photodarkening of germanium-selenium glasses induced by below-bandgap light

PHOTODARKENING OF GERMANIUM-SELENIUM GLASSESINDUCED BY BELOW-BANDGAP LIGHT

By

CRAIG RUSSELL SCHARDT

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOLOF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2000

Copyright 2000

by

Craig Russell Schardt

To my parents, Jean and George Schardt.

iv

ACKNOWLEDGMENTS

It is my great pleasure to thank my advisor, Dr. Joseph Simmons, for his patience

and guidance throughout my years as a graduate student. He gives his students the

freedom to find their own research direction and the encouragement to produce quality

over quantity. I believe that his supervision has helped me to become a better researcher

and prepared me for the challenges I will face in my professional career. I also thank the

members of my committeeDr. Cammy Abernathy, Dr. Paul Holloway, Dr. Rolf

Hummel, and Dr. David Reitzefor all of their assistance and thoughtful comments.

I could not have completed this project without the excellent samples prepared by

Pierre Lucas and Lydia LeNiendre. I must also thank Pierre for the many papers he sent

me and the useful conversations we have had. My gratitude goes out to Dr. Li Wang for

teaching me how to set up and operate the Ti:Sapphire laser and to Mrs. Catherine J.

Simmons for all of her encouragement and advice.

Gwain A. Davis has been a friend and mentor to me outside of the lab. I would

like to thank him for all of his guidance in developing my leadership skills and for

showing me that people live up to your expectations of them.

Finally, I extend special thanks to my wife, Heather M. Mockler-Schardt, for her

love and support during my years as a graduate student. She has been my unwavering

companion from the beginning, and for this I am indebted to her.

v

TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ................................................................................................. iv

LIST OF TABLES........................................................................................................... viii

LIST OF FIGURES ........................................................................................................... ix

ABSTRACT...................................................................................................................... xii

CHAPTERS

1 INTRODUCTION...........................................................................................................1

Chalcogenide Glasses and Light..................................................................................... 1Electronic Properties................................................................................................... 2Optical Properties........................................................................................................ 4Nonlinear Index of Refraction and Absorption .......................................................... 5Vibrational Properties ................................................................................................. 7

Photoinduced Effects in Chalcogenide Glass ................................................................. 7Photodarkening ........................................................................................................... 8Photoinduced Anisotropy............................................................................................ 9Photoinduced Crystallization ...................................................................................... 9Photodiffusion and Photodoping............................................................................... 10Photoexpansion and Photoinduced Fluidity.............................................................. 10Summary of Photoinduced Effects ........................................................................... 11

Applications for Chalcogenide Glasses ........................................................................ 12Optical Limiting........................................................................................................ 12Infrared Fiber Optics................................................................................................. 14Photolithography....................................................................................................... 19Optical Switching...................................................................................................... 19Optical Computing.................................................................................................... 20

Contribution of This Research ...................................................................................... 22Systematic Study of a Variety of Compositions ....................................................... 23Ti:Sapphire Laser...................................................................................................... 24Measurement of Kinetics .......................................................................................... 25Raman Spectroscopy................................................................................................. 27Summary................................................................................................................... 27

vi

2 BACKGROUND...........................................................................................................29

Optical Physics.............................................................................................................. 29Absorption and Refraction........................................................................................ 29Dielectric Response .................................................................................................. 34

Germanium-Selenium Glass ......................................................................................... 40Amorphous Selenium................................................................................................ 43Amorphous Germanium Diselenide ......................................................................... 46Selenium-Rich Germanium-Selenium Glasses......................................................... 50

3 EXPERIMENTAL METHODS ....................................................................................53

Chalcogenide Glass Samples ........................................................................................ 53Glass Preparation ...................................................................................................... 53Spectroscopic Analysis ............................................................................................. 54

Photodarkening Measurements..................................................................................... 56Ti:Sapphire Laser...................................................................................................... 56Optical Arrangement................................................................................................. 58Data Acquisition and Analysis.................................................................................. 64Experiment Methodology ......................................................................................... 65

Raman Spectroscopy..................................................................................................... 67Raman Apparatus...................................................................................................... 69Experimental Raman Measurements ........................................................................ 72

4 MEASUREMENT OF OPTICAL PROPERTIES ........................................................75

Infrared Absorption Edge ............................................................................................. 75Visible Absorption Edge............................................................................................... 78

Measured Data .......................................................................................................... 80Extraction of Optical Properties................................................................................ 82

Discussion ..................................................................................................................... 90

5 BELOW-BANDGAP PHOTODARKENING ..............................................................96

Changes in Optical Properties Induced by Below-Bandgap Light ............................... 96Transmittance and Reflectance Changes ................................................................ 101Real and Imaginary Dielectric Response................................................................ 105Effect of Composition on Photodarkening ............................................................. 114The Kinetics of Photodarkening ............................................................................. 115Transient Darkening and Dark Recovery................................................................ 133

Mechanism of Permanent and Transient Below-Bandgap Photodarkening ............... 143Kolobovs Model of Dynamical Bond Formation .................................................. 147Dynamical Bonds and Photodarkening of Germanium Selenium-Glasses............. 152

6 RAMAN STUDIES OF STRUCTURE AND TEMPERATURE ..............................156

Structure Changes During Photodarkening ................................................................ 157

vii

Transmission Measurements................................................................................... 157Raman Scattering Results ....................................................................................... 159

Sample Temperature Measurements........................................................................... 161Calculation of Temperature from Raman Spectra .................................................. 161Temperature Measurements for the Germanium-Selenium Samples ..................... 163

Discussion of Raman Measurements .......................................................................... 166Proof of Athermal Photodarkening......................................................................... 167Permanent Photodarkening Without Obvious Structure Change............................ 168

7 CONCLUSIONS.........................................................................................................172

APPENDIX POLISHING PROCEDURE FOR GLASS SAMPLES ..........................180

REFERENCES ................................................................................................................183

BIOGRAPHICAL SKETCH ...........................................................................................196

viii

LIST OF TABLES

Table page

3-1: Glass compositions used in this study........................................................................53

3-2: Performance of neutral density filters at 800 nm wavelength....................................60

4-1: Fundamental infrared active vibrations observed in amorphous selenium andgermanium-selenium glasses .................................................................................78

4-2: Optical properties of germanium-selenium glasses calculated by applicationof the Curve Fitting Technique to the measured absorbance spectra ....................85

4-3: Optical properties of germanium-selenium glasses calculated by applicationof the Derivative Technique to the measured absorbance spectra.........................88

4-4: Reported values for the refractive index (n) of germanium-selenium glassesat 800 nm................................................................................................................91

4-5: Reported values for the absorption coefficient (α) of germanium-seleniumglasses at 800 nm ...................................................................................................92

4-6: Reported values for the optical bandgap (Ego) germanium-selenium glass at800 nm ...................................................................................................................93

5-1: Parameters determined by fitting Equation 5-8 to the data in Figure 5-17 ..............125

6-1: Temperature of germanium-selenium glasses during exposure to 800 nmlaser light..............................................................................................................165

ix

LIST OF FIGURES

Figure page

1-1: Typical band structure of lone-pair semiconductors ....................................................4

2-1: Typical imaginary dielectric response of a chalcogenide glass..................................37

2-2: Structural elements of germanium-selenium glass containing less than 33%germanium .............................................................................................................43

3-1: Typical spectral profile of the Ti:Sapphire laser operating in CW mode...................57

3-2: Experimental apparatus used for simultaneous measurement of transmissionand reflection during photodarkening of the chalcogenide glass samples.............59

3-3: Experimental apparatus for measurement of Raman scattering duringphotodarkening ......................................................................................................70

4-1: Infrared absorbance of germanium-selenium glasses showing the multi-phonon absorption peaks........................................................................................76

4-2: Measured absorbance of germanium-selenium glasses in the exponentialband tail region ......................................................................................................81

4-3: Measured transmittance versus energy for germanium-selenium glasses..................83

4-4: Index of refraction at 800 nm for germanium-selenium glasses ................................91

4-5: Absorption coefficient at 800 nm for germanium-selenium glasses ..........................92

4-6: Optical bandgap for germanium-selenium glasses.....................................................93

5-1: Transmittance and reflectance of GeSe9 during exposure to 800 nm laser light........97

5-2: Transmittance and reflectance of Ge3Se17 during exposure to 800 nm laserlight ........................................................................................................................98

5-3: Transmittance and reflectance of GeSe4 during exposure to 800 nm laser light........99

5-4: Transmittance and reflectance of GeSe3 during exposure to 800 nm laser light......100

x

5-5: Transmittance change of the GeSe9 sample at the highest laser power (52.6mW). ....................................................................................................................102

5-6: Transmittance change of the Ge3Se17 sample at the highest laser power (57.9mW). ....................................................................................................................104

5-7: The real and imaginary parts of the dielectric response of GeSe9 glass at 800nm, calculated from the data in Figure 4-1 ..........................................................108

5-8: The real and imaginary parts of the dielectric response of Ge3Se17 glass at800 nm, calculated from the data in Figure 5-2 ...................................................109



5-11: Comparison of the change in the imaginary part of the dielectric response at3.5 mW laser power .............................................................................................114

5-12: Comparison of the change in the imaginary part of the dielectric response at10 mW laser power ..............................................................................................116

5-13: The imaginary part of the dielectric response of Ge3Se17 glass showing thetwo stages of photodarkening ..............................................................................117

5-14: Typical fit of the Stage I darkening process using First Order and SecondOrder models of the photodarkening kinetics ......................................................119

5-15: The imaginary part of the dielectric response at the start of exposure...................121

5-16: The slope of the linear fits to the data of Figure 5-15 versus the compositionof the glass ...........................................................................................................123

5-17: The maximum change in the imaginary dielectric (∆ε2) observed duringStage I darkening .................................................................................................124

5-18: The value of the fluence at which the Stage I darkening has reached 50% ofits final value........................................................................................................126

5-19: The slope of the darkening with respect to the fluence (dε2/dΦ) at thebeginning of the photodarkening experiments.....................................................127

5-20: Permanent and transient photodarkening in GeSe9 ................................................133

5-21: Transmittance change in GeSe9 during photodarkening with 800 nm light...........134

5-22: Permanent and transient photodarkening in Ge3Se17 glass.....................................136

xi

5-23: Permanent changes occurring after the transient response during re-exposure of an already darkened spot in Ge3Se17 glass .......................................138

5-24: Permanent and transient photodarkening in GeSe4 glass .......................................139

5-25: Re-exposure of a spot on the GeSe4 sample...........................................................140

5-26: Dynamical bond formation in chalcogenide glass..................................................149

5-27: Diagram of the photodarkening process in chalcogenide glass..............................154

6-1: Typical Raman spectra of germanium-selenium glass and silica.............................156

6-2: Transmission change of GeSe9 during Raman measurements .................................158

6-3: Raman spectra from before and after darkening for GeSe9......................................159

6-4: Raman spectra from before and after darkening for Ge3Se17 ...................................160

6-5: Raman spectra from before and after darkening for GeSe4......................................160

6-6: Typical Stokes and anti-Stokes spectrum, and the temperature valuescalculated from this data ......................................................................................164

xii

Abstract of Dissertation Presented to the Graduate Schoolof the University of Florida in Partial Fulfillment of theRequirements for the Degree of Doctor of Philosophy

PHOTODARKENING OF GERMANIUM-SELENIUM GLASSESINDUCED BY BELOW-BANDGAP LIGHT

By

Craig Russell Schardt

August 2000

Chairman: Joseph H. SimmonsMajor Department: Materials Science and Engineering

Photosensitive processes reveal fascinating details about the relationship between

structure and properties in materials. Photosensitive materials and the control of their

behavior are also important for the growing field of optical communications.

Chalcogenide glasses are a class of photosensitive materials with optical, mechanical, and

chemical properties that make them candidate materials for such applications.

This dissertation reports on an investigation of the photodarkening of germanium-

selenium chalcogenide glasses. Experiments were performed on four compositions,

GeSe9, Ge3Se17, GeSe4, and GeSe3, prepared by a conventional bulk-melting technique.

These glasses were chosen because their structure is well characterized and because they

represent a fundamental, binary glass composition from which many other glasses are

derived. The compositions were photodarkened by light from a Ti:Sapphire laser. This

light, with a wavelength of 800 nm, is below the bandgap of the glass, but within the

exponential absorption tail. Below-bandgap light was chosen because it can induce

xiii

darkening in thick samples (≈1 mm for this project). From time-resolved measurements

of the transmittance and reflectance, we are able to calculate the light-induced changes in

the dielectric response function of the samples.

We find that the photodarkening has similar characteristics for all of the samples.

The darkening profile is intensity dependent and depends on both the fluence and the

flux. It proceeds in two stages, the first of which appears governed by reaction-rate

kinetics, and the second of which is highly composition dependent. We show that the rate

and the magnitude of the photodarkening depend on the ratio of germanium to selenium

with the maximum photosensitivity occurring for GeSe4. Transient processes are also

seen in the high-selenium compositions. Raman spectroscopy performed during

photodarkening reveals no obvious change in the short-range structure. Analysis of

Stokes and anti-Stokes scattering permit us to calculate the sample temperature. We show

that the temperature increases less than 5 °C above room-temperature during

photodarkening. This is the first direct experimental proof that photodarkening is

athermal. We discuss our results with respect to several models of photodarkening and

show that they are most consistent with the dynamical bond model.

1

CHAPTER 1INTRODUCTION

Chalcogenide Glasses and Light

Chalcogens are the atoms occupying column six of the periodic table−sulfur,

selenium, and tellurium. The common factor linking these elements is the presence of six

electrons in their outer valence shell. When neutral, the atoms have two electrons paired

in a filled s shell, two more in a filled p shell, and one each in the other two p shells. This

configuration leaves two unfilled states in p orbitals to participate in the formation of

chemical bonds. Thus, these atoms tend to form structures in which the chalcogen atom

has two covalent chemical bonds. Several estimates of the ionicity of the bonds suggest

that they are more than 80% covalent for a variety of chalcogenide compounds.1

With only two bonds, the atoms are relatively free to move by rotating around the

axis between the two bonding atoms. The bond angle at the chalcogen atom is also

flexible and the bond can easily open or close by several degrees. In a solid, an additional

constraint to motion is provided by ionic and Van DerWaals interactions with

neighboring atoms. The flexibility of chalcogenide chemical bonds causes these atoms to

readily form amorphous networks either alone, or with a variety of other atomic

constituents. Binary glasses can be formed that contain the heavier Group IV and V

elements and some of the Group VII elements.1 Binary mixtures with germanium and

arsenic are the most commonly studied because they have large glass-forming regions,

especially when selenium is the chalcogen atom. Increasing the number of components

2

tends to increase the glass-forming range,1 and ternary glasses have been formed with

components from every column of the periodic table.2 Typically, any amorphous material

containing an abundance of chalcogen atoms is referred to as a chalcogenide glass.

The chalcogenide glasses share two common properties that have a profound

impact on their interaction with light; their electronic structure and their phonon

vibrations. Electronically, the chalcogenide glasses behave as semiconductors. They have

a bandgap, and consequently they are transparent to a certain range of wavelengths of

light. The disorder of the network creates localized electronic states that extend into the

forbidden bandgap. These states have a significant effect on the electrical and optical

properties of the chalcogenide glasses. The transparent window extends far into the

infrared because the infrared side of the transparent region is determined by the phonon

energy of the material. The presence of large, heavy atoms shifts the phonons to lower

energy and therefore longer wavelengths. The low phonon energy makes the

chalcogenide glasses attractive as infrared optical materials.

Electronic Properties

Chalcogenide glasses are semiconductors and possess a definite bandgap. The

energy of the bandgap is sensitive to composition and can vary from 0.70 eV in GeTe2 to

3.24 eV in GeS2.3 The intrinsic dc conductivity in most chalcogenide glasses is low and

varies, with composition, over the range of 10-3 to 10-15 Ω-1-cm-1 at room temperature.2,4

Compositions containing tellurium tend to have the smallest bandgap and the highest

conductivity, while compositions containing sulfur have the largest bandgap and the

lowest conductivity. The low conductivity comes from the disorder of the amorphous

structure. The inherent disorder in an amorphous material creates localized electronic

3

states near the band edges.5 These cause low carrier mobility because they act as traps

and scattering centers for conduction band electrons and valence band holes. The

conduction mechanism is not well known and several models have been proposed such as

the Davis-Mott model and the small-polaron model.6 In the Davis-Mott model,

conduction occurs by one of three possible paths depending on the temperature. At low

temperatures, conduction occurs by electron hopping between midgap localized states.

Conduction by electrons excited into localized states at the band edges occurs at higher

temperatures. At even higher temperatures, electrons can be directly excited to extended

states. In the small-polaron model, the charge carriers are small-polarons and conduction

occurs by thermally activated hopping. The small-polaron model is the generally

accepted model for electronic conduction in oxide glasses.

The greatest difficulty in developing a model for glass conductivity is accounting

for the disorder of the glass. Because glasses lack translational symmetry, standard band

structure calculations, which are derived for a periodic arrangement of atoms and are so

successful for explaining electronic transport in crystalline materials, cannot be used.

Models must take into account the random disorder that leads to localized states in the

bandgap and at the band edges. The conduction properties of the glass depend on the

nature and density of the localized and delocalized states.

All of the chalcogenide-rich glasses appear to share a common electronic band

structure. The chalcogen atoms all have six valence electrons in an s2p4 configuration. As

noted before, the s shell and one p shell are completely full. The full p shell is known as a

lone-pair (LP) orbital. The other two half-filled p shells participate in the formation of

covalent bonds, so the chalcogen atoms are normally twofold coordinated. The valence

4

band of chalcogenide glasses consists of states from the p bonding (σ) and LP orbitals.

The LP electrons have higher energy than the bonding electrons, so the full LP band

forms the top of the valence band. The conduction band is formed by the antibonding

(σ*) band. The LP band falls between the σ and σ* bands, so the bandgap is about half of

the bonding-antibonding splitting energy.7 The σ* is about 4 eV above the LP band while

the σ band is about 4 eV below the LP band. The more tightly bound s band is about 10

eV below the p bands.8 Because the electrical properties are determined by the LP band,

these materials are called lone-pair semiconductors.7 An example of the band structure is

shown in Figure 1-1.

Optical Properties

Optical excitations of band edge electrons involve excitation of the lone-pair

electrons into the conduction band. Even in alloys, the optical behavior of the glass is

p (6)

σ* (2)

LP (2)

σ (2)

4 eV

4 eV

molecularstates

atomicstates

bands insolid

Conduction

Valence

Bonding

Figure 1-1: Typical band structure of lone-pairsemiconductors. Based on Kastner.7

5

strongly determined by the nature and environment of the lone-pair electrons. One of the

most interesting optical properties of the chalcogenide glasses it their inherent

photosensitivity. The photosensitivity is only observed when samples are in the

amorphous state,9 and is strongly influenced by the type of chalcogen atom and the nature

of the LP band. A frequently studied, but poorly understood, type of chalcogenide

photosensitivity is photodarkening. The photodarkening is observed as an increase in

absorption and a decrease (red-shift) in the bandgap of chalcogenide glasses illuminated

with light with energy above or just below the bandgap energy. Measurements of

photodarkening in various compositions of chalcogenide glass bear out the significance

of the chalcogen atom in determining the darkening behavior.10 Comparison of the

magnitude of photodarkening (as determined by the shift in the bandgap) for various

elemental and binary glasses shows that the chalcogen atom determines, to a large extent,

the magnitude of photodarkening. Sample microstructure and preparation also have a

significant effect on the photosensitivity of the glasses. In some glasses (As2S3 and

As2Se3), the photoinduced red-shift of the band edge can be prevented by the addition of

about 25 at.% copper.11 In these cases, it is believed that the metal atoms add a new level

above the lone-pair band.12 Optical transitions from the metal states to the conduction

band now dominate and the lone-pair electrons are no longer involved. By preventing

excitation of lone-pair electrons, the metal atoms prevent the photodarkening.

Nonlinear Index of Refraction and Absorption

The atomic constituents of chalcogenide glasses tend to have large electronic

polarizability. This leads to a high index of refraction in the transparent regime

typically, the index of refraction will be greater than 2.0. The interaction of any material

with a strong enough light field can lead to nonlinear optical behavior.13 The high

6

polarizability of the chalcogenide glasses causes them to exhibit the highest intrinsic

nonlinear response of any glass.14,15

Several nonlinear effects occur, but for our purposes, the most important effect in

the chalcogenide glasses is the nonlinear index of refraction, and the associated nonlinear

absorption coefficient. These effects can be regarded as intensity-dependent contributions

to the refractive index and absorption coefficient

Innn 20 += (1-1)

I20 ααα += , (1-2)

where n0 and α0 are the linear index of refraction and absorption coefficent, n2 and α2 are

the intensity-dependent contributions, and I is the intensity of the electromagnetic field.

A variety of measurements confirms the high nonlinear response of the

chalcogenide glasses. In As2S3 fibers, the nonlinear index at 1.55 µm is found to be two

orders of magnitude larger than that of silica glass at the same wavelength.16 The time

response of the nonlinearity was determined to be less than 100 fs, indicating that the

observed nonlinear refraction resulted from the electronic hyperpolarizability.

Amorphous selenium films have also been shown to exhibit large nonlinear response at

1.06 µm17 and 632.8 nm.18 Large values for the nonlinear refraction and absorption at

1.064 µm have been measured in As2S3, GeSe4 and Ge10As10Se80 glasses.19 Third-

harmonic generation, a nonlinear effect related to the nonlinear index, has also been

studied in the chalcogenide glasses.20,21 It was found that the third-harmonic generation

efficiency and the nonlinear index of refraction increase with the density of the glass20

and with the addition of selenium.20,22 The nonlinear properties are critical for optical

7

switching, computing and memory applications and control of the nonlinear response of a

material is necessary if it is to be used with high-intensity lasers.

Vibrational Properties

The chalcogenide glasses typically consist of large, heavy atoms, which are

covalently bonded. The large atomic mass causes the phonon vibrations to have low

energies. Because optically active phonons absorb light, the energy of the fundamental

phonons tends to set the ultimate limit for the long-wavelength infrared transparency of

materials.23 Materials with high phonon energies have multi-phonon absorption edges

that can extend into the mid- and near-infrared wavelengths. This is especially true of

materials with lightweight, strongly bound atoms such as silica glasses and polymers and

it limits their usefulness for infrared applications. Chalcogenide glasses typically have

transparent windows that extend into the far infraredbeyond 10 µm.24-26 This makes the

chalcogenide glasses candidate materials for infrared fiber optics and other optical

elements for infrared systems.27

Photoinduced Effects in Chalcogenide Glass

Many types of photosensitive processes are observed in the chalcogenide glasses.

Of these, photodarkening and photoinduced anisotropy have been the most thoroughly

studied. Other photoinduced effects such as changes in density, changes in viscosity,

diffusion of metals, crystallization, and decomposition have been observed. Two

important aspects of photoinduced effects in chalcogenide glasses must be kept in mind;

(1) they are light induced,28 and (2) they only occur in amorphous samples.9 This section

will provide a short overview of the photosensitive behavior of the chalcogenide glasses.

8

For more information, refer to the excellent review articles by Tanka28 and by Pfeiffer et

al.29

Photodarkening

When chalcogenide glasses are exposed to above- and near-bandgap light, the

absorption coefficient over a broad range of frequencies increases. The amount of

increase depends on the wavelength of the inducing light, the duration of exposure and

the intensity of the light. The photodarkening process involves a shift of the optical

absorption edge to lower energy30 and an increase in the band tail absorption. The

absorption change is permanent and can only be removed by annealing the glass at a

temperature near its glass transition temperature.29 Because the optical changes can be

removed by heat treatment, this is known as reversible photodarkening. Reversible

photodarkening has been observed in bulk glasses31 and well annealed thin films.32 The

photodarkening can be induced with above-bandgap or below-bandgap light, so long as

the light has sufficient energy to excite electrons from the LP band.33

An irreversible change in the optical properties (called photobleaching) has also

been observed in thin films but this appears to be a different process.34-36 Photobleaching

is only observed in freshly deposited films and cannot be reversed by heat treatment. The

photobleaching behavior is very sensitive to the film composition and deposition

technique and it appears to result from photoinduced annealing of the highly disordered

films. As the film is exposed, the glass structure becomes denser and the optical

properties approach those of an annealed sample that has been photodarkened.

The index of refraction of the glass also changes with photodarkening37 or

photobleaching.36 The refractive index change associated with the photodarkening is

9

expected from the Kramers-Kronig relations. The associated index change may prove

useful for the fabrication of optical structures in bulk glasses and in thin films.38

Photoinduced Anisotropy

As with all glasses, the chalcogenide glasses are optically isotropic, at least until

they are exposed to light.39 The glasses become optically anisotoropic when exposed to

polarized laser radiation,40 or even unpolarized laser light with the proper exposure

geometry.41 The anisotropy appears as polarization dependent changes in absorption and

index of refraction.40,42 The direction of the polarization can be controlled by the

polarization of the incident light and rotation of the incident polarization will cause

rotation of the axis of anisotropy in the glass.43 This process is completely optically

reversible and the anisotropy can be reoriented hundreds of times with no apparent

fatigue.44,45 Photoinduced anisotropy is distinct from the process of photodarkening,

which occurs concurrently in these samples. The photoinduced anisotropy is largest when

it is induced with light that is less energetic than the bandgap, but within the exponential

band tail.29 Because the photoinduced anisotropy is directional, it is often called a

vectoral effect to distinguish it from the scalar photodarkening.

Photoinduced Crystallization

Griffiths et al.46 discovered that exposure of films of GeSe2 to strongly absorbed

light with energy in the exponential band tail induces crystallization of the film. The

formation of micro-crystals has been confirmed by Raman spectroscopy of the

samples.46-49 Because of the crystallization, large changes in the optical properties of the

films occur. Like photodarkening, the photoinduced crystallization is thermally

reversible. This effect has been reported in a variety of chalcogenide glasses including

amorphous selenium50 and the stoichiometric IV-VI mixtures GeSe2, GeS2,48 and SiSe2.

51

10

This phenomenon is the basis for the partially polymerized cluster (PPC) model of the

structure of GeSe2 glass, which asserts that the structure of the glass is very similar to that

of the crystal of the same composition.47 The PPC model is not universally accepted,50

and other explanations exist for the photoinduced crystallization.51,52

Photodiffusion and Photodoping

Silver and copper rapidly diffuse into chalcogenide glasses during illumination.

This effect has been observed in various amorphous arsenic- and germanium-

chalcogenide glasses. The diffusing species distributes uniformly throughout the doped

layer and exhibits an abrupt diffusion front. The concentration of dopant is typically 25 to

30 at.% in the doped layer.53 The process works best when the doped composition is

within the stable glass-forming region of the ternary compound. For example, Ag diffuses

most readily into As3S7 to form the stable compound AgAsS2.53 The doped material

remains amorphous and the effect is not observed in the crystalline chalcogenides.53

Photodoping is most efficient when the light has the same energy as the bandgap of the

doped composition.54 The photodoping process can be easily distinguished from thermal

diffusion of the metal species. The photodoping is only weakly temperature dependent

and has an activation energy of 0.1 to 0.2 eV, 5 to 10 times lower than the activation

energy for thermal diffusion.54 The chemical differences between the doped and undoped

glass, and the ability to control the doping with light have led to several investigations of

the applicability of chalcogenide glasses for photolithography.53,55

Photoexpansion and Photoinduced Fluidity

Light induced expansion has been observed in both annealed films and melt-

quenched glasses.9 Thin film samples expand by about 0.5 % of their thickness when

exposed to above-bandgap light.9,56 The expansion is reversible and can be removed by

11

annealing the sample near its glass transition temperature, Tg. Photoexpansion of as much

as 3 % has been induced in films of As2S3 with below-bandgap illumination.33 The strong

correlation between photoexpansion and photodarkening supports the theory that

photodarkening results from photoinduced changes in the density of the glass, and the

associated shift of the bandgap and exponential band tail states.10,28,57

An interesting variation of the photoexpansion, reversible contraction and

dilation, has been observed in films of As50Se50.58 When a film is illuminated with

polarized, below-bandgap light, it contracts in the direction parallel to the electric-field

vector, and expands in the direction perpendicular to the electric-field vector. The change

in stress is the mechanical analog of the photoinduced anisotropy of the optical

properties.

In a related phenomenon, illumination causes reversible changes in the stress of a

thin film deposited on a silicon substrate.59 It can also cause permanent deformation of a

stressed film or fiber in a process called photoinduced fluidity.60 Under illumination, a

sample of As2S3 deforms viscously, with a viscosity estimated at 5 × 1012 poiseseveral

orders of magnitude lower than the dark viscosity of the same material. The photoinduced

fluidity increases with decreasing temperature, completely opposite of what would be

expected of a thermally induced change in viscosity.

Summary of Photoinduced Effects

Photosensitivity is an intrinsic property of the chalcogenide glasses. It leads to a

variety of interesting effects, which as a group can be labeled photoinduced structural

changes. The changes in structure are caused by the absorption of above- or below-

bandgap light and the subsequent relaxation of the excited state into a new, metastable

12

structure. The structural change is athermal, meaning that it does not result from sample

heating caused by light absorption, but all of the effects discussed (except photodoping)

are reversible by thermal annealing near Tg of the glass. The ability to control the

structure and properties of the chalcogenide glasses with light makes them uniquely

suitable for applications in optics and microfabrication. Some of these applications will

be discussed in the next section.

Applications for Chalcogenide Glasses

The optical properties of the chalcogenide glasses make them candidate materials

for a variety of optical applications. The wide range of compositions available, and the

associated wide variation in optical, thermal, and mechanical properties, should enable

glasses to be engineered to suit a particular need. For example, some of the applications

below will require a material with a large nonlinear index while others will require a

material with negligiblsy small nonlinear optical properties. These apparently

contradictory goals can be achieved in the chalcogenide glasses by adjusting the

composition to select the appropriate properties of the material at the desired operating

wavelength.

Optical Limiting

Current interest in materials for optical limiting is high. The military is interested

in protecting sensitive detectors from high-power enemy laser fire. High-intensity blasts

from infrared lasers can destroy the sensitive detectors used for guidance and military

surveillance. Such attacks could blind missiles or satellites, effectively disabling them.

