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Q NBS SPECIAL PUBLICATION 697

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

OM85

BASIC PROPERTIES OF

OPTICAL vr I i vriL MATERIALS iiini Mmm ill r\ &m

SUMMARIES OF PAPERS
he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

basis for the nation's physical measurement system, (2) scientific and technological services for industry and

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The Bureau's technical work is performed by the National Measurement Laboratory, the National

Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Center for Materials

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The National Measurement Laboratory

Provides the national system of physical and chemical measurement;

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furnishes essential services leading to accurate and uniform physical and

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produces, and distributes Standard Reference "Materials; and provides

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• Basic Standards2 • Radiation Research

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Programming Science and

Technology

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Conducts research and provides measurements, data, standards, reference

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'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Gaithersburg, MD 20899.

2 Some divisions within the center are located at Boulder, CO 80303. 'Located at Boulder, CO, with some elements at Gaithersburg, MD.
#ATION/a BVPW

£>F SlRUD/i.T.DB LIBRARY OM85

Basic Properties of Optical Materials

Summaries of Papers llo . , „ .,

Presented at the

Topical Conference on

Basic Properties of Optical Materials

Held at the National Bureau of Standards

Gaithersburg, Maryland, May 7-9, 1985

Edited by:

Albert Feldman

Center for Materials Science

Inorganic Materials Division

National Bureau of Standards

Gaithersburg, Maryland 20899

Sponsored by:

U.S. Department of Commerce

National Bureau of Standards

Center for Materials Science

Inorganic Materials Division

Center for Electronics and Electrical Engineering

Semiconductor Materials and Processes Division

American Physical Society

Air Force Office of Scientific Research

In Cooperation with:

Optical Society of America

SPIE—The International Society for Optical Engineering

e

t»T OF

2

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued April 1985
Library of Congress Catalog Card Number: 85-600534

National Bureau of Standards Special Publication 697

Natl. Bur. Stand. (U.S.), Spec. Publ. 697, 294 pages (Apr. 1985)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1985

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
Foreword

This Special Publication contains summaries of papers to be presented at

the Topical Conference on Basic Properties of Optical Materials to be held at

the National Bureau of Standards in Gaithersburg, Maryland on May 7-9, 1985.

The use of optical materials in advanced applications such as optical

signal processing, optical computing, integrated optics, optical coatings,

optical domes, and laser windows is placing increasingly stringent

requirements on material performance. The purpose of this conference is to

bring together researchers from industry, academia, and government to discuss

the physical and structural properties of optical materials as they affect

performance. The scope of the conference includes the measurement and theory

of basic properties of optical materials in bulk and in thin film form and

the dependence of these properties on atomic structure, morphological

structure, impurity content, and inhomogeneity . The principal topical areas

are:

- Influence of microstructure on properties

- Waveguide materials, guided modes, surface plasmons

- Nonlinear phenomena, bistability, photorefractive effect

- Semiconductors and modulated structures

- Thin films

- Organics and polymers

- Glasses

- Metals

- Electro-optic, magneto-optic materials

- Optical constants and other properties

- Ultraviolet, visible, infrared properties

- Optical spectroscopies

The importance of optical materials to the international research

community is attested to by the large number of papers from abroad,,

This publication contains summaries of 70 papers which include 17

invited papers. The manuscripts have been prepared by the authors in cameraready form, and any questions pertaining to their content should be addressed

to those authors.

Albert Feldman

Chairperson

iii
Program and Editorial Committee

Albert Feldman - Chairperson

National Bureau of Standards

Michael I. Bell

National Bureau of Standards

Bernard Bendow

The BDM Corporation

H. E. Bennett

Naval Weapons Center

Samuel Ditman

Naval Surface Weapons Center

H. P. R. Frederikse

Bureau of Standards

Alastair M. Glass

AT&T Bell Laboratories

Arthur H. Guenther

Air Force Weapons Laboratory

H. Angus Macleod

University of Arizona

Edward Palik

Naval Research Laboratory

Armand R. Tanguay, Jr.

University of Southern California

Van Wood

Battelle Memorial Institute

Acknowledgments

We wish to thank the following individuals for their invaluable

assistance in preparing for the conference and this summary: Kathy Kilmer,

Mary Nestor, Susan Roth, Carolyn Sladic, Kathy Stang, Lillian Ware, Judy

Wilson. Special thanks are due to Jane Walters, Kathy Gallo, and Brenda

Kefauver for typing the conference program, for retyping several of the

manuscripts, and for assembling and editing the completed Summary of Papers

Disclaimer

Certain commercial equipment, instruments, or materials may be

identified in this publication in order to adequately specify the

experimental procedure. In no case does such identification imply

recommendation or endorsement by the National Bureau of Standards, nor does

it imply that the material or equipment identified is necessarily the best

available for the purpose.

iv
CONTENTS

Page

Foreword iii

Keynote Address—Progress in Optical Materials Research 1 *I. P. Kaminow

EFFECTS OF MICROSTRUCTURE

Determination of Microstructure from Spectrophotometry and

Spectroellipsometry 5 *D. E. Aspnes

Light Scattering from Dielectric and Metallic Microstructures 11

*R. K. Chang and P. W. Barber

Characterization of Optical Materials and Surfaces Using

Time-Domain Ref lectometry 17

A. G. Lieberman

Theory of Light Scattering from a Rough Surface with a Nonlocal Inhomogeneous Dielectric Permittivity 21

J. M. Elson

INFRARED MATERIALS

Optical Properties of Metals in the Infrared - the Drude

Model, Problems with It, and Non-Local Optics 24

*D. W. Lynch

Separation of Drude and Band-to-Band Spectra in Polyvalent

Metals 28

D. Y. Smith and B. Segall

Status of Materials for Transmissive and Reflective Infrared

Components 32

*H. E. Bennett

Dimensional Stability 36

W. Primak

ORGANIC MATERIALS AND POLYMERS

Nonlinear Optical Properties of Organic Polymer Materials 40

*G. M. Carter, Y. J. Chen, M. F. Rubner, M. K. Thakur,

S. K. Tripathy, J. P. Georger, and J. V. Hryniewicz

Preparation of Organic Nonlinear Optical Materials for

Second Harmonic Generation 46

C. W. Dirk, R. J. Twieg, and G. Wagniere

Invited Presentation

v
Page

Optical Phase Transitions in Organo-Metallic Compounds 50

T. 0. Poehler and R. S. Potember

A Review of the Optical Data Analysis for Phthalocyanine

Conducting Polymer and Molecular-Metal Systems 54

W. J. McCarthy, C. R. Kannewurf, T. Inabe,

T. J. Marks, and R. L. Burton

Optical Properties of PBS 58

M. W. Williams, D. W. Young, J. C. Ashley, and

E. T. Arakawa

WAVEGUIDE MATERIALS AND SURFACE PLASMONS

Optical Constants and Harmonic Generation by Surface Plasmons 60

*H. J. Simon

Low Loss Thin Film Materials for Integrated Optics 65

*H. E. Jackson and J, T. Boyd

Quantitative Sampling in Planar Waveguides 71

P. W. Bohn

THIN FILMS

Relationship of Microstr ucture to Optical Properties of

Thin Films 74

*H. A. Macleod

The Microstr ucture and Optical Properties of Thin Films

Prepared by Molecular Beam Techniques 80

K. L. Lewis, A. M. Pitt, J. A. Savage, A. G. Cullis,

N. G. Chew, and L. Charlwood

A Simple Model of Inhomogeneity in Optical Thin Films ... 84

G. Deniau, F. Flory, and E. Pelletier

Optical Properties of Diamondlike Carbon Films on Semiconductors 86

G. H. Bu-Abbud, J. D. Lamb, J. E. Oh, and J. A. Woollam

Temperature Dependent Optical Properties of Silver Sulfide

Thin Films 89

R. L. Burton, H. Buhay, M. Nisar, J. L. Grieser, and

N. P. Murarka

Molecular Bonding in Optical Films Deposited by Ion-Beam

Sputtering 93

*C. Y. She

vi
Page

POSTER PAPERS

Highly Transparent Metal Films: Pt on InP 99

D. E. Aspnes, A. Heller, J. D. Porter, T. T. Sheng,

and R. G. Vadimsky

Calculation of the Electronic Structure of As.S. and As.Se,

4 4 4 4 Molecules 103

D. Babic and S. Rabii

Free-Carrier Absorption in a Thin Film Silver Sulfide

Galvanic Cell 106

R. L. Burton, H. Buhay, J. L. Grieser, and N. P. Murarka

Synthesis and Characterization of Stoichiometric CdPS

3 110

J. Covino, P. Dragovich, and C. Lowe-Ma

Optical Characterization of Thin Semiconducting Films on Transparent Substrates 115

