PHOTODARKENING OF GERMANIUM-SELENIUM GLASSES INDUCED BY BELOW-BANDGAP LIGHT
By
CRAIG RUSSELL SCHARDT
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2000 Copyright 2000
by
Craig Russell Schardt To my parents, Jean and George Schardt. 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 committee—Dr. Cammy Abernathy, Dr. Paul Holloway, Dr. Rolf
Hummel, and Dr. David Reitze—for 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.
iv TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ...... iv
LIST OF TABLES...... viii
LIST OF FIGURES ...... ix
ABSTRACT...... xii
CHAPTERS
1 INTRODUCTION...... 1
Chalcogenide Glasses and Light...... 1 Electronic Properties...... 2 Optical Properties...... 4 Nonlinear Index of Refraction and Absorption ...... 5 Vibrational Properties ...... 7 Photoinduced Effects in Chalcogenide Glass ...... 7 Photodarkening ...... 8 Photoinduced Anisotropy...... 9 Photoinduced Crystallization...... 9 Photodiffusion and Photodoping...... 10 Photoexpansion and Photoinduced Fluidity...... 10 Summary of Photoinduced Effects ...... 11 Applications for Chalcogenide Glasses ...... 12 Optical Limiting...... 12 Infrared Fiber Optics...... 14 Photolithography...... 19 Optical Switching...... 19 Optical Computing...... 20 Contribution of This Research...... 22 Systematic Study of a Variety of Compositions...... 23 Ti:Sapphire Laser...... 24 Measurement of Kinetics ...... 25 Raman Spectroscopy...... 27 Summary...... 27
v 2 BACKGROUND...... 29
Optical Physics...... 29 Absorption and Refraction...... 29 Dielectric Response ...... 34 Germanium-Selenium Glass ...... 40 Amorphous Selenium...... 43 Amorphous Germanium Diselenide ...... 46 Selenium-Rich Germanium-Selenium Glasses...... 50
3 EXPERIMENTAL METHODS ...... 53
Chalcogenide Glass Samples ...... 53 Glass Preparation ...... 53 Spectroscopic Analysis ...... 54 Photodarkening Measurements...... 56 Ti:Sapphire Laser...... 56 Optical Arrangement...... 58 Data Acquisition and Analysis...... 64 Experiment Methodology ...... 65 Raman Spectroscopy...... 67 Raman Apparatus...... 69 Experimental Raman Measurements ...... 72
4 MEASUREMENT OF OPTICAL PROPERTIES ...... 75
Infrared Absorption Edge ...... 75 Visible Absorption Edge...... 78 Measured Data ...... 80 Extraction of Optical Properties...... 82 Discussion...... 90
5 BELOW-BANDGAP PHOTODARKENING ...... 96
Changes in Optical Properties Induced by Below-Bandgap Light ...... 96 Transmittance and Reflectance Changes ...... 101 Real and Imaginary Dielectric Response...... 105 Effect of Composition on Photodarkening ...... 114 The Kinetics of Photodarkening ...... 115 Transient Darkening and Dark Recovery...... 133 Mechanism of Permanent and Transient Below-Bandgap Photodarkening ...... 143 Kolobov’s Model of Dynamical Bond Formation...... 147 Dynamical Bonds and Photodarkening of Germanium Selenium-Glasses...... 152
6 RAMAN STUDIES OF STRUCTURE AND TEMPERATURE ...... 156
Structure Changes During Photodarkening ...... 157
vi Transmission Measurements...... 157 Raman Scattering Results ...... 159 Sample Temperature Measurements...... 161 Calculation of Temperature from Raman Spectra ...... 161 Temperature Measurements for the Germanium-Selenium Samples ...... 163 Discussion of Raman Measurements...... 166 Proof of Athermal Photodarkening...... 167 Permanent Photodarkening Without Obvious Structure Change...... 168
7 CONCLUSIONS...... 172
APPENDIX POLISHING PROCEDURE FOR GLASS SAMPLES ...... 180
REFERENCES ...... 183
BIOGRAPHICAL SKETCH ...... 196
vii 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 and germanium-selenium glasses ...... 78
4-2: Optical properties of germanium-selenium glasses calculated by application of the Curve Fitting Technique to the measured absorbance spectra ...... 85
4-3: Optical properties of germanium-selenium glasses calculated by application of the Derivative Technique to the measured absorbance spectra...... 88
4-4: Reported values for the refractive index (n) of germanium-selenium glasses at 800 nm...... 91
4-5: Reported values for the absorption coefficient (α) of germanium-selenium glasses at 800 nm ...... 92
4-6: Reported values for the optical bandgap (Ego) germanium-selenium glass at 800 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 nm laser light...... 165
viii 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 transmission and reflection during photodarkening of the chalcogenide glass samples...... 59
3-3: Experimental apparatus for measurement of Raman scattering during photodarkening ...... 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 exponential band 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 laser light ...... 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
ix 5-5: Transmittance change of the GeSe9 sample at the highest laser power (52.6 mW)...... 102
5-6: Transmittance change of the Ge3Se17 sample at the highest laser power (57.9 mW)...... 104
5-7: The real and imaginary parts of the dielectric response of GeSe9 glass at 800 nm, calculated from the data in Figure 4-1 ...... 108
5-8: The real and imaginary parts of the dielectric response of Ge3Se17 glass at 800 nm, calculated from the data in Figure 5-2 ...... 109
5-9: The real and imaginary parts of the dielectric response of GeSe4 glass at 800 nm, calculated from the data in Figure 5-3 ...... 110
5-10: The real and imaginary parts of the dielectric response of GeSe3 glass at 800 nm, calculated from the data in Figure 5-4 ...... 111
5-11: Comparison of the change in the imaginary part of the dielectric response at 3.5 mW laser power ...... 114
5-12: Comparison of the change in the imaginary part of the dielectric response at 10 mW laser power ...... 116
5-13: The imaginary part of the dielectric response of Ge3Se17 glass showing the two stages of photodarkening ...... 117
5-14: Typical fit of the Stage I darkening process using First Order and Second Order 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 composition of the glass ...... 123
5-17: The maximum change in the imaginary dielectric (∆ε2) observed during Stage I darkening ...... 124
5-18: The value of the fluence at which the Stage I darkening has reached 50% of its final value...... 126
5-19: The slope of the darkening with respect to the fluence (dε2/dΦ) at the beginning 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
x 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 values calculated from this data ...... 164
xi Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
PHOTODARKENING OF GERMANIUM-SELENIUM GLASSES INDUCED BY BELOW-BANDGAP LIGHT
By
Craig Russell Schardt
August 2000
Chairman: Joseph H. Simmons Major 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
xii 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.
xiii CHAPTER 1 INTRODUCTION
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
1 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 3.24 eV in GeS2. 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
σ* (2) Conduction
4eV
p (6) LP (2) Valence
4eV
σ (2) Bonding
atomic molecular bands in states states solid
Figure 1-1: Typical band structure of lone-pair semiconductors. Based on Kastner.7
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 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
= + n n0 n2 I (1-1)
α = α +α 0 2I , (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
19 1.064 µm have been measured in As2S3, GeSe4 and Ge10As10Se80 glasses. 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 infrared—beyond 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
46 Griffiths et al. 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
50 48 51 amorphous selenium and the stoichiometric IV-VI mixtures GeSe2, GeS2, and SiSe2. 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
53 most readily into As3S7 to form the stable compound AgAsS2. 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
33 as 3 % has been induced in films of As2S3 with below-bandgap illumination. 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
58 dilation, has been observed in films of As50Se50. 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
12 sample of As2S3 deforms viscously, with a viscosity estimated at 5 × 10 poise—several
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 limiters—they 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
25 damaging fibers of Te2Se3.9As3.1I. 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
67 68 photoluminesce in Ge10As40Se25S25 glass and GeGaS glass. 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 measurement—from 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
81-83 demonstrated with As2S3-based fibers. 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 switches—when structured to produce NOR gates—provide 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
today’s 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 exposure—permitting 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 glasses—if 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. CHAPTER 2 BACKGROUND
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.
