A Dissertation

entitled

Spectroscopic Ellipsometry Studies of

II-VI Semiconductor Materials and Solar Cells

by

Jie Chen

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

December 2010

Copyright 2010, Jie Chen

This document is copyrighted material. Under copyright law, no parts of this document

may be reproduced without the expressed permission of the author.

iii

An Abstract of

Spectroscopic Ellipsometry Studies of II-VI Semiconductor Materials and Solar Cells

by

Jie Chen

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

The University of Toledo December 2010

The multilayer optical structure of thin film polycrystalline II-VI solar cells such as

CdTe is of interest because it provides insights into the quantum efficiency as well as the

optical losses that limit the short-circuit current. The optical structure may also

correlate with preparation conditions, and such correlations may assist in process

optimization. A powerful probe of optical structure is real time spectroscopic

ellipsometry (SE) that can be performed during the deposition of each layer of the solar

cell. In the CdCl2 post-deposition treatment process used for thin film polycrystalline

II-VI solar cells, the optical properties of each layer of the cell change during the process

due to annealing as well as to the elevated temperature. In this case, ex-situ SE before

and after treatment becomes a reasonable option to determine the optical structure of

CdCl2-treated CdTe thin film solar cells.

CdTe solar cells pose considerable challenges for analysis by ex-situ SE. First, the

iv

relatively large thickness of the as-deposited CdTe layer leads to considerable surface

roughness, and the CdCl2 post-deposition treatment generates significant additional

oxidation and surface inhomogeneity. Thus, ex-situ SE measurements in reflection from

the free CdTe surface before and after treatment can be very difficult. Second, SE from

the glass side of the cell is adversely affected by the top glass surface which generates a

reflection that is incoherent with respect to the reflected beams from the thin film

interfaces and consequently depolarization if collected along with these other beams. In

this research, the first problem is solved through the use of a succession of Br2+methanol

treatments that smoothens the CdTe free surface, and the second problem is solved

through the use of a 60° prism optically-contacted to the top glass surface that eliminates

the top surface reflection. In addition, the succession of a Br2+methanol treatment not

only smoothens the CdTe surface but also enables CdTe etching in a layer-by-layer

fashion. In this way, it has been possible to track the optical properties of the CdTe

component layer as a function of depth from the surface toward the CdS/CdTe interface

in order to gain a better understanding of the film structure.

In this study, ex-situ spectroscopic ellipsometry was applied first to investigate the

optical properties of the TEC-15 glass substrate, and then to extract the optical properties

of thin film CdTe and CdS both as-deposited and CdCl2-treated. After obtaining all the

optical properties of the solar cell component layer materials, a comprehensive ex-situ SE

analysis has been applied to extract the optical structure of a single thin film of

CdCl2-treated CdTe, and finally to obtain the optical structure of the CdCl2

v

post-deposition treated CdTe solar cell.

Based on the fundamental studies in this thesis, various aspects of the solar cell

structure after the complicated CdCl2 treatment have been determined. In future work

the role of the key parameters of CdCl2 post-deposition treatment process will be

explored including: the temperature and treatment time. As a result, a correlation will

be established between solar cell performance and film structure. Finally, an

understanding of how solar cell structure can be optimized to achieve the highest solar

cell performance may be possible through improved control of the CdCl2 post-treatment

process.

vi

Table of Contents

Abstract iii

Table of Contents vi

List of Tables ix

List of Figures xii

1 Introduction to Spectroscopic Ellipsometry 1

1.1 History…………………………………...………………...………………..…....1

1.2 Purpose…… …………………………………………………………...…..…….2

1.3 Data measured by ellipsometry…………………………………………………..3

1.4 Mathematical derivation…..……………………………………………………..5

1.5 Spectroscopic ellipsometer used in the study…………………………………..10

1.6 Data analysis……………………………………………………………………12

2 Introduction to CdTe-based Solar Cells…………………………………………..18

2.1 CdTe-based solar cell structures ……………………………………………….18

2.2 Deposition method and process steps…………………………………………..21

2.3 Application of spectroscopic ellipsometry as an analysis technique …………..22

3 Optical Properties of TEC-15 Glass…….………………………………………...26

3.1 Introduction……………………………………………………………………..26

vii

3.2 Experimental details…...………………………………………………………..28

3.3 Data analysis and results…………………...…………………………………...29

4 Verification of the Chemical Etching Process for CdTe Depth Profiling………52

4.1 Introduction……………………………………………………………………..52

4.2 Structural evolution of CdTe during etching: experimental details…………….54

4.3 Structural evolution of CdTe during etching: results and analysis ......…….......57

4.4 Detection of a-Te on etched CdTe: experiment details…………………………59

4.5 Detection of a-Te on etched CdTe: results and analysis………………………..60

5 Optical Properties of Thin Film CdTe and CdS before and after CdCl2

Post-deposition Treatment………………………………………………………...71

5.1 Introduction……………………………………………………………………..71

5.2 Optical properties of as-deposited CdTe and CdS films deposited on c-Si

substrates……..…………………………………………………………………72

5.3 Optical properties of CdCl2 post-deposition treated CdTe and CdS……………78

5.4 Etch-back profiling of CdTe thin film structure after post-deposition treatments...

…………………………………………………………………………………. 84

6 Optical Structure of As-deposited and CdCl2-treated CdTe Superstrate Solar

Cells…………………………………………………………………………………94

6.1 Introduction……………………………………………………………..………94

6.2 Experimental details…………………………………………………………….96

6.3 Results and discussion: film side and prism side measurements…..…………...97

viii

6.4 Results and discussion: through the glass measurements……………………..113

6.5 Summary………………………………………………………………………119

7 RTSE Analysis of CdTe Solar Cell Structures in the Substrate Configuration…..

………………………………………………………………………………………120

7.1 Introduction……………………………………………………………………120

7.2 Analysis of CdTe deposition on rough molybdenum…………………………121

7.3 Ex situ spectroscopic ellipsometry analysis of a CdTe solar cell in the substrate

configuration…………….……………………………………………………138

8 Spectroscopic Ellipsometry Studies of II-VI Alloy Films………………...…….152

8.1 Introduction……………………………………………………………………152

8.2 Top cell material candidates: Cd1-xMnxTe and Cd1-xMgxTe…………………...154

8.3 Bottom cell material: Cd1-xHgxTe……………………………………………..172

9 Summary and Future Directions………………………………………………...178

9.1 Summary………………………………………………………………………178

9.2 Future directions………………………………………………………………183

References 196

Appendix

A Dielectric functions 207

ix

List of Tables

4.1 Best fit parameters and confidence limits that define Eqs. (4.1) and (4.2) for the

dielectric function of a-Te. …..……………………………………………………..63

5.1 Fitting results for single crystal and thin film polycrystalline CdTe using an analytical

model consisting of four critical points and one T-L background

oscillator. …...………………………………………………………………………74

5.2 Fitting results for single crystal and thin film polycrystalline CdS using an analytical

model consisting of three critical points and one T-L background

oscillator…………………………………………………………………………….75

5.3 Best fit dielectric function parameters comparing single crystal, CdCl2-treated, and

as-deposited CdTe samples. ………………………………………………..……….79

5.4 Best fit dielectric function parameters for as-deposited CdS on a fused silica prism,

CdCl2-treated CdS on the prism, and. as-deposited CdS on

c-Si. ……………………………………………………………….………….……..83

x

6.1 Dielectric function library used in spectroscopic ellipsometry data analyses for CdTe

solar cells. ……………………………………………………………………..……98

6.2 Best fitting parameters added step by step to improve the mean square error (MSE) in

modeling through-the-glass SE measurements of a CdTe solar

cell. ………………………………………………………………………………..116

6.3 Multilayer stack thicknesses, non-uniformity, and compositions, the latter expressed

in terms of volume fractions, along with parameter confidence limits for the best fit

to SE data obtained through the glass. …………………………………………….118

7.1 CdTe bulk and surface roughness layer thicknesses for the top four CdTe bulk

layers. ……………………………………………………………………………..126

7.2 Five models used to evaluate the Mo overlayer thickness using reference dielectric

functions from the literature. ……………………………………………………...134

7.3 Best fit critical point and Tauc-Lorentz oscillator parameters describing the inverted

dielectric function of polycrystalline ZnTe:Cu. The exponents µn are fixed at the

single crystal values of Table 7.4. ………………………………………………...143

xi

7.4 Best fit critical point and Tauc-Lorentz oscillator parameters for single crystal ZnTe.

……………………………………………………………………………………..144

7.5 Best fitting parameters added step by step to improve the standard mean square error

(MSE) in the ellipsometric analysis of a CdTe solar cell in the substrate

configuration. ……………………………………………………………………..150

8.1 Deposition parameters used to prepare the CdxMg1-xTe and CdxHg1-xTe thin

films. ………………………………………………………………………………155

8.2 Critical point parameters of transition energy and width obtained in the fits to the

dielectric functions of Fig. 8.9. ……………………………………………………167

8.3 Critical point energies and E0 broadening parameters for two as-deposited

Cd1-xMgxTe alloys from spectroscopic ellipsometry. Also shown are corresponding

results for as-deposited and CdCl2-treated CdTe. …………………………………172

8.4 Energy position and width of the critical point generating the strongest peak in ε2 for

as-deposited thin film Cd1-xHgxTe. ………………………………………………..174

xii

List of Figures

1-1 Schematic representation of the electric field vector trajectory0( , )E r t

r r for an elliptically

polarized light wave at a fixed position 0rr

versus time. Q is the tilt angle between the

ellipse major axis a and the p-axis, measured in counterclockwise-positive sense

when facing the light source. χ is the ellipticity angle given by tan-1(b/a). …...........

……………………………..…………………………………………………………7

1-2 Reflection of a polarized light wave at an interface between two media. ……….…..9

1-3 Spectroscopic ellipsometer used in this research mounted in the ex-situ mode of

operation. …………………………………………………………………………...11

1-4 Simplified flow chart of the data analysis procedure. …………...…………………13

1-5 Optical model and physical structure of a c-Si wafer used as a substrate. .……...........

………………………………...………………………..…...………………...…….14

2-1 The substrate structure for CdTe solar cells. ……………………………………….19

xiii

2-2 The superstrate structure for CdTe solar cells. ……………………………………..19

3-1 The multilayer structure of the TEC-15 glass substrate. …………………………...28

3-2 Simple model deduced from the analysis of the transmittance and ellipsometric (ψ, ∆)

spectra of Figs. 3-3 – 3-5 for the soda lime glass substrate. The surface roughness

is obtained in a best fit of the (ψ, ∆) spectra. …………………..…………………..31

3-3 Best fit simulated and experimental normal incidence transmittance spectra T vs.

photon energy for an uncoated soda lime glass substrate used in the fabrication of

TEC glasses. ………………………………………………………………………..31

3-4 Best fit simulated and experimental ellipsometric angle ψ = tan−1 (|rp/rs|) vs. photon

energy for an uncoated soda lime glass substrate used in the fabrication of TEC

glasses. The angle of incidence is 60˚. …………………………………………..32

3-5 Best fit simulated and experimental ellipsometric angle ∆ = δp − δs vs. photon energy

for an uncoated soda lime glass substrate used in the fabrication of TEC glasses.

The angle of incidence is 60˚. ……………………………………………………...32

3-6 Index of refraction (left) and extinction coefficient (right) vs. wavelength for the

xiv

uncoated soda lime glass substrate. The index of refraction results are derived from

the ellipsometric ψ spectrum whereas the extinction coefficient results are derived

from the transmittance spectrum. The data values are tabulated in Appendix A. ......

………………………………………………………………………………………33

3-7 Model with best fitting parameters obtained in the analysis of the transmittance and

ellipsometric (ψ, ∆) spectra of Figs. 3.8 and 3.9 for the soda lime glass substrate

coated with a single layer of undoped SnO2. ……………………………………….34

3-8 Normal incidence transmittance T vs. photon energy for a soda lime glass substrate

coated with a single layer of undoped SnO2, the first layer in the fabrication of TEC

glasses. Experimental data (broken line) and a best fit simulation (solid line) are

shown. ………………………………………………………………………………35

3-9 Ellipsometric angles ψ and ∆ vs. photon energy for a soda lime glass substrate coated

with a single layer of undoped SnO2. Experimental data (broken lines) and best fit

simulations (solid lines) for an angle of incidence of 60˚ are shown. ………………..

………………………………………………………………………………………35

3-10 (a,b) Real and imaginary parts of the dielectric function ε1 and ε2 vs. photon energy

for undoped SnO2 that forms the first layer of TEC glasses; (c) analytical expression

xv

for the complex dielectric function of (a,b) along with the best-fit free parameters

and their confidence limits. ………………………………………………………...36

3-11 Model adopted for the analysis of the transmittance and ellipsometric (ψ, ∆) spectra

of Figs. 3.12 and 3.13 obtained on the soda lime glass substrate coated with a single

layer of SiO2. ……………………………………………………………………….37

3-12 Normal incidence transmittance T vs. photon energy for a soda lime glass substrate

coated with a single layer of SiO2, which is used as the second layer in the

fabrication of TEC glasses; experimental data (broken line) and a best fit simulation

(solid line) are shown. ……………………………………………………………...38

3-13 Ellipsometric angles ψ and ∆ vs. photon energy for a soda lime glass substrate

coated with a single layer of SiO2, which is used as the second layer in the

fabrication of TEC glasses; experimental data (broken lines) and a best fit simulation

(solid lines) are shown. ……………………………………………………………..38

3-14 (a) Real (solid line) and imaginary (broken line) parts of the dielectric function ε vs.

photon energy for SiO2 that forms the second layer of the TEC glasses. The

imaginary part of the dielectric function vanishes; (b) mathematical expression for

the dielectric function in (a) along with the best fitting parameters and their

xvi

confidence limits. ……………………………………………………..……………39

3-15 Real and imaginary parts of the dielectric function ε vs. photon energy for the SiO2

that forms the second layer of the TEC glasses (solid lines) for comparison with the

reference data of a thermally-grown SiO2 on crystalline silicon. ………………..……

………………………………………………………………………………………..39

3-16 Best fit sample structure for a soda lime glass substrate coated with a two layer stack

of undoped SnO2 and SiO2, which are the first two layers used in the fabrication of

TEC glasses. ………………………………………………………………………..40

3-17 Ellipsometric angles (ψ, ∆) at an angle of incidence of 60˚ and transmittance T at

normal incidence plotted versus photon energy for a soda lime glass substrate coated

with a two layer stack of undoped SnO2 and SiO2, which are the first two layers used

in the fabrication of TEC glasses. …………………………………………………..41

3-18 Best fit multilayer stack for a complete TEC-15 glass sample. The layered

structure includes thin undoped SnO2, thin SiO2, and thick doped SnO2:F with

surface roughness on top. The previously-determined dielectric functions were

used for the soda lime glass and the two thin layers. ………………………………43

xvii

3-19 Normal incidence transmittance T vs. photon energy for a complete TEC-15 glass

sample consisting of a soda lime glass substrate coated with layers of undoped SnO2,

SiO2, and top-most doped SnO2:F. Experimental data (broken line) and a best fit

simulation (solid line) are shown. ………………………………………………….43

3-20 Ellipsometric angles ψ and ∆ at a 60˚ angle of incidence plotted vs. photon energy

for a complete TEC-15 glass sample consisting of a soda lime glass substrate coated

with layers of undoped SnO2, SiO2, and top-most doped SnO2:F. The broken lines

indicate experimental spectra and the solid lines indicate the best fit

simulation. ………………………………………………………………………….44

3-21 Real and imaginary parts of the dielectric function ε1 and ε2 vs. photon energy for

doped SnO2:F that forms the top-most layer of TEC-15 glass. These results are

obtained as a best fit analytical expression at low energies where the film is

semitransparent and by an inversion of (ψ, ∆) data at high energies where the film is

opaque. ……………………………………………………………………………..44

3-22 (a) The analytical equation for the dielectric function of the top-most SnO2:F layer

of TEC-15 that holds below 4.4 eV; also shown is (b) a table of the best fit

parameters in the equation and their confidence limits. ……………………………45

3-23 Multilayer structure with best-fit parameters for a complete TEC-7 glass sample.

xviii

The layered structure includes thin undoped SnO2, thin SiO2, and a thick layer of

doped SnO2:F with surface roughness on top. The previously determined dielectric

functions for TEC-15 glass were used here for this TEC-7 glass sample. ……………

………………………………………………………………………………………47

3-24 Multilayer structure with best-fit parameters for a complete TEC-8 glass sample.

The layered structure includes thin undoped SnO2, thin SiO2, and a thick layer of

doped SnO2:F with surface roughness on top. The previously determined dielectric

functions for TEC-15 glass were used here for this TEC-8 glass sample. ……………

………………………………………………………………………………………47

3-25 Transmittance T vs. photon energy for a complete TEC-7 glass sample; experimental

data (broken line) and simulated results based on the ellipsometric model (solid line)

are shown (left). The difference between the two data sets is shown at the

right. ………………………………………………………………….…………….49

3-26 Normal incidence transmittance T vs. photon energy for a complete TEC-8 glass

sample; experimental data (broken line) and simulated results based on the

ellipsometric model (solid line) are shown (left). The difference between the two

data sets is shown at the right. ……………………………………………………...50

xix

3-27 For TEC-7 glass, the normal incidence scattering results predicted by combining

ellipsometry and normal incidence specular transmittance are shown in comparison

with experimental normal incidence integrated scattering data from a diffuse

transmission experiment. Different TEC-7 samples were used for the two different

data sets. ……………………………………………………………………………51

3-28 For TEC-8 glass, the normal incidence scattering results predicted by combining

ellipsometry and normal incidence specular transmittance are shown in comparison

with experimental normal incidence integrated scattering data from a diffuse

transmission experiment. Different TEC-8 samples were used for the two different

data sets. ……………………………………………………………………………51

4-1 A schematic of optical models used to evaluate a CdTe film by optical depth profiling

during both deposition and etching processes. ……………………….…………….56

4-2 The evolution of void volume fraction within the top 100 Å of the bulk layer as a

function of CdTe bulk layer thickness obtained during the deposition and etching

processes. …………………………………………………………………………...58

4-3 Schematic of the sample structural changes that occur in the last three etching steps

for a CdTe film on c-Si. The starting thickness of this CdTe film is 3500 Å. ………

xx

…………….…………………………………………………………………………60

4-4 Ellipsometric spectra for a smoothened CdTe film on a c-Si wafer measured at angle

of incidence of 63°. The broken lines represent data measured before the first

additional Br2+methanol etching step, and the solid lines represent data measured

after the 6th additional Br2+methanol etching step. The total etching time between

the two is 18 seconds. The starting CdTe thickness before any etching was 3 µm. ...

.………………………………………………………………………………………61

4-5 Ellipsometric spectra for a CdTe thin film on a crystalline Si substrate after the 36th

and 37th etch steps for comparison. The starting CdTe film thickness was 3500 Å. ..

.………………………………………………………………………………………64

4.6 Ellipsometric spectra for a CdTe thin film on a crystalline Si substrate with a starting

thickness of 3500 Å measured after the 37th (left) and 36th (right) etching steps (data

points). Also shown are their best fits (broken lines). ………………………..……..

.………………………………………………………………………………………64

4-7 Model and best-fit parameters used for the analysis of the ellipsometric spectra of Fig.

4.6 (left panel) collected after the 37th etching step applied to a CdTe film on a

crystalline Si substrate. Because the CdTe film is completely removed, this

xxi

analysis provides the structure of the c-Si substrate. MSE indicates the mean

square error in the fit. ………………………………………………………………65

4-8 Model and best fit parameters used for the analysis of the ellipsometric spectra of Fig.

4.6 (right panel) collected after the 37th etching step applied to a CdTe film on a

crystalline Si substrate. This analysis yields the structure of the a-Te layer on the

c-Si substrate. The void volume fraction in the a-Te layer has been obtained by

expressing the a-Te layer in this study of polycrystalline CdTe as a mixture of the

a-Te obtained in a previous study of single crystal CdTe along with a void

component. …………………………………………………………………………65

4-9 Real and Imaginary parts of the dielectric function ε1 and ε2 vs. photon energy for

a-Te generated through Br2+methanol etching of a polycrystalline CdTe film. ………

.………………………………………………………………………………………65

4-10 A comparison of the a-Te optical properties deduced in this study (see Fig. 4.9) with

the literature reference optical properties of a-Te from 1.5~6 eV, the latter obtained

by etching single crystal CdTe. …………………………………………………….66

4-11 Ellipsometric spectra for a CdTe thin film on a crystalline Si substrate with a starting

thickness of 3500 Å measured after the 35th etch step (left panel). Also shown is

xxii

the best fit and associated model deduced in the analysis of the ellipsometric spectra

in order to extract the a-Te/CdTe/c-Si structural parameters (right panel). …………...

.………………………………………………………………………………………68

4-12 Experimental and best fit spectra (left panel) along with the best fit parameters and

model (right panel) for comparison with the results of Fig. 4.11, but without

introducing an a-Te component into the model. Such a model leads to a higher

MSE. ………………………………………………………………………………..68

4-13 Ellipsometric spectra and the best fit (left panel) for a smoothened CdTe film with a

starting thickness of 3 µm obtained before the first additional etch after smoothening.

Also shown is the model and best fit parameters used in the analysis of the

ellipsometric spectra over the energy range of 2 to 6 eV in order to deduce the a-Te

volume fraction in the surface roughness layer (right panel). ………………………...

.………………………………………………………………………………………69

4-14 Experimental and best fit spectra (left panel) along with the best fit model and

parameters (right panel) for comparison with the results of Fig. 4.13, but without

introducing an a-Te component into the model. This ellipsometric analysis is

associated with a 3 µm thick smoothened CdTe film before the first additional etch

after smoothening. ………………………………………………………………….69

xxiii

4-15 Ellipsometric spectra and the best fit (left panel) for a smoothened CdTe film with a

starting thickness of 3 µm obtained after the 6th additional etch after smoothening.

Also shown is the model and best fit parameters used in the analysis of the

ellipsometric spectra over the energy range of 2 to 6 eV in order to deduce the

surface roughness thickness and the a-Te volume fraction in the CdTe structure (right

panel). ………………………………………………………………………………70

4-16 Experimental and best fit spectra (left panel) along with the best fit model and

parameters (right panel) for comparison with the results of Fig. 4.15 but without

introducing an a-Te component into the model. This ellipsometric analysis is

associated with a 3 µm thick smoothened CdTe film after the 6th additional etch. …...

…….…………………………………………………………………………………70

5-1 The room temperature dielectric functions of single crystal CdTe (broken lines) and a

CdTe film deposited at 188°C (solid lines). The downward arrows point to the

energy values of the four critical point transitions E0, E1, E1+∆1, and E2. ……………

……………………….………………………………………………………………73

5-2 Band structure of CdTe. …...………………………………………………………..74

xxiv

5-3 The room temperature ordinary dielectric functions of single crystal (wurtzite) CdS

(broken lines) in comparison with the polycrystalline thin film CdS deposited on c-Si

at 225 °C (solid line). The three downward arrows point to the energy values of the

critical point transitions. ……………………………………………………………75

5-4 (left) Best fit analytical models of the room temperature dielectric functions for two

CdTe films of thickness approximately 1000 Å, obtained from the same deposition

but with different post-deposition processing: as-deposited (no treatments; broken

line) and CdCl2-treated for 5 min at 387°C (solid line); (right) a comparison between

the CdCl2-treated CdTe film (solid line) and single crystal CdTe (broken line). ……..

.………………………………………………………………………………………78

5-5 A schematic of the sputtering chamber for CdTe/CdS deposition on a fused silica

prism. ……………………………………………………………………………….81

5-6 (left) Best fit analytical models for the room temperature dielectric functions of a CdS

film as-deposited on a fused silica prism measured from the prism side and on a c-Si

wafer measured from the ambient side; (right) best fit analytical model for the

room temperature dielectric functions of CdS measured from the prism side before

and after a 30 min CdCl2 treatment at 387°C. ……………………………………...82

xxv

5-7 Resonance energies En (upper panel) and linewidths Γn (lower panel) for the critical

point transitions in single crystal CdTe (broken lines) and in db ~ 1000 Å thick CdTe

films sputter-deposited at different temperatures (points), all measured at 15°C. ……

………………………………………………………………………………………85

5-8 Critical point energies (upper panel) and widths (lower panel) as functions of CdTe

bulk layer thickness during etching by Br2+methanol for co-deposited CdTe films

processed in three different ways: (i) as-deposited, (ii) annealed in Ar for 30 min,

and (iii) CdCl2 treated for 5 min. The deviations at low thickness are due to the onset

of semi-transparency at the E1 critical point energy. ……………………………….86

5-9 Relative void volume fractions as functions of CdTe bulk layer thickness during

etching by Br2+methanol for co-deposited CdTe films processed in three different

ways: (i) as-deposited, (ii) thermally annealed in Ar for 30 min, and (iii)

CdCl2-treated for 5 min. For the as-deposited and annealed films, the void fraction

is scaled relative to the observed highest density film. For the CdCl2-treated film,

the void volume fraction is scaled relative to single crystal CdTe. …………………...

.………………………………………………………………………………………88

5-10 Energy of the E1 transition (upper panel) and its width ΓE1 (lower panel) as

functions of CdTe bulk layer thickness in successive Br2+methanol etching steps for

xxvi

~3000 Å thick CdTe films. The two films were processed under identical conditions

including fabrication on c-Si wafer substrates and annealing in Ar at 387°C for 30

minutes. The data for experiment #1 are the same as those depicted in Fig. 5.8. …….

.………………………………………………………………………………………90

5-11 Energy of the E1 transition (upper panel) and its width ΓE1 (lower panel) as functions

of CdTe bulk layer thickness in successive Br2-methanol etching steps for ~3000 Å

thick CdTe films. The two films were processed under similar conditions including

fabrication on c-Si wafer substrates and CdCl2 treatment for 5 minutes. The data

for experiment #1 are the same as those depicted in Fig. 5.8. .......................................

.………………………………………………………………………………………90

5-12 Void volume fraction as a function of CdTe bulk layer thickness in successive

Br2-methanol etching steps for ~3000 Å thick CdTe films in a second experiment for

comparison with the results in Fig. 5.9. Two different post-deposition processing

procedures were used: (i) an anneal in Ar for 30 min, and (ii) a CdCl2-treatment for 5

min. For the Ar annealed films, the void fraction is scaled relative to the depth at

which the highest density is observed. For the CdCl2-treated film, the void volume

fraction is scaled relative to single crystal CdTe. The void structure for the film

annealed in Ar is attributed to structure in the as-deposited film (as in Fig. 5.8). In

contrast, the void structure for the CdCl2 treated film is associated with extensive

xxvii

near-surface roughness. …………………………………………………………….92

6-1 Evolution of the surface roughness thickness and a depth profile of the void volume

fraction plotted versus bulk layer thickness obtained in successive Br2+methanol

etching steps that reduce the bulk layer thickness of an as-deposited CdTe

component of a solar cell. …………………………………………………………..99

6-2 (a, left) Evolution of the surface roughness thickness and a depth profile of the void

volume fraction plotted versus bulk layer thickness obtained in successive

Br2+methanol etching steps that reduce the bulk layer thickness of the CdCl2-treated

CdTe component of a solar cell; (b, right) a schematic structure suggested from (a). ..

.……………………………………………………………………………………..100

6-3 (left) Depth profiles of the critical point energies of the E1, E1+∆1 and E2 transitions

in the as-deposited CdTe layer of a solar cell, plotted versus bulk layer thickness

obtained in successive Br2+methanol etching steps that reduce the bulk thickness;

(right) depth profiles of the linewidths of the E1, E1+∆1 and E2 transitions obtained in

the same experiment. ……………………………………………………………...103

6-4 (a, top left) Depth profiles of the critical point energies of the E1, E1+∆1 and E2

transitions in the CdCl2-treated CdTe layer of a solar cell, plotted versus the bulk

xxviii

layer thickness obtained in successive Br2+methanol etching steps that reduce the

bulk thickness; (b, top right) depth profiles of the linewidths of the E1, E1+∆1 and E2

transitions obtained in the same experiment; (c, bottom) a schematic structure

suggested from (b). ………………………………………………………………..104

6-5 Energies of the E1, E1+∆1, and E2 transitions as functions of CdTe bulk layer

thickness in successive etches of a CdCl2 treated CdTe solar cell that reach within

0.1 µm of the CdS/CdTe interface. ………………………………………………..106

6-6 Broadening parameters ΓE1, ΓE1+∆1, and ΓE2 as functions of CdTe bulk layer thickness

in successive etches of a CdCl2 treated CdTe solar cell that reach within 0.1 µm of

the CdS/CdTe interface. …………………………………………………………...106

6-7 Experimental pseudo-dielectric function spectra for the CdTe solar cell of Figs. 6.2

and 6.4 after the 15th etching step; also shown is the best fit using the structural

model of Fig. 6.8. …………………………………………………………………109

6-8 Structural model for the CdTe solar cell after the 15th etch step that provides the best

fit in Fig. 6.7. ……………………………………………………………………...109

6-9 Ex situ SE spectra in (ψ, ∆) (symbols) (a) from the free CdTe surface after 8

xxix

Br2+methanol etching steps and (b) from the prism/glass side without etching. The

best fit results (solid lines) yield the structural parameters in Figs. 6.10 and 6.11,

including the thicknesses of the CdTe roughness, CdTe bulk, CdTe/CdS interface,

and CdS bulk layers, as well as the volume fractions of CdS/CdTe in the interface

layer and void in the CdS bulk layer. ……………………………………………..110

6-10 The best fit results from the free CdTe surface after 8 Br2+methanol etching steps

yielding the thicknesses of the CdTe roughness, CdTe bulk, CdTe/CdS interface, and

CdS bulk layers, as well as the volume fractions of CdS/CdTe in the interface layer

and void in the CdS bulk layer. ……………………………………………………111

6-11 The best fit results from the prism/glass side without etching yielding the

thicknesses of the CdTe roughness, CdTe bulk, CdTe/CdS interface, and CdS bulk

layers, as well as the volume fractions of CdS/CdTe in the interface layer and void in

the CdS layer. ……………………………………………………………………...111

6-12 CdS and CdTe/CdS interface layer thicknesses deduced from spectra collected

through the prism/glass (solid line) and from spectra collected from the CdTe surface

in successive etches (points, dotted line extrema). ………………………………..113

6-13 Multilayer stack used to model the thicknesses and compositions of the individual

xxx

layers of the CdTe solar cell. The SE beam enters through the glass, and the

reflection from the top surface is blocked since it is incoherent with respect to the

reflection from the glass/film interface. …………………………………………..114

6-14 Step-by-step MSE reduction by adding one fitting parameter at a time. Starting

with the CdTe thickness as a variable, each additional parameter was subsequently

fitted. It was found that fitting the SnO2:F thickness provided the greatest

improvement in MSE among all 2-parameter attempts. Similar methodology was

used for all 12 parameters. Circular points indicate the best n-parameter fit with n

given at the top and the added parameter given in Table 6.2. …………………….115

6-15 Ellipsometric spectra (points) in ψ (top) and ∆ (bottom) at an angle of incidence of

60° as measured through the glass at a single point on a 3 x 3 cm2 CdTe solar cell

sample. The solar cell was treated with CdCl2 but no back contact processing was

performed. Also shown is a best fit (lines) using the model structure of Fig. 6.13

with the parameters listed in Table 6.3. …………………………………………...118

7-1 Time evolution of (ψ, ∆) at 5 photon energies selected from 706-point spectra

acquired during sputter deposition of CdTe on a Mo coated glass slide. The full

spectral acquisition time was 2 s and the angle of incidence was 65.68°. ………..122

xxxi

7-2 Flow chart of the three-iteration <MSE> minimization procedure for CdTe film

growth on a rough Mo film substrate. …………………………………………….127

7-3 The schematic structure describing the final optical model for deposition on rough

Mo. ………………………………………………………………………………..128

7-4 The schematic structures describing the interface filling (left) and bulk layer growth

(right) models for the first interface layer. ………………………………………...129

7-5 (Left) MSE, which is a measure of the quality of the fit to RTSE data, for the

complete CdTe deposition using optical models for the CdTe film consisting of one

bulk layer (broken line) and four bulk layers (solid line). In both cases a one-layer

model for surface roughness was employed; (right) the MSE for the model with four

bulk layers is shown on an expanded scale. ………………………………………130

7-6 Evolution of the surface roughness thickness versus deposition time determined using

a four-layer model for CdTe film growth on rough Mo. The spikes in the surface

roughness thickness result from the consideration of each bulk layer individually

with an independent surface roughness layer. In this case, the surface roughness

layer on the underlying layer is instantaneously transformed into an interface layer at

the vertical broken lines upon initial growth of the overlying layer, whose roughness

layer starts from zero thickness. …………………………………………………..132

xxxii

7-7 Time evolution of the CdTe overlayer volume percent during interface filling of the

underlying CdTe roughness layer for CdTe growth on Mo. ………………………132

7-8 (Left) Evolution of the individual bulk layer thicknesses versus deposition time

determined using a four-layer model for CdTe film growth on Mo; (right) evolution

of effective thickness of CdTe, including all bulk, interface, and surface layer

components. ……………………………………………………………………….133

7-9 Mo dielectric function at a nominal temperature of 200 °C acquired by inversion

assuming a Mo substrate roughness thickness of 79.6 Å (solid line). For the

overlying CdTe, four bulk layers and a roughness layer are used to describe the best

fit model. For the first bulk layer, the Mo/CdTe interface roughness, the CdTe bulk,

and CdTe surface roughness layer thicknesses di, db, ds, respectively, are determined

in a dynamic analysis, in which case the criterion is the minimum average MSE.

The Mo/CdTe interface roughness thickness di is taken to be the same as the Mo

substrate film roughness thickness. Also shown is the Mo dielectric function at room

temperature before heating to the deposition temperature as determined by inversion,

again assuming a Mo surface roughness layer thickness of 79.6 Å (broken line). …...

………………………………………………………………………………………134

7-10 Real (top panel) and imaginary (bottom panel) parts of the dielectric functions of the

xxxiii

four layers [(a)-(d)] of a CdTe thin film deposited on rough Mo. These results are

determined from inversion, after determining the CdTe roughness and bulk layer

thicknesses through minimization of the average MSE obtained throughout the layer

analysis; (e) also shown is a comparison of the first layer dielectric function of CdTe

deduced in this study with that of CdTe deposited on a smooth c-Si substrate at a

nominal temperature of 200 °C. In (b)-(d) comparisons are provided between the

dielectric function of a given layer and that of the layer underneath it. ………………

.……………………………………………………………………………………..137

7-11 Comparison of the surface roughness thickness at the end of the deposition for a

1496.5 Å thick CdTe film on Mo as deduced by RTSE with the relative surface

height distribution and rms roughness from AFM. ……………………………….138

7-12 A comparison of measured pseudo-dielectric functions (solid lines) for Mo thin

films deposited by sputtering (a) on glass and (b) on Kapton. Also shown are the

fits (broken lines) using a reference dielectric function for dense Mo determined

separately, and the multilayer models depicted in the insets. ……………………..140

7-13 Ellipsometric spectra (solid lines) and best fit (broken lines) using the structural

model and best fit parameters shown in the inset. The dielectric function is

determined simultaneously using a model assuming a sum of critical point structures.

xxxiv

The resulting dielectric function is shown in Fig. 7.14. …………………………..142

7-14 Dielectric function of thin film ZnTe:Cu prepared by magnetron sputtering with 1

wt.% Cu in the ZnTe target (solid lines). A model consisting of four critical points

in the band structure has been used in this analysis. The data points are literature

results for single crystal ZnTe. ……………………………………………………144

7-15 Step-by-step MSE reduction by adding one fitting parameter at a time. Starting with

the CdTe thickness as a variable, each additional parameter was subsequently fitted.

It was found that fitting the CdS thickness provided the greatest improvement in

MSE among all 2-parameter attempts. Similar methodology was used for all 14

parameters. Circles connected by the solid line indicate the best n-parameter fit with

n given at the top and the added parameter given in Table 7.5. …………………..147

7-16 Ellipsometric spectra for a CdTe solar cell deposited on Mo in the substrate

configuration (points). The cell was exposed to a CdCl2 treatment before this

measurement. The top contact of the solar cell is not incorporated over the area

probed, leading to the structure: ambient/CdS/CdTe/ZnTe:Cu/Mo. The solid line

depicts the optical model shown in Fig. 7.17. …………………………………….148

7-17 Optical model for a CdTe solar cell in the substrate configuration (excluding the top

xxxv

contact) deposited on a Mo film surface. This model and the best fit parameters

provide the solid line results in Fig. 7.16. ………………………………………...151

8-1 Current-voltage and normalized quantum efficiency spectra for a champion 16.5%

efficient CdTe/CdS thin-film solar cell. …………………………………………..152

8-2 Two-terminal tandem cell based on Cd1-xMgxTe and Cd1-xHgxTe absorbers. …………

.……………………………………………………………………………………..154

8-3 Real (a) and imaginary (b) parts of the pseudo-dielectric functions of RF sputtered

CdTe (Eg = 1.50 eV), Cd1-xMnxTe (Eg = 1.63 eV) and Cd1-xMgxTe (Eg = 1.61 eV)

films all in the as-deposited state; (c) Pseudo-dielectric function of as deposited

Cd1-xMnxTe samples after different storage times in laboratory ambient: (1)

immediately after Br2/methanol etch; (2) 3 weeks after deposition; and (3) 1.5 years

after deposition. …………………………………………………………………...158

8-4 Best fit (lines) to the second derivative of the experimental pseudo-dielectric function

(points) for the as-deposited Cd1−xMnxTe film of Fig. 8.3 (c: immediately after etch).

The three CP transitions, E1, E1 + ∆1, and E2, are indicated by arrows with best fit

energies of 3.352, 3.884, and 5.033 eV, respectively. The composition of x=0.06

can be estimated by the empirical relationship between E1, the strongest CP in this

xxxvi

case, and the composition. ………………………………………………………...160

8-5 Variation of the pseudo-dielectric function of as deposited Cd0.94Mn0.06Te with time

after Br2/methanol etching, measured in situ at room temperature during exposure to

laboratory ambient. ………………………………………………………………..161

8-6 Pseudo-dielectric functions of as-deposited and one-step and two-step CdCl2 treated

Cd0.94Mn0.06Te samples. …………………………………………………………...161

8-7 Index of refraction and extinction coefficient of amorphous TeO2. ……………….162

8-8 Pseudo-dielectric functions of as-deposited and CdCl2 treated Cd1-xMgxTe samples. ...

.……………………………………………………………………………………..163

8-9 Approximate dielectric functions, i.e., optical properties deduced with a best attempt

to eliminate surface effects, for as-deposited films and CdCl2-treated films obtained

by SE after Br2+methanol etching that improves the surface quality (points); (a)

CdTe; (b) Cd1-xMnxTe; (c) Cd1-xMgxTe; the solid lines show the results of fits to

extract critical point energies and widths. The result for the CdCl2-treated

Cd1-xMnxTe could not be fit with a critical point parabolic band model. ……………..

.……………………………………………………………………………………..166

xxxvii

8-10 Pseudo-dielectric function obtained directly from experimental (ψ, ∆) data using a

single interface conversion formula for a Cd1-xMgxTe sample prepared from a target

of CdTe (80 wt.%) + MgTe (20 wt.%) (CGT42). The solid line describes

experimental data and the dashed line describes the best fit result. The deduced

bulk and surface roughness layer thicknesses are shown. ………………………...169

8-11 Best fit analytical dielectric function obtained from an analysis of the experimental

(ψ, ∆) data for the Cd1-xMgxTe sample of Fig. 8.10 prepared from a target of CdTe

(80 wt.%) + MgTe (20 wt.%) (CGT42). …………………………………………..169

8-12 Pseudo-dielectric function obtained directly from experimental (ψ, ∆) data using a

single interface conversion formula for a Cd1-xMgxTe sample prepared from a target

of CdTe (60 wt.%) + MgTe (40 wt.%) (CGT92). The solid line describes

experimental data and the dashed line describes the best fit result. The deduced

bulk and surface roughness layer thicknesses are shown. ………………………...170

8-13 Best fit analytical dielectric function obtained from an analysis of the experimental

(ψ, ∆) data for the Cd1-xMgxTe sample of Fig. 8.12 prepared from a target of CdTe

(60 wt.%) + MgTe (40 wt.%) (CGT92). …………………………………………..171

xxxviii

8-14 Band gap of as-deposited thin film Cd1-xHgxTe as a function of the substrate

temperatures over the range from 23°C to 153°C. ………………………………..174

8-15 Dielectric functions from mathematical inversion and from the corresponding

analytical model fit for as-deposited Cd1-xHgxTe films prepared with different

substrate temperatures. ……………………………………………………………175

8-16 Comparison of the real (left) and imaginary (right) parts of the pseudo-dielectric

function of as-deposited and CdCl2 treated CdxHg1-xTe films, including results (a)

before and (b) after a single Br2/methanol etching step. ………………………….177

1

Chapter One

Introduction to Spectroscopic Ellipsometry

1.1 History

The very first ellipsometric studies were performed by Professor Paul Drude (1863~

1906), even though the term “ellipsometry” was not used at that time [1-1]

. Drude was

the first to derive the equations of ellipsometry, and was also the first to perform

experimental studies on both absorbing and transparent solids. The optical properties

determined in these ellipsometry studies were found to be quite accurate. In fact, when

Palik compared Drude’s results with those obtained 100 years later, the results were

amazingly close [1-2]

. Because of the absence of fast computation methods made possible

by the modern computer, Drude obtained the optical properties of solids at only a few

selected wavelengths [1-1].

After Paul Drude’s tremendous impact on ellipsometry development, very little

progress was reported in the succeeding 70 years. One exception was a 1945 article

authored by Alexandre Rothen who described the half-shade method to detect the

polarization state change of light upon reflection from a specular surface, and coined the

term “ellipsometry”[1-3]

. When laboratory computers became prevalent in the 1960s and

2

1970s, automated ellipsometers for diverse purposes were developed [1-4]

. Among the

different types of automated ellipsometers developed at that time, two major types are

still widely used in the spectroscopic mode of operation: (i) the rotating element

ellipsometer [1-5],

and (ii) the phase modulation (PM) ellipsometer [1-6]

. The photon

energy range of spectroscopic ellipsometry has increased significantly over the years

since D. E. Aspnes and A. A. Studna developed the first rotating analyzer spectroscopic

ellipsometer covering the full (near-infrared)-to-(near-ultraviolet) range [1-7]

. At the

same time, the instrument development focus was also placed on increasing the speed of

full spectroscopic measurement by incorporating a multichannel detection system in the

ellipsometer in order to acquire the entire spectral range essentially simultaneously [1-8]

.

As a result of this effort, the technique of real time spectroscopic ellipsometry (RTSE)

arose for analysis of thin film growth and materials processing.

1.2 Purpose

Spectroscopic ellipsometry is used to obtain the optical properties of materials of

interest in optical and electronic applications [1-9]

. Once optical properties of materials

are available, thin film thicknesses can be measured using optical models for single thin

film and multilayer samples. Advanced data analysis often enables measurement of

thickness and optical properties simultaneously [1-10, 1-11]

. The measurable thickness

range for ellipsometry varies from submonolayer to several microns. For spectroscopic

ellipsometry measurements of thickness, a wide spectral range is important since the light

must penetrate through the thin film, reflect from an underlying interface, return through

3

the film, and proceed to the detector. In studies of semiconductors, lower energy gap

materials such as CuInSe2 can be analyzed for thickness when the spectral range extends

deeper into the infrared. For energies below the semiconductor band gap, the light

remains unabsorbed and reflects from the bottom interface of the film, enabling wave

superposition and phase shifts that allow thickness to be determined. This demonstrates

the advantage of spectroscopic ellipsometers with an extended near-IR spectral range,

even below the 1.1 eV band gap of the most common Si diode detectors used in

ellipsometers. A similar advantage exists for spectroscopic ellipsometers with an

extended ultraviolet spectral range when characterizing the thickness of metal thin films.

In addition to thickness, other properties of a film can be determined through

ellipsometric measurements performed in real time during the deposition process [1-12].

These include roughness thickness on the surface of the film and the optical properties of

the film. From the latter, the film density deficit (represented by a volume fraction of

voids in the layer), film crystalline quality (represented by a defect density or average

grain size), alloy composition, and temperature may be determined. In fact, real time

measurements may also provide a depth profile of the film structure and properties, and

even area uniformity of the film.

1.3 Data measured by ellipsometry

An ellipsometric measurement provides the angles (ψ, ∆), corresponding to the

relative amplitude ratio (tanψ) and phase shift difference (∆) between the complex

4

amplitude reflection coefficients for pEr

and sEr

, the orthogonal linear electric field

components of a polarized light wave [1-13]

. These electric field components are parallel

( pEr

) and perpendicular ( sEr

) to the plane of incidence. (The overline arrow denotes a

complex vector in which case each vector component has a real amplitude and phase.)

The nature of pEr

and sEr

for a light wave will be further elucidated in the next section.

Thus, the quantity measured by ellipsometry is the ratio ρ% of the complex amplitude

reflection coefficients for the p-polarized field component ( pR% ) to that for the s-polarized

field component (sR% ):

tan∆= =

%

%%

p i

s

Rρ e

Rψ ; (1-1)

where

( )exp

ref

p

p p pinc

p

ER R i

Eδ= =

%% %

%, (1-2)

( )expref

ss s sinc

s

ER R i

Eδ= =

%% %

%. (1-3)

Here, the notational style of these equations will be summarized. Generally, the

subscripts p and s identify the wave characteristics for vector components parallel and

perpendicular to the plane of incidence, respectively. For example, δp and δs represent

the phase shifts of each orthogonal electric field component upon reflection. On the

other hand ( )p sE% denotes the p (s) orthogonal component of the electric field amplitude.

The superscripts “ref” and “inc” in Eqs. (1-2) and (1-3) refer to the electric field

components of the reflected and incident light waves.

5

As a result, the angles ψ and ∆ are defined by:

tan =%

%

p

s

R

Rψ , (1-4)

p sδ δ∆ = − . (1-5)

( )p sR% are also called the complex Fresnel coefficients. As a complex variable, ( )p sR%

provides information on the amplitude change and phase shift of the p (s) field

components of the wave upon its reflection from the sample. In fact, the complex

Fresnel coefficients provide the reflected-to-incident amplitude ratio and the

reflected-minus-incident phase shift for each orthogonal electric field component pEr

(or

sEr

) of the polarized light wave.

1.4 Mathematical derivation

In order to understand the derivation of optical properties from the ellipsometric

angles (ψ, ∆), it is necessary to understand first the mathematics of polarized light.

When the most general state of elliptically polarized light wave transmits through or

reflects from one or more interfaces between media at a non-normal angle of incidence,

the polarization change can be defined in terms of a change in tilt angle and ellipticity

angle of the general polarization ellipse. This change depends on the angle of incidence

and the optical properties and thicknesses of the media. The elliptically polarized state

of monochromatic light in any medium assumed to be isotropic can be described by

decomposing the beam into two orthogonal components which are linear and parallel ( pEr

)

6

as well as linear and perpendicular ( sEr

) to the plane of incidence. Both components are

plane waves and a superposition of such components is described by [1-14]

:

[ ]0( , ) exp ( )E r t E i q r tω= ⋅ −r rr r r

; (1-6)

where qr

is the complex propagation vector, ω is the wave frequency,

and 0Er

determines the polarization state of the wave. In this linear p-s basis,

0ˆ ˆp s

i i

p s p sE E E E e p E e sγ γ= + = +

r r r. (1-7)

For this general polarization state of the light wave, the endpoint of the vector 0Er

traces an ellipse as a function of time t during propagation at a fixed position 0rr

. A

complete cycle is made in a time 2π

τω

= . The plane wave also travels in space with a

phase velocity of Re( )

=%

vq

ω, and the endpoint of the field vector traverses one full

ellipse after a distance equal to the wavelength 2

Re( )=

%q

πλ . Here is %q defined as the

complex magnitude of the propagation vector: ˆ=r

%q qq .

7

Figure 1-1 Schematic representation of the electric field vector trajectory0( , )E r t

r r for an

elliptically polarized light wave at a fixed position 0rr

versus time. Q is the tilt angle

between the ellipse major axis a and the p-axis, measured in counterclockwise-positive

sense when facing the light source. χ is the ellipticity angle given by tan-1

(b/a).

In Equation 1-6, the wavevector qr

defines the propagation direction. If one

assumes qr

is parallel to the z-axis, the wave becomes:

[ ]0( , ) exp ( )= −r r

%E r t E i qz tω ; (1-8)

where

2 2

2 24 = + =

%% rrq i N

c c

πσω ωε

ω, (1-9)

or

=

%%q Nc

ω.

Here c is the speed of light in vacuum. At the light wave frequency ω, εr and σr denote

the real dielectric function and real optical conductivity of the medium in which the wave

p

0( , )E r tr r

b

a χ

Q

s

0r r=r r

8

travels, and N% is its complex index of refraction, where [1-15]

4 rr

N n ik iπσ

εω

= + = +

% . (1-10)

Here n is the (real) index of refraction, and k is the extinction coefficient of the medium.

It should be noted that Re( ) =%q nc

ω, so the phase velocity of the wave is

cv

n= and the

wavelength is 2 2

= =c

vn

π πλ

ω ω as expected. Next %q and N% are substituted into

Equation 1-8 to give

0( , ) exp expkz nz

E r t E i tc c

ω ωω

= − −

r rr. (1-11)

In addition to the complex index of refraction N% , the complex dielectric function ε%

is another commonly used quantity to describe the macroscopic optical properties of

solids [1-15], where:

2

1 2i Nε ε ε= + = %% , (1-12)

2 2

1 r n kε ε= = − , (1-13)

2

42r nk

πσε

ω= = . (1-14)

Ellipsometry measures the change in polarization state of the incident light caused by

reflection from one or more interfaces. When an incident linearly polarized light wave

reflects from a single interface between two media (see Fig. 1.2), the state of polarization

of the reflected beam can assume an elliptical state with the tilt and ellipticity angles

depending on the optical properties of the sample.