B. Edgerton and D. Shortt

Laser Propagation Through Fibers with Biquadratic Refractive

Index (Closed Form Solution) 119

F. Z. El-Halafawy, A. Y. Rezk, and E-S. A. El-Badawy

Densif ication of Zirconia Films by Coevaporation with Silica 122

A. Feldman and E. N. Farabaugh

Temperature Dependence of the VUV Optical Spectra and Band

Structure of Al

2 0

3 126

R. H. French and R. L. Coble

Raman Spectra of LiYF^ Crystal 130

F. X. Gan and H. Y. Chen

EPR Studies of Infrared-Transmitting Sulfide Ceramics 133

D. C. Harris, M. E. Hills, J. Covino, C. K. Lowe-Ma,

and R. W. Schwartz

Elastic Properties of Chemically Vapor-Deposited ZnS and

ZnSe 137

C. A. Klein and C. B. Willingham

Radiation Effects in a Glass-Ceramic (Zerodur) 141

N. Koumvakalis, M. G. Jani, and L. E. Halliburton

Infrared Characterization of Defect Centers in Quartz 145

H. G. Lipson

vii
Page

The Importance of Electron-Electron Correlation in the

Calculation of Second-Order Nonlinear Optical Properties

of Organic Molecules. The Case of Urea 150

B. M. Pierce

Diffuse Multilayer Analysis Using a Multiflux Method 154

S. 0. Sari

Optical Absorption in the Band Gap in High Purity Silicon 158

R. T. Swimm

Properties of Guided Modes in Bidirectional Anisotropic

Media 160

0. Schwelb

Calor imetric Measurement of Optical Absorption in Sapphire

at Visible, Near IR, and Near UV Wavelengths 164

A. B. Villaverde, R. T. Swimm, and M. Bass

Optical Properties of Ion Beam Irradiated Molybdenum Laser

Mirrors as Studied by Ellipsometry 167

J. A. Woollam, G. H. Bu-Abbud, D. L. Mathine, D. Poker,

D. Ingram, and P. Pronko

Crystal Field Energy Levels and Optical Absorption

Intensitites of Ni2* : MgF

2 169

B. Zhang, J-K. Zhu, and S-H. Liu

PROPERTIES FROM MILLIMETER TO X-RAY WAVELENGTHS

Status of Optical Constants of Solids from X-Ray to

MM-Wave Region 171

*E. D. Palik

Optical Constants at X-Ray Wavelengths 177

D. Y. Smith, A. E. Williamson, and T. I. Morrison

Vacuum Ultraviolet Loss in Magnesium Fluoride Films 181

0. R. Wood, II, P. J. Maloney, H. G. Craighead, and

J. E. Sweeney

Surface Erosion Induced by Electronic Transitions 184

R. F. Haglund, Jr., and N. H. Tolk

SEMICONDUCTORS AND QUANTUM WELL STRUCTURES

Dielectric Function and Interband Transitions in

Semiconductors ' 188

*M. Cardona

viii
Page

Band Structure and Density of States Changes for Doped

Gallium Arsenide 194

H. S. Bennett

Micro-Raman Study of Laser-Induced Damage 198

P. M. Fauchet, I. H. Campbell, and F. Adar

Optical Effects in Quantum Well Structures and Super lattices 202

*D. S. Chemla

Photoref lectance in GaAs/AlGaAs Multiple Quantum Wells 214

0. J. Glembocki, B. V. Shanabrook, N. Bottka,

W. T. Beard, and J. Comas

Picosecond Carrier Dynamics in a-Si 218

A. I. D'Souza, M. G. Roe, P. E. Wigen, and R. Messier

NONLINEAR OPTICAL MATERIALS AND THE PHOTOREFRACTIVE EFFECT

Photorefractive and Nonlinear-Optical Properties of New

Electrooptic Materials 222

*P. GUnter

Measurement of Defect and Transport Properties of

Electro-Optic Materials Using the Photorefractive Effect 226

M. B. Klein and G. C. Valley

Analysis of Scattering Patterns and Decay Dynamics of

Photorefractive Gratings in LiNbOg Crystals 229

J. K. Tyminski, R. C. Powell, H. C. Chow, and

M. J. Kleiwer

Use of Optical Phase Conjugation for Understanding Basic

Materials Properties 232

*R. W. Hellwarth

Measurement of Dielectric Properties of KTa ,_ xNbx0 234

D. Rytz, M. B. Klein, B. Bobbs, M. Matloubian, and

H. Fetterman

Refractive Indices and Thermo-Optic Coefficients of

Nonlinear Crystals Isomorphic to KH„P0 238

2 4 K. W. Kirby, C. S. Hoefer, and L. G. DeShazer

> Bismuth Silicon Oxide: Sample Variability Studied with

Thermally Stimulated Conductivity and Thermoluminescence 242

B. W. Holmes, J. E. Ludman, and C. L. Woods

ix
Page

NONLINEAR OPTICS AND BISTABILITY

Materials Requirements for Optical Logic and Bistable \

Devices 246

*N. Peyghambar ian and H. M. Gibbs

Mirrorless Optical Bistability in CdS 249

J. W. Haus, C. C. Sung, C. M. Bowden, and J. M. Cook

Nonlinear Optical Effects in Liquid Crystals .... 251

D. Armitage and S. M. Delwart

A Study of Second Harmonic Generation Coefficients and

Ultraviolet Absorption Edge of Barium Borate Crystal 255

J-K. Zhu, B. Zhang, and S-H. Liu

Soliton Transmission in Inhomogeneous Media with W-Tailored

Refractive Index 256

F. Z. El-Halafawy, E-S. A. El-Badawy, M. A. El-Gammal,

and M. H. Aly

GLASSES

Comparison of Vibrational Spectra of Heavy Metal Fluoride

Glasses with Those of "Common" Glasses 260

*B. Bendow

Sol Gel Coatings for Optical Applications (Paper not Available)

*D. R. Uhlmann

The Verdet Constant of Optical Glasses 266

H. J. Hoffman, W. W. Jochs, and G. Przybilla

Temperature Dependence of Magnetooptic Effects in

Mid-Infrared Fibers 270

H. Sato, Y. Azumai, and M. Saito

Optical Characterization of Devitrification for Cr 3+ -Doped

Zr-Ba-La-Al Fluoride Glass . 274

W. J. Miniscalco, L. J. Andrews, B. T. Hall, and

D. E. Guenther

Optical Study of Ge-P-Te and Ge-Se-Te Chalcogenide Glasses 278

L. Boehm, A. Bornstein, and S. Arie

Author Index 282

x
PROGRESS IN OPTICAL MATERIALS RESEARCH (KEYNOTE TALK)

Ivan P. Kaminow

AT&T Bell Laboratories

Crawford Hill Laboratory

Holmdel, New Jersey 07733

The advent of the laser in 1960 stimulated the need for research

in high quality optical materials. The last 25 years are

peppered with both great successes and disappointments in the

quest for practical materials for novel applications. I will

review a few examples pertinent to telecommunications

applications with an eye to future needs.

The initial challenge is usually to find any material that

exhibits a unique optical property to demonstrate a new

phenomenon or device. But a first success then leads to more

stringent demands on the material. Not only must the unique

property be enhanced, but, at the same time, ancillary

properties essential for practical implementation must also be

realized.

Optical Fibers ; Perhaps the most dramatic illustration of

success in optical materials research is the low-loss optical

fiber now widely used for telecommunications. It was well-known

in the 1960s that light — including laser light — could be

guided by an optical fiber with a high refractive index core and

lower index cladding. However, all the handbooks indicated

losses due to absorption in the most transparent glasses to be

about 1000 dB/km — much too large for long haul communications.

Then it was recognized that if impurities could be reduced

sufficiently (parts/billion), the transparency could be improved

to practical levels. The bulk oxides from which glasses were

made could not be economically purified to the required level.

However, chemical vapor techniques already known in the glass

and silicon industries led naturally to high purity silica

glasses. The starting materials, SiCl^ and O^i could be

obtained as high-purity reagents and the vapor pressures of

remnant transition metal chlorides in the liquid SiCl^ were low

enough that they were not transferred with the SiCl, vapor. The

demonstration of losses of 20 dB/km in 1970 marked the start of

the practical phase of fiber materials research. Over the past

15 years, not only has the loss been reduced to 0.16 dB/km —

near the theoretical limit — but a host of ancillary material

problems have been addressed; including, high mechanical

strength, new plastic coatings, efficient production methods,

minimal OH impurities, and new dopants for changing the

refractive index of silica.

l
Further applications call for entirely new fiber materials that

will transmit wavelengths, X, longer than 1.55 urn, where the

silica fibers have their minimum lo|s. Since the loss due to

Rayleigh scattering decreases as x , the hope is to realize

losses much less than 0.16 dB/km. But one must find glasses

with weak lattice vibration absorption at these wavelengths that

can be manufactured free of impurities (particularly OH), and

later, learn to make them strong, robust and cheap.

Semiconductor Lasers : Another example of success is the

development of methods for epitaxial growth of semiconductor

alloys to be employed in lasers and photodiodes to operate with

the low-loss silica fibers. The first important step toward a

practical device was the recognition of the need for a heteroepitaxial structure to confine the photons and electrons

to the same thin region. A liquid phase epitaxial (LPE) method

for growing a suitable double heterostructure (DH) AlGaAs/GaAs

wafer was developed and a low-threshold laser operating at 0,.8nm

was demonstrated in 1970. The next requirement was to find a

semiconductor compound with a bandgap corresponding to the

low-loss region -- 1.2-1.5jim — of the silica fibers. In 1976,

In

xGa^_xAs P, , which can cover the desired wavelength range,

was grown lattice-matched to InP, and was used in a

long-wavelength DH laser. Following the demonstration of laser

operation at that time, much effort has been devoted to growing

reproducible, large wafers without defects and with

well-controlled layer thickness and composition. A variety of

epitaxial methods have been studied: liquid phase, vapor phase

(VPE and MOVPE) and molecular beam epitaxy (MBE) . And, of

course, as these techniques have been perfected they suggest and

permit still more sophisticated applications, which in turn put

more demands on the material — on both its optical and

non-optical properties. The most recent advance is the

development of multi-quantum well structures.