29 30
Propagation of light in a material
The theory of the interaction of light with matter begins with Maxwell’s
relations.13 In the case of a linear, homogeneous, isotropic medium, these can be written
ρ ∇ ⋅ E = (2-1) ε
∇ ⋅ B = 0 (2-2)
∂B ∇ × E = − (2-3) ∂t
∂E ∇ × B = µσE + µε . (2-4) ∂t
The light is an electromagnetic wave propagating in space and time. Treating it as a plane
wave, the electric field can be described by
= []−ω E(x,t) E0 exp i(kx t) , (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 Maxwell’s 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 Maxwell’s 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
= [ε ∗ ω − ]ε P D ( ) 1 0 E(x,t) , (2-6)
where ε0 is the electric permittivity of free space. The material-specific information is
ε ∗ ω contained in the material’s dielectric response function,D ( ) . The dielectric response is a dimensionless function. It can be written in terms of its real and imaginary components as 31
ε ∗ ω = ε ω + ε ω D ( ) 1( ) i 2 ( ) . (2-7)
Solution of Maxwell’s equations shows that in a material k* is related to the dielectric response by
∗ c ∗ ε (ω) = k (ω) , (2-8) D ω
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,
[][ω 2 = ω) + κ (ω ) ]2 = ε ∗ ω N( ) n( i D ( ) . (2-9)
Here, n(ω) is the refractive index, and κ(ω) is the extinction coefficient. For the clarity of
ƒ ω ε ∗ the rest of the discussion, the explicit ( ) notation will be dropped, however D , 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:
ωn ωκ E(x,t) = E expi x −ωt exp− x . (2-10) 0 c c
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
cε 2ωκ −α I(x) = 0 E 2 exp− x = I e x . (2-11) 2 0 c 0
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
E N − N ρ = R = 2 1 . (2-12) + EI N2 N1
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,
A + T + R = 1. (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
(1− r)2 e−α d T = (2-14) 1− r 2 e−2α d
R = r(1−T e−α d ) , (2-15)
where r is the single surface reflectivity, which for the case of a sample in air is
2 2 ∗ (n −1) +κ r = ρρ = , (2-16) (n +1)2 +κ 2
and α from Equation 2-11 is
2ωκ 4πκ α = = , (2-17) c λ
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
α e- d:
2 2 −α 3 1− R 1 −α 2 1− R −α 1 ()d + − + ()d + − ()d − = e 1 2 T e 2 e 0 . (2-18) T T T T
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 2 x(t) d x(t) m + mΓ + kx(t) = −qE(t) , (2-19) dt 2 dt
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
= −iωt E(t) E0 e , (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
q 1 x(t) = − E(t) , (2-21) ()ω 2 −ω 2 + Γω m 0 i
where the natural frequency of the oscillator, ω0, is
k Γ 2 ω = − . (2-22) 0 m 4
The polarization of this oscillator is the charge times the displacement,
P(t) = −qx(t) , (2-23) so the dielectric response of a single oscillator can be found from Equation 2-6,
2 ∗ P(t) q 1 ε = 1+ = 1+ . (2-24) D ε ε ()ω 2 −ω 2 + Γω 0 E(t) 0m 0 i
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
2 ∗ 1 q N f ε = 1+ ∑ j j j . (2-25) D ε ()ω 2 −ω 2 + Γ ω 0 j m j 0 j i j
Equation 2-25 is the total dielectric response of a system of simple harmonic oscillators.
ε ∗ It is important to recognize that D 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
102
100
10-2 2 ε 10-4
10-6
-8 10 I II III VI
101 100 10-1 10-2 10-3 Photon Energy - hν (eV)
Figure 2-1: Typical imaginary dielectric response of a chalcogenide glass. Regions are: (I) electronic band-to-band transitions, (II) exponential absorption tail, (III) Rayleigh scattering and impurity absorption, and (IV) vibrational transitions.
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 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
Se Se
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
Ge
Se Se
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.
Se-Se Chain GeSe4/2 Tetrahedra
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 germanium atom. 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
6 ≈10 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
tetrahedra—analogous 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
104 of GeSe2 glass. Tronc et al. 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 Tronc’s 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
c line ( A1 ) but it is not present in the crystalline Raman spectrum. The intensity of both the
c 105 A1 and A1 lines is maximum at the GeSe2 composition.
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
c 106 the A1 line. The cluster, known as an “outrigger raft,” 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
107 scattering data 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
129 observation of two chemically inequivalent chalcogen sites in GeSe2 glass by I
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
Bridenbaugh’s “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
110 c al. proposed that the A1 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
c the A1 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
c species of atoms but not on their concentration in the glass. The A1 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
c of the ratio of A1 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
r = (4.0)x + (2.0)(1− x) , (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
96 amorphous selenium, this peak was assigned to a vibrational mode of Se8 rings, 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 Ge
Se Se Se Se
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. CHAPTER 3 EXPERIMENTAL 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 98 Ge3Se17 15 2.3 126 GeSe4 20 2.4 170 GeSe3 25 2.5 198
53 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
1 A = log . (3-1) 10 T
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
hν α(hν ) = α exp , (3-2) 0 σ
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 Intensity (arb.)
799.0 799.5 800.0 800.5 801.0 Wavelength - λ (nm)
Figure 3-1: Typical spectral profile of the Ti:Sapphire laser operating in CW mode.
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 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
Reflected Signal Detector Focusing Lens ND Filter
xxxxxxxxxx
xxxxxxxxxx Beam xxxxxxxxxx xxxxxxxxxx
xxxxxxxxxx
xxxxxxxxxx Splitter xxxxxxxxxx xxxxxxxxxx
xxxxxxxxxx
xxxxxxxxxx
xxxxxxxxxx
xxxxxxxxxx
Transmitted Sample Signal Detector Reference Signal Detector
Figure 3-2: Experimental apparatus used for simultaneous measurement of transmission and reflection during photodarkening of the chalcogenide glass samples.
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 r 2 I(r, z) = exp− 2 , (3-3) 2 πw w
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 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
I 2 P = , (3-4) π 2 IT w
where IT is the total power of the laser beam. The radius of the beam at any position along
the z direction is
2 = + z w(z) w0 1 , (3-5) z R 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
πw2 z = 0 . (3-6) R λ
Table 3-2: Performance of neutral density filters at 800 nm wavelength. ND Filter Measured OD (800 nm) 0.2 0.12 0.4 0.19 0.6 0.41 0.8 0.62 1.0 0.52 2.0 1.33 3.0 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
s′ ()s f −1 = 1+ . (3-7) []()− 2 + ()2 f s f 1 z R f
The size of the new waist is the magnification m,
w′ 1 m = 0 = . (3-8) 2 2 w0 []− ()+ () 1 s f z R f
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
2 2 W/(mW⋅cm ). For a total average power, IT, of 1 mW, the peak intensity is 70 W/cm .
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
1 V T = T (3-9) RT Vref
1 V R = R . (3-10) RR Vref
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
I(ω + Ω) Ω = exp− h . (3-11) ω − Ω I( ) k BT
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
To Raman Spectrometer Transmitted Signal Detector
Sample Focusing Lens
Beam ND Filter Splitter
xxxxxx
xxxxxx
xxxxxx From xxxxxx xxxxxx
xxxxxx
xxxxxx
Ti:Sapphire xxxxxx
xxxxxx
xxxxxx Laser xxxxxx xxxxxx
xxxxxx
xxxxxx Mirror
Reference Signal Detector
Figure 3-3: Experimental apparatus for measurement of Raman scattering during photodarkening.
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 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 magnitude—enough 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. CHAPTER 4 MEASUREMENT 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
75 76
Wavelength (µm) 10 12.5 15 17.5 20 22.5 25 1.2 0.8 GeSe 460 3 1.0 GeSe4 0.6 490 Ge Se 562 3 17 GeSe9 0.4 0.8 0.2 Area Fraction 0.6 0.0 10 15 20 25
Absorbance Composition (% Ge) 0.4
0.2 562 490 460 0.0 1000 900 800 700 600 500 400 Wavenumber (cm-1)
Figure 4-1: Infrared absorbance of germanium-selenium glasses showing the multi- phonon absorption peaks. Vertical lines indicate the positions of the peaks. The inset plots the areas of the three peaks (as fractions of the total area) against the composition of the sample.
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. 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,
127 four fundamental modes for the GeSe4/2 tetrahedra have been identified. 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 vibrations observed in amorphous selenium and germanium- selenium glasses. All of the selenium assignments are from Siemsen and Riccius128 and Lucovsky et al.96 and all 127 of the GeSe4/2 assignments are from Ohsaka. Observed Assignment Frequency (cm-1) 55 Se8, E2 97 Se8, E1; Se-chain, A2 123 GeSe4/2, ν2 138 Se-chain, E 195 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
6 GeSe9 Ge3Se17 GeSe 5 4 GeSe3
4
3 Absorbance 2
1
0 600 650 700 750 800 850 900 Wavelength (nm)
Figure 4-2: Measured absorbance of germanium-selenium glasses in the exponential band tail region
900 nm—the 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 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
hν α(hν ) = exp β + , (4-1) σ
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
1 GeSe9 Ge3Se17 GeSe 0.1 4 GeSe3
0.01
0.001 Transmittance 0.0001
1e-05
1e-06 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 hν (eV)
Figure 4-3: Measured transmittance versus energy for germanium-selenium glasses.