With laser pulse duration on the order of 10 to 100 ns, the damage will occur faster than a

mechanical device can react. One possible solution to protect against short laser bursts

13

involves placing a nonlinear optical material in front of the detector.61 Such a material

must be transparent to low-intensity infrared light in the wavelengths of interest, but must

react to high-intensity threats. Materials with a nonlinear index of refraction will have a

higher or lower index of refraction for the high-power pulses. The change in index of

refraction varies with the spatial profile of the beam, and the exposed region behaves as a

graded-index lens. The transient lens will defocus the laser on the detector plane, thereby

reducing the intensity of the attacking laser to safe levels and protecting the sensor.

Appropriate materials for optical limiting must have a high nonlinear index of

refraction. The chalcogenide glasses appear to posses appropriately large nonlinear

optical responses, especially in the near infrared regime, so they may be ideally suited for

protection against Nd:YAG lasers, one of the expected threats, operating at 1.06 µm. In

addition, they are predicted to have high nonlinear responses throughout their transparent

region and may be useful protection against other threat lasers in the mid- and far-

infrared.

Of course, the high nonlinear index is useless if the material is not transparent at

the desired observation wavelengths. Several materials that are expected to have high

nonlinear indexes have very poor transparency in the mid- and far-infrared. An example

of this is carbon-based polymers which tend to have strong molecular absorption in the

mid- and far-infrared. The chalcogenide glasses have excellent transparency over the

entire infrared range with windows typically extending from less than 1 µm to greater

than 12 µm in wavelength. Of key importance, is transparency in the atmospheric

windows of 3 to 5 µm and 8 to 14 µm, the two regions where atmospheric absorption is

a minimum. These two regions are important for remote detection, infrared imaging, and

14

night vision. Only impurity scattering reduces the transparency of chalcogenide glasses in

these regimes, and that can be controlled by careful processing and improved purification

methods.

Chalcogenide glasses may have one critical weakness as optical limitersthey

appear to have low damage thresholds. Intense optical radiation can cause permanent

changes in the glass ranging from darkening to melting and evaporation. These effects

may be exaggerated in the case of a glass with a positive nonlinear index at the attack

wavelength. The positive index causes additional focusing of the laser inside the glass,

leading to higher electric fields, which, in turn, lead to more self-focusing. If the laser

self-focusing is not limited, the field strength will eventually exceed the damage

threshold. Not much is known about the damage threshold in chalcogenide glasses or

how it varies with glass composition, laser wavelength, and peak pulse intensity.

Infrared Fiber Optics

Infrared fibers are of great technological importance for communication, imaging,

remote sensing, and laser power delivery.62 The chalcogenide glasses fit many of the

materials requirements for these varied applications.24 They have a high bandgap, long-

wavelength multiphonon edge, and low optical attenuation. They are chemically stable in

air and can be drawn into long core-clad fibers. They also have the potential to permit

new applications that are unachievable with current infrared materials.63

Fiber fabrication techniques

Chalcogenide fibers can be drawn via conventional fiber drawing technology.64 A

typical fiber optic has a core region surrounded by a cladding region. The core has a

higher index of refraction, and a smaller diameter than the cladding. Light injected into

the core at the proper angle will propagate down the fiber with very little loss because the

15

light is contained in the core by total internal reflection at the interface between the core

and the cladding.

Such a core-clad structure is easy to fabricate with chalcogenide glasses, as

described below.26,63-66 Compositions for the core and cladding are chosen to achieve the

proper difference in the index of refraction. Compositions must also be chosen which

have matched thermal expansion and the correct softening and flow behavior to permit

drawing fibers. A solid cylinder of the core material is placed inside a hollow cylindrical

sleeve of the cladding material to make a pre-form. The pre-form is placed into a fiber

pulling apparatus, heated to the point where it has the proper viscosity for fiber drawing,

and then drawn down into a fiber. By careful design of the pre-form, the final fiber will

have the desired core diameter surrounded by a sufficient thickness of cladding to

achieve proper optical confinement and mechanical properties. Such a technique has been

used commercially to prepare fibers of Ge-Se-Sb glass in excess of 1 km long.24 Square

fibers, which are useful for imaging and transmitting polarized light, can also be formed

with this technique.

The ease by which fibers can be drawn gives the chalcogenide glasses a

significant advantage over other infrared-transparent materials. Crystalline materials,

which can have wider transparent windows and lower theoretical attenuation, cannot

easily be formed into fibers. Techniques such as extrusion, coating, and pedestal growth

of single crystals have been suggested for the fabrication of such fibers, but all of these

methods are much more complicated than fiber drawing.27 Halide glasses are another

possible fiber material, however they are more difficult to work with and are much more

susceptible to environmental degradation than the chalcogenide glasses. The main

16

problem with chalcogenide fibers is the lack of techniques for fabricating glasses of

sufficient purity to approach the theoretical intrinsic scattering limits.27

Laser power delivery

The use of fiber optics to deliver high-power laser light has led to significant

advances in surgical techniques. Current optical fibers absorb in the mid- and far-

infrared, and cannot be used for delivery of light from lasers in this region of

wavelengths. Delivery of CO2 laser light, at either 9.6 or 10.6 µm, is particularly useful

because of the shallow penetration depth of human tissue at this wavelength.

Chalcogenide glasses are suitably transparent at this wavelength, however the low

damage threshold and large nonlinear response limit the maximum power which can be

carried in such fibers. Powers of up to 3 W at 10.6 µm have been carried without

damaging fibers of Te2Se3.9As3.1I.25 This may be sufficient for some applications,

however further research should lead to compositions with much higher power handling

capabilities.63

Fiber amplifier

Photoluminescence of erbium ions (Er3+) in a silica host permits direct

amplification of 1.55 µm communication signals. It would be beneficial to the

communications industry to directly amplify light at other wavelengths. This could be

achieved by doping a fiber with other rare-earth ions, but many of the other technically

significant rare-earth ions do not luminesce when embedded in silica. The broad, high-

energy phonon spectrum of the silica glass couples with the electronic levels of the rare-

earth ions and leads to excited state decay through non-radiative transitions.

Chalcogenide glasses have low energy phonons, which do not couple strongly with the

17

rare-earth ions. They can easily accommodate the large rare-earth ions and are

transparent at the important emission wavelengths. Erbium has been shown to

photoluminesce in Ge10As40Se25S25 glass67 and GeGaS glass.68 Even more significant is

the observation of luminescence from praseodymium,69,70 neodymium,71,72 and

dysprosium68,73 in chalcogenide glass hosts. By doping with different rare-earth ions,

fibers can be formed with optical gain at a variety of near- and mid-infrared

wavelengths.74

Gain and amplification can be improved by trapping the pumping wavelength

within the doped section of the fiber. In silica fibers, this is accomplished by writing a

grating at each end of the active segment of fiber. Gratings can also be written in

chalcogenide glass fibers by exploiting their intrinsic photosensitivity.75-77 In fact, rare-

earth doped chalcogenide glasses have greater photosensitivity than the undoped host

glasses.78,79 Doped chalcogenide glass fibers could thus be fabricated and deployed as

fiber amplifiers in a manner similar to that used with silica fibers today. The ability to

dope the fibers with a wide range of rare-earth ions and even transition metals will enable

amplification of communications signals over a much broader range of wavelengths. For

similar reasons, the chalcogenide glasses may be attractive for development of new types

of infrared fiber lasers.

Remote sensing

Chalcogenide glass fibers are likely to revolutionize the field of broadband

infrared sensing. Broadband sensing is used for temperature measurement, pollution

monitoring, and infrared source detection.24 In conventional applications, a detector must

be placed so that the object being monitored is in its line of sight. If the detector cannot

be placed in direct view of the object, light from the object can be relayed to the detector

18

with conventional infrared optics. Such a system cannot transmit light over very large

distances and it can be bulky and difficult to work with. A fiber-based system permits

remote monitoring by placing a fiber tip near the object to be measured. The fiber

transmits the infrared light to a remote detector with very low loss. The use of several

input fibers permits a single detection system to simultaneously monitor several

locations.

Infrared spectroscopy can also benefit from broadband infrared fibers. In this

application, a single fiber would carry light from a broadband infrared source to a remote

location for sensing and then back to a Fourier transform or dispersive spectroscopic

detection system. Removing the cladding from a short section of the fiber allows light to

leak from the fiber into the surrounding environment. The amount of light leakage will

depend on the absorptive properties of the surrounding environment. If the fiber is placed

into a liquid or gaseous environment, the maximum losses will occur at the characteristic

frequencies of the molecular vibrations of the chemicals present.25,26

Chalcogenide fibers are well suited for applications in remote sensing and

spectroscopy. Chalcogenide fibers are already available for some commercial infrared

spectroscopy systems. The transparent window is wide enough to cover the range of

wavelengths typically used for chemical analysis and temperature measurementfrom 2

to 25 µm. Because such systems are useful even with fibers that are only several meters

long, control of the impurity absorption is not as critical to proper device function, but

sensitivity can be improved by reduction of the impurities. The chalcogenide glasses are

also very stable and are not damaged by immersion in water or organic solvents.62 It is

19

conceivable that they could even be used in-vivo for real-time monitoring of blood

chemistry.

Photolithography

The photosensitive response of the chalcogenide glasses can be used to produce

high-resolution images and photolithographic resists. Photodoping of chalcogenide

glasses with silver has generated the most interest, however other photo-induced changes

could also be used for image replication. Photolithography with chalcogenide glass is

very similar to the conventional organic-resist process.53 A film of chalcogenide glass is

deposited on the substrate to be patterned. Chalcogenide films can be deposited by

several methods including evaporation, sputtering, and chemical vapor deposition (CVD).

A thin layer of silver is deposited over the chalcogenide glass and then the sample is

exposed with the desired pattern. In the illuminated areas, the silver diffuses into the

chalcogenide glass. The undoped chalcogenide can be removed with wet or dry etching;

leaving behind a negative resist. Such a process should be easy to incorporate in current

semiconductor fabrication systems. With proper methods, the resolution is expected to be

10 to 50 nm. A different technique, using electron-beam exposure, demonstrated 60 nm

resolution with dry etching.55

Optical Switching

With the proliferation of fiber optic networks, comes the need to switch signals

between different fiber segments. Traditionally, this switching has been done by

converting the optical signals into electrical signals and then using conventional

microcircuits to route the signals onto the proper fibers. The speed of these electronic

switches limits the speed of the entire optical network. The only way to overcome this

bottleneck is to develop switches that are completely optical. For example, Lucent

20

Technologies recently announced an all-optical switch that permits a tenfold increase in

throughput over conventional switches.80

High-speed optical switches can use nonlinear optical elements to direct the

signals. If chalcogenide glasses are used for such devices, the switching can be

accomplished by the nonlinear index of refraction. High-speed optical switching has been

demonstrated with As2S3-based fibers.81-83 Demultiplexing signals of 50 Gbit/s was

achieved and the system has the potential to exceed 100 Gbit/s operation.83

Switching can also be done with thin film devices. A thin film optical switch must

have waveguides and other optical elements to direct the flow of light to the active

regions of the switch.84 These waveguides could be formed on chalcogenide glasses

either by photodarkening,85 photodoping, or ion-exchange to create the proper variation

in the index of refraction. Gratings77 and other passive holographic structures86 can also

be formed by photodarkening.

Optical Computing

Optical switcheswhen structured to produce NOR gatesprovide the logic

gates of a simple optical computer. Much more complicated devices can be envisioned

which consist of combinations of these elements working together to effect optical

computation. A variety of optical structures fabricated on and in a single base material

would be the optical equivalent of the integrated electronic microcircuit. Just as the

electronic microcircuit is a critical component of modern computers, the optical

microcircuit will be a critical component of optical computers. Chalcogenide glasses have

the potential to be the basis for future optical computers much as silicon is the basis for

todays microprocessors and computer memories.

21

Active components are at the core of any computer. These elements permit

control of the flow of information based on previous inputs to the system (logic gates). A

switching element can be changed between on and off states by a signal on a control

line. In the on state, a signal can flow through the device; in the off state, the signal is

blocked. Switches can be combined to build up circuits that perform basic binary logic

operations. These circuits are known as logic gates and from them all computations can

be performed. In electronic circuits, the switches are transistors formed by doping

semiconductors. Optical circuits will rely on switches based on nonlinear optical behavior

of a host material such as the optical switching effects that have already been discussed.

Any optical microcircuit will require passive devices such as waveguides and

gratings to control the flow of optical information between the active elements. These

elements can be fabricated in a chalcogenide glass by several methods including

photodarkening and photodoping. The observation of grating formation in fibers is a

good indication that they can also be fabricated in films. Permanent photodarkening

produced by exposure to below-bandgap light may also permit fabrication of three-

dimensional interconnects by writing optical structures into the bulk of a chalcogenide

glass. Because it is not strongly absorbed, below-bandgap light can penetrate deep into a

chalcogenide sample. If the darkening process can be controlled by controlling the focal

point of the light within the sample or by creating appropriate interference patterns in the

bulk of the glass, then passive elements can be written anywhere throughout the thickness

of a bulk sample.

Because the chalcogenide glasses exhibit complex interactions with light, and

because the nature of these interactions can be controlled by changing the composition of

22

the glass, the chalcogenide glasses may provide the ideal base material for future optical

computing devices. The ability to build an entire circuit on a single chip of silicon was

critically important to the development of modern computers. The ability to fabricate

entire optical circuits on a single base material may be equally important for the

development of future systems such as optical computers or image analyzers.

The real possibilities of chalcogenide glasses have only been gleaned by some of

the cited research, but much more must be learned about the structure-property

relationships in chalcogenide glasses before we will know the true potential for these

glasses in the mentioned applications. The process of research itself can be expected to

reveal new and as yet unimagined possibilities for these unique glasses.

Contribution of This Research

The chalcogenide glasses will enhance or revolutionize many of the products that

operate with or on infrared light. Some examples of the potential benefits are presented in

this chapter. Chalcogenide infrared fibers are available today for spectroscopic

applications, but their applicability is still limited. Most of the other applications will

only be realized after much further study of the properties of chalcogenide glasses. All of

the applications depend on our ability to engineer glass compositions to meet the specific

requirements of the system. The tailoring of chalcogenide glasses for specific properties

is possible, but we do not know enough about most of the glass systems to choose

compositions wisely. It is the intent of this research to develop a basic understanding of

the optical behavior, especially the photodarkening, of a range of compositions from a

simple, binary chalcogenide system. These results may lead directly to applications, or

23

more likely, they may provide a foundation for other research into the optical behavior of

more complicated chalcogenide glass compositions.

Systematic Study of a Variety of Compositions

The intention of this research is to provide a systematic study of the optical

behavior of chalcogenide glasses as a function of composition. The range of potential

compositions is immense, but it centers about combinations of sulfur or selenium with

germanium or arsenic. This study has been limited to the simplest composition range: a

single, binary glass system containing germanium and selenium. Four compositions

between pure selenium and germanium diselenide were chosen. These are mixtures of

selenium with 10, 15, 20 and 25 at.% germanium. The glass structure within this range

varies from the polymer-like linear chains of amorphous selenium to the fully

interconnected three-dimensional silica-like network of GeSe2. The bandgap increases

from 1.9 to 2.4 eV and the glass transition temperature increases from 40 °C to 350 °C.

Many of the commercially important ternary and quaternary glasses can be formed by

alloying germanium-selenium glasses with other elements. Before the effect of alloying

on the photosensitive properties can be understood, we need to develop a better

understanding of the physics of the binary glass system.

Most of the optical studies to date have been performed on certain stoichiometric

compositions of glass. Extensive research has been performed on GeSe2 glass, but very

little has been performed on other compositions. It is unnecessary to limit research to the

stoichiometric compositions. Doing so makes it difficult or impossible to determine the

contributions one atom makes to the overall behavior of the system. The range of

germanium to selenium ratios will enable us to determine the individual roles of each

component and to examine the effect of structure without changing the chemical

24

components of the glass. The samples are cut from bulk pieces of well-annealed glass.

Using bulk glass for the samples instead of films eliminates the additional mesoscopic

complications of film deposition techniques such as columnar structure, composition

fluctuations, and film porosity.

Ti:Sapphire Laser

The choice of the excitation light source is important since it will determine what

excitations will occur in the material. In the past, darkening studies have been performed

with white-light sources, above-bandgap lasers, and below-bandgap lasers. Above-

bandgap refers to light sources with photon energy, hν, greater than the optical bandgap

of the sample, Eg, while below-bandgap refers to photons with less energy than the

bandgap. The most common below-bandgap lasers are HeNe at 632.8 nm and Kr+ at

647.1 nm. Both of these wavelengths are in the high absorption region of the exponential

band tail of the germanium-selenium glasses. For these studies, we chose a Ti:Sapphire

laser operating at a wavelength of 800 nm. The wavelength is still within the exponential

band tail of all of the compositions, however it is much further from the bandgap energy

than the shorter wavelengths used in previous studies. Photons of this wavelength are

about 0.5 eV less energetic than the band-to-band transitions. The absorption coefficient

is low at this wavelength, minimizing effects of sample heating and enabling the study of

darkening in bulk (≈1 mm thick) samples of glass. For simplicity, the excitation light is

also used as the probe of the optical properties. This avoids complications with the

alignment of two beams in the sample.

The Ti:Sapphire laser can operate in two modes, continuous wave (CW) and

mode-locked (ML). CW operation is similar to any other continuous laser source. The

25

laser cavity is not designed for stable CW operation, so the mode and frequency of the

laser are less stable than that of a standard CW source such as a HeNe or Ar+ laser.

Because of the lack of long-term stability of the CW operation of the laser, this mode is

only used for Raman spectroscopy. All of the darkening experiments were carried out

with the laser in ML operation. When the laser is mode-locked, it produces ultra-short

light pulses at high repetition rate. The pulses are only about 150 fs long, and they repeat

at 76 MHz. The corresponding pulse bandwidth is about 35 nm full-width half-maximum

(FWHM). The laser power is condensed into these short bursts of light, and consequently

the pulses have very high peak intensities with low to moderate average power. The high

intensity pulses facilitate the study of nonlinear processes. Of particular interest in this

work is the determination of whether the photodarkening process induced at this

wavelength is nonlinear. Knowing this will be useful in determining the mechanism for

the photodarkening process.

Measurement of Kinetics

Photodarkening is a time-dependent phenomenon, and understanding the kinetics

of the process is important for understanding the mechanism. Measurement of the

kinetics has been performed by recording the transmittance and reflectance of the

Ti:Sapphire laser beam as a function of the duration of exposure. The dielectric response

parameters ε1 and ε2 can be calculated from the measured transmittance and reflectance of

the sample. Analysis of these parameters provides information on how the observed

external response (change in transmittance and reflectance) is related to fundamental

changes in the dielectric properties of the material, which are, in turn, related to the

microstructure of the glass.

26

Measuring the nonlinearity of the darkening process is important for determining

the underlying mechanism. If the process is linear, it depends only on the total fluence of

photons. This would indicate that photodarkening is a simple phenomenon involving the

excitation of only single electrons. If, on the other hand, the process is nonlinear, then the

explanation of photodarkening will require a more complicated mechanism. Nonlinearity

indicates that several photons are involved in the process, either by multiphoton

excitation of electrons into higher energy levels, or by the excitation of several electrons

that jointly participate in the chemical changes necessary to bring about photodarkening.

From an application perspective, nonlinear photodarkening is interesting because it

would permit precise fabrication of three-dimensional darkened structures by control of

the laser intensity inside a bulk sample. For example, a photodarkened point could be

formed at the crossing of two lasers of sub-critical intensity.

The observed optical response of a material is related to the microstructure of the

material by the complex dielectric response function (ε*=ε1 + iε2). The frequency-

dependent dielectric response of a material is the linear sum of the contributions of all the

optically active species with response times faster than the period of the measurement

frequency. All of the observed properties such as transmittance and reflectance are

complicated functions of the dielectric response and do not exhibit simple linear

dependence on the population of oscillating species.

Unlike earlier research, we measure both the transmittance and the reflectance

during photodarkening and then we calculate the dielectric response from these values.

The interpretation of photodarkening in terms of changes in the dielectric function

27

facilitates structural interpretations of the data. Other researchers have reported only

transmittance changes and attempted to directly interpret the results.

The research presented here looks at the photodarkening as a means of

understanding the unique optical behavior of the chalcogenide glasses. Interest in this

phenomenon is not limited to the study fundamental glass physics. There exist several

potential applications in which controlled photodarkening of chalcogenide glasses could

be an important engineering tool. We will discuss the phenomena from both aspects. We

will consider the results as they pertain to understanding the physics of chalcogenide

glasses and as they pertain to the development of practical applications for these glasses.

Raman Spectroscopy

Raman spectroscopy is used in these studies as the primary tool for characterizing

structural changes that occur during photodarkening. Raman spectra are measured in the

wings of the 800 nm excitation wavelength, thus enabling the simultaneous monitoring of

structure and optical properties. The Raman spectra provide direct evidence of structural

changes that occur during photodarkening. They also provide information about the

sample temperature during exposurepermitting estimation of the magnitude of thermal

effects in the total photosensitivity of the germanium-selenium glasses. The temperature

measurement technique we use is applicable to temperature measurement in any material

and can be used to determine the thermal contribution to a variety of photoinduced

phenomena in chalcogenide glasses.

Summary

The goal of this work is a better understanding of the structural changes that occur

during photodarkening of germanium-selenium glasses. To achieve this goal, we measure

the optical and vibrational properties of the glasses before, during, and after

28

photodarkening. These properties are related to the structure of the glass and the kinetics

of their change reveals information about how the structure of the glass changes with

light exposure. The kinetics of photodarkening will be discussed in terms of theories for

the photoinduced changes of chalcogenide glasses.

Knowledge of the mechanism of photodarkening in chalcogenide glasses will lead

to the ability to engineer glasses for specific applications. Glasses with controlled

photosensitivity will facilitate a wide range of new optical applications. Remote infrared

sensors, high-bandwidth communications, optical data storage, and even optical

computing can be realized with the chalcogenide glassesif their properties can be

understood and controlled. The ultimate goal of this project is to provide some of the

knowledge that will enable the design of such novel optical devices.

29

CHAPTER 2BACKGROUND

Optical Physics

Optics is the study of the interaction of light with matter. Light is a quantized

electromagnetic wave; the quantum units of which are photons. Matter is a

conglomeration of atoms, which are composed of electrons, protons, and neutrons.

Photons interact with the charged particles in matter. The nature of this interaction

between light and matter is expressed in the dielectric response of the material. The

complex dielectric response, ε*, is also called the dielectric constant, an unfortunate

misnomer since it is a function of the wavelength of light. The entire interaction of light

with matter is contained in the dielectric response, and the dielectric response can be

calculated from information about the atomic and electronic structure of a material. So, if

the structure is known, the interaction with light can be calculated. Conversely, the

interaction of a material with light gives information about the structure of that material,

via the dielectric response function. The optics equations and the physics of the

interaction between light and matter will be discussed in this section.

Absorption and Refraction

In linear optics, two outcomes can occur when a photon interacts with matter. The

material can absorb the photon and it can alter the phase of the photon. The absorption

process leads to excitation of the material, and eventually heating or reemission of the

absorbed light. The phase change causes a change in the direction of propagation of the

light and leads to effects such as focusing by lenses and dispersion by prisms.

30

Propagation of light in a material

The theory of the interaction of light with matter begins with Maxwells

relations.13 In the case of a linear, homogeneous, isotropic medium, these can be written

ερ=⋅∇ E (2-1)

0=⋅∇ B (2-2)

t∂∂−=×∇ B

E (2-3)

t∂∂+=×∇ E

EB µεµσ . (2-4)

The light is an electromagnetic wave propagating in space and time. Treating it as a plane

wave, the electric field can be described by

[ ])(exp),( 0 tkxiEtxE ω−= , (2-5)

where k is the wavevector, x is the propagation vector, ω is the angular frequency, and t

is the time. In the general case of light traveling through a conducting medium, the

solution of Maxwells relations leads to a complex-valued k, denoted k∗ .The wavevector

is a function of the physical properties of the material which are themselves functions of

the wavelength of light. From Maxwells relations, we find that the interaction of light

with matter occurs because the light causes the matter to polarize. In most materials, the

degree of polarization, P, is proportional to the electric field, E(x,t), so that

[ ] ),(1)( 0 txEP D εωε −= ∗ , (2-6)

where ε0 is the electric permittivity of free space. The material-specific information is

contained in the materials dielectric response function, )(ωε ∗D . The dielectric response is

a dimensionless function. It can be written in terms of its real and imaginary components

as

31

)()()( 21 ωεωεωε iD +=∗ . (2-7)

Solution of Maxwells equations shows that in a material k* is related to the

dielectric response by

)()( ωω

ωε ∗∗ = kc

D , (2-8)

where c is the speed of light in vacuum. For convenience, a dimensionless value called

the complex refractive index, N(ω), is defined as the square root of the dielectric

response,

[ ] [ ] )(()( 22 ωεωκωω ∗=)(+)= DinN . (2-9)

Here, n(ω) is the refractive index, and κ(ω) is the extinction coefficient. For the clarity of

the rest of the discussion, the explicit ƒ(ω) notation will be dropped, however ∗Dε , N, and

all related quantities are still implicitly wavelength dependent.

Substitution of Equation 2-9 into Equation 2-5 via Equation 2-8 yields the

standard form for the propagation of an electromagnetic wave through a dielectric

medium:

−

−= x

ctx

c

niEtxE

κωωωexpexp),( 0 . (2-10)

The first exponential term is a traveling sinusoidal wave and the second term is an

exponential decay in the electric field strength with the distance traveled in the absorbing

medium. The power density of the wave is

xIxc

Ec

xI ακωε −=

−= e

2exp

2)( 0

20

0 . (2-11)

The absorption coefficient, α, is the rate at which the light energy decays as it penetrates

into the sample. Unlike κ, α has dimension and is typically given in units of cm-1.

32

Transmittance, reflectance, and absorptance

When a light wave crosses a boundary between two different materials, a portion

of the energy of the wave will be reflected. The reflection coefficient, ρ, is the ratio of the

electric field reflected at the boundary, ER, to incident electric field, EI. If the light is

normally incident on a boundary between two materials having complex dielectric

constants of N1 (incident medium) and N2 (transmitted medium), the reflection coefficient

is

+−==

12

12

NN

NN

E

E

I

Rρ . (2-12)

In many practical situations, the boundary of interest is between a solid material

and air. Because of the low density of air, and its limited polarizability at optical

frequencies, the dielectric response of air is approximately 1.0. This approximation is

very accurate for the visible and near-infrared frequencies of light.

Optical properties can be determined by shining light on a sample of material and

measuring the intensity of reflected and transmitted light as a function of wavelength.

The ratio of transmitted intensity to the incident intensity is known as the sample

transmittance, T. Similarly, the ratio of reflected intensity to incident intensity is the

reflectance, R, and the ratio of absorbed intensity to the incident intensity is the

absorptance, A. By conservation of energy,

1=++ RTA . (2-13)

So, if two of the quantities are measured, the third quantity is also known.

The typical experiment for determining optical properties involves the

measurement of spectral response of T and R from a sample in air. The light is incident

normal to the sample, and the sample is fabricated with two flat, parallel faces separated

33

by the thickness, d. In this geometry, the relationship between observed quantities and

optical properties is complicated by multiple internal reflections inside the sample.

Barnes and Czerny87 developed equations which express T and R in terms of the single

surface reflectivity, r, the absorption coefficient, α, and the sample thickness, d. These

equations were developed for thin films and account for multiple internal reflections and

interference effects. In the case of thick samples which are not too strongly absorbing, the

interference effects average out and the equations can be simplified to88

d

d

r

rT α

α

22

2

e1

e)1(−

−

−−= (2-14)

)e1( dTrR α−−= , (2-15)

where r is the single surface reflectivity, which for the case of a sample in air is

22

22

)1(

)1(

κκρρ

+++−== ∗

n

nr , (2-16)

and α from Equation 2-11 is

λπκωκα 42 ==

c, (2-17)

where λ is the wavelength of light in a vacuum, which is equal to 2πc/ω.

Combining Equations 2-14 and 2-15 and eliminating r leads to a cubic equation in

e-α d:

( ) ( ) ( ) 01

e21

e1

11

e2

2

2

23 =−

−

−+

+−

−+ −−−

TT

RT

TT

R ddd ααα . (2-18)

Finding the roots of Equation 2-18 is straightforward. Once the value of α is known, κ

and r can be calculated. The index of refraction, n, can then be calculated by rewriting

Equation 2-16 as a quadratic equation of n and solving by the binomial theorem. Finally,

34

the real and imaginary parts of the dielectric response (ε 1 and ε2) can be calculated from

Equation 2-9.

Dielectric Response

The above discussion shows that the observable optical properties of a material

are all related to the dielectric response. The response of a non-magnetic material to an

electric field depends on free charge carriers and polarizable units called dipoles. In an

insulator or intrinsic semiconductor, the number of free carriers is small, and their

influence can usually be neglected, so the dielectric response is determined by the types

of dipoles present. Three types of dipoles affect the visible and infrared properties of a

material: electronic, atomic, and orientational.89 The electronic dipoles are distortions of

the electric field surrounding the atoms of the material. Atomic, or ionic, dipoles occur

when the external electric field induces motion of positive and negative ions in the

material. Orientational dipoles are most common in gases and liquids. They occur when

permanent molecular dipoles rotate to align with the applied electric field.

