding a clearly defined nanocrystallite nucleation thickness. Films deposited under the conditions that yield the best solar cells should also be analyzed by a direct structural probe such as cross-sectional transmission electron microscopy (XTEM) to determine if the i-layer film incorporates any nanocrystalline component near its top surface.

(2) The studies performed in this Thesis research leading to the development of deposition phase diagrams for the Si:H i- and p-layer materials should also be extended to the bottom n-layer. The n-layer conditions, in particular the H2 dilution ratio, should be varied while maintaining fixed optimized conditions for the i- and p-layers. The n-layer structure has been shown to have significant impact on the performance of Si:H solar cells in the p-i-n superstrate configuration. In fact, in the p-i-n superstrate configuration,

267 an optimum solar cell fill-factor is obtained when the n-layer reaches a ~ 58 vol.% - 42 vol.% mixture of amorphous and nanocrystalline phases at its top surface. For the n-i-p solar cells in the substrate configuration, however, it is a greater challenge to fabricate such a nanocrystalline n-layer on ZnO as compared to an a-Si:H i-layer, the underlying layer of the p-i-n cell. Furthermore if an n-layer deposited on the back-reflector ZnO reaches a desired mixed phase structure, it will then behave as a seed layer for the critical i-layer in the n-i-p solar cell. As a result, the mixed phase n-layer in this solar cell configuration may lead to undesirable nanocrystals propagating within the i-layer. Hence in the n-i-p configuration, a high-quality protocrystalline n-layer material may optimize solar cell performance.

(3) The first studies resulting in a spatially-resolved phase diagram were reported for the top p-layer of an a-Si:H n-i-p solar cell structure on a flexible substrate. Such studies should be extended as well to the i-layer of the structure. In these future studies, contours lines that describe the i-layer near-surface nanocrystalline volume percentage should be drawn over the area of the substrate. These results can be obtained through an analysis of the ellipsometric spectra at high energies in order to ensure a short penetration depth within the i-layer. By superimposing these lines onto a map of the bulk i-layer thickness, the spatially-resolved phase diagram will result. This will contain more information than the p-layer diagram due to the identification of contours in the volume percentage. By correlating these data with solar cell performance, one can optimize the performance of solar cells over large area inexpensive substrates such as polymers having low glass transition temperatures. If possible, an optimized location on the solar cell

268 should also be evaluated by XTEM for possible crystallites within the amorphous phase at the top surface of the resulting i-layer.

(4) The understanding of Ag/ZnO back-reflectors achieved as described in

Chapter 4 should be applied to the solar cell device in future research. The goal is to increase the short circuit current (Jsc) without degradation of the other performance parameters so that the overall cell performance is increased. For that purpose, the Ag layer should be roughened in a controlled manner by increasing the deposition temperature above room temperature in the sputtering process to ensure a large grain size, which serves to reduce free carrier absorption. Depositing the initial ZnO layer on Ag at an elevated Ar pressure is expected to reduce the ZnO index of refraction to ~ 1.5 in the range of 700-800 nm. In this way the screening is reduced and the Ag/ZnO interface absorption peak is blue shifted above the back-reflector photon energy range of operation. The roughness of the Ag layer should be ~ 250 Å, as measured by RTSE. For this roughness thickness, the Ag/ZnO back-reflector studied here has demonstrated optimal scattering for maximization of Jsc. In addition to back-reflector fabrication on rigid substrates, similar structures should be developed and deposited on flexible substrates for optimized solar cell performance.

(5) RTSE data collection on moving flexible substrates was the greatest challenge when studying the nucleation and the growth of the ZnO during sputter deposition and the Si:H layers during PECVD on these substrates. Even a small warpage of the flexible substrate shifts the path of the reflected light away from the entrance of the detector unit.

In order to solve this problem, the roll-to-roll cassette should be modified so that the

269 flexible substrate always stays flat and taut near the region where the ellipsometer beam hits the substrate. This would also improve uniformity in the deposition processes.

(6) The thickness evolution during sputter deposition of the ZnO layer in the transient region of nucleation and early growth should be modeled beyond the simple inverse square variation. A deposition mechanism that includes scattering of the sputtered ZnO species from Ar atoms of the sputtering gas is required so that the model can better fit the measured data. The statistical processes of molecular scattering can be considered with rigorous simulation programs. Another aspect of the sputter deposition process of ZnO that could be explored is the possibility that the optical properties evolve with thickness due to a change in angle of the incident flux as the substrate moves from one end of the deposition zone to the other. It is known that glancing angle flux can lead to tilted columnar structures that may appear in the ZnO film at the interface to the Ag when the film is deposited in a physical vapor deposition process. In fact, such structures may be beneficial if a lower index of refraction is desired at the interface to the Ag in order to reduce screening and shift the confined plasmon band to higher energies.