converts the data into absorbance by Equation 3-1. The sample transmittance, which is
related to the sample optical properties, is therefore
T = 10− A . (4-2)
Wavelength can be transformed into photon energy, hν, by
1240 hν = , (4-3) λ 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. 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
(n −1) 2 r = . (4-4) (n +1) 2
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
102 135 coefficients) of the index of refraction of amorphous selenium and Ge20Se80 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 of the Curve Fitting Technique to the measured absorbance spectra. -1 Sample σ (meV) β n α800(cm ) Ego (eV) GeSe9 (3) 62.5 ±0.6 -24.2 ±0.3 2.62 ±0.03 1.79 ±0.07 1.946 ±0.004 Ge3Se17 (5) 66.7 ±1.5 -22.7 ±0.6 2.43 ±0.08 1.81 ±0.15 1.972 ±0.004 GeSe4 (4) 70.9 ±2 -21.3 ±0.7 2.38 ±0.05 1.76 ±0.23 2.001 ±0.003 GeSe3 (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,
dα 1 = α . (4-5) d(hν ) σ
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
dα 1 λ2 1 dT = . (4-6) d(hν ) d hc T d λ
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
T ≈ (1− r) 2 exp(−αd) . (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,
dα − ln(10) λ2 d A = . (4-8) d(hν ) d hc d λ
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,
dα 1 hν = exp β + , (4-9) d(hν ) σ σ or, by taking the natural logarithm of both sides,
dα 1 1 ln = ln + β + (hν ) . (4-10) d(hν ) σ σ
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,
r = 1− exp(αd − 2.303A) , (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,
+ 1 r n = . (4-12) 1− r
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 of the Derivative Technique to the measured absorbance spectra. -1 Sample σ (meV) β n α800(cm ) Ego (eV) GeSe9 (3) 59.6 ±0.3 -25.6 ±0.1 2.73 ±0.03 1.49 ±0.03 1.939 ±0.003 Ge3Se17 (5) 61.5 ±1.6 -25.0 ±0.7 2.61 ±0.06 1.32 ±0.13 1.959 ±0.004 GeSe4 (4) 66.2 ±1.2 -23.2 ±0.5 2.55 ±0.01 1.30 ±0.06 1.991 ±0.005 GeSe3 (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,
Aλ2 n 2 −1 = , (4-13) λ2 − λ2 0
where A and λ0 are fitting parameters and λ is the wavelength of the light. The second
form is the Wemple-DiDomenico136,137 equation,
E E n 2 −1 = d 0 , (4-14) 2 − 2 E0 E
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
2.8 Curve Fit Technique Derivative Technique Published Values 2.7
2.6
2.5
Index of Refraction 2.4
2.3
2.2 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Ge Concentration (Atomic Fraction)
Figure 4-4: Index of refraction at 800 nm for germanium-selenium glasses. Error bars indicate the standard deviation of the values estimated by the two techniques. See Table 4-4 for the sources of the published values.
Table 4-4: Reported values for the refractive index (n) of germanium-selenium glasses at 800 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 2.62 Wemple-DiDomenico Equation, Table 2 143 20 2.55 Sellmeier fit to data in Table 1 135 25 2.49 Wemple-DiDomenico Equation, Table 4 139 92
3.0 Curve Fit Technique Derivative Technique Published Values 2.5
2.0
1.5 Absorption Coefficient
1.0
0.5 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Ge Concentration (Atomic Fraction)
Figure 4-5: Absorption coefficient at 800 nm for germanium-selenium glasses. Error bars indicate the standard deviation of the values estimated by the two techniques. See Table 4-5 for the sources of the published values.
Table 4-5: Reported values for the absorption coefficient (α) of germanium-selenium glasses at 800 nm. -1 Glass (% Ge) α800 (cm ) Note Ref 0 2.9 Figure 4 138 25 0.986 Exponential Band Tail, Table 6 139 93
2.20 Curve Fit Technique Derivative Technique 2.15 Published Values
2.10 (eV) go 2.05
2.00
1.95 Optical Band Edge, E
1.90
1.85 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Ge Concentration (Atomic Fraction)
Figure 4-6: Optical bandgap for germanium-selenium glasses. Error bars indicate the standard deviation of the values estimated by the two techniques. See Table 4-6 for the sources of the published values.
Table 4-6: Reported values for the optical bandgap (Ego) germanium-selenium glass at 800 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 5 1.94 Exponential Tail (α=103), Figure 5 134 10 1.97 Exponential Tail (α=103), Figure 5 134 20 2.03 Exponential Tail (α=103), Figure 5 134 25 2.09 Exponential Tail (α=103), Figure 5 134 30 2.19 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. CHAPTER 5 BELOW-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.
96 97
0.6 GeSe9 I0 (mW) 1.43 0.5 3.29 8.53 28.1 0.4 52.6
0.3
Transmittance 0.2
0.1
0.0 0 50 100 150 200 250 Exposure Time (minutes)
0.4 GeSe9 I0 (mW) 1.43 3.29 8.53 0.3 28.1 52.6
0.2 Reflectance
0.1
0.0 0 50 100 150 200 250 Exposure Time (minutes)
Figure 5-1: Transmittance and reflectance of GeSe9 during exposure to 800 nm laser light. Each trace represents the exposure of an unexposed location beginning at time = 0. 98
0.6 Ge3Se17 I0 (mW) 0.441 0.5 0.917 3.51 9.88 0.4 18.9 35.9 57.9 0.3
Transmittance 0.2
0.1
0.0 0 50 100 150 200 250 300 350 Exposure Time (minutes)
0.4 Ge3Se17 I0 (mW) 0.441 0.917 0.3 3.51 9.88 18.9 35.9 0.2 57.9
Reflectance 0.1
0.0
-0.1 0 50 100 150 200 250 300 350 Exposure Time (minutes)
Figure 5-2: Transmittance and reflectance of Ge3Se17 during exposure to 800 nm laser light. Each trace represents the exposure of an unexposed location beginning at time = 0. 99
0.7 GeSe4 I0 (mW) 1.01 3.60 0.6 10.1 38.8
0.5
0.4 Transmittance
0.3
0.2 0 100 200 300 400 500 600 700 800 900 1000 Exposure Time (minutes)
0.4 GeSe4 I0 (mW) 1.01 3.60 10.1 38.8
0.3 Reflectance
0.2 0 100 200 300 400 500 600 700 800 900 1000 Exposure Time (minutes)
Figure 5-3: Transmittance and reflectance of GeSe4 during exposure to 800 nm laser light. Each trace represents the exposure of an unexposed location beginning at time = 0. 100
0.7 GeSe3 I0 (mW) 0.956 0.6 3.66 9.98 36.6 0.5
0.4
Transmittance 0.3
0.2
0.1 0 200 400 600 800 1000 1200 Exposure Time (minutes)
0.4 GeSe3 I0 (mW) 0.956 3.66 9.98 36.6
0.3 Reflectance
0.2 0 200 400 600 800 1000 1200 Exposure Time (minutes)
Figure 5-4: Transmittance and reflectance of GeSe3 during exposure to 800 nm laser light. Each trace represents the exposure of an unexposed location beginning at time = 0. 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
0.5 GeSe9 I0 (mW) 52.6 0.4
0.3
0.2 Transmittance
0.1
0.0 0 0.5 1 1.5 2 2.5 Exposure Time (minutes)
Figure 5-5: Transmittance change of the GeSe9 sample at the highest laser power (52.6 mW).
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 35.9 103
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 distorted—a 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
0.5 Ge3Se17 I0 (mW) 57.9 0.4
0.3
0.2 Transmittance
0.1
0.0 0 1 2 3 4 5 6 7 Exposure Time (minutes)
Figure 5-6: Transmittance change of the Ge3Se17 sample at the highest laser power (57.9 mW).
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. 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 powers—they 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,
t Φ(t) = ∫ I(t)dt , (5-1) 0
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
N Φ ≈ − (t) ∑ I n (t n t n−1 ) , (5-2) n=1 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 samples—further 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
9.0 GeSe9
8.0
7.0 1 ε 6.0 I0 (mW) 0 1.52 5.0 3.29 8.53 28.1 52.6 4.0 0.01 0.1 1 10 100 1000 Fluence (J)
600 I0 (mW) GeSe9 0 500 1.52 3.29 8.53 400 28.1 52.6 ) 6 10
× 300 ( 2 ε 200
100
0 0.01 0.1 1 10 100 1000 Fluence (J)
Figure 5-7: The real and imaginary parts of the dielectric response of GeSe9 glass at 800 nm, 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 the highest-power curve is marked with an error bar typical of the error for all of the measurements. 109
9.0 Ge3Se17
8.0
7.0 1 ε I0 (mW) 6.0 0 0.441 0.917 3.51 5.0 9.88 18.9 35.9 57.9 4.0 0.01 0.1 1 10 100 1000 Fluence (J)
400 I0 (mW) Ge3Se17 0 350 0.441 0.917 300 3.51 9.88 250 18.9 )
6 35.9
10 57.9
× 200 ( 2 ε 150
100
50
0 0.01 0.1 1 10 100 1000 Fluence (J)
Figure 5-8: The real and imaginary parts of the dielectric response of Ge3Se17 glass at 800 nm, 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 the highest-power curve is marked with an error bar typical of the error for all of the measurements. 110
9.0 GeSe4
8.0
7.0 1 ε 6.0
I0 (mW) 0 5.0 1.01 3.60 10.1 38.8 4.0 0.01 0.1 1 10 100 1000 Fluence (J)
1000 I0 (mW) GeSe4 900 0 1.01 800 3.60 10.1 700 38.8
) 600 6 10
× 500 ( 2 ε 400 300 200 100 0 0.01 0.1 1 10 100 1000 Fluence (J)
Figure 5-9: The real and imaginary parts of the dielectric response of GeSe4 glass at 800 nm, calculated from the data in Figure 5-3. The gray × on the left side of the graph (labeled “0”) is the value determined by the Derivative Technique. The first point of the highest-power curve is marked with an error bar typical of the error for all of the measurements. 111
9.0 GeSe3
8.0
7.0 1 ε 6.0
I0 (mW) 0 5.0 0.956 3.66 9.98 36.6 4.0 0.01 0.1 1 10 100 1000 Fluence (J)
450 I0 (mW) GeSe3 400 0 0.956 350 3.66 9.98 300 36.6 ) 6 250 10 × (
2 200 ε 150
100
50
0 0.01 0.1 1 10 100 1000 Fluence (J)
Figure 5-10: The real and imaginary parts of the dielectric response of GeSe3 glass at 800 nm, calculated from the data in Figure 5-4. The gray × on the left side of the graph (labeled “0”) is the value determined by the Derivative Technique. The first point of the highest-power curve is marked with an error bar typical of the error for all of the measurements. 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 power—a 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 enough—by 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 data—probably 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
400 Sample [I0 (mW)] GeSe [3.29] 350 9 Ge3Se17 [3.51] GeSe4 [3.60] 300 GeSe3 [3.66]
250 ) 6 10
× 200 ( 2 ε 150
100
50
0 0.01 0.1 1 10 100 1000 Fluence (J)
Figure 5-11: Comparison of the change in the imaginary part of the dielectric response at 3.5 mW laser power. All four compositions are shown. Exact values are shown in the key.