Simple harmonic oscillator

Any type of dipole can be modeled, to a first approximation, as a driven simple

harmonic oscillator. The motion of a simple harmonic oscillator can be found as the

solution to

)()(d

)(d

d

)(d2

2

tqEtkxt

txm

t

txm −=+Γ+ , (2-19)

where x(t) is the displacement of the charge as a function of time. The oscillating mass is

m, the damping force is mΓ and the restoring force is k. The right-hand side of Equation

2-19 is the forcing function caused by an oscillating electric field

tiEtE ω−= e)( 0 , (2-20)

35

with amplitude E0 and frequency ω acting on an oscillator of charge q. The classical,

steady-state solution of Equation 2-19 is

( ) )(1

)(22

0

tEim

qtx

ωωω Γ+−−= , (2-21)

where the natural frequency of the oscillator, ω0, is

4

2

0

Γ−=m

kω . (2-22)

The polarization of this oscillator is the charge times the displacement,

)()( tqxtP −= , (2-23)

so the dielectric response of a single oscillator can be found from Equation 2-6,

( ) ωωωεεε

Γ+−+=+=∗

im

q

tE

tPD 22

00

2

0

11

)(

)(1 . (2-24)

Matter is composed of many oscillators with different natural frequencies. If the

oscillators act independently, then the vibrational modes are orthogonal, and the total

response is the sum of the individual responses. Consider an oscillator j with a natural

frequency ω0j. A sample will have a certain density of these oscillators, Nj. In addition, a

quantum mechanical treatment of the simple harmonic oscillator reveals that the

polarization of each type of oscillator depends on its oscillator strength, fj. With these

modifications Equation 2-24 becomes

( )∑ Γ+−+=∗

j jj

jj

j

jD

i

fN

m

q

ωωωεε

220

2

0

11 . (2-25)

Equation 2-25 is the total dielectric response of a system of simple harmonic oscillators.

It is important to recognize that ∗Dε is directly proportional to Nj. The dielectric response

is the only optical property to obey this relationship, so it is the key parameter for relating

optical properties to structure.90

36

Light absorption by chalcogenide glasses

When discussing light interactions with matter we typically divide light into

different regions based on the wavelength, or energy, of the photons. Ultraviolet light

represents the highest energies of what is typically considered optical radiation. This

band extends from about 10 nm to 390 nm in wavelength. Photons in this range have

enough energy to excite electronic transitions in almost all materials. The photons may

even be energetic enough to cause bond breaking and damage in materials such as

polymers. The visible portion of the spectrum occurs at lower energy. Visible light,

defined by the range of wavelengths to which the human eye is sensitive, ranges from

390 nm to 780 nm in wavelength. Visible light is highly energetic compared to thermal

fluctuations (kBT) and will excite electronic transitions in many materials. The absorption

of light by electronic transitions gives rise to the color of many common substances. The

infrared region of the spectrum exists at energies below the visible. This encompasses the

wavelength range from 780 nm to 1 mm and is rather arbitrarily divided into regions of

near-, mid-, far-, and extreme-infrared.89 From 780 nm to about 3 µm is considered the

near-infrared region. Light in this range is still much more energetic than kBT and tends to

cause electronic transitions in semiconductors. The region from 3 to 6 µm is known as

the mid-infrared. Photons of this energy are less energetic than most electronic

transitions, except those of narrow-bandgap semiconductors and nearly-free electrons in

conductors. Molecular vibrations, especially of small molecules, couple strongly with

mid-infrared light. Water, carbon dioxide, and organic molecules have strong vibrational

absorption bands in this range of wavelengths. From 6 to 15 µm is considered the far-

infrared. These wavelengths are strongly absorbed by molecular vibrations and lattice

vibrations in solids. This region of wavelengths is important for thermography and

37

infrared imaging since a black body at room temperature will radiate energy with a peak

wavelength of about 9.89 µm.13 Wavelengths beyond 15 µm (up to 1 mm) are in the

extreme-infrared. These wavelengths will typically couple with molecular rotations and

some low energy molecular vibrations.

The specific interaction between light and matter will depend on the frequency of

the light and the chemical and electronic structure of the matter. Absorption of light will

occur when it is in resonance with any electronic or vibrational modes of the structure, so

long as those modes are optically active. Because of their structural and electronic

similarities, all of the chalcogenide glasses exhibit the same basic optical response. This

general optical behavior of a chalcogenide glass is shown schematically in Figure 2-1

10-8

10-6

10-4

10-2

100

102

10-310-210-1100101

ε 2

Photon Energy - hν (eV)

I II III VI

Figure 2-1: Typical imaginary dielectric response of a chalcogenide glass. Regions are:(I) electronic band-to-band transitions, (II) exponential absorption tail, (III) Rayleighscattering and impurity absorption, and (IV) vibrational transitions.

38

which depicts the imaginary part of the dielectric response as a function of wavelength. It

is divided into four significant regions, each of which will be discussed in more detail.

Region I: Band-to-band. The first region represents the highest-energy optical

transitions. Photons with energy greater than the bandgap will excite direct valence band

to conduction band transitions. This process results in free carriers, which produce

photoconductivity. Photoconductivity has been observed in germanium-selenium

glasses.91 The excited electrons can come from the band tail of localized states or

anywhere deeper in the valence band. Except for the presence of localized states at the

band edges, these are the same as direct transitions in crystalline semiconductors. The

absorption coefficient is extremely high (greater than 104 cm-1) making the material

effectively opaque to light with these wavelengths. Because the penetration depth is on

the order of 10 µm or less, photoinduced changes created by light in this region will be

limited to the surface of the glass. The forbidden band in chalcogenide glasses is typically

at energies of 0.7 to 3.3 eV, corresponding with band edge absorption in the near-infrared

to visible. The band edge can be shifted by changing the composition of the glass. Sulfur

based glasses have the highest bandgaps while tellurium glasses have the lowest.

Alloying with arsenic or germanium will increase the bandgap for compositions with an

excess of the chalcogen atoms over the stoichiomtric composition of GeX2 or As2X3, with

X representing the chalcogen. Photodarkening causes a decrease in the energy of the

optical band edge transition.

Region II: Band tail. Photons with energy slightly less than the bandgap will

interact with the band tail states. In this region, the absorption increases exponentially

with the energy of the photon. The presence of an exponential band tail at all

temperatures distinguishes amorphous semiconductors from their crystalline counterparts.

39

Localized electrons at the top of the valence band will be excited either to the bottom of

the conduction band or to exciton states with energies below the conduction band. In the

chalcogenide glasses, the localized electrons come from the lone-pair orbitals of the

chalcogen atoms. The band tail will typically extend 50 to 100 meV below the band edge

in chalcogenide glasses, but the exact shape of the tail is sensitive to the composition and

the processing of the glass. Photodarkening causes a change in the width of the

exponential band tail.

Light with energy in this region can cause structural changes without generating

free carriers. The entire process occurs near the localized state. Because the absorption

coefficient in this region is low, the penetration depth is large (≈1 cm) and photoinduced

changes can be produced quite deeply into the bulk of a glass sample.

Region III: Transparent window. In the midgap region, light is not absorbed by

the chalcogenide glass. This is the transparent window of the glass. The primary

mechanisms of loss are Rayleigh scattering from density fluctuations and absorption by

impurities and defects. These scattering processes can be controlled by careful processing

of the glass. Purification of the raw materials will minimize the intrinsic impurity

absorption while proper heat treatments will reduce the Rayleigh scattering.

The transparent window is the region in which optics such as fibers and lenses are

designed to operate. It may also be a region for nonlinear optical devices that have large

nonlinear indexes of refraction with low linear and nonlinear absorption. Light in this

region should not cause photoinduced changes since a single photon does not have

enough energy to directly excite a lone-pair electron into a conduction or exciton state.33

Chalcogenide glasses have rather high refractive indexes in this range of

wavelengths. Typically n is 2.5 or greater. Intrinsic absorption is very low, but impurities

40

can lead to significant absorption peaks within the transparent window. Just as in silica

glass, impurities must be eliminated in order to transmit light through fibers longer than a

few meters.

Region IV: Phonons. At long enough wavelengths, the photons have the same

energy as the phonons in the glass. This leads to absorption peaks from the fundamental

phonon resonances with a broad tail to higher energy known as the multiphonon edge.

Absorption of light in this range of frequencies will lead to lattice heating through the

direct creation of phonons. Because the chalcogenide glasses have low frequency

phonons, the multiphonon absorption edge is located in the mid- to far-infrared. This

edge limits the long wavelength transparency of all of the chalcogenide glasses. For

sulfur based glasses this can be in the 5 to 10 µm range. In glasses containing tellurium or

other heavy atoms, the transparent window can extend beyond 25 µm. The low frequency

of the multiphonon absorption edge makes chalcogenide glasses attractive for use as

infrared fiber optics.

The positions of the electronic and multiphonon edges, and the shape of the

exponential band tail are directly related to the composition of the glass. This provides a

unique opportunity to engineer optical devices with specific properties by choosing the

appropriate composition of the glass.

Germanium-Selenium Glass

As already discussed in the introduction, the chalcogenide glass family contains a

wide range of compositions. As one would expect, the wide range of compositions brings

with it a wide range of microstructures and physical properties. Like crystalline systems,

certain compositions exist that have distinct structures. Such compositions occur at

stoichiometric ratios of the constituent atoms such as GeSe2 or As2S3. Glasses can easily

41

be formed at non-stoichiometric ratios and these will have intermediate structures and

properties. Unlike most crystalline systems, the structural and physical changes are

continuous. The intermediate structures are homogeneous blends of the stoichiometric

structures with no boundaries. This provides enormous flexibility in the choice of

physical properties and microstructure, which translates into opportunity for engineering

glasses for specific needs. The amorphous structure defies easy characterization and

limits the usefulness of crystallography tools, such as X-ray diffraction, for determining

the structure. Despite extensive studies, the microstructure of many chalcogenide glasses

is still not well characterized.

For this project, binary glasses composed of germanium and selenium were

selected. Compositions with less than 33% germanium have the best glass forming

properties. Four such compositions were used in this study. The glasses fall between two

stoichiometric glasses: amorphous selenium (a-Se), and amorphous germanium

diselenide (a-GeSe2). The structure of these two endpoint compositions will be discussed

followed by a discussion of the properties of intermediate compositions.

Despite being amorphous, all glasses have structure. For descriptive purposes, the

structure is divided into three regions: short-, medium-, and long-range order. The short-

range order consists of nearest neighbors. Covalent glasses, such as the chalcogenide

glasses, have well defined short-range structure. Several probes of short-range order exist

including diffraction, X-ray absorption, and vibrational spectroscopy.92 Infrared and

Raman vibrational spectra of the chalcogenide glasses exhibit sharp features associated

with well defined atomic clusters.93 Medium-range structure is associated with order

occurring within several nearest-neighbor distances. The ring structure in silica glasses is

an example of medium-range structure. This structure is more difficult to identify since

42

direct measurement is rarely possible. The medium-range structure of chalcogenide

glasses is not well understood and both silica-like rings and large crystalline fragments

have been offered as explanation for the properties of these glasses.94 Long-range

structure (any ordering extending over hundreds of atoms) in a glass is, by definition,

non-existent. This can be readily verified by the lack of sharp peaks in X-ray diffraction

measurements, and this measurement is used as the basic test to determine if a material is

amorphous.

Glass short-range structure is frequently described in terms of structural units.1 In

the selenium rich germanium-selenium system two structural units are important. The

first is a simple chain-like structure of elemental selenium

SeSe

which is designated as SeSe2/2 or Sen. The second is a tetrahedral structure with a

germanium atom at the center and selenium atoms as the four corners

Se

Se

Se

Se

Ge

which is designated as GeSe4/2. Three-dimensional views of the structural units are shown

in Figure 2-2.

The structural units are based on the assumption that the number of neighbors an

atom will have is equal to the number of covalent bonds that atom can form. This is

known as the 8 - n rule with n being the column of the periodic table of the atom. An

additional assumption is that the glass is chemically ordered, meaning that heteropolar

bonds are preferred over homopolar bonds. In the selenium-rich glasses this mean that all

43

of the germanium will preferentially bond with selenium. No germanium-germanium

bonds should exist. Together, these two assumptions are the basis of the chemically

ordered continuous random network (COCRN) model of glass formation. There is strong

evidence that this model is valid in germanium-selenium glasses.92

Amorphous Selenium

The structure of liquid and amorphous selenium has been investigated by many

techniques. Among these are viscosity measurements of the liquid state,95 infrared and

Raman spectroscopy of crystalline and amorphous selenium,96 measurement of low-angle

X-ray diffraction,97 and neutron diffraction of liquid selenium.98 Models of the structure

have been devised based on comparisons with sulfur99 and tellurium100 and by simulation

using a Monte Carlo technique.97 All of the work indicates the presence of both ring- and

chain-like structures in amorphous selenium. The ring-like structures are Se8 molecules,

which also occur in the monoclinic form of crystalline selenium. The chain-like

structures are long polymeric Sen chains. These chains occur in crystalline trigonal

selenium.

GeSe4/2 TetrahedraSe-Se Chain

Figure 2-2: Structural elements of germanium-selenium glass containing less than 33%germanium. Large spheres are selenium atoms, and the small sphere is a germaniumatom.

44

The disorder of the amorphous state prevents exact description of the structure.

Despite this, some aspects of the short-range order are known for amorphous selenium.

The selenium-selenium bond length, as determined by neutron98 and X-ray97 radial

distribution functions, is 2.35 Å. The first coordination shell contains two atoms. The

bonding angle is approximately 105°,98 and the distance between second nearest

neighbors is 3.75 Å.97 These values are very close to the values observed in the

crystalline forms of selenium. Three selenium atoms will define a plane. The next atom

along the chain will extend out of this plane at an angle of 102°.101 This angle is known

as the dihedral angle. The position of the fifth atom along the chain will determine

whether the atoms form a closed eight-membered ring or a polymeric chain.

The presence of both Se8 rings and polymeric chains in amorphous selenium is

well agreed upon, but the ratios of these two structures are not well known. Probably the

best estimate comes from the work of Briegleib.98 He dissolved samples of amorphous

selenium, prepared by quenching from different temperatures, in CS2. Se8 rings are

highly soluble in CS2 but the polymeric selenium chains are almost insoluble. By

measuring the mass of selenium dissolved, he was able to estimate the concentration of

Se8 rings. For the samples equilibrated at the lowest temperature before quenching (about

100 °C), Brieglieb measured the highest Se8 ring concentration, which was greater than

55% selenium atoms in Se8 rings. Glasses prepared by water quenching will probably be

most similar to the samples equilibrated near the melting point of selenium. These glasses

were found to contain about 40% of the selenium atoms in the rings.

The remaining selenium atoms will exist in polymeric chains. The length of these

chains decreases rapidly with increasing temperature in liquid selenium, as is evident

from the viscosity data.95 Eisenberg and Tobolsky formulated a thermodynamic model

45

which predicts the ring-chain equilibrium in amorphous selenium.99 This model predicts

an average chain length of 104 atoms at the melting point of crystalline selenium (217

°C). The chain length in the super-cooled liquid is predicted by this model to go as high

as 105 atoms. Analysis of viscosity data by Keezer and Bailey95 places the chain length as

high as 105 atoms/chain at the melting point and an extrapolation of this data by the

Eisenberg and Toblosky theory predicts a maximum chain length greater than 106

atoms/chain in the super-cooled liquid. Misawa and Suzuki98 formulated a structural

model that predicts a similar degree of polymerization. Their model assumes that the

selenium polymerizes in the form of a disordered chain. The disordered chain can assume

both the ring and chain structures by changes in the dihedral angle of adjacent bonds.

This model predicts a complicated structure of interconnected rings and chains and

provides good fits to measured estimates of chain length. It also predicts the presence of

threefold coordinated selenium atoms, which must be present in order to provide charge

balance for the singly coordinated atoms at the chain ends.

Since both models assume that the structure is in thermodynamic equilibrium, it is

not clear how to apply the predictions to the amorphous solid state. The glass is a super-

cooled liquid, but the quenching process prevents the structure from assuming

thermodynamic equilibrium. The exact effects of quenching will depend on the

quenching rate and the kinetics of the reactions. The kinetics of the reactions in the

liquid, especially in the super-cooled state, should be very slow because of the high

viscosity. The ease of glass formation also suggests that atomic motions are extremely

slow in the liquid below the melting point. The experimentally determined degree of

polymerization at the melting point (≈105 atoms/chain by Keezer and Bailey) is therefore

a reasonable lower estimate of the average chain length in amorphous selenium. Based on

46

the thermodynamic theory of Eisenberg and Tobolsky, the chain length may increase to

≈106 atoms/chain before the glass cools to Tg. This degree of chain growth is probably

unlikely in glass quenched in water.

The chain length is important in predicting the structure of the glass and in

estimating the intrinsic number of singly and threefold coordinated selenium atoms,

which represent defects in the amorphous structure. The density of amorphous selenium

is 4.275 gm/cc,102,103 or about 3.26×1022 atoms/cc. Assuming that about 60% of the atoms

are present in chains, that the average chain length is 105 atoms, and that each chain has

two ends; then the number density of singly coordinated atoms can be estimated at about

4×1017 atoms/cc. An equal number of threefold coordinated atoms will also be present to

provide charge balance.

Amorphous Germanium Diselenide

The structure of the other terminal composition, germanium diselenide (GeSe2), is

much more controversial than the structure of amorphous selenium. Originally, it was

assumed that the COCRN model described GeSe2. Based on this model, the structure of

GeSe2 would consist of a three-dimensional network of edge and corner-sharing GeSe4/2

tetrahedraanalogous to the network structure of vitreous silica. The glass would have

no medium- or long-range order. An alternate interpretation of the Raman spectra led to

the molecular-cluster network (MCN) model. An MCN is still composed of linked

tetrahedra, however the tetrahedra are joined in clusters with distinct medium-range

order. These clusters are ribbon-like two-dimensional structures and their formation

requires that the chemical ordering be broken. Some concentration of homopolar bonds

must form to lead to the presence of clusters.

47

Raman scattering measurements have been used to support both structural models

of GeSe2 glass. Tronc et al.104 first reported Raman measurements of germanium-

selenium glasses. They identified two sharp features in the spectra of GeSe2 glass: one at

195 cm-1, and the other at 215 cm-1. In selenium-rich glasses, the 195 cm-1 peak was

found to vary in intensity with the concentration of germanium. This led to the

assignment of this peak to the to the A1 symmetric tetrahedral breathing-mode of the

GeSe4/2 molecular clusters. The variation in intensity of the second line does not show a

simple dependence on concentration, but it was guessed that a Se-Ge-Se vibration might

be the source. Nemanich et al.105 agreed with Troncs assignment of the lower peak

(which they measured at 202 cm-1) but suggested that the second line (which they

identified at 219 cm-1) was associated with a large molecular ring structure similar to the

rings found in silica glass. Since then, this line has been the source of much contention.

Because it always accompanies the A1 line, it has come to be known as the A1-companion

line ( cA1 ) but it is not present in the crystalline Raman spectrum. The intensity of both the

A1 and cA1 lines is maximum at the GeSe2 composition.105

In an attempt to explain the presence of the companion line Bridenbaugh et al.106

proposed that the glass had a structure similar to that of the high-temperature crystalline

(β) phase. The crystal consists of layered sheets of tetrahedra. In the glass, the width of

these sheets is assumed limited to the width of a few unit cells. The edges of the sheets

are terminated by Se-Se bonds and the vibration of these bonds is predicted to give rise to

the cA1 line. The cluster, known as an outrigger raft,106 has a composition of Ge6Se14. It

is composed of two corner-sharing chains linked by edge-sharing tetrahedra.

Compensating germanium-rich clusters must also be present to preserve stoichiometry.

These are assumed to be ethane-like molecules of Ge2Se6/2. Pressure-dependent Raman

48

scattering data107 also supports the presence of molecular clusters in GeSe2 glass and

Griffiths et al.46-48 used the MCN theory to explain their observations of photoinduced

crystallization in melt quenched GeSe2 glasses.

Further evidence for the presence of large molecular clusters was provided by the

observation of two chemically inequivalent chalcogen sites in GeSe2 glass by 129I

Mössbauer emission spectroscopy.108 The two chemically inequivalent sites are assigned

to a selenium atom that is bonded with two germanium atoms and a selenium atom that is

bonded with one germanium atom and another selenium atom. The latter occurs along the

edge of the outrigger rafts. The same researchers also identified two chemically

inequivalent germanium sites by 119Sn Mössbauer emission spectroscopy.109 These sites

are associated with germanium atoms in tetrahedral GeSe4/2 clusters and in ethane-like

Ge2Se6/2 clusters. To quantitatively explain the experimental results, they propose that the

glass is composed of molecular clusters of Ge22Se46. Though much larger than

Bridenbaughs outrigger raft, this cluster is still a fragment of the crystalline phase and

is bordered by Se-Se bonds.

The MCN theory is not universally accepted. To counter the theory, Nemanich et

al.110 proposed that the cA1 line could be equally well explained by the breathing-mode

vibration of two edge-sharing tetrahedra. Such a structure will be present in chemically

ordered amorphous GeSe2 and would be consistent with the COCRN theory. More recent

investigations of the Raman spectra,111 X-ray scattering,112,113 neutron scattering,114 and

infrared spectra115 contradict the outrigger raft models and support the assignment of

the cA1 vibration to edge-sharing tetrahedra.

The most extensive support for the COCRN model was presented by Sugai.50 By

comparing the behavior of Ge1-xSx, Ge1-xSex, Si1-xSx, and Si1-xSex, he developed a model

49

which depends only on one parameter, P, which is determined by the ratio of edge- to

corner-sharing tetrahedra in an ordered random network structure. P depends on the

species of atoms but not on their concentration in the glass. The cA1 line is assigned to the

vibration of edge-sharing tetrahedra and the A1 mode is assigned to the breathing-mode of

the corner-sharing tetrahedra. Both vibrations are assumed to be localized on their

respective molecular groups. This model correctly predicts the composition dependence

of the ratio of cA1 to A1 line intensity for all of the glass systems. The model can also

account for the threshold intensity for photoinduced crystallization in GeSe2 and SiSe2

and the differences in structure for above- and below-bandgap induced crystallization.51

Sugai suggests that the Mössbauer spectra can be explained by the chemical differences

between selenium and germanium atoms in corner-sharing and edge-sharing tetrahedra.

Because of this work, the COCRN model is still a strong candidate for explaining the

structure of amorphous GeSe2.

The short-range order of GeSe2 glass is composed of GeSe4/2 tetrahedra. Radial

distribution functions calculated from X-ray diffraction data reveal that the germanium-

selenium bond length is 2.37 Å with a root mean square displacement of 0.092 Å2.116 The

selenium atoms form the first coordination sphere around the germanium with a

coordination number of 4.0. Two germanium-germanium correlations are also observed:

one at 3.20 Å, and another at 3.58 Å. These are interpreted as the distances between

germanium atoms in adjacent edge-sharing and corner-sharing tetrahedra, respectively. A

selenium-selenium correlation is found at 3.87 Å, the distance between the selenium

atoms at the corners of the tetrahedra. The atomic arrangements in the tetrahedra and

between neighboring tetrahedra are close to that in the crystal.116

50

Selenium-Rich Germanium-Selenium Glasses

The intermediate compositions of germanium selenium glasses are often denoted

as GexSe1-x with x representing the atomic fraction of germanium in the structure. All of

the glasses used in this project contain less than 33% germanium (x < 0.33). These

glasses are also characterized by their average-coordination number, ⟨r⟩ , which is a

measure of the number of atoms with which an average atom is coordinated. For

amorphous selenium, ⟨r⟩ is 2.0, since all of the atoms are the same and all of them are

twofold coordinated. For mixtures of atoms with different coordination, ⟨r⟩ is calculated

by summing the products of the atomic fraction and the coordination number for all of

the atomic species in the glass. The germanium atoms are fourfold coordinated, so in the

binary germanium-selenium glasses

)1)(0.2()0.4( xxr −+= , (2-26)

where x is the atomic fraction of germanium. From this formula, ⟨r⟩ for the GeSe2 glass is

approximately 2.67.

The easiest way to understand the structure of these glasses is to consider the

addition of germanium to amorphous selenium. The germanium atoms are fourfold

coordinated, so they will act as cross-links between chains or rings of amorphous

selenium. The GeSe4/2 tetrahedra are distributed uniformly throughout the glass as is

predicted by the COCRN model. For low germanium concentrations, the corners of the

tetrahedra are connected by long chains of selenium. A broad peak on the Raman spectra

centered at 250 cm-1 is associated with the presence of Se-Se bonds.104,105 This peak is

also observed in pure selenium, and its relative intensity decreases monotonically with

increasing germanium content. This assignment seems non-controversial; however, in

amorphous selenium, this peak was assigned to a vibrational mode of Se8 rings,96 while in

51

germanium selenium mixtures, it is assigned to vibrations of selenium atoms in chain-like

structures.104 This apparent discrepancy has not been resolved.

As the germanium concentration increases, the selenium chains grow shorter. For

example, the chain length is about 25 atoms for 2% germanium and about 5 atoms for 8%

germanium.117 At a composition of 20% germanium, the adjacent tetrahedra are

connected by Se-Se bonds as shown in the following schematic:

Se

Se

Se

Se

Ge

Se

Se

Se

Se

Ge

No appreciable concentration of Ge-Se-Ge bonds is found for compositions

containing less than 20% germanium,118 lending support to the COCRN model. The

medium-range order of these structures is not known. They may form long ribbons or

they may branch out into two- or three-dimensional structures. At higher concentrations

of germanium, the tetrahedra begin to connect at their corners and eventually at their

edges and the structure becomes similar to amorphous GeSe2. Evidence of germanium-

germanium bonds is not observed for compositions with less than 30% germanium.119

Structural investigations of GexSe1-x glasses reveal that the short-range structure

changes little with germanium content.120,121 The germanium-selenium bond length (in

the tetrahedra) is ≈2.37 Å from 10% to 33% germanium. The Se-Ge-Se bond angle in the

GeSe4/2 tetrahedra is found to be between 108.3° and 109.2° for this same range of

compositions. The selenium-selenium chain bond is ≈2.37 Å, almost the same as for the

trigonal crystalline phase. In a sample with 17% germanium, no germanium-germanium

correlation is found within the first three coordination spheres.120 This is evidence that the

52

germanium tetrahedra are dispersed, and do not form edge- or corner-sharing structures

a result consistent with the COCRN model of chalcogenide glasses.

53

CHAPTER 3EXPERIMENTAL METHODS

Chalcogenide Glass Samples

Glass Preparation

Chalcogenide glass samples were prepared at the University of Rennes by a

standard bulk-melt technique.122 All samples are prepared from high-purity raw materials

(5 6N). To minimize contamination, the powders are placed under vacuum in glass

ampoules and heated to 250 °C. The heating and low pressure helps to remove any

surface contamination. Without leaving the vacuum, the powders are mixed in the proper

ratio and sealed in a silica ampoule. This ampoule is placed in a rocking furnace and

heated to 600 °C to melt the powder. The melts are held at this temperature for several

hours. During the hold, the ampoule is rocked to mix the melt and improve homogeneity.

After 24 hours, the ampoule is removed from the furnace and quenched in air. The

ampoule is sliced open to remove the rod of chalcogenide glass, which is about 8 mm in

diameter and varies in length depending on the quantity of glass produced. Compositions

containing 10, 15, 20, and 25% germanium were prepared in this way. The glass

Table 3-1: Glass compositions used in this study.Glass Designation %Ge ⟨⟨⟨⟨r⟩⟩⟩⟩ Tg (°°°°C)GeSe9 10 2.2 98Ge3Se17 15 2.3 126GeSe4 20 2.4 170GeSe3 25 2.5 198

54

composition, average coordination numbers, and glass transition temperatures are listed

in Table 3-1.

Optical samples are prepared by slicing transverse sections about 1 to 2 mm thick

from the bulk rod. These samples are polished to a high surface finish while maintaining

flat and parallel faces. Most of the samples were received polished, however a few had to

be polished in house. The sample polishing procedure used to prepare the samples is

documented in the Appendix. After polishing, the sample thickness was measured by a

micrometer with an accuracy of ±0.05 mm.

Spectroscopic Analysis

Measuring the linear optical properties is necessary for evaluating the accuracy of

our measurements, and verifying the composition of the samples. Composition analysis

by ICP was conducted elsewhere.122 The optical properties of the prepared samples were

measured by both ultraviolet/visible/near-infrared (UV/Vis/NIR) spectroscopy and

Fourier transform infrared (FTIR) spectroscopy. UV/Vis/NIR data are used for

comparison with photodarkening measurements and the FTIR spectra are used to identify

the glass composition and the presence of impurities in the samples.

UV/Vis/NIR spectra were measured from 500 to 3000 nm on a Perkin Elmer

Lambda 9 dual-beam spectrophotometer. Samples were mounted in the sample beam and

the reference beam was left empty. The intensity of the light in the UV/Vis/NIR

spectrometer is too low to cause photodarkening of the glasses. The results are processed

to permit estimation of the absorption coefficient and the linear index of refraction at

800nm. The methodology will be discussed in the results section.

55

The spectrometer measures transmittance (T) and records the data as absorbance

(A) which is defined as

=

TA

1log10 . (3-1)

If the surface reflections were negligible, A would be directly proportional to the

absorption coefficient (α) of the sample. With chalcogenide samples, the index of

refraction is high and consequently the surface reflections cannot be ignored.

Determination of the absorption coefficient is still possible; however, it requires two

assumptions. First, the band tail absorption is assumed to be accurately modeled by an

exponential curve of the form

=

σνανα h

h exp)( 0 , (3-2)

where σ is the width of the band tail and α0 is a scaling factor and hν is the energy of the

photon. Second, the index of refraction is assumed constant over the range of

wavelengths of the band tail. This is harder to justify since we know that any variation in

absorption will cause a variation in refraction. We turn to a pragmatic justification; in the

portion of the exponential band tail measured, the data is well fit by an exponential

function. This is especially true for the wavelength region beyond 700 nm. If the index

did have a large dispersion, it would distort the shape of the transmittance curve and an

exponential function would provide a poor fit.

FTIR spectroscopy was used to establish the far-infrared limit of the sample

transparency. The transmission spectra were measured on a Nicolet single-beam FTIR

over a range from 4000 to 400 cm-1 (2.5 to 25 µm). No further analysis was performed on

the data.

56

Photodarkening Measurements

Measurement of the kinetics of photodarkening induced by the Ti:Sapphire laser

is the primary result of this research. The wavelength of the Ti:Sapphire laser is farther

into the infrared than the wavelengths used in previous studies. It was not certain that

such a laser would produce darkening in the germanium-selenium glasses. The laser was

chosen because it produces high intensity pulses, which are ideal for studying electronic

nonlinear processes in materials. A custom optical apparatus was built to permit

simultaneous measurement of transmittance and reflectance of the exciting laser light.