9

. .

.

Medium 0

Medium 1

Plane of sample

Plane of incidence

p p

s s

s

p

reflected wave incident wave

θi θi

tθ%

s

p

transmitted wave

Figure 1-2 Reflection of a polarized light wave at an interface between two media.

For the ideal situation of a perfectly planar interface on the atomic scale with no

roughness, the optical properties of the reflecting medium can be derived from the

ellipsometric angles (ψ, ∆) as long as the optical properties of the incident medium and

the angle of incidence are known [1-13]. In the simplest case of reflection and transmission

at the perfectly planar interface between two isotropic media (see Fig. 1.2), the ratio of

the complex Fresnel reflection coefficients can be written:

cos cos

cos cos

cos cos

cos cos

s i a t

p a t s i

s a i s t

a i s t

N n

R n Nρ

R n N

n N

θ θ

θ θ

θ θ

θ θ

−

+ = = −

+

%%

% % %

%% %%

%%

, (1-15)

where na is the assumed real refractive index of Medium 0 (ambient, see Fig. 1.2), sN% is

the complex index of refraction of Medium 1 (substrate, see Fig. 1.2), iθ is the angle of

incidence and tθ% is the complex angle of refraction. cos %

tθ can be obtained from sin iθ ,

10

an , and sN% by using a complex form of Snell’s Law:

2 2 2sincos

s a i

t

s

N n

N

θθ

−= ±

%%

%. (1-16)

Then, eliminating cos tθ from Equation 1-15 yields:

( )( )( )( )

2 2 2 2 2 2 2

2 2 2 2 2 2 2

cos sin cos sin

cos sin cos sin

s i a s a i a i s a ip

ss i a s a i a i s a i

N n N n n N nRρ

R N n N n n N n

θ θ θ θ

θ θ θ θ

− ± −= =

± − −

% % %m%

%% % % %m

, (1-17)

2 2 2 2

2 2 2 2

sin cos sin

sin cos sin

a i i s a i

a i i s a i

n N nρ

n N n

θ θ θ

θ θ θ

−=

± −

%m%

%, (1-18)

and solving for 2

sN% yields:

2

2 2 2 21sin 1 tan

1s a i i

ρN n

ρθ θ −

= + +

%%

%. (1-19)

As a result, by using the dielectric function definition in Equation 1-12, sε% can be

obtained from

2

2 21sin 1 tan

1s a i i

ρ

ρε ε θ θ

−= +

+

%%

%. (1-21)

Therefore, if one knows (i) aε the dielectric function of the ambient; (ii) iθ the angle

of incidence, and (iii) (ψ, ∆) the measured ellipsometric angles, then one can determine

the dielectric function of the reflecting medium.

1.5 Spectroscopic ellipsometer used in the study

The spectroscopic ellipsometer used for the study described in this thesis was

manufactured by J. A. Woollam Company [1-16]

. The specific model used here was the

M-2000DI, which is a rotating-compensator multichannel ellipsometer. This

11

ellipsometer covers the photon energy range from 0.74 to 6.50 eV. One complete set of

spectra in the ellipsometric angles (ψ, ∆) (0.74~6.5 eV) can be collected as an average

over a minimum of two optical cycles in a time of (30.7 Hz)-1

= 32 ms; thus, the single

optical period is 16 ms. Here 30.7 Hz is the mechanical rotation frequency of the

compensator. In the case of real time SE applications, specifically for monitoring the

CdTe or CdS deposition process, acquisition times from 1 to 3 seconds were chosen. In

the case of the ex-situ SE applications, the data acquisition time of 10 seconds was

chosen to ensure a higher precision in the measured (ψ, ∆) spectra. As a result of the

multichannel detection capability, this spectroscopic ellipsometer is ideal for in-situ

process monitoring and quality control, and specifically for studies of the CdTe-based

solar cells as described in this thesis.

Figure 1-3 Spectroscopic ellipsometer used in this research mounted in the ex-situ

mode of operation.

The angle of incidence is adjustable for this ellipsometer. For ex-situ studies, the

ellipsometer is set at angles of incidence ranging from 45° to 75° at 5° intervals.

12

Measurements at different angles of incidence enable one to extract optical properties of

unknown materials with greater confidence. Analyses of all spectra apply either

numerical inversion or least-squares regression algorithms, or even combinations of these

two methods.

1.6 Data analysis

As described in Section 1.4, the ellipsometry measurement provides two angles

(ψ, ∆), which quantify the change in the state of polarization of the light wave upon

oblique reflection from the sample. Ellipsometry does not directly measure the optical

properties and thickness of a thin film; however, ψ and ∆ are functions of these

characteristics, which require data analysis for extraction [1-17]

. The starting point for such

analysis is an optical model for the sample. A general schematic of the analysis

procedure is illustrated in Fig. 1.4.

The first step in building an optical model for the sample requires identifying the

physical sequence of layers of the sample, including each layer’s thickness and optical

properties, the latter either as fixed functions, analytically defined functions with variable

parameters, or even continuously variable functions point by point. For each such

thickness and optical property variable, it is necessary to provide an estimated value to

begin the iteration. As an example, an optical model for a simple silicon substrate

sample is shown in Fig. 1.5. In general, building an optical model begins with the

simplest structure; however, complexities such as surface and interface roughness layers

13

can be added as required in order to improve the fit to the data and to conform with any

previously established understanding of the nature of the sample.

Figure 1-4 Simplified flow chart of the data analysis procedure.

Construct optical

model

Measurement

(ψ, ∆) versus E

(ψ, ∆) versus θi

Fit, compare

data and model

results

Results:

n, k versus E

thicknesses

Assign initial

values to variables

14

Figure 1-5 Optical model and physical structure of a c-Si wafer used as a substrate.

Calculated (ψ, ∆) spectra are first generated using the optical model with the initial

values assigned to the unknown parameters. Then these spectra are compared with the

experimental (ψ, ∆) spectra and iterative adjustments of the unknown parameters are

performed in a regression analysis intended to minimize the difference between the two

pairs of spectra. If the initial values of the unknown parameters differ substantially from

the overall best fit solution, however, then the regression algorithm may fail. The role

of this algorithm is to compute the corrections to the initial estimates that yield improved

agreement between the calculated and experimental spectra and ultimately the overall

best fit. What can occur instead is the identification of a local minimum in the quality

of fit when plotted in the space of the unknown free parameters, and as a result the

calculated spectra may differ substantially from the experimental spectra. In contrast, if

the initial estimates are close enough to the overall best fit solution, then through iterative

corrections, the algorithm can identify the global minimum in the quality of the fit, and as

db

ds

SiO2

SiO2/void

c-Si

db

n, k, (surface roughness)

n, k, (interface)

n, k, (film)

ds

n, k, (substrate)

di

SiO2/c-Si di

15

a result improved agreement between the calculated and experimental data is possible.

For this reason, the flow chart in Fig. 1.4 shows an iteration step not only in the

construction of the model but also in the variation of the initial values typically over a

grid in parameter space.

In addition to the simplest case of thicknesses as unknown parameters, the

least-squares regression method is commonly used to extract the complex dielectric

function of one or more materials in the model [1-17]

. When an unknown complex

dielectric function can be expressed as an analytically-defined function of several

wavelength-independent parameters such as electronic resonance energies (band gaps),

resonance amplitudes (oscillator strengths), and broadening parameters (inverse

excitation lifetimes), then the fitting procedure is similar to that of fitting simply

thicknesses. All the known values of the parameters are fixed in the model, and the

wavelength independent unknown parameters are estimated, including the thicknesses

and the optical property parameters. The (ψ, ∆) spectra associated with these initial

estimates are calculated and compared with the experimental (ψ, ∆) spectra. Then, the

least-squares regression algorithm is used to adjust the unknown parameters iteratively so

as to minimize the difference between the calculated and experimental ellipsometric

spectra. A mean square error (MSE) function is used as the criterion; the iterations are

terminated when MSE attains its minimum. If the initial estimates of the unknown

parameters are close enough to the correct values, then the global minimum can be

reached; if not, a local minimum can lead to erroneous parameter results.

16

In such analyses, the least-squares regression algorithm uses the weighted mean

square deviation given by [1-17]

:

2 2cal exp cal exp

exp exp1

1

2

Ni i i i

i

MSEN M ψ

ψ ψ

σ σ= ∆

− ∆ − ∆ = + − ∑ (1-22)

where N is the number of (ψ, ∆) data pairs versus wavelength or photon energy, and M is

the number of unknown free parameters determined in the analysis. Thus, the squares

of the differences between each pair of calculated and experimental data ( calψ ,expψ ) and

( cal∆ ,exp∆ ) at a given wavelength or photon energy indicated by the subscript i are

summed and divided by the standard deviations of the experimental data exp

ψσ and expσ ∆ ,

respectively, for the associated wavelength. As a result, spectral points that exhibit a

lower signal to noise ratio, typically at the highest photon energies (6.0~6.5 eV) are

weighted less heavily.

Once the fit for a given model is successful, a number of various models need to be

tested in order to improve the global fit to the data. These models generally start with

the simplest structure, e.g., a single film on a substrate, and then progress to more

complicated ones that include surface and interface roughness. Some complications

may be expected based on an understanding of how thin films grow. Others may be

unexpected and provide new insights. In particular for complicated models with many

parameters, the overall best fit parameters must be evaluated for their confidence limits

and possible pair-wise or multiple correlations. In addition, the best fit parameters must

be physically meaningful; obviously there should be no zero or negative thickness values.

17

For an intrinsic semiconductor, the index of refraction n must decrease smoothly with

increasing λ at wavelengths longer than that associated with the band gap. In this range,

k should remain at zero, because of the lack of absorption at photon energies below the

band gap. Obviously, k cannot be negative; otherwise, the light would be amplified in

traversing the material.

18

Chapter Two

Introduction to CdTe-based Solar Cells

2.1 CdTe-based solar cell structures

CdTe-based solar cells can be fabricated in both substrate and superstrate

configurations [2-1, 2-2, 2-3]. In the substrate configuration, sunlight enters the active layers

of the cell before reaching the underlying substrate, and thus the substrate need not be

transparent. A typical substrate-type deposition process would follow the sequence,

Mo/CdTe/CdS/In2O3:Sn. Indium-tin-oxide (ITO), denoted by the chemical formula

In2O3:Sn whereby Sn is the dopant, is a transparent conducting oxide (TCO) thin film

that functions as an electrical contact as well as a window layer through which sunlight is

transmitted [2-1]. In the superstrate configuration which is the configuration used by

industry, the sunlight enters the substrate first, and the substrate must be selected for low

absorption over the solar spectrum. Typically there will be a trade-off between low

absorption and low cost in module manufacturing. A typical deposition sequence in this

case is glass/SnO2:F/CdS/CdTe/Cu/Au. A common superstrate for the CdTe solar cell is

TEC glass manufactured by Pilkington. TEC glass is a soda-lime glass coated with

successive layers of undoped SnO2, SiO2, and F-doped SnO2, SnO2:F, to achieve the

19

desired sheet resistance, optical properties, and chemical stability. Another TCO used in

place of In2O3:Sn and SnO2:F in both substrate and superstrate solar cells is ZnO:Al,

aluminum-doped zinc oxide. Schematic examples of the substrate and superstrate

configurations are shown in Figs. 2-1 and 2-2.

Figure 2-1 The substrate structure for CdTe solar cells.

Figure 2-2 The superstrate structure for CdTe solar cells.

In this thesis, results for both substrate and superstrate solar cells will be presented;

however, the focus has been on solar cells using TEC-15 glass as the superstrate. This

glass has been used in module manufacturing and will be described in detail in Chapter 3.

The TEC-15 glass is ~ 3 mm thick and serves as a support for the active layers of the

solar cell. It is transparent, rigid, and inexpensive, and has the widest applications for

ground mounted PV systems. The critical component is the TCO layer, SnO2:F, which

Mo

CdTe

CdS

ITO

Ambient

front contact

back contact

Soda lime glass

SnO2:F

SnO2

SiO2

CdTe

CdS

Cu/Au back contact

front contact

TEC-15

Ambient

20

is the top-most layer of the TEC-15 glass and acts as the front contact electrode of the

solar cell.

The polycrystalline cadmium sulfide (CdS) layer is invariably an n-type

semiconductor, and serves as one side of the p-n heterojunction solar cell [2-1]. As a

material with a wide band gap of 2.43 eV at room temperature, CdS is transparent to

optical wavelengths as short as 510 nm. Because its thickness is relatively small

compared to that of CdTe, typically ~1000 Å, some fraction of the photons with energy

above 2.43 eV will still pass through the CdS layer to reach the CdTe layer.

The polycrystalline cadmium telluride (CdTe) is the active absorber layer and serves

as the p-type semiconductor of the heterojunction. It is an ideal absorber material

because its 1.5 eV band gap is very close to the theoretically calculated optimum value

for a single junction solar cell [2-4] under unconcentrated AM1.5 sunlight. It is an

efficient absorber above its band gap, and its high absorption coefficient results from the

direct nature of the band gap transition. Typically, the thickness of the CdTe layer in the

solar cell ranges from 2 to 4 µm in order to absorb a larger fraction of the light between

633 nm and 832 nm. The p-n junction consists of the CdTe layer in contact with the

CdS layer. Because the doping level in CdTe is much lower than that in the CdS, most

of the depletion region of the device is located within the CdTe layer.

The back contact studied in this dissertation uses copper (~ 30 Å) and gold (~ 200 Å)

in forming the electrode. Due to its high conductivity, a large thickness is not needed for

the gold layer.

21

2.2 Deposition method and process steps

The deposition method pioneered at the University of Toledo utilizes the radio

frequency (RF) magnetron sputtering technique for fabrication of both the CdTe and CdS

thin films [2-5]. The CdTe or CdS sputtering target, serving as one electrode, is driven by

a RF power source. This power source generates a plasma of ionized argon gas between

the target and the substrate platform, which serves as the second grounded electrode.

The RF potential drives the ions towards the surface of the target where they impact,

causing atoms to be dislodged from the target. These atoms travel to the substrate

surface where they are deposited. A magnetic field is applied to contain the plasma ions

near the surface of the target in order to increase the sputtering rate. The ions follow

helical paths around the magnetic field lines, an effect that enhances the ion density in the

plasma near the target. This also allows the plasma to be sustained at lower pressures.

The sputtered species are predominantly neutral atoms and are not affected by the

magnetic trap.

Solar cell fabrication in the superstrate configuration begins with the deposition of a

CdS thin film with a thickness of approximately 1300 Å on a SnO2:F coated soda lime

glass substrate [2-6]. Typical sputtering parameters for CdS include 50 Watts RF target

power and 10 mTorr Ar gas pressure. During deposition, the substrates are held at a

nominal temperature of 300°C. After CdS deposition, a CdTe film with a standard

thickness of approximately 2.4 µm is deposited on the CdS surface using similar

deposition conditions as for CdS. For selected depositions of this study, a nominal

22

substrate temperature of 200°C has been used for the CdTe. After the two

semiconductor depositions, a CdCl2 post-deposition treatment is generally applied to the

substrate/CdS/CdTe stack [2-7]. This treatment consists of exposure to an atmosphere of

vaporized CdCl2 with partial pressure at 3.6 mTorr, and for a standard thickness of CdTe,

is carried out for 30 minutes in a tube furnace set at 387 °C. The CdCl2 post-deposition

treatment is applied for different durations to cells with different CdTe layer thicknesses,

while setting the same treatment temperature [2-8]. For example, for a 1 µm thick CdTe

layer the treatment time is ~ 15 min.

The solar cell is finished with an evaporated Cu-Au back contact. Cu is deposited to

30 Å thickness and Au to 200 Å thickness [2-9]. The final step requires annealing the

solar cell for 45 minutes in air at 150 °C in order to diffuse the Cu into the CdTe. In this

step, the CdTe layer near the back contact becomes more heavily p-type doped [2-9]. For

the thinner CdTe cells, the annealing time for Cu diffusion must be reduced in order to

achieve the proper dopant distribution in the CdTe layer.

2.3 Application of spectroscopic ellipsometry as an analysis technique

In the development of real time spectroscopic ellipsometry (RTSE) as a probe for

CdTe-based solar cell characterization, a step-by-step research program is being

undertaken in order to separate out the various complexities that occur in the deposition

process and in the CdCl2 post-deposition treatment process. For the first real time

analyses of CdTe and CdS deposition processes, optical properties of the deposited layers

23

must be established simultaneously with the structural parameters such as bulk layer

thickness, void volume fraction profile, and surface roughness thickness. Such initial

analyses are typically done using ultra-smooth crystalline silicon substrates so that the

extracted optical properties are as accurate as possible [2-10]. Substrates with rough

surfaces require incorporation of an interface roughness layer into the film growth model

that adds greater uncertainty to the overall analysis.

Parameterization of the deposited layer optical properties in terms of useful

characteristics such as defect density or grain size, strain, and temperature then yields an

optical property database that enables real time analysis of subsequent, more complex

deposition processes and substrate structures [2-11]. In basic research studies on the

deposition process, details of the solar cell structure during its deposition beyond simple

thickness can be determined such as CdTe and CdS nucleation and coalescence

characteristics, surface roughness evolution versus thickness, void volume fraction depth

profile, deposition temperature, film stress, defect density or grain size, and CdTe and

CdS interface layer compositional depth profile at the interface between the materials.

These features can be used not only for basic research but also for process development

and troubleshooting. In addition, the database can be applied to the ex-situ analysis of

post-deposition treatments using a bromine-methanol step-wise etching process for depth

profiling. Finally these optical property databases established under ideal conditions of

growth on atomically smooth and well-characterized substrates such as c-Si wafers can

be applied on-line for production monitoring of the solar modules or for off-line mapping

24

of completed modules. Data obtained on the production line could potentially be

applied to monitor and control layer thicknesses, for example, in the production process.

In addition to the deposition parameters of the CdTe film, the CdCl2 post-deposition

treatment of the CdTe solar cell significantly influences the CdTe film structure and

optical properties [2-12]. The final goal of spectroscopic ellipsometry analysis is to

understand the effects of the key parameters of the CdCl2 post-deposition treatment

process, temperature and time, on the optical properties and structure of the CdS/CdTe

and relate these to the solar cell performance. Because of the complexity of the final

film structures to be treated, the Br2+methanol stepwise etching in conjunction with

ex-situ spectroscopic ellipsometry is a unique capability for characterizing CdTe film

depth profiles, such as void fraction and grain structure. Thus, this analysis procedure

makes it possible to perform time-reversed real time spectroscopic ellipsometry while

maintaining a smooth surface as the layers of the structure are etched away. Such an

approach in which numerous spectra are collected as a function of thickness during

etching provides sufficient information to determine depth profiles of the film properties

with confidence.

In Chapter 3 through Chapter 5, this thesis will focus on optical property database

development. In order to determine the structural parameters of CdTe-based solar cells,

the required database of optical properties must include not only CdTe and CdS but also

any substrate components. Chapter 3 will describe how the four sets of optical

properties for the materials of the TEC-15 glass substrate are extracted. These materials

25

include the soda lime glass, undoped SnO2, SiO2, and doped SnO2:F. In Chapter 4,

validity of stepwise etching for time reversed real time spectroscopic ellipsometry will be

demonstrated for the purpose of depth profiling CdTe thin films. Chapter 5 will

describe the determination of the optical properties of CdTe and CdS films before and

after the CdCl2 post-deposition treatment process. These results will be applied in

Chapter 6 along with an optical model to deduce the structure for superstrate solar cells.

Results in Chapter 7 focus on the development of a database and analysis of the complete

solar cell for the substrate configuration. In Chapter 8, the application of spectroscopic

ellipsometry will be described for the characterization of CdTe-based ternary alloys.

26

Chapter Three

Optical Properties of TEC-15 Glass

3.1 Introduction

The transparent electrically conducting (TEC) glass manufactured at low cost by

Pilkington North America is a durable, pyrolytically coated, soda lime glass. The

coating is available in various thicknesses on 3 mm thick soda lime glass which yields an

electrical sheet resistance from 6 to 8 Ohms/square (Ω/ ) for TEC-7, up to

approximately 5000 Ω/ for TEC-1000. The Ω/ value provides the resistance in

Ohms when current passes from one side of a square region of the coating surface or

interface to the opposite side, irrespective of the area of the square. Because of the

coating durability, TEC glass plates can be handled just like ordinary uncoated plates.

TEC glass can be used in many thermal and electrical applications including frost-free

refrigerator windows, defogging mirrors, touch screen displays, static-free windows,

liquid crystal displays, and superstrates and substrates for thin film photovoltaics.

Among the group of TEC glass products, TEC-15, TEC-7, and TEC-8 are the

transparent conducting oxide (TCO) coated products used most extensively in the

27

fabrication of CdTe thin film solar cells in the superstrate configuration. As a widely

used thin film transparent conductor, fluorine doped tin-oxide (SnO2:F) is the most

important layer of the three-layer TEC glass stack. This layer forms the top contact, and

thus serves to conduct the current generated in the semiconductor layers to the external

circuit. SnO2:F is relatively easy to deposit pyrolytically onto a heated substrate and is

quite stable chemically. TEC-15 has the appearance of uncoated glass due to the color

suppression characteristics of the three layer stack.

Before multilayer optical analysis can be applied to spectroscopic ellipsometry data

collected on thin film CdTe-based superstrate solar cells, a library of dielectric functions

ε = ε1 + iε2 is needed that includes all the component layers. In this chapter, an ex-situ

spectroscopic ellipsometry investigation is described that provides the four sets of optical

properties for the material components of TEC-15 glass. From bottom to top, these

materials include the soda lime glass substrate, undoped SnO2, SiO2, and SnO2:F. In

determining the optical properties of these materials, optical models were used to analyze

the measured ellipsometry and transmittance spectra. Because all the TEC glasses

exhibit the same multilayer structure, the optical properties deduced for each layer of the

TEC-15 glass are assumed to be applicable for the corresponding layers of the TEC-7 and

TEC-8 glasses in order to determine their thicknesses. For the TEC-7 and TEC-8

glasses, comparisons of the experimental and calculated transmission spectra, the latter

based on an ellipsometric analysis, will be presented in this Chapter as well. These

comparisons provide information on light scattering, so-called haze, and macroscopic

28

roughness. A schematic of the multilayer structure of TEC-15 glass is shown in Fig.

3-1.

Figure 3-1 The multilayer structure of the TEC-15 glass substrate.

3.2 Experimental details

The primary effort was focused on TEC-15 glass which exhibits the thinnest SnO2:F

layer, and thus the smoothest surface among the three glasses explored. As a result, the

measured data are least affected by scattering due to macroscopic roughness. In

addition to ex-situ ellipsometric spectra, normal incidence transmittance spectra were

collected for the TEC-15 components. The purpose of the latter spectra was to seek

higher accuracy extinction coefficient values for the components of the TEC-15 glass.

The ellipsometry measurement is sensitive to small changes in the polarization state of

the light, which in turn is measurably affected by even a monolayer change in the

thickness of a thin film. Because the ellipsometer measures the change in p-s ratio of

the electric fields of the light wave upon reflection from the sample surface, it is not very

sensitive to the extinction coefficient k, when the k-value is small (≤ 0.1). As a result, a

transmission measurement, which can provide more accurate values of k when its

Surface roughness

Soda lime glass

SnO2:F

SnO2

SiO2

29

magnitude is low, is used to supplement the ellipsometry measurement. The two data

sets are analyzed together using the same optical model.

TEC glass samples were provided by Pilkington North America; five samples were

prepared for this study. These samples include (i) uncoated soda lime glass, (ii)

SnO2/(soda lime glass), (iii) SiO2/(soda lime glass), (iv) SiO2/SnO2/(soda lime glass), and

(v) fully coated TEC-15 glass: SnO2:F/SiO2/SnO2/(soda lime glass). In addition,

separate samples of TEC-7 and TEC-8 glass were provided. Variable angle

spectroscopic ellipsometry and normal incidence transmittance measurements were

applied to study all samples.

Each sample was cut into two pieces. For the first piece, the backside of the sample

was roughened to remove the beam returning from the back side glass/air interface.

This beam will distort the ellipsometry spectra in ways that are difficult to model due to

the incoherence of this beam relative to the top side reflection. The ellipsometry data

were acquired at angles of incidence of 45°, 60° and 75°, and each acquisition time at a

given angle was 10 seconds. The second sample piece was kept “as-is” and measured

using normal incidence transmittance. The spectral range of all ellipsometry and

transmission measurements was 0.75~6.5 eV.

3.3 Data analysis and results

(i) Uncoated soda lime glass

The deduced substrate structure, which includes the bulk glass and a thin surface

30

roughness or modulation layer, is shown in Fig. 3-2. The best fit value for the thickness

of this layer (13 Å) is also given in Fig. 3-2. The transmittance spectrum measured on

the soda lime glass was first analyzed in order to determine its extinction coefficient k.

By fixing the index of refraction spectra of the soda lime glass using results from a

reference database as a first estimate [3-1], numerical inversion could be applied to the

transmittance spectra in order to deduce the extinction coefficient k. Then, the index of

refraction spectrum could be extracted by fitting ellipsometry spectra (ψ, ∆) as measured

on the back-surface roughened glass in a procedure that also provides the surface

modulation layer thickness. In this fitting procedure, the spectrum in k was fixed as that

obtained from transmittance analysis. This process was iterated by repeating the

inversion of the transmittance spectra using the index of refraction and sample structure

deduced from the ellipsometry spectra. As a check of the final results, an analysis of

both the transmittance and ellipsometric spectra was also applied in order to deduce n and

k simultaneously using a 100% weighting level of transmittance relative to ψ and ∆.

Once the optical properties have been determined in this analysis procedure, they have

been fitted by smooth analytical functions. The results are tabulated in Appendix A.

Experimental spectra for the transmittance, ψ and ∆ (broken lines), and their best fit

simulations (solid lines) using the final structure and optical properties are shown in Figs.

3-3, 3-4, and 3-5.

31

Figure 3-2 Simple model deduced from the analysis of the transmittance and ellipsometric (ψ, ∆) spectra of Figs. 3-3−3-5 for the soda lime glass substrate. The surface roughness is obtained in a best fit of the (ψ, ∆) spectra.

0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

0.8

1.0

simulation

exp.

Tra

nsm

itta

nce

Photon Energy (eV)

Soda Lime Glass substrate

θi =0

o

Figure 3-3 Best fit simulated and experimental normal incidence transmittance spectra T vs. photon energy for an uncoated soda lime glass substrate used in the fabrication of TEC glasses.

Considering Fig. 3-5, the ellipsometric spectra ∆ should be 0° throughout the spectral

range when the surface layer thickness is negligible and absorption is weak as is the case

for soda lime glass. The 13 Å surface roughness or modulation layer is justified by the

observation of a non-zero ∆ spectrum. This layer may also include contributions due to

surface contamination and/or differences in the chemical nature of the glass near the

surface. As a result, the relatively poor quality of the fit to ∆ is likely to be due to

inadequacies in the simple Bruggeman effective medium theory model for the optical

surface roughness 13.1 ± 0.1 Å

soda lime glass 3 mm MSE = 1.85

32

properties of the thin modulation layer. The analytical expressions that best fit the index

of refraction and extinction coefficient spectra for the uncoated soda lime glass are shown

in Fig. 3-6.

0 1 2 3 4 5 6 7

2

3

4

5

6

soda lime glass substrate

simulation

exp.

ψ (

de

gre

e)

Photon Energy (eV)

θi = 60

o

Figure 3-4 Best fit simulated and experimental ellipsometric angle ψ = tan−1 (|rp/rs|) vs. photon energy for an uncoated soda lime glass substrate used in the fabrication of TEC glasses. The angle of incidence is 60˚.

0 1 2 3 4 5 6 7

0

10

20

θi = 60

o

soda lime glass substrate

simulation

exp.

∆ (d

eg

ree

)

Photon Energy (eV) Figure 3-5 Best fit simulated and experimental ellipsometric angle ∆ = δp − δs vs. photon energy for an uncoated soda lime glass substrate used in the fabrication of TEC glasses. The angle of incidence is 60˚.

33

0 200 400 600 800 1000 1200 1400 1600 1800

1.5

1.6

1.7

Index o

f R

efr

actio

n

Wavelength (nm)

Soda lime glass substrate

0 200 400 600 800 1000 1200 1400 1600 18001E-7

1E-6

1E-5

1E-4

Soda lime glass substrate

Extinction C

oe

ffic

ient

Wavelength (nm)

Figure 3-6 Index of refraction (left) and extinction coefficient (right) vs. wavelength for the uncoated soda lime glass substrate. The index of refraction results are derived from the ellipsometric ψ spectrum whereas the extinction coefficient results are derived from the transmittance spectrum. The data values are tabulated in Appendix A.

(ii) SnO2/(soda lime glass)

Ellipsometry and transmittance spectra were measured on the soda lime glass

substrate coated with a single film of undoped SnO2. The analysis of this coated soda

lime glass substrate was performed similarly to that of the uncoated glass and used the

optical properties of the soda lime glass shown in Fig. 3-6. The deduced sample

structure is shown in Fig. 3-7, including the bulk glass and a two-layer (roughness/bulk)

model for the film. The best fit structural parameters obtained in the analysis are also

included in Fig. 3-7. The experimental and best fit simulated transmittance and

ellipsometric (ψ, ∆) spectra are given in Figs. 3-8 and 3-9, and the optical properties of

the undoped SnO2 used in the best fit simulations are shown in Fig. 3-10. These optical

property results are also tabulated in Appendix A.

The surface roughness layer on the film depicted in Fig. 3-7 is modeled as a mixture

34

of the underlying undoped SnO2 and void with a variable composition. The

parameterized expression used for the optical properties of the SnO2 in the fits of Figs.

3-8 and 3-9 employs the parameters given along with their confidence limits in Fig. 3-10.

The absorptive properties of the film can be assessed from the imaginary part of the

dielectric function ε2 shown in Fig. 3-10 (b). Due to the thinness of the SnO2 layer, the

absorption associated with values of ε2 below 0.01 is not definitive, however, and can be

approximated as 0. In fact, an ε2 value of 0.01 at 2.0 eV, corresponds to a k-value of

0.0026, an absorption coefficient of 5.3 x 102 cm-1, and a single pass absorbance of

0.16% in a 310 Å film. As a result, no significant influence on any of the optical

characteristics of the TEC glass stack results from this approximation.

Figure 3-7 Model with best fitting parameters obtained in the analysis of the transmittance and ellipsometric (ψ, ∆) spectra of Figs. 3-8 and 3-9 for the soda lime glass substrate coated with a single layer of undoped SnO2.

Soda Lime Glass 3 mm

SnO2 226 ± 2 Å

surface roughness 160 ± 1 Å

0.52 ± 0.01 / 0.48 ± 0.01 SnO2 / void

MSE = 3.81

35

0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

0.8

1.0

simulation

exp.

Tra

nsm

itta

nce

Photon Energy (eV)

SnO2/SLG

θi = 0

o

Figure 3-8 Normal incidence transmittance T vs. photon energy for a soda lime glass substrate coated with a single layer of undoped SnO2, the first layer in the fabrication of TEC glasses. Experimental data (broken line) and a best fit simulation (solid line) are shown.

0 1 2 3 4 5 6 7

4

8

12

16

SnO2/SLG

simulation

exp.

ψ (

deg

ree

)

Photon Energy (eV)

θi= 60

o

0 1 2 3 4 5 6 7

-100

0

100

200

300

SnO2/SLG simulation

exp.

∆ (

de

gre

e)

Photon Energy (eV)

θi = 60

o

Figure 3-9 Ellipsometric angles ψ and ∆ vs. photon energy for a soda lime glass substrate coated with a single layer of undoped SnO2. Experimental data (broken lines) and best fit simulations (solid lines) for an angle of incidence of 60˚ are shown.

36

0 1 2 3 4 5 6 7

3.2

3.6

4.0

4.4

ε 1

Photon Energy (eV)

(a) SnO2

0 1 2 3 4 5 6 7

1E-3

0.01

0.1

1

10(b) SnO

2

ε 2

Photon Energy (eV)

(c) Parameterization of dielectric function:

ε1 + iε2 = ε∞ − ADrudeΓDrude/(E2+iΓDrudeE) + ( )

2

1,T-L,n 2,T-L,n1

in=

ε + ε∑ + 1,Gaussian 2,Gaussianiε + ε

Here: gn

2,T-L,n1,T-L,n 2 2

E

ξε (ξ)dξ

ξ E

∞

ε =−∫ , and

2n 0n n gn

2,T-L,n gn2 2 2 2 20n n

2,T-L,n gn

A E C (E E ) 1ε E > E

(E E ) + C E E

ε 0 E E

−= ⋅

−

= ≤

,

21,Gaussian 2 2

0

( )2p d

E

∞ξε ξ

ε = ξπ ξ −∫ ,

2 2Gaussian Gaussian( ) ( )

2,Gaussian GaussianA (e e )E E E E− +

− −σ σε = − , and

Gaussian

2 ln(2)

Γσ =

Figure 3-10 (a,b) Real and imaginary parts of the dielectric function ε1 and ε2 vs. photon energy for undoped SnO2 that forms the first layer of TEC glasses; (c) analytical expression for the complex dielectric function of (a,b) along with the best-fit free parameters and their confidence limits.

An (eV) E0n (eV) Cn (eV) Egn (eV) ADrude (eV) ΓDrude (eV) ε∞

n = 1 20.564±1.380 4.825±0.052 2.647±0.063 3.236±0.025

5.303±4.020 0.026±0.020 0.357±0.213

n = 2 68.155±8.90018.992±1.31011.845±1.200 1.557±0.027

AGaussain (eV) EGaussian (eV) ΓGaussian (eV)

0.228±0.016 4.384±0.006 0.522±0.024

37

(iii) SiO2/(soda lime glass)

Transmittance and ellipsometry spectra on a soda lime glass substrate coated with a

single layer of SiO2 were measured and fit simultaneously at the 100% weighting level of

transmittance relative to ψ and ∆. The SiO2 is used as the second layer in the

fabrication of TEC glasses. The adopted sample structure, including the bulk glass and

a two-layer (roughness/bulk) model for the film is shown in Fig. 3-11. The best fit

structural parameters and their confidence limits are also shown. The surface roughness

is assumed to be a 0.5/0.5 volume fraction mixture of the underlying SiO2 and void.

The experimental transmittance and ellipsometric spectra along with their best-fit

simulations are shown in Figs. 3-12 and 3-13. The optical properties of the SiO2 used in

these simulations are shown in Fig. 3-14(a), and the data are tabulated in Appendix A.

A parameterized expression for the optical properties of the SiO2 is used as shown in Fig.

3-14(b), based on a two term Sellmeier expression and a separate pole term. Figure

3-15 shows the reference dielectric function for thermally-grown SiO2 on crystalline Si

[3-2] in comparison with the deduced dielectric function of the SiO2 film on the soda lime

glass.

Figure 3-11 Model adopted for the analysis of the transmittance and ellipsometric (ψ, ∆)

Surface roughness 35 ± 2 Å

Soda Lime Glass 3 mm

SiO2 315 ± 4 Å

MSE = 1.24

38

spectra of Figs. 3-12 and 3-13 obtained on the soda lime glass substrate coated with a single layer of SiO2.

0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

0.8

1.0

θi= 0

o

simulation

exp.

Tra

nsm

itta

nce

Photon Energy (eV)

SiO2/SLG

Figure 3-12 Normal incidence transmittance T vs. photon energy for a soda lime glass substrate coated with a single layer of SiO2, which is used as the second layer in the fabrication of TEC glasses; experimental data (broken line) and a best fit simulation (solid line) are shown.

0 1 2 3 4 5 6 75.5

6.0

6.5

7.0

7.5

SiO2/SLG

simulation

exp.

ψ (

de

gre

e)

Photon Energy (eV)

θi= 60

o

∆ (

de

gre

e)

0 1 2 3 4 5 6 70

5

10

15

20

25

θi= 60

o

SiO2/SLG

simulation

exp.

Photon Energy (eV)

Figure 3-13 Ellipsometric angles ψ and ∆ vs. photon energy for a soda lime glass substrate coated with a single layer of SiO2, which is used as the second layer in the fabrication of TEC glasses; experimental data (broken lines) and a best fit simulation (solid lines) are shown.

39

0 1 2 3 4 5 6 7

0.0

0.5

1.0

1.5

2.0

2.5

ε 1,

ε 2

Photon Energy (eV)

(a) SiO2

(b) Parameterization of the real part of the dielectric function:

ε1 = εoffset + A0/(E02−E2) + Apole/(E

2pole−E2); ε2 = 0;

Figure 3-14 (a) Real (solid line) and imaginary (broken line) parts of the dielectric function ε vs. photon energy for SiO2 that forms the second layer of the TEC glasses. The imaginary part of the dielectric function vanishes; (b) mathematical expression for the dielectric function in (a) along with the best fitting parameters and their confidence limits.

0 1 2 3 4 5 6 7

0.0

0.5

1.0

1.5

2.0

2.5

ε2

ε1

ε 1,

ε 2

Photon Energy (eV)

ε1 TEC SiO

2

ε2 TEC SiO

2

ε1 thermal SiO

2

ε2 thermal SiO

2

Figure 3-15 Real and imaginary parts of the dielectric function ε vs. photon energy for the SiO2 that forms the second layer of the TEC glasses (solid lines) for comparison with the reference data of a thermally-grown SiO2 on crystalline silicon[3-2].

A0 (eV2) E0 (eV) Apole (eV2) Epole (eV) εoffset

248.876 ± 1.458 14.544 ± 0.003 0.033±0.001 0 1.000 ± 0.009

40

(iv) SiO2/SnO2/(soda lime glass)

For the next set of results to be described, the SiO2 layer was deposited instead on the

SnO2/(soda lime glass) structure. The ellipsometry and transmittance data were fit

simultaneously using 100% weighting of transmittance relative to ψ and ∆ for this sample,

as well. The optical properties of the soda lime glass, the undoped SnO2, and the SiO2

used in the best-fit simulation are those shown in Figs. 3-6, 3-10, and 3-14, respectively.

Figure 3-16 shows the optical model applied in this case along with the best fit

parameters and their confidence limits. Figure 3-17 shows the best fit to the

ellipsometric spectra ψ and ∆, obtained using the model of Fig. 3-16.

Figure 3-16 Best fit sample structure for a soda lime glass substrate coated with a two layer stack of undoped SnO2 and SiO2, which are the first two layers used in the fabrication of TEC glasses.

Surface roughness 144 ± 2 Å

(0.63 ± 0.01)/(0.37 ± 0.01) SiO2/void

SiO2 253± 3 Å

SnO2 466 ± 1 Å

Soda Lime Glass 3 mm

MSE = 4.03

41

0 1 2 3 4 5 6 7

0

8

16

24

32

40

θi= 60

o

SiO2/SnO

2/SLG

simulation

exp.

ψ (

de

gre

e)

Photon Energy (eV)

0 1 2 3 4 5 6 7

-100

0

100

200

300

θi= 60

o

SiO2/SnO

2/SLG

simulation

exp.

∆ (

de

gre

e)

Photon Energy (eV)

0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

0.8

1.0

θi= 0

o

simulation

exp.

Tra

nsm

itta

nce

Photon Energy (eV)

SnO2/SiO

2/SLG

Figure 3-17 Ellipsometric angles (ψ, ∆) at an angle of incidence of 60˚ and transmittance T at normal incidence plotted versus photon energy for a soda lime glass substrate coated with a two layer stack of undoped SnO2 and SiO2, which are the first two layers used in the fabrication of TEC glasses.

The effective thicknesses of these layers as indicated in Fig. 3-16, including surface

roughness and bulk components, are larger than those of the individual layers. For the

SnO2 layer of the bi-layer the effective thickness is the bulk layer thickness, so that

deff(SnO2) = 466 Å. For the SiO2, one must also include the contribution of the

roughness layer, so that deff(SiO2) = 344 Å. For the individual layers, deff(SnO2) = 309

42

Å and deff(SiO2) = 333 Å.

(v) TEC-15 glass with SnO2:F/SiO2/SnO2/ (soda lime glass) structure

The assumed sample structure, including the bulk glass and a four-layer model for

the TEC-15 multilayer stack is shown in Fig. 3-18. The stack includes two ideal films

for the undoped SnO2 and the SiO2 and two layers -- roughness/bulk -- for the top-most

doped SnO2:F film. Figure 3-18 also shows the best-fit structural parameters of the

model along with their confidence limits. The previously-determined dielectric

functions were used for the soda lime glass, the thin undoped SnO2, and the SiO2. The

dielectric function of the SnO2:F and structural parameters were deduced simultaneously

in this analysis. In Figs. 3-19 and 3-20, the experimental transmittance and

ellipsometric spectra are shown along with the simulations obtained as the best fit using

at a 100% weighting level of transmittance relative to ψ and ∆. The optical properties

of the top-most doped SnO2:F used in the simulation are shown in Fig. 3-21 and tabulated

in Appendix A. The minimum ε2 value of 0.02 near 2.5 eV corresponds to a k value of

0.0027, an absorption coefficient of 6.8 x 102 cm-1, and a single pass irradiance loss of

2.5%, the latter value typical of high quality transparent conducting oxides. The

analytical expression for the complex dielectric function valid for photon energies below

4.4 eV is given in Fig. 3-22 along with the best fit parameters and their confidence limits.

This expression includes a two term Sellmeier expansion, one Lorentz oscillator, and one

Drude contribution. The dc electrical conductivity can be deduced from the Drude

amplitude AD according to σdc = ADε0/ħ = 2.87 x 103 (Ω⋅cm)−1, leading to a resistivity of

43

3.48 x 10-4 Ω⋅cm and a sheet resistance of ~ 10 Ω/.

Figure 3-18. Best fit multilayer stack for a complete TEC-15 glass sample. The layered structure includes thin undoped SnO2, thin SiO2, and thick doped SnO2:F with surface roughness on top. The previously-determined dielectric functions were used for the soda lime glass and the two thin layers.

0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

0.8

1.0

θi= 0

o

simulation

exp.

Tra

nsm

itta

nce

Photon Energy (eV)

SnO2:F/SiO

2/SnO

2/SLG

Figure 3-19 Normal incidence transmittance T vs. photon energy for a complete TEC-15 glass sample consisting of a soda lime glass substrate coated with layers of undoped SnO2, SiO2, and top-most doped SnO2:F. Experimental data (broken line) and a best fit simulation (solid line) are shown.

SiO2 222 ± 3 Å

SnO2:F 3533 ± 6 Å

SnO2 287 ± 3 Å

Soda Lime Glass 3 mm

MSE = 64.65

Surface roughness 273 ± 3 Å

0.60 ± 0.005 / 0.40 ± 0.005 SnO2:F / void

44

0 1 2 3 4 5 6 7

0

10

20

30

40

θi= 60

o

SnO2:F/SiO

2/SnO

2/SLG simulation

exp.

ψ (

de

gre

e)

Photon Energy (eV)

0 1 2 3 4 5 6 7

-100

0

100

200

300

θi= 60

o

SnO2:F/SiO

2/SnO

2/SLG simulation

exp.

∆ (

de

gre

e)

Photon Energy (eV)

Figure 3-20 Ellipsometric angles ψ and ∆ at a 60˚ angle of incidence plotted vs. photon energy for a complete TEC-15 glass sample consisting of a soda lime glass substrate coated with layers of undoped SnO2, SiO2, and top-most doped SnO2:F. The broken lines indicate experimental spectra and the solid lines indicate the best fit simulation.

0 1 2 3 4 5 6 7

0

1

2

3

4

5

6

7

ε 1

Photon Energy (eV)

SnO2:F

exact inversion

of (ψ, ∆) datafit to analytical

expression

0 1 2 3 4 5 6 70.01

0.1

1

ε 2

Photon Energy (eV)

SnO2:F

exact inversion

of (ψ, ∆) datafit to analytical

expression

Figure 3-21 Real and imaginary parts of the dielectric function ε1 and ε2 vs. photon energy for doped SnO2:F that forms the top-most layer of TEC-15 glass. These results are obtained as a best fit analytical expression at low energies where the film is semitransparent and by an inversion of (ψ, ∆) data at high energies where the film is opaque.

45

(a) Parameterization of the dielectric function E < 4.4 eV:

ε1 + iε2 = εoffset + A1/(E12−E2)+ ALΓLE0/(E

20−E2−iΓLE) − ADΓD/(E2+ iΓDE);

(b) Sellmeier:

A1 (eV2) E1 (eV) εoffset

207.561±4.905 8.857±0.001 1.003±0.070

Lorentz:

AL E0 (eV) ΓL (eV)

1.332±0.240 4.686±0.077 0.389±0.061

Drude:

AD (eV) ΓD (eV)

21.311±0.608 0.089±0.002

Figure 3-22 (a) The analytical equation for the dielectric function of the top-most SnO2:F layer of TEC-15 that holds below 4.4 eV; also shown is (b) a table of the best fit parameters in the equation and their confidence limits.

(vi) TEC-7 and TEC-8 glasses with SnO2:F/SiO2/SnO2/ (soda lime glass) structure

The sample structures deduced for TEC-7 and TEC-8 glasses are shown in Figs. 3-23

and 3-24. The best-fit structural parameters are included in the figures, as well. The

dielectric functions previously-determined from TEC-15 glass were used for the soda

lime glass, the thin undoped SnO2, thin SiO2, and thick doped SnO2:F layers of the

TEC-7 and TEC-8 samples. The incorporation of two additional fitting parameters was

attempted in this case because of the larger surface roughness and bulk SnO2:F film

thicknesses for the TEC-7 and TEC-8 glasses relative to TEC-15. One parameter is the

volume fraction of voids in the SnO2:F layer, which is incorporated due to the expected

coarser microstructure of the SnO2:F layers for the TEC-7 and TEC-8 glasses. The

other parameter describes the thickness non-uniformity of the layers. Thickness

non-uniformity arises due to the variation of one or more film thicknesses across the

46

sample surface.

If the film thickness varies over the area of the light beam, then the beam on the film

surface can be divided into components by a grid selected such that the thickness

variation is negligible over a given beam component. The resulting grid size must be

larger than the lateral coherence of the beam, estimated to be ~5-10 µm, otherwise

interference between neighboring beam components will occur. In the absence of

interference, the irradiances associated with all beam components will add and the

resulting reflected beam will be partially polarized. A thickness non-uniformity

parameter can then be determined in the analysis. This parameter describes the

percentage variation in film thickness within the overall probe beam area according to the

definition [(dmax−dmin)/dave]×100%. For the TEC-7, the observed ~7% non-uniformity is

not of the macroscopic variety, i.e. not a variation in thickness from one side of the beam

to the other, but rather is associated with surface roughness having an in-plane scale that

exceeds the lateral coherence length. As support for this interpretation, when thickness

non-uniformity is added as a free parameter into the TEC-15 fitting procedure, however,

the best-fit value is zero within confidence limits. This result is consistent with the fact

that this film has an in-plane roughness scale that is smaller than the TEC-7 and TEC-8,

which in turn is consistent with its thinner surface roughness layer.

47

Figure 3-23 Multilayer structure with best-fit parameters for a complete TEC-7 glass sample. The layered structure includes thin undoped SnO2, thin SiO2, and a thick layer of doped SnO2:F with surface roughness on top. The previously determined dielectric functions for TEC-15 glass were used here for this TEC-7 glass sample.

Figure 3-24 Multilayer structure with best-fit parameters for a complete TEC-8 glass sample. The layered structure includes thin undoped SnO2, thin SiO2, and a thick layer of doped SnO2:F with surface roughness on top. The previously determined dielectric functions for TEC-15 glass were used here for this TEC-8 glass sample.

The experimental normal incidence transmission data measured for the TEC-7 and

TEC-8 samples and the data calculated on the basis of the optical models deduced by

ellipsometry are shown in Fig. 3-25 (left) and Fig. 3-26 (left). Due to the existence of

SnO2:F 4708 ± 19 Å

0.97 ± 0.005 / 0.03 ± 0.005 SnO2:F / void

SiO2 222 ± 5 Å

SnO2 302 ± 6 Å

Soda Lime Glass 3 mm

Thickness non-uniformity 7.4% ± 0.8%; MSE = 87.6

Surface roughness 409 ± 4 Å

0.55 ± 0.005 / 0.45 ± 0.005 SnO2:F / void

SnO2:F 5672 ± 52 Å

0.92 ± 0.01 / 0.08 ± 0.01 SnO2:F / void

SiO2 294 ± 14 Å

SnO2 335 ± 14 Å

Soda Lime Glass 3 mm

Thickness non-uniformity 10.7% ± 0.8%; MSE = 156.2

Surface roughness 609 ± 7 Å

0.53 ± 0.01 / 0.47 ± 0.01 SnO2:F / void

48

thicker surface roughness layers on the TEC-7 and TEC-8 samples, some amount of

scattering is expected in the normal incidence transmission measurement. In theory, the

transmission spectra calculated on the basis of the model deduced by ellipsometry should

be approximately equal to the summation of the experimental normal incidence specular

transmission data and the total normal incidence scattering data integrated over all solid

angles.