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 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 intent—to provide a basis for reducing the data, and to permit discussion
of the intensity and composition dependence of the photodarkening. 116
400 Sample [I0 (mW)] GeSe [8.53] 350 9 Ge3Se17 [9.88] GeSe4 [10.1] 300 GeSe3 [9.98]
250 ) 6 10
× 200 ( 2 ε 150
100
50
0 0.01 0.1 1 10 100 1000 Fluence (J)
Figure 5-12: Comparison of the change in the imaginary part of the dielectric response at 10 mW laser power. All four compositions are shown. Exact values are shown in the key.
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. 117
400 I0 (mW) Ge Se 0.441 3 17 350 0.917 3.51 300 9.88 18.9 35.9 250 57.9 ) 6 10
× 200 ( 2 ε 150
100 II
50 I
0 0.01 0.1 1 10 100 1000 Fluence (J)
Figure 5-13: The imaginary part of the dielectric response of Ge3Se17 glass showing the two stages of photodarkening. The diagonal line (from top-left to bottom-right) divides the curves into two sections, which correspond with Stage I and Stage II darkening as labeled on the graph.
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 118
during the transition from the undarkened state to the darkened state the imaginary
dielectric response is
ε Φ) = ε + ∆ε ⋅ Φ ( 20 2 g( ) , (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
d g(Φ) = σ (1− g(Φ)) , (5-4) dΦ r
where σr is the inverse of the rate constant. With the boundary condition that g(0) = 0, the
solution is
Φ = − −σ Φ g( ) 1 exp( r ) . (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
180 Ge3Se17 [19 mW] First Order Model 160 Second Order Model
140 )
6 120 10 × ( 2
ε 100
80
60
40 0.01 0.1 1 10 Fluence (J)
Figure 5-14: Typical fit of the Stage I darkening process using First Order and Second Order models of the photodarkening kinetics.
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
d g(Φ) = (σ + β ⋅ g(Φ))(1− g(Φ)) , (5-6) dΦ r r
where βr is the linear change in the rate with the darkening. With the same boundary
condition as Equation 5-5, the solution is 120
1− exp(−sΦ) g(Φ) = . (5-7) bexp(−sΦ) +1
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
140 GeSe9 Ge3Se17 120 GeSe4 GeSe3
100 )
6 80 10 × ( 20
ε 60
40
20
0 0 10 20 30 40 50 60 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 Derivative Technique. The lines show linear fits to the data. For the GeSe9 and Ge3Se17 samples, the values 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 with fluence less than 0.1 J.
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 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
-5 2×10 —much 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
-5 presented in Figure 5-9 is reliable once the value of ε2 exceeds 2×10 .
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
1.2
1
0.8 /mW) 6 0.6 10 × ( 0 0.4 / dI 20 ε d 0.2
0
-0.2 0.1 0.15 0.2 0.25 Ge Concentration (Atomic Fraction)
Figure 5-16: The slope of the linear fits to the data of Figure 5-15 versus the composition of the glass. Error bars indicate the asymptotic standard error estimated by the curve fitting software.
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 124
160 GeSe9 Ge3Se17 140
120
100 ) 6 10
× 80 ( 2 ∆ε 60
40
20
0 0.1 1 10 100 Laser Power (mW)
Figure 5-17: The maximum change in the imaginary dielectric (∆ε2) observed during Stage I darkening. The lines indicate the best fits of a logarithmic relation to the data.
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,
∆ε = 2 (I) Alog10 (B I) , (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 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,
−1 1− g Φ(g) = ln , (5-9) s gb +1 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 to the data in Figure 5-17. Sample A (× 106) B (mW-1) GeSe9 37 ± 36 ± 1 Ge3Se17 43 ± 3 17 ± 6 126
2.0 GeSe9 Ge Se 1.8 3 17
1.6
1.4
1.2
(g) @ g = 0.5 (J) 1.0 Φ
0.8
Fluence, 0.6
0.4
0.2 0 10 20 30 40 50 60 Laser Power (mW)
Figure 5-18: The value of the fluence at which the Stage I darkening has reached 50% of its final value.
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. 127
250 GeSe9 Ge3Se17 ) -1 J
6 200 10 × ( Φ /d 2
ε 150
100
50 Initial Darkening Rate, d
0 0 10 20 30 40 50 60 Laser Power (mW)
Figure 5-19: The slope of the darkening with respect to the fluence (dε2/dΦ) at the beginning of the photodarkening experiments.
The other quantity of interest is the rate of the transition, which is the derivative
of Equation 5-3,
dε d g(Φ) 2 = ∆ε = ∆ε (σ + β ⋅ g(Φ))(1− g(Φ)) , (5-10) dΦ 2 dΦ 2 r r
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. 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-
145 photon absorption (2PA). 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
145 (3) -4 semiconductors predicts that χ should be proportional to (Eg) . 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
-4 be expected for a simple (Eg) 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
-4 the one on which the (Eg) 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 nonlinear—it 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 annealing—forming 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
120 Exposure [I (mW)] 0 GeSe9 115 First [3.21] Second [3.38] 110 105 100 ) 6 95 10 × (
2 90 ε 85 80 75 70 65 0.01 0.1 1 10 100 Fluence (J)
Figure 5-20: Permanent and transient photodarkening in GeSe9. The curve labeled “First” is from the first time that the spot was exposed. The laser was blocked for 7½ hours and then the spot was exposed for a second time for the “Second” curve, which is plotted with zero fluence at the start of the second exposure.
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 134
0.60 GeSe9
0.58
0.56
0.54 Transmittance 0.52
0.50
0.48 0 20 40 60 80 100 120 Time (m)
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 the transient portion of the darkening and its dark recovery.
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 recovery—occurring when the photodarkening light is off—is 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 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
220 Exposure [I0 (mW)] Ge Se First [19] 3 17 200 Second [3.6]
180
160 ) 6 10
× 140 ( 2 ε 120
100
80
60 0.01 0.1 1 10 100 Fluence (J)
Figure 5-22: Permanent and transient photodarkening in Ge3Se17 glass. The first exposure was at a power of 19 mW, and the re-exposure was at 3.6 mW.
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
148 the process. Frumar et al. 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 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 fluence—the exposure
history—of 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
260 Exposure [I (mW)] 0 Ge3Se17 240 First [19] Second [3.6] 220 First [3.5] 200 180 ) 6 160 10 × (
2 140 ε 120 100 80 60 40 0.01 0.1 1 10 100 Fluence (J)
Figure 5-23: Permanent changes occurring after the transient response during re-exposure of an already darkened spot in Ge3Se17 glass. The “Second” curve is plotted as a continuation of the “First [19 mW]” curve.
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. 139
1000
900
800 Exposure [I0 (mW)] First [3.7] 700 Second [10.5] 600 ) 6 10
× 500 ( 2 ε 400
300
200
100 GeSe4 0 0.01 0.1 1 10 100 Fluence (J)
Figure 5-24: Permanent and transient photodarkening in GeSe4 glass. The first exposure was at 3.7 mW and the second exposure was at 10.5 mW.
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 140
1000 Exposure [I0 (mW)] 900 First [3.7] Second [10.5] 800
700
600 ) 6 10
× 500 ( 2 ε 400
300
200
100 GeSe4 0 0.01 0.1 1 10 100 Fluence (J)
Figure 5-25: Re-exposure of a spot on the GeSe4 sample. The darkening continues along the Stage II curve, although the intensity is higher, and the experiment was stopped for two hours between the first and second exposures.
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. 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 quickly—within 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
d g(t) 1 1 = []G − g(t) − g(t) . (5-11) τ τ dt C D
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
− t g(t) = A1− exp , (5-12) τ
where
Gτ A = D , (5-13) τ +τ C D
and
1 1 1 = + . (5-14) τ τ τ C D
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:
ε = ε + ε Φ + ε 2 20 2P ( ) 2T (t) , (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 effect—it 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
10 As2S3 glass illuminated by a below-bandgap laser. 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 sample—the 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 GeSe4—exactly 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.