The time-dependent data was recorded with a digital computer for ease in data

processing.

Ti:Sapphire Laser

The laser used in the photodarkening and Raman measurements is an Ar+ pumped

Coherent Mira 900 Ti:Sapphire laser. The laser is capable of operating in two modes. In

the continuous wave (CW) mode the laser outputs a continuous beam with a center

frequency of 800 nm and a full-width half-max (FWHM) bandwidth of about 0.06 nm. A

typical spectral profile of the CW mode is shown in Figure 3-1. Because of the design of

the laser cavity, the laser mode is not completely stable in CW operation and the resulting

laser beam tends to flicker as the modes shift. Some attempts were made to adjust the

cavity to prevent the mode hopping, but they were unsuccessful. The best results came

with careful tuning of the full cavity, which produced a stable laser frequency (no

wavelength hopping), with minimal temporal variation. The operation of the laser was

confirmed by measurement with the same spectrometer used for the Raman

measurements. The laser instability made CW mode unsuitable for measuring

photodarkening, which is highly sensitive to the modal quality of the beam. The

57

instability was not a problem when the laser was used for Raman measurements. In fact,

the Raman measurements can only be made with the laser in the CW mode.

To achieve the ultra-short pulses, the laser is placed into mode-locked (ML)

operation. Mode-locking occurs when a large spread of laser frequencies are

superimposed inside the laser cavity. In the Ti:Sapphire laser, this spread has a bandwidth

of almost 35 nm. When all of the wavelengths are phase matched, the resulting intensity

profile has large, short spikes that occur at regular intervals on a long, flat background.

The spikes are only about 150 fs long and occur at 76 MHz (or with a spacing of a little

more than 13 ns). In the Mira 900, the mode locking is brought about by rapidly changing

the cavity length to promote multimode lasing. When a pulse begins to form it will have a

799.0 799.5 800.0 800.5 801.0

Inte

nsity

(ar

b.)

Wavelength - λ (nm)

Figure 3-1: Typical spectral profile of the Ti:Sapphire laser operating in CW mode.

58

much higher intensity in the laser crystal. This high intensity causes a nonlinear index

change in the Ti:Sapphire crystal that focuses the pulse more tightly than the free running

laser beam. By closing a slit located at the focus of the high intensity pulse, the CW

signal is blocked without removing power from the mode-locked pulse. Once the CW

mode is fouled, all of the power in the crystal will be fed into the pulse by stimulated

emission. The pulse is now stable in the cavity and will remain so as long as the slit is

kept closed. Once the ML state has been achieved, the laser operation is stable and it will

continue to produce pulses with no active intervention. At the exit of the laser is a beam

expander that increases the beam diameter and reduces its divergence. After passing

through the expander, the laser beam has a diameter of 1.2 mm and a far-field divergence

angle of 2×10-4 radians. Each individual pulse carries about 1.3×10-8 J per Watt of laser

power.

Optical Arrangement

The optical setup for measuring photodarkening is shown in Figure 3-2. After

leaving the beam expander, the laser beam passes through a 45° 70-30 beam splitter. The

reflected portion of the beam is directed into a thermopile detector. The signal from this

detector is acquired along with the transmitted and reflected signals from the sample and

is used to monitor the laser intensity fluctuations during the experiment. This signal is

called the laser reference signal. By recording the laser reference signal, the data can be

corrected for the laser power fluctuations that occur over the time span required to

conduct the darkening experiments.

The transmitted portion of the beam passes a filter holder. Neutral density (ND)

filters placed in the filter holder attenuate the laser beam to permit measurement of

59

darkening over a several order of magnitude range of laser powers. Because the filters are

designed for the visible, some are not as efficient in the near-infrared and the attenuation

is reduced at 800 nm. Table 3-2 lists the ND filters used and their corresponding optical

density (OD) as determined by measuring the light transmitted through the filters while

no sample was present in the sample mount.

After the ND filter, the laser is focused by a 25 mm diameter lens with a focal

length of 150 mm. The spot size of the beam at the focal point can be calculated from the

lens and laser beam parameters using the method developed by Self123 for Gaussian beam

optics. The normalized intensity distribution of a Gaussian beam is

−

=

2

22exp

2),(

w

r

wzrI

π, (3-3)

where I is the intensity and w is the radius of the beam (measured at 1/e2 of the peak

intensity). The description is based on a cylindrical coordinate system with r as the radial

coordinate and z as the longitudinal coordinate. The beam is cylindrically symmetric, so

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

TransmittedSignal DetectorSample

Reflected SignalDetector

Focusing Lens

Reference SignalDetector

ND FilterBeamSplitter

Figure 3-2: Experimental apparatus used for simultaneous measurement of transmissionand reflection during photodarkening of the chalcogenide glass samples.

60

there is no need for an angular coordinate. The coordinate system is oriented such that the

beam propagates along the z axis. The origin is located at the center of the portion of the

beam with the narrowest cross section, which is also known as the beam waist and

denoted by w0. The peak intensity, IP, at any position along the beam occurs at the center

(r = 0), and is

2

2

wI

I

T

P

π= , (3-4)

where IT is the total power of the laser beam. The radius of the beam at any position along

the z direction is

2

0 1)(

+=

Rz

zwzw , (3-5)

where zR is the Rayleigh range. The Rayleigh range describes the Lorentzian intensity

profile along the beam axis, and can be calculated from the waist radius and the

wavelength of light, λ, as

λπ 2

0wzR = . (3-6)

Table 3-2: Performance of neutraldensity filters at 800 nm wavelength.ND Filter Measured OD

(800 nm)0.2 0.120.4 0.190.6 0.410.8 0.621.0 0.522.0 1.333.0 1.94

61

By comparison with geometrical optics, Self derived a formula for a Gaussian

beam that is equivalent to the standard lens equation. A laser beam with a waist located at

a distance s from a lens of focal length f will be imaged to a position s′. The lens formula

for this arrangement can be written

( )( )[ ] ( )221

11

fzfs

fs

f

s

R+−−+=

′. (3-7)

The size of the new waist is the magnification m,

( )[ ] ( )220

0

1

1

fzfsw

wm

R+−=

′= . (3-8)

With these equations and the measured geometry, the beam size on the sample can be

calculated.

The peak incident intensity, IP, can be estimated from the above equations and the

geometry of the optical setup depicted in Figure 3-2. The wavelength, λ, of the laser is

800 nm and at the output of the laser, the waist, w0, is approximately 1.2 mm. The

focusing lens is 1.5 m from the laser and has a focal length of 150 mm. The sample is

located at the focus of the lens and the waist at the sample is estimated (from Equation 3-

8) as 30 µm. The time-averaged peak intensity (IP/IT) at the sample is therefore 70

W/(mW⋅cm2). For a total average power, IT, of 1 mW, the peak intensity is 70 W/cm2.

During the photodarkening experiments, the laser power at the sample was varied from

0.1 to 50 mW, so the peak intensity varied from about 7 to 3500 W/cm2.

The value of the normalized peak intensity is only reliable as an order of

magnitude estimate of the peak intensity, because the exact value is highly sensitive to

the initial beam waist. The value used for the waist is extracted from the laser manual and

is not considered accurate to more than ± 20%. With this uncertainty in the waist size, the

62

peak intensity is only accurate to ± 40%. The only way to reduce this inaccuracy is to

carefully characterize the laser at the sample position. However, this uncertainty does not

affect the accuracy of the measurements, it only affects the absolute value of the

intensity. If the laser power is doubled, the peak intensity is also doubled. For this reason,

most of the results are presented in terms of the total power, which is known to the

accuracy of the detectors± 2%.

The sample is mounted in a clip that is attached to an x-y-z translation stage. The z

axis of the stage is adjusted to position the sample at the focal point of the lens and the x

and y axes are used to position the sample in the laser beam. The accurate positioning

control permits a single sample to be used for multiple experiments by changing the

portion of the sample exposed to the laser. The x and y position of each exposure is

recorded and the sample is moved to an unexposed location for each new experiment.

Typically, spots were exposed on a square grid with each spot separated from its nearest

neighbors by approximately 0.5 mm. Occasionally, the beam was placed on a spot that

caused excessive distortion in the transmitted beam. This was indicative of poor surface

quality, or density fluctuations inside the sample. Such spots were marked as bad and the

experiment was restarted at a new location. A piece of front surface mirror was placed on

the sample holder so that it could be translated into the beam for calibration of the

reflection measurements. The front of the mirror was aligned with the front face of the

sample.

In front of the sample, and to one side of the laser beam, was a pick-off mirror.

This front surface mirror was positioned to direct the reflected light from the sample

surface into a silicon photodetector. The signal generated by this photodetector was

63

amplified and then acquired by computer. The intensity of this signal is proportional to

the reflectance of the sample. A calibration mirror (not shown) was used to determine the

signal for 100% reflectance before each experiment. The translation stage was adjusted (x

and y axes only) to position the calibration mirror in the laser beam, and the voltage from

the detector was recorded. The calibration mirror is assumed to be 100% reflective at 800

nm, so the recorded voltage corresponds with 100% reflectance. Light reflecting from the

front surface of the detector was directed to a screen about 1 m away. This was used to

observe the quality of the reflected beam and the alignment of the sample.

Behind the sample was a 60 mm focal length lens. This lens was needed to

refocus the transmitted beam onto another silicon detector. The signal generated by this

detector was acquired as the transmittance signal. Before each measurement, the sample

was moved out of the laser beam and the signal corresponding to 100% transmittance was

measured. Light reflected from the front face of the transmittance detector was also

directed onto the screen for monitoring the quality of the sample location and the

progress of the darkening experiment.

A silicon CCD camera was placed in front of the screen. A camera lens focused

the side-by-side transmittance and reflectance images onto the CCD, and the image was

displayed on a standard TV/VCR system. The monitor permitted easy viewing of the

alignment of the samples and was used to determine if spots were unsuitable for

measurement. The VCR was used to record examples of these images, but a detailed

analysis of the images is not part of the present study.

The system was realigned after inserting each sample. Alignment was done to

insure that the reflected beam from the sample was directed properly into the reflectance

64

detector. During alignment, the laser was attenuated by 4 orders of magnitude so as not to

induce any darkening of the alignment spot. First, the calibration mirror was positioned in

the beam and the entire sample mount was adjusted to position the reflected light slightly

inside the edge of the pick-off mirror. The pick-off mirror was then adjusted to place the

reflected spot at the center of the detector and the position of the reflected spot on the

screen was marked. The sample was then translated so that it was in the beam. The

position of the sample was adjusted (without changing the alignment of the sample

mount) so that the reflected spot was positioned at the same location on the screen.

Alignment of the reflected beam was verified visually by inspecting the beam position on

the pick-off mirror and on the detector.

Data Acquisition and Analysis

All data acquisition was performed on an IBM PC compatible computer with a

Data Acquisition Card (DAQ). The DAQ was set to measure a range of ± 1 volt with 12-

bit accuracy. Signals from all three detectors were collected simultaneously on three

channels of the card. The data acquisition was controlled by a custom program written in

LabVIEW 4.1.124 The program kept track of the raw voltage readings for each of the

three detectors and saved the data to disk for all further processing. Measurements were

typically recorded at 1 second intervals, although longer intervals were used for several

of the low-power, long-duration measurements. 1000 samples were collected per second

and averaged to obtain the recorded value. A second LabVIEW program was used to

calibrate the detectors so that the voltage data could be converted to transmittance and

reflectance values. The raw data was scaled by the measured scaling factors for 100%

transmittance and reflectance and this was recorded to disk.

65

After collection, the data was processed to determine the optical properties of the

sample from the transmittance and reflectance values. All additional processing was done

with programs written for this purpose in the Python125 programming language. The

programs implemented the calculations outlined in Chapter 2 for determining ε1 and ε2.

In addition, the code included estimation of errors for the calculated optical properties.

These errors were determined from the known uncertainties in the transmittance and

reflectance measurements.

Experiment Methodology

Before any experiment, the laser was turned on and allowed to warm-up for at

least half an hour. During setup, the laser was blocked to prevent any accidental exposure

of the sample. The sample was moved out of the laser beam so that the entire beam was

transmitted to the transmittance detector. While the laser was blocked, the calibration

program was started on the computer and the voltage signal from all three detectors was

measured. This dark voltage was subtracted from all other measurements to correct for

any baseline offset in the detectors.

The laser was unblocked and the reference signal, Vref, and the transmittance

signal, VT, were recorded in the lab book. The ratio, VT/Vref, was calculated and recorded

in the lab book as RT. Next, the calibration mirror was translated into the beam so that the

entire beam was reflected onto the reflectance detector. Again, the calibration program

was run and the reference, Vref, reflectance, VR, and the ratio, RR, of the two was

recorded. The laser was blocked and the calibration program was stopped.

The sample was translated into the laser beam at the position chosen for the

experiment. The data collection program was loaded and the transmittance and

66

reflectance ratios (RT and RR) were entered into the data collection program so that it

could record data as absolute transmittance and reflectance along with the raw voltage

values from the three detectors. Next, the program was executed. When first started, the

program records the dark signal coming from each of the detectors. This information is

used to eliminate the detector background signal from the measured data. Typically, the

background signal was two orders of magnitude less than the signal during the

measurements. After about thirty seconds, the laser was unblocked. When the program

detects a large change in the reference signal voltage, it stops acquiring the background

and begins recording the experimental data. During this stage, the program reads data

from each of the detectors and subtracts the respective background signals. These values

are denoted Vref, VR, and VT for the voltages from reference, reflectance, and

transmittance detectors respectively. The program calculates the transmittance, T, and

reflectance, R, by

=

ref

T

V

V1

TRT (3-9)

=

ref

R

V

V1

RRR . (3-10)

After doing the calculations, the program records the time since the beginning of

the exposure (in seconds), T, R, Vref, VR, and VT to an ASCII data file. This process is

repeated at each time-step for the entire experiment. At the end of the experiment, the

laser is again blocked and the setup for a new experiment begins. The data files are

analyzed to extract the relevant information for further analysis.

67

Raman Spectroscopy

Raman spectroscopy is a practical tool for analysis of photodarkening processes.

Because Raman spectra provide a direct optical probe of the phonon modes of a sample,

analysis of the spectra can provide information about the atomic structure and the

temperature of the sample. The Raman signal arises from the inelastic scattering of light

by Raman active optical-branch phonons. The inelastically scattered light is

omnidirectional, so it can be collected without interfering with the transmitted or

reflected fundamental beam. This permits Raman spectra to be collected while measuring

photodarkening. Because the same laser is used for darkening and Raman scattering, the

region of the sample being probed is the same as to the region being photodarkened. No

alignment problems complicate the experimental arrangement or the analysis of the

results. This is especially critical in the event that no structural or thermal changes are

observed since it eliminates misalignment as a possible explanation for the null result.

The process of Raman scattering can be imagined to start when a photon of

angular frequency ω interacts with an electron in the sample. Even if the photon does not

have enough energy to cause an electronic transition, it can still cause transient excitation

of the electron. When this happens, the electron is said to be in a virtual state. Virtual

states have exceptionally short, but finite, lifetimes. While the electron is excited, it can

interact with the lattice and absorb or emit phonons. Eventually, the excited electron

decays back to its original state and reemits a photon. The new photon will be shifted in

energy by an amount equal to the energy of the phonons that were absorbed or emitted.

Because the phonons are quantized, the new photons will be shifted from the exciting

68

wavelength by discrete amounts of energy equal to the energy of the phonon, Ω. This

change in energy is known as the Raman shift.

When the excited electron emits phonons, energy is transferred to the lattice, and

the Raman scattered photon has less energy than the exciting photon. The new photon has

a lower energy than the fundamental (ω - Ω). It can be observed on the long-wavelength

side of the fundamental, and the process is known as Stokes scattering. When the photon

gains energy from the lattice by absorption of phonons, it shifts to shorter wavelengths

and the photon is anti-Stokes scattered. The energy of the anti-Stokes photon is (ω + Ω).

The ratio of Stokes to anti-Stokes scattered light depends on the phonon energy and the

quantity of phonons in the lattice. At 0 K, the lattice is at rest and no phonons are present,

so light can be Stokes scattered by creating phonons, but it cannot be anti-Stokes

scattered because there are no phonons to absorb. As the lattice temperature increases, the

probability of anti-Stokes scattering also increases. The intensity of the Stokes scattered

light, I(ω - Ω), is proportional to the probability of phonon creation, while the intensity of

the anti-Stokes scattered light, I(ω + Ω), is proportional to the probability of phonon

annihilation. These probabilities can be found from the quantum mechanical treatment of

the simple harmonic oscillator.126 The ratio of the two intensities yields

Ω−=Ω−Ω+

TkI

I

B

hexp

)(

)(

ωω

. (3-11)

The absolute temperature can be determined simply by measuring the ratio of anti-Stokes

to Stokes scattered light at a particular Raman shift. This is the basis of using Raman as a

temperature probe. Because the intensity ratio depends only on the temperature, no

calibration is needed beyond that for measuring the intensities accurately.

69

Lattice vibrations are quantized, so the energy shifts have discrete values. In a

crystal, the quantization results in sharp Raman lines, the breadth of which is related to

the damping properties of the lattice. Typically, the peaks will have a Lorentzian profile

similar to the shape of the infrared absorption peaks of crystalline materials. In

amorphous materials, the phonon energies are broadened by the random variations in

bond lengths and angles. This lattice disorder is apparent in the broad Raman features

associated with amorphous samples, and the distortion causes them to assume Gaussian

or Voigt profiles.

Raman Apparatus

In order to achieve high fidelity of the Raman measurements, a second darkening

apparatus was assembled near the entrance slit of the spectrometer. The setup is shown in

Figure 3-3. The setup is designed to maximize the quality of the Raman spectra.

However, the transmitted data was monitored to confirm that the photodarkening process

was identical with the other configuration. All of our observations indicate the

photodarkening of the samples is identical with the photodarkening measured in the

previously described apparatus.

Optical arrangement

Laser light from the Ti:Sapphire laser was directed onto the spectrometer table by

several steering mirrors. Just as with the photodarkening apparatus, the laser light was

attenuated by ND filters before being focused onto the sample. A 25 mm diameter, 150

mm focal length lens focused the light, and a mirror was used to aim the light onto the

sample, which was placed directly in front of the spectrometer collection optics. The light

was incident on the sample at 45° to lessen the difficulty of aligning the collection optics.

The sample was also positioned slightly behind the focus to provide a larger exposed

70

region. The larger exposure spot makes alignment of the Raman collection optics easier.

A detector placed in the transmitted portion of the beam behind the sample measured the

intensity of the transmitted light. The transmitted and reference signals were recorded by

the computer data-acquisition system and saved for further analysis.

Because the sample is slightly behind focus, the power density in the sample is

not as high as it was for the other photodarkening measurements. This is advantageous

because the laser can be attenuated so that darkening does not occur during the Raman

measurements without decreasing the Raman signal so much that it is difficult to detect.

The power density can be calculated in the same manner as it was for the photodarkening

apparatus. The laser waist (radius) on the sample is about 0.3 mm, so the peak normalized

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

TransmittedSignal Detector

SampleFocusing Lens

Reference SignalDetector

ND FilterBeamSplitter

FromTi:SapphireLaser

Mirror

To RamanSpectrometer

Figure 3-3: Experimental apparatus for measurement of Raman scattering duringphotodarkening.

71

intensity is about 0.7 W/(mW⋅cm2). High total laser powers (20 to 40 mW) were used

during the experiments to compensate for the lower power density. In this way, the

exposure conditions were made similar for the photodarkening and Raman experiments.

Raman measurements were collected with the laser in CW mode at a power of about 0.25

mW, or a peak intensity of about 0.18 W/cm2.

Raman spectrometer

The Raman scattered light was collected by a 25 mm focal length lens placed

behind the sample. Placing the lens at the exit face of the sample reduced the spectral

background from scattering of the incident light off the front face of the sample. The

collection lens was positioned so that its focal point was within the sample, and the

Raman signal was maximized by adjusting the position of the laser with the steering

mirror. The collimated light from the collection lens was passed through a holographic

notch filter with a 300 cm-1 bandwidth centered at 12500 cm-1 (800 nm). The filter

attenuates the laser line by six orders of magnitudeenough to permit the use of a single

grating spectrometer to measure the Raman signal. The filter bandpass is very sharp and

spectral features as close as 170 cm-1 can be clearly resolved. A second lens focuses the

filtered light onto the entrance slit of the spectrometer. For these measurements, the

entrance slit was set to 200 µm. The Raman spectra are broad enough that a narrower slit

does not improve the resolution. The high throughput from the wide slit speeds

acquisition of weak signals. The spectrometer has a 640 mm single arm equipped with an

800x2000 pixel silicon CCD detector. The detector is cooled with liquid nitrogen to

minimize electronic background noise. Data from the CCD is collected by a computer,

which also controls the position of the spectrometer grating. For these experiments, the

72

computer was programmed to automatically record spectra at two grating positions. One

was chosen to be just below the laser line to record the Stokes shifted light and the other

was chosen just above the laser line to record the anti-Stokes shifted light. Together, the

two spectra contain all of the Raman information about the sample structure and

temperature.

Experimental Raman Measurements

Raman spectroscopy provides two types of information useful for understanding

the photodarkening process in chalcogenide glasses. The peaks in the Raman spectra

correspond with structural vibrations. Changes in the shape and position of these peaks

reveal changes in the structure. Changes such as the formation of homopolar bonds might

occur during photodarkening. If the structure changes enough to cause changes in the

optical properties, it may also cause changes in the Raman spectra. The structural change

will appear either as a new peak corresponding to a vibrational mode of the new structure

or as a change in the existing peaks corresponding to the change in the existing structure.

The Raman spectra can also be used to determine the absolute temperature of the

sample. The athermal nature of photodarkening is generally believed without evidence,28

however, no one has attempted to directly measure the temperature of the illuminated

region of the sample. A direct measurement can quantify the amount of heating of the

sample. By measuring this, it should be possible to separate the thermal changes from the

athermal ones and determine conclusively the role that temperature plays in

photodarkening.

Structure changes during photodarkening

Structural information is contained in either the Stokes or anti-Stokes Raman

spectrum, but the Stokes scattered light has higher intensity; therefore, it was used for all

73

of the structural comparisons. For these experiments, a sample was placed in the mount

and the system was aligned to maximize the Raman signal. The laser was blocked and the

sample re-positioned so that the beam would be incident on an unexposed spot. The laser

was set to CW mode and filters were placed in the beam path to attenuate the beam by

about two orders of magnitude. The laser was unblocked and the Stokes spectrum was

collected. The collection time was less than 5 minutes and the transmitted light was

monitored to verify that no darkening occurred during collection of the Raman spectrum.

When the collection was complete, the laser was blocked. The ND filters were removed

and the laser was set to ML operation. The laser was unblocked and transmittance data

were recorded just as they had been for the photodarkening measurements already

described. Darkening was carried out at moderate intensities. After the desired period of

darkening, the laser was blocked, switched to CW operation, and the filters replaced.

Another measurement of the Raman spectrum was performed. The Raman spectra were

usually collected within 5 minutes of the end of the photodarkening. For some of the

measurements, darkening was interrupted several times. During each interruption, the

Raman spectrum was measured.

Temperature changes during exposure

Temperature measurements were done using the same experimental arrangement

that was used for the structural studies. For these measurements, only CW operation was

used. This experiment is designed to determine how much heating of the sample was

being caused by absorption of the Ti:Sapphire laser light. For this, anti-Stokes and Stokes

spectra were measured at three different laser intensities. The intensity of the laser was

controlled by the same neutral density filters used in the other experiments. The laser

intensities spanned a range of two orders of magnitude, and they were chosen so that the

74

lowest intensity caused no photodarkening during the measurement period and the

highest intensity caused moderate photodarkening. Higher intensities were avoided

because the rapid change in transmission associated with the photodarkening could alter

the Raman spectra during the measurement and produce unreliable results.

75

CHAPTER 4MEASUREMENT OF OPTICAL PROPERTIES

Infrared Absorption Edge

The infrared transparency of any semiconductor is limited on the long wavelength

side by the multi-phonon absorption of light. In the chalcogenide glasses, the constituent

atoms are heavy enough that the fundamental phonon vibrations have low energy. The

phonon energy is below 400 cm-1 (25 µm) for germanium selenium glasses.127 Multi-

phonon processes occur at energies that are sums of the fundamental phonon energies, so

the multi-phonon absorption in chalcogenide glasses also occurs at low energy (long

wavelength). Again, citing germanium selenium glasses as the example, the multi-

phonon peaks tend to be below 1000 cm-1 (10 µm). The probability of a multi-phonon

event is inversely related to the number of phonons involved. Therefore, two- and three-

phonon processes may show up as distinct absorption peaks, while higher order processes

merge into a tail extending to higher energies (shorter wavelengths). This tail is known as

the multi-phonon edge. For optical fibers, the multi-phonon tail is an important limiting

factor on the long-wavelength transparency. For thin optical elements, such as windows

and lenses, the tail absorption is insignificant and the long-wavelength transparency is

limited by the two- and three-phonon peaks.

To determine the long wavelength edge of these samples, we measured their

transmittance with an FTIR. The samples were too thin to permit us to see the multi-

phonon edge; however, the multi-phonon peaks are clearly visible in Figure 4-1. Three

76

peaks can be seen, and their positions are indicated by vertical lines on the figure. The

areas of the three peaks can be determined by curve fitting with spectroscopic curve

fitting software. Scaling the peak areas to the total area of the three peaks permits

comparison of the different compositions. This is shown in the inset on Figure 4-1.

The peak at 490 cm-1 is quite clearly associated with selenium ring or chain

vibrations. Such a peak is also observed in amorphous selenium. Siemsen and Riccius128

assigned it to a two-phonon resonance of Se8 ring molecule. The assignment was based

on the observation of Lucovsky et al.96 that the fundamental peak at about 250 cm-1 seen

in amorphous selenium coincides well with a ring mode seen in α-monoclinic selenium.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

4005006007008009001000

10 12.5 15 17.5 20 22.5 25

Abs

orba

nce

Wavenumber (cm-1)

Wavelength (µm)

460

490

562

GeSe3 GeSe4 Ge3Se17 GeSe9

0.0

0.2

0.4

0.6

0.8

10 15 20 25

Are

a Fr

actio

n

Composition (% Ge)

460490562

Figure 4-1: Infrared absorbance of germanium-selenium glasses showing the multi-phonon absorption peaks. Vertical lines indicate the positions of the peaks. The insetplots the areas of the three peaks (as fractions of the total area) against the composition ofthe sample.

77

In a later paper, Martin et al.100 point out that an analogous vibration is seen in

amorphous tellurium, which does not form rings. They suggest that the vibration might

be due to a chain mode that is shifted in energy in the amorphous state. If the vibration

was due to a ring mode, we would expect it to vanish at a low concentration of

germanium because chemical ordering will cause the germanium atoms to turn any rings

into chains. Furthermore, in the 20% germanium glass, the germanium atoms are

connected by pairs of selenium atoms. This structure should not exhibit any of the ring

modes; however, the two selenium atoms and one germanium atom still form a structure

similar to the selenium chain. The vibration should be only slightly higher (≈1.4%) since

the germanium atom is slightly lighter than the selenium atom it is replacing in the chain.

The persistence of the 490 cm-1 vibration at and above 20% germanium concentration

indicates that it is most likely a second harmonic of the chain vibration rather than a

second harmonic of the ring mode.

The other two peaks are not seen in amorphous selenium. Both peaks increase in

intensity with increasing germanium content, so it is reasonable to assume that they are

related to the presence of GeSe4/2 tetrahedra in the glass. By using infrared spectroscopy,

four fundamental modes for the GeSe4/2 tetrahedra have been identified.127 Assignment of

these modes to the multi-phonon peaks at 460 and 562 cm-1 is beyond the scope of this

work. The small peak appearing around 800 cm-1 is most likely a three-phonon

absorption. In amorphous selenium, such a peak has been observed at about 750 cm-1 and

assigned to a three-phonon process.128 This peak also appears to be affected by the

presence of germanium, and it is not known which modes account for this vibration in the

germanium-selenium glasses.

78

Because the infrared absorption results from the presence of molecular species in

the glass, the frequency of the peaks remains nearly constant with changes in

composition. The infrared edge does not shift much with the addition of up to 33%

germanium to amorphous selenium. Above this germanium concentration, the glass will

consist of different molecular species, and the absorption edge might exhibit a distinct

shift. All of the compositions measured are transparent to at least 10 µm in the infrared.

Visible Absorption Edge

The visible absorption edge of semiconductors results from electronic transitions.

Photons with sufficient energy are absorbed when they excite electrons across the

forbidden bandgap. In traditional semiconductors, the electrons are excited from the top

of the valence band to the bottom of the conduction band. The transition can be either

direct, conserving energy and momentum; or indirect, conserving only energy. In

amorphous semiconductors, additional states exist just above the valence band and just

Table 4-1: Fundamental infrared active vibrationsobserved in amorphous selenium and germanium-selenium glasses. All of the selenium assignments arefrom Siemsen and Riccius128 and Lucovsky et al.96 and allof the GeSe4/2 assignments are from Ohsaka.127

ObservedFrequency (cm-1)

Assignment

55 Se8, E2

97 Se8, E1; Se-chain, A2

123 GeSe4/2, ν2

138 Se-chain, E195 GeSe4/2, ν4

257 Se8, E1

278 GeSe4/2, ν1

307 GeSe4/2, ν3

79

below the conduction band. These states are present because the disorder creates

localized electronic states. The localized states participate in the absorption process.

These so-called band tail states lead to an extension of the absorption into the bandgap.90

The absorption coefficient exhibits an exponential dependence on the energy of the light;

hence, it is often referred to as the exponential absorption tail. Because of its similarity

with a process first observed by Franz Urbach129 in crystalline semiconductors, the

exponential band tail is also known as an Urbach tail; however, this is a misnomer.