In comparison with the close agreement between the calculated and experimental

transmission spectra for the TEC-15 sample (Fig. 3-18), the corresponding data sets for

TEC-7 and TEC-8 samples differ considerably below 3.5 eV. Considering the values of

the microscopic surface roughness thicknesses of three TEC samples, these results can be

easily explained. TEC-15 glass has the smallest microscopic surface roughness

thickness among three samples ~275 Å, which means it has the smallest macroscopic

roughness as well, and thus, the smallest scattering loss. In this case, the experimental

data are closest to the calculated results and in fact, it was valid to use the transmittance

as a data component to be fitted in the analysis of Fig. 3-18. TEC-8 glass has the largest

microscopic surface roughness thickness, thus the largest macroscopic roughness

thickness, and as a result the largest scattering loss. This explains why the experimental

transmission for the TEC-8 glass exhibits the greatest deviation from the calculated

results.

Figures 3-25 (right) and 3-26 (right) show the differences between the calculated and

experimental transmission spectra for the TEC-7 and TEC-8 glass samples. This

49

difference approximates the total normal incidence scattering data integrated over all

angles. It is easily recognized that the transmission loss in TEC-8 glass is larger

because of a stronger scattering effect than that in TEC-7 glass.

In addition, in Figs. 3-27 and 3-28 the normal incidence scattering data for these

samples as predicted by the combination of ellipsometry and normal incidence specular

transmission has been compared with experimental normal incidence integrated

scattering data. The experimental scattering data were measured at Pilkington in a

diffuse transmission experiment using a different pair of TEC-7 and TEC-8 samples than

the ones measured in this investigation. From the comparison in Figs. 3-27 and 3-28,

the experimental scattering results are lower than the predictions over the 400 – 600 nm

and 1200 – 1500 nm wavelength ranges in both cases. One possible origin of this

difference may arise from the small collection aperture of the ellipsometer used to

measure the normal incidence specular transmittance relative to the apertures used to pass

the

0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

0.8

1.0

θi = 0°

Tra

nsm

itta

nce,

T

Photon Energy (eV)

simulation

exp. data

TEC-7 transmission

0 1 2 3 4 5 6 7-0.05

0.00

0.05

0.10

0.15

0.20

θi = 0°

∆T

Photon Energy (eV)

Difference between TEC-7 simulation

and exp. data

Figure 3-25 Transmittance T vs. photon energy for a complete TEC-7 glass sample; experimental data (broken line) and simulated results based on the ellipsometric model (solid line) are shown (left). The difference between the two data sets is shown at the right.

50

0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

0.8

1.0

Tra

nsm

itta

nce,

T

simulation

exp. data

TEC-8 transmission

Photon Energy (eV)

θi = 0°

0 1 2 3 4 5 6 7

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

∆T

Photon Energy (eV)

Difference between TEC-8 simulation

and exp. dataθ

i = 0°

Figure 3-26 Normal incidence transmittance T vs. photon energy for a complete TEC-8 glass sample; experimental data (broken line) and simulated results based on the ellipsometric model (solid line) are shown (left). The difference between the two data sets is shown at the right.

specularly reflected and transmitted beams in the measurement at Pilkington with an

integrating sphere. In such a case, near-specular scattering would be considered true

scattering by ellipsometry but rather as part of the specular beam in the integrating sphere

measurement, and hence not collected. This difference due to near-specular scattering

amounts to about 5% for TEC-7 and closer to 10% for TEC-8 at the high and low

energies.

Another possible origin of the difference may arise from different optical properties

of the SnO2:F layer in the three different types of TEC glass. If the absorbance in

TEC-7 and TEC-8 are underestimated with the use of the TEC-15 optical properties, then

the measured transmittance of the TEC-7 and TEC-8 would be lower than that predicted

by ellipsometry. This effect would contribute a positive term to the ∆T spectra in Figs.

3-25 and 3-26 that is not accountable by scattering. In fact, it is expected that the

increasing ∆T values at long wavelengths visible most clearly in Figs. 3-27 and 3-28 are

generated by a larger Drude contribution to the absorption in the TEC-7 and TEC-8

51

glasses compared to TEC-15. Improvements in the analysis of TEC-7 and TEC-8 using

the approach developed here for TEC-15 will be the subject of future research.

0 200 400 600 800 1000 1200 1400

0.0

0.1

0.2

0.3

To

tal in

teg

rate

d s

catt

eri

ng

Wavelength (nm)

TEC-7

Measured scattering by diffuse transmission

Predicted scattering by ellipsometry

and specular transmissionθ

i = 0°

Figure 3-27 For TEC-7 glass, the normal incidence scattering results predicted by combining ellipsometry and normal incidence specular transmittance are shown in comparison with experimental normal incidence integrated scattering data from a diffuse transmission experiment. Different TEC-7 samples were used for the two different data sets.

0 200 400 600 800 1000 1200 1400

0.0

0.1

0.2

0.3

0.4

TEC-8

Measured scattering by diffuse transmission

Wavelength (nm)

Predicted scattering by ellipsometry

and specular transmission

θi = 0°

Figure 3-28 For TEC-8 glass, the normal incidence scattering results predicted by combining ellipsometry and normal incidence specular transmittance are shown in comparison with experimental normal incidence integrated scattering data from a diffuse transmission experiment. Different TEC-8 samples were used for the two different data sets.

52

Chapter Four

Verification of the Chemical Etching Process for CdTe Depth Profiling

4.1 Introduction

A critical step in the fabrication of CdTe-based solar cells is the CdCl2 vapor

treatment performed near 400 °C in the presence of oxygen. This process step improves

the solar cell efficiency by a factor of two or more [4-1, 4-2]. Comparisons of as-deposited

and CdCl2 vapor-treated CdTe thin film materials have revealed significant near-surface,

interface, and bulk property differences. Considering the near-surface, the CdCl2

post-deposition treatment generates much thicker roughness and oxidized layers on the

treated film in comparison with the as-deposited film. Evidently the exposure to

chlorine and oxygen in the high temperature (~ 400 °C) environment during the treatment

leads to three-dimensional grain growth and oxidation of the surfaces of the large grains.

In addition, many bulk film and interface parameters that may impact the solar cell

performance are modified in the post-deposition CdCl2 treatment. These include the

physical characteristics such as thickness, density, and grain size and orientation for both

the CdTe and CdS films, as well as the composition profile of the interface region

between the two films. Changes also occur in the optical and electronic properties upon

53

treatment including the dielectric functions of the CdTe, CdS, and interface region, the

concentration and nature of the defects which control the free electron concentration, and

the mobility of photoinjected carriers.

Real time spectroscopic ellipsometry can be used to obtain dynamic information on

film growth and modification through analysis of the data acquired during thin film

deposition or post-deposition processing. During the CdCl2 post-deposition treatment,

however, the properties of several layers change simultaneously. In fact, the layers that

may change in their properties and thickness upon CdCl2 treatment include CdTe and

CdS, as well as the surface and interface layers: TCO/CdS, CdS/CdTe, and CdTe/oxide.

In order to separate out all the changes that occur during the post-deposition treatment

process, real time spectroscopic ellipsometry is avoided in favor of ex-situ spectroscopic

ellipsometry, accompanied by chemical etching for depth profiling. A comparison of

the depth profiling results with those obtained in real time on the as-deposited film

provides an effective comparison before/after deposition.

Depth profiling of the CdCl2-treated thin films by successive Br2+methanol etches of

the CdTe thin film layer has been applied in this thesis research. In previous research

the Br2+methanol etch has been successful in removing overlayers including native

oxides and surface roughness from opaque single crystal materials, such as CdTe, and

HgxCd1-xTe [4-3]. By performing spectroscopic ellipsometry during the etching process,

one can determine the extent to which oxide and roughness removal has been successful

by monitoring the maximum magnitude of the imaginary part of the pseudo-dielectric

54

function denoted <ε2> after each etching step. The pseudo-dielectric function is

calculated from the ideal single-interface ambient/bulk model. Thus, as the overlayers

are removed, the pseudo-dielectric function maxima determined from the (ψ, ∆) spectra

increase and approach the true values of the complex dielectric function of the opaque

CdTe film in this case. Thus, upon complete removal of the overlayers, an inverted

form of the complex Fresnel amplitude reflection ratio /% %p sR R yields the complex

dielectric function spectra of the opaque film directly from the (ψ, ∆) spectra.

In order to adapt successfully an etching technique previously demonstrated for

single crystals to the polycrystalline films of this study, it must be verified that the

chemical etching process does not modify the underlying film structure that one is

attempting to measure. In the following paragraphs, an experiment is described to

evaluate the validity of the etching method to be used for the CdCl2 treated CdTe-based

solar cell structure as described in Chapters 5 and 6. In fact, optical depth profiling

results for the CdTe film structure from real time spectroscopic ellipsometry are

compared with the corresponding results from ex-situ spectroscopic ellipsometry during

etch back.

4.2 Structural evolution of CdTe during etching: experimental details

Magnetron sputtering of the CdTe thin film used in this study was performed at a

radio frequency (rf) target power of 60 W, an Ar pressure of 18 mTorr, and an Ar flow

rate of 23 sccm. The substrate was a native oxide-covered crystalline Si (c-Si) wafer

55

held at a nominal temperature of 200°C [4-4]. The true temperature of the starting surface

just prior to deposition was estimated to be 130 ± 5°C, as determined in situ from an

analysis of the c-Si E1 and E2 critical points. A c-Si wafer substrate was used for this

deposition due to its smoothness. As a result, complications were avoided due to

substrate-induced surface roughness that evolves into interface roughness during

overlying film growth.

The design of the commercial rotating-compensator multichannel ellipsometer used

in this study is similar to that first developed to study the growth of Si:H-based materials

and solar cells [4-5]. The spectral range of the ellipsometer extends from ~0.75 to 6.5 eV,

and complete spectra in the ellipsometric angles (ψ, ∆) can be collected as an average

over a minimum of two optical cycles in a time of (30.7 Hz)-1 = 32.6 ms. Here 30.7 Hz

is the mechanical rotation frequency of the compensator. In the real time experiment

performed on the deposition of the CdTe film to be etched, complete (ψ, ∆) spectra were

collected in 1.95 seconds as an average over 60 such optical cycle pairs. A total of 705

spectral files were collected, corresponding to a set of time points from 2.38 s to 3216.3 s,

with a step of 4.56 s. Each spectral file includes 706 values of ψ and ∆, spanning

photon energies from 0.743 to 6.50 eV. Thus, during the 3213.9 s deposition time, the

instrument acquired (705)*(706)*(2) = 9.9546x105 experimental data values, filling about

15 Mbytes of computer memory. During the acquisition time for one set of (ψ, ∆)

spectra, an average thickness of CdTe of 2.4 Å accumulates at the bulk layer deposition

rate measured here (1.21 Å/s). Analyses of all spectra utilized a specialized

(mathematical inversion) / (least-squares regression) algorithm developed previously [4-6].

The angle of incidence for the RTSE measurement was 65.61°.

56

Figure 4-1 A schematic of optical models used to evaluate a CdTe film by optical depth profiling during both deposition and etching processes.

The large data set accumulated in this way during the deposition of the CdTe film was

analyzed over the energy range of 5~6.5 eV in order to achieve the highest depth

resolution possible. The absorption depth (α −1, where α is the absorption coefficient)

of single crystal CdTe decreases with increasing photon energy, reaching 100 Å at 5 eV.

A schematic of the optical models used in the analysis of the experiment including the

deposition and etching processes is shown in Fig. 4-1. The chemical etch of the CdTe

thin film was performed using a Br2+methanol solution prepared with 0.05 volume

percent Br2. Initially, the etching time was fixed at 3 seconds for each etch step, then

increased to 30 seconds and fixed.

57

4.3 Structural evolution of CdTe during etching: results and analysis

In order to verify the validity of the above approach, the same sample was studied in

real time during deposition and ex-situ during sequential etching, without a CdCl2

treatment in between the two measurements. A simple two-layer roughness/bulk model

was applied to analyze SE data collected in real time during deposition as well as ex-situ

after each chemical etch step. Figure 4-2 (solid line) shows the evolution of void

volume fraction in the top ~100 Å of the CdTe bulk layer as a function of the bulk layer

thickness (the latter as deduced from lower energy data) during the deposition process.

The abrupt upward step in void fraction represents a sharp microstructural transition,

characteristic of the relaxation of high compressive strain that occurs in the early stage of

film growth. This structural transition is only observed at low substrate temperatures (<

200 °C) and the resulting void structures that propagate throughout the film are likely to

be detrimental to the final solar cell performance. The discrete points in Fig. 4-2

collected after each etch step match the deposition results (solid line) very well −− given

the confidence limits and depth resolution of the analysis. Thus, for each CdTe bulk

thickness, the sample has the same structural profile as measured during both the

deposition and etching processes. This result shows that the etching process is the

reverse of the deposition process, and that etching does not modify the underlying film

structure, even when the underlying structure is inhomogeneous and varies significantly

with depth.

58

0 500 1000 1500 2000 2500 3000 3500-0.05

0.00

0.05

0.10

0.15

0.20

0.25

CdTe growth process CdTe etch process

void

vol

ume

frac

tion,

f v

bulk layer thickness, db (Å)

one-layer surfaceroughness model

analysis rangefor f

v: 5.0~6.5 eV

depth resolution1/α (5eV) ~ 100 Å

Figure 4-2 The evolution of void volume fraction within the top 100 Å of the bulk layer as a function of CdTe bulk layer thickness obtained during the deposition and etching processes.

One detail of interest must be considered in view of these results. Previous reports

have shown that a thin amorphous Te (a-Te) layer remains on the top surface of CdTe

single crystals after a Br2+methanol etch step [4-7,4-8]. The data of Fig. 4-2 show that this

thin a-Te layer, if it does exist for the polycrystalline CdTe film, has only a weak effect on

the determination of the sub-surface void fraction within the sample as long as the CdTe

layer is much thicker than the a-Te layer. Such conditions are satisfied due to the

expected thinness of the a-Te layer using the previous report as a guide. Another detail

must be addressed considering that, for the data acquired in these two processes, the

samples are at different temperatures, 130 °C for deposition and 25 °C for etching. For

the film structure during deposition, thermal expansion will occur at the elevated

temperature, and as a result, a difference in the thickness scales will exist relative to the

59

film structure at room temperature. Given the thermal expansion coefficient of single

crystal CdTe of 5.9x10−6 (°C)−1 at 25 °C, the thickness change that a 2000 Å thick CdTe

film undergoes upon heating to 130°C is (2000 Å)[5.9x10−6 (°C)−1](105 °C) = 1.2 Å,

which is inconsequential in this study.

4.4 Detection of a-Te on etched CdTe: experiment details

Two experiments have been designed in order to detect a-Te on etched CdTe films

and to extract its optical properties. In the first experiment, a 3 µm thick CdTe film was

deposited onto a c-Si wafer, and smoothened by Br2+methanol etching from a starting

surface roughness thickness of 500 Å to 50 Å, as characterized by spectroscopic

ellipsometry over the photon energy range from 0.75 to 1.5 eV. Once the surface

roughness has been reduced to its minimum, additional Br2+methanol etch steps have

been applied to this sample with spectroscopic ellipsometry measurements performed

before the first additional etch step and after each successive etch. The very rough

region at the surface of the starting CdTe is removed through successive 3 second etches,

leaving a smooth surface which increases the sensitivity of the analysis to the surface and

underlying CdTe. In the additional etches, also set at 3 second durations, the smooth

CdTe film was removed in a layer-by-layer fashion with a relatively constant roughness

thickness. The additional etches and measurements have provided the information

needed to evaluate the presence of an a-Te layer in the Br2+methanol etching process.

In the second experiment, a 3500 Å thick CdTe film was deposited on a c-Si wafer, and a

60

total of 37 Br2+methanol etch steps was applied to this sample until the CdTe thin film

was completely removed from the c-Si wafer. Spectroscopic ellipsometry

measurements were performed after each etch step. These measurements have been

used to extract the optical properties of the a-Te film generated in the Br2+methanol

etching process. The concept of this second experiment is shown in Fig. 4-3 through a

schematic of the sample structural changes. These layered structures are applied in the

modeling of the spectroscopic ellipsometry data.

Figure 4-3 Schematic of the sample structural changes that occur in the last three etching steps for a CdTe film on c-Si. The starting thickness of this CdTe film is 3500 Å.

4.5 Detection of a-Te on etched CdTe: results and analysis

Previous reports have shown that Br2+methanol treatments leave the surface of single

crystal CdTe covered with an optically identifiable amorphous Te layer [4-7, 4-8]. A

similar effect is expected for polycrystalline CdTe, which can be seen clearly by the

difference in the ellipsometric spectra of Fig. 4-4. Figure 4-4 shows two spectra for the

3 µm thick smoothened CdTe film on c-Si wafer measured at angle of incidence of 63°.

The dashed line represents the data measured before the additional Br2+methanol etching

C-Si

SiO2

CdTe a-Te

C-Si

SiO2

a-Te

C-Si

SiO2

35th etching 36th etching 37th etching

61

steps when the surface roughness has reached its minimum, and the solid line is acquired

after the 6th additional Br2+methanol etch step after a total etching time of 18 seconds.

Because the CdTe surface is already smooth after the first set of etching steps and the

deduced surface roughness thickness is not changing over the additional etching steps,

then the ellipsometric spectra measured after the 6th etch should be similar to that

measured before the 1st etch. Obviously, from Fig. 4-4, one concludes that changes have

occurred in the nature of the surface, even though the roughness layer thickness is not

changing significantly. It can be proposed that the changes are characterized by the

gradual conversion of a roughness layer associated with CdTe to a roughness layer

associated with the a-Te region.

15

20

25

30

2 3 4 5 680

100

120

140

160

ψ (d

egre

e)∆

(deg

ree)

6th Br+Me etch Before 1st etch

Photon Energy (eV)

Figure 4-4 Ellipsometric spectra for a smoothened CdTe film on a c-Si wafer measured at angle of incidence of 63°. The broken lines represent data measured before the first additional Br2+methanol etching step, and the solid lines represent data measured after the 6th additional Br2+methanol etching step. The total etching time between the two is

62

18 seconds. The starting CdTe thickness before any etching was 3 µm.

Based upon such a proposition, analysis is performed on the ellipsometric spectra

acquired in the second experiment described in Sec. 4.4 after the 36th and 37th etching

steps at an angle of incidence of 65°. The two experimental spectra are shown in Fig.

4-5 for comparison. Figure 4-6 shows the two spectra presented separately along with

the best-fit simulations in each case. Figures 4-7 and 4-8 also show the best-fit

structural parameters of the model along with their confidence limits. If the real and

imaginary parts of the dielectric function (ε1, ε2) of the a-Te were extracted from the

model of Fig. 4-8 without the assumption of voids, then a relatively weak oscillator

amplitude in ε2 would be obtained, but with a shape similar to that of the previous reports

on single crystal CdTe [4-7, 4-8]. The weak ε2 is attributed, in fact, to the large void

fraction in the a-Te derived from etching away the polycrystalline CdTe in comparison to

that derived from bulk single crystal CdTe. In an initial fit of the spectra of Fig. 4-6

(left), the a-Te dielectric function from the previous reports was used as a reference along

with a variable void volume fraction. In the final fit, an analytical model for the a-Te

dielectric function was used along with a fixed void fraction deduced from the initial fit.

The confidence limits on the void fraction in Fig. 4-8 are derived from the initial fit.

The resulting dielectric function deduced for the a-Te layer over the range of 0.75 to

6.5 eV is shown in Fig. 4-9. In Fig. 4-10, a comparison of these best fit spectra is

provided with the corresponding results for a-Te from measurements of single crystal

63

CdTe over the range of 1.5 to 6.0 eV from the previous reports [4-7, 4-8]. The analytical

expression for the real and imaginary parts of the dielectric function used in the best fit is

given as [4-9]:

2 ( ) 0;Eε = g

E E< (4.1)

2

02 2 2 2 2 2 2 2

0

( )( ) ( ) ( ) ;

( ) ( )g

g p

E E AE EE G E L E

E E E E E E

− Γε = =

− + − + Γ

gE E> . (4.2)

21 1 2 2

( )2( ) ( ) ,

gEE P d

E

∞ ξε ξε = ε ∞ + ξ

π ξ −∫

Here E is the photon energy and Eg is the band gap energy associated with band-to-band

transitions in the a-Te. For E>Eg, the imaginary part of the dielectric function includes

the product of two terms, the Lorentz oscillator function L(E) and the band edge function

G(E). The latter is based on the assumption of parabolic bands and a constant dipole

matrix element. In the Lorentz oscillator expression L(E), A is the amplitude, Γ is the

broadening parameter and E0 is the resonance energy. In the band edge function, Ep (>

Eg) defines a second transition energy (in addition to Eg), given by Ep+Eg. This second

transition energy separates the band edge region from the Lorentz oscillator region and

provides flexibility that is lacking in the more common Tauc–Lorentz expression [4-9].

Table 4.1 Best fit parameters and confidence limits that define Eqs. (4.1) and (4.2) for the dielectric function of a-Te.

An En (eV) Γn (eV) Eg (eV) Ep (eV) ε1 (∞)

38.79±1.97 2.949±0.053 2.867±0.075 0.909±0.103 0.497±0.154 2.819±0.143

64

15

20

25

30

35

40

0 1 2 3 4 5 6 7

100

120

140

160

180

ψ (d

egre

e)∆

(deg

ree)

36th etch 37th etch

Photon Energy (eV)

Figure 4-5 Ellipsometric spectra for a CdTe thin film on a crystalline Si substrate after the 36th and 37th etch steps for comparison. The starting CdTe film thickness was 3500 Å.

15

20

25

30

35

40

0 1 2 3 4 5 6 7

100

120

140

160

180

ψ (d

egre

e)∆

(deg

ree)

37th etch fit

Photon Energy (eV)

15

20

25

30

35

40

0 1 2 3 4 5 6 7

100

120

140

160

180

ψ (d

egre

e)∆

(deg

ree)

36th etch fit

Photon Energy (eV)

Figure 4-6 Ellipsometric spectra for a CdTe thin film on a crystalline Si substrate with a starting thickness of 3500 Å measured after the 37th (left) and 36th (right) etching steps (data points). Also shown are their best fits (broken lines).

65

Figure 4-7 Model and best-fit parameters used for the analysis of the ellipsometric spectra of Fig. 4-6 (left panel) collected after the 37th etching step applied to a CdTe film on a crystalline Si substrate. Because the CdTe film is completely removed, this analysis provides the structure of the c-Si substrate. MSE indicates the mean square error in the fit.

Figure 4-8 Model and best fit parameters used for the analysis of the ellipsometric spectra of Fig. 4-6 (right panel) collected after the 37th etching step applied to a CdTe film on a crystalline Si substrate. This analysis yields the structure of the a-Te layer on the c-Si substrate. The void volume fraction in the a-Te layer has been obtained by expressing the a-Te layer in this study of polycrystalline CdTe as a mixture of the a-Te obtained in a previous study of single crystal CdTe along with a void component.

0

5

10

15

20

ε 1

0 1 2 3 4 5 6 7

0

5

10

15

Photon Energy (eV)

ε 2

Figure 4-9 Real and Imaginary parts of the dielectric function ε1 and ε2 vs. photon energy for a-Te generated through Br2+methanol etching of a polycrystalline CdTe film.

native SiO2 20.5 Å

c-Si 2 mm

MSE = 7.669

Surface roughness 12.3 ± 0.1 Å

0.55 ± 0.01 / 0.45 ± 0.01 a-Te/void

native SiO2 20.5± 0.1 Å

c-Si 2 mm

MSE = 5.896

66

0

5

10

15

20 a-Te reference

ε 1

2 3 4 5 6

0

5

10

15

Photon Energy (eV)

ε 2

Figure 4-10 A comparison of the a-Te optical properties deduced in this study (see Fig. 4-9) with the literature reference optical properties of a-Te from 1.5 to 6 eV, the latter obtained by etching single crystal CdTe.

Now that the optical properties of a-Te have been determined, it is possible to apply

the results in a model of spectra collected in the two etching experiments in order to

improve the quality of fit to the data. A decrease in the MSE value will provide an

indicator of the correctness of the optical properties of a-Te layer obtained in this study.

Figure 4-11 shows the ellipsometric spectra and the best fit for the same etching

experiment as that in Fig. 4-6, but after the 35th etch step (left panel). The right panel

shows the optical model consisting of an a-Te/CdTe/c-Si structure along with the best fit

parameters, confidence limits, and MSE value. Figure 4-12 shows the modeling results

corresponding to Fig. 4-11 but without introducing an a-Te layer and using CdTe surface

roughness in the analysis instead. Similarly, Figures 4-13 and 4-14 compare the best fit

of the ellipsometric spectra before the first additional etch for the same experiment as that

67

of Fig. 4-4, comparing the modeling results with and without the a-Te layer. Finally in

Figs. 4-15 and 4-16 a comparison of the ellipsometric analysis after the 6th additional etch

step for the same experiment as that in Figs. 4-13 and 4-14, comparing the modeling

results with and without introducing the a-Te component into the model. In all three

situations, introduction of the a-Te component into the model lowers the MSE and thus,

improves the quality of the fit to the spectra. As a result, it can be concluded that the

optical properties of a-Te extracted in this study are reliable and useful.

Various features of the results of Figs. 4-11 to 4-16 are relevant for this and future

investigations. First it can be noted that it is not necessary to include the a-Te

component in order to obtain accurate structural information when the CdTe thickness is

much larger than the a-Te surface layer thickness. This is the case in Figs. 4-13-4-16.

In contrast when the CdTe is very thin, it becomes necessary to incorporate the a-Te

component for an accurate CdTe void volume fraction. This can be seen by comparing

Figs. 4-11 and 4-12. Second, for the thinner (3500 Å) as-deposited CdTe film, the a-Te

layer obtained even after many etching steps is relatively thin (14 Å) and dense as can be

seen from Fig. 4-11. In contrast, for the thicker (3 µm) as-deposited CdTe film, the a-Te

containing layer is thicker (50-60 Å), but with a much lower volume fraction of a-Te

(0.2-0.3) as can be seen from Figs. 4-13 and 4-15. In spite of the large physical

thickness of the layers in this case, the effective thickness is identical to that of the a-Te

layer on the thinner CdTe (13-14 Å). This comparison suggests that etching of the very

thick film leads to greater inhomogeneity in the surface layer.

68

native SiO2 20.5 Å

c-Si 2 mm

MSE = 13.33

Surface roughness 14 ± 0.4 Å

0.97 ± 0.03/0.03 ± 0.03 a-Te / void

CdTe 109 ± 1 Å

0.94 ± 0.01 / 0.06 ± 0.01 CdTe / void

a-Te at surface: deff = 13.5 Å

Surface roughness 78 ± 8 Å

0.11 ± 0.01/0.89 ± 0.01 CdTe / void

MSE = 22.11

CdTe 95 ± 1 Å

1.16 ± 0.01 / −0.16 ± 0.01 CdTe / void

native SiO2 20.5 Å

c-Si 2 mm

15

20

25

30

35

0 1 2 3 4 5 6 7

100

120

140

160

180

ψ (d

egre

e)∆

(deg

ree)

35th etch fit

Photon Energy (eV) Figure 4-11 Ellipsometric spectra for a CdTe thin film on a crystalline Si substrate with a starting thickness of 3500 Å measured after the 35th etch step (left panel). Also shown is the best fit and associated model deduced in the analysis of the ellipsometric spectra in order to extract the a-Te/CdTe/c-Si structural parameters (right panel).

15

20

25

30

35

0 1 2 3 4 5 6 780

100

120

140

160

180

ψ (d

egre

e)∆

(deg

ree)

35th etch fit

Photon Energy (eV)

Figure 4-12 Experimental and best fit spectra (left panel) along with the best fit parameters and model (right panel) for comparison with the results of Fig. 4-11, but without introducing an a-Te component into the model. Such a model leads to a higher MSE.

69

CdTe 137 ± 12 Å

0.85±0.01/0/0.15±0.01 CdTe/a-Te/void CdTe semi infinite substrate

0.95 ± 0.01 / 0.05 ± 0.01 CdTe / void

Surface roughness 59 ± 2 Å

0.22±0.01/0.29±0.02/0.49±0.01 a-Te/CdTe/void

MSE = 7.181

a-Te at surface: deff = 13 Å

a-Te at sub-surface: deff = 20.5 Å

Surface roughness 84 ± 0.7 Å

0.51 ± 0.01/0.49 ± 0.01 CdTe / void

CdTe semi infinite substrate

0.94 ± 0.01 / 0.06 ± 0.01 CdTe / void

MSE = 8.168

15

20

25

30

35

2 3 4 5 6

100

120

140

160

ψ (d

egre

e)∆

(deg

ree)

before 1st etch fit

Photon Energy (eV)

Figure 4-13 Ellipsometric spectra and the best fit (left panel) for a smoothened CdTe film with a starting thickness of 3 µm obtained before the first additional etch after smoothening. Also shown is the model and best fit parameters used in the analysis of the ellipsometric spectra over the energy range of 2 to 6 eV in order to deduce the a-Te volume fraction in the surface roughness layer (right panel).

15

20

25

30

35

2 3 4 5 6

100

120

140

160

ψ (d

egre

e)∆

(deg

ree)

before 1st etch fit

Photon Energy (eV)

Figure 4-14 Experimental and best fit spectra (left panel) along with the best fit model and parameters (right panel) for comparison with the results of Fig. 4-13, but without introducing an a-Te component into the model. This ellipsometric analysis is associated with a 3 µm thick smoothened CdTe film before the first additional etch after smoothening.

70

CdTe/a-Te 251 ± 11 Å

0.89±0.01/0.06±0.01/0.06±0.01 CdTe/a-Te/void CdTe semi infinite substrate

0.99 ± 0.01 / 0.01 ± 0.01 CdTe / void

Surface roughness 53 ± 2 Å

0.27 ± 0.01/0.73 ± 0.01 a-Te / void

MSE = 8.028

a-Te at surface: deff = 14 Å

a-Te at sub-surface: deff = 15 Å

CdTe semi infinite substrate

1.02 ± 0.01 / -0.02 ± 0.01 CdTe / void

Surface roughness 100 ± 4 Å

0.68 ± 0.01/0.32 ± 0.01 CdTe / void

MSE = 39.38

15

20

25

30

35

2 3 4 5 6

100

120

140

160

ψ

(deg

ree)

∆ (d

egre

e)

6th etch fit

Photon Energy (eV)

Figure 4-15 Ellipsometric spectra and the best fit (left panel) for a smoothened CdTe film with a starting thickness of 3 µm obtained after the 6th additional etch after smoothening. Also shown is the model and best fit parameters used in the analysis of the ellipsometric spectra over the energy range of 2 to 6 eV in order to deduce the surface roughness thickness and the a-Te volume fraction in the CdTe structure (right panel).

15

20

25

30

35

2 3 4 5 680

100

120

140

160

ψ (d

egre

e)∆

(deg

ree)

6th etch fit

Photon Energy (eV)

Figure 4-16 Experimental and best fit spectra (left panel) along with the best fit model and parameters (right panel) for comparison with the results of Fig. 4-15 but without introducing an a-Te component into the model. This ellipsometric analysis is associated with a 3 µm thick smoothened CdTe film after the 6th additional etch.

71

Chapter Five

Optical Properties of Thin Film CdTe and CdS before and after CdCl2

Post-deposition Treatment

5.1 Introduction

A description of the optical properties of the TEC-15 glass substrate components has

been provided in Chapter 3. Here in Chapter 5, the focus now shifts to the optical

properties of CdTe and CdS before and after the CdCl2 post-deposition treatment. The

optical properties of as-deposited CdTe and CdS films on single crystalline Si (c-Si)

substrates were determined as described previously [5-1]. Using this previous work on an

as-deposited CdTe film as a starting point, post-deposition CdCl2 treatment of the same

film was performed as part of this thesis, and its optical properties were obtained after the

treatment. In the case of CdS, a polycrystalline thin film prepared in the device

configuration on a fused silica prism enables measurements of the same CdS film through

the prism before and after CdCl2 treatment, without loss of spectral range.

As a first step toward studying the layers of the full solar cell, the CdTe film

structural changes upon CdCl2 treatment were investigated using spectroscopic

ellipsometry (SE) measurements of a CdTe film on a crystalline silicon (c-Si) substrate.

72

Because the c-Si is very smooth, the complexity of the data analysis is reduced as a result

of the smooth, well-characterized interface between the film and substrate. In addition,

the absence of an underlying CdS film, which is present in the solar cell structure, avoids

the complication of alloying of the CdTe with S due to S in-diffusion. Analyses of CdTe

films in CdCl2 treated solar cell structures are described later in Chapter 6, and in that

chapter the issue of S diffusion will be addressed.

Upon CdCl2 treatment, it was observed in this study that the optical properties of the

CdTe film on c-Si change dramatically as will be described in Sec. 5.3. The

modification experienced by the CdS film in the SiO2/CdS/CdTe structure as a result of

the CdCl2 treatment is weaker; however, in this case, additional research needs to be

performed in the future to explore the observed substrate dependence of the CdS optical

properties and the role of the post-deposition treatment.

5.2 Optical properties of as-deposited CdTe and CdS films deposited on c-Si substrates

The polycrystalline CdTe and CdS films of this study were magnetron sputtered

under conditions similar to those yielding 14%-efficient solar cells [5-2]. The CdTe

depositions were performed on native oxide-covered c-Si wafers in a system with two

chambers and a load-lock (built by AJA International, Inc.) using 60 W rf power applied

to the target, 18 mTorr Ar pressure, 23 sccm Ar flow, and a 10 ± 1 cm target-substrate

distance. The CdS depositions were performed similarly on c-Si in the two-chamber

system to obtain reference data, and on a fused silica prism in a separate single-chamber

73

system (built at Univ. Toledo) to explore the role of CdCl2 treatments; (Dr. Victor

Plotnikov is acknowledged for assistance in the fabrication of this sample). For both

CdS depositions, the rf power level was 50 W and the Ar pressure was 10 mTorr. As

noted earlier, c-Si substrates and an optical quality fused silica prism were used in both

cases due to their consistent optical properties and smoothness; thus, complications in

optical analysis arising from substrate-induced surface roughness and film/substrate

interface roughness were avoided. The true substrate temperatures T for the CdTe and

CdS depositions on c-Si were 188 °C and 225 °C, respectively, as determined in an in situ

SE calibration [5-3]. The nominal substrate temperature T was 200 °C for the CdS

deposition on the fused silica prism in the single-chamber system. In this case, a

measurement of true substrate temperature was not possible since real time SE was not

used to probe the film growth process.

1 2 3 4 5 6-4

-2

0

2

4

6

8

10

12

14

16

ε 1,ε

2

photon energy (eV)

E0

E1

E1+∆

1E

2

Figure 5-1 The room temperature dielectric functions of single crystal CdTe (broken lines) [5-4] and a CdTe film deposited at 188°C (solid lines) [5-5]. The downward arrows point to the energy values of the four critical point transitions E0, E1, E1+∆1, and E2 identified in the band structure of Fig. 5-2.

_______ 188 °C

- - - - Single crystal CdTe

74

Table 5.1 Fitting results for single crystal and thin film polycrystalline CdTe using an analytical model consisting of four critical points and one T-L background oscillator.

Figure 5-2 Band structure of CdTe [5-6].

An En (eV) Γn (eV) φn (degree) µn

EG ε∞

Single

crystal

CdTe

CP(E0) 7.283±0.407 1.491±0.004 0.041±0.006 −20.806±2.165 0.048±0.003

−2.975±0.343

CP(E1) 4.871±0.137 3.310±0.002 0.300±0.011 −6.149±4.598 1.089±0.054

CP(E1+∆1) 7.358±0.382 3.894±0.003 0.286±0.010 77.473±1.798 0.377±0.019

CP(E2) 5.320±0.261 5.160±0.003 0.923±0.034 −31.056±8.876 1.560±0.094

T-L 70.853±3.536 4.790±0.067 4.773±0.380 1.710±0.034

Film

CdTe at

188 °C

CP(E0) 8.928±0.314 1.527±0.007 0.089±0.018 −16.791±1.194 0.048

−4.120±0.301

CP(E1) 2.395±0.072 3.199±0.018 0.628±0.025 −75.501±5.900 1.089

CP(E1+∆1) 6.458±0.131 3.981±0.019 0.516±0.022 96.117±5.746 0.377

CP(E2) 1.862±0.092 5.208±0.023 0.958±0.048 9.523±6.253 1.560

T-L 73.089±4.033 4.790 3.733±0.136 1.710

E1 E1+∆1 E0

E2

75

0 1 2 3 4 5 6

0

2

4

6

8

film CdS Tdep

=225 OC

single crystal CdS

ε 1,ε

2

photon energy (eV)

E0

E1-A

E1-B

Figure 5-3 The room temperature ordinary dielectric functions of single crystal (wurtzite) CdS (broken lines) [5-7] in comparison with the polycrystalline thin film CdS deposited on c-Si at 225 °C (solid line) [5-1]. The three downward arrows point to the energy values of the critical point transitions. Table 5.2 Fitting results for single crystal and thin film polycrystalline CdS using an analytical model consisting of three critical points and one T-L background oscillator.

An En (eV) Γn (eV) φn (degree) µn

EG ε∞

Single

crystal

CdS

CP(E0) 6.720±0.756 2.399±0.003 0.209±0.008 −19.056±0.836 0.103±0.013

−1.463±0.595 CP(E1-A) 2.581±0.190 4.802±0.004 0.349±0.021 50.393±7.018 0.777±0.085

CP(E1-B) 5.586±0.327 5.518±0.008 0.689±0.046 101.96±4.870 0.489±0.058

T-L 90.770±5.560 6.262±0.043 3.421±0.232 3.501±0.046

Film CdS

at 225 °C

CP(E0) 6.739±0.071 2.426±0.004 0.127±0.008 −20.697±0.621 0.103

−1.597±0.103 CP(E1-A) 2.533±0.146 4.944±0.009 0.349±0.020 55.403±3.499 0.777

CP(E1-B) 5.458±0.112 5.400±0.018 0.620±0.026 79.673±5.466 0.489

T-L 94.931±8.038 6.262 4.602±0.282 3.501

For all dielectric functions in Figs. 5-1 and 5-3, experimental (ε1, ε2) results obtained

by inversion of (ψ, ∆) data were fit using an analytical model consisting of N critical

76

points (N=4 for CdTe and N=3 for CdS). The locations of the four critical point features

of CdTe are identified in the band structure diagram of Fig. 5-2. E0 represents the

fundamental band gap transition at the zone center Γ point, whereas the E1 complex is

attributed to transitions along the L line between the L6 valence and conduction bands and

between the L4,5 valence bands and the L6 conduction band. Each critical point was

modeled using an expression derived for Lorentzian broadened transitions between

parabolic bands [5-8]:

n n(i )n n n n=A e /2[E E i( /2)]φ µε Γ − − Γ (5.1)

Thus each critical point is fit with five parameters, an amplitude An, a phase φn, a

broadening parameter or linewidth Γn, a resonance or band gap energy En, and an

exponent µn. These parameters are given in Table 5.1 for single crystal and thin film

polycrystalline CdTe and in Table 5.2 for corresponding samples of CdS. Also included

in the dielectric function model was a single broad background Tauc-Lorentz oscillator

which was used to fit non-parallel-band transitions in energy regions between the critical

points. The background is modeled using the expression:

2

G 0 02 G2 2 2 2 2

0 0

E E A E Eε = (E E )

E (E E ) + E

− Γ Θ −

− Γ , (5.2)

where G(E E )Θ − is a unit step function, centered at E=EG such that Θ =1 when E > EG

and Θ =0 when E ≤ EG. This expression has four variable parameters, EG, the Tauc

band gap, A0, E0, and Γ0, the Lorentz oscillator resonance amplitude, energy, and

broadening parameter, respectively. These parameters are also included in Tables 5.1

77

and 5.2 along with ε∞, the constant contribution to the dielectric function. This constant

may be due to transitions above the measured spectral range. Negative values for ε∞

have been observed in similar such analyses of single crystal Si [5-9]; however, the origin

of such unphysical values is unclear.

The major difference between the polycrystalline thin film CdTe and single crystal

CdTe dielectric functions derive from the critical point broadening parameters or

linewidths, which are larger for the thin film most likely due to scattering of excited

carriers at grain boundaries which reduces the lifetimes. For CdS, however, it is

observed that the single crystal has equal or larger critical point widths than the thin film.

This effect is likely to be due to polishing damage at the near surface of the crystal in this

case. The differences in the critical point energies are due to in-plane strain in the thin

films, and these strain shifts are currently being quantified in order to use the dielectric

function to evaluate strain −− with the potential for on-line analysis [5-10]. The strain

probed in this case lies in the plane of the film since the probing optical field, even

though impinging on the film at oblique incidence, is strongly refracted so that the optical

field lies predominantly in the plane. The differences in the critical point amplitudes

can be attributed to either voids or tensile strain which decrease the An values or

compressive strain which increase these values. The exponents µn and the phases φn are

expected to be the same in the film and single crystal, and in fact, the µn values are fixed

for the thin films at values deduced for the single crystal. The observed differences in

the best fit φn may be attributed to changes in excitonic interactions due to grain structure

78

or defects.

5.3 Optical properties of CdCl2 post-deposition treated CdTe and CdS

In order to characterize the changes in the structure of the thin films of the solar cell

upon post-deposition treatment, the optical properties of the treated CdTe and CdS must

be obtained and compared to those of Section 5.2. The dielectric function of the

CdCl2-treated CdTe film deposited on a c-Si substrate was extracted in order to avoid

complications of S diffusion in the completed solar cell. The optical properties of the

treated CdTe are shown in Fig. 5-4.

-4

0

4

8

12

1 2 3 4 5 6

0

4

8

12

CdTe as-deposited

CdTe CdCl2 treated

ε 1

ε 2

Photon Energy (eV)

-4

0

4

8

12

1 2 3 4 5 6

0

4

8

12

CdTe single crystal

CdTe CdCl2 treated

ε 1

ε 2

Photon Energy (eV)

Figure 5-4 (left) Best fit analytical models of the room temperature dielectric functions for two CdTe films of thickness approximately 1000 Å, obtained from the same deposition but with different post-deposition processing: as-deposited (no treatments; broken line) and CdCl2-treated for 5 min at 387°C (solid line); (right) a comparison between the CdCl2-treated CdTe film (solid line) and single crystal CdTe (broken line).

79

Table 5.3 Best fit dielectric function parameters comparing single crystal, CdCl2-treated, and as-deposited CdTe samples.

An En (eV) Γn (eV) φn (degree) µn

EG ε∞

Single

crystal

CdTe

CP(E0) 7.283±0.407 1.491±0.004 0.041±0.006 −20.806±2.165 0.048±0.003

−2.975±0.343

CP(E1) 4.871±0.137 3.310±0.002 0.300±0.011 −6.149±4.598 1.089±0.054

CP(E1+∆1) 7.358±0.382 3.894±0.003 0.286±0.010 77.473±1.798 0.377±0.019

CP(E2) 5.320±0.261 5.160±0.003 0.923±0.034 −31.056±8.876 1.560±0.094

T-L 70.853±3.536 4.790±0.067 4.773±0.380 1.710±0.034

CdCl2

treated

CdTe

CP(E0) 7.701±0.169 1.503±0.005 0.061±0.011 −15.625±0.449 0.048

−3.756±0.175

CP(E1) 4.260±0.042 3.321±0.003 0.342±0.006 −3.146±1.034 1.089

CP(E1+∆1) 6.119±0.057 3.913±0.004 0.212±0.005 88.142±1.689 0.377

CP(E2) 4.756±0.040 5.214±0.003 0.840±0.010 −22.885±0.821 1.560

T-L 79.254±1.208 4.790 4.576±0.075 1.710

Film

CdTe at

188 °C

CP(E0) 8.928±0.314 1.527±0.007 0.089±0.018 −16.791±1.194 0.048

−4.120±0.301

CP(E1) 2.395±0.072 3.199±0.018 0.628±0.025 −75.501±5.900 1.089

CP(E1+∆1) 6.458±0.131 3.981±0.019 0.516±0.022 96.117±5.746 0.377

CP(E2) 1.862±0.092 5.208±0.023 0.958±0.048 9.523±6.253 1.560

T-L 73.089±4.033 4.790 3.733±0.136 1.710

As an example of the key role of the CdCl2 treatment, Fig. 5-4 and Table 5.3

compare best-fit analytical results for the room temperature dielectric functions of the

single crystal CdTe, as-deposited thin film CdTe, and thin film CdTe with the 5 min

CdCl2-treatment. The optical model used here is the same as that described in Section

5.2. The spectra in Fig. 5-4 for the treated film were obtained after a sufficient number

of etch cycles, so that its thickness matched that at which the as-deposited film was

measured (~ 1000 Å). It is clear from Table 5.3 that the CdCl2-treatment leads to a

significant narrowing of the critical points so as to be nearly indistinguishable from the

single crystal as shown in Fig. 5-4. This is an indication of an increase in grain size and

/or a reduction in defect density upon treatment.

80

The narrower higher energy critical points for the treated film may be due to its

higher quality surface compared to the single crystal. Also in Table 5.3 the critical point

energies of the treated film approach those of the single crystal, indicating that strain in

the film is relaxed as a result of the CdCl2 treatment. As a result, the primary difference

between the dielectric function of the CdCl2-treated film and the single crystal is the

presence of a small volume fraction of voids (0.01 ± 0.002) that exist preferentially near

the surface and reduce the amplitudes of the higher energy critical points.

It is more difficult to perform the corresponding experiment for CdCl2 treatment of

the CdS film. First, the effectiveness of the etching procedure which is used to remove

the thick oxide and surface roughness layers for determination of the treated CdTe

dielectric function, in fact, has yet to be successfully demonstrated for CdS. Second, in

order for post-deposition treatment studies of the CdS to be at all relevant for device

structures, the CdS must be capped with a layer of CdTe, as this layer is likely to have a

significant impact on the structural change upon treatment. Because an overlying CdTe

layer significantly attenuates the light irradiance entering the CdS from the CdTe/ambient

side at photon energies above the band gap of the CdTe, the use of a prism arrangement

has been explored in order to study the effect of treatment on the CdS. In this study,

CdS with an intended thickness of 3000 Å is deposited directly onto one face of a 60°

fused silica prism held at a nominal temperature of 200°C, and then over-deposited with

CdTe to an intended thickness of 5.0 µm. The true temperature of the surface of the

film is difficult to assess in this case and should be much lower than 200°C due to the

81

different geometry of the substrate holder necessitated by the prism and the lack of a real

time SE analysis capability on the deposition chamber (see Fig. 5-5). Finally the sample

structure and CdS dielectric function are measured by spectroscopic ellipsometry through

the prism side before and after the CdCl2-treatment.

CdS Target

Fused silica prism

substrate

Sputtering chamber

CdTe Target

Substrate holder

Ground Shield

Plasma

Heating wire

Figure 5-5 A schematic of the sputtering chamber for CdTe/CdS deposition on a fused silica prism (reproduced with permission from Victor Plotnikov, Ph.D. Thesis, University of Toledo, 2009).

Figure 5-6 (left) shows the analytically derived dielectric function of CdS

as-deposited on the prism and measured from the prism side, in comparison with that of

CdS as-deposited on c-Si at 225°C and measured from the ambient side. The dielectric

function of the CdS as-deposited on the prism is suppressed significantly in amplitude at

the higher energies, and the high energy critical point structure is very broad. Because

the light beam does not penetrate very deeply into the CdS at these higher energies, the

results are characteristic of the CdS at the prism interface which is apparently either a low

82

density material due to incomplete space filling during nucleation or instead a physical

mixture of the substrate material with CdS due to microscopic roughness. Alternatively,

a chemical mixture may occur at the interface due to intermixing induced by the impact

of sputtered species. The extensive broadening of the high energy critical points E1-A

and E1-B would suggest a nanocrystalline CdS character at the interface; however other

explanations for this such as a chemical interaction and diffusion are certainly possible.

Figure 5-6 (right) shows that the CdCl2 treatment process appears to densify the CdS, but

the material exhibits a similar interface nature as the as-deposited film.

0

2

4

6

8

1 2 3 4 5 6

0

2

4

6

8

CdS as deposited on prism

CdS as deposited on c-Si

ε 1

ε 2

Photon Energy (eV)

0

2

4

6

8

1 2 3 4 5 6

0

2

4

CdS as deposited

CdS CdCl2 treated

ε 1

on prism

ε 2

Photon Energy (eV)

Figure 5-6 (left) Best fit analytical models for the room temperature dielectric functions of a CdS film as-deposited on a fused silica prism measured from the prism side and on a c-Si wafer measured from the ambient side; (right) best fit analytical model for the room temperature dielectric functions of CdS measured from the prism side before and after a 30 min CdCl2 treatment at 387°C.

83

Table 5.4 Best fit dielectric function parameters for as-deposited CdS on a fused silica prism, CdCl2-treated CdS on the prism, and. as-deposited CdS on c-Si.