Kolobov’s 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
(1)
(2)
KEY: Electron Hole Normal Bond Dynamical Bond Chalcogen Atom
(3) Lone-Pair Orbital
Figure 5-26: Dynamical bond formation in chalcogenide glass. (1) Two photons excite two lone-pair electrons forming (2) two half-filled lone-pair orbitals. (3) The orbitals overlap 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
0 + ν → ∗ → ( 0 − 0 ) 2C2 2h 2C2 C3 C3 , (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:
2C 0 (original) 2 0 − 0 → 0 (C3 C3 ) 2C2 (new) . (5-17) − + + C1 C3 (VAP) 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 Kolobov’s model as it pertains to amorphous selenium, but EXAFS measurements have also been used to identify the formation of dynamical
151 bonds during illumination in amorphous As2Se3. 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
2 hν
Photo-excitation New Structure II Original Glass Dynamical Stage II Structure Bond I III Defects (VAPs) Transient State
Transient Permanent Photodarkening Photodarkening
Figure 5-27: Diagram of the photodarkening process in chalcogenide glass. Illumination causes 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 in optical properties. If, on the other hand, the dynamical bond decays back to the original structure, or to an intermediate, but transient, state, the optical properties will only display transient changes.
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 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. CHAPTER 6 RAMAN 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
Ge3Se17 SiO2 Intensity (arb.)
-200 -300 -400 -500 -600 -700 Raman Shift (cm-1)
Figure 6-1: Typical Raman spectra of germanium-selenium glass and silica. The sharp features in the Ge3Se17 spectra correspond with molecule-like short-range order.
156 157
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
c GeSe4/2 tetrahedra. The peak next to it is the A1 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
composition—indicating 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
1.00 GeSe9 0.98
0.96 ) 0 0.94
0.92
0.90
0.88
0.86 Transmission (relative to T 0.84
0.82
0.80 0 5 10 15 20 25 30 35 40 45 50 Time (m)
Figure 6-2: Transmission change of GeSe9 during Raman measurements. The breaks in the curve correspond with the collection of Raman spectra.
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 manner—even 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. 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
-1 scaled by the height of the GeSe4/2 (195 cm ) 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
GeSe9 Before Exposure After Exposure Intensity (arb.)
-180 -200 -220 -240 -260 -280 -300 -320 Raman Shift (cm-1)
Figure 6-3: Raman spectra from before and after darkening for GeSe9. 160
Ge3Se17 Before Exposure After Exposure Intensity (arb.)
-180 -200 -220 -240 -260 -280 -300 -320 Raman Shift (cm-1)
Figure 6-4: Raman spectra from before and after darkening for Ge3Se17.
GeSe4 Before Exposure After Exposure Intensity (arb.)
-180 -200 -220 -240 -260 -280 -300 -320 Raman Shift (cm-1)
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
4 − hcν µ −ν I(µ +ν ) exp = . (6-1) µ +ν µ −ν k BT I( )
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 added—the 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 = +ξ (ν ) , (6-2) ν ν T ( ) Tr ( ) 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
Temperature 340 Stokes anti-Stokes
320
300
280 Raman Intensity (arb.) Calculated Temperature (K)
260
160 180 200 220 240 260 280 300 320 Raman Shift (cm-1)
Figure 6-6: Typical Stokes and anti-Stokes spectrum, and the temperature values calculated from this data.
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 powers—1, 10,
and 75 mW—and the sample temperature at each laser power was calculated on a point-
-1 by-point basis. The raw temperature, Tr(ν), was calculated every 1 cm 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 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
temperature—especially 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 samples—despite 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 laser light. The peak intensity of the light is indicated in the row above the calculated temperature values. All of the temperatures were calibrated with a temperature response function 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 ±2.8 Ge3Se17 296 ±1.7 297 ±3.3 297 ±2.2 GeSe4 302 ±4.1 311 ±2.9 304 ±3.0 GeSe3 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. 167
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 model—indicating 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 photodarkening—those 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
47,49 crystallization of GeSe2. 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 170 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 motion—a 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.
Kolobov’s 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. CHAPTER 7 CONCLUSIONS
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.
172 173
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 compositions—the 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 process—creation 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 recovers—indicating 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 Kolobov’s 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 theories—the 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 °C—an 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. APPENDIX POLISHING 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:
180 181
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. REFERENCES
1. Z. U. Borisova, Glassy Semiconductors (Plenum Press, New York, 1981).
2. N. F. Mott and E. A. Davis, Electronic Processes in Non-Crystalline Materials, 2nd ed. (Clarendon Press, Oxford, 1979).
3. H. Tichá, L. Tichý, and V. Smrcka, “The temperature dependence of the optical gap in quasibinary chalcogenide glasses and their far infrared spectra,” Mater. Lett. 20, 189 (1994).
4. H. Fritzsche, “Electronic properties of amorphous semiconductors,” in Amorphous and Liquid Semiconductors, edited by J. Tauc (Plenum, New York, 1974), pp. 221.
5. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109 (5), 1492 (1958).
6. P. Nagels, “Electronic transport in amorphous semiconductors,” in Amorphous Semiconductors, edited by M. H. Brodsky (Springer-Verlag, Berlin, 1985), Vol. 36, pp. 113.
7. M. Kastner, “Bonding bands, lone-pair bands, and impurity states in chalcogenide semiconductors,” Phys. Rev. Lett. 28 (6), 355 (1972).
8. G. A. N. Connell, “Optical properties of amorphous semiconductors,” in Amorphous Semiconductors, edited by M. H. Brodsky (Springer-Verlag, Berlin, 1985), Vol. 36, pp. 73.
9. H. Hamanaka, K. Tanaka, and S. Iizima, “Reversible photostructural change in melt-quenched As2S3 glass,” Solid State Commun. 23, 63 (1977).
10. K. Tanaka, “Mechanisms of photodarkening in amorphous chalcogenides,” J. Non-Cryst. Solids 59 & 60, 925 (1983).
11. J. Z. Liu and P. C. Taylor, “Absence of photodarkening in bulk, glassy As2S3 and As2Se3 alloyed with copper,” Phys. Rev. Lett. 59 (17), 1938 (1987).
12. J. Z. Liu and P. C. Taylor, “Effect of Cu alloying on metastable photoinduced absorption in Cux(As0.4Se0.6)1-x and Cux(As0.4S0.6)1-x glasses,” Phys. Rev. B 41 (5), 3163 (1990).
183 184
13. J. H. Simmons and K. S. Potter, Optical Materials (Academic Press, San Diego, Calif. ; London, 1999).
14. H. Nasu and J. D. Mackenzie, “Nonlinear optical properties of glasses and glass- or gel-based composites,” Opt. Eng. 26 (2), 102 (1987).
15. E. M. Vogel, M. J. Weber, and D. M. Krol, “Nonlinear optical phenomena in glass,” Phys. Chem. Glasses 32 (6), 231 (1991).
16. M. Asobe, T. Kanamori, K. Naganuma, H. Itoh, and T. Kaino, “Third-order nonlinear spectroscopy in As2S3 chalcogenide glass fibers,” J. Appl. Phys. 77 (11), 5518 (1995).
17. R. R. Rojo, “Nonresonant nonlinear optical response of chalcogenide thin films to picosecond pulses,” in Second Iberoamerican Meeting on Optics, edited by D. Malacara, S. E. Acosta, R. R. Vera, Z. Malcara, and A. Morales (1996), pp. 397.
18. V. K. Tikhomirov, P. Lievens, N. Qamhieh, and G. J. Adriaenssens, “Detection of optical non-linearities in amorphous semiconductors by caustic crossing in an intensity-modulated laser beam,” J. Non-Cryst. Solids 198-200, 119 (1996).
19. F. Smektala, C. Quemard, L. L. Neindre, J. Lucas, A. Barthélémy, and C. D. Angelis, “Chalcogenide glasses with large non-linear refractive indices,” J. Non- Cryst. Solids 239, 139 (198).
20. H. Nasu, K. i. Kubodera, M. Kobayashi, M. Nakamura, and K. Kamiya, “Third- harmonic generation from some chalcogenide glasses,” J. Am. Ceram. Soc. 73 (6), 1794 (1990).
21. H. Nasu, J. Matsuoka, and K. Kamiya, “Second- and third-order optical non- linearity of homogeneous glasses,” J. Non-Cryst. Solids 178, 23 (1994).
22. T. Cardinal, K. A. Richardson, H. Shim, A. Schulte, R. Beatty, K. LeFoulgoc, C. Meneghini, J. F. Viens, and A. Villeneuve, “Non-linear optical properties of chalcogenide glasses in the system As-S-Se,” J. Non-Cryst. Solids 256&257, 353 (1999).
23. M. E. Lines, “The search for very low loss fiber-optic materials,” Science 226, 663 (1984).
24. P. Klocek, M. Roth, and R. D. Rock, “Chalcogenide glass optical fibers and image bundles: properties and applications,” Opt. Eng. 26 (2), 88 (1987).
25. C. Blanchetière, K. LeFoulgoc, H. L. Ma, X. H. Zhang, and J. Lucas, “Tellurium halide glass fibers: preparation and applications,” J. Non-Cryst. Solids 184, 200 (1995). 185
26. L. Le Neindre, F. Smektala, K. LeFoulgoc, X. H. Zhang, and J. Lucas, “Tellurium halide optical fibers,” J. Non-Cryst. Solids 242, 99 (1998).