(7) When fabricating solar cell devices on flexible polymer substrates most devices were either partially or fully shunted. The situation was serious in the case of a flexible polyimide substrate, as only ~ 5% of the devices were operable, whereas it was severe in the case of PEN substrate, in which case no devices were operable. The reason for the shunting is believed to be improper cleaning of the substrate. A large number of micron-sized particles on the surface of the substrate may create pinholes that serve as current pathways for photogenerated carriers. Improved cleaning procedures for both glass, as well as for the flexible polymer substrates, should be developed in a clean room

270 environment so that pinholes can be eliminated. Hydrogen or argon plasma cleaning may provide an alternative option for cleaning the polymer substrate in order to improve the device yield.

(8) Although thin film a-Si:H solar cells have been optimized for maximum performance through this Thesis research, a single-junction solar cell having a band gap of ~ 1.7 eV does not harvest solar radiation below this photon energy in the NIR spectral range. Hence, a tandem or even a triple-junction monolithic thin film Si:H-based solar cell is required as a more efficient photovoltaics technology. A controllable band gap engineering approach must developed to achieve a reduced band gap for the bottom i-layer in tandem cells and both the bottom and middle i-layers in triple junction thin film

Si:H-based solar cells. Significant earlier research has shown that germanium alloying can reduce the band gap, but not to the level required for the bottom cell in tandem and triple junction cells, due to the electronic degradation of alloys with band gaps less than ~

1.4 eV. In contrast, nanocrystalline Si:H with a band gap ~ 1.1 eV -- as low as that of single-crystal Si -- can serve as an improved bottom cell material. The thickness of these individual stacked cells in a monolithic configuration must be selected such that the same amount of current is produced in each. The deposition of the nanocrystalline i-layer for the bottom cell is facilitated by the desired nanocrystalline Si:H n-layer at the very bottom of the semiconductor stack. Moreover, an ultrathin, highly-defective p-layer can be deposited after completing each n-i-p solar cell structure so that the top p-layer of the underlying cell forms an effective recombination junction with the bottom n-layer of the overlying cell.

271 As described earlier, the goal of this Thesis research is to fabricate optimum performing thin film Si:H solar cells in the n-i-p substrate configuration, at first as single- junction small-area dot cells in the laboratory. The second step is to scale the structures to larger areas for applications in solar modules with minimum loss in power conversion efficiency due to deposition non-uniformity. RTSE has served as the primary tool in the optimization procedures for the small area dot cells. An in-situ mapping technology operable with the cell structure under vacuum is currently being developed to assist in the optimization of larger area cells. Based on such information, spatial non-uniformities in thickness and optical properties can be reduced through modifications of the deposition hardware. Toward this goal, flexibilities must be built into the deposition mechanics including, for example, adjustments of the in-flow of the source gases as well as the out- flow of the exhaust while ensuring laminar flow of these gases. Adjustments of the distance between the cathode plate and the substrate could also provide the flexibility needed.

272

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283

Appendix

A.1 Analytical Expressions

In this appendix, mathematical expressions are provided for the contributions to the complex dielectric function  = 1 + i used to represent the optical properties of the component layers of thin film Si:H photovoltaics. As presented in Chapters 3, 4, 5, and

6, the analytical equations for  used in this work include those describing the (i) Lorentz oscillator, (ii) Drude free carriers, (iii) Tauc-Lorentz oscillator, (iv) Critical-point parabolic-band (CPPB) oscillator, and (v) Cody-Lorentz oscillator. The following sections describe the mathematical form of each of these equations along with the corresponding fitting parameters. In each of the following equations, the constant contribution to the real part of the dielectric function 1 = 1offset is dropped since the most general form for the dielectric function requires a sum of the different component expressions below with a single constant contribution to 1.

A1.1. Lorentz oscillator

The Lorentz oscillator is a classical damped and driven harmonic oscillator that describes the fundamental interaction of an electromagnetic wave with a two-level atomic system. By considering a collection of such atomic oscillators within a solid, the complex dielectric function can be deduced, written as:

284 A Lorentz 22 (A.1) E0  E  i  E where A is an oscillator amplitude, E0 is the resonance energy of the atomic oscillator,  describes the broadening of the oscillator, and E (= ħ is the photon energy. All quantities are in eV units.

Equation (A.1) can be written in terms of the real and imaginary parts of the dielectric functions (Lorentz) = Lorentz) + i Lorentz) as:

22 AEE 0   1 Lorentz (A.2) 2 22 2 2 EEE0   

AE and, 2 Lorentz (A.3) 2 22 2 2 EEE0   

The variables A, , and E0 are the fitting parameters of the Lorentz oscillator that proceed to define the dielectric function. In Woollam software, the amplitude parameter A is defined as A = A x Eo such that the new amplitude parameter A has the dimension of energy. All the tabulated values of the Lorentz oscillator amplitudes in Chapters 2, 3, 4, and 5 are based on this assumption of the Woollam software.