Table 5.4 shows a comparison of the parameters used in the analytical model for the

three dielectric functions of Fig. 5-6. A comparison of the critical point energies reveals

that the CdCl2 treatment leads to a reduction in the E0 energy from the as deposited value

to a value closer to the single crystal. This effect would appear to be characteristic of

strain relaxation, as also occurs in the case of CdCl2 treatment of CdTe. The situation

for the E1A transition is likely to be more complicated. A single, broad E1 peak for the

as-deposited film on the fused silica prism is an indication of a film without preferential

orientation of the crystallites. In contrast, the clear E1A-E1B doublet for the as-deposited

film on c-Si is an indication of preferential c-axis orientation. The observed significant

shift of oscillator strength to higher energy upon treatment could also be due to a change

An En (eV) Γn (eV) φn (degree) µn

EG ε∞

CdS as

deposited

on prism

CP(E0) 6.236±0.030 2.498±0.001 0.226±0.003 −24.268±0.297 0.103

0.198±0.023

CP(E1-A) 0.316±0.051 4.880±0.100 1.178±0.284 −32.194±39.738 1.861±0.858

CP(E1-B) 4.474±0.129 5.286±0.026 1.084±0.090 108.21±2.472 0.324±0.005

T-L 57.711±5.145 6.262 14.828 3.501

CdCl2

treated

CdS on

prism

CP(E0) 2.180±0.106 2.453±0.004 0.486±0.013 −34.041±3.277 0.473±0.030

9.153±4.829

CP(E1-A) 1.628±0.498 4.923±0.223 2.507±0.271 −123.88±10.262 1.197±0.195

CP(E1-B) 11.961±4.281 5.354±0.007 0.944±0.114 172.96±4.398 0.148±0.092

T-L 75.427±5.834 6.810±0.262 9.145±1.009 1.804±0.021

CdS as

deposited

on c-Si

CP(E0) 6.739±0.071 2.426±0.004 0.127±0.008 −20.697±0.621 0.103

−1.597±0.103

CP(E1-A) 2.533±0.146 4.944±0.009 0.349±0.020 55.403±3.499 0.777

CP(E1-B) 5.458±0.112 5.400±0.018 0.620±0.026 79.673±5.466 0.489

T-L 94.931±8.038 6.262 4.602±0.282 3.501

84

in the grain texture that leads to preferential c-axis orientation. Clearly further work

needs to be undertaken, in particular to understand whether the differences in the

as-deposited dielectric functions of CdS on c-Si and CdS on fused silica are due to

top-surface vs. back surface measurement method or due to differences in the nature of

deposition on the two substrates.

5.4 Etch-back profiling of CdTe thin film structure after post-deposition treatments

Analysis results are presented next that focus on the effects of post-deposition

processing on the structural depth profile of CdTe films deposited on native

oxide-covered c-Si substrates. Sequential etching was applied to three ~ 3000 Å thick

CdTe films co-deposited on c-Si substrates held at 188°C. These films were exposed to

the following post-deposition processing conditions: (i) as-deposited (i.e., no treatments),

(ii) thermally annealed at 387°C in an atmosphere of Ar for 30 min, and (iii) CdCl2

treated also at 387°C, but for 5 min. The Br2 concentration used in this study for

etching was 0.05 vol.% in methanol. For each sample, the etch-profiling method was

performed using successive immersion steps in Br2+methanol, with each etch step

leading to a ~ 300 Å reduction in the bulk layer thickness. Because of the relative

smoothness of the as-deposited CdTe on c-Si substrates (compared, for example, to

depositions on rough TEC glasses), the successive etching treatments led to very smooth

surfaces from which high accuracy dielectric function determinations were possible. In

addition, the absence of an underlying CdS film in this case avoided the complication of

85

alloying of CdTe due to S in-diffusion that may be especially notable in the later stages of

etching as the CdTe is fully removed. This complication will be discussed further in

Chapter 6.

Figure 5-7 Resonance energies En (upper panel) and linewidths Γn (lower panel) for the critical point transitions in single crystal CdTe (broken lines) and in db ~ 1000 Å thick CdTe films sputter-deposited at different temperatures (points), all measured at 15°C [5-10].

Figure 5-7 highlights the consistent differences between the critical point

parameters of as-deposited CdTe films and the single crystal. The latter is characteristic

86

of CdCl2-treated CdTe as shown in Fig. 5-6 (right). Results for five different

as-deposited films prepared at different substrate temperatures from 188 °C to 304 °C

reveal the following characteristics relative to the single crystal: (i) higher energy E0,

E1+∆1, and E2 critical point transitions, (ii) lower energy E1 transitions such that the spin

orbit splitting energy is larger than in the single crystal, and (iii) broader critical points

with the E1 transition showing the largest variation with substrate temperature. In the

next paragraph, the focus will be on the E1 critical point in an evaluation of the effect of

the CdCl2 treatment on the structural depth profile of the CdTe film.

etching

etching

Figure 5-8 Critical point energies (upper panel) and widths (lower panel) as functions of CdTe bulk layer thickness during etching by Br2+methanol for co-deposited CdTe films processed in three different ways: (i) as-deposited, (ii) annealed in Ar for 30 min, and (iii) CdCl2 treated for 5 min. The deviations at low thickness are due to the onset of semi-transparency at the E1 critical point energy.

87

Figure 5-8 presents the depth profiles in the E1 critical point energy and width

relative to those of the single crystal values. These results provide information on the

depth profiles in the strain and grain size, respectively, throughout the film. New

experimental results [5-11] suggest that the E1 transition shifts to lower energy with

increasing strain consistent with a stress shift of (−0.2 eV/GPa). With this new insight,

the depth profiles in the critical point energies take on greater meaning. Similarly, Fig.

5-9 presents depth profiles in the void fraction that provide information on the structural

uniformity.

For the as-deposited CdTe film, the red-shift of E1 relative to the single crystal

value in the top panel of Fig. 5-8 suggests significant strain in this film over the studied

depth range of 1500-2000 Å; (the depth is measured relative to the substrate interface at 0

Å). The maximum E1 energy shift of −0.12 eV at a depth of 1500 Å corresponds to a

stress level of 0.6 GPa, which is consistent with results for these as-deposited films in Fig.

5-7. The depth profile in the void volume fraction in Fig. 5-9 provides additional

indirect evidence for this strain. The film is observed to undergo a structural transition

near 1500 Å whereby the strain is ultimately relaxed (after 2000 Å thickness) through

generation of voids and their continued evolution with thickness as shown in Fig. 5-9.

The lower panel of Fig. 5-8 shows that the as-deposited film has a very large broadening

parameter ΓE1 ~ 0.6 ± 0.15 eV which appears to be decreasing with increasing thickness

(or distance from the substrate interface). This is indicative of a very small grain size (~

10 nm) which appears to be increasing with thickness [5-11].

88

Upon annealing of the CdTe film in Ar, the strain nearest the substrate is

significantly reduced as the grain size increases (reduced ΓE1). Even after 30 min of

annealing in Ar, however, there is no significant reduction in the grain size within 500 Å

of the surface, and the strain in this region increases somewhat relative to the

as-deposited film (as indicated by the lower E1 energy). Figure 5-9 shows that the void

fraction in the surface region is reduced upon annealing in Ar and thus, the structure of

the film becomes more uniform throughout the thickness.

Figure 5-9 Relative void volume fractions as functions of CdTe bulk layer thickness during etching by Br2+methanol for co-deposited CdTe films on c-Si processed in three different ways: (i) as-deposited, (ii) thermally annealed in Ar for 30 min at 387˚C, and (iii) CdCl2-treated for 5 min at 387˚C. For the as-deposited and annealed films, the void fraction is scaled relative to the observed highest density film. For the CdCl2-treated film, the void volume fraction is scaled relative to single crystal CdTe.

89

A 5 min CdCl2 treatment leads to an E1 energy within 10 meV (i.e., within

experimental error) of the single crystal value throughout the thickness, suggesting a fully

strain-relaxed film. In addition, ΓE1 has been reduced significantly to a constant value

of ΓE1 ~ 0.30 ± 0.02 eV throughout the bulk of the film, indicating a significant increase

in grain size. Finally the CdCl2 treatment leads to a uniform void volume fraction

throughout most of the bulk of the film: 0.05 ± 0.02. Considerably more scatter exists

in these CdCl2 treated data, however, compared with those of the other samples, possibly

an effect of the Br2+methanol etching of a large-grained, relatively thin film. Figure 5-9

shows that voids have been pushed to the near-surface region of the CdCl2 treated film

which is likely to be the result of a much larger surface roughness layer thickness.

Finally, it should be noted that the void fractions for the as-deposited and Ar annealed

films in Fig. 5-9 are plotted relative to that of the as-deposited film at the minimum

thickness of ~1250 Å. For this material, which is under significant compressive stress

(0.6 GPa), the apparent density is ~0.03 higher than that of single crystal CdTe. For the

CdCl2 treated film, the observed void fraction of 0.05 ± 0.02 is scaled relative to the

single crystal.

90

Figure 5-10 Energy of the E1 transition (upper panel) and its width ΓE1 (lower panel) as functions of CdTe bulk layer thickness in successive Br2+methanol etching steps for ~3000 Å thick CdTe films. The two films were processed under identical conditions including fabrication on c-Si wafer substrates and annealing in Ar at 387°C for 30 minutes. The data for experiment #1 are the same as those depicted in Fig. 5-8.

Figure 5-11 Energy of the E1 transition (upper panel) and its width ΓE1 (lower panel) as functions of CdTe bulk layer thickness in successive Br2-methanol etching steps for ~3000 Å thick CdTe films. The two films were processed under similar conditions including fabrication on c-Si wafer substrates and CdCl2 treatment for 5 minutes. The data for experiment #1 are the same as those depicted in Fig. 5-8.

CdCl2 treated

Experiment # 1

∆ Experiment # 2

CdCl2 treated

Experiment # 1

∆ Experiment # 2

Annealed CdTe

Experiment # 1

∆ Experiment # 2

Annealed CdTe

Experiment # 1

∆ Experiment # 2

91

The results of Figs. 5-8 and 5-9 can be clearly understood in terms of CdTe grain

growth and strain relaxation effects of the CdCl2 treatment, and can even identify clear

differences in behavior between the CdCl2 treatment and simply annealing in Ar. In

further experiments, the reproducibility of the etch-profiling studies of such films has

been explored with the goal being to corroborate the above interpretation.

Figure 5-10 shows the Ar annealing behavior of thin (3000-3300 Å) CdTe films on

c-Si substrates from two independent experiments for comparison. The solid squares

are the same results as shown in Fig. 5-8, and the open triangles denote the results of a

second experiment performed on a different sample prepared and annealed under

identical conditions. The annealing behavior is reasonably well reproduced in the two

experiments, considering that the film thickness in the second experiment is somewhat

lower. In both experiments, the E1 energy lies ~ 20 meV lower than that of single

crystal CdTe, indicating residual stress of ~0.1 GPa, and the width ΓE1 increases toward

the surface, indicating a smaller near-surface grain size in both experiments.

Figure 5-11 shows results for E1 and ΓE1 from the two experiments on CdTe films in

which CdCl2 treatments were applied for 5 min. The results of the first experiment have

been presented earlier in Fig. 5-8. This first experiment was performed with a CdCl2

treatment temperature of 387°C, whereas the second was performed using a higher

temperature of 397°C. Another difference between the two experiments -- the age of the

prepared CdCl2 sources -- was deemed insignificant. More importantly, for both

experiments, the treatment was the first one for each of the two CdCl2 vapor sources.

92

Although the overall results of the two experiments of Fig. 5-11 are similar, certain

details in the second experiment suggest an effect of the higher temperature. First, for

the second experiment, the grain size increases more significantly toward the surface than

in the first experiment. In fact, the broadening parameter in the top 500 Å of the film

drops below that of single crystal CdTe. This effect may reflect a dielectric function for

the single crystal CdTe from the reference [5-4] that may be influenced either by

experimental errors or by greater near-surface damage. Second, a comparison of Fig.

5-12 with Fig. 5-9 shows that the void profile in the second experiment is not nearly as

uniform as in the first. This feature is likely due to the higher temperature which leads

to a densification of the underlying large grain crystalline material at the expense of

significant roughness with surface connected voids that extend well into the film. A hint

of this effect appears for the CdCl2 treated film in Fig. 5-9, but the effect appears quite

strongly in Fig. 5-12.

Experiment #2 CdCl2 treated CdTe film

Experiment #2 Ar annealed CdTe film

Figure 5-12 Void volume fraction as a function of CdTe bulk layer thickness in successive Br2-methanol etching steps for ~3000 Å thick CdTe films in a second experiment for comparison with the results in Fig. 5-9. Two different post-deposition

93

processing procedures were used: (i) an anneal in Ar for 30 min, and (ii) a CdCl2-treatment for 5 min. For the Ar annealed films, the void fraction is scaled relative to the depth at which the highest density is observed. For the CdCl2-treated film, the void volume fraction is scaled relative to single crystal CdTe. The void structure for the film annealed in Ar is attributed to structure in the as-deposited film (as in Fig. 5-8). In contrast, the void structure for the CdCl2 treated film is associated with extensive near-surface roughness.

In the above studies, it is clear that a short 5 min CdCl2 treatment is observed to have

a more significant effect in relaxing strain and enhancing grain growth than a 30 min

anneal in Ar. This reveals the reactive nature of the CdCl2 treatment. These studies

suggest clear directions for future work which should involve the effects of treatment

time and temperature on the depth profiles of the strain and grain size. This may enable

one to study the kinetics of grain growth and the separate roles of the surface and

substrate interface in this process.

94

Chapter Six

Optical Structure of As-deposited and CdCl2-treated CdTe Superstrate Solar Cells

6.1 Introduction

The multilayer optical structure of thin film solar cells is of interest because it

provides insights into the optical quantum efficiency as well as the optical losses that

limit the short-circuit current [6-1]. The optical structure may also identify

process-property relationships that assist in process optimization. A powerful probe of

optical structure is real time spectroscopic ellipsometry (SE) [6-2] that can be performed

during the deposition of each layer of the solar cell as well as during post-deposition

processing. In some circumstances, however, the deposition or processing geometry

precludes optical access; in this case, ex-situ SE becomes the only option.

The CdTe solar cell poses considerable challenges for analysis by ex-situ SE [6-3].

First, the relatively large thickness of the as-deposited CdTe layer leads to considerable

surface roughness, and the conventional CdCl2 post-deposition treatment generates

significant additional oxidation and surface inhomogeneity. Thus, ex-situ SE

measurements in reflection from the free CdTe surface can be very difficult if not

impossible. Second, SE performed from the glass side of the solar cell is adversely

95

affected by the top glass surface which generates an incoherent reflection and consequent

depolarization.

In this research, the problem of the free CdTe surface is solved through the use of

Br2+methanol treatments that etch and smoothen the CdTe [6-4]. The problem of the free

glass surface is solved through the use of a 60° prism optically-contacted to the top glass

surface that eliminates the top surface reflection. In an additional approach, the top

surface reflection is eliminated through spatial filtering of the reflected beam, which is

possible due to the relatively thick glass substrate.

In this chapter, comprehensive ex-situ spectroscopic ellipsometry studies are

described that have been applied to investigate the multilayer optical structure of thin

film CdTe solar cells in the superstrate configuration before and after the CdCl2 treatment.

Dielectric functions have been obtained by SE for all layers of these cells as described in

previous chapters. As a result, a reference library for ex-situ analysis of CdTe solar cells

is available. The library used in this chapter is shown in Table 6.1. With the

Br2+methanol layer-by-layer etching, it has been possible to gain a better understanding

of the underlying structure for the as-deposited CdTe film by tracking the optical

properties of the CdTe layer as a function of depth from the surface and proximity to the

CdS/CdTe interface. In order to evaluate the role of the CdCl2 treatment, such

experiments have also been performed on the treated solar cell. In the latter

experiments, ex-situ SE is performed from the CdTe film side in the etching process and

also from the glass side either by (i) using a 60° fused silica prism optically contacted to

96

the soda lime glass substrate with index matching fluid, or (ii) blocking the top surface

reflection using an iris.

6.2 Experimental details

In this study, the CdS and CdTe layers of the cells were prepared by rf magnetron

sputtering [6-5] but no back contact deposition and anneal were performed. The CdS

depositions were performed directly on TEC-15 glass substrates at a nominal deposition

temperature of 160°C using 50 W rf power applied to the target, 10 mTorr Ar pressure, 23

sccm Ar flow, and a 10 ± 1 cm distance between the target and the substrate. The CdTe

depositions were performed similarly on each CdS film, with the exception that the

nominal deposition temperature was 180 °C; (Dr. Jennifer Drayton is acknowledged for

deposition of these samples). Thus, the layered structure of the cells studied here

includes TEC-15 glass coated with sputtered CdS and CdTe. Some of these cell

structures were subjected to a 30-min. CdCl2 treatment at 387°C. Ex-situ SE has been

applied for analysis of the CdTe-based solar cells before and after the CdCl2 treatment.

In order to perform reliable measurements from the CdTe free surface, the rough surface

region was removed through successive Br2+methanol etches, leaving a much smoother

surface suitable for SE measurements. In a series of etches applied to the CdTe cell

structures, the CdTe layer was also removed step by step, which provided a useful

method for optical depth profiling of the structures.

97

Additional experiments were carried out in which the same CdCl2 treated solar cell

structure was probed in two ex-situ SE measurements, one from the CdTe film side and

the other from the glass substrate side. In order to perform reliable measurements from

the glass side of the solar cell in this comparison, a 60° fused silica prism was contacted

with index-coupling fluid to the soda lime glass of the solar cell substrate, thus

suppressing the incoherent reflection from the top ambient/glass interface. These two

measurements can be compared to achieve greater confidence in the analysis of glass side

measurement, which could be adversely affected by stress in the prism and glass substrate

as well as by imperfect index-matching to the prism. Furthermore, experimental SE

measurements from the free CdTe side performed in successive etches can be used (i) for

assessing the confidence limits on the parameters that describe the underlying structure,

as well as (ii) for depth profiling of the CdTe high energy critical point parameters as has

been described previously in Chapter 5.

6.3 Results and discussion: film side and prism side measurements

By performing numerous etching/measurement cycles, this process simulates a real

time spectroscopic ellipsometry measurement, but reversed in time. Figure 6-1 shows the

CdTe surface roughness layer thickness and bulk layer void volume fraction during

etching of the as-deposited solar cell. Each point represents an etching step that leads to

a reduction in the bulk layer thickness of the CdTe, starting from an initial value of 2.4

µm. The thickness of the CdTe is determined from an analysis of spectroscopic data at

98

low energies (≤ 1.45 eV) where thin film interference oscillations are present. The

surface roughness thickness and bulk layer void volume fraction are determined from the

data at high energies (≥ 3 eV) where the CdTe is opaque and high surface sensitivity is

attained.

Table 6.1 Dielectric function library used in spectroscopic ellipsometry data analyses for CdTe solar cells.

Material Description File name Soda lime

glass TEC-15

component “SLG_pilkington_TEC15_20c_userdefined_02162006.mat”

SnO2 TEC-15

component “SnO2_pilkington_TEC15_20c_drudecppb_09172009.mat”

SiO2 TEC-15

component “SiO2_pilkington_TEC15_20c_cauchypole_02172006.mat”

SnO2:F TEC-15 component

“SnO2F_pilkington_TEC15_20c__inver.go_09152009.mat”

CdS

Sputtered nominal 400 °C (Figs. 6-1, 6-2,

6-7, 6-9)

“CdS_UT_Tser320C_20C_GO_12032005.mat”

CdTe

Sputtered nominal 200 °C (Figs 6-2, 6-4); Single crystal (Figs. 6-1, 6-3,

6-5, 6-6, 6-7, 6-9)

“CdTe_UT_Tser188C_20C_inver_06212004.mat”

Figure 6-1(a) shows that after about 7 etching steps the surface roughness and void

fraction stabilize with very small variations thereafter. With successive etching steps,

the surface roughness shows random fluctuations over the range of 42-47 Å whereas the

void fraction (scaled relative to that at the etch step when the highest density CdTe is

obtained) lies in the narrow range of 0.01-0.02. The void fraction for this sample is

99

uniform over a wide range of bulk layer thicknesses, from 0.4 to 1.6 µm. For a CdTe

film of this starting bulk layer thickness (2.4 µm), there is also a thick region of

surface-connected microvoids that extends 0.8 µm into the film and is interpreted in the

model as a “bulk” layer. A very high void fraction (~ 0.3) is obtained in the top 0.2 µm

of the bulk layer. This material is readily removed in the etching process.

Figure 6-2 shows the CdTe surface roughness layer thickness and bulk layer void

volume fraction during etching of the CdCl2 treated solar cell. These results show that

after about 5 etching steps the surface roughness and void fraction stabilize with weak

variations thereafter. In this case with successive etching steps, the surface roughness

shows random fluctuations over the range of 20-40 Å whereas the void fraction (scaled

relative to single crystal CdTe) lies in the range of −0.01-0.06, and is tentatively

attributed to a density deficit in the grain boundary regions. Figure 6-2 (b) shows a

proposed schematic of the film structure. The surface roughness thickness and void

fraction exhibit greater fluctuations for the CdCl2 treated solar cell possibly due to the

larger grained structure which leads to greater non-uniformity in the etching process.

4000 8000 12000 16000 20000 24000

0.0

0.1

0.2

0.340

50

60

70

void

vol

ume

frac

tion,

f v

asc42 as deposited CdTe:etching process

CdTe bulk thickness, db (Å)

depth resolution1/α (3 eV) ~ 400 Å

surf

ace

roug

hnes

sth

ickn

ess,

ds (

Å)

low Energy for db: 1.0 ~ 1.45 eV

high E range for (ds, f

v): 3.0 ~ 6.5 eV

Figure 6-1 Evolution of the surface roughness thickness and a depth profile of the void

100

volume fraction plotted versus bulk layer thickness obtained in successive Br2+methanol etching steps that reduce the bulk layer thickness of an as-deposited CdTe component of a solar cell.

Figure 6-2 (a, left) Evolution of the surface roughness thickness and a depth profile of the void volume fraction plotted versus bulk layer thickness obtained in successive Br2+methanol etching steps that reduce the bulk layer thickness of the CdCl2-treated CdTe component of a solar cell; (b, right) a schematic structure suggested from (a).

Additional information on the depth profile of the structure can be deduced from

analyses of the energies and widths of the critical point transitions. The results of such

analyses when applied to the as-deposited CdTe solar cell, are depicted in Fig. 6-3. The

critical point energies show a systematic variation with etching to a bulk layer depth of

0.5 µm. This can be attributed to an increase in compressive strain with increasing

thickness for the as-deposited CdTe film. Figure 6-3 also shows that the broadening

parameter values (or linewidths) are relatively constant, but are quite large compared with

those of the CdCl2 treated CdTe of Fig. 6-4. For the E1, E1+∆1, and E2 transitions, the

2.1 µm

1.8 µm

0.20-0.30 void fraction 0.3 µm

0.02-0.05 void fraction

(b) (a)

0.5 void fraction 0.01 µm

5000 10000 15000 20000

0.00

0.15

0.30

asc34 treatedetching process

low E range for db : 1.0 ~ 1.45 eV

high E range for (ds, f

v) : 3.0 ~ 6.0 eV

void

vol

ume

frac

tion,

f v

bulk layer thickness, db (Å)

depth resolution1/α(3 eV) ~ 400 Å

20

40

60

80

100

120

surf

ace

roug

hnes

sth

ickn

ess,

ds (

Å)

101

broadening values for the as-deposited film at 0.8 µm are 0.45, 0.48, and 1.08 eV,

respectively. The corresponding values for the CdCl2-treated films are 0.30, 0.30, and

0.98 eV, respectively. These results suggest that the as-deposited CdTe film has a

smaller grain size.

For the corresponding Br2+methanol etching results shown in Fig. 6-4(a), obtained

on the CdCl2-treated solar cell, the energies remain essentially constant with etching from

below the surface region to a depth of 0.8 µm. This result shows that the effects of the

CdCl2 treatment in the CdTe solar cell are not only to increase the grain size, but also to

relax strain in the film. A second experiment performed with higher depth resolution,

however, shows that as the CdS interface is approached, detectable shifts occur that may

be attributed either to residual interface strain and/or to the presence of S in the CdTe.

Unfortunately, it is not possible to probe through the CdS/CdTe interface since etching

studies of a single CdS film show that it is severely roughened and ultimately

delaminated by the Br2+methanol etch.

Figure 6-4(b) shows results for the depth profile of the linewidths of the prominent

E1, E1+∆1, and E2 critical points. The widths associated with the surface layer are

typically broader possibly due to the presence of an inhomogeneous region generated by

the CdCl2 treatment. The widths reach a minimum once the surface layer is removed

and the bulk film void fraction stabilizes below 0.06. It should be noted that the E1

linewidth shows behavior opposite to this possibly due to correlation with the nearby

E1+∆1 linewidth. As etching of the CdTe progresses toward the CdS interface, all three

102

broadening parameters increase. This effect may be attributed to CdTe crystallite

growth in the CdCl2 treatment that progresses from the surface to the CdS interface,

leaving a structure such as that shown in the schematic of Fig. 6-4(c). Alternatively, an

alloying effect of S with CdTe may be a possible explanation; however; this explanation

is not favored due to the lack of systematic variations in the critical point energies.

The results in Fig. 6-4(b) for the critical point widths can be understood using a

simple model of independent line broadening mechanisms each described by h∆νi ~ h/τi

(in photon energy), whereby the resulting transition lifetime is given as: 1/τ = 1/τ1 +

1/τ2 + 1/τ3 +… [6-6] Here ‘1’, ‘2’, and ‘3’ indicate, for example, the processes of phonon

scattering, impurity scattering, and grain boundary scattering. The latter process can be

written as 1/τ3 = υ/R, where υ is the electron group velocity and R is the average grain

radius. For a polycrystalline material in which grain boundary scattering controls the

variation in linewidth, the result h∆ν ≡ Γ = Γb + (hυ/R) is obtained, where (hυ/R) is the

grain boundary scattering term and Γb is the single crystal width [6-6]. In fact Γb is

typically controlled by phonon scattering, which leads to a dependence of Γb on the

measurement temperature. Thus, the simple schematic of the sample structure in Fig.

6-4(c), could account for the increase in transition widths with increasing depth as shown

in Fig. 6-4(b). When impurity scattering is the dominant mechanism, for example,

considering S atoms in a random CdTe1-xSx (x < 0.1) alloy, then R can be considered as

proportional to the average distance between atoms.

103

Figure 6-3 (left) Depth profiles of the critical point energies of the E1, E1+∆1 and E2 transitions in the as-deposited CdTe layer of a solar cell, plotted versus bulk layer thickness obtained in successive Br2+methanol etching steps that reduce the bulk thickness; (right) depth profiles of the linewidths of the E1, E1+∆1 and E2 transitions obtained in the same experiment.

104

Figure 6-4 (a, top left) Depth profiles of the critical point energies of the E1, E1+∆1 and E2 transitions in the CdCl2-treated CdTe layer of a solar cell, plotted versus the bulk layer thickness obtained in successive Br2+methanol etching steps that reduce the bulk thickness; (b, top right) depth profiles of the linewidths of the E1, E1+∆1 and E2 transitions obtained in the same experiment; (c, bottom) a schematic structure suggested from (b).

A similar analysis was applied to a second CdCl2-treated solar cell structure

co-deposited with the structure of Figs. 6-2 and 6-4 again using the high energy range of

2.1 µm

1.5 µm

0.20-0.30 void fraction

0.02-0.03 void fraction

0.5 void fraction 0.01 µm

(c)

8000 12000 16000 20000

5.17

5.18

5.19

5.20

E2 (

eV)

bulk layer thickness, db (Å)

energy of E2 transition (5.160 eV)

3.32

3.34

3.36

3.38

energy of E1 transition (3.310 eV)

asc34 treated: etching processlow E range for d

b : 1.0 ~1.45 eV

high E range for (ΓE1

, ΓE1+∆1

, ΓE2

) : 3.0 ~ 6.0 eV

E1 (

eV)

3.892

3.896

3.900energy of E

1+∆

1 transition (5.894 eV)

E1+∆

1 (eV

)

8000 12000 16000 20000

0.95

1.00

1.05

ΓE

2 (e

V)

bulk layer thickness, db (Å)

width of E2 transition (5.160 eV)

0.25

0.30

0.35

0.40

width of E1 transition (3.310 eV)

asc34 treated: etching processlow E range for d

b : 1.0 ~1.45 eV

high E range for (ΓE1

, ΓE1+∆1

, ΓE2

) : 3.0 ~ 6.0 eV

ΓE

1 (e

V)

0.30

0.35 width of E1+∆

1 transition (5.894 eV)

ΓE

1+∆

1 (eV

)(a) (b)

105

the spectra collected during etching to determine depth profiles in the energies and

linewidths of the CPs. The purpose of this analysis is to assess the reproducibility of the

observed behavior in Fig. 6-4 while achieving a greater depth resolution and approaching

closer to the CdS/CdTe interface.

Figure 6-5 shows the energies of the E1, E1 + ∆1, and E2 transitions versus CdTe

thickness all from successive etches. The data in the energies in Fig. 6-5 show relatively

weak variations; however, as the CdS interface region is approached, E2 -- which appears

to be a more sensitive indicator of structural deviations from the single crystal --

increases systematically, possibly due to interface compressive strain or to in-diffusion of

S. The very weak shifts in E1, E1 + ∆1, which appear only at the end of etching below a

bulk layer thickness of 2000 Å, are not consistent with compressive strain; thus,

in-diffusion of S seems to be a more likely possibility to explain the behavior of the E2

transition.

The broadening parameters corresponding to each critical point have also been

investigated. Figure 6-6 shows that ΓE1, ΓE1 + ∆1, and ΓE2 all increase gradually, an effect

which corroborates similar results obtained from the co-deposited solar cell presented

previously in Fig. 6-4(b). This effect may be due to grain size reductions and/or to the

effects of S alloying when the interface is approached, as in the case of the energy E2

described in the previous paragraph. Given the small differences in the energies in Fig.

6-5 compared to crystal CdTe, strain is unlikely to cause the significant broadening

effects in Fig. 6-6.

106

c-CdTe E1+∆1 = 3.894 eV

Figure 6-5 Energies of the E1, E1+∆1, and E2 transitions as functions of CdTe bulk layer thickness in successive etches of a CdCl2 treated CdTe solar cell that reach within 0.1 µm of the CdS/CdTe interface.

Figure 6-6 Broadening parameters ΓE1 , ΓE1+∆1, and ΓE2 as functions of CdTe bulk layer thickness in successive etches of a CdCl2 treated CdTe solar cell that reach within 0.1 µm of the CdS/CdTe interface.

In order to understand better the variation of the critical point parameters in CdTe

solar cell structures, the results of Figs. 6-5 and 6-6 can be considered in view of similar

107

results on thin films in Chapter 5. First, the Chapter 5 results (Fig. 5-8, top) suggest that

interface strain is not a significant factor for the CdCl2-treated sample structure, and thus,

any weak variations in the energies in Fig. 6-5 may be more likely due to alloying.

Second, considering the depth profile of the broadening parameters in Fig. 5-8 (bottom),

such results for the Ar annealed film are interpreted to suggest that grain boundaries

remain fixed at the surface but grain growth occurs sub-surface. In contrast, the CdCl2

treatment is shown to generate a more rapid grain growth effect not only well into the

bulk but also on the surface. Thus, a key role of the CdCl2 treatment is to generate

uniform grain growth throughout the thickness. The results in Figs. 6-4 (b) and 6-6

suggest that grain growth does not extend all the way to the CdS interface in the solar cell,

possibly due to the role of the CdS in pinning the grain boundaries or the diffusion of S

which may suppress grain growth. Alternatively, the CdCl2 treatment for the cells of

Figs. 6-4 (b) and 6-6 may not be fully optimized.

In addition to the structural analyses of Figs. 6-1 – 6-6 that focus on the high energy

SE data for the CdTe surface roughness and structural depth profiles, it is also possible to

extract characteristics of the underlying CdS and its layered structure from the low energy

data. This information is obtained from the same low energy data range that provides

the CdTe bulk layer thicknesses, plotted along the abscissas in Figs. 6-1 – 6-6. Figure

6-7 shows the deduced pseudo-dielectric function (solid lines) from SE measurement

after the 15th etch step for the CdCl2 treated sample of Figs. 6-2 and 6-4. Also shown in

Fig. 6-7 is the least-squares regression analysis best fit (broken lines). A simple

108

multilayer model that leads to this best fit with a relatively small number of free

parameters, seven in all, is shown in Fig. 6-8. It incorporates the glass substrate,

including (i) a fixed optical structure as obtained in a previous analysis of uncoated

TEC-15 consisting of SnO2 (267 Å); SiO2 (215 Å); and SnO2:F (3178 Å); (ii) an

interfacial roughness layer of fixed thickness between the TEC-15 and the CdS whose

fixed thickness is chosen to match the surface roughness thickness measured from the

uncoated TEC-15 (296 Å) and whose composition is a fixed 0.5/0.5 effective medium

mixture of the overlying and underlying materials; (iii) a CdS layer of variable thickness

and void volume fraction; (iv) a single interface layer of variable thickness between the

CdS and CdTe modeled as an effective medium of the two materials with variable

composition; and (v) the bulk CdTe and its 0.5/0.5 CdTe + void surface roughness layer,

both of variable thickness. The amorphous Te layer on the etched surface is neglected

in this study since it has little effect on the deduced parameters when the CdTe layer is

thick.

Because the starting TEC-15 transparent conducting oxide exhibits a surface

roughness layer with a thickness of approximately 300 Å, roughness is sure to propagate

throughout the structure and thus occurs at each interface. As a result, any layers that

are generated at the critical CdS/CdTe interface by the chemical interaction between the

CdS and CdTe are modulated by roughness. Thus, as a first approximation, a single

effective medium layer of CdS+CdTe of variable composition is used to represent the

layer at the CdS/CdTe interface.

109

Figure 6-7 Experimental pseudo-dielectric function spectra for the CdTe solar cell of Figs. 6-2 and 6-4 after the 15th etching step; also shown is the best fit using the structural model of Fig. 6-8.

Figure 6-8 Structural model for the CdTe solar cell after the 15th etch step that provides the best fit in Fig. 6-7.

CdTe/void = 0.5/0.5 35 ± 0.4 Å CdTe surface

roughness

CdTe bulk

CdTe/CdS interface

CdS bulk

CdS/SnO2:F interface

SnO2:F

SiO2

SnO2

Soda lime glass

CdTe/void=0.96±0.01/0.04±0.01 14529± 32 Å

CdTe/CdS = 0.51±0.02/0.49±0.02 935± 10 Å

CdS/void = 0.93±0.01/0.07±0.01 1247± 25 Å

CdS/SnO2:F = 0.5/0.5 296 Å

SnO2:F = 1.00 3178 Å

SiO2 = 1.00 215 Å

SnO2 = 1.00 267 Å

glass = 1.00 semi-inf.

Fixed TEC15 structure

Low energy data provide:

CdTe, CdS, and interface

thicknesses, along with their

compositions

High energy data provide:

CdTe surface roughness

CdTe composition and grain size or defect density

2 3 4 5 6-5

0

5

10

<ε2>

PHOTON ENERGY (eV)

-5

0

5

10

<ε 1>

Fit asc34 etch 15th

1.0 1.5 2.0-5

0

5

<ε2>

PHOTON ENERGY (eV)

5

10

<ε1>

Fit asc34 etch 15th

asc34 15th step

110

After the structural analysis of Figs. 6-7 and 6-8 was performed, confidence in the

method was sought by performing two more analyses on a second CdCl2 treated solar cell

structure deposited under the same conditions, one analysis from the film side and the

other from the glass substrate side through a prism in optical contact with the free surface

of the glass. Separate sample pieces from the same solar cell deposition were studied in

these two analyses. The previously deduced dielectric function library in Table 6.1 was

used in the analysis of the ex-situ SE data in Fig. 6-9 acquired from the CdTe free surface

after 8 etching steps and from the prism/glass substrate side without CdTe etching. The

structural models of Figs. 6-10 and 6-11 used in the analysis of both data sets shown in

Fig. 6-9 are the same as that of Fig. 6-8; simple models with six free parameters yielded

the fits in Fig. 6-9.

Figure 6-9 Ex situ SE spectra in (ψ, ∆) (symbols) (a) from the free CdTe surface after 8 Br2+methanol etching steps and (b) from the prism/glass side without etching. The best fit results (solid lines) yield the structural parameters in Figs. 6-10 and 6-11, including the thicknesses of the CdTe roughness, CdTe bulk, CdTe/CdS interface, and CdS bulk layers, as well as the volume fractions of CdS/CdTe in the interface layer and void in the CdS bulk layer.

15

30

45

60

0.9 1.0 1.1 1.2 1.3 1.4 1.5-150

0

150

300

Data: glass side Fit

ψ (d

egre

e)

(b)

∆ (d

egre

e)

Photon Energy (eV)

0

4

8

12

16

0.9 1.0 1.1 1.2 1.3 1.4 1.5-150

0

150

300

ψ (d

egre

e)

(a)

∆ (d

egre

e)

Data: 8 th etch Fit

Photon Energy (eV)

111

Figure 6-10 The best fit results from the free CdTe surface after 8 Br2+methanol etching steps yielding the thicknesses of the CdTe roughness, CdTe bulk, CdTe/CdS interface, and CdS bulk layers, as well as the volume fractions of CdS/CdTe in the interface layer and void in the CdS bulk layer.

Figure 6-11 The best fit results from the prism/glass side without etching yielding the thicknesses of the CdTe roughness, CdTe bulk, CdTe/CdS interface, and CdS bulk layers, as well as the volume fractions of CdS/CdTe in the interface layer and void in the CdS layer.

Figures 6-10 and 6-11 show the multilayer models of the sample structures, the latter

depicting the placement of a 60o fused silica prism on top of the free surface of the glass

substrate. In this configuration, an index-matching fluid proves vital in eliminating

unwanted incoherent reflections. Considering the assumptions and simplifications of the

model, the agreement in the structural parameters listed in the two figures is excellent.

Good agreement is obtained even in the CdTe/CdS interface layer composition although

112

this layer should require a more complex model that includes not only interface

roughness modeled using an effective medium approximation, but also interdiffusion [6-7]

modeled using stable phase CdTe1-xSx and CdS1-xTex alloy dielectric functions.

As final supporting results for the overall approach, the CdS layer and CdTe/CdS

interface thicknesses have been deduced from spectra collected at the CdTe free surface

in 24 successive etches as shown in Fig. 6-12. In the 25 analyses, the same model was

used for all the spectra, now obtained as a function of CdTe bulk thickness before and

after each etching step. These fits should provide independent values for CdS/CdTe

interface layer thickness and CdS bulk layer thickness since the unprocessed (ψ, ∆)

spectra data vary rapidly with CdTe bulk layer thickness due to variations in the

interference pattern as shown in Fig. 6-9 (left panel). In fact, these independent values

should be constant since the etching does not affect the sub-surface material, and any

variations provide a measure of the uncertainty in these values. For the selected optical

model to be justified, the confidence limits for the interface thickness and composition

must be smaller than the values themselves. In fact maximum deviations of ±2-3%

from the average values are obtained and the average values lie within the confidence

limits of the analyses performed on spectra collected through the prism/glass.

113

Figure 6-12 CdS and CdTe/CdS interface layer thicknesses deduced from spectra collected through the prism/glass (solid line) and from spectra collected from the CdTe surface in successive etches (points, dotted line extrema).

Among the key final results of Fig. 6-12 include a 1000 Å thick interface region of

(CdS+CdTe) and a 1030 Å thick layer of CdS. The (CdS+CdTe) interface layer for this

sample is found to be a 0.7/0.3 vol. fraction mixture of CdTe/CdS; however, this mixture

merely provides a dielectric function that approximates that of the interface region and

should not be interpreted physically. Further studies of the optical properties of the

interface are in progress [6-8].

6.4 Results and discussion: through the glass measurements

SE measurements directly through the top glass have been performed using a method

in which the reflection from the glass/film-stack interface is collected whereas the

reflection from the ambient/glass interface is blocked. Invasive prism attachment is

avoided by eliminating the top glass surface reflection, an approach that is more practical

for off-line or on-line cell and module mapping applications. An example of such SE

114

data analysis for a magnetron sputtered CdTe solar cell is demonstrated here in a

step-by-step process in which additional fitting parameters are introduced while

observing a measure of the quality of the fit. The goal is to increase the complexity of

the optical model systematically over the six and seven parameter models of Figs. 6-8,

6-10, and 6-11 by incorporating additional thicknesses and volume fractions and

determining the parameters that are most important in ensuring a good fit. The most

complicated optical model used for analysis of through-the-glass SE spectra collected on

CdTe solar cells on glass superstrates shown in Fig. 6-13 includes a total of 12 variable

parameters with satisfactory confidence limits on all parameters.

TEC-15

structure

(ψ, ∆)

CdTe (d, ∆d/d)

CdTe/CdS interface (d & fCdTe )

CdS +void (d & fv)

SnO2:F + CdS (d & fCdS)

SiO2 (d)

SnO2 (d)

Surface roughness (d, fv)

Soda lime glass (ambient)

Figure 6-13 Multilayer stack used to model the thicknesses and compositions of the individual layers of the CdTe solar cell. The SE beam enters through the glass, and the reflection from the top surface is blocked since it is incoherent with respect to the reflection from the glass/film interface.

115

0 10 20 30 40 50 60

0.10

0.12

0.14

0.16

0.18

0.20

0.22 112 121098765431

MS

E

Steps

Step-by-step MSE reduction

number of fitting parameters

Figure 6-14 Step-by-step MSE reduction by adding one fitting parameter at a time. Starting with the CdTe thickness as a variable, each additional parameter was subsequently fitted. It was found that fitting the SnO2:F thickness provided the greatest improvement in MSE among all 2-parameter attempts. Similar methodology was used for all 12 parameters. Circular points indicate the best n-parameter fit with n given at the top and the added parameter given in Table 6.2.

The SE spectra collected at one spot on the 3 x 3 cm2 CdTe solar cell and at angles of

incidence of 60° and 65° were modeled over the spectral range from 0.75 to 3.0 eV,

below the glass absorption onset. Figure 6-14 shows the step-by-step reduction in mean

square error (MSE), expressed in terms of the deviations in the real and imaginary parts

of ρ ≡ tanψ exp(i∆), obtained by adding best fitting parameters one at a time. Table 6.2

shows the sequence of fitting parameters that are introduced in order of importance to

obtain the best n-parameter fit (n = 2, 3, 4…12). Figure 6-15 shows the SE data and the

best final 12-parameter fit. The best fit parameters are shown in Table 6.3 along with

116

their confidence limits.

Table 6.2 Best fitting parameters added step by step to improve the mean square error (MSE) in modeling through-the-glass SE measurements of a CdTe solar cell.

# of fitting parameters Best fitting parameter to add to

improve MSE MSE

1 CdTe thickness 0.2208

2 SnO2:F thickness 0.1735

3 CdTe non-uniformity 0.1565

4 CdS thickness 0.1448

5 CdTe surface

roughness (50/50) 0.1363

6 Void fraction in CdTe roughness 0.1134

7 CdS volume fraction in SnO2:F 0.1056

8 SiO2 thickness 0.1010

9 Void volume fraction in CdS 0.0968

10 CdS/CdTe interface

thickness (50/50) 0.0883

11 SnO2 thickness 0.0881

12 CdTe volume fraction in CdS/CdTe

interface 0.0860

The fitting parameter sequence in Table 6.2 is understandable in that the thickest

layers have the greatest impact in the step-by-step fitting procedure. As a result this

new analysis approach also provides information on the starting TEC-15, namely, the

thicknesses of the SnO2 at the glass interface, the intermediate SiO2 layer, and the doped

117

conducting SnO2:F layer without assuming fixed values. For the solar cell, the analysis

provides additional information on possible modification of the SnO2:F by

over-deposition of CdS, as well as the standard parameters of CdS thickness, its void

fraction, the combined CdS/CdTe interface roughness-interaction thickness, and the CdTe

thickness. As shown in Fig. 6-13, a mixture of SnO2:F and CdS is used to model the

interaction between the two materials when CdS is deposited on the TEC-15; however,

the exact nature of this interaction will be the subject of more detailed future studies. It

is not clear if the modification is simulating the effect of CdS penetrating the roughness

and near surface void structure or, alternatively, if there is a uniform modification of the

SnO2:F properties. Other approaches to describe the interaction, e.g., a modification in

the free electron density or mobility in SnO2:F has not yet achieved success. The

interaction layer between the CdS and the CdTe has been described as a simple effective

medium of the two materials that simulates interface roughness, although a more realistic

approach may be to use alloy layers in addition to the effective medium layer as

described previously. It should be noted that the deduced CdS thickness of 1225 ± 14 Å

is in good agreement with the intended CdS thickness of 1300 Å.

118

Figure 6-15 Ellipsometric spectra (points) in ψ (top) and ∆ (bottom) at an angle of incidence of 60° as measured through the glass at a single point on a 3 x 3 cm2 CdTe solar cell sample. The solar cell was treated with CdCl2 but no back contact processing was performed. Also shown is a best fit (lines) using the model structure of Fig. 6-13 with the parameters listed in Table 6.3.

Table 6.3 Multilayer stack thicknesses, non-uniformity, and compositions, the latter expressed in terms of volume fractions, along with parameter confidence limits for the best fit to SE data obtained through the glass.

Soda lime glass

SnO2 thickness 339 ± 13 Å

SiO2 thickness 157 ± 5 Å

SnO2:F thickness

CdS volume fraction

3123 ± 24 Å

2.3% ± 0.5%

CdS thickness

Void volume fraction

1225 ± 14 Å

13.5% ± 0.6%

CdTe/CdS interface thickness

CdTe volume fraction

868 ± 32 Å

73.3% ± 1.6%

CdTe bulk thickness

CdTe thickness nonuniformity

19702 ± 43 Å

3.1% ± 0.1%

CdTe surface

roughness thickness

Surface void fraction

851 ± 16 Å

28.4% ± 0.7%

Ambient

The new analysis procedure, through-the-glass SE, is useful in determining the

119

optical structure of CdTe solar cells for off-line or on-line analysis in a mapping mode.

This method is useful because it is non-destructive, and the large roughness layer

thickness of the CdTe does not present a problem. Analysis of the SE data using a

step-by-step analysis methodology identifies the important thicknesses and compositional

parameters for successful optical characterization of the solar cell.

6.5 Summary

Ex-situ spectroscopic ellipsometry has been applied to perform multilayer analyses

of CdTe solar cell structures. This capability exploits a database obtained from both

ex-situ and in-situ measurements that includes the dielectric functions of all component

layers of the cell. As a supplementary tool, Br2+methanol etching was used to reduce

the CdTe bulk layer thickness in a layer-by-layer fashion for depth profiling purposes.

The SE measurements made after a variable number of etching steps enables tracking of

changes in the critical point energies and broadening parameters near the surface, in the

bulk CdTe, and near the CdS/CdTe interface. This capability was used to smoothen the

CdTe free surface so that measurements of the multilayer stack can be performed for

correlation with through-the-glass measurements of the solar cell. Good agreement is

obtained between the CdS thickness and CdS/CdTe interface layer thickness between the

two measurement approaches. Thus, the validity of the through-the-glass method of

solar cell analysis has been supported through this study.

120

Chapter Seven

RTSE Analysis of CdTe Solar Cell Structures in the Substrate Configuration

7.1 Introduction

In the conventional configuration for thin film CdTe solar cells used in both research

and manufacturing, one starts with a glass superstrate which is coated with a transparent

conducting oxide top contact [7-1]. In this configuration, the CdS window layer of the

heterojunction is deposited on the transparent conductor first and the CdTe active

photovoltaic layer is deposited on top of the CdS. In this sequence, the heterojunction is

protected from the ambient by the much thicker layer of CdTe. Furthermore, since the

CdTe surface is exposed to the ambient in this configuration, the CdTe layer can be

treated with CdCl2 just prior to p+ back contact formation.

In the reverse or substrate configuration, one cannot apply the same sequence of

operations. In this case, because the CdTe layer is deposited first, the back contact is

formed simultaneously with the deposition process, rather than as a separate step.

Furthermore the CdCl2 treatment must then be performed either after the CdTe deposition,

which is not likely to leave an optimum surface for subsequent heterojunction formation,

or after the CdS deposition, which is not likely to produce a favorable effect on the CdS

121

surface for subsequent top contact formation. As a result CdTe solar cells in the

substrate configuration have not reached the level of performance of cells in the

superstrate configuration [7-2].

In this Chapter, results of a real time spectroscopic ellipsometry (SE) study of CdTe

film growth on Mo, which is a standard back contact metal used in the substrate

configuration, are presented, and the information content of such SE measurements will

be discussed in detail. Ex situ SE results for a completed solar cell in the same substrate

configuration will also be presented and discussed.

7.2 Analysis of CdTe deposition on rough molybdenum

Figure 7-1 shows the time evolution of (ψ, ∆) at 5 photon energies selected from the 706

spectral positions acquired during CdTe sputter deposition at 50 W target power and 18

mTorr Ar pressure; (Dr. Anthony Vasko is acknowledged for deposition of this sample,

and additional measurement assistance of Dr. Jian Li is acknowledged). The substrate

was a glass slide coated with thin film Mo, held at a nominal temperature of 200°C.

This corresponds to a true temperature of 237°C when a crystalline Si wafer substrate is

used. The full spectral acquisition time was 2 s and the angle of incidence of the

measurement was 65.68°. This was the first real time experiment performed during

CdTe deposition using the SE system described in Chapter 1. The Mo film was also

prepared by magnetron sputtering and was found to exhibit a surface roughness ~80 Å

122

0 10 20 30 40 50

0

20

40

60

80

0 10 20 30 40 50

-100

0

100

200

300

1.166eV

6.500 eV

1.653 eV

2.637 eV

ψ (d

egre

e)

Time (min)

0.743 eV

1.166 eV

2.637 eV1.653 eV

6.500 eV

0.743 eV

∆ (d

egre

e)

Time (min) Figure 7-1 Time evolution of (ψ, ∆) at 5 photon energies selected from 706-point spectra acquired during sputter deposition of CdTe on a Mo coated glass slide. The full spectral acquisition time was 2 s and the angle of incidence was 65.68°.

thick. The analysis results obtained here for the Mo optical properties can be applied in

future studies of solar cells in the substrate configuration.