27. B. Bendow, H. Rast, and O. H. El-Bayoumi, “Infrared fibers: an overview of prospective materials, fabrication methods, and applications,” Opt. Eng. 24 (6), 1072 (1985).
28. K. Tanaka, “Photoinduced structural changes in chalcogenide glasses,” Reviews of Solid State Sci. 4 (2 & 3), 511 (1990).
29. G. Pfeiffer, M. A. Paesler, and S. C. Agarwal, “Reversible photodarkening of amorphous arsenic chalcogens,” J. Non-Cryst. Solids 130, 111 (1991).
30. L. Tichy, H. Ticha, P. Nagels, and R. Callaerts, “Photoinduced optical changes in amorphous Se and Ge-Se films,” J. Non-Cryst. Solids 240, 177 (1998).
31. V. M. Lyubin and V. K. Tikhomirov, “Novel photo-induced effects in chalcogenide glasses,” J. Non-Cryst. Solids 135, 37 (1991).
32. K. Oe, Y. Toyoshima, and H. Nagai, “A reversible optical transistion in Se-Ge and P-Se-Ge glasses,” J. Non-Cryst. Solids 20, 405 (1976).
33. K. Tanaka and H. Hisakuni, “Photoinduced phenomena in As2S3 glass under sub- bandgap excitation,” J. Non-Cryst. Solids 198-200, 714 (1996).
34. S. Rajagopalan, B. Singh, P. K. Bhat, D. K. Pandya, and K. L. Chopra, “Photo- induced optical effects in obliquely deposited amorphous Se-Ge films,” J. Appl. Phys. 50 (1), 489 (1979).
35. M. Okuda, T. T. Nang, and T. Matsushita, “Photo-induced absorption changes in selenium-based chalcogenide glass films,” Thin Solid Films 58, 403 (1979).
36. E. Márquez, A. M. Bernal-Oliva, J. M. González-Leal, T. Prieto-Alcón, and R. Jiménez-Garay, “On the irreversible photo-bleaching phenomenon in obliquely- evaporated GeS2 glass films,” J. Non-Cryst. Solids 222, 250 (1997).
37. V. K. Tikhomirov and S. R. Elliott, “The anisotropic photorefractive effect in bulk As2S3 glass induced by polarized subgap laser light,” J. Phys.: Condens. Matter 7, 1737 (1995).
38. V. Boev, E. Sleeckx, M. Mitkova, P. Markovsky, P. Nagles, and K. Zlatanova, “Holographic investigations of photoinduced changes in PECVD Ge-Se thin films,” Vacuum 47 (10), 1211 (1996).
39. K. Tanaka, “Light-induced anisotropy in amorphous chalcogenides,” Science 277, 1786 (1997). 186
40. J. Hajtó, I. Jánossy, and G. Forgács, “Laser-induced optical anistropy in self- supporting amorpuhous GeSe2 films,” J. Phys. C.: Solid State Phys. 15, 6293 (1982).
41. V. K. Tikhomirov and S. R. Elliott, “Metastable optical anisotropy in chalcogenide glasses induced by unpolarized light,” Phys. Rev. B 49 (24), 17476 (1994).
42. V. M. Lyubin and V. K. Tikhomirov, “Photoinduced optical anisotropy in the chalcogenide glass As2S3,” JETP Lett. 51 (10), 587 (1990).
43. V. M. Lyubin and V. K. Tikhomirov, “Photodarkening and photoinduced anisotropy in chalcogenide vitreous semiconductor films,” J. Non-Cryst. Solids 114, 133 (1989).
44. T. Kósa and I. Jánossy, “Kinetics of optical reorientation in amorphous GeSe2 films,” Philos. Mag. B 64 (3), 355 (1991).
45. T. Kósa and I. Jánossy, “On the kinetics of the reorientation of light-induced anisotropy in a-GeSe2 films,” J. Non-Cryst. Solids 137&138 (981) (1991).
46. J. E. Griffiths, G. P. Espinosa, J. P. Remeika, and J. C. Phillips, “Reversible reconstruction and crystallization of GeSe2 glass,” Solid State Commun. 40, 1077 (1981).
47. J. E. Griffiths, G. P. Espinosa, J. P. Remeika, and J. C. Phillips, “Reversible quasicrystallization in GeSe2 glass,” Phys. Rev. B 25 (2), 1272 (1982).
48. J. E. Griffiths, G. P. Espinosa, J. C. Phillips, and J. P. Remeika, “Raman spectra and athermal laser annealing of Ge(SxSe1-x)2 glasses,” Phys. Rev. B 28 (8), 4444 (1983).
49. E. Haro, Z. S. Xu, J. F. Morhange, M. Balkanski, G. P. Espinosa, and J. C. Phillips, “Laser-induced glass-crystallization phenomena of GeSe2 investigated by light scattering,” Phys. Rev. B 32 (2), 969 (1985).
50. S. Sugai, “Stochastic random network model in Ge and Si chalcogenide glasses,” Phys. Rev. B 35 (3), 1345 (1987).
51. S. Sugai, “Two-directional photinduced crystallization in GeSe2 and SiSe2 glasses,” Phys. Rev. Lett. 57 (4), 456 (1986).
52. M. Balkanski, “Structural transformations in glassy GeSe2 induced by laser irradiation,” in Physics of Disordered Materials, edited by D. Adler, H. Fritzsche, and S. R. Ovshinsky (Plenum, New York, 1985), pp. 505. 187
53. K. Tanaka, “Physics and applications of photodoping in chalcogenide glass,” J. Non-Cryst. Solids 137&138, 1021 (1991).
54. S. R. Elliott, “Photodissolution fo metals in chalcogenide glasses: a unified mechanism,” J. Non-Cryst. Solids 137&138, 1031 (1991).
55. A. V. Kolobov, “Photo-induced atomic processes in vitreous chalcogenides,” J. Non-Cryst. Solids 164-166, 1159 (1993).
56. H. Hamanaka, K. Tanaka, and S. Iizima, “Reversible photostructural change in melt-quenched GeS2 glass,” Solid State Commun. 33, 355 (1980).
57. K. Tanaka, “Photo-induced phenomena in amorphous semiconductors,” in Fundamental physics of amorphous semiconductors : proceedings of the Kyoto Summer Institute, Kyoto, Japan, September 8-11, 1980, edited by F. Yonezawa (Springer-Verlag, New York, 1981), Vol. 25, pp. 104.
58. P. Krecmer, A. M. Moulin, R. J. Stephenson, T. Rayment, M. E. Welland, and S. R. Elliott, “Reversible noncontraction and dilation in a solid induced by polarized light.,” Science 277, 1799 (1997).
59. E. Skordeva, K. Christova, M. Tzolov, and Z. Dimitrova, “Photoinduced changes of mechanical stress in amorphous Ge-As-S(Se) film/Si substrate systems,” Appl. Phys. A 66, 103 (1998).
60. H. Hisakuni and K. Tanaka, “Optical microfabrication of chalcogenide glasses,” Science 270, 974 (1995).
61. E. W. VanStryland, Y. Y. Wu, D. J. Hagan, M. J. Soileau, and K. Mansour, “Optical limiting with semiconductors,” J. Opt. Soc. Am. B 5 (9), 1980 (1988).
62. T. Miyashita and T. Manabe, “Infrared optical fibers,” IEEE J. Quantum Electron. QE-18 (10), 1432 (1982).
63. J. S. Sanghera and I. D. Aggarwal, “Active and passive chalcogenide glass optical fibers for IR applications: a review,” J. Non-Cryst. Solids 257, 6 (1999).
64. T. Kanamori, Y. Terunuma, S. Takahashi, and T. Miyashita, “Chalcogenide glass fibers for mid-infrared transmission,” J. Lightwave Tech. LT-2 (5), 607 (1984).
65. T. Katsuyama, S. Satoh, and H. Matsumura, “Scattering loss characteristics of selenide-based chalcogenide glass optical fibers,” J. Appl. Phys. 71 (9), 4132 (1992).
66. J. Kobelke, J. Kirchhof, M. Scheffler, and A. Schwuchow, “Chalcogenide glass single mode fibres - preparation and properties,” J. Non-Cryst. Solids 256&257, 226 (1999). 188
67. S. Ramachandran and S. G. Bishop, “Excitation of Er3+ emission by host glass absorption in sputtered films of Er-doped Ge10As40Se25S25 glass,” Appl. Phys. Lett. 73 (22), 3196 (1998).
68. Y. Guimond, J.-L. Adam, A.-M. Jurdyc, H. L. Ma, J. Mugnier, and B. Jacquier, “Optical properties of antimony-stabilised sulphide glasses doped with Dy3+ and Er3+ ions,” J. Non-Cryst. Solids 256&257, 378 (1999).
69. A. M. Jurdyc, C. Garapon, B. Jacquier, Y. Meresse, G. Fonteneau, and J. L. Adam, “Laser spectroscopy of Pr3+ doped germanium sulfide based glasses,” J. Non-Cryst. Solids 213&214, 231 (1997).
70. V. K. Tikhomirov, K. Iakoubovskii, P. W. Hertogen, and G. J. Adrianssens, “Visible luminescence from Pr-doped sulfide glasses,” Appl. Phys. Lett. 71 (19), 2740 (1997).