Electrooptics and Non-linear Optics : The non-linear optical

materials in some sense represent a disappointment. KDP — or,

chemically, KH2?0^ — and its isomorphs were known as

piezoelectric, ferroelectric and electrooptic materials in 1935,

well before the invention of the laser. When the laser came

along, they were obvious choices for the first high-speed

modulators and for the demonstration of optical second harmonic

generation, since both applications require non-centrosymmetric

(piezoelectric) transparent crystals. After 25 years of

research, there is still no substitute for KD2P0

4

in many

important applications. True, the available size of2the

crystals has increased^substantially from about 1 cm in

cross-section to 10 cm . But still one would prefer a non-water

soluble crystal with larger non-linear optical coefficients —

while retaining the excellent optical quality, UV transparency,

freedom from optical damage, high resistivity, and low

dielectric constant. During the 1960s, I and others hunted

2
through mineralogical collections looking for natural crystals

with the required symmetry and range of transparency to test for

their electrooptic and non-linear optical coefficients. In the

few cases that led to interesting materials, one then had the

problem of finding or growing large crystals with good physical

and electrical properties. Meanwhile, crystal growers set out

to synthesize oxides with suitable symmetry and transparency - often following the clues offered by the previously-known

synthetic piezoelectric and ferroelectric oxides, such as

BaTiO-, KNbO^, LiNbO^ and LiTaO.,, all of which had been

synthesized in the 1940s as a result of research on high

dielectric constant and ferroelectric materials. Their large

linear polarizabilities suggested large non-linear

polarizabilities . Many ABO, crystals and their solid solutions

were synthesized and studied. The solutions never really worked

well because uniform crystal growth was not possible. Some

compound oxides showed large electrooptic coefficients due to

the proximity of the ferroelectric Curie temperature to the

operating temperature. However, the corresponding high

dielectric constant lead to poor high frequency modulator

performance. Finally, after many years of study, LiNbO~ and

LiTaO^ have emerged as the best materials for many electrooptic

and non-linear optic applications, because they exhibit

reasonably large non-linear coefficients and can be grown in

large crystals of good quality. Still, these crystals have many

shortcomings for the sophisticated device applications that had

been proposed in the 1960s and 1970s: the non-linear

coefficients are too small for efficient tunable parametric

oscillators or harmonic generators and the materials suffer an

optical damage (photorefractive) effect at wavelengths of

interest

.

In the 1970s, I had hoped that an understanding of the

microscopic origins of the electrooptic and non-linear optic

coefficients would provide guidance to synthesizing the optimum

crystal — and I understand that some researchers still have

this hope — but, practically speaking, only the

"seat-of-the-pants" approach has worked. That is, intuitive

people have guessed at compounds that might exhibit the desired

optical property and still be growable, and then have tried them

out

.

Photonic Structures : In the absence of the ideal material, one

can also look for innovations in the device structure. Since

these non-linear effects are strong functions of field strength,

the interaction efficiency can be improved by confining the

interaction to the smallest allowed cross-section and assuring

good overlap of all the fields involved. The use of optical

waveguides eliminates diffraction and allows uniform interaction

over a path of many wavelengths. Thus, in the 1970s researchers

looked for methods to make waveguides in non-linear materials.

The most widely used process for waveguide electrooptic

modulators has turned out to be diffusion of titanium into

3
LiNbO,, since it is simple to employ using standard

photolithographic methods. Although it has been on the horizon

for a long time, it now looks as though integrated optics

devices employing Ti:LiNbO^ waveguides are on the verge of

application in telecommunications. Here again however,

Ti:LiNbO~ was one of the early combinations tried and

demonstrated, and subsequent efforts have not improved matters.

Thus, we were not able to make metal-diffused guides in any

other electrooptic oxides or semiconductors.

Certainly efforts to make good waveguides in semiconductor

materials as conveniently as the Ti:LiNbO^ guides, in such a way

that they will be compatible with the heteroepitaxial lasers

mentioned above, offers a worthy challenge to the optical

materials community. Not only could such electrooptic waveguide

devices be integrated with semiconductor lasers and detectors,

they could all be integrated together on the same chip with the

transistor circuits to drive them — the so called "integrated

optoelectronic structure". Further down the road is the

"photonic structure" in which optical signals switch other

optical signals leading to pure optical logic and switching.

Such devices will depend upon extremely large non-linear optical

interactions

.

Optical materials research has had a remarkable record of

success in making lightwave telecommunications a reality. As

the field becomes more sophisticated, many challenges remain,

and others are sure to develop, that require new approaches to

making high performance materials while working within the

physical constraints defined by the periodic table.

4
DETERMINATION OF MICROSTRUCTURE FROM SPECTROPHOTOMETRY

AND SPECTROELLIPSOMETRY

D. E. Aspnes

Bell Communications Research, Inc., Murray Hill, N.J. 07974

That microstructure can profoundly influence optical properties of materials has been

known essentially from the first investigations of the electromagnetic response of macroscopic media. 1 ' 2 "Microstructure" is used here in the standard materials science sense, referring to spatial inhomogeneities on the scale of about 1 to 25 nm. These are inhomogeneities large enough so that the separate regions possess their own dielectric identity, yet

small compared to the wavelength of light.

Can one reverse the procedure and use optical properties to determine microstructure?

Yes, within limits. The major difficulty is that optical data take the form of transmitted

or reflected intensities or of ratios of complex reflectances, whereas one really wants to

know microstructural properties such as average compositions, void fractions, and interface and surface region thicknesses. To go from optical data to microstructure one needs

to model, that is, to devise idealized mathematical representations for given samples that

allow their optical properties to be calculated analytically in terms of available data and

the sample parameters of interest. Given a model, one can either use the optical data as a template and apply least-squares regression to systematically best-fit the model parameters

to the data, or else use the optical data as input to allow the model equations to be solved

explicitly for one or more of the parameters of the model. Complicated samples are usually analyzed by the first approach, while the determination of oxide thicknesses is an example of the second approach. With present capabilities it is now possible to analyze

composite bulk or thin film samples that are anisotropic, macroscopically inhomogeneous,

microscopically rough, covered with adsorbed layers, or have finite interface and surface

region thicknesses.

The present summary deals primarily with the modeling problem, and will cover topics

that in my opinion have not been adequately discussed elsewhere. References to more

detailed treatments of specific topics will be given as needed. I shall be concerned with

the analysis of spectral data taken with the sample under static conditions, the usual

situation for materials characterization, rather than single-wavelength data taken under

dynamic conditions, the usual situation for process characterization.

The essential requirements for accurate microstructural analysis are accurate data for the

sample and all possible constituents, and an accurate model of the sample. Recent

advances in instrumentation, in particular the development of fast, automatic spectroellipsometers, have virtually solved the instrumentation and data accuracy problems, and

recent needs for nondestructive, in situ analyses of materials, surfaces, and interfaces in

semiconductor technology have greatly expanded the data base needed for model calculations. These data have also been essential to the development of analytical procedures,

5
which can also be considered a solved problem.

In contrast, the determination of the model that accurately represents a given sample is an

open-ended problem that is definitely not solved. McPhedran et al.

3 have recently discussed some aspects of this topic as it applies to spectrophotometry. In brief, one faces a challenge analogous to the black-box problem of electrical engineering: the microstructural details of the sample are not know but must be deduced from available data.

Mathematicians term this a problem of the inverse type, loosely describable as a situation

where one is given the answer and asked to find the problem. Difficulties include the possible existence of different but apparently equally valid models, overlooked models, inadequate data, no confidence in the parameters determined, convergence to a wrong solution,

and doubts that all relevant sample properties have actually been included in the model.

Considerable physical insight may also be needed to construct the model. The recom- mended procedure is to start with the simplest possible model until it proves to be inadequate and to take advantage of all the information available, whether it comes from optical data or from other sources.

At present, the primary objectives of optical microstructural analysis are to establish the

reliability of specific models and confidence in the results. That these are now the main

challenges represents considerable progress, as anyone who recalls the Ellipsometry

Conferences of the 1960's and 1970's can attest. Reliability and confidence are esta- blished by successful overdetermination, that is, by showing that data taken under

different conditions lead to the same parameters, or equivalently by showing that optical

properties calculated from model parameters determined under one set of conditions accurately predict optical properties observed under another. Different conditions are obtained

by varying parameters under direct experimental control such as the angle of incidence or the wavelength of light.

An inspection of the optical characterization literature in, e.g., Applied Optics or in any of a number of reviews,4

will show that almost anything that can be varied has been varied,

including not only wavelength and angle of incidence but also film thickness, ambient

refractive index, and numbers and types of overlayers. The most useful, convenient, and

powerful variable by far is the wavelength of light, not only because it can be changed

without affecting the sample but also because optical properties are themselves strong

functions of wavelength through intrinsic polarizabilities, long-range order, interference,

and other phenomena. In fact, a wavelength scanning capability is almost mandatory for

any serious microstructural analysis effort because single-wavelength measurements do not

return enough information to allow models to be cross-checked. Since optical properties are generally slow functions of the angle of incidence, a consequence of SnelPs Law is going from less dense to more dense media, this parameter is much less useful than the

wavelength in establishing independent conditions although it does affect sensitivities to interface regions under optically thick films. 5 The use of film thickness as a variable is risky because microstructure tends to evolve with deposition. The use of different

ambients also cannot be recommended because of the tendency of porous films to absorb

ambient material, a well known phenomenon in the optical coatings field. 6

The model is the weak link in any optical microstructural analysis, so the following limita6
tions should be kept in mind. A model is an idealized representation of a sample and con- sequently is an approximation. As such, it can always be pushed too far, even if it accurately describes all major observable sample characteristics. If adequate data are not

available, the model may not represent the sample properly. Models are usually expressed

in terms of macroscopic parameters, which are themselves averages over microscopic

phenomena that may be extremely complex. While macroscopic parameters are very useful for practical purposes (consider the relative advantages of working with pressure and

temperature or with the position and velocity of each molecule in a macroscopic sample of a gas), many problems can only be solved by using techniques such as transmission electron microscopy that are destructive but have the spatial resolution necessary to access microstructure directly. Also, the values of macroscopic parameters such as compositions

deduced from effective medium theory depend on microscopic properties such as grain

shapes that cannot be studied directly by optical techniques. However, limit theorems7-9 can be used to determine the ranges of uncertainty of such parameters even if nothing is known about the microstructure in detail.