7.2.1 MSE minimization for the analysis of CdTe/Mo

The analysis of the spectra for the experiment of Fig. 7-1 used a two-variable,

time-averaged, mean-square error (MSE) minimization procedure over selected time

intervals. The time averaged MSE serves as a criterion to obtain the correct structural

evolution as well as the optical properties of the deposited CdTe film, as a multilayer

within the selected time intervals. Even the structure and optical properties of the Mo

thin film can be determined in the procedure. Each selected time interval during

deposition has been separated into two components in the average MSE minimization

123

procedure. In one component, film growth occurs as a bulk/roughness structure with

variables db and ds which are the bulk and surface roughness layer thicknesses,

respectively. In the other component, film growth occurs through the filling of the

rough interface between the underlying and growing materials as an interface/roughness

structure with variables fi and ds, where fi is the volume fraction of new material filling

the roughness of the underlying material and ds is the surface roughness layer thickness

on the growing film. Additional details on the two analysis components will be given in

the following paragraphs. In order to achieve the desired results, one seeks to maintain

the MSE value below ~5 throughout the time range of the deposition. In this analysis

procedure, four time intervals have been selected in all, leading to four individual layers

in the CdTe film growth process, and the average MSE minimization procedure has been

applied to the growth of each layer.

For the first CdTe layer, the time interval for the average MSE minimization

procedure was 3.303~13.936 min and the energy range in the MSE calculation was

0.74~6.5 eV. Minimization of the average MSE for this layer requires the following

nine steps, grouped in three iterations.

Iteration A: Estimate Mo roughness thickness

Step 1. A value di is estimated for the surface roughness thickness on the Mo

substrate.

Step 2. Numerical inversion software is applied to the in-situ experimental data (ψ,

∆) collected before initiation of the deposition to deduce the dielectric function (ε1, ε2) of

124

the bulk Mo based on the value di from Step 1.

Step 3. A least-squares regression model is created, using a previously-determined

reference dielectric function for CdTe [7-3] as an initial approximation. A dynamic

growth analysis is performed over the 3.303~13.936 min time range and the

time-averaged MSE, denoted <MSE> is determined. The starting time is selected to

ensure that filling of the substrate/film interface roughness has occurred as described later,

and the ending point is selected to maintain an acceptable MSE versus time, typically less

than 5.

Step 4. The di value is adjusted and Steps 2 and 3 are repeated. The two results for

the <MSE> are compared and continued iterative adjustments in di are made until the

minimum <MSE> is found. Finally, di is fixed at the value that minimizes <MSE>.

Iteration B: Estimate CdTe structure and optical properties

Step 5. With the optimum di value fixed from Iteration A, further estimates are

made for a pair of values for the CdTe bulk and surface roughness layer thicknesses (db,

ds).

Step 6. Inversion of the experimental data (ψ, ∆) is performed next to deduce the

dielectric function (ε1, ε2) of CdTe at the ending time 13.936 min.

Step 7. Using the inverted CdTe dielectric function, dynamic growth analysis is

performed over the time range 3.303~13.936 min, in order to determine <MSE>.

Step 8. Steps 6 and 7 are iterated using successive adjustments in (db, ds) within a

two-dimensional grid, until the minimum <MSE> is found. The minimum <MSE> then

125

yields the best fit results for db(t), ds(t) and for the inverted CdTe dielectric function.

Iteration C: Refine Mo roughness thickness as well as the CdTe structure and

optical properties

Step 9. Next, rather than using the CdTe reference dielectric function of Step 3, the

inverted dielectric function of Step 8 is used in a repetition of Steps 1, 2, 3, and 4. This

refinement provides an improved value of di. Steps 5, 6, 7, 8, and 9 are then repeated

with the refined di value. A final iteration is performed for internal consistency.

The final results of Steps 1−9 are as follows. The minimum average MSE and the

interface roughness thickness are given by: <MSE>min = 2.98 and di = 79.6 Å. The best

fit bulk and surface roughness layer thicknesses at the ending time of 13.936 min are db =

423 Å; ds = 56.7 Å. These results are summarized in the first entry of Table 7.1.

The average MSE minimization procedure has also been applied for the other three

CdTe layers. For each of these three layers, the minimization steps were performed in a

similar way as those in the analysis of the first CdTe growth layer; however, now di can

be fixed at the final result from the first layer analysis and only Iteration B is needed.

Thus, one only need to estimate the pair of (db, ds) values and invert the experimental (ψ,

∆) data to obtain the dielectric function (ε1, ε2) of the CdTe at the ending time. With the

resulting CdTe dielectric function, dynamic growth analysis is performed, the <MSE> is

extracted, and the process is iterated through adjustments of (db, ds) until <MSE>min is

found. For the growth analysis with <MSE> = <MSE>min the db and ds values are

correct and the associated inverted dielectric function for CdTe is also correct.

126

These three successive <MSE> minimizations based on Iteration B have yielded the

following results. The second CdTe layer covered the time range of 15.229~23.024 min,

and analysis employed the energy range 1.2~6.5 eV; <MSE>min was obtained at db = 313

Å and ds = 54.5 Å. The third CdTe layer analysis used the ranges 24.246~34.480 min

and 1.0 ~ 6.5 eV; <MSE>min was obtained at db = 404 Å; ds = 66.0 Å. The fourth and

topmost CdTe layer analysis used the ranges 36.002~40.948 min and 1.5~6.5 eV;

<MSE>min was obtained at db = 108 Å; ds = 67.0 Å. These results for all four layers are

summarized in Table 7.1.

Table 7.1 CdTe bulk and surface roughness layer thicknesses for the top four CdTe bulk layers.

Time range (min) db (Å) ds (Å) Data analysis energy range (eV) <MSE>min

3.303~13.936 423 56.7 0.74~6.5 2.98

15.229~23.024 313 54.5 1.20~6.5 2.60

24.246~34.480 404 66.0 1.00~6.5 8.71

36.002~40.948 108 67.0 1.50~6.5 1.30

The overall <MSE> minimization can be described by a flow chart as shown in Fig.

7-2 for the most complicated case of the first CdTe layer. The schematic structure of the

full CdTe layer stack is shown in Fig. 7-3.

127

Figure 7-2 Flow chart of the three-iteration <MSE> minimization procedure for CdTe film growth on a rough Mo film substrate.

Y

Use the CdTe dielectric function deduced in Step 7 instead

of the reference CdTe dielectric function, and return to Step

1 in order to refine di value; minimum.

Minimum <MSE>; best fit di, (db, ds)

Y Step 4. Minimum <MSE> ? N

C

Step 1. Estimate di, the Mo substrate

surface roughness layer thickness.

Step 2. Apply inversion routine to the exp. data (ψ, ∆) obtained just prior

to deposition to deduce the dielectric function (ε1, ε2) of the bulk Mo.

Step 3. Apply reference dielectric function for CdTe, and

perform dynamic growth analysis over the time range

3.303~13.936 min, to extract the average MSE.

Minimum <MSE>; best fit di.

Step 5. Fix di at the best fit value, and estimate

CdTe (db, ds) at the ending time t = 13.936.

Step 7. Perform dynamic CdTe growth

analysis over the time range 3.303~13.936

min, to determine the average MSE.

Step 9. Minimum <MSE> ?

A

B

Step 8. Minimum <MSE> ?

Iterations

N

N

Adjust the (db, ds) values.

Step 6. Perform inversion of the exp. data (ψ, ∆) to

deduce the dielectric function (ε1, ε2) of CdTe.

Adjust the di value.

Minimum <MSE>; best Mo, CdTe

structures and dielectric functions

Final results :

<MSE>=2.98; di=79.6 Å; db=423 Å;

ds=56.7 Å.

Y

128

Figure 7-3 The schematic structure describing the final optical model for deposition on rough Mo.

Each of the four CdTe bulk layers will be associated with an interface layer adjacent

to the underlying material which is filled in upon deposition of the overlying material.

During each interface filling time, db is set to zero. The Bruggeman EMA has been used

to model the dielectric function of the interface layer. The volume percent void in the

interface layer is one fitting parameter which is varied in the interface filling analysis for

modeling purposes. Therefore, during each interface filling time, the void volume

percent should decrease from 50% to 0% as the overlying material volume percent

increases from 0% to 50%. The first interface layer is a three-component composite of

materials including Mo (50%), (void + CdTe) (50%), and the other three topmost

interface layers are three-component composites of materials including the lower CdTe

d2j+1 = d2j,end + (0.5−fi)d2j,end + 0.5ds

d2j = d2j-1,end + 0.5(ds−d2j-1,end) + db

d4 = d3,end + 0.5(ds−ds3,end) + db

d3 = d2,end + (0.5−fi)ds2,end + 0.5ds

d2 = d1,end + 0.5(ds−ds1,end) + db

d1 = (0.5−fi)di + 0.5ds di1 Mo

db1

di2

db2

di3

db3

di4

db4

ds

Ambient

first CdTe bulk layer first interface roughness

second interface roughness

third interface roughness

fourth interface roughness

second CdTe bulk layer

third CdTe bulk layer

fourth CdTe bulk layer

surface roughness

129

film (50%), and (void + the upper CdTe film) (50%). For the interface layer filling

analysis, the first interface layer (0~3.277 min) used the energy range (0.74~6.5 eV).

The second, third, and fourth interface layers spanned the time ranges of (14.012~15.229

min), (23.024~24.246 min), and (34.480~36.002 min), respectively, using the energy

ranges of 1.5~6.5 eV in all cases. A detail of the structural evolution of the first

interface and bulk CdTe layers is shown in Fig. 7-4.

Figure 7-4 The schematic structures describing the interface filling (left) and bulk layer growth (right) models for the first interface layer.

7.2.2 Structural evolution

The fit quality is given by the magnitude of the MSE which degrades rapidly for

deposition times t > 15.5 min. This result is shown in Fig. 7-5 (left) (broken line). The

goal of the multilayer model is to determine if this MSE degradation can be attributed to

the evolution of the dielectric function with accumulated bulk layer thickness. Such an

effect can be modeled using a succession of layers, each having a dielectric function

determined independently, whereas the same model for the surface roughness layer can

be used throughout.

Figure 7-5 (right) includes the results for the MSE from the four-layer model (solid

line) on an expanded scale in which case the quality of the fit remains very good (MSE<5)

di

ds (0.5/0.5): (CdTe #1/void)

(0.5/0.5): (Mo/CdTe #1)

db

Mo di ds

Mo

(0.5/0.5): (CdTe #1/void)

(0.5/0.5−fi/fi): (Mo/CdTe #1/void)

130

for the full ~40 min deposition process. In the final film structure, the effective

thicknesses of the four layers including the interface filling regions are (interface to

surface) 491, 369, 465, and 174 Å, for a total effective thickness of 1499 Å. The sharp

minima at 14, 23, 34.4, and 37.5 min in the four-layer MSE indicate the times at which

the dielectric functions of the four layers were determined.

Figure 7-5 (Left) MSE, which is a measure of the quality of the fit to RTSE data, for the complete CdTe deposition using optical models for the CdTe film consisting of one bulk layer (broken line) and four bulk layers (solid line). In both cases a one-layer model for surface roughness was employed; (right) the MSE for the model with four bulk layers is shown on an expanded scale.

Figures 7-6, 7-7 and 7-8 show the final results of such modeling, in which case four

separate bulk layers are used along with a single evolving surface roughness layer.

Although the best fit leads to an improvement in MSE as shown in Fig. 7-5 (left) (i.e., by

a factor of ~40), the exact origin of the improvement requires further study as will be

seen from an inspection of the four dielectric functions in Sec. 7.2.3. The evolution of

the surface roughness layer thickness (Fig. 7-6), the overlying material volume fraction

during the interface filling region (Fig. 7-7), the bulk layer thickness for all four CdTe

131

component layers (Fig. 7-8, left), and the effective thickness or mass per unit area (Fig.

7-8, right) versus deposition time have all been deduced using the four-layer model for

the CdTe film. The broken line jumps in the surface roughness thickness ds result from

the consideration of each bulk layer individually with an independent surface roughness

layer thickness. At the jumps, the surface roughness on the underlying layer is

instantaneously transformed into an interface roughness layer with the subsequent

development of roughness on the overlying layer starting from ds = 0 Å. The continuity

of ds before generation and after filling of the interface layers is an indication of the

internal consistency of the analysis. The evolution of the accumulated effective

thickness versus deposition time is determined from adding the following components:

(i) First interface filling layer: d1 = (0.5−fi) *di+0.5*ds, where db=0, 0 ≤ fi ≤ 0.5, t0 ≤ t < t1;

(ii) First bulk layer: d2 = d1,end + 0.5*(ds−ds1,end) + db, where t1 ≤ t < t2;

(iii) Second interface filling layer: d3 = d2,end + (0.5−fi)*ds2,end + 0.5*ds, where t2 ≤ t < t3;

(iv) Second bulk layer: d4 = d3,end + 0.5*(ds−ds3,end) + db, where t3 ≤ t < t4

………

In these equations, dj,end and dsj,end are the values of the effective thickness and the

surface roughness thickness at the end of the time range for layer j. The end of the time

range for the jth bulk layer t2j is defined somewhat arbitrarily in order to maintain an MSE

that is acceptably low (e.g. less than ~ 5), and the end of the time range for the jth

interface filling layer t2j+1 is defined such that the void fraction fi reaches zero. In

addition, the interface void fraction fi is related to the overlying material volume fraction

132

fm=0.5−fi.

Figure 7-6 Evolution of the surface roughness thickness versus deposition time determined using a four-layer model for CdTe film growth on rough Mo. The spikes in the surface roughness thickness result from the consideration of each bulk layer individually with an independent surface roughness layer. In this case, the surface roughness layer on the underlying layer is instantaneously transformed into an interface layer at the vertical broken lines upon initial growth of the overlying layer, whose roughness layer starts from zero thickness.

0 10 20 30

0

10

20

30

40

50

f m

Time (min) Figure 7-7 Time evolution of the CdTe overlayer volume percent during interface filling of the underlying CdTe roughness layer for CdTe growth on Mo.

f m (

%)

133

Figure 7-8 (Left) Evolution of the individual bulk layer thicknesses versus deposition time determined using a four-layer model for CdTe film growth on Mo; (right) evolution of effective thickness of CdTe, including all bulk, interface, and surface layer components.

7.2.3 Optical properties

In Fig. 7-9, the Mo dielectric function is shown, valid for the nominal deposition

temperature of 200 °C. These results were deduced by inversion after determination of

the Mo surface roughness thickness value of 79.6 Å, through the 3D <MSE>

minimization procedure. In this <MSE> minimization procedure, an independent

dynamic analysis provides interface, bulk, and surface roughness thicknesses, di, db, ds,

respectively, that describe the structural evolution of CdTe growth on the rough Mo film.

134

0 1 2 3 4 5 6 70

10

20

30

40

50

ε 2

Photon energy (eV)

-10

-5

0

5 inversion di = 79.6 Å at nom. 200 °C

inversion di = 79.6 Å at R.T.

ε 1

Figure 7-9 Mo dielectric function at a nominal temperature of 200 °C acquired by inversion assuming a Mo substrate roughness thickness of 79.6 Å (solid line). For the overlying CdTe, four bulk layers and a roughness layer are used to describe the best fit model. For the first bulk layer, the Mo/CdTe interface roughness, the CdTe bulk, and CdTe surface roughness layer thicknesses di, db, ds, respectively, are determined in a dynamic analysis, in which case the criterion is the minimum average MSE. The Mo/CdTe interface roughness thickness di is taken to be the same as the Mo substrate film roughness thickness. Also shown is the Mo dielectric function at room temperature before heating to the deposition temperature as determined by inversion, again assuming a Mo surface roughness layer thickness of 79.6 Å (broken line).

In an attempt to corroborate the surface roughness thickness on Mo from the starting

room temperature (ψ, ∆) spectra, reference dielectric functions for Mo [7-4], MoO3 [7-5] and

MoOx [7-5] were applied in conjunction with the models of Table 7.2.

Table 7.2 Five models used to evaluate the Mo overlayer thickness using reference dielectric functions from the literature.

91.2 ± 2.5 Å

50%/50%

81.9 ± 2.9 Å

50%/50%

86.4 ± 2.9 Å

50%/50%

117.4 ± 2.3 Å

50%/50%

121.6 ± 2.3 Å

50%/50%

ds [fi/(1−fi)]

MSE 273.1 238.5 267.6 190.9 188.4

Mo

Mo/void

Ambient

Mo

MoO3/void

Ambient

Mo

MoOx/void

Ambient

Mo

MoO3/Mo

Ambient

Mo

MoOx/Mo

Ambient

Model 1 Model 2 Model 3 Model 4 Model 5

ds [fi/(1−fi)]

135

The results of Table 7.2 show that the Mo substrate roughness thickness of 79.6 Å

deduced through the 3D <MSE> minimization procedure is close (within 12 Å) to the

corresponding model that applies reference dielectric function results (Model 1).

Figure 7-10 (a-d) shows the real (top) and imaginary (bottom) parts of the dielectric

functions of the four CdTe layers that comprise the film deposited on the Mo covered

glass substrate. Each of these CdTe dielectric functions has been determined by

numerical inversion, incorporating the full underlying film structure and after

determining the surface roughness and bulk layer thicknesses through minimization of

the <MSE> in a dynamic analysis of the growing layer. Figures 7-10(b-d) include

comparisons of the dielectric functions of two successive layers. Comparison of the

successive dielectric functions leads to two observations. First, using the range of

energies greater than ~2.5 eV, no significant differences in the void fraction, critical point

energies, and critical point widths are observed. This suggests a relatively uniform layer

throughout the thickness. Second, for the range of energies below 2.5 eV, artifacts are

observed, and these increase in amplitude with the increase in layer number. These two

observations lead to the conclusion that the increase in MSE in Fig. 7-5 for the one bulk

layer model is not due to non-uniformity with depth, but rather other features of the

measurement or model such as a spatial distribution of thicknesses over the surface of the

beam or inadequacies of the model for the Mo substrate interface. Such features do not

affect the data quality in the opaque regime above 2.5 eV for each layer.

136

For comparison in Fig. 7-10(e), the solid line is the dielectric function deduced in a

study of CdTe deposited on a c-Si substrate as reported by Li [7-6]. The sample on c-Si

was deposited at a substrate temperature of 188 °C, an rf power of 60 W, and an Ar

pressure of 18 mTorr. The ε1 spectra at low energies suggest that the void volume

fraction is consistently higher for the component layers of the CdTe film on Mo. In fact,

the first layer CdTe film material on Mo can be described as an effective medium of the

CdTe film material on Si plus voids; the deduced volume fraction of voids is 0.10. This

result indicates that the void volume fraction in thin film CdTe may depend on the

substrate and in particular its surface roughness thickness. Because the comparison in

Fig. 7-10(e) is for the first CdTe bulk layer on Mo, it appears that in the case of the Mo

substrate, voids develop immediately in the deposition process, likely an effect of

shadowing by the roughness on the Mo. Later in this chapter, an ex situ spectroscopic

ellipsometry analysis of a CdTe solar cell on ZnTe:Cu/Mo will be performed to evaluate

the ability to characterize the full solar cell in the substrate configuration.

0 1 2 3 4 5 6 7

0

2

4

6

8

10

ε 2

Photon energy (eV)

-2

0

2

4

6

8

10

12

ε 1

CdTe/Mo layer # 1

0 1 2 3 4 5 6 7

0

2

4

6

8

10

ε 2

Photon energy (eV)

-2

0

2

4

6

8

10

12

ε 1

CdTe/Mo layer # 2CdTe/Mo layer # 1

(a) (b)

137

0 1 2 3 4 5 6 7

0

2

4

6

8

10

ε 2

Photon energy (eV)

-2

0

2

4

6

8

10

12

ε 1

CdTe/Mo layer # 3CdTe/Mo layer # 2

0 1 2 3 4 5 6 7

0

2

4

6

8

10

ε 2

Photon energy (eV)

-2

0

2

4

6

8

10

12

ε 1

CdTe/Mo layer # 4CdTe/Mo layer # 3

0 1 2 3 4 5 6 7

0

2

4

6

8

10

12

ε 2

Photon energy (eV)

-2

0

2

4

6

8

10

12

ε 1

CdTe/Mo layer #1 CdTe/c-Si

Figure 7-10 Real (top panel) and imaginary (bottom panel) parts of the dielectric functions of the four layers [(a)-(d)] of a CdTe thin film deposited on rough Mo. These results are determined from inversion, after determining the CdTe roughness and bulk layer thicknesses through minimization of the average MSE obtained throughout the layer analysis; (e) also shown is a comparison of the first layer dielectric function of CdTe deduced in this study with that of CdTe deposited on a smooth c-Si substrate at a nominal temperature of 200 °C [7-6]. In (b)-(d) comparisons are provided between the dielectric function of a given layer and that of the layer underneath it.

7.2.4 Comparison of RTSE and AFM

Lastly, it is of interest to compare the roughness thickness for the final CdTe film on

the Mo coated glass substrate as deduced by RTSE with that obtained by atomic force

microscopy (AFM) using a 1 x 1 µm2 image area. The RTSE/AFM comparison results

are in reasonable agreement as shown in Fig. 7-11, where the root-mean-square (rms)

(c) (d)

(e)

138

value from AFM is indicated. Considering the surface height distribution from AFM, it

is clear that spectroscopic ellipsometry is not sensitive to area fractions of surface

asperities and depressions at the level of ~ 0.3 or less.

Figure 7-11 Comparison of the surface roughness thickness at the end of the deposition for a 1496.5 Å thick CdTe film on Mo as deduced by RTSE with the relative surface height distribution and rms roughness from AFM.

7.3 Ex situ spectroscopic ellipsometry analysis of a CdTe solar cell in the substrate

configuration

The goal of ex situ spectroscopic ellipsometry (SE) studies of solar cells in the

substrate configuration is two-fold. First, the substrate configuration precludes

transmission measurements for optical analysis of the solar cells. Thus, a reflection

measurement is the only choice for optical analysis, and ellipsometry is the most

powerful reflection measurement available. With such a measurement, it may be

possible to establish a sufficient in-depth understanding of the growth processes so that

they can be optimized for highest efficiency solar cells. Second, SE may be developed

Roughness ds = 67.1 Å

asperities depressions

139

as an in-line monitor of substrate-type solar cells, for example in a roll-to-roll process.

7.3.1 Metallic back contact for CdTe solar cells in the substrate configuration

Figure 7-12 shows a comparison of measured pseudo-dielectric functions (solid

lines) for the Mo thin films deposited (a) on glass and (b) on Kapton, two possible

substrates used for rigid and flexible solar modules, respectively. Thus, these Mo films

serve as the first deposited or back contact layer of the CdTe solar cells in the substrate

configuration. The pseudo-dielectric functions of Fig. 7-12 are calculated directly from

the ellipsometry spectra using an optical model consisting of a single perfect interface

between the ambient and the film. Thus, the pseudo-dielectric function approaches the

true dielectric function of the film only when the film is opaque and its surface is

atomically smooth and oxide-free. Both oxides and surface roughness on an opaque

film lead to deviations of the pseudo-dielectric function from the true dielectric function.

In addition, semitransparent films also generate strong differences between the two due to

the presence of back reflected light and associated interference fringes.

In the real time SE studies described earlier in this Chapter, the dielectric function

for Mo at room temperature has been established and this has been used in the optical

modeling of the pseudo-dielectric functions in Fig. 7-12. In fact, the Mo sample used as

a reference was fabricated on a smooth glass substrate and was analyzed using a (surface

roughness)/(semi-infinite bulk) optical model. Using this reference, the ex situ

ellipsometric spectra of Fig. 7-12 can be analyzed by applying the corresponding optical

model to deduce the microscopic structure of these samples. The results at the left in

140

Fig. 7-12 are for the Mo film deposited on glass, and reveal an excellent fit to the data

-15

-10

-5

0

Exp. data fit data

<ε 1>

0 1 2 3 4 5 6 70

10

20

30d

b

Mo/void = 0.54 ± 0.02/0.46 ± 0.02

PHOTON ENERGY (eV)

<ε 2>

Mosemi-inf

84 ± 3 Å

(a)

ds

MSE = 17.9

0

5

Exp. data fit data

<ε1>

0 1 2 3 4 5 6 70

10MSE = 28.2

Mo/void = 0.32 ± 0.01/0.69 ± 0.01

PHOTON ENERGY (eV)

<ε2>

db

Mo/void = 0.49 ± 0.01/0.51 ± 0.01

semi-inf

608 ± 3 Å ds

(b)

Figure 7-12 A comparison of measured pseudo-dielectric functions (solid lines) for Mo thin films deposited by sputtering (a) on glass and (b) on Kapton. Also shown are the fits (broken lines) using a reference dielectric function for dense Mo determined separately, and the multilayer models depicted in the insets.

(broken lines) using a model of bulk Mo (no density deficit relative to the reference) with

a 84 Å thick surface roughness layer on top. This is consistent with the results for the

reference Mo film which was prepared under similar conditions and exhibited a

roughness thickness of ~ 80 Å, as determined in the analysis of CdTe over-deposition.

The results at the right in Fig. 7-12 are for Mo deposited on Kapton; these results are

considerably different, particularly in terms of the overall magnitude of the dielectric

function at low energies. In addition, ε1 does not become negative for this film at low

energies. This suggests that the film lacks conducting channels in the plane of the film

and so the electrons behave as bound electrons at the frequencies of the optical field. In

fact, a fit to the ellipsometric data suggests a very thick roughness layer (~ 600 Å) which

141

is nearly opaque. Beneath this layer there appears to be a region of even larger density

deficit (~70%) in the bulk Mo film. It is not clear whether this density deficit is due to

true voids or to roughness at the interface to the Kapton substrate. The impact of the

resulting microstructure on solar cell performance is unclear; however, it is evident that

ex situ SE can be used to characterize the substrate metal optical properties and structure

and the effects of the substrate on overlying film optical properties and structure.

7.3.2 Transparent p+ back contact for CdTe solar cells

In order to develop a complete optical model for the CdTe solar cell in the substrate

configuration, it is also necessary to extract the optical properties of the ZnTe p+

semiconductor back contact in a structure that is easier to analyze than the completed

solar cell. As a result, these studies were performed using ZnTe deposited by magnetron

sputtering directly onto a glass substrate; (Dr. Viral Parikh is acknowledged for the

deposition of this sample). Doping ZnTe p-type was possible using Cu, and the Cu

content in the ZnTe sputtering target is 1 wt.%. Figure 7-13 shows the raw ellipsometric

spectra and the best fit that provides the bulk and surface roughness layer thicknesses

(5237 Å and 90 Å, respectively). In this analysis the dielectric function is modeled as a

sum of four critical point structures, three to match the peaks observed most clearly in ψ

in Fig. 7-13 and the fourth to simulate the gradual absorption onset. A fifth

Tauc-Lorentz oscillator simulates a broad background absorption centered above 6 eV.

The best fit result is shown in Fig. 7-14 as the solid lines. Handbook data [7-7] for single

142

0

10

20

30

exp.data fit

ΨΨ ΨΨ (

degr

ee)

0 1 2 3

-100

0

100

200

300

PHOTON ENERGY (eV)

∆∆ ∆∆ (

degr

ee)

exp.data fit

3 4 5 6 7

ZnTe:Cusurface roughness

ZnTe:Cu

glass

90.4 ±0.9 Å

5236.6 ±1.1 Å

1 mm

ZnTe:Cusurface roughness

ZnTe:Cu

glass

90.4 ±0.9 Å

5236.6 ±1.1 Å

1 mm

PHOTON ENERGY (eV)

crystal ZnTe are also shown in Fig. 7-14 as the points. Significant differences can be

observed between the results for the doped thin film sample presented here and the

Figure 7-13 Ellipsometric spectra (solid lines) and best fit (broken lines) using the structural model and best fit parameters shown in the inset. The dielectric function is determined simultaneously using a model assuming a sum of critical point structures. The resulting dielectric function is shown in Fig. 7-14.

handbook results for the single crystal. The differences are likely to be due to the heavy

Cu doping as well as the fine-grained polycrystallinity of the thin film. The three higher

energy critical points at 3.61, 4.15, and 5.27 eV mirror those in the single crystal, but are

consistently broader; however, the band gap critical point expected at ~ 2.2 eV in the thin

film could not be detected in spite of considerable efforts to incorporate it into the model.

Instead, an oscillator at ~ 1.8 eV with a very large width of ~ 1 eV is needed to fit the low

energy spectra. Thus, the disappearance of the 2.2 eV band gap structure is interpreted

as a true effect, not an artifact of the analysis, since the band gap critical points in

ψ

143

undoped CdTe-based alloys of similar thickness on glass are easily observable using the

same method of analysis. As a result, the severely broadened band edge absorption is

interpreted as an effect of the Cu incorporation in the film which is likely to be

significantly greater than typical doping levels in semiconductors. Tables 7.3 and 7.4

provide the parameterized results for polycrystalline ZnTe:Cu and single crystal ZnTe

assuming four critical point oscillators and one Tauc-Lorentz oscillator, the latter serving

as the broad back ground.

The critical point oscillator expression is given by:

ε = Σn [Anexp(iφn)] [Γn/(2En−2E−iΓn)]µn. (7.1)

The free parameters include amplitudes, resonance energies, broadening parameters,

phases, and exponents, respectively: (An, En, Γn, φn, µn);

n = 1, 2, 3, 4. For the thin

film ZnTe:Cu, the exponents µn are fixed at the best fit values from the analysis of single

crystal ZnTe data.

Table 7.3 Best fit critical point and Tauc-Lorentz oscillator parameters describing the inverted dielectric function of polycrystalline ZnTe:Cu. The exponents µn are fixed at the single crystal values of Table 7.4.

CPPB

oscillator An En(eV) Γn(eV) φn µn ε1 offset

1 4.10 ± 0.42 1.78 ± 0.14 0.96 ± 0.22 −124.34 ± 10.76 0.08 2.79 ± 0.61

2 2.69 ± 0.06 3.61 ± 0.01 0.72 ± 0.01 −112.82 ± 3.34 2.09 3 11.86 ± 0.67 4.14 ± 0.01 0.55 ± 0.02 45.02 ± 2.92 0.38 4 6.64 ± 0.23 5.27 ± 0.01 1.28 ± 0.02 −19.90 ± 3.10 1.52

T-L oscillator An En (eV) Γn (eV) Eg (eV)

1 36.24 ± 11.89 6.35 ± 0.18 4.28 ± 0.46 1.49 ± 0.49

144

Table 7.4 Best fit critical point and Tauc-Lorentz oscillator parameters for single crystal ZnTe [7-7].

CPPB

oscillator An En(eV) Γn(eV) φn µn ε1 offset

1 8.05 ± 0.45 2.21 ± 0.03 0.20 ± 0.03 −37.31 ± 9.34 0.08 -3.64 ± 0.75

2 4.85 ± 0.09 3.58 ± 0.01 0.50 ± 0.01 −78.30 ± 3.48 2.09 3 16.09 ± 1.01 4.25 ± 0.02 0.51 ± 0.03 137.85 ± 9.29 0.38 4 3.43 ± 0.20 5.22 ± 0.02 0.77 ± 0.05 −35.46 ± 7.67 1.52

T-L oscillator An En (eV) Γn (eV) Eg (eV)

1 219.76 ± 19.98 4.74 ± 0.06 2.86 ± 0.06 2.48 ± 0.06

Figure 7-14 Dielectric function of thin film ZnTe:Cu prepared by magnetron sputtering with 1 wt.% Cu in the ZnTe target (solid lines). A model consisting of four critical points in the band structure has been used in this analysis. The data points are literature results for single crystal ZnTe [7-7].

7.3.3 Optical analysis of the CdTe solar cell in the substrate configuration

In the optical analysis of the CdTe solar cell in the substrate configuration, a device

is studied here that is complete with the exception of the top contact; (Dr. Anthony Vasko

is acknowledged for deposition of this sample, and Dr. Jian Li is acknowledged for

145

measurement assistance). Thus, the top surface from which the light beam reflects is

CdS, which is relatively rough. After the CdS deposition, this solar cell was treated

with CdCl2 at a temperature of 387 °C for a duration of 30 min. In order to analyze the

structure of the solar cell, a reference set of dielectric functions is adopted including CdS

obtained at room temperature using in situ SE for a film prepared in the same sputtering

chamber at a substrate temperature of 310 °C, a rf power level at the target of 50 W, an Ar

pressure of 10 mTorr, and an Ar flow of 23 sccm. The spacing between the target and

the substrate was ~ 10 cm and the substrate was a smooth c-Si substrate for ease of

analysis. Single crystal CdTe was also used as a reference, as obtained from real time

SE of a film prepared by molecular beam epitaxy in a literature study [7-8]. The two

other dielectric functions include that of ZnTe:Cu, obtained as described above (see Figs.

7-13 and 7-14), and Mo, obtained in the real time SE study of CdTe deposition on

Mo/glass. In the latter analysis, correction was made for the surface roughness layer on

the Mo film.

A step-by-step analysis, in which one free parameter is introduced at a time, was

developed specifically for ex situ studies of CdTe solar cells. As each parameter is

introduced, a measure of the quality of the fit is observed, with the goal being to increase

the complexity of the optical model by incorporating additional thicknesses and

compositions, and in this way, determine which parameters are most important for a high

quality fit and which parameters are unnecessary.

Figure 7-15 shows the step-by-step reduction in the mean square error (MSE)

146

obtained by adding best fitting parameters one at a time. The MSE is expressed in terms

of the standard deviations of the real and imaginary parts of ρ ≡ tanψ exp(i∆). Figure

7-16 shows the experimental spectroscopic ellipsometry data for the CdTe solar cell on

the Mo surface in the substrate configuration. The data from 0.75 to 2.5 eV are shown

on an expanded scale relative to those over the range from 2.5 to 6.5 eV. The fringe

pattern over the range from 0.75 to 1.5 eV provides information on the CdTe thickness

and the modulation of these fringes provides information on the optical properties and

thicknesses of the materials underneath the CdTe. The single fringe over the range from

1.5 to 2.3 eV provides information on the CdS thickness and the modulation of this fringe

provides information on the underlying (opaque) CdTe. The data above 2.5 eV provides

information on the critical points of the CdS. Even very small details of the cell

structure can be inferred from the raw data, as described next.

First, the critical points of the CdS are broadened compared to the film deposited on

crystal Si from which the reference data were obtained. This broadening may be due to

oxidation at the surface as a result of the CdCl2 treatment. Alternatively, the effect may be

due to a smaller grain size in the CdS when it is deposited on a CdTe thin film as

compared to when it is deposited on bulk crystal Si. Finally, the effect may be due to

interdiffusion of the CdS and CdTe. A second observation is that the CdS band gap

appearing in the data is lower than that in the model, suggesting either interdiffusion or

differences in strain between the reference film deposited on crystal Si and the solar cell

of Fig. 7-16 deposited on CdTe. In spite of these small deviations, a reasonably good fit

147

(solid line) can be obtained using the model shown in Fig. 7-17. It should be

emphasized that this represents a first attempt at analyzing solar cells in the substrate

configuration and improved results are expected by breaking the structure down and

developing optical properties more relevant to the structure. For example, the optical

properties of the CdS can be obtained from a single-layered sample that has been exposed

to the same CdCl2 treatment as the solar cell.

0 10 20 30 40 50 60 70 80

0.2

0.4

0.6

0.8 14131211102 98765431

MS

E/1

000

Steps

Step-by-step MSE reduction

number of fitting parameters

Figure 7-15 Step-by-step MSE reduction by adding one fitting parameter at a time. Starting with the CdTe thickness as a variable, each additional parameter was subsequently fitted. It was found that fitting the CdS thickness provided the greatest improvement in MSE among all 2-parameter attempts. Similar methodology was used for all 14 parameters. Circles connected by the solid line indicate the best n-parameter fit with n given at the top and the added parameter given in Table 7.5.

148

0

10

20

30

40 Exp. data fit

ΨΨ ΨΨ (

degr

ee)

0.5 1.0 1.5 2.0

-100

0

100

200

300

PHOTON ENERGY (eV)

∆∆ ∆∆ (

degr

ee)

Exp. data fit

3 4 5 6 7

PHOTON ENERGY (eV)

Figure 7-16 Ellipsometric spectra for a CdTe solar cell deposited on Mo in the substrate configuration (points). The cell was exposed to a CdCl2 treatment before this measurement. The top contact of the solar cell is not incorporated over the area probed, leading to the structure: ambient/CdS/CdTe/ZnTe:Cu/Mo. The solid line depicts the optical model shown in Fig. 7-17.

The fitting parameter sequence in Table 7.5 is understandable in that the thickest

layers have the greatest impact in the step-by-step fitting procedure. When the initial

estimate of a fitting parameter is close to its best fitting result, this fitting parameter will

be added into the model at a lower priority in the sequence, an example being the ZnTe

thickness. The results provide information on the ZnTe thickness and void fraction, the

ZnTe/Mo interface thickness, its Mo volume fraction, as well as the CdS thickness, and

149

void fraction, the combined CdS/CdTe interface roughness-interaction thickness, its CdTe

fraction, and the CdTe thickness, and void fraction, all shown in Fig. 7-17. Also

determined is the percent non-uniformity, which describes the thickness distribution over

the area of the probe beam.

The following comments can be made regarding the deduced structure of Fig. 7-17.

The high void fraction in the Mo substrate is consistent with the study of individual such

layers as noted above. Apparently these voids are not completely filled in by the

overlying deposition of ZnTe:Cu. The model is not able to discern roughness at the

CdTe/ZnTe:Cu interface, not because it does not exist, but rather, because the optical

properties of the two materials do not exhibit sufficient contrast to detect it. The ~1300

Å thick interface layer between the CdS and CdTe is attributed to a combination of

interface roughness and alloying. The volume fractions in the layers of the structure

also convey some information; however, some results require closer scrutiny. The CdTe

(3% void) of this substrate solar cell structure appears to be similar in density to that

typically observed in CdCl2 treated superstrate cells (typically 1-3% voids). The CdS in

the substrate cell appears to be denser than that in superstrate cells. Finally, the low

volume fraction of Mo in the Mo/ZnTe interface layer seems incongruous in view of the

higher Mo fraction in the surface layers of the bare Mo film as shown in Fig. 7-12. This

result needs to be studied in greater detail in future analyses. Generally such difficult

analyses are a work in progress -- like the cell itself -- and will improve as more is

learned about the optical properties and microstructure. For example, a three

150

component effective medium approximation may be needed to describe the ZnTe:Cu/Mo

interface, consisting of Mo, ZnTe:Cu, and finally void. In this way, voids trapped at the

substrate interface can be quantified.

Table 7.5 Best fitting parameters added step by step to improve the standard mean square error (MSE) in the ellipsometric analysis of a CdTe solar cell in the substrate configuration.

# of fitting parameters Best fitting parameter added to

improve MSE Standard MSE

1 CdTe thickness 764.2

2 CdS thickness 475.7

3 Mo void volume fraction 214

4 CdS roughness thickness

(50/50) 113.3

5 ZnTe/Mo interface thickness

(50/50) 86.05

6 CdTe void volume fraction 67.84

7 Mo volume fraction in ZnTe 53.02

8 CdS roughness void volume

fraction 40.05

9 CdTe non-uniformity 36.4

10 CdS/CdTe interface thickness

(50/50) 35.54

11 CdS void volume fraction 34.93

12 CdTe volume fraction in

CdS/CdTe interface 34.33

13 ZnTe void volume fraction 33.95

14 ZnTe thickness 33.87

151

CdS surface roughness thickness Surface void fraction

159 ± 5 Å 0.25 ± 0.01

CdS thickness Void volume fraction

2433 ± 9 Å 0.007 ± 0.003

CdS/CdTe interface thickness CdTe volume fraction

1348 ± 20 Å 0.835 ± 0.009

CdTe thickness Void volume fraction

CdTe thickness non-uniformity

13715 ± 66 Å 0.030 ± 0.003 3.8% ± 0.2%

CdTe/ZnTe interface thickness 0

ZnTe thickness Void volume fraction

1120 ± 114 Å −0.026 ± 0.011

ZnTe/Mo interface thickness Mo volume fraction

293 ± 63 Å 0.195 ± 0.061

Mo void volume fraction 0.395 ± 0.027

Figure 7-17 Optical model for a CdTe solar cell in the substrate configuration (excluding the top contact) deposited on a Mo film surface. This model and the best fit parameters provide the solid line results in Fig. 7-16.

152

Chapter Eight

Spectroscopic Ellipsometry Studies of II-VI Alloy Films

8.1 Introduction

In the single junction superstrate solar cell configuration, the highest efficiency for a

CdTe device prepared by sputtering is 14% [8-1] and the corresponding result for

close-spaced sublimation is 16.5% [8-2]. The latter champion solar cell has the following

characteristics: VOC = 845 mV, JSC = 25.9 mA/cm2, and FF (fill factor) = 75.5%. The

current-voltage (J-V) and quantum efficiency (QE) curves of the champion cell are

shown in Figure 8-1.

Figure 8-1 Current-voltage and normalized quantum efficiency spectra for a champion 16.5% efficient CdTe/CdS thin-film solar cell [8-2].

153

In order to improve on these cell efficiencies, materials and devices for tandem cell

structures have been investigated in the research laboratory [8-3]. Instead of using a

single junction device based on CdTe with a near-optimum band gap of 1.5 eV, the top

cell absorber material of the tandem must have a wider band gap, and the bottom cell

absorber material must have narrower band gap. A practical conversion efficiency of

25% has been predicted for a two-junction two-terminal polycrystalline thin-film tandem

cell with energy band gaps of 1.14 eV for the bottom cell and 1.72 eV for the top cell [8-4].

CdTe-based ternary alloy materials, such as Cd1-xMgxTe and Cd1-xMnxTe are attractive

due to the flexibility of controlling their band gaps through the molar composition x, and

as a result, these materials have been considered as wide band gap top cell candidates for

such tandem cells as shown in Fig. 8-2. In addition to the II-VI alloys with wide band

gaps, the alloy Cd1-xHgxTe is a possible narrow band gap bottom cell candidate.

Cd1-xHgxTe is flexible enough to tailor the band gap from −0.15 eV for x = 1, i.e.

semimetallic, to 1.5 eV for x = 0 [8-5].

Spectroscopic ellipsometry is an excellent non-contacting technique for investigating

thin-film semiconductor optical properties, electronic structure, and surface and bulk

microstructure. This technique has been applied for materials evaluation in order to

explore the opportunities and identify the potential difficulties in the fabrication of II-VI

materials for top cells in two-junction devices with either monolithic two-terminal (see

Fig. 8-2) or mechanically stacked four-terminal structures. In this research, two top cell

materials, Cd1-xMnxTe and Cd1-xMgxTe, the latter with a band gap as wide as 1.98 eV,

154

were measured. These films were obtained by sputtering in order to assess their

suitability in tandem PV devices with a Cd1-xHgxTe bottom cell. The widest band gap

Cd1-xMgxTe was obtained from a target of 60 wt.% CdTe and 40 wt.% MgTe. Also in

this research, Cd1-xHgxTe thin films with a band gap variation from 0.81 eV to 1.58 eV

were measured. These films were obtained by sputtering using a target of 60 wt.%

CdTe and 40 wt.% HgTe through a variation of the deposition temperature.

Figure 8-2 Two-terminal tandem cell based on Cd1-xMgxTe and Cd1-xHgxTe absorbers.

8.2 Top cell material candidates: Cd1-xMnxTe and Cd1-xMgxTe

8.2.1 Cd1-xMnxTe and Cd1-xMgxTe preparation

The Cd1-xMnxTe and Cd1-xMgxTe films described in this section were magnetron

sputtered on soda-lime glass substrates from targets fabricated from 87 wt. % CdTe and

13 wt. % MnTe, and from 80 wt. % CdTe and 20 wt. % MgTe, respectively; (Viral Parikh

is acknowledged for the deposition of these samples). A first estimate of the

composition of the as-deposited alloys films was made on the basis of the optical

Cd1-xMgxTe

ZnO CdS

ZnTe

Cd1-xHgxTe

ZnO CdS

Cu/Au

glass

155

absorption edge determined from the transmission spectra. The Cd1-xMnxTe film

thickness was typically about 1 µm; Cd1-xMgxTe films were thinner -- about 0.2 µm.

The deposition conditions for CdxMg1-xTe are shown as the first two entries of Table 8.1.

Table 8.1 Deposition parameters used to prepare the CdxMg1-xTe and CdxHg1-xTe thin films.

Rf power (W) Pressure (mTorr) Substrate temp (°C)

CdTe 20 18 250 CdxMg1-xTe

(20 wt.% MgTe) 50 20 200

CdxMg1-xTe (40 wt.% MgTe)

50 5 290

CdxHg1-xTe 27 10 23 CdxHg1-xTe 27 10 44 CdxHg1-xTe 27 10 70 CdxHg1-xTe 27 10 85 CdxHg1-xTe 27 10 97 CdxHg1-xTe 27 10 153

A CdCl2 post-deposition treatment was performed as an important step in fabricating

solar cells using the alloys as the active layers. Several effects of the CdCl2 treatment

are believed to enhance the solar cell performance of the alloy films, including relaxing

the strain, increasing the grain size, improving the alloy/CdS interface, and reducing the

lattice mismatch there [8-6]. For evaluation purposes, the CdCl2 treatment was performed

on a 2 cm × 3 cm piece of each sample placed in a 2.5 cm diameter quartz tube. The

CdCl2 source was fabricated by forming a saturated methanol solution of the chloride and

evaporating it from the surface of a heated glass plate. The sample was placed above

156

the source plate with the film side facing the plate and a 1 mm gap between the two. A

typical 30 minute CdCl2 treatment was performed on the Cd1-xMgxTe films at a

temperature of 387°C. To treat the Cd1-xMnxTe films, two post-deposition approaches

were evaluated. In one approach, the CdCl2 vapor treatment was carried out on the

films under the same conditions as for Cd1-xMgxTe. In the other, a two-step process was

applied in which a high temperature annealing step was carried out at 520°C for 10

minutes under 2% H2/Ar, followed by the standard CdCl2 vapor treatment at 385°C for 30

minutes in dry air.

In order to compare the optical results before and after CdCl2 treatment, pure CdTe

films of more than 1 µm in thickness were magnetron sputtered onto soda-lime glass at

250°C. For these CdTe films, a CdCl2 treatment in dry air ambient was performed at a

temperature of 387°C with different times optimized depending on the film thicknesses.

8.2.2 Data analysis and results

A rotating compensator multichannel spectroscopic ellipsometer with a 0.75 - 6.5 eV

photon energy range was used to investigate the optical properties of the as-deposited and

annealed films. The information extracted from SE measurements is very useful for

assessing the surface and bulk characteristics of the samples.

As-deposited Cd1-xMgxTe and Cd1-xMnxTe optical properties

Figure 8-3(a-b) shows the pseudo-dielectric functions of RF magnetron sputtered

CdTe, Cd1-xMnxTe, and Cd1-xMgxTe films in the as-deposited state. The thicknesses of

157

CdTe, Cd1-xMnxTe and Cd1-xMgxTe films are 1.41 µm, 1.0 µm and 0.18 µm, respectively.

The band gaps of 1.63 eV for the Cd1-xMnxTe film and 1.61 eV for the Cd1-xMgxTe film

were estimated from optical transmission measurements. These two alloy films as well

as the CdTe film are transparent below their band gaps, and the spectral density of

interference fringes in the lower energy range of ~ 0.75 eV to 2.0 eV scales with the film

thickness. In the high energy range of 2.0 eV to 6.5 eV, features are observed

corresponding to the higher energy band gaps at the critical points (CPs) in the joint

density of states. The nature of these CPs and the information that can be extracted

from them will be discussed shortly.

A comparison of pseudo-dielectric functions over the high energy range for the

Cd1-xMnxTe film of Fig. 8-3(a-b) after Br2/methanol etch and after selected times of long

term laboratory storage is given in Fig. 8-3(c). The freshly-deposited sample exhibits

higher amplitudes in < ε > than a sample that has been stored for a period of time. The

data for the Cd1-xMnxTe sample in Figure 8-3(a-b) were taken one week after film

deposition. Thus, it is reasonable to interpret the relatively low dielectric function

amplitudes of the stored samples to surface oxidation. By tracking <ε2 > values during

Br2/methanol chemical etching processes, one can develop an optimum procedure to

remove the oxide, and achieve the most abrupt interface to the ambient as this leads to

maximum <ε2 >. For the results in Figure 8-3(c), the E1, E1 + ∆1, and E2 critical-point

structures can be seen clearly in all spectra. The sample measured immediately after

etching by Br2/methanol chemical solution showed the highest amplitudes of the

158

pseudo-dielectric function in the higher energy region. In fact, the maximum values in

Fig. 8-3(c) are in accord with those of epitaxial films [8-7] and bulk crystals [8-8]. Thus,

the pseudo-dielectric function after etching is expected to be very close to true dielectric

function with only small deviations due to residual surface roughness or a thin Te-rich

surface layer generated by the etching process.

1 2 3 4 5 6

0

4

8

12

16

CdMgTe

CdMnTe

CdTe

Energy (eV)

< e

1>

1 2 3 4 5 6

0

4

8

12

16

1 2 3 4 5 6

0

4

8

12

16

1 2 3 4 5 6

-4

0

4

8

CdMgTe

Energy (eV)

1 2 3 4 5 6

-4

0

4

8

< e

2>

CdMnTe

CdTe

1 2 3 4 5 6

-4

0

4

8

<ε 1

>

<ε 2

> Cd1-xMnxTe

Cd1-xMgxTe

Cd1-xMnxTe

Cd1-xMgxTe

CdTe CdTe

(a) (b)

Figure 8-3 Real (a) and imaginary (b) parts of the pseudo-dielectric functions of RF sputtered CdTe (Eg = 1.50 eV), Cd1-xMnxTe (Eg = 1.63 eV) and Cd1-xMgxTe (Eg = 1.61 eV) films all in the as-deposited state; (c) Pseudo-dielectric function of as deposited Cd1-xMnxTe samples after different storage times in laboratory ambient: (1) immediately after Br2/methanol etch; (2) 3 weeks after deposition; and (3) 1.5 years after deposition.