71. A. Belykh, L. Glebov, C. Lerminiaux, S. Lunter, M. Mikhailov, A. Plyukhin, M. Prassas, and A. Przhevushii, “Spectral and luminescence properties of neodymium in chalcogenide glasses,” J. Non-Cryst. Solids 213&214, 238 (1997).
72. L. S. Griscom, J.-L. Adam, and K. Binnemans, “Optical study of halide modified sulfide glasses containing neodymium ions,” J. Non-Cryst. Solids 256&257, 383 (1999).
73. Y. B. Shin and J. Heo, “Mid-infrared emissions and energy transfer in Ge-Ga-S glasses doped with Dy3+,” J. Non-Cryst. Solids 256&257, 260 (1999).
74. B. Cole, L. B. Shaw, P. C. Pureza, R. Mossadegh, J. S. Sanghera, and I. D. Aggarwal, “Rare-earth doped selenide glasses and fibers for active applications in the near and mid-IR,” J. Non-Cryst. Solids 256&257, 253 (1999).
75. K. Shiramine, H. Hisakuni, and K. Tanaka, “Photoinduced Bragg reflector in As2S3 glass,” Appl. Phys. Lett. 64 (14), 1771 (1994).
76. K. Tanaka, N. Toyosawa, and H. Hisakuni, “Photoinduced Bragg gratings in As2S3 optical fibers,” Optics Lett. 20 (19), 1976 (1995).
77. A. Zakery, P. J. S. Ewen, and A. E. Owen, “Photodarkening of As-S films and its application in grating fabrication,” J. Non-Cryst. Solids 189-200, 769 (1996).
78. V. K. Tikhomirov, G. J. Adriaenssens, and A. J. Faber, “Photoinduced anisotropy and photorefraction in Pr-doped Ge-Ga-S glasses,” J. Non-Cryst. Solids 213&214, 174 (1997).
79. V. K. Tikhomirov, “Photoinduced effects in undoped and rare-earth doped chalcogenide glasses: review,” J. Non-Cryst. Solids 256-257, 328 (1999). 189
80. Lucent Technologies, “Lucent Technologies teams with Tellium to offer optical switching products for advanced data networks,” (Lucent Technologies, 1999 URL: http://www.lucent.com/press/1299/991214.nsa.html).
81. M. Asobe, T. Kanamori, and K. i. Kubodera, “Applications of highly nonlinear chalcogenide glass fibers in ultrafast all-optical switches,” IEEE J. Quantum Electron. 29 (8), 2325 (1993).
82. M. Asobe, T. Ohara, I. Yokohama, and T. Kaino, “Low pwer all-optical switching in a nonlinear optical loop mirror using chalcogenide glass fibre,” Electron. Lett. 32 (15), 1396 (1996).
83. K. Uchiyama, T. Morioka, M. Saruwatari, M. Asobe, and T. Ohara, “Error free all-optical demultiplexing using a chalcogenide glass fibre based nonlinear optical loop mirror,” Electron. Lett. 32 (17), 1601 (1996).
84. A. M. Andriesh, “Properties of chalcogenide glasses for optical waveguides,” J. Non-Cryst. Solids 77&78, 1219 (1985).
85. S. Ramachandran and S. G. Bishop, “Low loss photoinduced waveguides in rapid thermally annealed films of chalcogenide glasses,” Appl. Phys. Lett. 74 (1), 13 (1999).
86. A. Kikineshy, “Structural phototransformations and optical recording in Se/As2S3 multilayer films,” Opt. Eng. 34 (4), 1040 (1995).
87. R. Bowling Barnes and M. Czerny, “Concerning the reflection power of metals in thin layers for the infrared,” Phys. Rev. 38, 338 (1931).
88. W. Nazarewicz, P. Rolland, E. da Silva, and M. Balkanski, “Abac chart for gast calculation of the absorption and reflection coefficients,” Appl. Optics 1 (3), 369 (1962).
89. E. Hecht, Optics, second ed. (Addison-Weley, Reading, MA, 1988).
90. J. L. Hartke and P. J. Regensburger, “Electronic states in vitreous selenium,” Phys. Rev. 139 (3A), A970 (1965).
91. Z. El Gharras, A. Bourahla, and C. Vautier, “Role of photoinduced defects in amorphous GexSe1-x photoconductivity,” J. Non-Cryst. Solids 155, 171 (1993).
92. G. Lucovsky and T. M. Hayes, “Short-range order in amorphous semiconductors,” in Amorphous Semiconductors, edited by M. H. Brodsky (Springer-Verlag, Berlin, 1985), Vol. 36, pp. 215.
93. J. C. Phillips, “Topology of covalent non-crystalline solids I: short-range order in chalcogenide alloys,” J. Non-Cryst. Solids 34, 153 (1979). 190
94. J. C. Phillips, “Topology of covalent non-crystalline solids II: medium-range order in chalcogenide alloys and a-Si(Ge),” J. Non-Cryst. Solids 43, 37 (1981).
95. R. C. Keezer and M. W. Bailey, “The structure of liquid selenium from viscosity measurements,” Mater. Res. Bull. 2, 185 (1967).
96. G. Lucovsky, A. Mooradian, W. Taylor, G. B. Wright, and R. C. Keezer, “Identification of the fundamental vibrational modes of trigonal, α-monoclinic and amorphous selenium,” Solid State Commun. 5, 113 (1967).
97. R. Kaplow, T. A. Rowe, and B. L. Averbach, “Atomic arrangement in vitreous selenium,” Phys. Rev. 168 (3), 1068 (1968).
98. M. Misawa and K. Suzuki, “Structure of chain molecule in liquid selenium by time-of-flight pulsed neutron diffraction,” Trans. Japan Inst. Metals 18, 427 (1977).
99. A. Eisenberg and A. V. Tobolsky, “Equilibrium polymerization of selenium,” J. Polymer Sci. 46, 19 (1960).
100. R. M. Martin, G. Lucovsky, and K. Helliwell, “Intermolecular bonding and lattice dynamics of Se and Te,” Phys. Rev. B 13 (4), 1383 (1976).
101. M. Misawa and K. Suzuki, “Ring-chain transition in liquid selenium by a disordered chain model,” J. Physical Soc. Jpn. 44 (5), 1612 (1978).
102. W. Burkhardt, A. Feltz, and P. Bussemer, “The influence of structure of diffferent arsenic chalcogenide glasses on the dispersion parameters of a Sellmeier and a Lorentz-Lorenz relation,” J. Non-Cryst. Solids 89, 273 (1987).
103. U. Senapati, K. Firstenberg, and A. K. Varshneya, “Structure-property inter- relations in chalcogenide glasses and their practical implications,” J. Non-Cryst. Solids 222, 153 (1997).
104. P. Tronc, M. Bensoussan, and A. Brenac, “Optical-absorption edge and Raman scattering in GexSe1-x glasses,” Phys. Rev. B 8 (12), 5947 (1973).
105. R. J. Nemanich, S. A. Solin, and G. Lucovsky, “First evidence for vibrational excitations of large atomic clusters in amorphous semiconductors,” Solid State Commun. 21, 273 (1977).
106. P. M. Bridenbaugh, G. P. Espinosa, J. E. Griffiths, J. C. Phillips, and J. P. Remeika, “Microscopic origin of the companion A1 Raman line in glassy Ge(S,Se)2,” Phys. Rev. B 20 (10), 4140 (1979). 191
107. K. Murase, T. Fukunaga, Y. Tanaka, K. Yakashiji, and I. Yunoki, “Investication of large molecular fragments in glassy Ge1-x(Se, or S)x,” Physica B 117B&118B, 962 (1983).
108. W. J. Bresser, P. Boolchand, P. Suranyi, and J. P. de Neufville, “Direct evidence for intrinsically broken chemical ordering in melt-quenched glasses,” Phys. Rev. Lett. 46 (26), 1689 (1981).
109. P. Boolchand, J. Grothaus, W. J. Bresser, and P. Suranyi, “Structural origin of broken chemical order in a GeSe2 glass,” Phys. Rev. B 25 (4), 2975 (1982).
110. R. J. Nemanich, F. L. Galeener, J. C. Mikkelsen, Jr., G. A. N. Connell, G. Etherington, A. C. Wright, and R. N. Sinclair, “Configurations of a chemically ordered continuous random network to describe the structure of GeSe2 glass,” Physica B 117B&118B, 959 (1983).
111. O. Matsuda, K. Inoue, and K. Murase, “Resonant Raman study of crystalline GeSe2 in relation to amorphous states,” Solid State Commun. 75 (4), 303 (1990).
112. P. H. Fuoss and A. Fischer-Colbrie, “Structure of a-GeSe2 from X-ray scattering measurements,” Phys. Rev. B 38 (3), 1875 (1988).
113. A. Fischer-Colbrie and P. H. Fuoss, “X-ray scattering studies of intermediate- range order in amorphous GeSe2,” J. Non-Cryst. Solids 126, 1 (1990).
114. R. L. Cappelletti, M. Cobb, D. A. Drabold, and W. A. Kamitakahara, “Neutron scattering and ab initio molecular-dynamics study of vibrations in glassy GeSe2,” Phys. Rev. B 52 (13), 9133 (1995).