Urbach found that the band tail in several crystalline semiconductors had an exponential

relationship with the photon energy and that the slope of the exponent was proportional to

1/kBT. The proportionality constant is close to 1.0 for several materials including those

originally studied by Urbach. Amorphous semiconductors also have a region of

absorption that is exponentially dependent on the photon energy, but, contrary to the

Urbach rule, the slope of the exponential absorption tail is nearly independent of

temperature.130 Though several authors have attempted to relate both crystalline and

amorphous absorption tails to a unified theoretical model, no clear explanation has

emerged,130-132 and it is still quite possible that the two absorption processes are

unrelated. This distinction is significant, but it is frequently ignored in the published

literature.

Knowing the optical properties of the glasses at the exposure wavelength is

critical for understanding the photodarkening process. The optical properties, specifically

n and α, of the annealed glass samples represent the starting state from which the

darkening process proceeds. Accurate determination of these values permits us to

evaluate the various mechanisms that might account for the photodarkening process. For

80

example, if the absorption is high, we might expect sample heating to play a significant

role in the process. Independent knowledge of these values also permits us to estimate the

accuracy of the measurements made using the photodarkening apparatus. Comparison of

n and α (or ε1 and ε2) measured at the beginning of photodarkening with their values

determined by spectrophotometry permits estimation of the accuracy of the

photodarkening apparatus.

Initially we looked to the published literature for these values. While much

information is available for amorphous selenium, very little of it can be used to determine

the optical properties at 800 nm. In addition, almost no information is available about the

optical properties of germanium-selenium glasses. Because of the limited amount of

information in the literature, we had to measure the values directly.

The most common ways to measure the optical properties are to measure normal

incidence reflection and transmission simultaneously or to measure the transmission

through samples of different thickness. Neither of these methods was practical for our

samples. However, because the wavelength of interest is within the exponential band tail,

the optical properties can be determined by measuring only the sample transmission and

then using curve fitting techniques to extract the relevant information. Two different

curve fitting methods were used. Both methods will be discussed and the results

compared. The values of n and α obtained with either method agree well with published

values.

Measured Data

The measurement of transmission was described in Chapter 3. For determining

near-infrared optical properties, the transmission of samples was measured from 600 to

81

900 nmthe low absorption portion of the exponential band tail. The higher absorption

portion of the band tail and the optical band edge could not be measured because the

samples were too thick. At least two samples of each composition were measured. The

samples of the same composition had different thickness but often the difference was

small. The results of the measurements are shown in Figure 4-2.

The data in Figure 4-2 is displayed in terms of the absorbance, a unitless quantity

that is related to the transmittance by Equation 3-1. From this figure, we can see that the

exponential band tail shifts to lower frequencies (higher energies) with increasing

germanium content. The noisy flat region on the left-hand side of the graph is just the

detection limit of the spectrophotometer. The real absorbance increases by several more

0

1

2

3

4

5

6

600 650 700 750 800 850 900

Abs

orba

nce

Wavelength (nm)

GeSe9Ge3Se17GeSe4GeSe3

Figure 4-2: Measured absorbance of germanium-selenium glasses in the exponential bandtail region

82

orders of magnitude before reaching a maximum. The band-to-band absorption maximum

in amorphous selenium occurs at about 4.0 eV (310 nm).133 On the right-hand side of the

graph, all of the compositions have the same absorbance. In this region, the absorption

coefficient is low and the only loss of transmitted light comes from surface reflections.

Extraction of Optical Properties

The exponential absorption tail is described by Equation 3-2, repeated here in a

slightly modified, but equivalent, form

+=

σνβνα h

h exp)( , (4-1)

where β=ln(α0). This form is used because it is computationally more stable in curve

fitting routines.

In the region of the exponential band tail, two techniques can be used for

extracting n and α from the measured transmission of a single sample. The first method is

to directly fit the measured data with a function that assumes that the absorption

coefficient is exponential and the index of refraction is constant. The second method is to

fit the derivative of the measured transmittance with an exponential function. The

parameters for the absorption tail can be extracted from this fit, and the index can then be

calculated from the fit and the original data. This technique was developed by Oheda134

and applied to germanium-selenium glasses; however, he did not publish the fit

parameters, so his data cannot be used to determine the actual absorption coefficients.

The spectrophotometer records sample absorbance, A, as a function of

wavelength, λ, but the spectrophotometer actually measures transmittance, T, and

83

converts the data into absorbance by Equation 3-1. The sample transmittance, which is

related to the sample optical properties, is therefore

AT −=10 . (4-2)

Wavelength can be transformed into photon energy, hν, by

λν 1240=h , (4-3)

where λ is the wavelength of light measured in nm, and hν is the energy of the photons in

eV. The result of applying Equations 4-2 and 4-3 to the data from Figure 4-2, is shown in

Figure 4-3. These equations are presented because data in this form can be easier to work

with in the techniques discussed here.

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1

Tra

nsm

ittan

ce

hν (eV)


Figure 4-3: Measured transmittance versus energy for germanium-selenium glasses.

84

Curve fitting technique

Consider the equation for normal transmission through a thick sample with two

flat parallel faces, given in Chapter 2 as Equation 2-14. The transmission depends on two

factors, the absorption coefficient, α, and the single surface reflectivity, r. Since the

transmission measurement is done in the region of the exponential absorption tail, the

absorption coefficient as a function of photon energy can be modeled by Equation 4-1.

This provides two adjustable parameters, β and σ, for fitting the measured transmission.

The single surface reflectivity is described by Equation 2-16. Because the

absorption coefficient in this portion of the band tail is small (less than 100 cm-1), the

extinction coefficient, κ, is tiny (≈10-4) and its contribution to the reflection can be

neglected. The single surface reflection can then be written as

2

2

)1(

)1(

+−=

n

nr . (4-4)

This equation provides one more adjustable parameter, n, for fitting the measured data. If

we assume that n is constant over the range of wavelengths measured, then the data can

be fully described by a model with three adjustable parameters. The assumption of a

constant index of refraction is not generally true for wavelengths of light near an

absorption change; however, we can estimate the size of the error introduced by this

assumption by examining published data. Published values (in the form of Sellmeier

coefficients) of the index of refraction of amorphous selenium102 and Ge20Se80135 indicate

that the index of refraction over the range of wavelengths from 700 to 1000 nm varies by

less than 5%. While this is hardly a constant value, it will only introduce an error of about

±2.5% in the final value determined for the index of refraction. This error is on the same

85

order as the other errors in this measurement and does not lead to a significant decrease in

the accuracy of the optical parameters determined in this manner.

The measured data can be fit by using Equations 2-14, 4-1, and 4-4 in a program

that performs nonlinear curve fitting. The solution will depend on only three independent

parameters, σ, β, and n. From these, the optical properties at any wavelength within the

exponential band tail can be calculated. The results of the curve fitting procedure are

given in Table 4-2. In addition to the three curve fitting parameters, the table also lists

two calculated values: the absorption coefficient at 800 nm, α800, and the optical

bandgap, Ego. The absorption coefficient is calculated by solving Equation 4-1 at 800 nm

with the values of σ and β given in the table. The optical bandgap is estimated134 as the

energy at which the calculated absorption coefficient is 103 cm-1.

All of the values shown are the average of the values obtained by fitting several

different spectra. The number of spectra used in each case is listed in parenthesis after the

sample composition. Each term in the table is followed by its uncertainty, which is

calculated as the standard deviation of the values used for the average. This uncertainty is

an indication of the repeatability of the technique and not a true measure of the absolute

error in the measurement.

Table 4-2: Optical properties of germanium-selenium glasses calculated by application ofthe Curve Fitting Technique to the measured absorbance spectra.Sample σσσσ (meV) ββββ n αααα800(cm-1) Ego (eV)GeSe9 (3) 62.5 ±0.6 -24.2 ±0.3 2.62 ±0.03 1.79 ±0.07 1.946 ±0.004Ge3Se17 (5) 66.7 ±1.5 -22.7 ±0.6 2.43 ±0.08 1.81 ±0.15 1.972 ±0.004GeSe4 (4) 70.9 ±2 -21.3 ±0.7 2.38 ±0.05 1.76 ±0.23 2.001 ±0.003GeSe3 (6) 74.1 ±0.8 -20.9 ±0.3 2.34 ±0.07 1.01 ±0.06 2.062 ±0.003

86

Derivative fitting technique

The other method for extracting the optical properties from the band tail region of

an amorphous material was developed by Oheda.134 He recognized that, in the case of an

exponential band tail, the derivative of α is also an exponential function,

ασν

α 1

)d(

d =h

. (4-5)

Taking the derivative eliminates the contribution of the surface reflections, which are

assumed constant. The slope of the derivative is directly related to the slope of the

absorption edge, which can be found by fitting a straight line to the derivative data

plotted on a semi-log scale.

The relationship between the measured transmission and the derivative of the

absorption coefficient dα/d(hν) is

λλ

να

d

d11

)d(

d 2 T

Thcdh= . (4-6)

This relationship is derived from Equation 2-14 with two assumptions. The first is that

the term in the denominator is approximately equal to 1.0 and the transmission can be

written as

)exp()1( 2 drT α−−≈ . (4-7)

This is a good approximation since R2exp(-2αd) is less than 0.1 when α is greater than 1

cm-1. The second assumption is that the single surface reflection is independent of

wavelength. This is equivalent to the assumption that the index of refraction is constant.

The validity of this assumption has already been discussed.

Oheda designed an apparatus to directly measure 1/T(dT/dλ). The derivative of

the transmission thus measured was used in Equation 4-6 to calculate the derivative of the

87

absorption coefficient. In our case, we measure the absorbance not its derivative.

Combining Equation 4-6 with Equation 4-2,

λλ

να

d

d)10ln(

)d(

d 2 A

hcdh

−= . (4-8)

The derivative of the absorbance, dA/dλ, can be calculated numerically and all of the

other values are known, so dα/d(hν) can be found from the data.

From Equations 4-1 and 4-5,

+=

σνβ

σνα h

hexp

1

)d(

d, (4-9)

or, by taking the natural logarithm of both sides,

)(11

ln)d(

dln ν

σβ

σνα

hh

+

+

=

. (4-10)

This is the equation of a straight line when ln(dα/d(hν)) is plotted against hν. The slope

of the line is (1/σ) and the intercept is (ln(1/σ) + β). By fitting with a straight line, it is

possible to find the values of both adjustable parameters (σ and β) necessary to describe

the exponential absorption tail.

The final unknown parameter is the index of refraction, n. Since the absorption

coefficient as a function of wavelength is now known, the index of refraction can be

calculated directly from the measured data. This can be done by substituting Equation 4-2

into Equation 4-7 and then solving for the single surface reflectance,

)303.2exp(1 Adr −−= α , (4-11)

where α is the absorption coefficient calculated from the derivative data. Application of

this equation to the absorbance data yields the reflectance of the sample as a function of

88

wavelength. Essentially, this is the portion of the absorbance not accounted for by the

calculated absorption coefficient. The index of refraction can be calculated by solving

Equation 4-4 for n. Assuming that the index is greater than 1.0,

−+=

r

rn

1

1. (4-12)

The results obtained by this method for σ, β, and n are given in Table 4-3. The

format of this table is the same as the format of Table 4-2 and the values of α and Ego

were calculated in the same manner as they were for the Curve Fit Technique. The value

given for the index of refraction is calculated by averaging the calculated values of n over

a range of wavelengths because averaging reduces the noise of the measurement and

improves the accuracy. The range from 795 to 805 nm was used for the estimate of the

index at 800 nm.

Comparison with published values

In order to evaluate the two methods for determining the band tail optical

properties of the germanium-selenium glasses, the data are compared with values

available in the literature. Only values for n and α at 800 nm are used for the comparison.

They were determined either by directly reading them from a graph or by calculating the

value at 800 nm from functions fit to experimental data. Data reported on film samples

Table 4-3: Optical properties of germanium-selenium glasses calculated by application ofthe Derivative Technique to the measured absorbance spectra.Sample σσσσ (meV) ββββ n αααα800(cm-1) Ego (eV)GeSe9 (3) 59.6 ±0.3 -25.6 ±0.1 2.73 ±0.03 1.49 ±0.03 1.939 ±0.003Ge3Se17 (5) 61.5 ±1.6 -25.0 ±0.7 2.61 ±0.06 1.32 ±0.13 1.959 ±0.004GeSe4 (4) 66.2 ±1.2 -23.2 ±0.5 2.55 ±0.01 1.30 ±0.06 1.991 ±0.005GeSe3 (6) 68.8 ±0.5 -22.9 ±0.2 2.49 ±0.05 0.74 ±0.01 2.047 ±0.004

89

was not used since the deposition process often leads to microstructures which are

different from that of well-annealed glass samples.

The dispersion of the refractive index, n, is usually reported in one of two forms.

The first is the Sellmeier dispersion formula13 for a single resonance,

20

2

22 1

λλλ−

=− An , (4-13)

where A and λ0 are fitting parameters and λ is the wavelength of the light. The second

form is the Wemple-DiDomenico136,137 equation,

220

02 1EE

EEn d

−=− , (4-14)

where Ed and E0 are the fitting parameters and E is the energy of the light. Table 4-4 lists

the refractive index values found in the literature. The Ref column indicates the source

of the value and the Note column indicates how the value was determined from that

source. Most of the published values were for amorphous selenium but a few sources

were available for germanium-selenium mixtures. The values are plotted in Figure 4-4

along with the values obtained by the Curve Fit Technique and the Derivative Technique.

Table 4-5 lists the published values of the absorption coefficient and Table 4-6

lists the published values of the optical bandgap (Ego). The value of the absorption

coefficient at 800 nm was only found in two sources. In one paper,138 the absorption in

the exponential region was reported graphically. The value at 800 nm was read directly

from the graph. In the other paper,139 the equation for the exponential absorption tail was

given and the value was calculated from this equation. The experimentally determined

absorption coefficients and the published values are shown in Figure 4-5.

90

The optical bandgap was determined in several ways. One of the methods was

that of Tauc, Grigorovici, and Vancu.140 In their method, the optical bandgap is found by

plotting (αhν)1/2 vs. hν in the region of wavelengths shorter than the exponential band

tail. The absorption process in this region is due to band-to-band transitions and the

absorption coefficient is high (≥ 104). The plotted data are fit with a straight line and the

bandgap is found as the intercept of this line with the x-axis. A different technique, based

on fitting the measured dielectric response in the interband region was used in one

reference.133 In this paper, the complex dielectric response was measured by ellipsometry

and the data was fit with a model proposed by Jellison and Modine.141 The bandgap is

then extracted from the fitting parameters of the model. The final method that is used to

determine the bandgap is that of Oheda.134 The absorption data in the band tail region is

fit with an exponential model given in Equation 4-1. The energy at which the absorption

becomes 103 cm-1 is calculated from this model and reported as the estimated optical

bandgap. This is the same method used to estimate the bandgap for the experiments

reported here. Figure 4-6 shows the published and experimentally determined values of

the optical bandgap.

Discussion

It is clear from the three graphs that the optical parameters determined by both the

Curve Fit Technique and the Derivative Technique are in close agreement with one

another. The data also appears to agree well with the published values.

Looking at Figure 4-4 we can see that the estimates of the index of refraction

using the Derivative Technique are 4 to 7% higher than the estimates using the Curve

Fitting Technique. The opposite is true of the absorption coefficient, seen on Figure 4-5.

91

2.2

2.3

2.4

2.5

2.6

2.7

2.8

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Inde

x of

Ref

ract

ion

Ge Concentration (Atomic Fraction)

Curve Fit TechniqueDerivative Technique

Published Values

Figure 4-4: Index of refraction at 800 nm for germanium-selenium glasses. Error barsindicate the standard deviation of the values estimated by the two techniques. See Table4-4 for the sources of the published values.

Table 4-4: Reported values for the refractive index (n) of germanium-selenium glasses at800 nm.Glass (% Ge) n800 Note Ref

0 2.59 Sellmeier Equation 102

0 2.63 Wemple-DiDomenico Equation 142

0 2.61 Sellmeier Equation 133

0 2.58 Wemple-DiDomenico Equation 137

0 2.69 Wemple-DiDomenico Equation, Table 2 143


20 2.55 Sellmeier fit to data in Table 1 135


92

0.5

1.0

1.5

2.0

2.5

3.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Abs

orpt

ion

Coe

ffic

ient



Published Values

Figure 4-5: Absorption coefficient at 800 nm for germanium-selenium glasses. Error barsindicate the standard deviation of the values estimated by the two techniques. See Table4-5 for the sources of the published values.

Table 4-5: Reported values for the absorption coefficient (α) of germanium-seleniumglasses at 800 nm.Glass (% Ge) αααα800 (cm-1) Note Ref

0 2.9 Figure 4 138

25 0.986 Exponential Band Tail, Table 6 139

93

1.85

1.90

1.95

2.00

2.05

2.10

2.15

2.20

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Opt

ical

Ban

d E

dge,

Ego

(eV

)



Published Values

Figure 4-6: Optical bandgap for germanium-selenium glasses. Error bars indicate thestandard deviation of the values estimated by the two techniques. See Table 4-6 for thesources of the published values.

Table 4-6: Reported values for the optical bandgap (Ego) germanium-selenium glass at800 nm.Glass (% Ge) Ego (eV) Note Ref

0 1.86 Tauc Bandgap from Table 1 144

0 1.94 Tauc Bandgap 142

0 1.87 Jellison-Modine Model 133

0 1.945 Exponential Tail (α=103), Figure 5 134






94

Here, the values calculated by the Derivative Technique are 20 to 30% lower than the

values calculated by the Curve Fitting Technique. In both figures the error bars associated

with the Derivative Technique are smaller than those associated with the Curve Fitting

Technique for the same composition. The difference in error bars between different

compositions is indicative of the variation in quality and thickness of the different

samples.

The optical bandgap data shown in Figure 4-6 displays the best agreement

between the two techniques. The estimated values of the optical bandgap differ by less

than 1% for all of the glasses measured. The small error bars indicate that the sample-to-

sample variation in this value was extremely small for glasses of the same composition.

In comparing the two techniques, we can see that the trends in the data are

identical for both techniques. The random variation of the Derivative Technique is

smaller than the random variation of the Curve Fitting Technique. The Curve Fitting

Technique appears to favor higher absorption coefficients and, consequently, lower index

of refraction values. The differences in the estimated absorption coefficients result from

small differences in the values of the parameters σ and β determined by fitting the

exponential model to the experimental data. Interestingly, the value of the optical

bandgap, which is calculated from σ and β, is almost identical for the two techniques.

This may indicate that the curve fitting methods used are more accurate for the regions of

higher absorption coefficient. The effect of the refractive index also becomes less

significant at higher absorption coefficient.

The scarcity of data from other sources makes it difficult to evaluate which

method is most accurate. Despite this, it appears that the Derivative Technique is the

95

better method for determining the optical properties. It exhibits lower sample to sample

variation than the Curve Fitting Technique and therefore is more precise. It also produces

values of the index of refraction that agree very well with published values (obtained by

minimum-deviation method and thin film transmission measurements) for two different

compositions from three different authors. The values of the index of refraction are

generally less sensitive than the values of the absorption coefficient to the sample

preparation. Scattering from density fluctuations and small inhomogeneities will lead to

an apparent increase in the absorption coefficient with little or no change in the index of

refraction. This reduces the significance of the single published value of the absorption

coefficient that agrees well with the value determined by the Curve Fitting Technique for

the GeSe3 composition. For all of these reasons, we choose to use the values determined

by the Derivative Technique as the optical properties of the germanium selenium glasses.

Looking at Table 4-3, we can see that σ increases with increasing germanium

content. The width of the tail is directly related to σ; hence, the exponential band tail is

wider for glasses with higher germanium content. The source of the exponential

absorption is not understood; however, it has been suggested that the width of the tail is a

measure of the degree of structural distortion present in the amorphous lattice.134 The

band tail states are associated with the lone-pair electrons of the selenium atoms, so, if σ

is a measure of the distortion of the localized states, then the addition of germanium

increases the distortion around the selenium atoms.

96

CHAPTER 5BELOW-BANDGAP PHOTODARKENING

Photodarkening is a light-induced change in the transmittance of a sample. This

can quite easily be measured by exposing the sample to a laser of known power and

measuring the intensity of light transmitted through the sample. By also recording the

intensity of the signal reflected by the sample, the optical properties ε1 and ε2 can be

calculated. Since these properties are related to the structure of the sample, changes in

their value indicate changes in the structure of the sample. Measuring the kinetics of the

process at different laser powers provides information about the mechanism of the

structural change. This chapter presents measurements of the kinetics of photodarkening

in germanium-selenium glasses.

Changes in Optical Properties Induced by Below-Bandgap Light

A computer controlled data-acquisition system records the voltages generated by

three photodetectors. Two detectors are used to monitor the amount of light transmitted

and reflected by the sample. Another detector is used to monitor the laser beam intensity,

thus providing a reference signal for scaling the signals from the other detectors. By

calibrating the system before the experiment, the voltages can be converted by the

computer into the percent of light transmitted and reflected. The time dependence of

these two values is recorded to a file and the change in dielectric properties is calculated

from the recorded values.

97

0.0

0.1

0.2

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0.4

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0.6

0 50 100 150 200 250

Tra

nsm

ittan

ce

Exposure Time (minutes)

GeSe9 I0 (mW)1.433.298.5328.152.6

0.0

0.1

0.2

0.3

0.4

0 50 100 150 200 250

Ref

lect

ance


GeSe9 I0 (mW)1.433.298.5328.152.6

Figure 5-1: Transmittance and reflectance of GeSe9 during exposure to 800 nm laserlight. Each trace represents the exposure of an unexposed location beginning at time = 0.

98

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Ge3Se17 I0 (mW) 0.441 0.917 3.51 9.88 18.9 35.9 57.9

-0.1

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0.3

0.4

0 50 100 150 200 250 300 350

Ref

lect

ance


Ge3Se17 I0 (mW) 0.441 0.917 3.51 9.88 18.9 35.9 57.9

Figure 5-2: Transmittance and reflectance of Ge3Se17 during exposure to 800 nm laserlight. Each trace represents the exposure of an unexposed location beginning at time = 0.

99

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GeSe4 I0 (mW)1.013.6010.138.8

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GeSe4 I0 (mW)1.013.6010.138.8


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GeSe3 I0 (mW)0.9563.669.9836.6

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GeSe3 I0 (mW)0.9563.669.9836.6


101

Transmittance and Reflectance Changes

Several measurements of photodarkening were performed at each power on each

sample. Typical results for the observed changes in transmittance and reflectance are

shown in Figure 5-1 through Figure 5-4. All of the studied compositions of germanium-

selenium glass undergo large changes in their transmittance and reflectance during

exposure to 800 nm laser light. The transmittance for all of the samples decreases in a

manner consistent with photodarkening. The change in transmittance occurs more rapidly

for high laser powers than for low laser powers. This is expected for any process in which

the rate of change is controlled by the intensity of the light. The number of photons

incident on the sample is proportional to the power of the laser, so higher laser powers

are equivalent to higher photon fluxes and therefore they lead to faster darkening. More

significant is the observation that the total change in transmittance appears to be a

function of the incident intensity for all of the samples. This is evidence that the process

of photodarkening in germanium-selenium glasses is intensity dependent or, in other

words, optically nonlinear. The total darkening depends not only on the photon fluence

(the time-integrated number of photons that pass through the sample) but also on the

photon flux (the rate at which photons pass through the sample). If the total darkening

were only a function of the fluence, then photodarkening would be a linear process in

which each absorbed photon creates one defect. The dependence on flux as well as

fluence shows that the photodarkening depends on excitation by multiple photons to

produce a single defect. The reflectance also decreases; however, since the reflectance

includes a significant portion of reflected light from the back surface of the samples, this

does not necessarily indicate a decrease in the index of refraction.

102

Despite the general similarities, each sample displays distinct characteristics. The

most striking differences can be seen in the rate of darkening and in the exact shape of

the darkening curves. Looking first at the sample with the least germanium (GeSe9),

shown in Figure 5-1, we can see that the transmittance decreases monotonically with

exposure time for the three lowest laser powers. The next higher power (35.9 mW) causes

a steep initial decrease followed by an increase and then a larger and slower decrease in

transmittance. The increase in transmittance and reflectance indicates that light is capable

of inducing recovery as well as darkening. The recovery is only observed in the GeSe9

sample. The highest power (52.6 mW) causes such a rapid change in the transmittance

that it is difficult to see on the graph, so it is redrawn as Figure 5-5. This power also

causes a steep decrease in transmittance followed by a small increase just as for the 35.9

0.0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5 2 2.5

Tra

nsm

ittan

ce


GeSe9 I0 (mW)52.6

Figure 5-5: Transmittance change of the GeSe9 sample at the highest laser power (52.6mW).

103

mW power. However, after the increase, the transmittance decreases rapidly to almost

zero. The reflectance also decreases rapidly to almost zero. After exposure to the 52.6

mW power, the surface of the sample appears distorteda bulge appears on the surface

at the location of the irradiated spot. The bulge occurs on both the front and back surfaces

of the sample. The surface of the bulge is shiny, but surrounding it is a frosty ring. This

ring is about twice the diameter of the bulge. Such a change is not observed at any of the

locations exposed to lower power.

The transmittance and reflectance changes for the Ge3Se17 sample are shown in

Figure 5-2. For a given power, the amount of darkening is greater in this sample than in

the GeSe9 sample, but the process occurs more slowly in the higher germanium content

glass. The Ge3Se17 composition does not exhibit the recovery period seen in GeSe9.

Instead, at any power above 1 mW, the transmittance decreases rapidly and then the

change appears to saturate. After a period of time, which is power dependent, the

transmission decreases again. The rate of the second decrease is slower than the initial

rate. Eventually the second decrease reaches a limiting value, which is also dependent on

the laser power. At the highest power (57.9 mW) the darkening process appears similar to

that at the lower exposure powers except at the end. This can be seen in Figure 5-6.

Instead of reaching a limiting transmittance value, the transmittance decrease slows.

Then, quite abruptly, the transmittance and reflectance both decrease to almost zero. This

is very much like the effect observed in the GeSe9 sample exposed to the highest laser

intensity. After exposure, the surface of the sample showed evidence of damage similar

to the damage seen on the GeSe9 glass. The Ge3Se17 sample required more than twice the

exposure time for the damage to occur.

104

The photodarkening of the GeSe4 sample is shown in Figure 5-3. The

transmittance curves show a monotonic decrease for all laser powers. The transmittance

exhibits an initial decrease and then a slowing in the rate of decrease. This is followed by

another period of transmittance decrease much like that seen in the Ge3Se17 sample. The

total decrease in transmittance is larger for this sample than for the two samples that

contain less germanium, and the process takes longer to reach its limiting value. The final

transmittance change is almost the same for all of the spots independent of the laser

power. One measurement was made at a laser power of 55 mW but problems with the

calibration make the data unusable. After ten minutes of exposure at the 55 mW power,

the sample did not show any signs of damage.

0.0

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0.3

0.4

0.5

0 1 2 3 4 5 6 7

Tra

nsm

ittan

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Ge3Se17 I0 (mW) 57.9

Figure 5-6: Transmittance change of the Ge3Se17 sample at the highest laser power (57.9mW).

105

Figure 5-4 shows the photodarkening of the GeSe3 sample. Of all the samples

studied, this sample contains the highest concentration of germanium and it shows the

slowest darkening response for a given laser power. The first stage of the darkening

process appears similar to that of the other samples. The second stage, while similar to

that of the GeSe4 sample, exhibits temporal fluctuations in the transmittance and

reflectance. The ripples occur consistently at all laser powersthey can be seen at

different sample locations and a variety of laser powers. They are not seen in the other

compositions.

Real and Imaginary Dielectric Response

The change in transmittance indicates a change in the structure of the samples

during illumination. The structure change may be a change in the amorphous state of the

material, or it may be the creation of defects. This change in structure leads to a change in

the electronic properties of the material. The optical band edge may shift or a new

absorption process may occur by the formation of new defects that behave as color

centers. Thus, the change in physical structure leads to a change in optical properties.

To further characterize the photoinduced change in structure, the optical

properties must be calculated from the transmittance and reflectance. Neither the

transmittance nor reflectance is directly related to the structure; however, the dielectric

response terns ε1 and ε2 are because they are a linear sum of all of the contributions from

the optically active structural elements. The calculation of ε1 and ε2 requires finding the

roots of a third order equation and has already been described in Chapter 2. This step was

carried out after the data was collected by a program written for this purpose.

106

By realizing that the process is light induced, it becomes evident that using time

as the independent variable is incorrect. The process does not depend on the time of

exposure; it depends on the number of photons that strike the sample. This quantity is the

fluence, Φ, which is the temporal integral of the flux,

∫=Φt

ttIt0

d)()( , (5-1)

where t is the time, and I(t) is the incident light intensity at time t. The fluence, Φ, has

units of Joules when I is in Watts and t is in seconds. In any experiment, the data is

sampled at discrete times. The above integral can then be approximated for the Nth

measurement by the summation

∑=

−−≈ΦN

nnnn ttIt

11 )()( , (5-2)

where tn is the time at which the nth data point was measured, In is the laser intensity at

that time, and the data points are numbered from zero. The rest of the photodarkening

data presented in this chapter will be graphed with the fluence as the independent

variable. In addition, the use of a logarithmic scale for the x axis (fluence) facilitates

comparison of the photodarkening process at different laser powers. The results for the

four compositions are presented in Figure 5-7 through Figure 5-10.

Analysis of the transmittance and reflectance data reveals that the changes

observed are caused almost entirely by a photoinduced increase in the imaginary portion

of the dielectric response, ε2. This corresponds with an increase in absorption by the

samples. Some changes are also observed in ε1 during darkening, but they are almost the

same size as the error and do not show the clear trends observed in the ε2 results. The ε1

values are much more sensitive to the surface finish. We expect that this explains the

107

spot-to-spot variation that makes the results difficult to interpret. It is worth noting that

the ε2 data does not appear to suffer from the uncertainty or the inconsistency associated

with the ε1 data despite the fact that they are both calculated from the same raw data. This

indicates that the method we use is best applied to measuring changes in absorption and

is rather insensitive to changes in the index of refraction. For completeness, the ε1 data

will be shown with the ε2 data for all of the samples.