Also, the values obtained depend on the accuracy of the data base. For example, Johnson

and Christy 10 used reflectance and transmittance measurements to determine the dielectric properties of a number of metal films deposited on room-temperature substrates by

evaporation at moderate (10~5 torr) pressures. These data probably differ from the true

bulk dielectric responses of the respective metals by amounts of the order of 10% due to the inefficient packing of the metal grains in the films. Any microstructural analysis using

these data as reference data must take this uncertainty into account. As materials

preparation procedures improve, reference data become more accurate, but the process is an evolutionary one. As another example, the maximum amplitude of the "best" dielectric function spectrum of amorphous Si has increased gradually from 20 to about 30 over

the past 15 years, primarily because of improvements in deposition procedures. Indications that the intrinsic dielectric properties of a-Si may have finally been obtained follow

because the dielectric properties of material prepared by three different ways in three

different laboratories (and measured by two different optical techniques) are now in very

good agreement. 11 But the possibility of further improvements cannot be ruled out.

I now consider specific details, beginning with available information and its determination.

The optical probe is polarized light, which carries four pieces of information in the form

of the amplitudes and phases of the two orthogonal components of the electric field. Reflection or transmission changes these amplitudes and phases to new values. Consequently, four pieces of data can be obtained in principle about a sample during any single

optical measurement. In reflectance measurements these four data are expressed as two

complex reflectances, r

s and rp

, which describe the effect of the sample on the electric field

components parallel and perpendicular, respectively, to the plane of incidence. The fact

that only four data are available is a severe limitation and shows that multiple measure- ments are necessary. The actual situation is even less favorable: photometric techniques

(reflectometry) that deal with intensities determine only two data (in two separate measurements), the amplitudes of r

s and rp

, and ellipsometric measurements that deal with

polarization states also determine only two data (in a single measurement), the complex

reflectance ratio r_/r

s

. The latter quantity is analogous to an impedance. Because it is

7
easier to accurately measure impedances than power levels, and because such measure- ments are less susceptible to experimental artifacts, it is easier to reach a given level of

accuracy with ellipsometry than with reflectometry even though the ultimately attainable

levels of accuracy are the same.

The biggest experimental impediment to accuracy is not instrumentation but sample

preparation. For example, careful sample preparation is the reason why the dielectric properties of single-crystal Ge determined by Archer 12 from discrete-wavelength ellipsometric

data and those determined by Donovan et al. 13 from reflectance data agree within several

percentage points of each other and with those determined from recent spectroellipsometric data 14 in a field where discrepancies of 10-20% are not uncommon. Ideally,

samples should be clean, flat, and damage-free, and maintained that way by keeping them

in an inert atmosphere during measurement. Proper sample preparation simplifies microstructural analysis by eliminating complexity at the experimental level rather than forcing

it to be dealt with during data analysis. The real-time data acquisition capabilities and

better submonolayer sensitivities of presently operating automatic spectroellipsometers

allow surface conditions to be assessed during the sample preparation process, guaranteeing that the best possible surfaces can be obtained before spectral data are acquired for

analysis. A comprehensive discussion of methods of obtaining accurate data by ellipsometry has been given elsewhere. 15

The theoretical tools needed for microstructural characterization are the n-phase model,

effective medium theory, and least-squares regression analysis. 16 The n-phase model is the

mathematical prescription for calculating complex reflectances and transmittances from

the Fresnel reflection and propagation equations for a stratified medium consisting of the

substrate, (n-2) overlayers, and the ambient. Each layer is assumed to be uniform, but

graded interfaces can be accommodated by subdividing them into thin laminations. The

most convenient, comprehensive, and practical treatment of the n-phase model is that

recently given by Yeh. 17 All necessary equations are provided in a form readily adaptable

to numerical analysis, and are completely general in that optically anisotropic materials are treated as well. Numerical analysis is necessary because of the arcane nature of the

calculations and because almost all quantities involved are complex.

The purpose of effective medium theory (EMT) is to describe the dielectric function, e, of

a composite in terms of those of its constituents and microstructure. The physical basis is straightforward: the application of an external field causes local displacements of charge

within the material which manifests itself as screening charge at the boundaries of the

separate microscopic regions. This screening charge modifies the local electric _and dis^

placement field e*(f) and d(r) and therefore the average or macroscopic fields E and D

that are actually observed. For any medium, € can be calculated (at least in principle) by

solving the microscopic field problem exactly, and then spatially averaging the solution.

The dielectric function is then obtained from the relation D = e E.

This prescription is simple, but it shows why the biggest theoretical impediment to accu- racy is the EMT. It shows that each sample has its own EMT, and since the local fields

depend on the relative values of the dielectric functions of the constituents, the EMT is different in principle for each wavelength. Since this challenge is too much to accommo8
date in practice, one resorts to idealized microstructures for which analytic solutions are

available. The Maxwell Garnett (MG) model 1 is derived from the electrostatic solution

for isolated spheres in an infinite host dielectric and approximately describes cermet or coated-sphere microstructures, while the Bruggeman effective medium approximation 18 (EMA) is derived from the MG theory by a self-consistency assumption that allows it to be applied to aggregate or random microstructures. While the derivation of the MG

expression implies that its range of validity is limited to small volume fractions of the

inclusion phase, Smith 19 has shown that it also applies for coated spherical ellipsoidal or spherical particles such that the dipolar component of the field outside the coated particle

vanishes. The big difference between the MG and the EMA theories from a conceptual

point of view is that the MG theory represents a microstructure for which the internal

field pattern is always stationary, consisting of spatially fixed dipolar corrections to a background uniform field, whereas the self-consistency inherent in the EMA is an attempt

to represent a microscopic field pattern that changes with the relative dielectric function

values of the separate constituents. The dielectric function for a two-phase composite can

be written in general as

20

.€ ~ €b

f

€a~ ch , ,

eb~ €h ( — . v = f

a —; + fa —; ; (la)

€ +K€h *a + * €h

cb + " ch

qyb + (i-q>*h(fa

C

€a+W nM

(l-q)eh + q(fa€b + fbCa)

'

where €a , eb

, and eh are the dielectric functions of the separate phases a, b and the host

phase h, fa and fb are the respective volume fractions, and q = 1/(1 + k) is the depolarization factor that takes the values 0, 1/3, 1/2, and 1 for no screening, three dimensionally

isotropic, two dimensionally isotropic, and maximum screening, respectively. The host

dielectric function has the values €a or €b for the MG theories and e for the EMA. Arbitrary degrees of freedom in composition and microstructure do not lead to arbitrary values

of c because the parameters themselves have limited ranges, as described in simple

geometrical constructions by various limit theorems7-9

discussed elsewhere.20 The limit

theorems are written in terms of macroscopic observables such as relative volume fractions

and isotropy in two or three dimensions and can be used to establish the intrinsic uncertainties in the parameters obtained by the application of Eqs. (1) to optical data.

In principle q, fa (or y, and eh

all have the status of adjustable parameters, but some

assumptions are usually made. These typically take the form of specific values, such as q — 1/3 for systems that are expected to be isotropic in three dimensions, and/or the

EMA approximation eh = e for systems that are expected to have a random or aggregate

microstructure. Although the MG and EMA theories are identical to first order when the

volume fraction of one of the phases becomes small, for comparable volume fractions the

predicted spectral lineshapes for e are sufficiently different so that the two microstructures

are usually readily distinguishable from optical spectra. The EMA is found to describe

rather well the dielectric properties of a wide range of thin film systems owing to their

essentially random microstructure, but not surprisingly, there are numerous examples

where neither simple theory is adequate to describe the data. Au-Si02 cermets discussed

9
by Gittleman and Abeles2

fall into this category, as do the Rh films recently measured

by Arndt et al. 22 Equation (lb) shows that q and €h are not independent, but that the

assumption of a particular form for €h will affect q and vice versa. Since the choice of €h

is not always ckarcut, uncertainties are introduced in the optically determined values of q. The limit theorems show that particle shapes become particularly important whenever the

dielectric functions of the constituents are significantly different, as might be expected

from the relative efficiencies by which needle- and disc-shaped inclusions screen themselves from externally applied fields. When the dielectric functions of the constituents are

similar, then compositional differences are the important variables.

The final step is to determine the best fit parameters by linear regression analysis. 16

A number of applications can be found in two recent reviews by the author.23' 24

REFERENCES

1. J. C. M. Garnett, Philos. Trans. R. Soc. London 203, 385 (1904); A205, 237

(1906).

2. H. A. Lorentz, Theory of Electrons, 2nd ed. (Teubner, Leipzig, 1916).

3. R. C. McPhedran, L. C. Botter, D. R. McKenzie, and R. P. Netterfield, Appl. Opt.

23, 1197 (1984).

4. F. Abeles, in Physics of Thin Films 6, ed. by G. Hass and R. E. Thun (Academic,

New York 1971).

5. J. B. Theeten and D. E. Aspnes, Thin Solid Films 60, 183 (1979).

6. J. P. Borgogno, F. Flory, P. Roche, B. Schmitt, G. Albrand, E. Pelletier and H. A.

Macleod, Appl. Opt. 23, 3567 (1984).

7. Z. Hashin and S. Shtrikman, J. Appl. Phys. 33, 3125 (1962).

8. D. J. Bergman, Phys. Rev. Lett. 44, 1285 (1980).

9. G. W. Milton, Appl. Phys. Lett. 37, 300 (1980).

10. P. B. Johnson and R. W. Christy, Phys. Rev. B6, 4370 (1972); B9, 5056 (1974).

11. D. E. Aspnes, A. A. Studna, and E. Kinsbron, Phys. Rev. B29, 768 (1984).

12. R. J. Archer, Phys. Rev. 110, 354 (1958).

13. T. M. Donovan, E. J. Ashley, and H. E. Bennett, J. Opt. Soc. Am. 53, 1403

(1963).