A1.2. Drude free charge carriers

The Drude expression describes the free carrier effects on the dielectric response of a material. It exhibits a similar form as the Lorentz oscillator, but with a zero resonance energy, i.e., E0= 0. The complex dielectric functions associated with the

Drude free carriers is given by:

A Drude   (A.4) E2  i E

285 where A is the amplitude,  is the broadening, and E (= ħis the photon energy.

In terms of the resistivity  and the scattering time , the Drude form can be written as:

2 Drude   (A.5)   2 0  E  i E where 0 is the permittivity of the free space. The resistivity  is related to the effective charge carrier mass m*, the carrier concentration N, and the electronic charge e according to:

m*  , (A.6) Ne2 

and the scattering time is given by

 (A.7) 

The Drude expression given in Eq. (A.5), can be written in terms of real and imaginary parts of the dielectric functions, (Drude) = Drude) + i Drude) as:

22E Drude   (A.8) 1   2 4 2 2 0  EE  

3 E and, Drude (A.9) 2   2 4 2 2 0  EE  

The quantities  and  are the fitting parameters of the Drude free electron expression, which generates the dielectric function.

286 A1.3 Critical-point parabolic-band (CPPB) oscillator

The critical-point parabolic-band (CPPB) oscillator models the shape of the dielectric function at an interband critical point (CP). The shape of a critical point oscillator depends on five parameters including the (i) amplitude A, (ii) threshold energy

E0, (iii) broadening parameter , (iv) phase projection factor , and (v) exponent . The complex dielectric function contribution from a single CPPB oscillator is given by (Leng et al., 1998):

 i  CPPB Ae  (A.10) 2E0  2E  i 

The exponent  can assume the values of 1/2 , 0, and 1/2 depending on whether the

CP’s are 1-D, 2-D, or 3-D in nature. In this work, only the 1-D CP oscillator has been used, and so its contribution to the complex dielectric function becomes:

 CPPB Aei (A.11) 2E0  2E  i 

The parameters A, E0, , and  become the fitting parameters of the specific 1-D CPPB oscillator, which together generate the single CPPB contribution to the dielectric function.

A1.4 Tauc-Lorentz oscillator

The Tauc-Lorentz oscillator function is used to model the dielectric function of an amorphous solid. Just above the optical band gap in the absorption onset region, the imaginary part of the dielectric function of the Tauc-Lorentz model follows the Tauc Law

287 2 2 formula 2  (E  Eg) / E , where Eg is the Tauc optical band gap of the material. In this work, the Tauc-Lorentz oscillator is used to model the Ag/ZnO interface optical properties in the UV region. Multiple Tauc-Lorentz oscillators can be assigned a common band gap energy Eg. The nanocrystalline i-layer described in Chapter 3 has been modeled by using two Tauc-Lorentz oscillators.

The mathematical form of the Tauc-Lorentz oscillator is first defined in terms of the imaginary part of the dielectric function 2, and then the real part 1 is obtained from the Kramers-Kronig transformation. In the Kramers-Kronig transformation, a unit contribution to the real part of the dielectric function is removed. When using a single dielectric function contribution or multiple contributions, a single constant term is re-incorporated, denoted 1offset. Following Jellison and Modine (Jellison and Modine,

1996), one can write:

2 AE C E E 1 0g  2gTLEE  2  E EECE2 2 2 2 (A.12)  0 

0 E Eg

2    and, T  L  P2 d  (A.13) 1 E 22  g E  where A is the amplitude, E0 is the resonance energy, and C is the broadening parameter that describes the oscillator. Hence, there are four fitting parameters in a single Tauc-

Lorentz oscillator expression, A, E0, C and Eg, used to model the dielectric function of an amorphous material.

288 A1.5 Cody-Lorentz oscillator

The Cody-Lorenz oscillator model, developed by Ferlauto et al. (Ferlauto et al.,

2002), is also designed for amorphous solids. All amorphous n-, i-, and p-layers in this

Thesis research are modeled using the Cody-Lorentz oscillator. It is similar to the Tauc-

Lorentz in that it defines the optical band gap energy Eg and a Lorenzian absorption peak.

However, the two models behave differently in the absorption onset region. The Tauc-

2 2 Lorentz model follows the Tauc Law formula 2  (E  Eg) / E , whereas Cody-Lorentz

2 model follows 2  (E  Eg) which is Cody's modification of the Tauc Law. The

Ferlauto et al. publication also includes an Urbach term, which describes the absorption below the band gap primarily due to structural and thermal disorder in the material. The

Tauc-Lorentz model is based on the assumptions of parabolic bands and a constant- momentum matrix element (CM-ME), whereas the Cody-Lorentz model is based on the assumptions of parabolic bands and a constant dipole matrix element (CD-ME).