In general, ε1 is nearly constant within the accuracy of these measurements and

does not vary in a consistent manner with the incident power. The only exception is seen

in the high power exposure of the GeSe9 and Ge3Se17 samples. A large decrease in ε1 is

seen which corresponds to the large, sudden drop in reflectance and transmittance shown

in Figure 5-5 and Figure 5-6. Since this is most likely caused by damage to the sample, it

should not be considered a real change in dielectric properties but, instead, a side effect

of the change in the sample surface during damage. In the other cases, the differences in

ε1 are most likely an indication of variations in the surface quality on a point-to-point

basis. The sample with the largest variation in ε1, GeSe9, also had the worst surface

quality of all of the samplesfurther corroborating this interpretation.

The values of ε1 for all samples at all powers are consistently higher than the value

determined using the Derivative Technique on spectrophotometry data discussed in the

previous chapter. This may be an indication that the mirror used to calibrate the

reflectance detector was less than 100% reflective at 800 nm. An error of a few percent

would account for this discrepancy. Because of the problems with accurate measurement

of ε1, the rest of the discussion will concentrate on the ε2 data.

108

4.0

5.0

6.0

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9.0

0.01 0.1 1 10 100 1000

ε 1

Fluence (J)

GeSe9

I0 (mW)0

1.523.298.5328.152.6

0

100

200

300

400

500

600

0.01 0.1 1 10 100 1000

ε 2 (

×106 )

Fluence (J)

GeSe9I0 (mW)0

1.523.298.5328.152.6

Figure 5-7: The real and imaginary parts of the dielectric response of GeSe9 glass at 800nm, calculated from the data in Figure 5-1. The gray × on the left side of the graph(labeled 0) is the value determined by the Derivative Technique. The first point of thehighest-power curve is marked with an error bar typical of the error for all of themeasurements.

109

4.0

5.0

6.0

7.0

8.0

9.0

0.01 0.1 1 10 100 1000

ε 1

Fluence (J)

Ge3Se17

I0 (mW)0

0.4410.9173.519.8818.935.957.9

0

50

100

150

200

250

300

350

400

0.01 0.1 1 10 100 1000

ε 2 (

×106 )

Fluence (J)

Ge3Se17I0 (mW)0

0.4410.9173.519.8818.935.957.9

Figure 5-8: The real and imaginary parts of the dielectric response of Ge3Se17 glass at 800nm, calculated from the data in Figure 5-2. The gray × on the left side of the graph(labeled 0) is the value determined by the Derivative Technique. The first point of thehighest-power curve is marked with an error bar typical of the error for all of themeasurements.

110

4.0

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6.0

7.0

8.0

9.0

0.01 0.1 1 10 100 1000

ε 1

Fluence (J)

GeSe4

I0 (mW)0

1.013.6010.138.8

0

100

200

300

400

500

600

700

800

900

1000

0.01 0.1 1 10 100 1000

ε 2 (

×106 )

Fluence (J)

GeSe4I0 (mW)0

1.013.6010.138.8


111

4.0

5.0

6.0

7.0

8.0

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0.01 0.1 1 10 100 1000

ε 1

Fluence (J)

GeSe3

I0 (mW)0

0.9563.669.9836.6

0

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100

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450

0.01 0.1 1 10 100 1000

ε 2 (

×106 )

Fluence (J)

GeSe3I0 (mW)0

0.9563.669.9836.6


112

The graphs of ε2 as a function of fluence produce a consistent picture of the

photodarkening of the different compositions. Looking first at Figure 5-7, the graph for

GeSe9, the change in ε2 exhibits an S-shaped fluence dependence. This is characteristic of

an exponential function plotted on a semi-logarithmic scale and will be discussed in more

detail later in this chapter. In addition, we see that the value of ε2 at the beginning of the

exposure depends on the intensity of the laser. This might be associated with a fast

transient nonlinearity, which may or may not be related to the photodarkening process.

The recovery seen in the transmittance is evident at the two highest power exposures, and

the darkening continues after the recovery. The rate of darkening and the degree of

darkening are both dependent on the laser powera sign that a nonlinear process is

involved in the formation of the photodarkened state.

Figure 5-8 shows that the same features are present in the Ge3Se17 photodarkening

process: the characteristic S-curve is evident at all powers, and the position and height of

the curve depend on the laser power. In addition, almost all of the curves show a second

darkening process occurring after the S-curve has leveled off. This second process

appears as a linear increase in ε2 against the logarithm of the fluence. The second process

begins at lower fluence for higher exposure powers, indicating that its onset is dependent

on the laser power. The slope, though, does not depend on laser power and is almost the

same for all of the curves shown. The ε2 data also tends to exhibit more fluctuations

during this part of the darkening than it does during the first part. The only curves that do

not show this behavior are the two lowest power exposures. It seems clear that this is

only because the experiments were not continued for long enoughby visual

extrapolation from the other curves, the onset would have required several days at these

113

powers. At the highest exposure powers, the Ge3Se17 sample appears to undergo a

recovery similar to that seen in the GeSe9 sample. Such a process was not apparent from

the transmittance dataprobably because the recovery is smaller than in the GeSe9

sample and it occurs later in the darkening process.

The GeSe4 sample (Figure 5-9) shows a large difference in darkening behavior

from the two previous samples. The most obvious difference is the large photodarkening

change, which is more than twice as great as the change in ε2 for the other samples. The

S-shaped portion of the curve is hard to discern and the second portion produces to a

much larger increase in ε2. The second process appears to reach saturation, and the value

of this saturation looks like it might be the same for the different darkening powers. No

recovery is evident, and the initial value of ε2 is less sensitive to power than in the

samples with lower germanium concentrations.

The most striking differences are seen in the photodarkening of the GeSe3 sample

shown in Figure 5-10. Here, the S-shaped portion of the curve is almost nonexistent.

Initially the change in ε2 is much smaller than that observed in the other samples.

Eventually, the darkening transitions into the second portion; however, this transition

occurs at the greatest fluence of any of the glass compositions studied. In the other

samples, the transition to the second regime is a smooth one, but, for the GeSe3

composition, the transition involves an abrupt increase in ε2 followed by a linear increase

with the logarithm of the fluence. While the other samples showed fluctuations in ε2

during the second part of the darkening, the fluctuations are much larger and more

regular for the GeSe3 glass. As in the other samples, the onset of this process depends on

the incident laser power and the slope appears to be independent of the power.

114

Effect of Composition on Photodarkening

One of the goals of this project is to study the effect of germanium concentration

on the photodarkening of germanium-selenium glasses. To facilitate the comparison, the

ε2 data is plotted for all four compositions at a fixed incident laser intensity. Figure 5-11

shows the results when all of the samples are exposed at about 3.5 mW and Figure 5-12

shows the results at 10 mW. These figures are representative of the results observed at all

laser powers.

The trend in sensitivity to photodarkening is common to the two graphs. Both the

position of the S-curve and the onset of the linear portion move to lower fluence as the

0

50

100

150

200

250

300

350

400

0.01 0.1 1 10 100 1000

ε 2 (

×106 )

Fluence (J)

Sample [I0 (mW)] GeSe9 [3.29]Ge3Se17 [3.51] GeSe4 [3.60] GeSe3 [3.66]

Figure 5-11: Comparison of the change in the imaginary part of the dielectric response at3.5 mW laser power. All four compositions are shown. Exact values are shown in thekey.

115

germanium concentration increases to 20% germanium (GeSe4). The sensitivity then

drops significantly with further increase in the germanium concentration, and the 25%

germanium sample (GeSe3) shows the least sensitivity of any of the compositions. The

magnitude of the darkening is the largest for the GeSe4 glass followed by the Ge3Se17

glass. GeSe3 has the least change in ε2 until it reaches the second portion, then it darkens

enough to exceed that of the GeSe9 sample. This can be seen in Figure 5-12. The slope of

the second regime of the GeSe4 sample is significantly steeper than the slope of the

second regime for the other samples.

The Kinetics of Photodarkening

The qualitative results provide some insight into the nature of the photodarkening

process. It is apparent that the GeSe4 composition is the most sensitive to

photodarkening, the compositions with lower concentrations of germanium show

recovery, and compositions with higher concentrations of germanium show almost no

darkening until large fluence is reached.

Quantitative values are needed to get a better understanding. The extraction of

quantitative data requires finding a function that represents the process and then fitting

the data to that model. The parameters determined by the fit can be used to compare the

darkening behavior as a function of both power and composition. To this end, we propose

a model to describe the darkening results. The model is not based on any assumption

about the process; instead, it is based on mathematical relations that describe the shape of

the changes in ε2. As such, the model may not be a unique description of the data, but it

will server our intentto provide a basis for reducing the data, and to permit discussion

of the intensity and composition dependence of the photodarkening.

116

In the previous discussion, it has already been suggested that the photodarkening

process can be divided into two regions or stages. The distinction between the two stages

is based on the characteristic curves that describes the change in ε2 as a function of

fluence. In the first stage, Stage I, the darkening is characterized by an S-shaped

dependence on fluence. In the second stage, Stage II, the darkening shows a linear

dependence on the logarithm of the fluence. Figure 5-13 shows the data for the Ge3Se17

sample with a line drawn to indicate the transition from Stage I to Stage II darkening.

Stage I is the portion below and to the left side of the diagonal line and Stage II is the

portion above and to the right. The transition between the two stages is power dependent.

The model will deal with each stage separately.

0

50

100

150

200

250

300

350

400

0.01 0.1 1 10 100 1000

ε 2 (

×106 )

Fluence (J)

Sample [I0 (mW)] GeSe9 [8.53]Ge3Se17 [9.88] GeSe4 [10.1] GeSe3 [9.98]

Figure 5-12: Comparison of the change in the imaginary part of the dielectric response at10 mW laser power. All four compositions are shown. Exact values are shown in the key.

117

In forming the model, it is necessary to assume that the dielectric response varies

linearly with the degree of darkening. This assumption is consistent with the sum rule of

optical physics, which states that the dielectric response of a material is the linear sum of

all of the contributions of the individual oscillators. Before darkening, the material will

have some intrinsic absorption, ε20. For excitation by light in the exponential band tail,

this will be caused by light absorption by localized electronic states near the bandgap

energy. The darkening process creates some type of change in the glass structure leading

to additional absorption. In the fully darkened state (the state at which no further

darkening occurs), the absorption will have increased by an amount ∆ε2. At any point

0

50

100

150

200

250

300

350

400

0.01 0.1 1 10 100 1000

ε 2 (

×106 )

Fluence (J)

Ge3Se17

I

II

I0 (mW)0.4410.9173.519.8818.935.957.9

Figure 5-13: The imaginary part of the dielectric response of Ge3Se17 glass showing thetwo stages of photodarkening. The diagonal line (from top-left to bottom-right) dividesthe curves into two sections, which correspond with Stage I and Stage II darkening aslabeled on the graph.

118

during the transition from the undarkened state to the darkened state the imaginary

dielectric response is

)(( 220 Φ⋅∆+=)Φ gεεε , (5-3)

where Φ is the fluence and g(Φ) is a function which describes the degree of darkening as

a function of fluence.

Stage I photodarkening

The S-shaped curve in a semi-log plot is typical of an exponential relationship

that has a zero-point offset and a saturation value. This indicates that the Stage I

photodarkening may be governed by a rate equation. In this case, the transition function,

g(Φ), varies from 0 at the beginning of the experiment to 1 when the darkening has

saturated. The simplest such equation is a first order transition which can be described by

the differential equation

))(1()(d Φ−=

ΦΦ

gd

grσ , (5-4)

where σr is the inverse of the rate constant. With the boundary condition that g(0) = 0, the

solution is

)exp(1)( Φ−−=Φ rg σ . (5-5)

Combining Equation 5-5 with Equation 5-3 leads to an equation with three adjustable

parameters, ε20, ∆ε2, and σr. This equation can be fit to the Stage I portion of the Ge3Se17

data with nonlinear curve fitting software. While the function does have a shape similar

to the S-shape seen in Figure 5-13, it fails to fit the sharpness of the transition and it

underestimates the ε2 values at low fluence. A higher order rate equation is needed to

properly model the Stage I photodarkening.

119

In a second order transition, the rate, σr, is itself a function of the degree of

darkening. The form of the variation in σr depends on the process of photodarkening.

Since this is not known, it is necessary to make an assumption. The simplest such

assumption is that the rate varies linearly with the magnitude of the darkening, g(Φ). The

differential form for this type of second order reaction is

))(1))((()(d Φ−Φ⋅+=

ΦΦ

ggd

grr βσ , (5-6)

where βr is the linear change in the rate with the darkening. With the same boundary

condition as Equation 5-5, the solution is

40

60

80

100

120

140

160

180

0.01 0.1 1 10

ε 2 (

×106 )

Fluence (J)

Ge3Se17 [19 mW]First Order Model

Second Order Model

Figure 5-14: Typical fit of the Stage I darkening process using First Order and SecondOrder models of the photodarkening kinetics.

120

1)exp(

)exp(1)(

+Φ−Φ−−=Φ

sb

sg . (5-7)

Two substitutions were made to simplify the above equation: s=σr+βr and b=βr/σr.

Substituting Equation 5-7 into Equation 5-3 yields an equation with four adjustable

parameters. These are then fit to the data using nonlinear curve fitting software. A typical

fit of the data is shown in Figure 5-14, which shows the best fit achieved with both the

first and second order equations.

The second-order equation provides a consistently better fit for all of the data.

Because of this, it has been used to fit the Stage I portions of the data for GeSe9 and

Ge3Se17. For GeSe9, the higher power curves could not be reliably fit because of the

recovery peak that obscured the top of the S-curve. Not enough of the Stage I curve was

available to permit fitting for the GeSe4 and GeSe3 samples at any of the powers.

The improved fit from the use of a second order model suggests that the

photodarkening process is governed by a second order rate equation. The results of the

fitting are useful for comparing the photodarkening process in samples with different

compositions, but more theoretical work is needed before any conclusions can be drawn

about the reaction rate of the Stage I photodarkening. Without an underlying theory, the

purpose of fitting the ε2 data with Equation 5-7 is data reduction. The fit provides four

parameters that describe each curve. Two of the parameters have physical significance:

ε20, the estimated value of ε2 at the beginning of exposure (before any photoinduced

changes have occurred); and ∆ε2, the maximum change in ε2 during Stage I

photodarkening.

121

The results for ε20 are shown in Figure 5-15. The values for GeSe9 and Ge3Se17

were determined by the curve fitting technique just discussed. In the case of the GeSe9,

the curve fitting could only be applied to the measurements made at exposure intensities

of 10 mW or less. The onset of recovery in GeSe9 and of Stage II darkening in the GeSe4

and GeSe3 samples obscured the top of the Stage I portion making it impossible to fit

with the proposed model. Instead, the ε20 values for these compositions were determined

from the raw photodarkening data by averaging the ε2 data collected at the beginning of

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60

ε 20

(×10

6 )

Laser Power (mW)


Figure 5-15: The imaginary part of the dielectric response at the start of exposure, ε20

(open symbols). The solid symbols (at 0 mW) are the values calculated by the DerivativeTechnique. The lines show linear fits to the data. For the GeSe9 and Ge3Se17 samples, thevalues are obtained from fitting the photodarkening data with Equation 5-7. For GeSe4

and GeSe3, the values are from averaging all of the photodarkening data points withfluence less than 0.1 J.

122

the experiment. A fluence of 0.1 J was chosen as the upper cut-off for the averaging.

Values determined in this same manner for GeSe9 and Ge3Se17 were found to be larger

than the values determined by the curve fit, but the difference was less than 10%. All of

the data from the measurements on GeSe4 exposed at laser power less than 10 mW were

excluded because most of the values were so close to zero that they had to be the result of

experimental error. The GeSe4 sample was the thinnest sample studied. It appears that the

sample was too thin for reliable measurements of the absorption when the absorption

coefficient was low. The error associated with this sample were typically on the order of

2×10-5much larger than the calculated values of ε2 at the beginning of the

photodarkening experiments. The error remains nearly constant for the entire

measurement, so the data becomes more reliable as the sample darkens and the data

presented in Figure 5-9 is reliable once the value of ε2 exceeds 2×10-5.

The lines on Figure 5-15 show least-squares linear fits to the data points for the

different compositions. The fact that all of the lines have nonzero slopes indicates that the

glasses have intrinsic, intensity-dependent absorption. The value of ε20 is an estimate of

the value within the first second of light exposure. This means that it is an intrinsic

property of the undarkened sample. As such, it is possible that this is a measure of a very

fast transient nonlinear absorption in the glasses at the laser wavelength of 800 nm. The

nonlinear absorption may be due to an electronic or a thermal effect. Within the range of

powers measured, the power dependence is well approximated by a straight line. Such a

linear relationship with power is indicative of a third order nonlinear effect such as two-

photon absorption.13

123

Figure 5-16 displays the slopes of the lines from Figure 5-15 as a function of the

glass composition. The slope is a minimum for the GeSe4 glass (20% Ge)indicating

that the nonlinear absorption term is the smallest for this composition. The error bars for

the GeSe4 sample are large because of the limited number of points available and because

of their large scatter. However, the trend is obvious from the other values shown on the

graph.

The total change in ε2 induced by the light exposure during Stage I is expressed

by the ∆ε2 parameter. This is a measure of the difference between the starting and ending

values of the S-shaped curve. The magnitude of photodarkening, ∆ε2, is independent of

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0.1 0.15 0.2 0.25

dε20

/ dI

0 (×

106 /m

W)


Figure 5-16: The slope of the linear fits to the data of Figure 5-15 versus the compositionof the glass. Error bars indicate the asymptotic standard error estimated by the curvefitting software.

124

the starting value, ε20, and therefore independent of any intrinsic nonlinear effects that are

not the result of the darkened state. Values for ∆ε2 could only be determined for the

GeSe9 (at exposure of 10 mW or less) and Ge3Se17 samples since these were the only

compositions which could be fit properly with the Stage I model. The values are shown in

Figure 5-17. Also on the figure are lines showing the least squares fit of the data with a

logarithmic model,

)(log)( 102 IBAI =∆ε , (5-8)

where A and B are the fitting constants, and I is the exposure power. The values of these

parameters are listed in Table 4-2. The logarithmic relationship between the maximum

0

20

40

60

80

100

120

140

160

0.1 1 10 100

∆ε2

(×10

6 )

Laser Power (mW)

GeSe9Ge3Se17

Figure 5-17: The maximum change in the imaginary dielectric (∆ε2) observed duringStage I darkening. The lines indicate the best fits of a logarithmic relation to the data.

125

change in ε2 and the laser intensity is very similar to the observed red-shift of the

bandgap energy during photodarkening. In As2S3 glass, it is found that the induced shift

in the bandgap, ∆E, is proportional to the logarithm of the inducing light intensity for

both above-bandgap28 and below-bandgap33 photodarkening when the experiment is

preformed at room temperature. The shift is almost independent of the intensity when the

experiment is performed at 100 K.

The other two parameters of the curve fit, s and b, do not have direct meaning, but

they can be used to calculate other interesting values that describe the darkening process.

One such quantity is the amount of energy required to induce 50% of the total change in

ε2. This value can be determined by rewriting Equation 5-7 to express Φ as a function of

g,

+

−−=Φ1

1ln

1)(

gb

g

sg , (5-9)

and then solving for Φ at g=0.5. The midpoint is chosen arbitrarily, any other point

between 0 and 1 could also be chosen and the trend with respect to laser power would be

the same.

The value of the fluence at 50% of the darkening is shown in Figure 5-18 for

GeSe9 and Ge3Se17. The Ge3Se17 data exhibits a nearly linear decrease in the fluence

Table 5-1: Parameters determined by fitting Equation 5-8 tothe data in Figure 5-17.

Sample A (×××× 106) B (mW-1)GeSe9 37 ± 3 6 ± 1Ge3Se17 43 ± 3 17 ± 6

126

required for 50% darkening with the laser power. The only exception to this occurs at low

power (less than 3 mW) where fluence required increases with increasing intensity. Not

enough data is available to determine if this is a real trend. The trend for the GeSe9

sample is harder to discern because of the limited range of powers over which the values

could be extracted. Despite this, the data does appear to show a positive trend with

increasing power similar to the low power trend in the Ge3Se17 sample. The graph also

shows that the midpoint of the darkening in GeSe9 occurs at higher fluence than in

Ge3Se17 for a given power. This indicates that the Ge3Se17 sample is more

photosensitive at 800 nm than the GeSe9 sample.

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 10 20 30 40 50 60

Flue

nce,

Φ(g

) @

g =

0.5

(J)

Laser Power (mW)

GeSe9Ge3Se17

Figure 5-18: The value of the fluence at which the Stage I darkening has reached 50% ofits final value.

127

The other quantity of interest is the rate of the transition, which is the derivative

of Equation 5-3,

))(1))(((d

)(d

d

d22

2 Φ−Φ⋅+∆=ΦΦ∆=

Φgg

grr βσεεε

, (5-10)

where dg(Φ)/dΦ comes from Equation 5-6. The estimated slope at the start of the

experiments is shown in Figure 5-19. For both compositions, the slope increases with

increasing power. The relationship also appears to be a linear one in both cases. The

darkening rate in the Ge3Se17 sample is faster than the rate in the GeSe9 sample.

0

50

100

150

200

250

0 10 20 30 40 50 60

Initi

al D

arke

ning

Rat

e, d

ε 2/d

Φ (

×106 J

-1)

Laser Power (mW)

GeSe9Ge3Se17

Figure 5-19: The slope of the darkening with respect to the fluence (dε2/dΦ) at thebeginning of the photodarkening experiments.

128

Discussion of Stage I photodarkening

The results obtained from the study of the Stage I photodarkening reveal many

interesting aspects about the optical and photosensitive properties of the germanium-

selenium glasses. The model used to describe Stage I photodarkening is based on a

second order reaction rate equation. This implies that the rate of photodarkening is a

function of the degree of photodarkening. From this model, four parameters were

determined which describe the entire Stage I process. The first parameter, ε20, is

associated with an intrinsic property of the undarkened glass samples while the other

three parameters are associated with the photodarkening process.

The intensity dependence of ε20 reveals the presence of an intrinsic nonlinear

absorption process in all of the glasses. We can observe that the nonlinear absorption is

the largest in the GeSe9 composition and the smallest in the GeSe4 sample. In addition,

the relationship between ε20 and laser power is linear for all of the compositions. A linear

dependence on the intensity is a sign of a third order nonlinear process.13

Nonlinear absorption of below-bandgap light in a semiconductor is due to two-

photon absorption (2PA).145 The slope of ε20 versus the intensity, I0, is proportional to the

third order susceptibility, χ(3). A model for the two-photon absorption in

semiconductors145 predicts that χ(3) should be proportional to (Eg)-4. All other things

being equal, materials with larger bandgaps should have smaller two-photon absorption

rates. For the germanium-selenium glasses, this means that the slope of ε20 versus I0

(dε20/dI0) should decrease monotonically with increasing germanium content. Looking at

Figure 5-16 this is not the case. Instead, the slope decreases with increasing germanium

concentration up to the composition of GeSe4 and then increases for GeSe3. The rate of

129

decrease in ε20 with increasing germanium concentration is also much steeper than would

be expected for a simple (Eg)-4 dependence.

The germanium-selenium glasses do not show the expected behavior for 2PA.

This discrepancy can be explained in two ways; either the nonlinear absorption process is

not due to 2PA, or the structure of the chalcogenide glasses has a larger effect on the

magnitude of the 2PA than the shift in bandgap. The structure effect may arise from a

deviation of the glass band structure from the ideal, parabolic model. A composition-

dependent deviation from parabolic bands would lead to a different density of states than

the one on which the (Eg)-4 relationship is based. This will drastically alter the transition

probabilities for 2PA and cause the apparent deviation from the predicted behavior. Not

enough information is available to determine which is the proper explanation. The second

explanation seems reasonable, since the structure of the glasses changes significantly

with increasing germanium content. This does not rule out the first possibility although

there is no evidence for other nonlinear processes such as excited state absorption (ESA)

in these glasses. It would be interesting to investigate the source of the nonlinear

absorption and the reason for the composition dependence in the germanium-selenium

glasses.

The similarity of ε2 curves when plotted against fluence and the ability to model

the darkening as a function of the fluence both demonstrate that the fluence is a proper

variable for describing the photodarkening process. However, it is not sufficient. If it

were, all of the photodarkening curves would overlap when plotted against fluence.

Instead, the composition and flux are also needed to describe the photodarkening process.

130

The three parameters that describe the Stage I photodarkening all display power

dependence. The full curves for Stage I darkening could only be fit to the data for GeSe9

and Ge3Se17, so the meaning of the results is not as clear as it is for the ε20 data. Despite

the difficulty in comparing compositions, it is still worth considering. The magnitude of

the change in ε2 at saturation, ∆ε2, is dependent on the logarithm of the exposure power.

This same logarithmic power dependence is observed in the saturation value of the

bandgap shift during photodarkening of other chalcogenide glasses.28 The midpoint

fluence, Φ(g=0.5), is also power dependent; however, the exact relationship is difficult to

establish. In GeSe9, it appears to increase linearly with the laser power, but in Ge3Se17 it

appears to increase with intensity at low intensity and then decrease with intensity at high

intensity. The initial rate of darkening, dε2/dΦ, increases linearly with power for both

compositions. The power dependence of all three parameters shows that the

photodarkening is nonlinearit involves the interaction of multiple photons. Two-photon

processes will be proportional to I while higher order multi-photon processes will be

proportional to higher powers of the light intensity. The linear power dependence of

dε2/dΦ indicates that it is a two-photon process.

Comparing the results for the GeSe9 and Ge3Se17 samples shows that the Ge3Se17

sample is more sensitive to photodarkening than the GeSe9 sample. This can be seen by

the larger change in ε2, the steeper rate of darkening, and the lower value of the fluence at

the midpoint of the darkening for Ge3Se17. By looking at Figure 5-11 it appears that the

GeSe4 sample is even more photosensitive than Ge3Se17, while in Figure 5-12 the GeSe3

sample shows almost no Stage I photodarkening. The photosensitivity increases with

131

germanium concentration up to 20% after which the photosensitivity decreases rapidly

with further increase in the germanium concentration.

The compositional trend in photosensitivity is opposite the observed

compositional trend in ε20 behavior, which exhibits a minimum at the 20% germanium

composition. The nonlinear absorption process and the photodarkening may compete in

these glasses, so that glasses with higher nonlinear absorption have lower

photosensitivity. The sharp reduction in photosensitivity of GeSe3 with only a small

increase in nonlinear absorption from GeSe4 indicates that the correlation probably does

not exist. In addition, the decrease in photosensitivity for the GeSe3 glass is evidence

against the assumption that photosensitivity is proportional to the glass transition

temperature.10 While this theory might be supported by the increase in photosensitivity

from GeSe9 to GeSe4, the GeSe3 glass has the highest glass transition temperature of all

the samples, yet it is the least photosensitive. In such a model, the only effect of the

germanium is to increase the glass transition temperature. In all other ways, germanium is

passive and the photodarkening is caused by structural rearrangement of the chalcogen

atoms. The present results indicate that the germanium is an active participant in the

photodarkening process in germanium-selenium glasses. Because photosensitivity is

temperature dependent in the chalcogenide glasses,29 it would be useful to measure the

photosensitivity and nonlinear absorption at low temperature to see if the observed

relationships persist.

Stage II photodarkening

In Stage I, the photodarkening shows a behavior governed by a reaction rate type

equation. In Stage II, the photodarkening exhibits a linear relationship with the logarithm

132

of the fluence. For the two samples with the least germanium, the Stage II darkening

includes periods of decreasing ε2 with increasing fluence. These periods signify a

recovery process caused by an unknown mechanism. For the other two samples, the

recovery is not seen. The Stage II darkening appears to reach saturation in the GeSe4

sample, but this does not happen for any of the other compositions. This may be because

none of the experiments continued long enough for the Stage II darkening to reach

saturation in the other samples. The darkening process in the GeSe3 glass exhibits rapid

fluctuations not seen in the darkening of the other samples.

The differences in Stage II from one sample to the next make it difficult to

suggest a model from which quantitative comparisons can be made. The overall process

seems highly composition dependent. The observation of recovery in GeSe9 and Ge3Se17

might indicate that the sample is annealingforming a rearranged structure with a

reduction in the darkening. The annealing process may occur when the increased

absorption from the darkening causes sample heating sufficient to cause thermal

rearrangement of the atoms. However, it may also be photoinduced. After the Stage I

darkening saturates, the photons may excite structural changes that lead to a decrease in

the absorption coefficient.

Similar darkening profiles were reported by Ducharme et al. for films of arsenic-

sulfur glass excited by above-bandgap light.146 They attribute the logarithmic increase in

absorption to the formation of the same defects that cause midgap absorption. These

defects are believed to be distinct from the ones associated with the Stage I darkening

process. They have only been observed in samples darkened at low temperature (below

180 K) and they anneal out as the sample is raised to room temperature. It would be quite

133

remarkable if our observations show the formation of stable midgap defects at room

temperature. The defects that cause midgap absorption are associated with light-induced

electron-spin resonance (ESR) in the chalcogenide glasses,147 so measurement of ESR on

these samples during darkening could be used to determine if stable midgap paramagnetic

defects are forming at room temperature.

Transient Darkening and Dark Recovery

In a few of the experiments, a darkened spot on the sample was re-exposed after

the initial darkening. This re-exposure was usually done within 24 hours of the original

darkening experiment. The intent of these measurements was to see if the induced

65

70

75

80

85

90

95

100

105

110

115

120

0.01 0.1 1 10 100

ε 2 (

×106 )

Fluence (J)

GeSe9Exposure [I0 (mW)]First [3.21]Second [3.38]

Figure 5-20: Permanent and transient photodarkening in GeSe9. The curve labeled Firstis from the first time that the spot was exposed. The laser was blocked for 7½ hours andthen the spot was exposed for a second time for the Second curve, which is plotted withzero fluence at the start of the second exposure.

134

darkening remained after the laser light was removed from the sample. It was found that,

for all samples, the exposed spot showed a permanent change in transmittance; however,

the spot also showed some recovery of the transmittance. The amount of recovery

depends on the sample composition. This type of recoveryoccurring when the

photodarkening light is offis called dark recovery. It is not the same as the light

induced recovery observed during exposure in the GeSe9 and Ge3Se17 samples.