14. D. E. Aspnes and A. A. Studna, Phys. Rev. B27, 985 (1983).

15. D. E. Aspnes, in Handbook of Optical Constants of Solids, ed. E. E. Palik

(Academic, New York, 1985).

16. D. E. Aspnes, J. B. Theeten, and F. Hottier, Phys. Rev. B20, 3292 (1979).

17. P. Yeh, J. Opt. Soc. Am. 69, 742 (1979); Surface Sci. 96, 41 (1980).

18. D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).

19. G. B. Smith, J. Phys. D10, L39 (1977).

20. D. E. Aspnes, Thin Solid Films 89, 249 (1982).

21. J. I. Gittleman and B. Abeles, Phys. Rev. B15, 3273 (1977).

22. D. P. Arndt et al., Appl. Opt. 23, 3571 (1984).

23. D. E. Aspnes, J. de Physique Colloque C10, 3 (1983).

24. D. E. Aspnes, SPIE Proc. 452, 60 (1983).

10
LIGHT SCATTERING FROM DIELECTRIC AND METALLIC MICROSTRUCTURES

Richard K. Chang

Section of Applied

New

Yale University

Physics and Center for Laser Diagnostics

Haven, Connecticut 06520

and

Peter W. Barber

Department of

CI ark son University

Electrical and Computer Engineering

Potsdam, New York 13676

Introduction

The generalized Lorenz/Mie formalism can be used to calculate the elastic

scattering (e.g., extinction and scattering cross sections) and the

internal electromagnetic field distributions 1 of axisymmetric micro-objects

(e.g., cylinders, spheres, and spheroids) with complex refractive index

(ft = n + ik) and characteristic size a. The electromagnetic fields inside

and on the surface of the microparticles can be enhanced at specific values

of the size parameter x = 2ira/X (where X is the optical wavelength) . For

dielectric microparticles with x >> 1, morphology-dependent resonances

occur at nearly regularly spaced wavelength intervals. For metallic

microparticles, even with x < 1, localized surface plasmon resonances can occur at several wavelengths with vastly different electromagnetic field

enhancement factors and spectral linewidths.

Recent experimental interests have been directed toward the exploitation of

the enhanced electromagnetic, field intensity at these resonances. For

dielectric microparticles in particular, morphology-dependent resonances

have been applied to the determination of the following properties of

individual droplets flowing in a linear stream: (a) evaporation and

condensation rates; (b) interfacial surface tension and bulk viscosity;

and (c) nonlinear optical properties such as lasing and coherent Raman

processes. For metallic microparticles, localized surface plasmon reso- nances have been applied to the species determination of molecular adsorbates via the surface enhanced Raman scattering. In this presentation,

research results from collaborative work at Yale, Cornell, and Clarkson

Universities will be briefly reviewed.

Evaporation and Condensation Rates

Shifts in the wavelength of the morphology-dependent resonances have been

used to measure extremely small changes in the radius of spherical liquid

droplets. A modified Berglund-Liu vibrating orifice droplet generator was used to generate highly monodispersed (1 part in 10 5

) liquid droplets with

Dielectric Microparticles

11
a radius in the 10-50 um range. Since the morphology-dependent resonances

associated with fluorescence emission are spectrally narrower than those

associated with elastic scattering, the droplets were impregnated with

fluorescent dyes and excited by a pulsed UV N2 laser. The resonances from

different droplets successively further downstream of the orifice were noticed to shift monotonically to shorter wavelengths indicative of a decrease in the radius due to evaporation, as shown in Figs. 1(a) and 1(b).

These resonances shifted to longer wavelengths when the droplets increased

in radius as a result of being in a saturated vapor environment, as shown

in Fig. 1(c). The wake of preceding droplets in the linear stream significantly decreased the evaporation rate of individual droplets relative to

that of an isolated droplet. Small radius changes of 1 part in 10^ have

been observed. 2

Interfacial Surface Tension and Bulk Viscosity

A spherical droplet which has been perturbed by a laser pulse (impulse

function) distorts a droplet from a sphere to an equal volume spheroid. The

freely damped oscillation of the droplet shape (from a sphere to an oblate

and/or prolate spheroid) has a characteristic frequency and a damping

constant (as shown in Fig. 2), which are related to the interfacial surface

tension and bulk viscosity of the droplet. 3 Small amplitude shape distortions of 1 part in 10^ have been observed.

Nonlinear Optical Properties

The incident wavelength or the internally generated radiation at a shifted

wavelength can be tuned to be commensurate with one of the many morphologydependent resonances, i.e., single resonance conditions (with either input

or output waves) or double resonance conditions (with both input and output

waves) can be satisfied. At the input resonance, the large internal

electromagnetic field can increase nonlinear optical phenomena. At the

output resonance, the liquid-air interface can provide a wavelength selective optical feedback (with high Q) which greatly lowers the input intensity

necessary to achieve lasing 4, or stimulated Raman scattering. 5 Molecular

composition identification by stimulated Raman scattering and other coherent

Raman processes 6 in droplets will be compared with those processes for an equal volume sample without an optical boundary.

Metallic Microparticles

7 The surface-averaged electromagnetic intensity of metallic spheres and

spheroids 8 can be greatly enhanced for certain combinations of incident

wavelength. For metals with a small imaginary component of the bulk

dielectric constant [e (w) = e-^u)) + i£2 ( w ) ] > the largest enhancement factor

is calculated to occur when the size of the microparticle is much less than

the incident wavelength (the electrostatic limit) . For metals with larger

£2 (w) , the maximum enhancement occurs when the size extends well into the

electrodynamic region. However, the enhancement in the latter case is

greatly reduced from that in the former case. Recent calculations of the

enhanced surface field for a few catalytically important metals will be

g compared with those for Ag, which is known to exhibit surface enhanced

Raman scattering. For example, Fig. 3 shows the enhancement at the tip of

a 2:1 Pt spheroid as a function of size and incident wavelength. For the

12
size range shown, the maximum enhancement of 76 occurs at a = 101 nm and

X = 710 nm. Preliminary experimental results on the inelastic emission from

discrete 2000 A-sized metal microstructures designed and fabricated by

e-beam lithography at the National Research and Resources Facilities for

Submicron Structures at Cornell University will be presented. 10

We wish to acknowledge the collaboration of our colleagues at Yale (M. B.

Long, S.-X. Qian, B. Schlicht, J. B. Snow, H.-M. Tzeng, and K. F. Wall), at

Cornell (E. D. Wolf) , and Clarkson (M. P. Cline) . We also acknowledge the

partial support of this work by the Air Force Office of Scientific Research

(Grant No. F49620-82-K-005) , the Army Research Office (Grants No. DAAG29-82-

K004 at Yale and DAAG29-84-K-0054 at Clarkson) , and the Gas Research

Institute (Basic Research Grant No. 5083-260-0795)

.

References

1. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation

(Academic, New York, 1969); C. F. Bohren and D. R. Huffman, Absorption

and Scattering of Light by Small Particles (Wiley, New York, 1983)

.

2. H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9, 273

(1984) .

3. H.-M. Tzeng, M. B. Long, R. K. Chang, and P. W. Barber, "Laser-Induced

Distortions of Flowing Droplets Deduced from Morphology-Dependent

Resonances in Fluorescence Spectra," submitted to Opt. Lett.

4. H.-M. Tzeng, K. F. Wall, M. B. Long, and R. K. Chang, Opt. Lett. 9_, 499

(1984).

5. J. B. Snow, S.-X. Qian, and R. K. Chang, "Stimulated Raman Scattering

from Individual Water and Ethanol Droplets at Morphology-Dependent

Resonances," Opt. Lett., in press.

6. S.-X. Qian, J. B. Snow, and R. K. Chang, "Coherent Raman Mixing and

Coherent Anti-Stokes Raman Scattering from Individual Micron-Sized

Droplets," to be published.

7. B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, Phys.

Rev. B 24, 649 (1981)

.

8. P. W. Barber, R. K. Chang, and H. Massoudi, Phys. Rev. Lett. 50_, 997

(1983); ibid., Phys. Rev. B 2_7, 7251 (1983).

9. M. P. Cline, P. W. Barber, and R. K. Chang, "Surface-Enhanced Electric

Fields on Pt, Ir, Ni, Pd, and Rh Spheroids," to be published.

10. Burghard Schlicht (Yale) and Edward D. Wolf (Cornell), private communication .

13
I I I I 522.0 522.5 523.0 523.5 nm

FLUORESCENCE WAVELENGTH

Fig. 1. The single laser shot fluorescence spectra from 8 to 10 spatially

resolved droplets emerging from a Berglund-Liu generator into

several different environments: (a) ambient, (b) higher temperature, and (c) high ambient ethanol vapor pressure (EtOH Pvapor) at

room temperature. Shifts to shorter wavelengths and longer wavelengths correspond to evaporation and condensation, respectively.

[Figure from ref. 2.]

14
FLUORESCENCE

J L I 596 597 598

WAVELENGTH (nm)

Fig. 2. Fluorescence spectra from laser-perturbed droplets downstream from

the Berglund-Liu generator. Each droplet is perturbed by two coun- terpropagating Ar+ laser beams at locations indicated by the two

arrows. The subsequent freely damped oscillations of morphologydependent resonances from droplets downstream yield a shape oscillation frequency and damping constant corresponding to a quadrupole

shape distortion with L = 2 and m = 0. [Figure from ref. 3.]

15
Fig. 3. Electro dynamic results of the intensity enhancement at the tip of

a Pt spheroid. The dependence of this enhancement on the semi

major axis length (a) and the incident wavelength (XQ

) is plotted

for a Pt spheroid with a:b = 2 and immersed in air.