2 3 4 5 6-2

0

2

4

6

8

10

12

3

21

E2

E1

E1+∆

1

< ε

1>

Energy (eV)2 3 4 5 6

-2

0

2

4

6

8

10

12

2

E2

E1+∆

1E1

1

3

< ε

2>

Energy (eV)(C)

159

Once the maximum value of <ε2> is obtained through etching, the resulting spectra as in

Fig. 8-3(c) (immediately after etch), interpreted as an approximation to the true dielectric

function, can be further interpreted through CP analysis. Although the imaginary part of

the dielectric function is most closely related to the absorptive behavior of films and thus

the joint density of electronic states, however, both real and imaginary parts encode this

information due to the Kramers-Kronig relationships. The fundamental and higher band

gap energies determined from the CP features provide information on the alloy

composition and strain whereas the broadening energies of the CP features provide

information on the crystalline grain size arising from the polycrystalline structure. The

band structure parameters of a single CP, including the band gap and broadening energies

can be deduced from both parts of ε(E) by fitting to a standard analytic line shape [8-9]

0( ) / [(2 2 ) ]iE Ae E E iφ µ µε = Γ − + Γ , (8-1)

where A is the CP amplitude, Γ and φ are the Lorentzian broadening energy and phase

angle, and E0 and µ are the threshold energy and exponent, the latter defined by the

nature of the singularity in the electronic joint density of states. These parameters are

readily determined by fitting second-derivative spectra d2ε(E)/dE2. For the ternary alloy

system, once relationships have been established between the molar composition x and

the CP energies in the band structure, as determined from the dielectric function ε(E),

usually from studies of single crystals, such relationships can be used to estimate the

composition of any unknown alloy [8-9,8-10]. Figure 8-4 shows the experimental

second-derivative spectra in the pseudo-dielectric function <ε(E)> of an as-deposited

160

Cd1-xMnxTe sample, along with best fit results obtained using Eq. (8-1).

2 3 4 5 6

-100

0

100d2<ε

1>/dω

2

d2<ε2>/dω

2

E2 (5.033 eV)

E1 (3.352 eV)

E1+∆

1 (3.884 eV)

d2<

ε>

/ d

ω2

Energy (eV)

Figure 8-4 Best fit (lines) to the second derivative of the experimental pseudo-dielectric function (points) for the as-deposited Cd1−xMnxTe film of Fig. 8-3 (c: immediately after etch). The three CP transitions, E1, E1 + ∆1, and E2, are indicated by arrows with best fit energies of 3.352, 3.884, and 5.033 eV, respectively. The composition of x=0.06 can be estimated by the empirical relationship between E1, the strongest CP in this case, and the composition [8-7].

Returning to the results of Fig. 8-3(c), very large changes in the pseudo-dielectric

function induced by sample exposure to laboratory ambient can be observed by SE.

This effect can be explored in greater detail by RTSE. Figure 8-5 shows the continuous

variation in the pseudo-dielectric function of the 3-week-old Cd0.94Mn0.06Te sample

immediately after Br2/methanol etching and upon exposure to air. For such

measurements, the native oxide layer was removed by 0.01-0.02% Br2/methanol in a few

seconds of etching time. Upon exposure of the resulting clean sample to air, the

pseudo-dielectric function does not change much during the initial several minutes;

however, with increasing time both real and imaginary parts of the pseudo-dielectric

function gradually decrease. In fact, the imaginary part of the pseudo-dielectric function

near the E1 + ∆1 CP energy (~ 3.88 eV) decreased by 5% over a one hour period.

161

Figure 8-5 Variation of the pseudo-dielectric function of as deposited Cd0.94Mn0.06Te with time after Br2/methanol etching, measured in situ at room temperature during exposure to laboratory ambient.

1 2 3 4 5 6

0

4

8

12

16

20 As-deposited One-step

385 oC 30 min with CdCl2

Two-step first 520 oC 10 min in H

2,

then 385 oC 30 min with CdCl2

<ε 1

>

Energy (eV)1 2 3 4 5 6

-4

0

4

8

12

16

20

As-deposited One-step

385 oC 30 min with CdCl2

Two-step first 520 oC 10 min in H

2,

then 385 oC 30 min with CdCl2

< ε

2 >

Energy (eV)

Figure 8-6 Pseudo-dielectric functions of as-deposited and one-step and two-step CdCl2 treated Cd0.94Mn0.06Te samples.

Optical properties of CdCl2-treated and Cd1-xMnxTe and Cd1-xMgxTe

Figure 8-6 shows the pseudo-dielectric function of as-deposited (3-week-old) and

annealed Cd0.94Mn0.06Te samples. Using the dielectric functions obtained from the

Br2/methanol-etched Cd0.94Mn0.06Te sample and assuming Te oxide (TeO2) on the surface,

the latter shown in Fig. 8-7 [8-11], a simple 3-layer model of oxide/Cd0.94Mn0.06Te/glass

could be employed to fit the experimental results for the as-deposited sample. The

1 2 3 4 5 6

-2

0

2

4

6

8

10

12

14

16

18

Tim

e in

cre

asi

ng

0.5 min 3.5 min 6.5 min 9.5 min 18 min 38 min 58 min

<

ε1>

Energy (eV)1 2 3 4 5 6

-8

-6

-4

-2

0

2

4

6

8

10

12

Tim

e in

cre

asi

ng

0.5 min 3.5 min 6.5 min 9.5 min 18 min 38 min 58 min

< ε

2>

Energy (eV)

162

thickness of TeO2 layer was found to be ~ 35 Å. For the annealed sample, however, it

was difficult to fit the experimental data due to lack of reference dielectric functions for

the surface layer components. In particular, for the sample that was vapor treated with

CdCl2 at 385°C, the pseudo-dielectric function was much different from that of the

as-deposited samples. It was further observed that even after the treated films were

etched using several etching steps of 0.04 volume % Br2 in methanol, the

pseudo-dielectric function showed much different spectral behavior from that of the

as-deposited sample. This suggests that the top layer is substantially modified during

treatment, both chemically and morphologically; however, there remains the possibility

that the behavior is due to a thick metallic oxide generated during treatment that does not

respond to the Br2 methanol etch in the same way as the native oxide.

Figure 8-7 Index of refraction and extinction coefficient of amorphous TeO2.

163

Figure 8-8 Pseudo-dielectric functions of as-deposited and CdCl2 treated Cd1-xMgxTe samples.

Figure 8-8 shows the pseudo-dielectric function of as-deposited and CdCl2-treated

Cd1-xMgxTe samples. For the CdCl2-treated Cd1-xMgxTe sample, much less deterioration

in the bulk optical characteristics is observed compared with CdCl2 treated Cd1-xMnxTe,

suggesting that the CdCl2 treatment is effective for Cd1-xMgxTe PV devices. Most

importantly, the critical point structure of the Cd1-xMgxTe is retained upon treatment with

a clear narrowing of the widths.

Dielectric functions of as-deposited and CdCl2 treated samples over the energy range

of 3.0 ~ 6.0 eV are accumulated in Fig. 8-9 (a-c). For these measurements, the films

were previously etched using one or more steps, each consisting of brief immersion in a

0.04 volume % Br2 in methanol solution. The original intent of this process was to

remove oxides that are observed to develop on as-deposited and CdCl2-treated CdTe

films due to their exposure to the laboratory and treatment ambients. Interestingly, for

CdTe it has been found that successive etching steps lead to a significant step-wise

smoothening of the film surface simultaneously with decreasing bulk layer thickness due

1 2 3 4 5 6

0

4

8

12

16

20 As-deposited

387oC 30 min CdCl2 treated

< ε

1>

Energy (eV)1 2 3 4 5 6

-4

0

4

8

12

16

20 As-deposited

387oC 30 min CdCl2 treated

< ε

2>

Energy (eV)

164

to step-wise film dissolution. In fact, a roughness layer of thickness of up to a micron or

more can be eliminated in several successive etching steps, and ultimate stabilization of

the roughness thickness at ~20-40 Å can be observed. It is under stable, smooth-surface

conditions that the measurements on CdTe of Fig. 8-9(a) are made. Under these

conditions, the dielectric function deduced from the measured ellipsometry spectra is

reasonably representative of the true dielectric function, enabling determination of the

critical point energies and widths by dielectric function fitting. It is known that the

etching treatments lead to a Te-rich surface layer (~10 Å) [8-12]; however, its effect is

expected to be smaller than that of the residual roughness and has been neglected in this

study.

Figure 8-9(c) compares the approximate dielectric function of Br2/methanol-etched

Cd1-xMgxTe in the as-deposited (left) and CdCl2-treated (right) states. This Cd1-xMgxTe

film was sputter-deposited to a thickness of 0.18 µm on a soda-lime glass slide. The

results in Fig. 8-9(c) may differ somewhat from the true dielectric function due to the

presence of the residual roughness and a Te-rich surface layer. The key observation in

the comparison of the panels of Fig. 8-9(c) is that noted earlier in Fig. 8-8, namely, the

critical points E1, E1+∆1, and E2 are clearly observed at similar energy positions in both

sample states. Any observed shifts may be due to incomplete accounting of surface

effects. In fact, all critical points become sharper upon CdCl2 treatment. This is an

indication that the composition of the film is retained upon treatment and that the

crystalline grain size increases significantly, as well. For comparison, in Fig. 8-9(a),

165

which depicts the corresponding results for CdTe (i.e., with no alloying), similar behavior

is observed. In contrast, for Cd1-xMnxTe in Fig. 8-9(b), the CdCl2 treatment leads to a

complete loss of the critical point structures and these cannot be recovered by continued

etching. This demonstrates that the treatment leads to a significant chemical

modification of the Cd1-xMnxTe film, most likely phase segregation and oxidation of the

Mn, which can account for its poor performance when incorporated into actual devices.

The fact that the Cd1-xMgxTe does not experience such a modification upon CdCl2

treatment and retains the band structure characteristics of the as-deposited film (along

with a significant increase in grain size) has demonstrated its promise for the

development of devices from this material.

Quantitative information can be obtained from fits to the approximate dielectric

functions of Figs. 8-9(a) and 8-9(c) which provide the energy positions and widths of the

dielectric function peaks. These results are given in Fig. 8-9 as the solid lines for all

films except for the CdCl2-treated Cd1-xMnxTe in which case the critical point structure is

lost. The critical point parameters including the energy positions Ej and widths Γj are

presented in Table 8.2. Among the key observations of Table 8.2 include:

(i) retention of the critical point structure for Cd1-xMgxTe upon CdCl2 treatment

without a significant change in the energy positions (in consideration of surface

variations), indicating success of alloying in the CdCl2-treated films;

(ii) reduction of the critical point transition widths upon CdCl2 treatment for the

CdTe and Cd1-xMgxTe, an indication of an increase in grain size or a reduction in defect

166

density;

Figure 8-9 Approximate dielectric functions, i.e., optical properties deduced with a best attempt to eliminate surface effects, for as-deposited films and CdCl2-treated films obtained by SE after Br2+methanol etching that improves the surface quality (points); (a) CdTe; (b) Cd1-xMnxTe; (c) Cd1-xMgxTe; the solid lines show the results of fits to extract critical point energies and widths. The result for the CdCl2-treated Cd1-xMnxTe could not be fit with a critical point parabolic band model.

(a)

(b)

(c)

167

(iii) increase of the critical point transition widths for the as-deposited alloys

compared with the as-deposited CdTe, possibly due to a smaller grain size in the

as-deposited alloy films; and

(iv) similar critical point widths for the CdCl2-treated CdTe and Cd1-xMgxTe,

indicating the effectiveness of the treatment in improving the alloy.

Table 8.2 Critical point parameters of transition energy and width obtained in the fits to the dielectric functions of Fig. 8-9.

CdTe

as-dep. CdTe

CdCl2-treat. Cd1-xMgxTe

as-dep. Cd1-xMgxTe CdCl2-treat.

Cd1-xMnxTe as-dep.

Cd1-xMnxTe CdCl2-treat.

E0 (eV) 1.497 1.499 1.615 1.633 1.548 --- E1 (eV) 3.274 3.331 3.354 3.303 3.363 ---

Γ(Ε1) (eV) 0.411 0.200 0.480 0.216 0.430 --- E1+∆1 (eV) 3.844 3.883 3.901 3.878 3.914 ---

Γ(E1+∆1) (eV) 0.484 0.368 0.520 0.309 0.483 --- E2 (eV) 5.193 5.208 5.179 5.197 5.182 ---

Γ(E2) (eV) 0.993 0.796 1.252 0.879 1.215 ---

Furthermore, two additional Cd1-xMgxTe samples prepared by magnetron sputtering

from alloy targets were studied in detail by ex situ SE. The goal of this study was to

compare the previously-described as-deposited film prepared with low Mg content and

band gap of Eg = 1.615 eV with those prepared under conditions leading to higher Mg

content. This comparison was performed on as-deposited films without CdCl2 treatment.

For the sample labeled CGT42, the target was CdTe (80 wt.%) + MgTe (20 wt.%), and

Cd1-xMgxTe deposition was performed on a soda lime glass substrate at a temperature of

200°C using 50 W rf power at the target, 20 mTorr Ar pressure, and 30 sccm Ar flow.

168

The deposition time was 2 hours, and the final Cd1-xMgxTe film thickness was ~ 0.3 µm.

For the much higher Mg content sample labeled CGT92, the target was CdTe (60 wt.%) +

MgTe (40 wt.%), and Cd1-xMgxTe deposition was performed on an aluminosilicate glass

substrate at a temperature of 290°C using 50 W rf power at the target, 5 mTorr Ar

pressure, and 30 sccm Ar flow. In this case, the deposition time was 6 hours, and the

Cd1-xMgxTe film thickness was ~ 2.9 µm.

Spectroscopic ellipsometry was performed on these two samples at angles of

incidence of 60° and 65°, respectively. The photon energy range was standard:

0.74~6.50 eV. A two-layer surface-roughness/bulk model for the film was used to

analyze the experimental data (ψ, ∆). The dielectric function of the bulk layer was

modeled using a sum of critical point oscillator terms, each of the form of Eq. (8-1),

given by

ε = εTL + 41j=Σ [Ajexp(iφj)][Γj/(2Ej − 2E − iΓj)]

µj. (8-1)

Here oscillators labeled j = 1, 2, 3, 4 correspond to the E0 (band gap), E1, E1+∆1, and E2

critical point transitions. An additional oscillator, denoted εTL, is modeled using the

Tauc-Lorentz expression in order to simulate a broad background in ε. Each of the

critical point oscillators has five free parameters: amplitude Aj, energy Ej, width Γj, phase

φj, and exponent µj. In this analysis, the focus is on the critical point energies Ej and the

width Γ0 of the lowest band gap critical point.

169

0 1 2 3 4 5 6 7-4

0

4

8

12

<ε2>

<ε1>

<ε 1, ε

2>

Photon Energy (eV)

CdMgTe 42

db = 2908 Å

glass

CdMgTe

roughness ds = 94 Å

ambient

Figure 8-10 Pseudo-dielectric function obtained directly from experimental (ψ, ∆) data using a single interface conversion formula for a Cd1-xMgxTe sample prepared from a target of CdTe (80 wt.%) + MgTe (20 wt.%) (CGT42). The solid line describes experimental data and the dashed line describes the best fit result. The deduced bulk and surface roughness layer thicknesses are shown.

0 1 2 3 4 5 6 7

0

4

8CdMgTe 42

ε2

ε1

ε 1, ε2

Photon Energy (eV)

E0 = 1.71 eV , Γ

E0 = 0.13 eV

Figure 8-11 Best fit analytical dielectric function obtained from an analysis of the experimental (ψ, ∆) data for the Cd1-xMgxTe sample of Fig. 8-10 prepared from a target of CdTe (80 wt.%) + MgTe (20 wt.%) (CGT42).

The energies can provide information on the band gaps, alloying, and strain, whereas

the width of the E0 critical point provides information on defects, grain size, and disorder.

Cd1-xMgxTe

CGT42

Cd1-xMgxTe

CGT42

170

Figure 8-10 shows the pseudo-dielectric function data for the lower Mg content

Cd1-xMgxTe sample (CGT42) and the best fit to these data. Figure 8-11 shows the true

dielectric function of this Cd1-xMgxTe film which is extracted in the best fit. The

deduced band gap, 1.71 eV, and the broadening parameter is 0.13 eV. This band gap

corresponds to a molar composition of x = 0.15 using the relationship established

previously [8-7]. Optical transmission spectroscopy yielded a band gap value in

agreement with the SE result.

0 1 2 3 4 5 6 7

0

4

8CdMgTe 92

<ε2>

<ε1>

< ε

1, ε2 >

Photon Energy (eV)

db = 28887 Å

glass

CdMgTe

roughness ds = 137 Å

ambient

Figure 8-12 Pseudo-dielectric function obtained directly from experimental (ψ, ∆) data using a single interface conversion formula for a Cd1-xMgxTe sample prepared from a target of CdTe (60 wt.%) + MgTe (40 wt.%) (CGT92). The solid line describes experimental data and the dashed line describes the best fit result. The deduced bulk and surface roughness layer thicknesses are shown.

Cd1-xMgxTe

CGT92

171

0 1 2 3 4 5 6 7

0

4

8ε

2

ε1

ε 1, ε2

Photon Energy (eV)

E0 = 1.98 eV, Γ

E0 = 0.16 eV CdMgTe 92

Figure 8-13 Best fit analytical dielectric function obtained from an analysis of the experimental (ψ, ∆) data for the Cd1-xMgxTe sample of Fig. 8-12 prepared from a target of CdTe (60 wt.%) + MgTe (40 wt.%) (CGT92).

Figures 8-12 and 8-13 show the corresponding results for the higher Mg content

sample (CGT92). The band gap of this film is 1.98 eV, and the broadening parameter is

0.16 eV. The band gap corresponds to a composition [8-7] of x = 0.30, indicating a linear

relationship between film molar and target wt. % composition for CdTe and the two alloy

samples with a slope of 0.0075/wt.% MgTe.

Table 8.3 shows the values of the fundamental gap energy E0 and its width, as well

as the energies of the higher energy critical points E1, E1+∆1, E2, for the two Cd1-xMgxTe

samples. Also shown for comparison are the corresponding results for pure CdTe before

and after the CdCl2 treatment. The shifts in the energies of critical points upon CdCl2

treatment for CdTe in this case are due to relaxation of strain and the narrowing of the E0

peak is due to an increase in grain size. It is clear that the E0 band gap increases as the

target alloy composition increases; the use of 20 wt.% MgTe in the target does not lead to

Cd1-xMgxTe

CGT92

172

significant broadening of the E0 transition relative to pure untreated CdTe. However, 40

wt.% MgTe leads to a significant broadening effect as a result of either a smaller grain

size or increased disorder in the film due to alloying. The non-monotonic behavior

observed in the E1 and E1+∆1 higher energy gaps with alloying are likely to be due to

changes in electronic structure as well as to strain in the films.

Table 8.3 Critical point energies and E0 broadening parameters for two as-deposited Cd1-xMgxTe alloys from spectroscopic ellipsometry. Also shown are corresponding results for as-deposited and CdCl2-treated CdTe.

CdTe

CdCl2-treat. CdTe

Untreated

Cd1-xMgxTe 42

(20 wt.% MgTe)

Cd1-xMgxTe 92

(40 wt.% MgTe) E0 (eV) 1.503 1.527 1.710 1.983

Γ(E0) (eV) 0.061 0.089 0.128 0.161

E1 (eV) 3.321 3.199 3.567 3.479 E1+∆1 (eV) 3.913 3.981 3.725 3.816

E2 (eV) 5.214 5.208 5.175 5.143

8.3 Bottom cell material: Cd1-xHgxTe

8.3.1 Cd1-xHgxTe film preparation

Efforts have also focused on the optical characterization of as-deposited Cd1-xHgxTe

films grown at different substrate temperatures for use as a bottom cell absorber material.

The Cd1-xHgxTe films were deposited by rf magnetron sputtering as described in Table

8.1 on 1 mm thick soda-lime glass, using a sputtering target containing CdTe (60 wt.%) +

HgTe (40 wt.%). Individual films were grown at substrate temperatures of 23°C, 44°C,

70°C, 85°C, 97°C, and 153°C. This substrate deposition temperature range is of

173

greatest interest in order to avoid metallic Hg inclusions [8-13]. All such films were

deposited at an Ar pressure of 10 mTorr and an RF power of 27 W; (Dr. Viral Parikh is

acknowledged for deposition of these samples). In addition, CdCl2 post-deposition

treatments were performed on the Cd1-xHgxTe films. The higher temperature of the

post-deposition process in CdTe has been shown to increase the grain size and thus

improve the efficiency of the cells. A two stage process was explored for the

Cd1-xHgxTe consisting of an anneal in an inert gas at 387°C and then a CdCl2 vapor

treatment at the same temperature. Optical characterization was performed in order to

determine the band gap variation with substrate temperature. Thus, ex situ

spectroscopic ellipsometry data were acquired on as-deposited and CdCl2-treated

Cd1-xHgxTe films before and after Br2/methanol etching.

8.3.2 Results and discussion

Figure 8-14 shows the band gaps of the Cd1-xHgxTe films in the as-deposited state for

different substrate temperatures, whereas Fig. 8-15 shows comparisons of the dielectric

functions from the inversion process and from the corresponding analytical model fit.

Table 8.4 also shows the energy and width of the critical point with the strongest peak in

ε2 as described in Fig. 8-15.

174

20 40 60 80 100 120 140 160

0.8

1.0

1.2

1.4

1.6

Ban

dgap

(eV

)

Substrate Temperature (C) Figure 8-14 Band gap of as-deposited thin film Cd1-xHgxTe as a function of the substrate temperatures over the range from 23°C to 153°C. Table 8.4 Energy position and width of the critical point generating the strongest peak in ε2 for as-deposited thin film Cd1-xHgxTe.

Temperature (°C) E (eV) Γ (eV) 23 3.30 1.97 44 3.11 2.50 70 3.44 1.64 85 3.47 1.89 97 3.49 1.77 153 3.51 0.85

175

Figure 8-15 Dielectric functions from mathematical inversion and from the corresponding analytical model fit for as-deposited Cd1-xHgxTe films prepared with different substrate temperatures.

The agreement between the two methods for dielectric function determination

supports the validity of the functional form of the analytical model. Figure 8-14 shows

0 1 2 3 4 5 6 7-2

0

2

4

6

8

10

12

14 g.o. fit inversion inversion

e1,e

2

eV

Ts = 23°CEg = 1.58 eV

0 1 2 3 4 5 6 7-2

0

2

4

6

8

10

12

14 g.o. fit inversion inversion

e1,e

2

eV

Ts = 44°CEg = 1.57 eV

0 1 2 3 4 5 6 7-2

0

2

4

6

8

10

12

14 g.o. fit inversion inversion

e1,e

2

eV

Ts = 70°CEg = 1.51 eV

0 1 2 3 4 5 6 7-2

0

2

4

6

8

10

12

14 g.o. fit inversion inversion

e1,e

2

eV

Ts = 85°CEg = 1.15 eV

0 1 2 3 4 5 6 7-2

0

2

4

6

8

10

12

14 g.o. fit inversion inversion

e1,e

2

eV

Ts = 97°CEg = 1.37 eV

0 1 2 3 4 5 6 7-2

0

2

4

6

8

10

12

14

e1,e

2

eV

g.o. fit inversion inversion

Ts = 153°CEg = 0.81 eV

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that the band gap decreases abruptly at a substrate temperature of about 75°C. At low

temperatures the band gaps are close to that of CdTe, however, the dielectric function

shape is inconsistent with polycrystalline CdTe. It is possible that nanoscale Hg

inclusions exist, giving rise to a broad plasmon resonance centered near 3.5 eV. The

semiconductor component of all films except that grown at the highest temperature must

have a very small grain size or high defect density in accordance with the large

broadening values. In the film prepared at the highest temperature of 153°C,

semiconducting Cd1-xHgxTe with x ~ 0.4 appears to have been obtained with a larger

grain size [8-14]. These trends are confirmed by XRD measurements which reveal that

the films grown at 85°C and 97°C consist of small grains coalesced to form larger grains

with diffuse grain boundaries.

Figure 8-16 presents a comparison of the pseudo-dielectric functions of as-deposited

and CdCl2 treated Cd1-xHgxTe films, including the results for each of the two samples

before and after a single Br2+methanol etching step. The key observations of Fig. 8-16

include (i) the blue shift of the critical point energies for Cd1-xHgxTe upon CdCl2

treatment, indicating the loss of Hg content in the alloy film after the treatment; and (ii)

reduction of the critical point transition widths for the Cd1-xHgxTe upon CdCl2 treatment,

an indication of an increase in grain size or a reduction in defect density. This

post-deposition treatment has proven to be the most challenging aspect of Cd1-xHgxTe and

other alloy film preparation and further work is needed to optimize these processes

specifically for the alloys.

177

0 1 2 3 4 5 6 7-2

0

2

4

6

8

10

12

14

16 As developed As developed 1st etch step CdCl

2 treated

CdCl2 treated 1st etch step

<ε1>

Photon energy (eV)

0 1 2 3 4 5 6 7-6

-4

-2

0

2

4

6

8

10

12

<ε2>

Photon energy (eV)

As developed As developed 1st etch step CdCl

2 treated

CdCl2 treated 1st etch step

E1

E1+∆

1E

2

E1

E1+∆

1E

2

Cd1-x

HgxTe critical points blue shift after CdCl

2 treatment

Figure 8-16 Comparison of the real (left) and imaginary (right) parts of the pseudo-dielectric function of as-deposited and CdCl2 treated CdxHg1-xTe films, including results (a) before and (b) after a single Br2/methanol etching step.

178

Chapter Nine

Summary and Future Directions

9.1 Summary

The most significant accomplishment of this thesis research is the first demonstration

of ex-situ spectroscopic ellipsometry (SE) performed through the glass superstrate for

non-destructive evaluation of CdTe solar cells in the configuration used widely by

industry. This measurement approach avoids the problem of the very rough free surface

of CdTe, which makes quantitative optical measurements from the film side extremely

difficult, if not impossible. The validity of such through-the-glass measurements has

been corroborated by ex-situ SE measurements from the film side of the solar cell

performed destructively after smoothening the CdTe film surface with a succession of

Br2+methanol etching steps. The measurement approach in which the CdTe solar cell is

probed non-destructively through the glass has a wide variety of applications including:

(i) off-line mapping of large area coated glass plates, (ii) on-line monitoring of such

plates, as well as (iii) interpreting quantum efficiency measurements in terms of optical

and electronic losses.

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In Chapter 3 of this thesis, ex-situ SE was shown to provide the four sets of optical

properties of the materials that comprise the Pilkington TEC-15 glass superstrate of the

CdTe solar cell. These materials include the soda lime glass superstrate material, and

the SnO2, SiO2, and SnO2:F thin film materials deposited in on-line coating processes.

The dielectric functions of these four materials were measured from the film side in each

case, and they serve as a database that enables analysis of CdCl2-treated and untreated

CdTe solar cells in measurements through the glass or from the film side. Both

ellipsometry and transmittance experiments have been performed on the set of TEC-15

samples, and the optical models have been selected for each material so as to fit the

measured ellipsometry and transmittance spectra simultaneously and thereby provide

accurate dielectric functions of the component materials of the superstrate.

In the thesis research described in Chapter 4, a Br2+methanol step-wise chemical

etching process has been developed that both reduces the bulk thickness of the CdTe and

smoothens its surface, but without introducing measurable changes in the underlying thin

film structure. In studies that demonstrate this capability, in-situ real time SE and

ex-situ SE measurements have been compared, the latter in conjunction with repetitive

chemical etching. By comparing the CdTe thin film structure during deposition as

monitored by real time SE with that during the etching process using ex-situ SE, it has

been shown that the etching process is the reverse of the deposition process. This means

that for each CdTe bulk layer thickness during growth or etching, the underlying bulk

layer of the sample has the same void fraction profile.

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In Chapter 5, the Br2+methanol etching procedure has been demonstrated for the

analysis of CdTe structural modifications by CdCl2 treatments. This approach is

preferred over in-situ real time SE studies of CdCl2 treatment because in the real time

studies many aspects of the sample structure are likely to change simultaneously, making

interpretation extremely difficult. In Chapter 5, the power of Br2+methanol etch

profiling was demonstrated first in studies of ~3000 Å thick CdTe films on crystalline Si

substrates processed in three different ways: (i) as-deposited, (ii) thermally annealed in Ar

gas for 30 min, and (iii) CdCl2 treated for 5 min. For such films, depth profiles in the

relative void volume fraction and the critical point energies and widths as functions of

CdTe bulk layer thickness during etching by Br2+methanol have provided information on

microstructure, grain size, and strain. As a result, it has been demonstrated that the

CdCl2 treatment relaxes the strain in the CdTe network and generates a relatively uniform

grain structure throughout the thickness of the thin films. Differences in the depth

profiles between Ar annealed and CdCl2 treated films suggest that in the former case, a

fine grained structure is retained at the surface.

Also in Chapter 5, the optical properties of CdCl2 treated CdTe and CdS were

presented, and comparisons made with the optical properties of the as-deposited films.

The changes that occur in the optical properties of CdTe and CdS upon CdCl2 treatment

are significant and demonstrate the necessity of expressing these optical properties in

terms of photon-energy independent parameters that describe the critical point features.

These parameters in turn can be expressed in terms of the physical properties such as

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mean free path or grain size and stress. With such a database, it then becomes possible

to use the physical properties as free parameters in the optical analysis of CdCl2-treated

solar cells. This more advanced approach will be undertaken in future work.

In the research effort described in Chapter 6, the database consisting of optical

properties of the TEC-15 and semiconductor components of the CdTe solar cell has been

applied to analyze the CdS/CdTe solar cell structure obtained after CdCl2 post-deposition

treatment. The measurements of the solar cell structure were performed

non-destructively from the glass superstrate side using a 60° prism contacted to the glass

superstrate with index matching fluid. As described earlier in this summary, the

metrological capability developed here is the most significant accomplishment of this

thesis research due to its potential application for on-line monitoring and off-line

mapping of complete modules.

Also in Chapter 6, the application of ex-situ spectroscopic ellipsometry was

described for analyzing the structure of the thin film CdTe solar cell destructively using a

succession of Br2+methanol etching treatments. In this way, the optical properties of the

CdTe component of the cell could be determined as a function of depth from the surface

and proximity to the CdS/CdTe interface. Using this method of depth profiling, a better

understanding of the overall film structure could be obtained in comparison with the

non-destructive method. In addition to providing a depth profiling capability, the

destructive method has also been useful in corroborating the structure measured

non-destructively through the glass superstrate.

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In Chapters 7 and 8, the application of ex-situ spectroscopic ellipsometry to more

advanced problems in the development of CdTe-based solar cell materials and devices

was described.

First, in the research described in Chapter 7, ex-situ SE has provided the thicknesses

and structural properties of CdTe solar cells in the substrate configuration in which case

the CdTe is deposited directly on opaque Mo metal. Although ex-situ SE in the

substrate configuration has the advantage that there is no overlying glass to limit the

spectral range that reaches the semiconductors, the basic problem in this configuration is

the surface roughness on the top-most transparent conductor, or CdS layer in the full or

partial device configuration, respectively. There is less motivation at this time to

address these issues since all current manufacturing processes for CdTe solar cells exploit

the superstrate configuration.

Second, in the research described in Chapter 8, ex-situ SE has been applied to study

the CdTe based ternary alloys Cd1-xMnxTe, Cd1-xMgxTe, and Cd1-xHgxTe, which are

potential absorber layer components of sputtered II-VI tandem solar cells. In this study

it was shown that ex-situ SE could provide the critical point band gaps and broadening

parameters from which the success of alloying could be assessed. By repeating such

measurements after the CdCl2 treatments, the ability of such treatments to generate the

desired increase in grain size while maintaining the desired alloy composition and band

gap could also be assessed. As a result, it was shown that ex-situ SE could be used in

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conjunction with absorber materials fabrication for the development of sputtering and

post-deposition processes to be adopted in device structures.

9.2 Future directions

The most pressing goal of future research is to identify a robust optical model that

can be used for all CdTe based solar cells such that small changes in materials properties

such as CdS and CdTe layer thicknesses, void fractions, mean free paths or grain sizes,

strain, and uniformity can be determined non-invasively in the actual solar cell

configuration. Possible modifications of the TCO layers of the superstrate by CdS

over-deposition is also of interest. Although accuracy is not necessarily needed,

sensitivity to changes is a key goal. If the optical model can be optimized, then it may

be possible to achieve accuracy and sensitivity simultaneously. Along the way, it will

be helpful to correlate spectroscopic ellipsometry (SE) results with other methods such as

cross-sectional transmission electron microscopy (XTEM) and secondary ion mass

spectrometry (SIMS) in order to better understand the nature of the interactions at the

CdS/CdTe and SnO2:F/CdS interfaces in the solar cells. In particular, it is important to

improve the SnO2:F/CdS interface model and understand how the SnO2:F may be

modified by CdS over-deposition and post-deposition treatments. In this section, more

detailed suggestions for future studies to continue this thesis research will be reviewed in

order of the relevant chapter.

184

Additional improvement in the analysis of TCO-coated glass superstrates, an

extension of the TEC glass studies of Chapter 3, is an important direction for future

research. For the complete TCO stack, the simulated spectra are not in close agreement

with experimental data over two regions of the photon energy range. The largest

deviations occur at the lowest energies (< 1.0 eV) where the Drude behavior dominates.

Four different complexities may be evaluated in greater detail in the future so as to

improve the fitting in this region: (i) additional layers in the optical model, such as

interface roughness between pairs of bulk layers; (ii) additional terms in the analytical

model for the top-most SnO2:F, which is the most strongly absorbing layer; (iii)

non-uniformity over the area of the beam due to macroscopic scale roughness; and (iv)

non-uniformity with depth due, for example, to a void volume fraction or free carrier

concentration gradient. Although some of these approaches have been attempted

individually, they have not been evaluated in combination. Also in the region near

4.50-4.75 eV, where a transition from SnO2:F semi-transparency to opacity is observed,

improved modeling results will require a closer match between the regimes where an

analytical function is assumed for the dielectric function and where exact inversion is

applied. This may require (i) an improved analytical model for the absorption onset

and/or (ii) more advanced inversion methods that incorporate not only the surface

roughness thickness, but also the bulk layer thickness.

The focus in this thesis has been on the development of an optical database for

TEC-15, the most common coated superstrate used for CdTe solar cells. Other types of

185

coated TEC glass deserve similar attention, such as TEC-7 and TEC-8, as well as coated

glass from other manufacturers. TEC-7 and TEC-8 may be used for solar cells in which

light scattering or "haze" is desirable, e.g., cells with thin (< 1 µm) CdTe layers or with

thin film silicon absorber layers. Results reported in Chapter 3 suggest that the optical

properties of the top-most SnO2:F of TEC-7 and TEC-8, differ from those of TEC-15, and

these TEC glass types should be reanalyzed on the basis of this assumption. Of recent

interest are the high resistivity transparent top layers typically undoped or weakly doped

SnO2, called "HRT" or "buffer" layers, which are incorporated as a fourth layer of

experimental TEC glass stacks. The ultimate challenge is to characterize the optical

properties of these layers in the full multilayer configuration consisting of

glass/SnO2/SiO2/SnO2:F/HRT. In summary, future research must involve standardizing

the analysis procedure for TEC-15 so that it is applicable for other TEC glasses.

Furthermore, standardized procedures are also needed for the analysis of the four-layer

stacks, applied to cases in which samples of the HRT layer on simpler substrates are

unavailable.

In Chapter 4, step-wise Br2+methanol etching was evaluated for depth-profiling of

CdCl2 treated and untreated CdTe thin film materials and solar cells while retaining a

smooth surface for high quality optical measurements throughout the process. In this

chapter, it was shown how a residual amorphous tellurium (a-Te) layer ~13-14 Å in

effective thickness could be detected and characterized under certain circumstances.

The presence of this layer was neglected in the depth-profiling studies of CdTe thin film

186

materials in Chapter 5 and solar cells in Chapter 6. This simplification was based on

modeling performed for very thick CdTe layers, namely that the impact of the a-Te layer

on the deduced film structure is minimal. Further work needs to be done, however, in

order to evaluate the validity of this simplification under all circumstances. For

example, when the surface roughness region of a CdTe solar cell is completely etched

away, the void fraction in the CdTe reaches a sharp minimum. Future work must be

performed to determine if this minimum continues to be observed when a-Te is included

in the optical model, or if it is an artifact of neglecting the a-Te. In addition, the effect

on critical point analyses that results from incorporating a-Te in the optical model must

be evaluated. A more detailed analysis involving analytical removal of a known

thickness of a-Te may provide a better understanding of the CdTe solar cell depth profiles

in the mean free path or grain size and film strain. Although very good consistency has

been observed in the depth profiles for the CdTe material in Chapter 5, the depth profiles

for the CdTe solar cells in Chapter 6, in particular the critical point energies, were not

easily interpretable, possibly as a result of simultaneous variations in film strain and

sulfur in-diffusion. Very accurate critical point analyses will be needed in the future to

separate out these effects.

In Chapter 5, clear differences between the optical properties of CdCl2 treated and

untreated CdTe have been characterized and understood in terms of differences in strain,

which shifts the critical point energies, and differences in defect density or grain size,

which changes the broadening parameters. For CdS, however, the dielectric function of

187

a thin film as-deposited on a fused silica prism and measured through the prism differs

considerably from those of thin films as-deposited on crystalline Si substrates and

measured from the film side at a thickness of 500 Å. The motivation for such a study

was to characterize the change in dielectric function of CdS upon CdCl2 treatment using a

configuration that corresponds more closely to the actual device, i.e., an underlying oxide

and an overlying CdTe layer such that the free surface of the CdS is not exposed during

the treatment. In the prism deposition experiment described in Chapter 6, the origin of

the differences in the as-deposited materials must be studied in greater detail in the future

through additional experimentation. The low amplitude of the dielectric function in the

high energy range is of particular interest. Even the CdCl2 treatment does not restore

this amplitude to the level observed for CdS deposited on crystalline Si and measured

from the film side. Future experiments may determine if this effect is (i) due to extrinsic

differences in the deposition process, e.g., higher interface contamination levels or lower

substrate temperature associated with deposition on the prism, (ii) specific to the interface

structure of CdS on fused SiO2, or (iii) intrinsic to the CdS interface in general which

becomes evident using light from the substrate side with a very short penetration depth

(photon energies > 4 eV).

The future directions designed to extend studies of the step-wise etching for

materials and solar cells decribed in Chapters 5 and 6, respectively, must focus on the role

of temperature and time in the Ar annealing and CdCl2 treatment processes. For the

thinner CdTe materials on crystalline substrates, one may be able to establish the nature

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of the grain growth processes. For example, in the case of annealing in Ar gas, grain

growth appears to start from the substrate interface with pinned grain boundaries at the

surface, whereas for CdCl2 treatment, the mechanism is clearly different with both

near-surface and sub-surface grain growth occurring. In the case of the solar cell

structures, by exploring the kinetics versus temperature and time one may be able to

separate out effects of grain growth in CdTe from those of CdS in-diffusion.

In the research described Chapter 7, a novel approach for real time spectroscopic

ellipsometry (RTSE) analysis has been applied to a CdTe deposition in the substrate

configuration on Mo. In this analysis, which involves a synthesis of exact inversion and

least squares regression analysis methods, excellent fits to the data have been obtained

with a low mean square error. In spite of these excellent fits, the resulting inverted

dielectric functions show artifacts indicating that improvements in the multilayer model

for the substrate/film are required. These improvements may include (i) incorporation

of thickness non-uniformity over the cross-section of the optical beam or (ii) application

of a multilayer or graded model to describe the CdTe/Mo interface or even an alternative

effective medium theory. Because of the uncertainty involved in modeling rough

interfaces between the CdTe and its substrate, a case in point being the CdTe/Mo

interface, subsequent studies to extract high accuracy dielectric functions of the CdTe

have used the smoothest possible substrates -- single crystal silicon wafers. In the future,

if complete solar cells are to be studied successfully by real time SE, such issues

involving rough interfaces must addressed comprehensively.

189

As described in the inroductory pararaph of this section, the key studies in Chapters 6

and 7 on ex situ SE of CdTe solar cells in the superstrate and substrate configurations

represent works in progress, and significant improvements are to be expected through

additional future studies. Promising future directions will be outlined in the following

paragraphs. This discussion provides a roadmap that future research should follow,

continuing from the foundation established through this initial thesis research. It is also

recommended, because of the complexity of the models being developed, that a

step-by-step procedure be undertaken as described in Chapters 6 and 7 in which case the

number of free parameters of the model is increased successively. With this approach,

the success or failure of the suggestions for improvement made below can be

quantitatively evaluated.

Tin side characteristics of the glass superstrate

Analysis of through-the-glass spectroscopic ellipsometry on superstrate CdTe solar

cells may benefit from a detailed analysis of the reflection from the Sn side of the glass,

i.e., the side through which the light enters. The modeling of the bare soda lime glass as

described in Chapter 3 was performed using uncoated glass from the side opposite to the

Sn side. The focus of an improved analysis will be on characterization of the optical

properties of the Sn side using the dielectric function of the opposite side from Chapter 3

as the underlying base material. One or two layers may be required to characterize the

residual Sn clusters on the glass surface as well as atomic Sn diffused into the glass.

190

The Sn side reflection must be taken into account carefully when considering the

polarization changes that occur when the incident and specularly reflected light beams,

the latter from the glass/film interface, crosses the Sn side interface. In addition to the

more detailed analysis of the Sn side of the glass for through-the-glass SE, it will also be

important to characterize the strain in the glass. The effect of strain in the superstrate

glass is similar to that of strained windows in real time ellipsometry, and the successful

correction procedures are expected to consist of zone averaged measurements as well as

an offset correction in the ellipsometric angle ∆.

SnO2:F/CdS interface

The surface roughness on the TEC-15 SnO2:F is up to ~300 Å thick, and when high

resistivity transparent layers are added to the top of the TEC glass, the roughness can

increase even further. This surface roughness is likely to appear as interface roughness

when the CdS is deposited on the superstrate surface. As the superstrate of the CdTe

solar cell becomes rougher, it becomes more difficult to determine all the characteristics

of the solar cell because one must use thicker effective medium layers at the rough

interfaces, and effective medium theories generally involve considerable uncertainty. In

the analysis of the superstrate solar cell, however, when one attempts to incorporate a

SnO2:F/CdS effective medium mixture as an interface roughness layer, the thickness of

this layer expands to the entire thickness of the SnO2:F, and the CdS volume fraction

decreases to relatively small values. The interpretation of this observation is that the

dominant effect of the interaction between the SnO2:F and CdS is not interface roughness,

191

but rather modification of the SnO2:F layer either in the CdS deposition process or in the

CdCl2 treatment. Future experiments for modeling improvement include characterizing

TEC-15 glass not only before solar cell deposition, but also after all cell processing, in

the latter case after removing both the CdTe and CdS layers by etching. In such

experiments, one may be able to identify the optical characteristics of the SnO2:F layer

that change upon cell processing, e.g., free carrier concentration, optical absorption onset,

and/or void fraction, as well as the key processing parameters that lead to the change in

optical properties. Once this information is available, then it may be possible to include

both interface roughness and SnO2:F modification in the ex situ SE modeling of the solar

cell.

Optical properties of CdS and CdTe

The poorer fits to the ex situ ellipsometric spectra for the superstrate and substrate

solar cells in the neighborhood of the CdTe and CdS fundamental band gaps and high

energy critical points may be attributed to mean free paths, grain sizes, or strain levels in

the solar cell layers that may be different than those in the layers used to extract the

reference dielectric functions. Layer interdiffusion may also contribute to the

differences. As a result, improvements in fitting can be expected if such effects can be

incorporated in the modeling. For example, for the superstrate solar cell of Chapter 6,

the fringe pattern in ψ just below the band gap is more pronounced in the data than in the

model, an indication of a longer mean free path or larger grain size in the solar cell than

in the CdTe material used for reference data. Furthermore, for the substrate solar cell

192

analysis of Chapter 7, the CdS layer band gap is noticeably lower and the CdTe band gap

is higher in the experimental data than in the model, possibly indicating that the stress in

the CdS is lower and that in the CdTe is higher than in the reference materials. These

simple observations made on the basis of (ψ, ∆) comparisons could be made quantitative

through a parameterization of the CdS and CdTe reference dielectric functions explicitly

in terms of mean free path, stress, and alloying generated by inter-diffusion.

CdS/CdTe interface thickness

The thickness of the CdS/CdTe interface layer for both superstrate and substrate solar

cells has been observed to lie in the range of 800-1400 Å. In the case of the superstrate

solar cells, this thickness is significantly greater than the expected interface roughness

layer if the thin CdS layer were to conformally cover the SnO2:F of the TEC-15 without

generation of additional roughness. As an alternative approach to using a single layer

model for the CdS/CdTe, a three layer model may be implemented in future research.

The layers at the interfaces to the bulk CdS and CdTe layers would be CdS-rich and

CdTe-rich layers, respectively, representing the interdifusion regions, and the intervening

layer would represent the interface roughness. It would be reasonable to fix the

composition of the latter at ~0.5/0.5 CdS/CdTe for stability in the modeling when using

three interface layers.

Two different approaches could be used for modeling the optical functions of the two

interface layers in the three layer model. The first method is the simplest, involving the

use of effective medium theories that incorporate small volume fractions of CdTe in CdS

193

and CdS in CdTe. This approach may be applicable if interdiffusion occurs through the

grain boundaries, and thin regions at the boundary regions then assume the composition

of the adjoining layer. Alternatively, ternary alloys of CdS1-x Tex with a small Te content

in CdS, and CdTe1-xSx with a small S content in CdTe could be assumed based on a

model of uniform bulk interdiffusion. .For this latter approach, the dielectric functions of

metastable ternary alloys are available; however. future efforts must focus on determining

the dielectric functions of the stable alloy phases that form at the elevated temperatures of

solar cell processing.

CdTe properties and roughness thickness

For future improvement of the ex situ analysis of both superstrate and substrate CdTe

solar cells, the ability to incorporate void profiles of various functional forms must be

included in the modeling. As detailed in Chapters 4-6, real time SE measurements have

shown clearly that complicated void profiles can exist in the as-deposited CdTe films and

solar cells, and that these profiles are suppressed in the CdCl2 treatment processes. The

results of Chapter 6 do suggest small deviations in density for the CdCl2 treated CdTe,

however, which may lead to significant effects in ex situ modeling when accumulated

throughout the thickness of 2-3 µm films. Also for the superstrate solar cell analyzed

through the glass in Chapter 6, the surface roughness on the CdTe at the back of the solar

plays an important role due to its effect on the back-reflected light beam. In fact, the

CdTe roughness parameters are the fifth and sixth most important ones in the

12-parameter model. Improvements may be possible in this case through the use of

194

multiple layers to describe the roughness, or even a graded layer. It is also of interest to

test effective medium approximations other than that of Bruggeman for comparisons of

the fitting quality.

The p+ doped back contact

For the CdTe solar cell in the superstrate configuration studied by ex situ SE analysis

(Chapter 6), the p+ back contact treatment consisting of in-diffusion of a 30 Å layer of Cu

has not been applied. It is of interest to explore the optical properties of this back

contact material to determine if changes can be detected in the mean free path as derived

from the widths of the critical points. Such an experimentation is best performed after

CdCl2 treatment followed by a Br2+methanol etch that leads to a smooth and

well-characterized surface, from which it is easiest to detect changes upon Cu

in-diffusion.

For the CdTe solar cell in the substrate configuration, as described in Chapter 7, the

p+ back contact ZnTe:Cu has been studied in detail. This thin film material shows clear

evidence of heavy doping in the form of a significantly broadened absorption onset. In

fact, if this material is to be used as a transparent back contact, improvements in optical

properties will be needed since a significant absorption tail exists even below 2 eV.

Reduction in low energy absorption may be possible through a reduction in the doping

level. Finally, analysis of the p+ back contacts used in superstrate and substrate solar

cells may benefit from infrared spectroscopic ellipsometry which may be able to detect

the free carrier absorption in the contact regions or in discrete heavily doped layers.

195

A final area of research that deserves additional future study follows from the alloy

research of Chapter 8. In general for future progress in this area, a closer correlation

between the ex situ SE measurements of the alloys before and after CdCl2 treatment and

the device measurements would be helpful in order to establish the relationships between

fundamental materials properties and device performance. Both real time SE

measurements and Br2+methanol etching experiments would also be helpful to establish

the role of the CdCl2 treatment in modifying the structure of the film throughout the

depth. Such experiments may help to guide future improvements in the post-depositon

treatment processes. Finally, solar cell depositions using individual binary targets would

enable continuous compositional ranges to be obtained in a single deposition across the

superstrate surface, and such materials and cells can then be characterized by mapping SE

in terms of their band gaps. This approach would enable expeditious study and

subsequent optimization of alloy composition not possible with discrete ternary targets.