At the start of the second exposure, the value of ε2 is not as large as it had been at

the end of the first exposure. Some portion of the darkening recovered at room

temperature after the inducing light was turned off. During the second exposure, ε2

0.48

0.50

0.52

0.54

0.56

0.58

0.60

0 20 40 60 80 100 120

Tra

nsm

ittan

ce

Time (m)

GeSe9

Figure 5-21: Transmittance change in GeSe9 during photodarkening with 800 nm light.The light source was blocked several times during the exposure to demonstrate thetransient portion of the darkening and its dark recovery.

135

quickly increases to the same value that it had at the end of the first exposure. The

transient period is shown in Figure 5-20. The lighter curve shows the first exposure of the

spot and the darker curve shows the response of the spot to re-exposure. The re-exposure

occurred approximately 7½ hours after the end of the first exposure. At the beginning of

the second exposure, ε2 is lower than it was at the end of the first exposure, but it has not

returned to the value it had at the beginning of the first exposure. This difference is the

permanent darkening from photoinduced structural changes. We observed that ε2 does not

recover more than this even if the sample is left unexposed for several days.

During the second exposure, ε2 increases to the value it had at the end of the first

exposure. The S-shaped curve indicates that the transient response follows a rate equation

much like the permanent response. Unlike the permanent response, the transient response

can be induced repeatedly by blocking the laser light and then re-exposing the sample.

An excellent example of the repeated formation and recovery of the transient darkening is

shown in Figure 5-21. This figure shows the transmittance of a sample of GeSe9 during a

two-hour experiment. To create this figure, a virgin spot was exposed the 800 nm light

for one hour causing the spot to darken completely to saturation. The laser was then

blocked, corresponding with the first gap in the data. After 30 seconds, the laser was

unblocked and the transmittance was recorded. It is evident that the sample had recovered

a portion of the transmittance it had lost during the first exposure. The laser was left

unblocked long enough for the sample to re-darken to the level it had been at the end of

the first exposure. This process was repeated with the laser blocked for 1 minute, 2

minutes, and 10 minutes. Each time, the sample transmittance increases when the laser is

blocked and then it decreases when the sample is exposed. The transient portions

136

observed after each cycle are almost identical with one another and are distinct from the

darkening process observed when the sample is first exposed.

At the end of the experiment, the laser was repeatedly blocked for 25 seconds and

then unblocked for 5 seconds. This provides a means to display the recovery of the

sample darkening. This is not a direct measure of the transient recovery, since the

frequent exposure does not permit the sample to fully recover; however, it does illustrate

the process. Frumar et al.148 observed similar behavior in a film of As2S3 under above-

bandgap excitation.

The transient darkening can be observed in other samples also. Figure 5-22 shows

the transient darkening response of Ge3Se17. For this example, a virgin spot was darkened

60

80

100

120

140

160

180

200

220

0.01 0.1 1 10 100

ε 2 (

×106 )

Fluence (J)

Ge3Se17Exposure [I0 (mW)]First [19]Second [3.6]

Figure 5-22: Permanent and transient photodarkening in Ge3Se17 glass. The first exposurewas at a power of 19 mW, and the re-exposure was at 3.6 mW.

137

at a laser power of 19 mW. Three hours after the first darkening experiment, the spot was

exposed to light at 3.6 mW. The figure shows the dark recovery and the transient

darkening response followed by a period of additional Stage II darkening. The transient

darkening causes ε2 to return almost entirely to the value that was reached by the first

19mW darkening. This is an indication that the sample has been permanently changed by

its exposure at 19 mW and that this change is distinct from the change that would be

caused by darkening at a lower or higher power. This verifies the observation that the

darkening is nonlinear and that it is a function of the cumulative fluencethe exposure

historyof the sample spot. The difference between ε2 at the top of the transient portion

of the second exposure and the final value of ε2 from the first exposure indicates that the

magnitude of the transient response is also intensity dependent.

The continuation of Stage II darkening can be seen more clearly in Figure 5-23,

where the second exposure has been plotted as a function of the total accumulated

fluence. This is done by adding the fluence at the end of the first experiment to the

fluence of the second experiment. For reference, the darkening of the Ge3Se17 sample

exposed at 3.6 mW is also shown. Despite the different histories represented by the three

curves, the slope of the Stage II portion of all three curves is nearly identical. This

supports the observation that the slope of Stage II darkening is nearly independent of

power and of exposure history. The only part of Stage II darkening that is power

dependent is the onset fluence. Beyond this, it shows that once Stage II darkening has

been initiated it can be continued at a lower power. The total fluence, had it been

accumulated at the lower power, would not have been sufficient to initiate Stage II

138

darkening, but once the Stage II process is started, it can be continued by any further

exposure. Once Stage II darkening has begun, it is the dominant process.

If the Stage II darkening is the result of structural damage, then this behavior can

be explained. During Stage I, the sample darkening is uniform throughout the exposed

area. Stage II begins when the sample darkening becomes non-uniform because sample

damage changes the homogeneity of the sample at the illuminated spot. Inhomogeneous

regions cause variations in the spatial profile of the laser, and the associated scattering

and index variations cause focusing of the light within the sample. The high intensity

causes additional sample damage, which further alters the profile of the laser.

40

60

80

100

120

140

160

180

200

220

240

260

0.01 0.1 1 10 100

ε 2 (

×106 )

Fluence (J)

Ge3Se17Exposure [I0 (mW)]First [19]Second [3.6]First [3.5]

Figure 5-23: Permanent changes occurring after the transient response during re-exposureof an already darkened spot in Ge3Se17 glass. The Second curve is plotted as acontinuation of the First [19 mW] curve.

139

Unlike the lower germanium samples, the GeSe4 glass shows almost no dark

recovery or transient darkening. This is shown in Figure 5-24. For this experiment, the

sample was first exposed at 3.7 mW and then exposed at 10 mW two hours later. There is

no evidence of dark recovery and almost no transient portion. Unlike the other samples,

the little transient response seen appears to be a decrease in the dielectric response of the

sample. The lack of dark recovery has been confirmed by holding the sample for longer

periods before re-exposure. Samples that were held for up to 24 hours showed no sign of

dark recovery regardless of the initial exposure intensity.

The upward trend seen in the data is a continuation of the Stage II darkening. This

is more evident in Figure 5-25 where the second exposure is graphed as a function of the

0

100

200

300

400

500

600

700

800

900

1000

0.01 0.1 1 10 100

ε 2 (

×106 )

Fluence (J)

GeSe4

Exposure [I0 (mW)]First [3.7]Second [10.5]

Figure 5-24: Permanent and transient photodarkening in GeSe4 glass. The first exposurewas at 3.7 mW and the second exposure was at 10.5 mW.

140

total fluence. After a brief and apparently negative transient response, the Stage II

darkening continues as if it had not been interrupted.

The dark recovery as a portion of total darkening is the largest in the sample with

the least germanium, GeSe9, and decreases with an increase in the germanium content of

the sample. In the above observations, less recovery was observed in the Ge3Se17 sample

and almost no recovery is observed in the GeSe4 sample. This trend can be explained by

assuming that dark recovery is a thermally activated process and that the energy barrier is

proportional to Tg. Laser problems prevented measurements on the GeSe3 sample. Since

this sample has the highest Tg, it should also have no dark recovery.

0

100

200

300

400

500

600

700

800

900

1000

0.01 0.1 1 10 100

ε 2 (

×106 )

Fluence (J)

GeSe4

Exposure [I0 (mW)]First [3.7]Second [10.5]

Figure 5-25: Re-exposure of a spot on the GeSe4 sample. The darkening continues alongthe Stage II curve, although the intensity is higher, and the experiment was stopped fortwo hours between the first and second exposures.

141

If the dark recovery is thermally activated, then, given enough time, the darkening

should completely recover. However, our observations indicate that the transmittance

recovers quicklywithin hours. Samples held for longer do not show further recovery.

From this, we postulate that the change responsible for the transient darkening and dark

recovery is not the same as the change responsible for the permanent darkening. The two

states may represent completely separate photoinduced processes or they may represent

two stages of the darkening process. More data will be needed to verify that the dark

recovery does not lead eventually to total recovery of the photodarkening.

The transient darkening and dark relaxation appear to arise from the photoinduced

creation and thermal decay of transient defects. If this is the case, a simple equation can

be derived to model the transient optical properties of the germanium-selenium glasses.

Let us consider that in a volume of chalcogenide glass there exist a number, G, of photo-

active sites without explicitly defining what a site is. The transient process seems to be

associated with selenium chains; however, we cannot tell whether the process requires

single selenium atoms, selenium-selenium bonds, or longer chains of selenium atoms.

Assume for now that the number of sites is constant. When the sample is annealed, all of

the sites equilibrate to their ground state. In the ground state, they do not absorb light.

Intense light interacts with the sites and causes them to become excited. In the excited

state, the site absorbs light. The number of excited sites is g(t), and the rate of excitation

is related to the intensity of the light and the probability that a photon will excite an

unexcited site. For simplicity, we will assume that the excitation rate can be described by

an excitation (creation) time constant, τC, which depends on the photon flux.

142

The excited state decays to the ground state through a thermally activated process.

This process can be characterized by a time constant for decay, τD. The decay rate is a

function of the sample temperature and may depend on Tg and the structure of the glass.

The rate of change in the number of excited sites, dg(t)/dt, is

[ ] )(1

)(1

d

)(dtgtgG

t

tg

DC ττ−−= . (5-11)

The solution is a single exponential rate equation. If the sample has been left unexposed

for long enough, all of the defect sites will be in the ground state. The boundary condition

is g(0) = 0, and the solution is

−−=

τt

Atg exp1)( , (5-12)

where

DC

DGA

τττ+

= , (5-13)

and

DC τττ111 += . (5-14)

Equation 5-12 provides excellent fits to the transient darkening observed in GeSe9 and

Ge3Se17. From Equation 5-14 we can deduce that the lifetime of the excited state, τD,

must be greater than the time constant τ. The value of τ can be determined by fitting the

transient darkening data with Equation 5-12, and this can be used as an estimate of the

lower limit on τD. Therefore, the lifetime of the excited state is greater than 250 seconds

in GeSe9 and greater than 120 seconds in Ge3Se17. If more measurements of the transient

darkening had been made, we would be able to estimate the values of τC and τD

143

accurately. Thorough observations of the transient darkening should be the topic of future

research.

Mechanism of Permanent and Transient Below-Bandgap Photodarkening

The results presented in this chapter identify several sources that contribute to the

total absorption of the sample. The microstructural origin of the darkening processes is

not known; however, the intensity and time dependence of the darkening provides insight

into the nature of these microstructural changes.

We choose to describe the darkening process as a change in the imaginary

dielectric response, ε2, of the sample because ε2 can be described as the linear sum of

contributions from all of the optically active centers in the sample. Other parameters,

such as transmittance or absorption coefficient, are not linearly related to the glass

microstructure. The total change in the sample optical properties has at least three distinct

contributions. These can be summarized by the following equation for the imaginary

dielectric response:

)()( 22202 tTP εεεε +Φ+= , (5-15)

where Φ is the total fluence from this exposure and all past exposures (since the last time

the sample was annealed), and t is the time since the beginning of the current exposure.

All of the terms of the above equation are implicitly intensity dependent.

The first term, ε20, is the intrinsic value of the imaginary dielectric response. It is

intensity dependent, as has already been demonstrated in the previous section. The source

of ε20 appears to be distinct from the sources of the photoinduced darkening. We cannot

determine the rise-time of this contribution, but we know that it is much less than one

second. The origin of this term is most likely two-photon absorption excited by the high

144

electric field of the ultra-short laser pulses from the Ti:Sapphire laser. Darkening induced

by less intense sources may not exhibit a noticeable ε20 contribution.

The second term, ε2P(Φ), is the permanent darkening induced by light exposure. It

results from permanent changes in the structure of the glass caused by interaction with

photons that have energies within the exponential band tail of the glass. The permanent

darkening is a cumulative effectit depends on the total fluence on the sample since the

first exposure. The sample remembers the past exposures and, after a brief transient

period, further darkening occurs from the point at which it left off at the end of the prior

exposure. It is important to point out that the cumulative nature of the permanent effect

means that it is directly related to metastable structural changes. It cannot be explained by

sample heating or any other transient state induced by the light.

The permanent change observed by us is the portion of the darkening associated

with the red-shift in the bandgap and the change in the band tail reported by other

researchers. This is often called reversible darkening because the transmittance of a

darkened sample can be restored by annealing.29 Based on other peoples results, the

permanent darkening should be removed by annealing at temperatures less than 50 °C

below the samples glass transition temperature. This property of the photodarkened state

is well-established, and, though we have not shown that the permanent change we

observe can be removed by annealing, we predict that the darkening induced in these

samples could be removed by appropriate annealing.

Many authors report that the thickness of films increases during photodarkening

with above-bandgap light.29 Recently a 3% change in thickness has been observed in

As2S3 glass illuminated by a below-bandgap laser.10 Tanaka has termed this effect giant

145

photoexpansion. We also observe photoexpansion at the illuminated spots on our

samples; however, we have not studied this aspect of photodarkening. The

photoexpansion may be related to the transition between Stage I and Stage II

photodarkening. Stage I may be the process of defect formation without large-scale

atomic motion. As more defects are created, the structure becomes more disordered and

atomic motion can occur. Stage II darkening may be the change in optical properties

associated with this atomic motion. Stage II darkening is also similar to the darkening

caused by the formation of midgap defects; however, such defects are not known to be

stable at room temperature.

The third term, ε2T(t), is the transient change in optical properties observed during

re-exposure. This portion of the darkening completely recovers when the exciting light is

removed. It is associated with the formation of transient defects that decay at room

temperature. The transient darkening and dark relaxation can be repeated through many

cycles at room temperature. The transient darkening depends on the intensity of the light

and on the time of exposure.

The composition dependence of the photodarkening reveals information about the

roles of the constituent atoms in the overall effect. We beleive that photodarkening occurs

in a two step process (the basis of this model will be discussed below). First the light is

absorbed causing an atom to move into an excited state, and then the state relaxes either

back to the original state or into the metastable photodarkened state. The selenium atoms

appear to be responsible for the absorption of light and the formation of the

photodarkened state. The germanium atoms appear to be responsible for stabilizing the

photodarkened state.

146

It is already well established that the selenium lone-pair electrons are involved in

the absorption of light. Our results indicate that selenium-selenium bonds are necessary

for efficient excitation by below-bandgap light. This is based on the very low

photosensitivity of the GeSe3 samplethe only sample with a significant fraction (50%)

of the selenium atoms not bonded to other selenium atoms. The selenium-selenium bonds

may be needed to impart sufficient flexibility in the structure to permit atomic

rearrangement. The excitation step is therefore proportional to the concentration of

selenium-selenium bonds in the glass.

The magnitude of permanent photodarkening increases with increasing

germanium content. The transient state, however, decreases with the addition of

germanium. This indicates that the germanium acts to stabilize the structure changes

associated with photodarkening. It may be that the germanium atoms stabilize the

structure of the glass and reduce the likelihood of thermal relaxation at room temperature.

This is in agreement with the measured Tg for these glasses. It is also possible that the

germanium atoms provide permanent electronic traps. For example, an electron generated

by light absorption could trap at the germanium atom while the associated hole could trap

on a selenium atom. This generates a charged defect pair that might be much more stable

than the case where both the hole and electron localize on selenium atoms. In either case,

the stability of the darkened state is proportional to the germanium concentration.

The total permanent photodarkening is the product of the probability of excitation

and the probability of formation of a stable defect. The first term is proportional to the

density of selenium-selenium bonds and the second term is proportional to the density of

germanium atoms. Simple estimates of these values show that such a product would have

147

a maximum value somewhere between Ge3Se17 and GeSe4exactly the composition

dependence we obtain experimentally for the maximum photosensitivity. Compositions

on the selenium-rich side of the maximum can be more easily excited, but the glass

contains fewer permanent traps. Compositions on the germanium-rich side of the

maximum have ample traps, but the structure is not effectively excited by the below-

bandgap light.

Kolobovs Model of Dynamical Bond Formation

A description of photodarkening in amorphous selenium, developed by Kolobov

et al.,149 provides a structural explanation for the observed results in germanium-selenium

glasses. The theory is based on measurements of extended X-ray absorption fine structure

(EXAFS) in an amorphous selenium film.150 The EXAFS is measured before, during, and

after light exposure while the sample is maintained at 30 K. The low temperature is

needed to retain the photoinduced changes, which, in selenium, anneal out at room

temperature. During illumination, the average coordination number and the mean-square

relative displacement (MSRD) increase from the values measured before illumination.

After the light is turned off, the average coordination number returns to its pre-

illumination value, but the MSRD remains significantly higher. Annealing the sample at

room temperature (Tg ≈40 °C) reduced the MSRD back to its pre-illumination value. The

increase in MSRD is interpreted as a sign of increased structural disorder in the glass.

The increased disorder is believed to cause a decrease in the bandgap and an increase in

the light absorption.

The normalized coordination number increases 4% during illumination. The

increase indicates that some of the selenium atoms are becoming threefold coordinated.

148

In amorphous selenium, the formation of threefold coordinated selenium atoms must

occur in pairs. Two neighboring twofold coordinated selenium atoms form a bond and

become threefold coordinated. This structure is called a dynamical bond,149 and it is a

transient state only occurring during illumination. Additional evidence for the presence of

a transient state has been provided by Raman spectroscopy151 and X-ray photoelectron

spectroscopy.152

If the increased coordination is an indication of the formation of dynamical bonds

then the photodarkening can be explained by a simple model. A photon with sufficient

energy excites a lone-pair electron on the chalcogen atom. In the EXAFS experiments,

this was accomplished with above-bandgap light. Since the lone-pair orbitals form the top

of the valence band, above-bandgap light can excite an electron from the valence to the

conduction band. The hole left behind when the electron is excited is trapped on the

chalcogenide atom. When below-bandgap light is used, the light does not have enough

energy to create free electron-hole pairs; however, it can excite electrons from the band

tails. The band tails consist of the lone-pair states that have become localized because of

the disorder of the amorphous semiconductor. Below-bandgap light will excite an

electron either into the conduction band or into an exciton-like state. We do not know

which process is occurring; however, the low energy of the exciting light would favor the

creation of excitons. It will also favor the excitation of the electrons in the most

disordered environments since these states will be the ones that extend the furthest into

the bandgap. The excited electron leaves behind a hole trapped on the chalcogen atom

just as for of above-bandgap excitation, and two excited lone-pair orbitals can combine to

form a new bond. The process of photo-excitation and dynamical bond formation is

149

hν

hν

(3)

(2)

(1)

Electron

Lone-PairOrbital

Hole

ChalcogenAtom

KEY:

Normal Bond

Dynamical Bond

Figure 5-26: Dynamical bond formation in chalcogenide glass. (1) Two photons excitetwo lone-pair electrons forming (2) two half-filled lone-pair orbitals. (3) The orbitalsoverlap and form a dynamical bond. The excited electrons are shown as excitons in (2)and as a biexciton in (3).

150

illustrated in Figure 5-26. To form the bond, the separation between the atoms must be

close to the covalent bond length (≈2.4 Å) and the holes must have opposite spins. The

newly formed bond is the dynamical bond believed to be responsible for the observed

increase in the coordination number of the illuminated amorphous selenium. The

formation of these new bonds causes local distortion around the threefold coordinated

atoms, which has the effect of increasing the MSRD.

If the formation of the dynamical bonds is thought of as a chemical reaction then

it can be described by the formula

( )03

032

02 222 CCChC −→→+ ∗ν , (5 -16)

where C represents a chalcogen atom with the coordination given by the subscript and the

charge given by the superscript. The asterisk (*) denotes that the atom is in an excited,

but neutral, state.

An interesting aspect of this process is that it requires two photons to create one

dynamical bond and, therefore, the process is inherently power dependent. The rate of

creation of dynamical bonds should vary linearly with the intensity of the illumination. If

the lifetime of the excited state is long, the process will have weak intensity dependence;

if the lifetime is short, the process will have strong intensity dependence.

The dynamical bond is a non-equilibrium structure. It can only be detected during

illumination and it decays after the light is turned off. The EXAFS data was collected for

between 50 minutes and two hours, so the lifetime of the dynamical bond must be less

than 30 minutes. Otherwise, it would have been detected in the EXAFS measurements

after the sample had been illuminated. This restriction does not put much of a limit on the

151

lifetime of the dynamical bonds, but it does mean that they can not be the source of the

permanent darkening.

The decay of the dynamical bonds can take one of three paths. The first path, path

I, occurs when the dynamical bond to breaks and the system returns to its original

configuration. This process leads to no permanent change in the structure, and therefore

no permanent photodarkening. In the second path, path II, the dynamical bond does not

decay. Instead, other bonds break which allow the structure to return to the twofold

coordination. The new structure will tend to be more disordered than the original

structure, and this increased disorder will cause a decrease in the bandgap and an increase

in the absorption. The third path, path III, involves the formation of a charged defect pair

called a valence alternation pair (VAP). This occurs when a bond breaks on only one of

the threefold coordinated chalcogen atoms and the formerly threefold coordinated

chalcogen becomes twofold coordinated. The excited electrons recombine with the two

holes created when the bond breaks and a threefold and a singly coordinated atom are left

in the structure. The threefold coordinated atom will have a positive charge and the singly

coordinated atom will have a negative charge. The average coordination number is

restored by the formation of the VAP, even though the individual chalcogen atoms are

not twofold coordinated. Unlike the dynamical bond, this defect is stable and can exist for

long times in the chalcogenide glasses. The change in average bond length and the

presence of charged defects should alter the optical properties of the sample. The decay

of the dynamical bonds can be represented by the formula:

+→−

+− )(

)(2

)(2

)(

31

02

02

03

03

VAPCC

newC

originalC

CC . (5-17)

152

The most probable pathway for decay is not known. It is likely that all three decay

pathways happen and that the glass structure is the determining factor for the dominant

pathway. In arsenic-chalcogenide glasses, researchers have observed homopolar bond

formation148 and electron-spin resonance (ESR)153 after photodarkening. The homopolar

bonds would be formed by path II while the ESR signal will most likely come from the

formation of charged defects through path III.

Dynamical Bonds and Photodarkening of Germanium-Selenium Glasses

So far, we have discussed Kolobovs model as it pertains to amorphous selenium,

but EXAFS measurements have also been used to identify the formation of dynamical

bonds during illumination in amorphous As2Se3.151 In this glass, the selenium

coordination increases during illumination, but the arsenic coordination decreases. The

MSRD of both types of atoms increases during illumination. When the light is turned off,

the MSRD decreases slightly but does not return to the pre-exposure value indicating that

an increase in structural disorder is responsible for the reversible photodarkening. The

coordination number for the selenium decreases but remains higher than the initial value

and the coordination number for the arsenic increases but remains lower than the initial

value. The similarity of these observations with those from selenium EXAFS leads to the

conclusion that the same mechanism of photodarkening is active in both materials. The

dynamical bonds should occur in any amorphous system containing chalcogen atoms,154

so they should also form during illumination in the germanium-selenium glasses that are

the topic of this research.

The dynamical bond mechanism provides an explanation for the photodarkening

results presented in this chapter. Illumination of the samples leads to the formation of

dynamical bonds. The optical properties are altered by the presence of these bonds

153

because they induce strain in the surrounding environment and because the excited

electrons are capable of absorbing light. Dynamical bonds that decay through path I will

cause only transient changes in the optical properties of the glass. This means that the

dynamical bonds could be the transient state responsible for transient photodarkening and

dark recovery seen in the low-germanium samples. The possibility that the dynamical

bond decays to a different type of transient state should also be considered. This may be

necessary to account for the rather long lifetime of the transient state at room temperature

(at least 2 to 4 minutes by our measurements). The transient state and the permanent

structure change may differ only in the size of the energy barrier between the excited and

ground states. If this is so then the dark recovery of the transient darkening is similar to

structural relaxation and it should obey a Kohlrausch type relationship.

Permanent changes in the optical properties will be brought about by the decay of

dynamical bonds through paths II and III. During the exposure of an annealed spot, both

the permanent and transient processes occur simultaneously. This may explain why a

second order rate equation is needed to describe the Stage I photodarkening. The

permanent change cannot occur without the formation of the transient state, so the Stage I

darkening curve is the convolution of the darkening from transient and permanent

changes. Eventually, the number of permanently darkened sites reach a limit after which

new permanent changes cannot occur without destroying other regions of permanent

change. This saturation of permanent darkening is the reason that Stage I darkening has

an upper limit. The power dependence of Stage I darkening arises from the inherent

power dependence of the dynamical bond formation. The increase in the darkening rate

with power can be attributed to the intensity dependence of the equilibrium between the

154

creation and thermal decay of dynamical bonds. The increase in the magnitude of Stage I

photodarkening with power can be explained by the higher density of dynamical bonds in

a sample illuminated by intense light. The more dynamical bonds the greater the total

strain energy and the more likely that metastable disordered states will be created.

Darkening does not stop at the end of Stage I in any of the samples measured. It

continues, but with a different character. Stage II darkening appears to depend on the

logarithm of the fluence with almost no intensity dependence in the slope. Stage II

darkening does not begin until at least some Stage I darkening has occurred, and once it

Original GlassStructure

DynamicalBond

NewStructure

TransientState

2 hν

TransientPhotodarkening

PermanentPhotodarkening

Defects(VAPs)

Photo-excitation

IIII

II

Stage II

Figure 5-27: Diagram of the photodarkening process in chalcogenide glass. Illuminationcauses the formation of dynamical bonds. If the dynamical bond decays to form a new(stable) structure or a charged defect, the sample will exhibit a permanent change inoptical properties. If, on the other hand, the dynamical bond decays back to the originalstructure, or to an intermediate, but transient, state, the optical properties will onlydisplay transient changes.

155

begins, it is the dominant mechanism for darkening. The Stage II darkening continues

even if the exposure is stopped and then restarted some time later, while Stage I

darkening is not seen after the initial exposure. The change in darkening behavior

indicates a change in the mechanism of photodarkening.

The increase in structural disorder and the formation of charged defects causes

stress to accumulate in the glass network. Illumination continues to cause atomic motion

through the formation and decay of dynamical bonds; however, now the built-up stress

field is an additional driving force for the atomic motion. In order to relieve the stress, the

atomic motion may lead to void formation and growth. The presence of voids will

increase the scattering of the sample and therefore cause an apparent increase in the

absorption. Voids will also lower the density of the sample and cause the expansion

observed by other authors. If the change in optical properties during Stage II is entirely

caused by the formation and growth of voids then the density and structural disorder of

the glass surrounding the voids could remain nearly constant. Only below-bandgap light

can lead to large expansion since only it will create voids through the entire thickness of

the sample. Above-bandgap light can create stress and voids near the surface of a sample

but not within the bulk. This idea is supported by the giant photoexpansion of As2Se3

glass and by the observation of photoinduced light scattering in As2S3 glass exposed to

below-bandgap illumination.31 To verify this description of Stage II darkening, we will

have to show that the expansion does not occur until the onset of Stage II darkening and

that the amount of expansion can be correlated with the duration of Stage II darkening.

156

CHAPTER 6RAMAN STUDIES OF STRUCTURE AND TEMPERATURE

One remarkable feature of the chalcogenide glasses is their Raman spectra. The

Raman peaks are exceptionally sharp for an amorphous material. A typical germanium-

selenium glass Raman spectrum (Stokes) is shown in Figure 6-1. For comparison, the

Raman spectrum of silica is also shown. Silica has a long broad plateau-like feature that

extends from the laser line to almost 500 cm-1. In this same region, germanium-selenium

-700-600-500-400-300-200

Inte

nsity

(ar

b.)

Raman Shift (cm-1)

Ge3Se17SiO2

Figure 6-1: Typical Raman spectra of germanium-selenium glass and silica. The sharpfeatures in the Ge3Se17 spectra correspond with molecule-like short-range order.

157

glasses with less than 33% Ge show three distinct peaks at 195 cm-1, 215 cm-1 and 255

cm-1. The lowest energy peak is associated with the breathing-mode vibration of the

GeSe4/2 tetrahedra. The peak next to it is the cA1 line, which is of uncertain origin. As was

discussed in Chapter 2, it may come from Se-Se pairs or from edge-sharing tetrahedra.

The highest energy peak is associated with a vibration of Sen chains or Se8 rings. The

relative intensities of the two main peaks vary monotonically with the concentration of

germanium in the sample. The central positions of the peaks vary only slightly with

compositionindicating that the fundamental vibrations are rather insensitive to their

environment.

Structure Changes During Photodarkening

Transmission Measurements

High sensitivity to short-range order makes Raman useful for studying structure

changes associated with photodarkening. To look for these changes, a sample was

darkened by light from the Ti:Sapphire laser in the apparatus described in Chapter 3.

Before the sample was darkened, a Raman spectrum was collected at the location to be

darkened. The Raman data was collected with the laser in low-power, CW operation to

not induce any darkening and the transmission through the sample was monitored to

verify this. The laser was then adjusted to high-power, ML operation and the sample was

darkened for a set time. After which, a Raman spectrum was collected with the laser at

low power, the laser was set back to high-power, and the darkening process was

continued. This was repeated several times as can be seen in Figure 6-2. The Raman

spectra were collected during the breaks in the transmission data and at the beginning and

the end of the experiment.

158

The transmission changes are in good qualitative agreement with those observed

in the transmittance-reflectance measurements of the previous chapter. The darkening

proceeds in the same mannereven exhibiting the recovery characteristic of the GeSe9

composition. When the experiment is restarted after the Raman measurement, the

transmission shows a rapid decrease indicative of the transient change followed by

continued progress along the permanent darkening curve. Darkening of Ge3Se17 and

GeSe4 also exhibit good agreement with that observed in the transmittance-reflectance

measurements. GeSe3 was not examined because it exhibits almost no photodarkening at

the exposure powers used in this part of the research.

0.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

0 5 10 15 20 25 30 35 40 45 50

Tra

nsm

issi

on (

rela

tive

to T

0)

Time (m)

GeSe9

Figure 6-2: Transmission change of GeSe9 during Raman measurements. The breaks inthe curve correspond with the collection of Raman spectra.