16
CHARACTERIZATION OF OPTICAL MATERIALS AND SURFACES

USING TIME-DOMAIN REFLECTOMETRY

A. G. Lieberman

National Bureau of Standards

Gaithersburg, Maryland 20899

The generation of femtosecond duration laser pulses containing only a few oscillations of coherent light has recently been achieved using pulse

compression techniques (1). Such ultrashort pulses have broad spectral

bandwidths which may encompass the material and structural resonances of a reflecting medium. The effects of these resonances upon the reflected

waveform could provide a novel method for characterizing the optical

properties of a material or evaluating the surface finish of a manufactured

object. The purpose of this paper is to explore the features of timedependent optical pulse scattering from dispersive materials having smooth

surfaces, from perfect conductors having randomly rough surfaces, and from

materials exhibiting both dispersion and surface roughness.

For optical pulses structured as planewaves of a particular

polarization the scattering process can be entirely characterized by a single entity, the impulse response function. This function, denoted R(t),

is physically equivalent to the field induced on the scattering surface by

the incidence of a planewave of impulsive form. In the present analysis

the electric field is assumed to be polarized perpendicular to the plane of

incidence and the scattering medium is treated as a homogeneous material

half-space. For a material having a perfectly smooth surface, the impulse

response function is the inverse Fourier or Laplace transform of the

Fresnel reflection coefficient for the electric field. For a material

having a randomly rough surface, a statistically defined scattering

coefficient is used instead.

The Green's function describing the propagation of the reflected or scattered impulsive field is obtained by retarding the impulse response

function. That is to say, the argument of R(t) must be delayed by the time

it would take for a wave leaving the surface and traveling with speed c in

the direction of specular reflection to reach a given observation point.

For a planewave of arbitrary waveform, the scattered field is simply the

convolution in time of the waveform with the Green's function.

In practice, the required inverse transformations are not usually

available in mathematical handbooks because the contour integrals are extremely difficult or impossible to evaluate exactly. An algorithm was consequently devised for expanding the reflection or scattering coefficient

into a series of terms which could be individually transformed from the

frequency domain to the time domain (2). The results of applying this

algorithm to a number of model materials are shown in the accompanying

table. The first four examples describe materials having smooth surfaces;

the last example relates to a perfect conductor having a randomly rough

surface.

17
The Debye material model is useful for treating relaxation phenomena

in polar dielectrics and semiconductors. Reflection is characterized by

the relaxation time x, the static susceptibility function x(°)> and the

angle of incidence 8^ The impulse response waveform is shown for normal

incidence (8^ = 0). The Lorentz model treats resonant dispersion in nonpolar dielectrics and other materials whose molecules (atoms or electrons)

behave as harmonic oscillators (as opposed to rigid rotators). In this

case, the binding frequency u) Q

, the oscillator strength w , and the viscous

damping rate (linewidth) v, characterize a specific resonance of the

medium. The waveform displayed in the figure corresponds to v = oip/8,

co 0

= u) D

, and 9.^ = 0. The Drude model for electronic conduction in a metal

or a semiconductor results from setting the binding frequency to 0 to zero

in the Lorentz model. The oscillator strength ajp now represents the plasma

frequency for a collective oscillation of the free electron gas. By

further eliminating the viscous damping the impulse response of a cold,

collisionless plasma results.

A metal surface characterized as smooth, lossless and infinitely

conducting (v = 0 and w = ») is an ideal reflector incapable of dispersing

an incident waveform, i.e., R(t) = -6(t). As such it provides a useful,

but fictitious, comparison standard for evaluating the dispersive effects

of surface roughness. The final entry in the accompanying taDle describes

the impulse response for scattering in the direction of specular reflection

by a randomly rough perfect conductor. Conditions of normal incidence are assumed so that no surface element is shadowed from the incident radiation

by any other element. Also, the distribution of surface heights about the

mean surface plane is assumed to be Gaussian with root-mean-square height

arms* Tne usual Fresnel-Kirchoff diffraction formula (3) has been applied

to evaluate the scattering of a unit intensity, monochromatic planewave.

In performing the integration, the tilt of the surface normal on each

element of the rough surface relative to the normal to the mean plane has

been disregarded. This would appear to limit the application of the theory

to surfaces of small arms

or gentle slopes, and has the effect of treating

the surface as a phase screen. Namely, the field-induced surface current

has the same magnitude as that induced upon a plane reflector occupying

the mean surface, whereas the phase at each location varies proportionately

with the random surface height. The application of the inverse Fourier

transform to the scattered monochromatic field gives R(t). Note from the

expression in the table that in the limit of a perfectly smooth surface

(arms

* 0), R(t) * -6(t), as it should.

The foregoing expressions may be applied as follows to materials which

are simultaneously dispersive and rough. For conditions of normal incidence

and normal scattering, the Fresnel-Kirchoff formula is easily generalized to

account for the reflectivity of the medium. Since the Fresnel reflection

coefficient for a perfect conductor is -1, the generalization is accomplished

by multiplying the scattered field amplitude by the negative value of the

Fresnel reflection coefficient for the dispersive medium. (Describing the

reflectivity by a Fresnel coefficient is an approximation consistent with the

phase screen approximation.) In the time domain, the impulse response

function for the simultaneously rough and dispersive medium is given by the

convolution of the impulse response for the rough, perfect conductor with the

negative of R(t) for the dispersive bulk material.

18
The waveform upon reflection for an actual optical pulse is evaluated as a convolution of this incident signal with the overall impulse response of the

medium. Since an incident physical pulse would have finite bandwidth,

shortcomings in the derivation of R(t) for large and small arms

/* tend

to become suppressed in the computation of the reflected pulse.

References

(1) Halbout, J.-M.; Grischowski, D. 12 femtosecond compressed laser pulses.

J. Opt. Soc. Am. 74: 1337; 1984.

(2) Lieberman, A. G. Transient state analysis of plane electromagnetic waves reflected from dispersive material surfaces. Nat. Bur. Stand. (U.S.)

Tech. Note 1202; 1985. 69 p.

(3) Born, M.; Wolf, E. Principles of optics. New York: Pergamon Press;

1980. 375-382.

19
IMPULSE RESPONSE FUNCTIONS

DEBYE POLAR DIELECTRIC

,B«„ = -(i)-

, I1 (^)..p[-(i^.),]

T'~ rcos 2 0j/X(O)

.8

.4 ^ 0 a -4

_ Q -.12

<

f

> 1 2 t/r 3 4

COLLISIONLESS PLASMA

R(t)/a>p =-(2/ojpt) J 2 (ct»pt)

(up : cup/cos 0|

.1

0 ?

- 1

AC -.3

-.4

j^f**^

1 1 1 1 1 1 1 I

< > 8 (Opt 24 32

DRUDE METAL

' 1, 'Jv, ,„ (3/2, n) ["(dipt) 2 ~| n

, R t /COp = --((WD

t) 2- (-1)" — ' — ln ^t/2

4

p l„=0 (3,n)nl L VX J

.08 ^ -08

— -

fiC -.24

-.32 1/ i i i i i i i > 8 (Opt 24 32

LORENTZ DIELECTRIC

R(t)/co p =--(a>pt) 2. (-D n 7—-r~ ; p

I J n(^ c

t) 4 <n=0 (3,n)n! L 2(t» c

t J n c

\ e

-I/t/2

.16 .a 08 3 o H -08

-.16

-.24

(

1 1 1 1 1 1 1 1

) 8 a>£t 24 32

ROUGH PERFECT CONDUCTOR

R(t)/(Oco = ^= exp -(OJcot) 2

/4j

OJ co = C/ /2 a rmg

.2 o

1

3

0 ^ -.1 £ -2

-.3

1 « 2 Wco* 8 8

20
THEORY OF LIGHT SCATTERING FROM A ROUGH SURFACE WITH A

NONLOCAL INHOMOGENEOUS DIELECTRIC PERMITTIVITY

J. M. Elson

Michelson Laboratory, Physics Division

Naval Weapons Center, China Lake, California 93555

First-order perturbation theory can be used to predict the combined effect of

surface roughness and dielectric inhomogeneities on the scattering of light

from optical surfaces. Figure 1 shows log 1

0

[ (dP/dfi)/PQ ] versus polar angle

of scattering, where (dP/dfO/P0 is the differential scattered power dP per

unit solid angle dQ, normalized to incident power PQ . The angle of incidence

is 60 deg from the normal, and the wavelength is 6328 A. The circles and

squares are scattered light measurements for a mirror with an evaporated

silver coating. The measurements were taken in the plane of incidence for pand s-polarized light, respectively. They may be compared to the theoretical

predictions (solid and dashed curves) for angle-resolved scattering due to

surface roughness only , with p- and s-polarization incident, respectively.

The data and curves to the right of the specular direction of 60 deg are for

scattering directions away from the specular and toward the incident beam

(backscattering) . The angle -60 deg is literally the retroscattering

direction. The data and curves to the left of 60 deg are in directions beyond

the specular direction and away from the incident beam (forward scattering).