196

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207

Appendix A Dielectric functions

A.1 Dielectric function of uncoated soda lime glass

nm n k 190.76 1.649 1.65E-05 192.33 1.6458 1.77E-05 193.91 1.6428 1.91E-05 195.49 1.6398 2.06E-05 197.06 1.6369 2.24E-05 198.64 1.6341 2.43E-05 200.22 1.6313 2.64E-05 201.8 1.6287 2.87E-05

203.37 1.6261 3.12E-05 204.95 1.6236 3.39E-05 206.53 1.6212 3.68E-05 208.11 1.6189 3.99E-05 209.69 1.6166 4.32E-05 211.27 1.6144 4.67E-05 212.85 1.6123 5.03E-05 214.43 1.6102 5.42E-05 216.01 1.6081 5.82E-05 217.59 1.6062 6.23E-05 219.18 1.6042 6.66E-05 220.76 1.6024 7.09E-05 222.34 1.6006 7.53E-05 223.92 1.5988 7.98E-05 225.51 1.5971 8.43E-05 227.09 1.5954 8.88E-05 228.67 1.5938 9.33E-05 230.26 1.5922 9.77E-05 231.84 1.5906 0.00010202 233.42 1.5891 0.00010622 235.01 1.5877 0.00011026 236.59 1.5862 0.00011413 238.18 1.5848 0.0001178 239.76 1.5835 0.00012124 241.35 1.5821 0.00012444 242.94 1.5808 0.00012737 244.52 1.5796 0.00013002 246.11 1.5783 0.00013237 247.69 1.5771 0.00013442 249.28 1.5759 0.00013617 250.87 1.5748 0.0001376 252.45 1.5736 0.00013873

254.04 1.5725 0.00013957 255.63 1.5715 0.00014012 257.22 1.5704 0.00014042 258.8 1.5694 0.00014049 260.39 1.5684 0.0001404 261.98 1.5674 0.00014013 263.57 1.5664 0.00013962 265.16 1.5655 0.00013884 266.74 1.5646 0.00013778 268.33 1.5637 0.00013641 269.92 1.5628 0.00013473 271.51 1.5619 0.00013275 273.1 1.5611 0.00013045 274.69 1.5603 0.00012785 276.28 1.5595 0.00012497 277.87 1.5587 0.0001218 279.46 1.5579 0.00011837 281.05 1.5571 0.0001147 282.64 1.5564 0.00011081 284.23 1.5556 0.00010673 285.82 1.5549 0.00010247 287.41 1.5542 9.81E-05

289 1.5535 9.36E-05 290.59 1.5529 8.90E-05 292.18 1.5522 8.43E-05 293.77 1.5515 7.97E-05 295.36 1.5509 7.50E-05 296.95 1.5503 7.04E-05 298.54 1.5497 6.58E-05 300.13 1.5491 6.14E-05 301.72 1.5485 5.70E-05 303.31 1.5479 5.27E-05 304.9 1.5473 4.86E-05 306.49 1.5468 4.47E-05 308.08 1.5462 4.10E-05 309.68 1.5457 3.74E-05 311.27 1.5451 3.40E-05 312.86 1.5446 3.08E-05 314.45 1.5441 2.78E-05 316.04 1.5436 2.50E-05 317.63 1.5431 2.25E-05

319.22 1.5426 2.01E-05 320.81 1.5422 1.79E-05 322.41 1.5417 1.59E-05

324 1.5412 1.41E-05 325.59 1.5408 1.24E-05 327.18 1.5403 1.10E-05 328.77 1.5399 9.62E-06 330.36 1.5395 8.43E-06 331.95 1.539 7.37E-06 333.55 1.5386 6.43E-06 335.14 1.5382 5.61E-06 336.73 1.5378 4.88E-06 338.32 1.5374 4.25E-06 339.91 1.537 3.70E-06 341.5 1.5366 3.23E-06 343.1 1.5362 2.81E-06 344.69 1.5359 2.46E-06 346.28 1.5355 2.16E-06 347.87 1.5351 1.90E-06 349.46 1.5348 1.68E-06 351.05 1.5344 1.50E-06 352.64 1.5341 1.34E-06 354.24 1.5337 1.21E-06 355.83 1.5334 1.09E-06 357.42 1.5331 9.99E-07 359.01 1.5328 9.20E-07 360.6 1.5324 8.53E-07 362.19 1.5321 7.97E-07 363.78 1.5318 7.49E-07 365.38 1.5315 7.08E-07 366.97 1.5312 6.74E-07 368.56 1.5309 6.44E-07 370.15 1.5306 6.18E-07 371.74 1.5303 5.96E-07 373.33 1.53 5.76E-07 374.92 1.5297 5.59E-07 376.51 1.5295 5.43E-07 378.1 1.5292 5.28E-07 379.69 1.5289 5.15E-07 381.29 1.5286 5.03E-07 382.88 1.5284 4.91E-07

208

384.47 1.5281 4.81E-07 386.06 1.5279 4.70E-07 387.65 1.5276 4.61E-07 389.24 1.5274 4.51E-07 390.83 1.5271 4.42E-07 392.42 1.5269 4.34E-07 394.01 1.5266 4.26E-07 395.6 1.5264 4.18E-07

397.19 1.5262 4.10E-07 398.78 1.5259 4.02E-07 400.37 1.5257 3.95E-07 401.96 1.5255 3.88E-07 403.55 1.5253 3.81E-07 405.14 1.525 3.74E-07 406.73 1.5248 3.68E-07 408.32 1.5246 3.61E-07 409.91 1.5244 3.55E-07 411.5 1.5242 3.49E-07

413.09 1.524 3.43E-07 414.68 1.5238 3.37E-07 416.27 1.5236 3.32E-07 417.86 1.5234 3.27E-07 419.45 1.5232 3.21E-07 421.04 1.523 3.16E-07 422.63 1.5228 3.11E-07 424.22 1.5226 3.07E-07 425.81 1.5224 3.02E-07 427.4 1.5222 2.98E-07

428.99 1.522 2.93E-07 430.57 1.5219 2.89E-07 432.16 1.5217 2.85E-07 433.75 1.5215 2.81E-07 435.34 1.5213 2.77E-07 436.93 1.5212 2.74E-07 438.52 1.521 2.70E-07 440.11 1.5208 2.67E-07 441.7 1.5206 2.64E-07

443.28 1.5205 2.60E-07 444.87 1.5203 2.57E-07 446.46 1.5202 2.54E-07 448.05 1.52 2.52E-07 449.64 1.5198 2.49E-07 451.22 1.5197 2.46E-07 452.81 1.5195 2.44E-07 454.4 1.5194 2.42E-07

455.99 1.5192 2.40E-07 457.58 1.5191 2.37E-07 459.16 1.5189 2.35E-07 460.75 1.5188 2.34E-07 462.34 1.5186 2.32E-07 463.93 1.5185 2.30E-07 465.51 1.5183 2.29E-07 467.1 1.5182 2.27E-07 468.69 1.5181 2.26E-07 470.27 1.5179 2.25E-07 471.86 1.5178 2.24E-07 473.45 1.5176 2.22E-07 475.04 1.5175 2.22E-07 476.62 1.5174 2.21E-07 478.21 1.5172 2.20E-07 479.8 1.5171 2.19E-07 481.38 1.517 2.19E-07 482.97 1.5169 2.18E-07 484.56 1.5167 2.18E-07 486.14 1.5166 2.18E-07 487.73 1.5165 2.18E-07 489.31 1.5164 2.18E-07 490.9 1.5162 2.18E-07 492.49 1.5161 2.18E-07 494.07 1.516 2.18E-07 495.66 1.5159 2.19E-07 497.24 1.5158 2.19E-07 498.83 1.5156 2.20E-07 500.42 1.5155 2.20E-07

502 1.5154 2.21E-07 503.59 1.5153 2.22E-07 505.17 1.5152 2.23E-07 506.76 1.5151 2.24E-07 508.34 1.515 2.25E-07 509.93 1.5149 2.27E-07 511.51 1.5147 2.28E-07 513.1 1.5146 2.30E-07 514.68 1.5145 2.31E-07 516.27 1.5144 2.33E-07 517.85 1.5143 2.35E-07 519.44 1.5142 2.36E-07 521.02 1.5141 2.38E-07 522.61 1.514 2.41E-07 524.19 1.5139 2.43E-07 525.78 1.5138 2.45E-07

527.36 1.5137 2.47E-07 528.95 1.5136 2.50E-07 530.53 1.5135 2.53E-07 532.12 1.5134 2.55E-07 533.7 1.5133 2.58E-07 535.28 1.5132 2.61E-07 536.87 1.5131 2.64E-07 538.45 1.513 2.67E-07 540.04 1.5129 2.71E-07 541.62 1.5129 2.74E-07 543.21 1.5128 2.77E-07 544.79 1.5127 2.81E-07 546.37 1.5126 2.85E-07 547.96 1.5125 2.89E-07 549.54 1.5124 2.92E-07 551.12 1.5123 2.97E-07 552.71 1.5122 3.01E-07 554.29 1.5121 3.05E-07 555.87 1.5121 3.09E-07 557.46 1.512 3.14E-07 559.04 1.5119 3.19E-07 560.63 1.5118 3.23E-07 562.21 1.5117 3.28E-07 563.79 1.5116 3.33E-07 565.37 1.5116 3.38E-07 566.96 1.5115 3.44E-07 568.54 1.5114 3.49E-07 570.12 1.5113 3.54E-07 571.71 1.5112 3.60E-07 573.29 1.5112 3.66E-07 574.87 1.5111 3.72E-07 576.46 1.511 3.78E-07 578.04 1.5109 3.84E-07 579.62 1.5108 3.90E-07 581.2 1.5108 3.97E-07 582.79 1.5107 4.03E-07 584.37 1.5106 4.10E-07 585.95 1.5105 4.17E-07 587.53 1.5105 4.23E-07 589.12 1.5104 4.31E-07 590.7 1.5103 4.38E-07 592.28 1.5103 4.45E-07 593.86 1.5102 4.52E-07 595.45 1.5101 4.60E-07 597.03 1.51 4.68E-07

209

598.61 1.51 4.76E-07 600.19 1.5099 4.84E-07 601.78 1.5098 4.92E-07 603.36 1.5098 5.00E-07 604.94 1.5097 5.09E-07 606.52 1.5096 5.17E-07 608.1 1.5096 5.26E-07

609.69 1.5095 5.35E-07 611.27 1.5094 5.44E-07 612.85 1.5094 5.53E-07 614.43 1.5093 5.62E-07 616.01 1.5092 5.72E-07 617.6 1.5092 5.81E-07

619.18 1.5091 5.91E-07 620.76 1.509 6.01E-07 622.34 1.509 6.11E-07 623.92 1.5089 6.21E-07 625.5 1.5088 6.32E-07

627.09 1.5088 6.42E-07 628.67 1.5087 6.53E-07 630.25 1.5087 6.64E-07 631.83 1.5086 6.74E-07 633.41 1.5085 6.86E-07 634.99 1.5085 6.97E-07 636.58 1.5084 7.08E-07 638.16 1.5084 7.20E-07 639.74 1.5083 7.31E-07 641.32 1.5082 7.43E-07 642.9 1.5082 7.55E-07

644.48 1.5081 7.67E-07 646.06 1.5081 7.80E-07 647.65 1.508 7.92E-07 649.23 1.508 8.05E-07 650.81 1.5079 8.17E-07 652.39 1.5078 8.30E-07 653.97 1.5078 8.43E-07 655.55 1.5077 8.56E-07 657.13 1.5077 8.70E-07 658.71 1.5076 8.83E-07 660.29 1.5076 8.97E-07 661.88 1.5075 9.11E-07 663.46 1.5075 9.25E-07 665.04 1.5074 9.39E-07 666.62 1.5074 9.53E-07 668.2 1.5073 9.67E-07

669.78 1.5072 9.82E-07 671.36 1.5072 9.96E-07 672.94 1.5071 1.01E-06 674.52 1.5071 1.03E-06 676.1 1.507 1.04E-06 677.68 1.507 1.06E-06 679.26 1.5069 1.07E-06 680.85 1.5069 1.09E-06 682.43 1.5068 1.10E-06 684.01 1.5068 1.12E-06 685.59 1.5067 1.13E-06 687.17 1.5067 1.15E-06 688.75 1.5066 1.17E-06 690.33 1.5066 1.18E-06 691.91 1.5065 1.20E-06 693.49 1.5065 1.22E-06 695.07 1.5064 1.23E-06 696.65 1.5064 1.25E-06 698.23 1.5064 1.27E-06 699.81 1.5063 1.28E-06 701.39 1.5063 1.30E-06 702.97 1.5062 1.32E-06 704.55 1.5062 1.34E-06 706.13 1.5061 1.35E-06 707.71 1.5061 1.37E-06 709.29 1.506 1.39E-06 710.87 1.506 1.41E-06 712.45 1.5059 1.43E-06 714.03 1.5059 1.44E-06 715.61 1.5058 1.46E-06 717.19 1.5058 1.48E-06 718.77 1.5058 1.50E-06 720.35 1.5057 1.52E-06 721.93 1.5057 1.54E-06 723.51 1.5056 1.55E-06 725.09 1.5056 1.57E-06 726.67 1.5055 1.59E-06 728.25 1.5055 1.61E-06 729.83 1.5055 1.63E-06 731.41 1.5054 1.65E-06 732.99 1.5054 1.67E-06 734.57 1.5053 1.69E-06 736.15 1.5053 1.71E-06 737.73 1.5052 1.73E-06 739.31 1.5052 1.75E-06

740.89 1.5052 1.77E-06 742.47 1.5051 1.79E-06 744.05 1.5051 1.81E-06 745.63 1.505 1.83E-06 747.21 1.505 1.85E-06 748.78 1.505 1.87E-06 750.36 1.5049 1.89E-06 751.94 1.5049 1.91E-06 753.52 1.5048 1.93E-06 755.1 1.5048 1.95E-06 756.68 1.5048 1.97E-06 758.26 1.5047 1.99E-06 759.84 1.5047 2.01E-06 761.41 1.5046 2.03E-06 762.99 1.5046 2.05E-06 764.57 1.5046 2.07E-06 766.15 1.5045 2.09E-06 767.73 1.5045 2.12E-06 769.31 1.5045 2.14E-06 770.88 1.5044 2.16E-06 772.46 1.5044 2.18E-06 774.04 1.5043 2.20E-06 775.62 1.5043 2.22E-06 777.2 1.5043 2.24E-06 778.77 1.5042 2.26E-06 780.35 1.5042 2.28E-06 781.93 1.5042 2.31E-06 783.5 1.5041 2.33E-06 785.08 1.5041 2.35E-06 786.66 1.5041 2.37E-06 788.24 1.504 2.39E-06 789.81 1.504 2.41E-06 791.39 1.504 2.43E-06 792.97 1.5039 2.45E-06 794.54 1.5039 2.47E-06 796.12 1.5038 2.50E-06 797.7 1.5038 2.52E-06 799.27 1.5038 2.54E-06 800.85 1.5037 2.56E-06 802.42 1.5037 2.58E-06

804 1.5037 2.60E-06 805.58 1.5036 2.62E-06 807.15 1.5036 2.64E-06 808.73 1.5036 2.66E-06 810.3 1.5035 2.69E-06

210

811.88 1.5035 2.71E-06 813.45 1.5035 2.73E-06 815.03 1.5034 2.75E-06 816.6 1.5034 2.77E-06

818.18 1.5034 2.79E-06 819.75 1.5033 2.81E-06 821.33 1.5033 2.83E-06 822.9 1.5033 2.85E-06

824.47 1.5033 2.87E-06 826.05 1.5032 2.89E-06 827.62 1.5032 2.91E-06 829.19 1.5032 2.94E-06 830.77 1.5031 2.96E-06 832.34 1.5031 2.98E-06 833.91 1.5031 3.00E-06 835.49 1.503 3.02E-06 837.06 1.503 3.04E-06 838.63 1.503 3.06E-06 840.2 1.5029 3.08E-06

841.77 1.5029 3.10E-06 843.35 1.5029 3.12E-06 844.92 1.5029 3.14E-06 846.49 1.5028 3.16E-06 848.06 1.5028 3.18E-06 849.63 1.5028 3.20E-06 851.2 1.5027 3.22E-06

852.77 1.5027 3.24E-06 854.34 1.5027 3.25E-06 855.91 1.5026 3.27E-06 857.48 1.5026 3.29E-06 859.05 1.5026 3.31E-06 860.62 1.5026 3.33E-06 862.19 1.5025 3.35E-06 863.76 1.5025 3.37E-06 865.32 1.5025 3.39E-06 866.89 1.5024 3.41E-06 868.46 1.5024 3.43E-06 870.03 1.5024 3.44E-06 871.59 1.5024 3.46E-06 873.16 1.5023 3.48E-06 874.73 1.5023 3.50E-06 876.29 1.5023 3.52E-06 877.86 1.5022 3.53E-06 879.43 1.5022 3.55E-06 880.99 1.5022 3.57E-06

882.56 1.5022 3.59E-06 884.12 1.5021 3.60E-06 885.68 1.5021 3.62E-06 887.25 1.5021 3.64E-06 888.81 1.5021 3.66E-06 890.38 1.502 3.67E-06 891.94 1.502 3.69E-06 893.5 1.502 3.71E-06 895.06 1.502 3.72E-06 896.62 1.5019 3.74E-06 898.19 1.5019 3.76E-06 899.75 1.5019 3.77E-06 901.31 1.5019 3.79E-06 902.87 1.5018 3.81E-06 904.43 1.5018 3.82E-06 905.99 1.5018 3.84E-06 907.55 1.5017 3.85E-06 909.1 1.5017 3.87E-06 910.66 1.5017 3.88E-06 912.22 1.5017 3.90E-06 913.78 1.5016 3.91E-06 915.34 1.5016 3.93E-06 916.89 1.5016 3.94E-06 918.45 1.5016 3.96E-06

920 1.5015 3.97E-06 921.56 1.5015 3.99E-06 923.11 1.5015 4.00E-06 924.67 1.5015 4.02E-06 926.22 1.5015 4.03E-06 927.77 1.5014 4.05E-06 929.33 1.5014 4.06E-06 930.88 1.5014 4.07E-06 932.43 1.5014 4.09E-06 933.98 1.5013 4.10E-06 935.53 1.5013 4.11E-06 937.08 1.5013 4.13E-06 938.63 1.5013 4.14E-06 940.18 1.5012 4.15E-06 941.73 1.5012 4.17E-06 943.27 1.5012 4.18E-06 944.82 1.5012 4.19E-06 946.37 1.5011 4.20E-06 947.91 1.5011 4.22E-06 949.46 1.5011 4.23E-06

951 1.5011 4.24E-06

952.55 1.5011 4.25E-06 954.09 1.501 4.26E-06 955.63 1.501 4.28E-06 957.18 1.501 4.29E-06 958.72 1.501 4.30E-06 960.26 1.5009 4.31E-06 961.8 1.5009 4.32E-06 963.34 1.5009 4.33E-06 964.88 1.5009 4.34E-06 966.41 1.5009 4.36E-06 967.95 1.5008 4.37E-06 969.49 1.5008 4.38E-06 971.02 1.5008 4.39E-06 972.56 1.5008 4.40E-06 974.09 1.5007 4.41E-06 975.63 1.5007 4.42E-06 977.16 1.5007 4.43E-06 978.69 1.5007 4.44E-06 980.22 1.5007 4.45E-06 981.75 1.5006 4.46E-06 983.28 1.5006 4.47E-06 984.81 1.5006 4.48E-06 986.34 1.5006 4.49E-06 987.87 1.5006 4.50E-06 989.4 1.5005 4.51E-06 990.92 1.5005 4.51E-06 992.45 1.5005 4.52E-06 993.97 1.5005 4.53E-06 995.49 1.5005 4.54E-06 997.01 1.5004 4.55E-06 998.54 1.5004 4.56E-06 1000.1 1.5004 4.57E-06 1012.3 1.5002 4.63E-06 1015.8 1.5002 4.65E-06 1019.2 1.5001 4.67E-06 1022.6 1.5001 4.68E-06 1026.1 1.5001 4.70E-06 1029.5 1.5 4.72E-06 1032.9 1.5 4.73E-06 1036.3 1.4999 4.75E-06 1039.8 1.4999 4.76E-06 1043.2 1.4998 4.78E-06 1046.6 1.4998 4.79E-06 1050 1.4998 4.81E-06

1053.5 1.4997 4.82E-06

211

1056.9 1.4997 4.84E-06 1060.3 1.4996 4.85E-06 1063.8 1.4996 4.86E-06 1067.2 1.4996 4.88E-06 1070.6 1.4995 4.89E-06 1074 1.4995 4.90E-06

1077.5 1.4994 4.91E-06 1080.9 1.4994 4.93E-06 1084.3 1.4994 4.94E-06 1087.7 1.4993 4.95E-06 1091.2 1.4993 4.97E-06 1094.6 1.4993 4.98E-06 1098 1.4992 4.99E-06

1101.5 1.4992 5.00E-06 1104.9 1.4991 5.02E-06 1108.3 1.4991 5.03E-06 1111.7 1.4991 5.04E-06 1115.2 1.499 5.06E-06 1118.6 1.499 5.07E-06 1122 1.499 5.08E-06

1125.4 1.4989 5.10E-06 1128.9 1.4989 5.11E-06 1132.3 1.4989 5.12E-06 1135.7 1.4988 5.14E-06 1139.2 1.4988 5.15E-06 1142.6 1.4988 5.16E-06 1146 1.4987 5.17E-06

1149.4 1.4987 5.19E-06 1152.9 1.4987 5.20E-06 1156.3 1.4986 5.21E-06 1159.7 1.4986 5.22E-06 1163.2 1.4986 5.24E-06 1166.6 1.4985 5.25E-06 1170 1.4985 5.26E-06

1173.4 1.4985 5.27E-06 1176.9 1.4984 5.28E-06 1180.3 1.4984 5.29E-06 1183.7 1.4984 5.30E-06 1187.2 1.4983 5.31E-06 1190.6 1.4983 5.32E-06 1194 1.4983 5.33E-06

1197.4 1.4982 5.34E-06 1200.9 1.4982 5.35E-06 1204.3 1.4982 5.36E-06 1207.7 1.4981 5.36E-06

1211.2 1.4981 5.37E-06 1214.6 1.4981 5.38E-06 1218 1.4981 5.39E-06

1221.5 1.498 5.39E-06 1224.9 1.498 5.40E-06 1228.3 1.498 5.40E-06 1231.7 1.4979 5.41E-06 1235.2 1.4979 5.41E-06 1238.6 1.4979 5.41E-06 1242 1.4978 5.41E-06

1245.5 1.4978 5.42E-06 1248.9 1.4978 5.42E-06 1252.3 1.4978 5.42E-06 1255.8 1.4977 5.42E-06 1259.2 1.4977 5.42E-06 1262.6 1.4977 5.42E-06 1266.1 1.4976 5.42E-06 1269.5 1.4976 5.41E-06 1272.9 1.4976 5.41E-06 1276.4 1.4976 5.41E-06 1279.8 1.4975 5.40E-06 1283.2 1.4975 5.40E-06 1286.7 1.4975 5.40E-06 1290.1 1.4975 5.39E-06 1293.5 1.4974 5.38E-06 1297 1.4974 5.38E-06

1300.4 1.4974 5.37E-06 1303.8 1.4973 5.36E-06 1307.3 1.4973 5.35E-06 1310.7 1.4973 5.34E-06 1314.1 1.4973 5.33E-06 1317.6 1.4972 5.32E-06 1321 1.4972 5.31E-06

1324.4 1.4972 5.30E-06 1327.9 1.4972 5.28E-06 1331.3 1.4971 5.27E-06 1334.7 1.4971 5.26E-06 1338.2 1.4971 5.24E-06 1341.6 1.4971 5.23E-06 1345 1.497 5.21E-06

1348.5 1.497 5.19E-06 1351.9 1.497 5.18E-06 1355.4 1.497 5.16E-06 1358.8 1.4969 5.14E-06 1362.2 1.4969 5.12E-06

1365.7 1.4969 5.11E-06 1369.1 1.4969 5.09E-06 1372.5 1.4969 5.07E-06 1376 1.4968 5.05E-06

1379.4 1.4968 5.03E-06 1382.9 1.4968 5.01E-06 1386.3 1.4968 4.98E-06 1389.7 1.4967 4.96E-06 1393.2 1.4967 4.94E-06 1396.6 1.4967 4.92E-06 1400 1.4967 4.90E-06

1403.5 1.4966 4.87E-06 1406.9 1.4966 4.85E-06 1410.4 1.4966 4.83E-06 1413.8 1.4966 4.81E-06 1417.2 1.4966 4.78E-06 1420.7 1.4965 4.76E-06 1424.1 1.4965 4.73E-06 1427.6 1.4965 4.71E-06 1431 1.4965 4.69E-06

1434.5 1.4964 4.66E-06 1437.9 1.4964 4.64E-06 1441.3 1.4964 4.62E-06 1444.8 1.4964 4.59E-06 1448.2 1.4964 4.57E-06 1451.7 1.4963 4.54E-06 1455.1 1.4963 4.52E-06 1458.6 1.4963 4.50E-06 1462 1.4963 4.47E-06

1465.4 1.4963 4.45E-06 1468.9 1.4962 4.43E-06 1472.3 1.4962 4.40E-06 1475.8 1.4962 4.38E-06 1479.2 1.4962 4.36E-06 1482.7 1.4961 4.33E-06 1486.1 1.4961 4.31E-06 1489.6 1.4961 4.29E-06 1493 1.4961 4.27E-06

1496.5 1.4961 4.25E-06 1499.9 1.496 4.23E-06 1503.4 1.496 4.21E-06 1506.8 1.496 4.19E-06 1510.2 1.496 4.17E-06 1513.7 1.496 4.15E-06 1517.1 1.4959 4.13E-06

212

1520.6 1.4959 4.11E-06 1524 1.4959 4.09E-06

1527.5 1.4959 4.07E-06 1530.9 1.4959 4.05E-06 1534.4 1.4959 4.04E-06 1537.8 1.4958 4.02E-06 1541.3 1.4958 4.00E-06 1544.7 1.4958 3.99E-06 1548.2 1.4958 3.97E-06 1551.7 1.4958 3.95E-06 1555.1 1.4957 3.94E-06 1558.6 1.4957 3.92E-06 1562 1.4957 3.91E-06

1565.5 1.4957 3.90E-06 1568.9 1.4957 3.88E-06 1572.4 1.4956 3.87E-06 1575.8 1.4956 3.86E-06 1579.3 1.4956 3.85E-06 1582.7 1.4956 3.83E-06 1586.2 1.4956 3.82E-06 1589.7 1.4956 3.81E-06 1593.1 1.4955 3.80E-06 1596.6 1.4955 3.79E-06 1600 1.4955 3.78E-06

1603.5 1.4955 3.77E-06 1606.9 1.4955 3.76E-06 1610.4 1.4955 3.75E-06 1613.9 1.4954 3.74E-06 1617.3 1.4954 3.73E-06 1620.8 1.4954 3.72E-06 1624.2 1.4954 3.71E-06 1627.7 1.4954 3.70E-06 1631.2 1.4953 3.69E-06 1634.6 1.4953 3.68E-06 1638.1 1.4953 3.67E-06 1641.5 1.4953 3.66E-06 1645 1.4953 3.65E-06

1648.5 1.4953 3.64E-06 1651.9 1.4952 3.63E-06 1655.4 1.4952 3.62E-06 1658.9 1.4952 3.60E-06 1662.3 1.4952 3.59E-06 1665.8 1.4952 3.58E-06

1669.3 1.4952 3.56E-06

213

A.2 Dielectric function of SnO2

eV ε1 ε2

6.5004 3.3297 1.1928

6.4471 3.3326 1.1992

6.3947 3.3362 1.2058

6.3432 3.3405 1.2127

6.2924 3.3456 1.2197

6.2425 3.3515 1.2269

6.1933 3.3581 1.2341

6.1448 3.3655 1.2414

6.0972 3.3738 1.2487

6.0502 3.3828 1.256

6.0039 3.3927 1.2632

5.9584 3.4034 1.2702

5.9135 3.4149 1.2771

5.8692 3.4272 1.2836

5.8257 3.4404 1.2899

5.7827 3.4544 1.2958

5.7404 3.4691 1.3012

5.6987 3.4846 1.3061

5.6575 3.5009 1.3105

5.617 3.5178 1.3142

5.577 3.5355 1.3173

5.5376 3.5537 1.3196

5.4987 3.5725 1.3211

5.4604 3.5919 1.3217

5.4226 3.6116 1.3214

5.3853 3.6318 1.3201

5.3485 3.6522 1.3178

5.3122 3.6728 1.3145

5.2764 3.6935 1.31

5.241 3.7141 1.3045

5.2062 3.7347 1.2979

5.1717 3.7549 1.2902

5.1378 3.7748 1.2814

5.1042 3.7941 1.2716

5.0711 3.8127 1.2609

5.0384 3.8306 1.2494

5.0062 3.8475 1.2372

4.9743 3.8634 1.2246

4.9429 3.8783 1.2116

4.9118 3.8921 1.1987

4.8811 3.905 1.1859

4.8508 3.9169 1.1736

4.8209 3.9282 1.1618

4.7913 3.939 1.1509

4.7621 3.9496 1.141

4.7332 3.9604 1.1319

4.7047 3.9717 1.1238

4.6765 3.9838 1.1164

4.6486 3.997 1.1096

4.6211 4.0117 1.1029

4.5939 4.0279 1.0961

4.567 4.0457 1.0887

4.5405 4.065 1.0802

4.5142 4.0858 1.0702

4.4882 4.1077 1.0584

4.4626 4.1304 1.0444

4.4372 4.1536 1.0279

4.4121 4.1767 1.0089

4.3873 4.1992 0.98722

4.3627 4.2207 0.96303

4.3384 4.2407 0.93647

4.3144 4.2589 0.90779

4.2907 4.2749 0.87732

4.2672 4.2885 0.84541

4.244 4.2996 0.81247

4.221 4.3079 0.7789

4.1983 4.3137 0.7451

4.1758 4.3168 0.71142

4.1536 4.3174 0.67821

4.1315 4.3158 0.64576

4.1098 4.312 0.6143

4.0882 4.3064 0.58403

4.0669 4.2992 0.55508

4.0458 4.2906 0.52755

4.0249 4.2808 0.50149

4.0042 4.2701 0.47692

3.9837 4.2587 0.45382

3.9635 4.2467 0.43215

3.9434 4.2343 0.41186

3.9235 4.2217 0.39288

3.9039 4.2089 0.37512

3.8844 4.196 0.35851

3.8652 4.1832 0.34297

3.8461 4.1704 0.3284

3.8272 4.1578 0.31474

3.8085 4.1453 0.30191

3.79 4.133 0.28984

3.7716 4.1209 0.27847

3.7534 4.109 0.26775

3.7355 4.0973 0.25761

3.7176 4.0858 0.24802

3.7 4.0746 0.23894

3.6825 4.0635 0.23033

3.6652 4.0527 0.22216

3.648 4.042 0.2144

3.631 4.0316 0.20703

3.6142 4.0214 0.20003

3.5975 4.0113 0.19337

3.5809 4.0014 0.18704

3.5646 3.9917 0.18103

3.5483 3.9822 0.17531

3.5322 3.9728 0.16989

3.5163 3.9636 0.16473

3.5005 3.9546 0.15985

3.4848 3.9458 0.15521

3.4693 3.9371 0.15083

3.4539 3.9285 0.14668

3.4387 3.9202 0.14275

3.4236 3.912 0.13905

3.4086 3.9039 0.13556

3.3938 3.896 0.13228

3.3791 3.8883 0.12919

3.3645 3.8807 0.1263

214

3.35 3.8733 0.12359

3.3357 3.8661 0.12106

3.3215 3.859 0.11871

3.3074 3.8521 0.11652

3.2934 3.8454 0.1145

3.2795 3.8389 0.11264

3.2658 3.8325 0.11093

3.2522 3.8263 0.10937

3.2386 3.8204 0.10795

3.2252 3.8147 0.10664

3.212 3.8093 0.10534

3.1988 3.804 0.10406

3.1857 3.7989 0.10279

3.1727 3.7939 0.10154

3.1599 3.7891 0.1003

3.1471 3.7844 0.099079

3.1345 3.7798 0.09787

3.1219 3.7754 0.096675

3.1095 3.771 0.095493

3.0971 3.7667 0.094324

3.0849 3.7626 0.093169

3.0727 3.7585 0.092027

3.0607 3.7545 0.090898

3.0487 3.7506 0.089782

3.0368 3.7468 0.088678

3.025 3.743 0.087586

3.0134 3.7393 0.086507

3.0018 3.7357 0.08544

2.9902 3.7321 0.084385

2.9788 3.7286 0.083341

2.9675 3.7252 0.08231

2.9563 3.7218 0.081289

2.9451 3.7185 0.08028

2.934 3.7153 0.079283

2.923 3.7121 0.078296

2.9121 3.7089 0.07732

2.9013 3.7058 0.076355

2.8905 3.7027 0.075401

2.8799 3.6997 0.074457

2.8693 3.6968 0.073523

2.8588 3.6939 0.0726

2.8483 3.691 0.071687

2.838 3.6881 0.070784

2.8277 3.6853 0.069891

2.8175 3.6826 0.069008

2.8074 3.6799 0.068134

2.7973 3.6772 0.06727

2.7873 3.6745 0.066415

2.7774 3.6719 0.06557

2.7676 3.6694 0.064734

2.7578 3.6668 0.063906

2.7481 3.6643 0.063088

2.7384 3.6618 0.062279

2.7289 3.6594 0.061479

2.7194 3.6569 0.060687

2.7099 3.6546 0.059904

2.7006 3.6522 0.059129

2.6913 3.6499 0.058363

2.682 3.6476 0.057605

2.6728 3.6453 0.056856

2.6637 3.643 0.056114

2.6547 3.6408 0.055381

2.6457 3.6386 0.054655

2.6368 3.6364 0.053937

2.6279 3.6343 0.053227

2.6191 3.6321 0.052525

2.6103 3.63 0.05183

2.6016 3.6279 0.051143

2.593 3.6259 0.050463

2.5844 3.6238 0.049791

2.5759 3.6218 0.049126

2.5675 3.6198 0.048468

2.559 3.6178 0.047817

2.5507 3.6159 0.047173

2.5424 3.6139 0.046536

2.5342 3.612 0.045906

2.526 3.6101 0.045283

2.5178 3.6082 0.044667

2.5098 3.6063 0.044057

2.5017 3.6045 0.043454

2.4937 3.6026 0.042858

2.4858 3.6008 0.042268

2.4779 3.599 0.041684

2.4701 3.5972 0.041107

2.4623 3.5955 0.040536

2.4546 3.5937 0.039971

2.4469 3.592 0.039412

2.4393 3.5903 0.03886

2.4317 3.5886 0.038313

2.4242 3.5869 0.037773

2.4167 3.5852 0.037238

2.4092 3.5835 0.036709

2.4018 3.5819 0.036186

2.3945 3.5802 0.035669

2.3872 3.5786 0.035157

2.3799 3.577 0.034651

2.3727 3.5754 0.034151

2.3655 3.5738 0.033656

2.3584 3.5722 0.033166

2.3513 3.5707 0.032682

2.3443 3.5691 0.032203

2.3373 3.5676 0.03173

2.3303 3.5661 0.031262

2.3234 3.5646 0.030799

2.3165 3.5631 0.030341

2.3097 3.5616 0.029888

2.3029 3.5601 0.02944

2.2961 3.5586 0.028998

2.2894 3.5572 0.02856

2.2827 3.5557 0.028127

2.2761 3.5543 0.027699

2.2695 3.5529 0.027276

2.263 3.5515 0.026857

2.2564 3.5501 0.026444

2.2499 3.5487 0.026035

2.2435 3.5473 0.025631

2.2371 3.5459 0.025231

215

2.2307 3.5445 0.024836

2.2244 3.5432 0.024445

2.2181 3.5418 0.024059

2.2118 3.5405 0.023677

2.2056 3.5392 0.0233

2.1994 3.5379 0.022927

2.1932 3.5365 0.022558

2.1871 3.5352 0.022194

2.181 3.534 0.021834

2.175 3.5327 0.021478

2.1689 3.5314 0.021126

2.163 3.5301 0.020779

2.157 3.5289 0.020435

2.1511 3.5276 0.020096

2.1452 3.5264 0.01976

2.1393 3.5251 0.019429

2.1335 3.5239 0.019101

2.1277 3.5227 0.018778

2.1219 3.5215 0.018458

2.1162 3.5202 0.018142

2.1105 3.519 0.01783

2.1048 3.5179 0.017522

2.0992 3.5167 0.017218

2.0936 3.5155 0.016917

2.088 3.5143 0.01662

2.0825 3.5132 0.016327

2.077 3.512 0.016037

2.0715 3.5108 0.015751

2.066 3.5097 0.015468

2.0606 3.5086 0.015189

2.0552 3.5074 0.014914

2.0498 3.5063 0.014642

2.0444 3.5052 0.014373

2.0391 3.5041 0.014108

2.0338 3.503 0.013846

2.0286 3.5019 0.013588

2.0233 3.5008 0.013333

2.0181 3.4997 0.013081

2.0129 3.4986 0.012833

2.0078 3.4975 0.012588

2.0027 3.4964 0.012346

1.9976 3.4954 0.012107

1.9925 3.4943 0.011872

1.9874 3.4933 0.01164

1.9824 3.4922 0.01141

1.9774 3.4912 0.011184

1.9724 3.4901 0.010961

1.9675 3.4891 0.010741

1.9625 3.4881 0.010524

1.9577 3.4871 0.010311

1.9528 3.486 0.0101

1.9479 3.485 0.0098917

1.9431 3.484 0.0096867

1.9383 3.483 0.0094847

1.9335 3.482 0.0092855

1.9288 3.481 0.0090893

1.924 3.4801 0.0088959

1.9193 3.4791 0.0087053

1.9146 3.4781 0.0085175

1.91 3.4771 0.0083325

1.9053 3.4762 0.0081503

1.9007 3.4752 0.0079709

1.8961 3.4742 0.0077941

1.8915 3.4733 0.0076201

1.887 3.4723 0.0074488

1.8825 3.4714 0.0072801

1.878 3.4705 0.0071141

1.8735 3.4695 0.0069507

1.869 3.4686 0.00679

1.8646 3.4677 0.0066318

1.8601 3.4667 0.0064762

1.8557 3.4658 0.0063231

1.8514 3.4649 0.0061726

1.847 3.464 0.0060246

1.8427 3.4631 0.0058791

1.8383 3.4622 0.005736

1.834 3.4613 0.0055955

1.8298 3.4604 0.0054573

1.8255 3.4595 0.0053216

1.8213 3.4586 0.0051883

1.817 3.4578 0.0050575

1.8128 3.4569 0.0049289

1.8087 3.456 0.0048027

1.8045 3.4551 0.0046789

1.8004 3.4543 0.0045574

1.7962 3.4534 0.0044382

1.7921 3.4526 0.0043213

1.7881 3.4517 0.0042067

1.784 3.4508 0.0040943

1.7799 3.45 0.0039842

1.7759 3.4492 0.0038763

1.7719 3.4483 0.0037706

1.7679 3.4475 0.0036671

1.7639 3.4467 0.0035658

1.76 3.4458 0.0034667

1.756 3.445 0.0033697

1.7521 3.4442 0.0032749

1.7482 3.4434 0.0031821

1.7443 3.4426 0.0030915

1.7405 3.4417 0.003003

1.7366 3.4409 0.0029166

1.7328 3.4401 0.0028322

1.729 3.4393 0.0027499

1.7252 3.4385 0.0026696

1.7214 3.4377 0.0025913

1.7176 3.437 0.0025151

1.7139 3.4362 0.0024408

1.7101 3.4354 0.0023685

1.7064 3.4346 0.0022982

1.7027 3.4338 0.0022299

1.699 3.4331 0.0021635

1.6954 3.4323 0.002099

1.6917 3.4315 0.0020365

1.6881 3.4308 0.0019759

1.6844 3.43 0.0019171

1.6808 3.4292 0.0018602

1.6772 3.4285 0.0018052

216

1.6737 3.4277 0.0017521

1.6701 3.427 0.0017008

1.6666 3.4262 0.0016514

1.663 3.4255 0.0016037

1.6595 3.4248 0.0015579

1.656 3.424 0.0015139

1.6525 3.4233 0.0014716

1.6491 3.4226 0.0014311

1.6456 3.4218 0.0013924

1.6422 3.4211 0.0013555

1.6387 3.4204 0.0013202

1.6353 3.4197 0.0012867

1.6319 3.419 0.001255

1.6285 3.4183 0.0012249

1.6252 3.4176 0.0011965

1.6218 3.4169 0.0011698

1.6185 3.4162 0.0011448

1.6152 3.4155 0.0011215

1.6118 3.4148 0.0010998

1.6085 3.4141 0.0010798

1.6053 3.4134 0.0010613

1.602 3.4127 0.0010445

1.5987 3.412 0.0010294

1.5955 3.4113 0.0010158

1.5922 3.4107 0.0010038

1.589 3.41 0.0009934

1.5858 3.4093 0.0009846

1.5826 3.4086 0.0009773

1.5795 3.408 0.0009716

1.5763 3.4073 0.0009674

1.5731 3.4067 0.0009648

1.57 3.406 0.0009636

1.5669 3.4054 0.000964

1.5637 3.4047 0.0009659

1.5606 3.4041 0.0009693

1.5576 3.4034 0.0009742

1.5545 3.4028 0.00098

1.5514 3.4022 0.0009858

1.5484 3.4015 0.0009917

1.5453 3.4009 0.0009975

1.5423 3.4003 0.0010034

1.5393 3.3997 0.0010093

1.5363 3.3991 0.0010153

1.5333 3.3985 0.0010212

1.5303 3.3978 0.0010272

1.5273 3.3972 0.0010332

1.5244 3.3966 0.0010392

1.5214 3.396 0.0010453

1.5185 3.3954 0.0010513

1.5156 3.3948 0.0010574

1.5127 3.3943 0.0010636

1.5098 3.3937 0.0010697

1.5069 3.3931 0.0010759

1.504 3.3925 0.001082

1.5011 3.3919 0.0010882

1.4983 3.3913 0.0010945

1.4954 3.3907 0.0011007

1.4926 3.3902 0.001107

1.4898 3.3896 0.0011133

1.487 3.389 0.0011196

1.4842 3.3885 0.001126

1.4814 3.3879 0.0011323

1.4786 3.3873 0.0011387

1.4758 3.3868 0.0011451

1.4731 3.3862 0.0011516

1.4703 3.3856 0.001158

1.4676 3.3851 0.0011645

1.4649 3.3845 0.001171

1.4622 3.384 0.0011776

1.4595 3.3834 0.0011841

1.4568 3.3829 0.0011907

1.4541 3.3823 0.0011973

1.4514 3.3818 0.0012039

1.4487 3.3812 0.0012106

1.4461 3.3807 0.0012172

1.4435 3.3801 0.0012239

1.4408 3.3796 0.0012306

1.4382 3.3791 0.0012374

1.4356 3.3785 0.0012441

1.433 3.378 0.0012509

1.4304 3.3774 0.0012577

1.4278 3.3769 0.0012646

1.4252 3.3764 0.0012714

1.4227 3.3759 0.0012783

1.4201 3.3753 0.0012852

1.4176 3.3748 0.0012922

1.4151 3.3743 0.0012991

1.4125 3.3738 0.0013061

1.41 3.3732 0.0013131

1.4075 3.3727 0.0013201

1.405 3.3722 0.0013271

1.4025 3.3717 0.0013342

1.4 3.3712 0.0013413

1.3976 3.3706 0.0013484

1.3951 3.3701 0.0013556

1.3927 3.3696 0.0013627

1.3902 3.3691 0.0013699

1.3878 3.3686 0.0013771

1.3854 3.3681 0.0013844

1.383 3.3676 0.0013916

1.3806 3.3671 0.0013989

1.3782 3.3666 0.0014062

1.3758 3.3661 0.0014135

1.3734 3.3656 0.0014209

1.371 3.3651 0.0014283

1.3687 3.3646 0.0014357

1.3663 3.3641 0.0014431

1.364 3.3636 0.0014505

1.3616 3.3631 0.001458

1.3593 3.3626 0.0014655

1.357 3.3621 0.001473

1.3547 3.3616 0.0014805

1.3524 3.3611 0.0014881

1.3501 3.3606 0.0014957

1.3478 3.3601 0.0015033

1.3455 3.3596 0.0015109

1.3433 3.3591 0.0015186

217

1.341 3.3586 0.0015263

1.3388 3.3582 0.001534

1.3365 3.3577 0.0015417

1.3343 3.3572 0.0015495

1.3321 3.3567 0.0015572

1.3299 3.3562 0.001565

1.3277 3.3557 0.0015729

1.3255 3.3553 0.0015807

1.3233 3.3548 0.0015886

1.3211 3.3543 0.0015965

1.3189 3.3538 0.0016044

1.3167 3.3534 0.0016123

1.3146 3.3529 0.0016203

1.3124 3.3524 0.0016282

1.3103 3.3519 0.0016363

1.3081 3.3515 0.0016443

1.306 3.351 0.0016523

1.3039 3.3505 0.0016604

1.3018 3.35 0.0016685

1.2997 3.3496 0.0016766

1.2976 3.3491 0.0016848

1.2955 3.3486 0.0016929

1.2934 3.3482 0.0017011

1.2913 3.3477 0.0017093

1.2893 3.3472 0.0017176

1.2872 3.3468 0.0017258

1.2851 3.3463 0.0017341

1.2831 3.3459 0.0017424

1.2811 3.3454 0.0017507

1.279 3.3449 0.0017591

1.277 3.3445 0.0017675

1.275 3.344 0.0017759

1.273 3.3436 0.0017843

1.271 3.3431 0.0017927

1.269 3.3426 0.0018012

1.267 3.3422 0.0018097

1.265 3.3417 0.0018182

1.263 3.3413 0.0018267

1.2611 3.3408 0.0018352

1.2591 3.3404 0.0018438

1.2572 3.3399 0.0018524

1.2552 3.3395 0.001861

1.2533 3.339 0.0018697

1.2514 3.3386 0.0018783

1.2494 3.3381 0.001887

1.2475 3.3377 0.0018957

1.2456 3.3372 0.0019044

1.2437 3.3368 0.0019132

1.2418 3.3363 0.0019219

1.2399 3.3359 0.0019307

1.2249 3.3323 0.0020028

1.2207 3.3313 0.0020232

1.2166 3.3303 0.0020437

1.2126 3.3293 0.0020644

1.2085 3.3283 0.0020852

1.2045 3.3274 0.0021062

1.2005 3.3264 0.0021273

1.1965 3.3254 0.0021485

1.1926 3.3244 0.0021699

1.1887 3.3234 0.0021914

1.1848 3.3225 0.0022131

1.1809 3.3215 0.0022349

1.1771 3.3205 0.0022568

1.1732 3.3195 0.0022789

1.1695 3.3185 0.0023011

1.1657 3.3176 0.0023235

1.1619 3.3166 0.002346

1.1582 3.3156 0.0023687

1.1545 3.3147 0.0023915

1.1509 3.3137 0.0024145

1.1472 3.3127 0.0024376

1.1436 3.3118 0.0024608

1.14 3.3108 0.0024842

1.1364 3.3098 0.0025078

1.1328 3.3089 0.0025315

1.1293 3.3079 0.0025553

1.1258 3.3069 0.0025793

1.1223 3.306 0.0026035

1.1188 3.305 0.0026278

1.1154 3.3041 0.0026522

1.1119 3.3031 0.0026768

1.1085 3.3021 0.0027016

1.1052 3.3012 0.0027265

1.1018 3.3002 0.0027515

1.0984 3.2993 0.0027767

1.0951 3.2983 0.0028021

1.0918 3.2974 0.0028276

1.0885 3.2964 0.0028533

1.0853 3.2954 0.0028791

1.082 3.2945 0.0029051

1.0788 3.2935 0.0029312

1.0756 3.2926 0.0029575

1.0724 3.2916 0.002984

1.0692 3.2907 0.0030106

1.0661 3.2897 0.0030374

1.0629 3.2888 0.0030643

1.0598 3.2878 0.0030914

1.0567 3.2868 0.0031186

1.0536 3.2859 0.003146

1.0506 3.2849 0.0031736

1.0475 3.284 0.0032013

1.0445 3.283 0.0032292

1.0415 3.2821 0.0032573

1.0385 3.2811 0.0032855

1.0355 3.2802 0.0033139

1.0326 3.2792 0.0033424

1.0296 3.2782 0.0033711

1.0267 3.2773 0.0034

1.0238 3.2763 0.003429

1.0209 3.2754 0.0034582

1.018 3.2744 0.0034876

1.0152 3.2734 0.0035171

1.0123 3.2725 0.0035468

1.0095 3.2715 0.0035767

1.0067 3.2706 0.0036067

1.0039 3.2696 0.0036369

1.0011 3.2687 0.0036673

218

0.99836 3.2677 0.0036979

0.99561 3.2667 0.0037286

0.99287 3.2658 0.0037595

0.99015 3.2648 0.0037905

0.98744 3.2638 0.0038218

0.98475 3.2629 0.0038532

0.98208 3.2619 0.0038847

0.97941 3.2609 0.0039165

0.97677 3.26 0.0039484

0.97413 3.259 0.0039805

0.97151 3.258 0.0040128

0.96891 3.2571 0.0040452

0.96632 3.2561 0.0040778

0.96374 3.2551 0.0041106

0.96117 3.2542 0.0041436

0.95862 3.2532 0.0041768

0.95608 3.2522 0.0042101

0.95356 3.2513 0.0042436

0.95105 3.2503 0.0042773

0.94855 3.2493 0.0043112

0.94607 3.2483 0.0043452

0.94359 3.2474 0.0043794

0.94113 3.2464 0.0044138

0.93869 3.2454 0.0044484

0.93625 3.2444 0.0044832

0.93383 3.2435 0.0045182

0.93142 3.2425 0.0045533

0.92902 3.2415 0.0045886

0.92664 3.2405 0.0046241

0.92427 3.2395 0.0046598

0.9219 3.2385 0.0046957

0.91956 3.2376 0.0047317

0.91722 3.2366 0.004768

0.91489 3.2356 0.0048044

0.91258 3.2346 0.004841

0.91028 3.2336 0.0048778

0.90798 3.2326 0.0049149

0.9057 3.2316 0.004952

0.90344 3.2306 0.0049894

0.90118 3.2296 0.005027

0.89893 3.2286 0.0050647

0.8967 3.2276 0.0051027

0.89447 3.2266 0.0051408

0.89226 3.2256 0.0051791

0.89006 3.2246 0.0052177

0.88787 3.2236 0.0052564

0.88569 3.2226 0.0052953

0.88351 3.2216 0.0053344

0.88135 3.2206 0.0053737

0.8792 3.2196 0.0054132

0.87707 3.2186 0.0054529

0.87493 3.2176 0.0054928

0.87282 3.2166 0.0055328

0.87071 3.2156 0.0055731

0.86861 3.2146 0.0056136

0.86652 3.2136 0.0056543

0.86444 3.2126 0.0056951

0.86237 3.2115 0.0057362

0.86031 3.2105 0.0057775

0.85826 3.2095 0.0058189

0.85622 3.2085 0.0058606

0.85419 3.2075 0.0059025

0.85217 3.2064 0.0059446

0.85016 3.2054 0.0059868

0.84815 3.2044 0.0060293

0.84616 3.2034 0.006072

0.84417 3.2023 0.0061149

0.8422 3.2013 0.006158

0.84023 3.2003 0.0062013

0.83828 3.1992 0.0062448

0.83633 3.1982 0.0062885

0.83439 3.1972 0.0063325

0.83246 3.1961 0.0063766

0.83054 3.1951 0.0064209

0.82862 3.1941 0.0064655

0.82672 3.193 0.0065102

0.82482 3.192 0.0065552

0.82294 3.1909 0.0066004

0.82106 3.1899 0.0066458

0.81919 3.1888 0.0066914

0.81732 3.1878 0.0067372

0.81547 3.1867 0.0067832

0.81362 3.1857 0.0068294

0.81179 3.1846 0.0068759

0.80996 3.1836 0.0069225

0.80814 3.1825 0.0069694

0.80632 3.1815 0.0070165

0.80452 3.1804 0.0070638

0.80272 3.1793 0.0071114

0.80093 3.1783 0.0071591

0.79915 3.1772 0.0072071

0.79737 3.1762 0.0072553

0.79561 3.1751 0.0073037

0.79385 3.174 0.0073523

0.7921 3.1729 0.0074011

0.79035 3.1719 0.0074502

0.78862 3.1708 0.0074995

0.78689 3.1697 0.007549

0.78517 3.1686 0.0075987

0.78345 3.1676 0.0076486

0.78174 3.1665 0.0076988

0.78004 3.1654 0.0077492

0.77835 3.1643 0.0077998

0.77667 3.1632 0.0078507

0.77499 3.1621 0.0079018

0.77332 3.1611 0.0079531

0.77165 3.16 0.0080046

0.77 3.1589 0.0080563

0.76835 3.1578 0.0081083

0.7667 3.1567 0.0081605

0.76507 3.1556 0.008213

0.76344 3.1545 0.0082656

0.76181 3.1534 0.0083185

0.7602 3.1523 0.0083717

0.75859 3.1512 0.008425

0.75698 3.1501 0.0084786

0.75539 3.149 0.0085325

219

0.7538 3.1478 0.0085865

0.75221 3.1467 0.0086408

0.75064 3.1456 0.0086954

0.74907 3.1445 0.0087501

0.7475 3.1434 0.0088051

0.74594 3.1423 0.0088604

0.74439 3.1411 0.0089158

0.74285 3.14 0.0089715

220

A.3 Dielectric function of SiO2

eV ε1 ε2 6.5004 2.4689 0 6.4471 2.4629 0 6.3947 2.4571 0 6.3432 2.4515 0 6.2924 2.4461 0 6.2425 2.4408 0 6.1933 2.4357 0 6.1448 2.4307 0 6.0972 2.4259 0 6.0502 2.4213 0 6.0039 2.4167 0 5.9584 2.4123 0 5.9135 2.408 0 5.8692 2.4039 0 5.8257 2.3998 0 5.7827 2.3959 0 5.7404 2.3921 0 5.6987 2.3883 0 5.6575 2.3847 0 5.617 2.3812 0 5.577 2.3777 0 5.5376 2.3744 0 5.4987 2.3711 0 5.4604 2.3679 0 5.4226 2.3648 0 5.3853 2.3618 0 5.3485 2.3588 0 5.3122 2.3559 0 5.2764 2.3531 0 5.241 2.3504 0 5.2062 2.3477 0 5.1717 2.345 0 5.1378 2.3425 0 5.1042 2.34 0 5.0711 2.3375 0 5.0384 2.3351 0