159

Raman Scattering Results

The Stokes Raman spectra from before, during, and after the darkening

experiments showed no differences. This can be seen in graphs of Raman spectra taken

before and after darkening for GeSe9 (Figure 6-3), Ge3Se17 (Figure 6-4), and GeSe4

(Figure 6-5). The spectrum are presented with the background removed and the data

scaled by the height of the GeSe4/2 (195 cm-1) peak. The background was estimated by

fitting a line to the data with Raman shift larger than 325 cm-1. This line was then

subtracted from all of the data.

For all three samples, the before and after Raman spectra are indistinguishable

even though the transmission decreased by 10% or more. Raman spectroscopy can not

distinguish between the undarkened glass and the glass that has been permanently

-320-300-280-260-240-220-200-180

Inte

nsity

(ar

b.)

Raman Shift (cm-1)

GeSe9 Before ExposureAfter Exposure

Figure 6-3: Raman spectra from before and after darkening for GeSe9.

160

-320-300-280-260-240-220-200-180

Inte

nsity

(ar

b.)

Raman Shift (cm-1)

Ge3Se17 Before ExposureAfter Exposure

Figure 6-4: Raman spectra from before and after darkening for Ge3Se17.

-320-300-280-260-240-220-200-180

Inte

nsity

(ar

b.)

Raman Shift (cm-1)

GeSe4 Before ExposureAfter Exposure

Figure 6-5: Raman spectra from before and after darkening for GeSe4.

161

photodarkened. This is evidence that photodarkening is not the result of changes in the

short-range order of the germanium-selenium glass.

Sample Temperature Measurements

Another set of Raman measurements were done to investigate the effect of

absorption of the laser light on the sample temperature for the purpose of identifying any

thermal contribution to the change in the sample optical properties. The measurements

could not be made during photodarkening because the bandwidth of the pulsed laser light

is to broad to be used for Raman spectroscopy. Instead, the sample was exposed to CW

laser light with powers equivalent to the pulsed laser powers used for photodarkening.

Since thermal processes are slow compared to the repetition rate of the laser, the CW

light should induce the same amount of sample heating as pulsed light of the same power.

The samples, initially at room temperature, were exposed for about 2 minutes to the laser

light during which time Stokes and anti-Stokes Raman spectra were recorded. The

absolute temperature of the sample can be found from proper analysis of this data. Three

different laser powers were used, one which was too low to induce any photodarkening or

sample heating and two more which were equivalent to powers at which photodarkening

was observed.

Calculation of Temperature from Raman Spectra

The intensity of the Raman scattering is related to the absolute temperature, T, by

−+

+−=

−)(

)(exp

4

νµνµ

νµνµν

I

I

Tk

hc

B

. (6-1)

This is a modified form of the Equation 3-11. The laser and phonon frequencies, now in

wavenumber, are µ and ν respectively. A new term has also been addedthe first

162

parenthesis on the right-hand-side of the equation. This term corrects for the scattering

probability, which is proportional to 1/λ4.

Two other corrections are also necessary. The first is the proper removal of the

scattered light background present in the spectrum from non-Raman scattering processes.

The background can be seen in Figure 6-1 in the region of data with Raman shift greater

than 330 cm-1. This portion of the data can be fit with a straight-line approximation that

can then be used as an estimate of the background over the entire measurement range.

The second correction is for the spectral response of the spectrometer optics and

detection system. Variations in the spectral sensitivity of the Raman spectrometer will

lead to errors in the calculated value of the temperature. The spectral response can be

found through a complicated spectrophotometric calibration process, but this method,

involving the use of standard lamps, is difficult to apply and highly prone to error. A

better method for calibrating Raman spectra was proposed by Malyj and Griffiths.155

Their method calibrates the spectrometer with the Raman spectra of a standard material at

a known temperature. A correction factor is found from the difference between the

known sample temperature and the temperature calculated from Equation 6-1. This

correction factor can then be applied to any other Raman spectra measured with the same

instrument and experimental conditions.

Malyj and Griffiths used silica as the standard and measured the spectra with a

visible laser as the source. The calibration can be found by recognizing that Equation 6-1

is valid for any Stokes/anti-Stokes data pairs. For a given Raman shift, ν, T can be

calculated from the ratio of the intensity at µ+ν and µ-ν. The Raman spectra are

measured at discrete points, so by aligning the Stokes and anti-Stokes spectra properly, T

163

can be calculated at each of the data points. They used the broad plateau from 100 to 480

cm-1 in silica to calculate Τ over a continuous range of Raman shifts. The temperature

thus calculated is called the raw temperature, Tr. The actual temperature, T, is related to

the raw temperature, Tr, by

)()(

1

)(

1 νξνν

+=rTT

, (6-2)

where ξ is the temperature response function representing the temperature correction for

the spectral response of the Raman system. All three values are shown as functions of the

Raman shift, ν, to indicate that they are calculated on a point-by-point basis for the

spectrum. Because silica does not absorb light from the Raman excitation laser, it

remains at room temperature (295 K) during the measurement. The temperature response

function, ξ, can be found from the silica raw temperature and the known sample

temperature and then applied to any other temperature measurement performed with the

same system.

Temperature Measurements for the Germanium-Selenium Samples

The same method for spectral correction was used in this project; however instead

of silica, we used the broad Raman peaks of the germanium-selenium samples for the

calibration. This offers the advantage that the calibration is most accurate in the same

region of Raman shifts as the unknown measurements. It is also easier to collect high

quality Raman spectra from the chalcogenide glasses since they are much better Raman

emitters at 800 nm than silica. To determine the temperature response function, the

Raman spectra of a sample is measured at very low power (1 mW total, or ≈0.5 W/cm2

peak intensity) and ξ(ν) is then calculated just as for the silica standard. The germanium-

164

selenium glasses are only weakly absorbing of 800 nm light, so the temperature increase

caused by such a low intensity of light is negligible, and it is reasonable to assume that

the sample remains at room temperature. The Ge3Se17 composition was used as the

calibration standard.

Measurements were then made on all of the samples at three laser powers1, 10,

and 75 mWand the sample temperature at each laser power was calculated on a point-

by-point basis. The raw temperature, Tr(ν), was calculated every 1 cm-1 over the range of

160 to 320 cm-1. The raw temperature was then corrected by a straight line fit to ξ(ν) to

get the measured value of the sample temperature, T(ν). The straight-line fit was used to

260

280

300

320

340

160 180 200 220 240 260 280 300 320

Cal

cula

ted

Tem

pera

ture

(K

)

Ram

an I

nten

sity

(ar

b.)

Raman Shift (cm-1)

TemperatureStokes

anti-Stokes

Figure 6-6: Typical Stokes and anti-Stokes spectrum, and the temperature valuescalculated from this data.

165

avoid introducing the noise in ξ(ν) as a second source of random noise in the temperature

measurements. Figure 6-6 shows typical Stokes and anti-Stokes spectra and T(ν)

calculated from this data.

The range from about 200 to 300 cm-1 exhibited the least scatter in the calculated

temperatureespecially between 200 and 260 cm-1, the centers of the two peaks. The

broad peak at 260 cm-1, the Se-Se chain vibration, is present and well resolved in all of

the glass compositions. The estimate of the actual sample temperature, T, was made by

averaging the values of T(ν) from 250 to 270 cm-1. The standard deviation calculated on

the same interval is an estimate of the random error associated with the value of T. The

results are presented in Table 4-2.

It can be seen that the temperature of the sample is increased only slightly by laser

intensities high enough to induce photodarkening. Comparison of the temperature

measured at the highest intensity with that at the lowest intensity reveals that the increase

is 5 °C or less for all of the samplesdespite the two order of magnitude increase in the

incident intensity. This increase is about the same as the standard deviation of the

measurements themselves.

Table 6-1: Temperature of germanium-selenium glasses during exposure to 800 nm laserlight. The peak intensity of the light is indicated in the row above the calculatedtemperature values. All of the temperatures were calibrated with a temperature responsefunction calculated from the low-power Ge3Se17 measurement (light gray cell).

Temperature (K)Sample

0.5 W/cm2 5 W/cm2 40 W/cm2

GeSe9 291 ±2.5 292 ±2.6 293 ±2.8Ge3Se17 296 ±1.7 297 ±3.3 297 ±2.2GeSe4 302 ±4.1 311 ±2.9 304 ±3.0GeSe3 295 ±7.2 295 ±4.7 298 ±5.3

166

Variations in the temperature from one sample to the next are the result of using

only one calibration curve for all of the calculations. Measurements for a single sample

were conducted without removing the sample from the mount or changing its position.

Slight differences in the mounting and surface quality of the samples appears to affect the

spectral response of the entire Raman system. Within any column, these variations

amount to an uncertainty of about ±5 °C, or about the same as the uncertainty of the

measured temperatures. The point that shows the greatest deviation is for GeSe4

measured at 5 W/cm2. This is probably an experimental error caused by misalignment of

the Stokes and anti-Stokes spectra. The large standard deviation for the GeSe3 sample

occurs because the Se-Se peak at 260 cm-1 is the smallest for this compositions and,

therefore, the most susceptible to background noise.

Discussion of Raman Measurements

Raman spectroscopy measures optical phonons, which are characteristic of the

sample structure. These phonons provide information on the temperature and short-range

order of the glasses, so Raman spectroscopy provides a direct probe of local structure

changes caused by photodarkening. The acquisition of Raman spectra is simple and non-

intrusive, making it ideal for studying photoinduced changes in chalcogenide glasses. The

high Raman scattering yield of the chalcogenide glasses permits rapid collection of the

Raman spectra, and time-resolved study is possible since several Raman spectra can be

collected during the course of a photodarkening experiment. Finally, proper analysis of

the Raman spectra can provide experimental insight into unanswered questions about the

photodarkening process.

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Proof of Athermal Photodarkening

Until now, the photodarkening process has been assumed athermal. While this

assumption appears to be supported by other experimental observations, it has never been

verified directly. In addition, thermal processes do occur at very high laser powers. For

example, we have observed melting and decomposition of the germanium-selenium

samples when exposed to intense Ti:Sapphire and CO2 laser light. There is even a theory

that the photodarkening of chalcogenide glasses can best be explained by structural

relaxation from local heating by photon absorption.156 This model, known as the local

heating model (LHM), predicts that structural changes occur when micro-regions of the

glass are heated to temperatures greater than Tg. Distinguishing between thermal and

athermal processes is necessary for developing a theory to explain the process of

photoinduced changes in chalcogenide glasses.

The Raman temperature measurements presented here provide the first direct

evidence that sample heating is not the cause of the photodarkening. Our measurements

show that sample heating by exposure to 800 nm light is insufficient to cause thermal

annealing of the glass. The temperature change is not even enough to cause thermo-

optical changes, which might appear as transient changes in the sample optical properties.

Photodarkening is therefore a process of direct photo-excitation of the glass structure and

subsequent rearrangement to a new structure with distinctly different optical properties.

This is in direct contradiction with the LHM modelindicating that it is not the correct

explanation for the below-bandgap photodarkening of germanium-selenium glasses.

Beyond the results for below-bandgap photodarkening, Raman temperature

measurement is a general technique that can be applied to the study of many other

photoinduced phenomena. Direct determination of the temperature can be used to study

168

the onset of thermal damage in samples exposed to high laser power. Sample heating can

also be monitored as a function of photon energy. Strongly absorbed wavelengths of light

might cause much more sample heating and alter the darkening process.

Heating chalcogenide glasses during exposure is known to reduce the magnitude

of photodarkening,157 and thermal relaxation removes the photoinduced changes.158 The

heating increases the relaxation rate and therefore reduces the total photodarkening. This

process may explain the logarithmic relationship between the laser intensity and the

magnitude of Stage I photodarkening shown in Chapter 5 (Figure 5-17). The

photodarkening at higher powers is limited by the associated sample heating, which will

have a greater effect at higher temperatures. The higher powers induce greater darkening

but may also heat the sample more, causing faster relaxation. The net effect of the two

counteracting processes is a sublinear relationship between light intensity and the

magnitude of photodarkening. Thermal relaxation process may also be present in the

recovery of transmission observed in the GeSe9 sample at high intensity. The apparatus

used for measuring sample temperature was designed for low intensity measurements, so

the presented results do not address sample heating at high laser intensities (greater than

100 W/cm2). More temperature measurements will have to be done to determine the

magnitude of sample heating at high intensities.

Permanent Photodarkening Without Obvious Structure Change

The permanent photodarkening does not appear to change the Raman spectra of

the samples from that of the undarkened state. The breadth, width, and positions of the

peaks remain constant throughout the photodarkening process. Macroscopically, the glass

is the same before and after darkening.

169

Raman spectroscopy should be sensitive to bonding changes involving 1% or

more of the atoms. Not seeing any changes in the Raman spectra of the photodarkened

glass means that photodarkening must result from changes in only a small portion of the

total glass structure or from changes in the medium- and long-range glass structure.

While the Raman data does not establish the structure of the photodarkened state, it does

exclude certain types of structural changes from being the source of the

photodarkeningthose which involve large changes in the glass short-range order.

Crystallization is one of the changes that can be ruled out. The formation of

crystals will produce sharp Raman peaks corresponding to the vibrational modes of the

crystalline lattice. These crystalline Raman peaks are observed in photoinduced

crystallization of GeSe2.47,49 Lack of these peaks shows that in our experiments the

samples remain amorphous during the entire process of photodarkening. The

photoinduced structural change must be one that preserves the amorphous long-range

order of the glass but produces a state with distinct optical properties from the annealed

glass.

We also see no evidence of the breakdown of the COCRN. In these glasses, the

formation of germanium-germanium bonds would break the chemical order and change

the optical properties.159 Formation of homopolar germanium bonds should be

accompanied by the growth of a Raman peak at about 180 cm-1.111 No such peak is

observed even in the most germanium-rich sample.

Our results contradict observations of homopolar bond formation in arsenic-sulfur

glasses.160,161 Other researchers have reported large changes in the Raman spectra of

photodarkened films at or near the stoichiometric As2S3 composition. Arsenic-rich

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compositions showed the greatest tendency to form homopolar bonds. The formation of

homopolar bonds has also been used to explain changes in the EXAFS spectra of

illuminated arsenic-sulfur and germanium-selenium glasses.162

This discrepancy can be explained by recognizing that all of the samples used in

this project were on the selenium-rich side of the stoichiometric composition (33% Ge),

so formation of germanium-germanium bonds is impossible without significant atomic

diffusion. According to other work, approximately 7% of the atoms must change position

in order to explain the experimental results.161 Our results show that the photodarkening

we observe is not the result of photoinduced diffusion and rearrangement of the atoms.

Homopolar bond formation is only possible when these bonds can form by short-range

atomic motiona condition only met by the stoichiometric and chalcogen-poor glasses.

Photodarkening can occur without homopolar bond formation. This leads to the

question of what role homopolar bonds play in the photodarkened state. Our data does

not provide an explanation, but it suggests that either photodarkening occurs by different

mechanisms in chalcogen-rich and chalcogen-poor glasses, or it occurs by the same

mechanism and homopolar bond formation is a secondary effect observed only in

chalcogen-poor compositions.

Charged defect formation is another possible explanation for the photodarkening

of chalcogenide glasses. Charged defects, such as valence-alternation pairs (VAPs), can

cause large changes in the optical properties in low concentrations.163 VAPs have been

estimated to form in concentrations of 1018 to 1020 cm-3.153 Such low concentrations (less

than 1%) might not be detected by Raman scattering. The large changes in optical

171

properties result from the presence of the defect electronic states near the middle of the

bandgap.

Changes in medium-range order would also be difficult to detect with Raman

scattering. The arrangement of the molecular sub-units can change without inducing

significant changes in the actual structure of those sub-units. The coordination of the

individual constituents is unaltered by darkening, but the covalent bond angles and

intermolecular distances could change. A model of this process is the bond-twisting

model.10,28,164 In this model, photoinduced bond twisting increases the disorder of the

glass, broadening and distorting the valence band. This change in the valence band

decreases the bandgap and broadens the exponential absorption tail.

Kolobovs model of photoinduced dynamical bond formation provides an

athermal process by which these structure changes can occur. This model of

photodarkening is completely consistent with the results presented in this and the

previous chapter.

172

CHAPTER 7CONCLUSIONS

The goal of this project was to advance the understanding of structure-property

relationships as they apply to the photodarkening process in chalcogenide glasses.

Chalcogenide glasses were chosen because they exhibit unique optical properties that

make them applicable to the growing field of optical communications. The goal was

accomplished by studying a characteristic chalcogenide glass system (germanium-

selenium) with experimental techniques that measure the optical properties of the sample,

monitor the change in optical properties with light exposure, and reveal the structure of

the glass during photodarkening. Several compositions from one glass system were

studied to elucidate the role played by the constituent atoms in the total photodarkening

process. Our results agree with the theory of photodarkening proposed by Kolobov et al.;

however, they also highlight the inadequacy of current theories at predicting the actual

photodarkening response of any specific chalcogenide glass. No single theory predicts the

range of optical changes observed in our experiments.

The chalcogenide glasses are of technological importance because of their wide

infrared transparency and their photosensitivity. The glasses are suitable for fabrication of

optical elements including traditional optics, thin film devices, and core-clad fiber optics

capable of operating at wavelengths from the visible to the far-infrared (beyond 10 µm).

Almost all chalcogenide glasses exhibit photosensitive changes in properties, especially

when illuminated by photons with energies above, or slightly below the bandgap energy

of the glass.

173

One of the photosensitive processes, photodarkening, can be used to fabricate

optical structures in a chalcogenide glass such as Bragg gratings, waveguides, and

holographic devices. Photodarkening of the glass by below-bandgap illumination permits

the fabrication of these structures deep within a sample not just on the surface, as is the

case for the strongly absorbed, above-bandgap light. Application of photodarkening to

fabrication of actual devices has been limited by a lack of understanding of the darkened

state and the process by which it forms. Recently several researchers have demonstrated

the fabrication of gratings in chalcogenide films and fibers. The experimental and

theoretical results presented in this dissertation reveal new information on the formation

of the photodarkened state induced by below-bandgap light and the effect of glass

composition on that process.

The chalcogenide glasses studied are from one of the simplest chalcogenide

compositionsthe binary system consisting of germanium and selenium. Compositions

of the glass used were GeSe9, Ge3Se17, GeSe4, and GeSe3. They were chosen to be on the

selenium-rich side of the stoichiometric composition, GeSe2. The structure of the

selenium-rich glasses consists of isolated GeSe4/2 tetrahedra linked by chains of selenium

atoms. The length of these chains depends on the amount of excess selenium. In the

annealed state, the germanium atoms are always fourfold coordinated and the selenium

atoms are always twofold coordinated. It is well known that selenium, or one of the other

chalcogen atoms (sulfur or tellurium), is necessary for photodarkening; however, the

effect of germanium has not received much study.

A Ti:Sapphire laser was used as the below-bandgap light source for inducing

photodarkening. The laser operates at a wavelength of 800 nm (1.55 eV) while the

174

bandgap of the glasses ranges from 1.95 for GeSe9 to 2.2 eV for GeSe3. The bandgap and

undarkened optical properties of the glasses at 800 nm were measured to supplement the

limited information on these properties available from published sources. Two techniques

for calculating the optical properties in the exponential band tail region were used. One

method, the Curve Fitting Technique, is based on fitting the measured transmittance

spectrum with a model for the exponential increase in the absorption coefficient with

photon energy. The other, the Derivative Technique, is based on calculating the

derivative of the transmittance spectrum with respect to wavelength and calculating the

exponential absorption parameters from a straight-line fit of this data. Both of these

techniques are simple to apply and require only a single spectral measurement of the

glass. Both give consistent results and the values obtained are in good agreement with the

limited amount of published data.

Photodarkening of the glasses was performed in a custom apparatus that permits

time-resolved, quantitative measurement of sample transmittance and reflectance during

light exposure. The simultaneous measurement of these two properties permits us to

calculate the optical dielectric response function (ε*) of the sample. A technique for

doing the calculations is presented along with an analysis of the data. Since the dielectric

response function is directly related to the sample structure, we can interpret the changes

induced by photodarkening in terms of changes in the glass structure. This is a significant

improvement from previous research, which has concentrated only on the transmittance

changes during light exposure. The transmittance alone is not a unique function of the

optical properties of the material and, therefore, does not provide a good measure of

structure changes.

175

Because of their reliance on the transmittance data, most researchers treat

photodarkening as a simple process of light induced creation of a single type of defects.

The light exposure will cause defects to be created until some saturation point at which

the sample is fully darkened. From analysis of our data, though, we find that the

permanent photodarkening induced by below-bandgap light occurs in two stages. Each of

the stages has distinct kinetics and dependence on the laser intensity (flux) and product of

the flux and the total exposure time (fluence). All of the samples were found to exhibit a

fast, intensity-dependent transient absorption typical of a two-photon absorption process.

A slower, transient absorption was also observed in the GeSe9 and Ge3Se17 samples. This

differed from the permanent photodarkening in that it went away when the inducing light

source was removed.

We show that the fluence dependence of the first stage of photodarkening (Stage

I) can be described by an equation derived from second order reaction rate kinetics. From

fits of this equation to the data for GeSe9 and Ge3Se17 (the only two samples in which

Stage I developed fully before the onset of Stage II) we show that the photodarkening is

flux dependent. The flux dependence means that the underlying mechanism of

photodarkening is a multi-photon processcreation of a single structural defect requires

the coordinated absorption of at least two photons. The rate of Stage I photodarkening

increases with flux, as does the magnitude of the change in optical properties at

saturation. Higher exposure intensity causes faster darkening and a larger total change.

The intensity dependence of permanent photodarkening may be useful for the fabrication

of bulk optical devices in which appropriate control of the laser intensity can permit

fabrication of three-dimensional structures.

176

Stage II darkening appears as a linear increase in the absorption when plotted on a

semi-log graph. The slope of the linear relation is insensitive to the flux, but the onset of

Stage II is very sensitive to the flux and occurs at lower fluence when the sample is

exposed to higher flux. The exact process of Stage II darkening is highly composition

dependent. In the low-germanium samples, GeSe9 and Ge3Se17, absorption actually

recovers slightly at the onset of Stage II, while in the GeSe3 sample the absorption

displays rapid fluctuations about the linear trend. The difference in kinetics between

Stage I and Stage II darkening means different types of defects are formed during the

different stages of darkening. We observe that Stage II darkening follows Stage I

darkening in all of the glasses. This is interpreted as an indication that the photoinduced

changes which occur during Stage I are precursors for the changes which occur during

Stage II.

A transient darkening process is seen when an already darkened spot is re-

exposed with laser light. At the start of the second exposure, the absorption is lower than

it was at the end of the first; however, it rapidly increases to the same level of absorption.

Photodarkening then continues as if the exposure had not been interrupted. This transient

phenomenon occurs because one of the defects that contributes to the darkened state

recovers to the undarkened state at room temperature. Only a portion of the total

absorption change recoversindicating that the observed absorption increase is the sum

of contributions from permanent and transient defect states. We believe that the transient

absorbing state may be a pair of threefold coordinated selenium atoms (dynamical

bonds). These are the same as the defects that act as the mechanism for the formation of

permanent darkening in Kolobovs model. The only experimental evidence of these

177

defects comes from in situ EXAFS studies, so this may be the first optical evidence of the

existence of dynamical bonds during the photodarkening. Measurement of the creation

and decay rates of the transient contribution can provide information about the kinetics

and lifetime of the transient state. This information cannot be determined by EXAFS but

can be measured optically.

Our results demonstrate the large effect that glass composition has on the

photodarkening process. Both the rate and the magnitude of Stage I photodarkening

increase with increasing germanium content up to the GeSe4 (20% Ge) composition.

Higher concentrations of germanium cause a sharp decrease in the Stage I

photodarkening. Stage II darkening is also sensitive to composition. The onset of Stage II

photodarkening occurs at the lowest fluence, for a given laser intensity, at the GeSe4

composition. The effect on transient absorption is the largest in GeSe9 where the transient

contribution is responsible for more than half of the measured change in absorption. The

transient absorption decreases with increasing germanium content and is almost

unobservable in GeSe4. We find that GeSe4 is the composition with the maximum

photosensitivity. Previous studies, which have concentrated on single glass compositions,

have not revealed such an optimum composition for maximizing permanent

photodarkening.

The composition dependence reveals the roles of germanium and selenium in the

photodarkening process. Selenium is necessary for the excitation process. The data we

present shows that selenium-selenium bonds must be present for the formation of the

transient state. The germanium, on the other hand, helps to stabilize the darkened state.

At the optimum ratio of 20% Ge, every selenium atom is bound to one germanium and

178

one selenium atom. This maximizes the cooperation between the excitation process and

the decay of the excited state to the metastable darkened state.

Raman spectroscopy was used to monitor the structure of the glasses. Comparison

of spectra taken before and after photodarkening reveals no change in the short-range

structure. From this information, we rule out two current theories of photodarkening:

photoinduced crystallization and homopolar bond formation. Raman spectroscopy would

reveal evidence of the structure changes associated with either of these processes. Two

other theoriesthe bond-twisting model and the formation of charged defects (VAPs)

would not lead to changes in the Raman spectra. Both processes are reasonable

explanations for the observed photodarkening behavior.

By analysis of the Stokes and anti-Stokes Raman spectra collected during

photodarkening, we are able to directly determine the sample temperature while the

sample is being photodarkened. Our results confirm that the temperature of the sample

does not increase significantly above room temperature during photodarkening.

Therefore, photodarkening is an athermal process. The largest increase in temperature

was less than 5 °Can increase too small to cause thermal relaxation of the glass. Many

researchers already assume that photodarkening is athermal, but this result is the first

experimental proof.

The combined study of structure and properties has led to new insights into the

photodarkening of chalcogenide glasses. We have presented several new results,

including evidence of the cooperative effect of germanium and selenium atoms in

producing permanent photodarkening, observation of a transient optical absorption which

may be an intermediate step in the photodarkening process, and proof of the athermal

179

nature of photodarkening. Much more research remains to be done as we try to develop

practical devices based on photosensitivity in chalcogenide glasses. We hope that this

dissertation will stimulate further research into this complicated and fascinating field.

180

APPENDIXPOLISHING PROCEDURE FOR GLASS SAMPLES

Careful polishing was needed to assure that the glass samples were of proper

thickness and had smooth and parallel faces. The method presented in this appendix was

found to produce samples with the desired qualities.

Germanium-selenium glass samples were sliced from the bulk glass rod with a

diamond saw. Water was used as the cutting fluid. Because the glass is soft, the saw was

set to a low speed. To prevent fracture, only enough weight to keep the sample in solid

contact with the blade was placed on the sample. After the sample was cut, a piece of 320

grit silicon carbide sandpaper was used to remove any protrusions or rough edges.

A polishing jig (South Bay Technologies Lapping Fixture) was used during

polishing to create the flat parallel faces of the sample. The sample was mounted to the

fixture with thermoplastic adhesive. Care was taken to avoid heating the sample above Tg

during the bonding process. A small quantity of the adhesive was placed on the sample

mount and the mount was heated on a hot plate until the adhesive began to flow. The

sample was placed on the adhesive near the center of the mount and the mount was

removed from the hot plate. A weight placed on the sample ensured that the adhesive

layer was thin and the bottom sample face was parallel to the surface of the mount. The

mount was secured to the polishing fixture and the height on the fixture was adjusted to

permit polishing of the sample surface. The polishing was carried out in the following

steps:

181

1. Remove the saw damage by lapping with 9.5 µm alumina powder in water on

a glass plate. This provides fast material removal and can be used to quickly

thin a sample to a desired thickness.

2. Polish with 3.0 µm alumina powder in water on a glass plate.

3. Polish with 1.0 µm alumina powder in water on a nylon polishing cloth with a

steel backing plate.

4. Polish with 1.0 µm diamond in oil on a nylon cloth with a steel backing plate.

The following notes are relevant to the entire process:

• All polishing was done in a fume hood to prevent inhalation of the polishing

byproducts.

• The glass is soft, so only light pressure was used. Application of excessive

pressure caused the appearance of pitting, even with the fine polishing media.

• Latex gloves were worn and changed after each polishing stage.

• The sample and polishing fixture were cleaned carefully between each

polishing step with water and absolute ethanol. Acetone was not used since it

dissolves the mounting adhesive.

After the first face was polished, the sample was demounted by placing the

sample and mount in a beaker of acetone (sample face-up). The beaker was set in an

ultra-sonic cleaner and sonicated until the sample was free from the mount. Acetone was

used to remove any remaining mounting adhesive from the sample. The sample was

rinsed in absolute ethanol and dried. The sample was remounted onto the polishing

fixture with the polished side down and the polishing procedure was repeated. Samples as

thin as 0.18 mm were produced by careful lapping during the polishing of the second

182

face. Once the second face was polished, the sample was removed from the fixture and

carefully cleaned with acetone and absolute ethanol.

A final polish was then applied to both faces to achieve the best optical quality.

This final polish was also used on samples which had developed a frosty surface film

from long exposure to air. The final polish was done with ¼ µm diamond in oil on a

nylon polishing cloth with a steel backing plate. The sample was held against the

polishing cloth with one finger (latex gloves were worn for this procedure). It was

polished for about 100 figure-8s with moderate finger pressure. Then it was polished for

100 more with very slight finger pressure. The same was done for the other face. The

sample was carefully cleaned with acetone and dried, and it was then ready for the

experiments.

183

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BIOGRAPHICAL SKETCH

Craig Russell Schardt received his bachelor of science degree in mechanical

engineering from Florida International University in December of 1993. As an

undergraduate, he worked with Dr. W. Kinzy Jones conducting research on advanced

ceramic materials for microelectronics packaging. This experience led to his interest in

materials science. In January of 1994, he moved to the University of Florida to begin a

doctoral program in materials science and engineering under the guidance of Dr. Joseph

H. Simmons. In addition to his studies, he served as president and treasurer of the Canoe

Club and was an active member of the Sport Clubs Council. In the spring of 1999, he was

inducted into the Florida Alpha Chapter of Tau Beta Pi, the national engineering honor

society.

photodarkening of germanium-selenium glasses induced by below-bandgap light

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