Careful examination shows that in the backscattering direction the predicted

polarization ratio is larger than the measured data. In the forward

direction, the predicted polarization ratio is smaller than the measured

data. Thus, in order to obtain better agreement between roughness scattering

theory and these experimental data, the theory curves need to be brought

closer together in the backscattering direction and further apart in the

forward scattering direction. Such a discrepancy as this is frequently seen

in practice, and so Figure 1 does not represent a unique situation. 1

First-order perturbation methods of roughness-induced light scattering do not

offer an opportunity to correct this discrepancy, as can be seen by the

following argument. The ensemble-averaged, angle-resolved scattering formula

can be written

f <d?r

>= Npr l 2 + M2 ]g r (i)

o

where | pr | 2 gr and | s r | 2 gr are the contributions to scattering intensity which are p- and s-polarized, respectively. The r subscript refers to

roughness as a source of scattering. The pr and s r are independent of

surface topography; whereas, gr is the power spectral density of surface

roughness. The polarization ratio of scattered light can thus be written

Rr=|Pr

/ s r |

2

• (2)

21
which is independent of surface roughness, since the power spectral density

cancels out. In other words, the Rr is independent of roughness statistics. Thus, the prediction from Eq. (2) is that Rr will be the same for

different mirrors provided that such parameters as angles of incidence and

scattering, optical constants, and wavelength are held constant. However,

polarization ratio measurements do vary between samples of the same material.

An additional source of scattering may be the explanation for this

disagreement between roughness scattering theory and measured data.

If it is assumed that dielectric inhomogeneities , in addition to roughness,

are present, then perturbation theory may be applied to calculate the scattered fields due to both sources. In this case, the angle-resolved scattering

depends on the autocorrelation properties of the surface roughness [as in Eq.

(1)], the dielectric inhomogeneities [analogous to Eq. (1)], and the statistical cross-correlation between the roughness and dielectric random variables.

In this case, the angle-resolved scattering formula may be written in the

general form

1 dPA T~ <TT>

= A g

r + B

*d + C *rd • (3)

o

where gr , g<j, and g r(j are the power spectral densities associated with

the autocorrelation properties of the roughness, dielectric inhomogeneities,

and the cross-correlation properties between the roughness and dielectric perturbations, respectively. The d subscript refers to dielectric inhomogeneity.

The resulting polarization ratio has the general form

l pr! 2gr + b g

d

+ C grd

R , = p5 , (4) rd |s

r

| 2 gr+ e gd+ f g

rd

which is now dependent on the statistical properties of a given mirror. By

juggling the roughness and dielectric statistics, especially the cross- correlation between them, Rr(j can be increased or decreased relative to the

roughness-only result, and the experimental reflectance curves can be

accurately fitted by theory. If g<j = gr(j = 0, Eq. (4) reduces to the

roughness-only result, as discussed previously. 2

References

1. J. M. Bennett, J. M. Elson, and J. P. Rahn, Proc. SPIE 401 , 234 (1983).

2. J. M. Elson, Phys. Rev. B 30, 5460 (1984).

22
FIGURE 1. Roughness Theory-Experiment

Discrepancy.
OPTICAL PROPERTIES OF METALS IN THE INFRARED - THE DRUDE MODEL, PROBLEMS

WITH IT, AND NON-LOCAL OPTICS

David W. Lynch

Department of Physics and Ames Laboratory-USDOE

Iowa State University

Ames, Iowa 50011

The infrared optical properties of metals are frequently described by a free-electron gas model, the Drude model. This model has only two parameters, an electron scattering time, t, and the plasma frequency, o)p = (4irNe 2 /m) 1 /2 . It can be derived simply from a classical picture for the

electrons, or from the Boltzmann equation. Quantum mechanically, it represents the photoexcitation of a conduction electron accompanied by the scattering of the electron by a phonon or impurity. The frequency-dependent

dielectric function is given 5 by

2 2 2

e(w) = e + ie = 1 - P + i L

1 2 ,,2 2 / 1 , 2 2

\

1+W T 0) ( 1+0) T ) The conductivity, a material function alternate to e, has a real part

g(u) = a(0) with o(0) = Ne^ = V

HtA2 m 4lT

A common test for the applicability of this model is a plot of u)£ 2 vs. e,-l

which should be a straight line. In many cases, when data over a limited

wavelength region are used, the plot yields a satisfactory straight line, even for materials for which the free-electron contribution to e is known

not to be the only one. In such cases the parameters derived from the data

will not be meaningful. We discuss several situations for which the Drude

model is known not to be valid, despite its use in the literature.

The infrared is taken here to mean the region between 1 and 50 ym wavelength, and we assume temperatures are around room temperature, except as noted below. In this range the excitations of the free electrons are the

only excitations to consider only if interband transitions are negligible.

There are just a few elemental metals for which this is so, and all are monovalent: the five alkali metals and the three noble metals. In principle, all polyvalent metals have interband transitions extending to arbitrar

ily low energies. The practical problem here is to whether the low-energy

interband contributions to e are negligible with respect to the Drude con- tribution in a given spectral region and at a particular temperature. For

the transition metals and rare earths, and presumably the actinides, the

region of strong interband contributions to e depends primarily on the

crystal structure, and is roughly the region above 1 eV for b.c.c. -structured metals, above 0.1 eV for h.c. p. -structured metals, and above 0.05 eV

for f.c.c. structured materials. In principle, all these metals have inter

band transitions at still lower energies, but their contribution to e is

relatively small compared to the Drude term. Despite this, the Drude model

has been fit successfully over a limited energy range to optical data for

2 4
some of the transition metals. There appears to be no simple structurebased rule for the polyvalent simple metals. If we take aluminum as an example, there is an interband absorption peak around 0.5 eV, which has a tail extending to lower energy. In fact, band structure calculations show

that there are' regions in the Brillouin zone where two bands cross at the

Fermi energy, leading to intraband absorption at arbitrarily low energies.

The 0.55 eV interband structure is difficult to detect at room temperature

because of the dominance of the Drude contribution. It probably has not

affected significantly the fit to the Drude model. At lower temperatures

the Drude contribution diminishes, and the interband term becomes relatively

mor e impor t ant

There have been a number of studies of the alkali metals, which should have

a well-defined threshold for interband transitions, predictable from reliable Fermi surface measurements. Significant absorption has been found

below this energy, some of it reproducible. Until the origin of this is

clear, one must be suspicious of Drude parameters obtained in the spectral

region near this "anomalous" absorption. A recent suggestion is that it

arises from excitations to or from surface states, and a calculation indicates that the expected magnitude is correct. Similar optical effects of

surface states have been seen in electroref lectance measurements on Ag

around 1 eV, i.e., well inside the Drude region. In this case, however, the

observed efects are very small and require that the surface be predominantly

100 or 110 planes. Such effects of surface states probably do not affect

the extraction of Drude parameters from data on Ag, but they could have an effect on the alkali metals.

We now discuss some limited aspects of non-local optics at the surface of a metal and how this affects the interpretation of optical measurements. We assume the metal can be described by a single dielectric function, later to

be extended to two functions. This implies that the metal is completely

homogeneous right up to the surface, where it terminates. We thereby ignore

surface relaxation and the tail-off of the electron distribution into the vacuum. We simplify the above free-electron dielectric function for two

regions in the infrared, where oj « up. If ojt « 1 ,22 2 t e

l * 1 - V e 2

* w

p w

a(u) * a(0)

2_ / 2a> A = 1 - R

(R and A are reflectance and absorbance at normal incidence on a semiinfinite sample.) This is the Hagen-Rubens or classical skin effect region,

If wt » 1 we have the relaxation region in which

2 2

1 2 2

3

0) 0) T

a (u) q(0)

2 2

A = v

25
In a relatively pure metal, t will increase by a large factor, the resistivity ratio, as the sample is cooled to 4.2 K. The measured absorbance

falls only a little as the sample is cooled, and the low temperature value

of A is far larger than the Drude theory predicts. Classically, the radiation penetrates to a depth characterized by the classical skin depth, 6Q =

c/(2ira)a(0)) 1/2 . At room temperature the mean free path of the electrons, 1 = Vpt, is much shorter than 5 Q

. At low temperatures, the mean free path can be much larger, depending on the impurity and defect concentration in the

individual sample. 1 can even be larger than 6 6 0wt, in the relaxation

region. When the mean free path is not much less than the classical skin

depth, we speak of the region of the anomalous skin depth, and non-local

optics must be introduced. Local optics uses a local constitutive relation,

e.g., J a£. (Cubic crystals are assumed.) This means that at each point

r in space and t in time the current density is proportional to the electric

field at that r and t. The constant of proportionality contains an average

of the electron velocity, i.e., the response of the electrons to the applied

field E at r and t. When the mean free path is large compared to the skin

depth, the velocity at a point r, t is not proportional to the field there,

but rather depends on the field at other points and earlier times, going

back along its trajectory to its previous collision. The electric field is

not constant over this path. The relationship between 5 and £ is now an integral one

J(f ,t) - TMsL j R[U(f ,f )] fixp (_ W/1) d

3 W R

* |t|«

with R = r" - t

1 and t

1 = t - |r|/vf

, a retarded time. Important contributions come only from a volume around r of the order of the the mean free

path in radius. This is a non-local relationship, and to the extent that

the effect is a large one, it means that one can no longer define a local

constitutive relation, J aE, that has any meaning. Just as the time

dependence of the electronic response can be Fourier transformed to give

individual frequency components, in a periodic solid, the r",r' dependence

becomes the simpler dependence on r-r', which Fourier transforms to a wave vector dependence. This means that for non-local optics, the conductivity

depends separately on the frequency and wave vector. A measurement at a fixed frequency involves a response function that is integrated over all wave vectors.

A second reason for the introduction of non-local optics is the occurrence

of surface charge induced on the surface of the metal by p-polarized radiation at non-normal incidence. The boundary condition on the normal component of t leads to a surface charge density, one of zero thickness in classical electromagnetism. The uncertainty principle dictates that this will

spread into a finite thickness, often of the order of the Thomas-Fermi

screening length, about 1 A for metals. When one Fourier analyzes this

spatial distribution, a large spread of wave vectors results, and these must

be summed to get the response to an incident wave of a single frequency.