115. A. M. Efimov, “The IR spectra of non-oxide glasses of various types: crucial differences and their origin,” J. Non-Cryst. Solids 213&214, 205 (1997).
116. Y. Nagata, S. Kokai, O. Uemura, and Y. Kameda, “Short-range order in amorphous Ge(Se1-xSx)2,” J. Non-Cryst. Solids 169, 104 (1994).
117. J. M. Saiter, A. Assou, J. Grenet, and C. Vautier, “Relaxation processes and structural models in glassy chalcogenide materials: application to the Se1-xGex alloys,” Philos. Mag. B 64 (1), 33 (1991).
118. P. Tronc, “Medium-range order and cohesive energy in GexSe1-x glasses,” J. Phys. France 51, 675 (1990).
119. A. Boukenter and E. Duval, “Comparison of inelastic light and neutron scattering in Se1-xGex glasses: structure and light-vibration coupling coefficient frequency dependence,” Philos. Mag. B 77 (2), 557 (1998). 192
120. P. Armand, A. Ibanez, Q. Ma, D. Raoux, and E. Philippot, “Structural characterization of germanium selenide glasses by differential anomalous X-ray scattering,” J. Non-Cryst. Solids 167, 37 (1993).
121. N. Ramesh Rao, P. S. R. Krishna, S. Basu, B. A. Dasannacharya, K. S. Sangunni, and E. S. R. Gopal, “Structural correlations in GexSe1-x glasses - a neutron diffraction study,” J. Non-Cryst. Solids 240, 221 (1998).
122. L. Le Neindre, “Optimisation de fibres optiques double indice pour la transmission dans le domaine 3 - 13 µm et leurs applications comme capteur chimique ou de temperature,” Doctoral Dissertation, University of Rennes I, 1997.
123. S. A. Self, “Focusing of spherical Gaussian beams,” Appl. Optics 22 (5), 658 (1983).
124. National Instruments, LabVIEW (National Instruments, 1996 URL: http://www.ni.com/labview/).
125. Stichting Mathematisch Centrum, Python (Stichting Mathematisch Centrum, Amsterdam, 1995 URL: http://www.python.org/).
126. C. Kittel, Introduction to Solid State Physics, 7th ed. (John Wiley & Sons, New York, 1996).
127. T. Ohsaka, “Infrared spectra of glassy Se containing small amounts of S, Te, As, or Ge,” J. Non-Cryst. Solids 17, 121 (1975).
128. K. J. Siemsen and H. D. Riccius, “Multiphonon processes in amorphous selenium,” J. Phys. Chem. Solids 30, 1897 (1969).
129. F. Urbach, “The long-wavelength edge of photographic sensitivity and the electronic absorption of solids,” Phys. Rev. 92 (5), 1324 (1953).
130. J. Szczyrbowski, “The exponential shape of the optical absorption edge tail,” Phys. Status Solidi (b) 105, 515 (1981).
131. J. D. Dow and D. Redfield, “Toward a unified theory of Urbach's rule and exponential absorption edges,” Phys. Rev. B 5 (2), 594 (1972).
132. D. J. Dunstan, “Evidence for a common origin of the Urbach tails in amorphous and crystalline semiconductors,” J. Phys. C: Solid State Phys. 30, L419 (1982).
133. T. Innami, T. Miyazaki, and S. Adachi, “Opical constants of amorphous Se,” J. Appl. Phys 86 (3), 1382 (1999).
134. H. Oheda, “The exponential absorption edge in amorphous Ge-Se compounds,” Jpn. J. Appl. Phys. 18 (10), 1973 (1979). 193
135. L. G. Aio, A. M. Efimov, and V. F. Kokorina, “Refractive index of chalcogenide glasses over a wide range of compositions,” J. Non-Cryst. Solids 27, 299 (1978).
136. S. H. Wemple and M. DiDomenico, Jr., “Optical dispersion and the structure of solids,” Phys. Rev. Lett. 23 (20), 1156 (1969).
137. S. H. Wemple, “Refractive-index behavior of amorphous semiconductors and glasses,” Phys. Rev. B 7 (8), 3767 (1973).
138. R. S. Caldwell and H. Y. Fan, “Optical properties of tellurium and selenium,” Phys. Rev. 114 (3), 664 (1959).
139. P. Klocek and L. Colombo, “Index of refraction, dispersion, bandgap, and light scattering in GeSe and GeSbSe glasses,” J. Non-Cryst. Solids 93, 1 (1987).
140. J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15, 627 (1966).
141. G. E. Jellison, Jr. and F. A. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69 (3), 371 (1996).
142. P. Nagels, E. Sleeckx, R. Callaerts, E. Márquez, J. M. González, and A. M. Bernal-Oliva, “Optical properties of amorphous Se films prepared by PECVD,” Solid State Commun. 102 (7), 539 (1997).
143. M. F. Kotkata, K. M. Kandil, and M. L. Thèye, “Optical studies of disorder and defects in amorphous GexSe1-x films as a function of composition,” J. Non- Cryst. Solids 164-166, 1259 (1993).
144. H. Adachi and K. C. Kao, “Dispersive optical constants of amorphous Se1-xTex films,” J. Appl. Phys. 51 (12), 6326 (1980).
145. M. Sheik-Bahae, D. C. Hutchings, D. J. Hagan, and E. W. Van Stryland, “Dispersion of bound electronic nonlinear refraction in solids,” IEEE J. Quantum Electron. 27 (6), 1296 (1991).
146. S. Ducharme, J. Hautala, and P. C. Taylor, “Photodarkening profiles and kinetics in chalcogenide glasses,” Phys. Rev. B 41 (17), 12250 (1990).
147. S. R. Elliott and K. Shimakawa, “Model for bond-breaking mechanisms in amorphous arsenic chalcogenides leading to light-induced electron-spin resonance,” Phys. Rev. B 42 (16), 9766 (1990).
148. M. Frumar, P. Firth, and A. E. Owen, “Reversible photodarkening and the structural changes in As2S3 thin films,” Philos. Mag. B 50 (4), 463 (1984). 194
149. A. V. Kolobov, H. Oyanagi, K. Tanaka, and K. Tanaka, “Structural study of amorphous selenium by in situ EXAFS: observation of photoinduced bond alternation,” Phys. Rev. B 55 (2), 726 (1997).
150. A. V. Kolobov, H. Oyanagi, K. Tanaka, and K. Tanaka, “Photostructural changes in amorphous selenium: an in situ EXAFS study at low temperature,” J. Non- Cryst. Solids 198-200, 709 (1996).
151. A. V. Kolobov, H. Oyanagi, A. Roy, and K. Tanaka, “Role of lone-pair electrons in reversible photostructural changes in amorphous chalcogenides,” J. Non-Cryst. Solids 227-230, 710 (1998).
152. H. Jain, S. Krishnaswami, A. C. Miller, P. Krecmer, S. R. Elliott, and M. Vlcek, “In situ high-resolution X-ray photoelectron spectroscopy of light-induced changes in As-Se glasses,” J. Non-Cryst. Solids in publication (2000).
153. D. K. Biegelsen and R. A. Street, “Photoinduced defects in chalcogenide glasses,” Phys. Rev. Lett. 44 (12), 803 (1980).
154. G. Pfeiffer and M. A. Paesler, “Identification of IRO structures in photodarkening: a high pressure study of As2S3,” J. Non-Cryst. Solids 114, 130 (1989).
155. M. Malyj and J. E. Griffiths, “Stokes/anti-Stokes Raman vibrational temperatures: reference materials, standard lamps, and spectrophotometric calibrations,” Appl. Spectrosc. 37 (4), 315 (1983).
156. V. K. Malinovsky, “Excitation relaxation processes in amorphous and vitreous materials,” J. Non-Cryst. Solids 90, 37 (1987).
157. K. Kimura, H. Hakata, K. Murayama, and N. T, “Interrelation between glass transition and reversible photostructural change in a-As2S3,” Solid State Commun. 40, 551 (1981).
158. V. L. Averianov, A. V. Kolobov, B. T. Kolomiets, and V. M. Lyubin, “Thermal and optical bleaching in darkened films of chalcogenide vitreous semiconductors,” Phys. Status Solidi (a) 57, 81 (1980).
159. S. R. Elliott, “A unified model for reversible photostructural effects in chalcogenide glasses,” J. Non-Cryst. Solids 81, 71 (1986).
160. M. Frumar, A. P. Firth, and A. E. Owen, “A model for photostructural changes in the amorphous As-S system,” J. Non-Cryst. Solids 59&60, 921 (1983).
161. M. Frumar, M. Vlcek, Z. Cernosek, Z. Polák, and T. Wágner, “Photoinduced changes of the structure and physical properties of amorphous chalcogenides,” J. Non-Cryst. Solids 213&214, 215 (1997). 195
162. L. F. Gladden, S. R. Elliott, and G. N. Greaves, “Photostructural changes in bulk chalcogenide glasses: an EXAFS study,” J. Non-Cryst. Solids` 106, 189 (1988).
163. R. A. Street, “Non-radiative recombination in chalcogenide glasses,” Solid State Commun. 24, 363 (1977).
164. K. Tanaka, “Photo-induced dynamical changes in amorphous As2S3 films,” Solid State Commun. 34, 201 (1980). 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.
196