5.0062 2.3328 0 4.9743 2.3305 0 4.9429 2.3283 0 4.9118 2.3261 0 4.8811 2.3239 0 4.8508 2.3218 0 4.8209 2.3198 0 4.7913 2.3178 0 4.7621 2.3158 0 4.7332 2.3139 0 4.7047 2.312 0 4.6765 2.3101 0 4.6486 2.3083 0 4.6211 2.3065 0 4.5939 2.3048 0 4.567 2.3031 0

4.5405 2.3014 0 4.5142 2.2998 0 4.4882 2.2982 0 4.4626 2.2966 0 4.4372 2.295 0 4.4121 2.2935 0 4.3873 2.292 0 4.3627 2.2906 0 4.3384 2.2891 0 4.3144 2.2877 0 4.2907 2.2863 0 4.2672 2.285 0 4.244 2.2837 0 4.221 2.2823 0

4.1983 2.2811 0 4.1758 2.2798 0 4.1536 2.2785 0 4.1315 2.2773 0 4.1098 2.2761 0 4.0882 2.2749 0 4.0669 2.2738 0

4.0458 2.2726 0 4.0249 2.2715 0 4.0042 2.2704 0 3.9837 2.2693 0 3.9635 2.2683 0 3.9434 2.2672 0 3.9235 2.2662 0 3.9039 2.2652 0 3.8844 2.2642 0 3.8652 2.2632 0 3.8461 2.2622 0 3.8272 2.2613 0 3.8085 2.2603 0

3.79 2.2594 0 3.7716 2.2585 0 3.7534 2.2576 0 3.7355 2.2567 0 3.7176 2.2558 0

3.7 2.255 0 3.6825 2.2541 0 3.6652 2.2533 0 3.648 2.2525 0 3.631 2.2517 0 3.6142 2.2509 0 3.5975 2.2501 0 3.5809 2.2493 0 3.5646 2.2486 0 3.5483 2.2478 0 3.5322 2.2471 0 3.5163 2.2463 0 3.5005 2.2456 0 3.4848 2.2449 0 3.4693 2.2442 0 3.4539 2.2435 0 3.4387 2.2429 0 3.4236 2.2422 0 3.4086 2.2415 0

3.3938 2.2409 0 3.3791 2.2402 0 3.3645 2.2396 0 3.35 2.239 0

3.3357 2.2383 0 3.3215 2.2377 0 3.3074 2.2371 0 3.2934 2.2365 0 3.2795 2.2359 0 3.2658 2.2354 0 3.2522 2.2348 0 3.2386 2.2342 0 3.2252 2.2337 0 3.212 2.2331 0 3.1988 2.2326 0 3.1857 2.232 0 3.1727 2.2315 0 3.1599 2.231 0 3.1471 2.2304 0 3.1345 2.2299 0 3.1219 2.2294 0 3.1095 2.2289 0 3.0971 2.2284 0 3.0849 2.2279 0 3.0727 2.2274 0 3.0607 2.227 0 3.0487 2.2265 0 3.0368 2.226 0 3.025 2.2256 0 3.0134 2.2251 0 3.0018 2.2247 0 2.9902 2.2242 0 2.9788 2.2238 0 2.9675 2.2233 0 2.9563 2.2229 0 2.9451 2.2225 0 2.934 2.2221 0

221

2.923 2.2216 0 2.9121 2.2212 0 2.9013 2.2208 0 2.8905 2.2204 0 2.8799 2.22 0 2.8693 2.2196 0 2.8588 2.2192 0 2.8483 2.2188 0 2.838 2.2184 0 2.8277 2.2181 0 2.8175 2.2177 0 2.8074 2.2173 0 2.7973 2.2169 0 2.7873 2.2166 0 2.7774 2.2162 0 2.7676 2.2159 0 2.7578 2.2155 0 2.7481 2.2152 0 2.7384 2.2148 0 2.7289 2.2145 0 2.7194 2.2141 0 2.7099 2.2138 0 2.7006 2.2135 0 2.6913 2.2131 0 2.682 2.2128 0 2.6728 2.2125 0 2.6637 2.2122 0 2.6547 2.2118 0 2.6457 2.2115 0 2.6368 2.2112 0 2.6279 2.2109 0 2.6191 2.2106 0 2.6103 2.2103 0 2.6016 2.21 0 2.593 2.2097 0 2.5844 2.2094 0 2.5759 2.2091 0 2.5675 2.2088 0 2.559 2.2085 0

2.5507 2.2082 0 2.5424 2.2079 0 2.5342 2.2077 0 2.526 2.2074 0

2.5178 2.2071 0 2.5098 2.2068 0 2.5017 2.2066 0 2.4937 2.2063 0 2.4858 2.206 0 2.4779 2.2058 0 2.4701 2.2055 0 2.4623 2.2052 0 2.4546 2.205 0 2.4469 2.2047 0 2.4393 2.2045 0 2.4317 2.2042 0 2.4242 2.204 0 2.4167 2.2037 0 2.4092 2.2035 0 2.4018 2.2032 0 2.3945 2.203 0 2.3872 2.2027 0 2.3799 2.2025 0 2.3727 2.2023 0 2.3655 2.202 0 2.3584 2.2018 0 2.3513 2.2016 0 2.3443 2.2013 0 2.3373 2.2011 0 2.3303 2.2009 0 2.3234 2.2007 0 2.3165 2.2004 0 2.3097 2.2002 0 2.3029 2.2 0 2.2961 2.1998 0 2.2894 2.1996 0 2.2827 2.1993 0 2.2761 2.1991 0 2.2695 2.1989 0

2.263 2.1987 0 2.2564 2.1985 0 2.2499 2.1983 0 2.2435 2.1981 0 2.2371 2.1979 0 2.2307 2.1977 0 2.2244 2.1975 0 2.2181 2.1973 0 2.2118 2.1971 0 2.2056 2.1969 0 2.1994 2.1967 0 2.1932 2.1965 0 2.1871 2.1963 0 2.181 2.1961 0 2.175 2.1959 0 2.1689 2.1957 0 2.163 2.1955 0 2.157 2.1953 0 2.1511 2.1951 0 2.1452 2.1949 0 2.1393 2.1948 0 2.1335 2.1946 0 2.1277 2.1944 0 2.1219 2.1942 0 2.1162 2.194 0 2.1105 2.1938 0 2.1048 2.1937 0 2.0992 2.1935 0 2.0936 2.1933 0 2.088 2.1931 0 2.0825 2.193 0 2.077 2.1928 0 2.0715 2.1926 0 2.066 2.1924 0 2.0606 2.1923 0 2.0552 2.1921 0 2.0498 2.1919 0 2.0444 2.1918 0 2.0391 2.1916 0

2.0338 2.1914 0 2.0286 2.1913 0 2.0233 2.1911 0 2.0181 2.1909 0 2.0129 2.1908 0 2.0078 2.1906 0 2.0027 2.1905 0 1.9976 2.1903 0 1.9925 2.1901 0 1.9874 2.19 0 1.9824 2.1898 0 1.9774 2.1897 0 1.9724 2.1895 0 1.9675 2.1893 0 1.9625 2.1892 0 1.9577 2.189 0 1.9528 2.1889 0 1.9479 2.1887 0 1.9431 2.1886 0 1.9383 2.1884 0 1.9335 2.1883 0 1.9288 2.1881 0 1.924 2.188 0 1.9193 2.1878 0 1.9146 2.1877 0 1.91 2.1875 0

1.9053 2.1874 0 1.9007 2.1872 0 1.8961 2.1871 0 1.8915 2.187 0 1.887 2.1868 0 1.8825 2.1867 0 1.878 2.1865 0 1.8735 2.1864 0 1.869 2.1862 0 1.8646 2.1861 0 1.8601 2.186 0 1.8557 2.1858 0 1.8514 2.1857 0

222

1.847 2.1855 0 1.8427 2.1854 0 1.8383 2.1853 0 1.834 2.1851 0 1.8298 2.185 0 1.8255 2.1849 0 1.8213 2.1847 0 1.817 2.1846 0 1.8128 2.1845 0 1.8087 2.1843 0 1.8045 2.1842 0 1.8004 2.1841 0 1.7962 2.1839 0 1.7921 2.1838 0 1.7881 2.1837 0 1.784 2.1835 0 1.7799 2.1834 0 1.7759 2.1833 0 1.7719 2.1831 0 1.7679 2.183 0 1.7639 2.1829 0 1.76 2.1828 0 1.756 2.1826 0 1.7521 2.1825 0 1.7482 2.1824 0 1.7443 2.1822 0 1.7405 2.1821 0 1.7366 2.182 0 1.7328 2.1819 0 1.729 2.1817 0 1.7252 2.1816 0 1.7214 2.1815 0 1.7176 2.1814 0 1.7139 2.1812 0 1.7101 2.1811 0 1.7064 2.181 0 1.7027 2.1809 0 1.699 2.1808 0 1.6954 2.1806 0

1.6917 2.1805 0 1.6881 2.1804 0 1.6844 2.1803 0 1.6808 2.1802 0 1.6772 2.18 0 1.6737 2.1799 0 1.6701 2.1798 0 1.6666 2.1797 0 1.663 2.1796 0

1.6595 2.1794 0 1.656 2.1793 0

1.6525 2.1792 0 1.6491 2.1791 0 1.6456 2.179 0 1.6422 2.1789 0 1.6387 2.1787 0 1.6353 2.1786 0 1.6319 2.1785 0 1.6285 2.1784 0 1.6252 2.1783 0 1.6218 2.1782 0 1.6185 2.1781 0 1.6152 2.1779 0 1.6118 2.1778 0 1.6085 2.1777 0 1.6053 2.1776 0 1.602 2.1775 0

1.5987 2.1774 0 1.5955 2.1773 0 1.5922 2.1772 0 1.589 2.177 0

1.5858 2.1769 0 1.5826 2.1768 0 1.5795 2.1767 0 1.5763 2.1766 0 1.5731 2.1765 0

1.57 2.1764 0 1.5669 2.1763 0 1.5637 2.1762 0

1.5606 2.1761 0 1.5576 2.1759 0 1.5545 2.1758 0 1.5514 2.1757 0 1.5484 2.1756 0 1.5453 2.1755 0 1.5423 2.1754 0 1.5393 2.1753 0 1.5363 2.1752 0 1.5333 2.1751 0 1.5303 2.175 0 1.5273 2.1749 0 1.5244 2.1748 0 1.5214 2.1747 0 1.5185 2.1745 0 1.5156 2.1744 0 1.5127 2.1743 0 1.5098 2.1742 0 1.5069 2.1741 0 1.504 2.174 0 1.5011 2.1739 0 1.4983 2.1738 0 1.4954 2.1737 0 1.4926 2.1736 0 1.4898 2.1735 0 1.487 2.1734 0 1.4842 2.1733 0 1.4814 2.1732 0 1.4786 2.1731 0 1.4758 2.173 0 1.4731 2.1729 0 1.4703 2.1728 0 1.4676 2.1727 0 1.4649 2.1726 0 1.4622 2.1725 0 1.4595 2.1724 0 1.4568 2.1723 0 1.4541 2.1722 0 1.4514 2.1721 0

1.4487 2.1719 0 1.4461 2.1718 0 1.4435 2.1717 0 1.4408 2.1716 0 1.4382 2.1715 0 1.4356 2.1714 0 1.433 2.1713 0 1.4304 2.1712 0 1.4278 2.1711 0 1.4252 2.171 0 1.4227 2.1709 0 1.4201 2.1708 0 1.4176 2.1707 0 1.4151 2.1706 0 1.4125 2.1705 0 1.41 2.1704 0

1.4075 2.1703 0 1.405 2.1702 0 1.4025 2.1701 0

1.4 2.17 0 1.3976 2.1699 0 1.3951 2.1698 0 1.3927 2.1697 0 1.3902 2.1696 0 1.3878 2.1695 0 1.3854 2.1694 0 1.383 2.1693 0 1.3806 2.1693 0 1.3782 2.1692 0 1.3758 2.1691 0 1.3734 2.169 0 1.371 2.1689 0 1.3687 2.1688 0 1.3663 2.1687 0 1.364 2.1686 0 1.3616 2.1685 0 1.3593 2.1684 0 1.357 2.1683 0 1.3547 2.1682 0

223

1.3524 2.1681 0 1.3501 2.168 0 1.3478 2.1679 0 1.3455 2.1678 0 1.3433 2.1677 0 1.341 2.1676 0 1.3388 2.1675 0 1.3365 2.1674 0 1.3343 2.1673 0 1.3321 2.1672 0 1.3299 2.1671 0 1.3277 2.167 0 1.3255 2.1669 0 1.3233 2.1668 0 1.3211 2.1667 0 1.3189 2.1666 0 1.3167 2.1665 0 1.3146 2.1664 0 1.3124 2.1664 0 1.3103 2.1663 0 1.3081 2.1662 0 1.306 2.1661 0 1.3039 2.166 0 1.3018 2.1659 0 1.2997 2.1658 0 1.2976 2.1657 0 1.2955 2.1656 0 1.2934 2.1655 0 1.2913 2.1654 0 1.2893 2.1653 0 1.2872 2.1652 0 1.2851 2.1651 0 1.2831 2.165 0 1.2811 2.1649 0 1.279 2.1648 0 1.277 2.1647 0 1.275 2.1647 0 1.273 2.1646 0 1.271 2.1645 0

1.269 2.1644 0 1.267 2.1643 0 1.265 2.1642 0 1.263 2.1641 0 1.2611 2.164 0 1.2591 2.1639 0 1.2572 2.1638 0 1.2552 2.1637 0 1.2533 2.1636 0 1.2514 2.1635 0 1.2494 2.1634 0 1.2475 2.1634 0 1.2456 2.1633 0 1.2437 2.1632 0 1.2418 2.1631 0 1.2399 2.163 0 1.2249 2.1622 0 1.2207 2.162 0 1.2166 2.1618 0 1.2126 2.1616 0 1.2085 2.1614 0 1.2045 2.1612 0 1.2005 2.161 0 1.1965 2.1608 0 1.1926 2.1606 0 1.1887 2.1604 0 1.1848 2.1602 0 1.1809 2.16 0 1.1771 2.1598 0 1.1732 2.1595 0 1.1695 2.1593 0 1.1657 2.1591 0 1.1619 2.1589 0 1.1582 2.1587 0 1.1545 2.1585 0 1.1509 2.1583 0 1.1472 2.1581 0 1.1436 2.1579 0

1.14 2.1577 0

1.1364 2.1575 0 1.1328 2.1573 0 1.1293 2.1571 0 1.1258 2.1569 0 1.1223 2.1566 0 1.1188 2.1564 0 1.1154 2.1562 0 1.1119 2.156 0 1.1085 2.1558 0 1.1052 2.1556 0 1.1018 2.1554 0 1.0984 2.1552 0 1.0951 2.155 0 1.0918 2.1548 0 1.0885 2.1546 0 1.0853 2.1543 0 1.082 2.1541 0 1.0788 2.1539 0 1.0756 2.1537 0 1.0724 2.1535 0 1.0692 2.1533 0 1.0661 2.1531 0 1.0629 2.1529 0 1.0598 2.1527 0 1.0567 2.1525 0 1.0536 2.1522 0 1.0506 2.152 0 1.0475 2.1518 0 1.0445 2.1516 0 1.0415 2.1514 0 1.0385 2.1512 0 1.0355 2.151 0 1.0326 2.1508 0 1.0296 2.1506 0 1.0267 2.1503 0 1.0238 2.1501 0 1.0209 2.1499 0 1.018 2.1497 0 1.0152 2.1495 0

1.0123 2.1493 0 1.0095 2.1491 0 1.0067 2.1488 0 1.0039 2.1486 0 1.0011 2.1484 0

0.99836 2.1482 0 0.99561 2.148 0 0.99287 2.1478 0 0.99015 2.1476 0 0.98744 2.1473 0 0.98475 2.1471 0 0.98208 2.1469 0 0.97941 2.1467 0 0.97677 2.1465 0 0.97413 2.1463 0 0.97151 2.146 0 0.96891 2.1458 0 0.96632 2.1456 0 0.96374 2.1454 0 0.96117 2.1452 0 0.95862 2.1449 0 0.95608 2.1447 0 0.95356 2.1445 0 0.95105 2.1443 0 0.94855 2.1441 0 0.94607 2.1438 0 0.94359 2.1436 0 0.94113 2.1434 0 0.93869 2.1432 0 0.93625 2.143 0 0.93383 2.1427 0 0.93142 2.1425 0 0.92902 2.1423 0 0.92664 2.1421 0 0.92427 2.1418 0 0.9219 2.1416 0 0.91956 2.1414 0 0.91722 2.1412 0 0.91489 2.1409 0

224

0.91258 2.1407 0 0.91028 2.1405 0 0.90798 2.1403 0 0.9057 2.14 0 0.90344 2.1398 0 0.90118 2.1396 0 0.89893 2.1394 0 0.8967 2.1391 0 0.89447 2.1389 0 0.89226 2.1387 0 0.89006 2.1384 0 0.88787 2.1382 0 0.88569 2.138 0 0.88351 2.1377 0 0.88135 2.1375 0 0.8792 2.1373 0 0.87707 2.1371 0 0.87493 2.1368 0 0.87282 2.1366 0 0.87071 2.1364 0 0.86861 2.1361 0 0.86652 2.1359 0 0.86444 2.1357 0 0.86237 2.1354 0 0.86031 2.1352 0 0.85826 2.135 0 0.85622 2.1347 0 0.85419 2.1345 0 0.85217 2.1342 0 0.85016 2.134 0 0.84815 2.1338 0 0.84616 2.1335 0 0.84417 2.1333 0 0.8422 2.1331 0 0.84023 2.1328 0 0.83828 2.1326 0 0.83633 2.1323 0 0.83439 2.1321 0 0.83246 2.1319 0

0.83054 2.1316 0 0.82862 2.1314 0 0.82672 2.1311 0 0.82482 2.1309 0 0.82294 2.1307 0 0.82106 2.1304 0 0.81919 2.1302 0 0.81732 2.1299 0 0.81547 2.1297 0 0.81362 2.1294 0 0.81179 2.1292 0 0.80996 2.129 0 0.80814 2.1287 0 0.80632 2.1285 0 0.80452 2.1282 0 0.80272 2.128 0 0.80093 2.1277 0 0.79915 2.1275 0 0.79737 2.1272 0 0.79561 2.127 0 0.79385 2.1267 0 0.7921 2.1265 0 0.79035 2.1262 0 0.78862 2.126 0 0.78689 2.1257 0 0.78517 2.1255 0 0.78345 2.1252 0 0.78174 2.125 0 0.78004 2.1247 0 0.77835 2.1245 0 0.77667 2.1242 0 0.77499 2.124 0 0.77332 2.1237 0 0.77165 2.1235 0

0.77 2.1232 0 0.76835 2.1229 0 0.7667 2.1227 0 0.76507 2.1224 0 0.76344 2.1222 0

0.76181 2.1219 0 0.7602 2.1217 0 0.75859 2.1214 0 0.75698 2.1211 0 0.75539 2.1209 0 0.7538 2.1206 0 0.75221 2.1204 0 0.75064 2.1201 0 0.74907 2.1198 0 0.7475 2.1196 0 0.74594 2.1193 0 0.74439 2.1191 0 0.74285 2.1188 0

225

A.4 Dielectric function of SnO2:F

eV ε1 ε2

6.5004 3.9713 4.0149 6.4471 3.8365 3.9148 6.3947 4.0079 3.9887 6.3432 4.041 4.0674 6.2924 4.1187 3.9552 6.2425 4.1532 3.9855 6.1933 4.1876 3.9881 6.1448 4.2819 3.9916 6.0972 4.3261 3.9426 6.0502 4.3707 3.9117 6.0039 4.4314 3.868 5.9584 4.5232 3.9396 5.9135 4.5773 3.8937 5.8692 4.6024 3.872 5.8257 4.6925 3.8377 5.7827 4.755 3.8735 5.7404 4.828 3.8354 5.6987 4.891 3.8227 5.6575 4.9459 3.7736

5.617 5.0635 3.8069 5.577 5.1365 3.8102

5.5376 5.2317 3.7544 5.4987 5.2471 3.7339 5.4604 5.3437 3.7248 5.4226 5.4337 3.7151 5.3853 5.5346 3.6793 5.3485 5.62 3.5867 5.3122 5.6826 3.5601 5.2764 5.7345 3.5325

5.241 5.7963 3.5341 5.2062 5.8783 3.4751 5.1717 5.9604 3.5094 5.1378 6.0616 3.4719 5.1042 6.1636 3.4253 5.0711 6.2959 3.389 5.0384 6.3878 3.3222

5.0062 6.5153 3.2727 4.9743 6.5892 3.2482 4.9429 6.6857 3.1561 4.9118 6.7541 3.0728 4.8811 6.8624 2.9625 4.8508 6.8828 2.8423 4.8209 6.9286 2.8191 4.7913 6.8787 2.713 4.7621 6.8868 2.666 4.7332 6.8607 2.5396 4.7047 6.8106 2.3692 4.6765 6.7108 2.17 4.6486 6.5733 1.9544 4.6211 6.4086 1.7318 4.5939 6.2269 1.5118

4.567 6.0375 1.3012 4.5405 5.8478 1.1047 4.5142 5.6671 0.92812 4.4882 5.501 0.77349 4.4626 5.3554 0.64218 4.4372 5.2368 0.53621 4.4121 5.1496 0.455 4.3873 5.1007 0.40485 4.3627 4.9976 0.36189 4.3384 4.9634 0.32464 4.3144 4.9301 0.29291 4.2907 4.8976 0.26542 4.2672 4.8663 0.24169

4.244 4.8361 0.22099 4.221 4.8071 0.20295

4.1983 4.7793 0.18707 4.1758 4.7528 0.17307 4.1536 4.7272 0.16065 4.1315 4.7029 0.14965 4.1098 4.6794 0.13975 4.0882 4.657 0.13093 4.0669 4.6353 0.12296

4.0458 4.6146 0.11577 4.0249 4.5946 0.10925 4.0042 4.5753 0.10334 3.9837 4.5568 0.097956 3.9635 4.5388 0.093011 3.9434 4.5215 0.088501 3.9235 4.5048 0.08436 3.9039 4.4885 0.080529 3.8844 4.4728 0.077006 3.8652 4.4575 0.073734 3.8461 4.4427 0.070718 3.8272 4.4283 0.067919 3.8085 4.4143 0.065308

3.79 4.4007 0.062875 3.7716 4.3875 0.060622 3.7534 4.3747 0.058505 3.7355 4.362 0.056515 3.7176 4.3498 0.054663

3.7 4.3378 0.052917 3.6825 4.3262 0.051279 3.6652 4.3147 0.049737

3.648 4.3036 0.04829 3.631 4.2927 0.04693

3.6142 4.282 0.045637 3.5975 4.2716 0.044418 3.5809 4.2614 0.043262 3.5646 4.2514 0.042167 3.5483 4.2416 0.041141 3.5322 4.2319 0.040162 3.5163 4.2225 0.03923 3.5005 4.2132 0.03834 3.4848 4.2042 0.037502 3.4693 4.1952 0.036701 3.4539 4.1865 0.035942 3.4387 4.1778 0.03522 3.4236 4.1693 0.03453 3.4086 4.161 0.033871

3.3938 4.1528 0.033239 3.3791 4.1447 0.032638 3.3645 4.1368 0.032069

3.35 4.129 0.03152 3.3357 4.1213 0.030999 3.3215 4.1137 0.030498 3.3074 4.1062 0.030019 3.2934 4.0989 0.029569 3.2795 4.0917 0.029131 3.2658 4.0845 0.028709 3.2522 4.0775 0.028309 3.2386 4.0706 0.027921 3.2252 4.0637 0.027551

3.212 4.0569 0.027199 3.1988 4.0502 0.026859 3.1857 4.0436 0.02654 3.1727 4.0371 0.026221 3.1599 4.0307 0.025929 3.1471 4.0243 0.02564 3.1345 4.018 0.025359 3.1219 4.0119 0.0251 3.1095 4.0057 0.024849 3.0971 3.9997 0.0246 3.0849 3.9936 0.024369 3.0727 3.9877 0.02415 3.0607 3.9818 0.023929 3.0487 3.9761 0.02373 3.0368 3.9703 0.02353

3.025 3.9647 0.023341 3.0134 3.959 0.023159 3.0018 3.9534 0.022989 2.9902 3.948 0.022821 2.9788 3.9425 0.02266 2.9675 3.9371 0.02251 2.9563 3.9317 0.022359 2.9451 3.9264 0.02222

2.934 3.9212 0.02209

226

2.923 3.916 0.02196 2.9121 3.9108 0.02184 2.9013 3.9057 0.02172 2.8905 3.9006 0.02161 2.8799 3.8956 0.0215 2.8693 3.8906 0.0214 2.8588 3.8856 0.0213 2.8483 3.8808 0.02121

2.838 3.8759 0.02113 2.8277 3.8711 0.02104 2.8175 3.8663 0.02097 2.8074 3.8615 0.02089 2.7973 3.8568 0.02082 2.7873 3.8521 0.02076 2.7774 3.8475 0.02069 2.7676 3.8428 0.02063 2.7578 3.8382 0.02058 2.7481 3.8337 0.02053 2.7384 3.8292 0.02048 2.7289 3.8247 0.02044 2.7194 3.8202 0.0204 2.7099 3.8158 0.02036 2.7006 3.8114 0.02033 2.6913 3.807 0.02029

2.682 3.8026 0.02027 2.6728 3.7983 0.02024 2.6637 3.794 0.02022 2.6547 3.7897 0.0202 2.6457 3.7855 0.02018 2.6368 3.7812 0.02017 2.6279 3.7771 0.02016 2.6191 3.7729 0.02015 2.6103 3.7687 0.02014 2.6016 3.7646 0.02014

2.593 3.7605 0.02014 2.5844 3.7564 0.02014 2.5759 3.7523 0.02014 2.5675 3.7482 0.02015

2.559 3.7443 0.02015

2.5507 3.7402 0.02016 2.5424 3.7362 0.02018 2.5342 3.7322 0.02019

2.526 3.7283 0.02021 2.5178 3.7244 0.02023 2.5098 3.7204 0.02025 2.5017 3.7166 0.02027 2.4937 3.7127 0.0203 2.4858 3.7088 0.02032 2.4779 3.7049 0.02035 2.4701 3.7011 0.02038 2.4623 3.6973 0.02042 2.4546 3.6935 0.02045 2.4469 3.6897 0.02049 2.4393 3.6859 0.02052 2.4317 3.6821 0.02056 2.4242 3.6783 0.02061 2.4167 3.6746 0.02065 2.4092 3.6709 0.02069 2.4018 3.6672 0.02074 2.3945 3.6635 0.02079 2.3872 3.6598 0.02084 2.3799 3.6561 0.02089 2.3727 3.6524 0.02094 2.3655 3.6488 0.021 2.3584 3.6451 0.02105 2.3513 3.6415 0.02111 2.3443 3.6379 0.02117 2.3373 3.6342 0.02123 2.3303 3.6307 0.02129 2.3234 3.6271 0.02136 2.3165 3.6235 0.02142 2.3097 3.6199 0.02149 2.3029 3.6163 0.02156 2.2961 3.6128 0.02163 2.2894 3.6092 0.0217 2.2827 3.6057 0.02177 2.2761 3.6022 0.02185 2.2695 3.5986 0.02192

2.263 3.5951 0.022001 2.2564 3.5916 0.02208 2.2499 3.5881 0.022159 2.2435 3.5846 0.02224 2.2371 3.5811 0.02232 2.2307 3.5777 0.0224 2.2244 3.5742 0.02249 2.2181 3.5707 0.02257 2.2118 3.5673 0.02266 2.2056 3.5638 0.02275 2.1994 3.5604 0.02284 2.1932 3.557 0.022929 2.1871 3.5535 0.02302

2.181 3.5501 0.02312 2.175 3.5466 0.023211

2.1689 3.5433 0.023309 2.163 3.5398 0.023411 2.157 3.5364 0.0235

2.1511 3.533 0.0236 2.1452 3.5296 0.02371 2.1393 3.5262 0.02381 2.1335 3.5228 0.02391 2.1277 3.5195 0.02402 2.1219 3.5161 0.024119 2.1162 3.5127 0.02423 2.1105 3.5093 0.02434 2.1048 3.506 0.024449 2.0992 3.5026 0.02456 2.0936 3.4992 0.02467

2.088 3.4959 0.02478 2.0825 3.4925 0.024901

2.077 3.4892 0.025011 2.0715 3.4858 0.025131

2.066 3.4825 0.02524 2.0606 3.4791 0.025361 2.0552 3.4758 0.025481 2.0498 3.4725 0.0256 2.0444 3.4692 0.025729 2.0391 3.4658 0.025849

2.0338 3.4625 0.025969 2.0286 3.4592 0.026101 2.0233 3.4559 0.026229 2.0181 3.4525 0.026349 2.0129 3.4492 0.026479 2.0078 3.4459 0.02661 2.0027 3.4426 0.026741 1.9976 3.4392 0.026871 1.9925 3.4359 0.027011 1.9874 3.4327 0.027139 1.9824 3.4293 0.02728 1.9774 3.426 0.02741 1.9724 3.4227 0.027549 1.9675 3.4194 0.027691 1.9625 3.4161 0.027829 1.9577 3.4128 0.027971 1.9528 3.4095 0.028111 1.9479 3.4062 0.028259 1.9431 3.4029 0.0284 1.9383 3.3996 0.02854 1.9335 3.3963 0.02869 1.9288 3.393 0.028841

1.924 3.3897 0.028989 1.9193 3.3864 0.02914 1.9146 3.3831 0.029289

1.91 3.3798 0.029441 1.9053 3.3765 0.029589 1.9007 3.3732 0.02974 1.8961 3.3699 0.0299 1.8915 3.3667 0.030059

1.887 3.3633 0.03021 1.8825 3.36 0.030371

1.878 3.3567 0.030532 1.8735 3.3534 0.030691

1.869 3.3502 0.03085 1.8646 3.3468 0.031012 1.8601 3.3436 0.031179 1.8557 3.3403 0.031339 1.8514 3.3369 0.031512

227

1.847 3.3337 0.03167 1.8427 3.3303 0.031842 1.8383 3.3271 0.032009

1.834 3.3238 0.032178 1.8298 3.3205 0.032352 1.8255 3.3172 0.03252 1.8213 3.3138 0.032692

1.817 3.3106 0.032868 1.8128 3.3073 0.033038 1.8087 3.3039 0.033221 1.8045 3.3007 0.0334 1.8004 3.2973 0.033571 1.7962 3.2941 0.033748 1.7921 3.2908 0.033928 1.7881 3.2874 0.034112

1.784 3.2841 0.0343 1.7799 3.2808 0.034478 1.7759 3.2775 0.034659 1.7719 3.2741 0.03485 1.7679 3.2708 0.035039 1.7639 3.2675 0.035218

1.76 3.2642 0.035411 1.756 3.2609 0.035598

1.7521 3.2575 0.035789 1.7482 3.2542 0.035989 1.7443 3.2509 0.036178 1.7405 3.2475 0.036372 1.7366 3.2442 0.036569 1.7328 3.2409 0.036761

1.729 3.2375 0.036962 1.7252 3.2342 0.037162 1.7214 3.2308 0.037361 1.7176 3.2275 0.03756 1.7139 3.2241 0.037762 1.7101 3.2208 0.037959 1.7064 3.2175 0.03817 1.7027 3.2141 0.03837

1.699 3.2108 0.038579 1.6954 3.2074 0.038783

1.6917 3.204 0.03899 1.6881 3.2007 0.039202 1.6844 3.1974 0.039408 1.6808 3.194 0.039618 1.6772 3.1906 0.039828 1.6737 3.1872 0.040042 1.6701 3.1839 0.04026 1.6666 3.1804 0.040472

1.663 3.1771 0.040688 1.6595 3.1737 0.040909

1.656 3.1704 0.041129 1.6525 3.167 0.041348 1.6491 3.1635 0.041572 1.6456 3.1602 0.041789 1.6422 3.1567 0.042012 1.6387 3.1534 0.042227 1.6353 3.15 0.042458 1.6319 3.1466 0.042688 1.6285 3.1432 0.042907 1.6252 3.1397 0.043141 1.6218 3.1364 0.043368 1.6185 3.1329 0.043601 1.6152 3.1295 0.043833 1.6118 3.1262 0.044057 1.6085 3.1227 0.044297 1.6053 3.1192 0.044533

1.602 3.1158 0.044771 1.5987 3.1124 0.044998 1.5955 3.109 0.045241 1.5922 3.1056 0.045476

1.589 3.1021 0.045718 1.5858 3.0987 0.045958 1.5826 3.0953 0.046198 1.5795 3.0917 0.046454 1.5763 3.0883 0.046691 1.5731 3.0849 0.046937

1.57 3.0814 0.047181 1.5669 3.0779 0.047433 1.5637 3.0745 0.047676

1.5606 3.0711 0.047926 1.5576 3.0675 0.048184 1.5545 3.0641 0.048432 1.5514 3.0606 0.048679 1.5484 3.0571 0.048943 1.5453 3.0537 0.049189 1.5423 3.0501 0.049451 1.5393 3.0466 0.049713 1.5363 3.0431 0.049973 1.5333 3.0396 0.050222 1.5303 3.0362 0.050491 1.5273 3.0327 0.050748 1.5244 3.0291 0.051013 1.5214 3.0257 0.051268 1.5185 3.0221 0.051541 1.5156 3.0186 0.051803 1.5127 3.0151 0.052074 1.5098 3.0115 0.052344 1.5069 3.008 0.052613

1.504 3.0045 0.052881 1.5011 3.001 0.053148 1.4983 2.9974 0.053423 1.4954 2.994 0.053697 1.4926 2.9904 0.05397 1.4898 2.9868 0.054252

1.487 2.9832 0.054533 1.4842 2.9797 0.054803 1.4814 2.9761 0.055082 1.4786 2.9726 0.05536 1.4758 2.9691 0.055646 1.4731 2.9655 0.055932 1.4703 2.962 0.056207 1.4676 2.9583 0.0565 1.4649 2.9547 0.056783 1.4622 2.9511 0.057074 1.4595 2.9475 0.057364 1.4568 2.944 0.057654 1.4541 2.9404 0.057942 1.4514 2.9368 0.058229

1.4487 2.9333 0.058515 1.4461 2.9296 0.05881 1.4435 2.9259 0.059115 1.4408 2.9224 0.059407 1.4382 2.9188 0.0597 1.4356 2.9152 0.060001

1.433 2.9115 0.060301 1.4304 2.9079 0.0606 1.4278 2.9043 0.060898 1.4252 2.9007 0.061195 1.4227 2.897 0.061512 1.4201 2.8934 0.061807 1.4176 2.8897 0.062122 1.4151 2.8862 0.062414 1.4125 2.8825 0.062727

1.41 2.8788 0.063039 1.4075 2.8752 0.063349

1.405 2.8715 0.063659 1.4025 2.8679 0.063977

1.4 2.8642 0.064284 1.3976 2.8605 0.064603 1.3951 2.8569 0.064917 1.3927 2.8531 0.065244 1.3902 2.8495 0.065546 1.3878 2.8458 0.06587 1.3854 2.8421 0.066193

1.383 2.8384 0.066525 1.3806 2.8347 0.066845 1.3782 2.831 0.067165 1.3758 2.8273 0.067493 1.3734 2.8236 0.06781

1.371 2.82 0.068136 1.3687 2.8162 0.068474 1.3663 2.8125 0.068797

1.364 2.8087 0.069133 1.3616 2.8051 0.069454 1.3593 2.8014 0.069787

1.357 2.7976 0.07012 1.3547 2.7939 0.070461

228

1.3524 2.7901 0.070791 1.3501 2.7864 0.071129 1.3478 2.7827 0.071467 1.3455 2.779 0.071803 1.3433 2.7751 0.072153

1.341 2.7714 0.072486 1.3388 2.7676 0.072834 1.3365 2.7639 0.073165 1.3343 2.7601 0.07352 1.3321 2.7563 0.073864 1.3299 2.7525 0.074216 1.3277 2.7487 0.074567 1.3255 2.745 0.074908 1.3233 2.7412 0.075257 1.3211 2.7374 0.075614 1.3189 2.7337 0.07596 1.3167 2.73 0.076305 1.3146 2.7261 0.076665 1.3124 2.7224 0.077017 1.3103 2.7185 0.077384 1.3081 2.7148 0.077724

1.306 2.711 0.078089 1.3039 2.7071 0.078452 1.3018 2.7033 0.078815 1.2997 2.6995 0.079176 1.2976 2.6956 0.079535 1.2955 2.6918 0.079904 1.2934 2.6881 0.080261 1.2913 2.6843 0.080626 1.2893 2.6803 0.081008 1.2872 2.6766 0.081361 1.2851 2.6728 0.081723 1.2831 2.6689 0.082101 1.2811 2.665 0.082478 1.279 2.6613 0.082845 1.277 2.6574 0.08322 1.275 2.6535 0.083592 1.273 2.6497 0.083974 1.271 2.6458 0.084344

1.269 2.642 0.084723 1.267 2.6381 0.085101 1.265 2.6343 0.085477 1.263 2.6305 0.085851

1.2611 2.6265 0.086244 1.2591 2.6227 0.086616 1.2572 2.6188 0.087015 1.2552 2.615 0.087385 1.2533 2.6111 0.087782 1.2514 2.6071 0.088167 1.2494 2.6034 0.088542 1.2475 2.5995 0.088935 1.2456 2.5956 0.089327 1.2437 2.5917 0.089717 1.2418 2.5878 0.090106 1.2399 2.5839 0.090494 1.2249 2.5522 0.093724 1.2207 2.5435 0.094619 1.2166 2.5346 0.09554 1.2126 2.5255 0.096477 1.2085 2.5167 0.097396 1.2045 2.5076 0.098342 1.2005 2.4987 0.099281 1.1965 2.4897 0.10022 1.1926 2.4806 0.10119 1.1887 2.4714 0.10216 1.1848 2.4624 0.10313 1.1809 2.4533 0.1041 1.1771 2.4441 0.10509 1.1732 2.4351 0.10606 1.1695 2.4257 0.10707 1.1657 2.4166 0.10806 1.1619 2.4075 0.10906 1.1582 2.3982 0.11008 1.1545 2.3889 0.1111 1.1509 2.3794 0.11215 1.1472 2.3702 0.11317 1.1436 2.3608 0.11422

1.14 2.3514 0.11527

1.1364 2.342 0.11632 1.1328 2.3327 0.11737 1.1293 2.3232 0.11845 1.1258 2.3137 0.11952 1.1223 2.3042 0.1206 1.1188 2.2947 0.12168 1.1154 2.285 0.1228 1.1119 2.2756 0.12388 1.1085 2.266 0.12499 1.1052 2.2561 0.12614 1.1018 2.2466 0.12724 1.0984 2.237 0.12836 1.0951 2.2273 0.12951 1.0918 2.2175 0.13065 1.0885 2.2078 0.13179 1.0853 2.1978 0.13298

1.082 2.1882 0.13412 1.0788 2.1783 0.13531 1.0756 2.1684 0.13648 1.0724 2.1585 0.13766 1.0692 2.1487 0.13884 1.0661 2.1386 0.14006 1.0629 2.1288 0.14125 1.0598 2.1188 0.14247 1.0567 2.1088 0.14369 1.0536 2.0988 0.14491 1.0506 2.0886 0.14617 1.0475 2.0787 0.1474 1.0445 2.0685 0.14866 1.0415 2.0583 0.14992 1.0385 2.0482 0.15118 1.0355 2.0381 0.15244 1.0326 2.0276 0.15375 1.0296 2.0176 0.155 1.0267 2.0072 0.15631 1.0238 1.9969 0.15762 1.0209 1.9866 0.15892

1.018 1.9764 0.16023 1.0152 1.9658 0.16158

1.0123 1.9556 0.16289 1.0095 1.9451 0.16424 1.0067 1.9346 0.16559 1.0039 1.9241 0.16695 1.0011 1.9137 0.1683

0.99836 1.903 0.16968 0.99561 1.8925 0.17106 0.99287 1.8819 0.17245 0.99015 1.8713 0.17384 0.98744 1.8607 0.17524 0.98475 1.85 0.17665 0.98208 1.8393 0.17806 0.97941 1.8286 0.17949 0.97677 1.8179 0.18092 0.97413 1.8071 0.18236 0.97151 1.7963 0.18381 0.96891 1.7855 0.18526 0.96632 1.7746 0.18673 0.96374 1.7638 0.1882 0.96117 1.7529 0.18968 0.95862 1.742 0.19116 0.95608 1.731 0.19266 0.95356 1.72 0.19416 0.95105 1.709 0.19567 0.94855 1.698 0.19719 0.94607 1.6869 0.19872 0.94359 1.6758 0.20025 0.94113 1.6647 0.2018 0.93869 1.6536 0.20335 0.93625 1.6424 0.20491 0.93383 1.6312 0.20648 0.93142 1.62 0.20805 0.92902 1.6088 0.20963 0.92664 1.5975 0.21123 0.92427 1.5862 0.21283 0.9219 1.5749 0.21444

0.91956 1.5635 0.21605 0.91722 1.5521 0.21768 0.91489 1.5407 0.21931

229

0.91258 1.5293 0.22095 0.91028 1.5178 0.2226 0.90798 1.5064 0.22426 0.9057 1.4948 0.22593

0.90344 1.4833 0.2276 0.90118 1.4717 0.22929 0.89893 1.4601 0.23098 0.8967 1.4485 0.23268

0.89447 1.4369 0.23439 0.89226 1.4252 0.23611 0.89006 1.4135 0.23783 0.88787 1.4017 0.23957 0.88569 1.39 0.24131 0.88351 1.3782 0.24306 0.88135 1.3664 0.24482 0.8792 1.3546 0.24659

0.87707 1.3427 0.24837 0.87493 1.3308 0.25016 0.87282 1.3188 0.25195 0.87071 1.3069 0.25376 0.86861 1.2949 0.25557 0.86652 1.2829 0.25739 0.86444 1.2709 0.25922 0.86237 1.2589 0.26106 0.86031 1.2468 0.26291 0.85826 1.2347 0.26477 0.85622 1.2225 0.26664 0.85419 1.2104 0.26851 0.85217 1.1982 0.2704 0.85016 1.1859 0.27229 0.84815 1.1737 0.27419 0.84616 1.1614 0.2761 0.84417 1.1492 0.27802 0.8422 1.1368 0.27995

0.84023 1.1245 0.28189 0.83828 1.112 0.28384 0.83633 1.0996 0.28579 0.83439 1.0872 0.28776 0.83246 1.0747 0.28973

0.83054 1.0622 0.29172 0.82862 1.0498 0.29371 0.82672 1.0372 0.29572 0.82482 1.0246 0.29773 0.82294 1.012 0.29975 0.82106 0.99934 0.30178 0.81919 0.98667 0.30382 0.81732 0.97405 0.30587 0.81547 0.9613 0.30793 0.81362 0.94859 0.31 0.81179 0.93576 0.31207 0.80996 0.92297 0.31416 0.80814 0.91012 0.31627 0.80632 0.89732 0.31836 0.80452 0.8844 0.32048 0.80272 0.87151 0.3226 0.80093 0.85858 0.32474 0.79915 0.8456 0.32688 0.79737 0.83265 0.32904 0.79561 0.81958 0.3312 0.79385 0.80654 0.33337 0.7921 0.79346 0.33557

0.79035 0.7804 0.33775 0.78862 0.76723 0.33996 0.78689 0.75408 0.34216 0.78517 0.74087 0.34439 0.78345 0.7277 0.34662 0.78174 0.71448 0.34885 0.78004 0.70121 0.3511 0.77835 0.6879 0.35337 0.77667 0.67454 0.35564 0.77499 0.66118 0.35792 0.77332 0.6478 0.36021 0.77165 0.63443 0.36252

0.77 0.62094 0.36484 0.76835 0.60748 0.36716 0.7667 0.59403 0.36948

0.76507 0.58046 0.37183 0.76344 0.56691 0.37418

0.76181 0.55339 0.37653 0.7602 0.53972 0.37891

0.75859 0.52609 0.38129 0.75698 0.51249 0.38367 0.75539 0.49874 0.38608 0.7538 0.48502 0.38849

0.75221 0.47133 0.3909 0.75064 0.45749 0.39336 0.74907 0.44369 0.3958 0.7475 0.42991 0.39824

0.74594 0.41607 0.4007 0.74439 0.40216 0.40318 0.74285 0.3882 0.40567