The equation for 2 defining the Cody-Lorentz oscillator is given by:

E1 EE t  2tC  L  exp 0  E  E EEu 2 (A.14) EE g  AE E G(E)L(E).EE 0  22t EEE2  EEE2 2   2 2   gp  0 

The function G(E) in Eq. (A.14) defines the Cody absorption behavior whereas L(E) defines the Lorentz oscillator behavior. The parameter Et is the energy at which the

Urbach tail absorption transitions to the band-to-band excitations. The parameter Eu is the Urbach absorption tail slope that gives the rate at which the Urbach absorption exponentially decays with energy below Et. The parameter Ep allows the user to define the energy Eg + Ep at which the function transitions from Cody absorption behavior to

289 Lorentz oscillator absorption behavior. As before, the quantities A, E0, and  are the amplitude, energy, and broadening parameters, and Eg is the band gap energy. Applying

the continuity condition at E = Et, the parameter E1 becomes E1 = Et G(Et) L(Et). Finally, as in the case of Tauc-Lorentz model, the real part of the dielectric function 1 in the

Cody-Lorentz oscillator model is obtained from the Kramers-Kronig transformation of 2

(Eq. A.13). In this case, the unity contribution to 1 is handled as described in Sec. A1.

In this Thesis research, however, the Urbach tail absorption is neglected for all amorphous materials. Hence Et is set to Eg in Cody-Lorentz modeling so that E1 → 0, implying that 2 → 0 for E < Eg.

A2. Parameter Coupling of the Cody-Lorentz Oscillator for High Quality PV

Materials

The five free parameters of the Cody-Lorentz oscillator including amplitude (A), energy (E0), broadening parameter , band gap Eg, and transition energy Ep have been correlated with the optical band gap Eg(T&R), as measured by transmission and reflection spectroscopy. This correlation is used to generate the dielectric functions of high quality

PV materials at room temperature from a single parameter (Collins and Ferlauto, 2005a).

This correlation covers the range of Eg(T&R) from 1.30 eV to 1.95 eV. The mathematical expressions of these correlations are as follows.

A = 64.7 + 7.05 Eg(T&R) for Eg(T&R) ≤ 1.8 eV (A.15)

A = 435 + 289 Eg(T&R) for Eg(T&R) > 1.8 eV (A.16)

E0 = 3.32 + 0.280 Eg(T&R) for Eg(T&R) ≤ 1.8 eV A.17)

E0 = 5.31  0.825 Eg(T&R) for Eg(T&R) >1.8 eV (A.18)

290  = 3.79 – 0.906 Eg(T&R) for Eg(T&R) ≤ 1.8 eV (A.19)

 = 6.68 + 4.88 Eg(T&R) for Eg(T&R) > 1.8 eV (A.20)

Ep = 0.777 + 108 Eg(T&R) for Eg(T&R) ≤ 1.8 eV (A.21)

Ep = 14.7 + 8.82 Eg(T&R) for Eg(T&R) > 1.8 eV (A.22)

Eg = 0.343 + 0.770 Eg(T&R) (A.23)

By replacing Eg(T&R) with the Cody optical band gap (Eg) through Eq. (A.23), the new coupling equations between the Cody-Lorentz parameters and Eg become:

A = 61.56 + 9.16 Eg for Eg ≤ 1.73 eV (A.24)

A = 563.736 + 375.325 Eg for Eg > 1.73 eV (A.25)

E0 = 3.195 + 0.364 Eg for Eg ≤ 1.73 eV (A.26)

E0 = 5.689 – 1.104 Eg for Eg > 1.73 eV (A.27)

 = 4.194 – 1.177 Eg for Eg ≤ 1.73 eV (A.28)

 = 8.854 + 6.338 Eg for Eg > 1.73 eV (A.29)

Ep= 1.258 + 1.403 Eg for Eg ≤ 1.73 eV (A.30)

Ep = 18.629 + 11.455 Eg for Eg > 1.73 eV (A.31)

These coupling equations, from A.24 through A.31, have been used to model the amorphous i-layer and p-layer optical properties at room temperature in several situations in this Thesis research. These expressions have become very useful in modeling mapping spectroscopic ellipsometry data to fit the multilayer structure with a reduced number of fitting parameters, and reduced correlations between parameters. Moreover, these coupling relations, together with the temperature coefficients of the Cody-Lorentz parameters as given by Podraza et al. (Podraza et al., 2006), can be used to introduce both optical band gap and temperature as free parameters.

291 The constant, dispersionless contribution, 1offset, to the real part of the dielectric function can deviate from unity due to absorption well outside the spectral range under study. This constant is a parameter of interest that can contribute to the dielectric function in addition to the parameters of each of the mathematical expressions. It is equivalent to the parameter denoted 1∞ that one often encounters in the literature.

292