The surface charge density gives rise to longitudinal electric fields, while

the fields of the electromagnetic wave are transverse. Two dielectric functions are now needed, a longitudinal and a transverse, except at normal

26
incidence. Both depend on both frequency and wave vector, but in the limit

of zero wave vector, they become equal. However, for non-normal incidence,

both are needed. Both dielectric functions may be obtained from calculations of varying degrees of sophistication. Once obtained, they may be used

for comparison with experiment, but because e (o),k) is not measured in the

infrared (although some high resolution electron energy loss measurements

are approaching this) a measurable quantity must be calculated from the

dielectric functions. This is the surface impedance 2, 4tr/c times the ratio

of the surface electric to magnetic fields, from which the reflectance can

be calculated as

2 R = Z -

4tt

Z +

4tt c~

If A « 1 A » £ Re(Z)

Z may be calculated. It not only depends on the model for the electron gas

and the surface, but on a boundary condition imposed on the electron momentum at the surface. A fraction p of the electrons is assumed to scatter

specularly at the surface, with the remainder scattering perfectly diffusely. At normal incidence in the Hagen-Rubens region the absorbance is

_ / 2a) + (1 _ )£ r p

T 8

c

3 V

F

which agrees with the Drude result if all scattering is specular, The

result for the relaxation region is

2

A = p I £*)&3

2 2

c + (1 - p)l

4

^c

in which the scattering time does not even appear. Holstein pointed out

that there is an additional process contributing to A, a second-order one in

which a photon excites an electron and a momentum-conserving phonon. It

contributes an additive term to A of

A = A !_D

H 5 f

1 V

in which 9^ is the Debye temperature and T is a relatively high temperature

(not that of the measurement of A) at which the electron-phonon scattering

time is t.

The anomalous skin effect completely dominates the low temperature infrared

optical properties of pure metals. At room temperature it produces a cor- rection that is of the order of a few percent at most (in A, still less in

R) , depending on wavelength. To the extent that it is present, it weakens

the concept of a frequency-dependent function to describe the optical properties. The use of such a function, e.g., e, to predict optical properties

other than the one from which it was derived, can lead to errors.

27
SEPARATION OF DRUDE AND BAND-TO-BAND SPECTRA IN POLYVALENT METALS

D. Y. Smith*

Argonne National Laboratory

Argonne, Illinois 60439

and

B. Segall

Case Western Reserve University

Cleveland, Ohio 44106

The problem of separating intra- and interband contributions to optical

properties has been reexamined with the goal of minimizing the dependence of

the separation on specific models. This was prompted by a desire to compare

the recently published*" theoretical interband spectrum of aluminum with

reflectance measurements. Unfortunately, such a comparison is complicated

because intra- and interband effects are almost inextricably intermeshed in

2 -ft

J the data. Several prior analyses have involved restrictive assumptions

regarding the interband component. However, we present here an approach that uses general qualitative features of the theory combined with experimental

data over a wide energy range that reduces the assumptions required and yields

a more reliable separation.

Interband absorption arises from electron-hole excitations and may be treated

in one-electron theory. Band structure calculations show that for aluminum

there are two principal interband excitations^ * ^ arising from transitions

between pairs of parallel bands^'^ near zone boundaries. These parallel-band

absorptions have sharp onsets at the zone-boundary energy gaps--estimated from

Fermi-surface, data to lie at ~0.5 and ~1.6 eV--followed by long high-energy

tails. In addition, detailed band calculations*" » predict a weak absorption

extending to zero energy and substantial broadening of the parallel-band

transitions.

Intraband absorption involves creation of an electron-hole pair within a band

and its simultaneous scattering by phonons. For co >> w(Debye), the intraband

contribution to the dielectric function has the "free-electron" Drude form*^

f 2 e (to) = 1 - ft /w(uH-i/T ) . (1)

P

ftp & t , the intraband plasma frequency and relaxation time, are constants.

In principle, the intra- and interband contributions may be separated because,

below the lowest parallel-band absorption, the Drude term dominates. The

reflectance of unoxidized aluminum films at room temperature is shown in

Fig. 1 after Bennett et al . 3 That of a good Drude "metal" is given in the

inset. Comparison of the two suggests that the measured spectrum is Drudelike below ~0.2 eV in accord with the theoretical expectations. For

2 -fi(o(Debye) = 0.07 eV 4 "fiw ^ 0.2 eV the reflectance has a frequency depen1/2 dence intermediate between a Hagens-Rubens form— In [R (a)) ] * - (2w/Tra ) , -1 HR -1

°

(D << t << ft —and the Dingle value — In [R (w) ] = - ft /2ira , t < w << ft —

p D p o p

Work supported by the U. S. Department of Energy.

28
where a is the dc conductivity. In this intermediate regime the reflectance

o 13

may be fit using the modified Kronig formula

In [R^((o)] « - (2w/-rrao

) 1/2

[(l+a)

2 T2

) 1/2

- wt]

1/2

. (2)

However, even the small (± 0.1%) error in the reflectance data of Bennett

et al . translates into a large uncertainty in the Drude parameters, namely:

12 eV ^ m 4 29 eV and 0.06 eV Ik" 1 ^0.2 eV. Note that the Dingle plateau

(indicated by a dashed line) does not develop because of the onset of the

strong interband transitions.

An alternative is to seek a separation of the intra- and interband components

of the dielectric function e(o)) = e'(w) + i e"(w) obtained from an analysis of

the reflectance measurements. The e(w) for Bennett et al .

' s^ data has been

given by Shiles et al . ^ One approach employs theoretical guidance as to the

form of the interband contribution. An obvious choice is the analytical model

of Ashcroft and Sturm 1 ^ which, together with a Drude term, may be fit to e(u)).

This method has been applied previously^*** and was tested here. Our experience was that, if no interrelation was assumed between the various parameters,

a broad and poorly defined minimum—especially for lifetimes—occurred in the

least-squares fitting. Moreover, the two-band model does not account for

interaction with other bands and introduces a bias into the separation.

To avoid these problems we employed the general, rather than the specific

features of the interband spectrum, in particular the dominant parallel-band

absorptions at ~0.5 and ~1.6 eV. These make distinctive contributions to

e'(oj) in the form of regions of anomalous dispersion. Hence, one expects the

total e'(oo) consists of (a) the Drude contribution with (b) two superimposed

oscillatory dispersions at each of the parallel-band absorptions; see Fig. 2.

The fitting procedure consists of searching for values of the Drude parameters

that give an intraband contribution to e'(w) which (a) fits the experimental

e'(o)) curve in the Drude region below 0.2 eV; but which (b) passes through the

29
Fig. 2. Comparison of the

experimental e'(u>) after Shiles

et al . with a trial Drude

contribution satisfying the

criteria of fitting experiment at

low energies, and passing through

regions of anomalous intraband

dispersion. Note y = t"*.

0.0 -

Y

3.0 oo

6.00 2.0 ENERGY (eV)

experimental e'(w) curve near the expected positions of the parallel-band

absorptions so as to form a monatonically increasing "background" on which the

anomalous interband dispersions are superimposed. In ambiguous cases the

regions where the crossings occur may be located using d [ e

' (w) ] /dw. These

requirements were found to be highly constraining for aluminum yielding

•fiOp = 12.5 ± 0.3 eV, and t = 1.06 ± 0.12 x 10" 14 sec.

A comparison with literature values is given in Table 1. Early studies, such

as that of Mendlowitz,^ involved fits above 2-2.5 eV and forced all the con- duction-band oscillator strength into the Drude term; the resulting t is too

small. Bennett et al . assumed both Q and a from independent experiments.

Ehrenreich et alT*" and Powell 5 separated the 1.5 eV transition, but included

the 0.5 eV transition in their Drude term. Dresselhaus et al . and Mathewson

and Myers^ (M & M) accounted for both principal interband transitions; the

latter via a fit of the Ashcrof t-S turm model^ to ellipsometric measurements

Q from 0.7 - 2.5 eV. Benbow and Lynch0 also accounted for both transitions, but

assumed ft (via the optical mass) following Ashcrof t and Sturm.

The present room temperature results and those of M & M agree nearly within

the estimated uncertainty. M & M's high value of ft may arise because their

measurements extended to only 0.7 eV--well above thl Drude region. However,

Table I. Aluminum Drude Parameters and Oscillator Strength f

f (in electrons/atoms)

Source

Temp

(K)

Kl

P (eV) (10

T 14 sec)f

f (e/a)

a opt<°>

(10 sec Mendlowitz (1960), Ref. 2 RT 14.1 0.12 2.40 0.44

Bennett et al. (1966), Ref. 3 RT 14.7 0.801 2.60 3.18

Ehrenreich et al. (1963) Ref. 4 RT 12.7 0.512 1.94 1.52

Powell (1970T, Ref. 5 RT 12.2 0.66 1.80 1.81

Dresselhaus et al. (1971), Ref. 6 RT 12.9*0.7 0.5*0.2 2.0±0.2 1.60*0.8

Mathewson and Myers (1972), Ref. 7 RT 13.0 1.02 2.03 3.14

Benbow and Lynch (1975), Ref. 8 4.2 12.7 1.10 1.94 3.25

Smith and Segall (present work) RT 12.5*0.3 1.06*0.12 1.88±0.09 3.00*0.30

Electrical Conductivity, Ref. 15 RT 3.18-3.39

30
in both cases the optical fa = ft t/4it1 and electrical conductivities are

o p equal to within the uncertainty or the separation. The values of t and a Q

given by Dresselhaus et al.^ is in disagreement with M & M and the present

work; the reason is not "cTear from their publication.

Fig. 3. Interband

conductivity of

aluminum. The experimental curve is for the room- temperature reflectance data of Bennett

et al. as analyzed by

Shiles et_ a_l_. The

theoretical results of

Szmulowicz and Segall

are based on parameterized APW band

calculations.

i c_> Ld

</) inO

12.0-

INTERBAND CONDUCTIVITY FOR ALUMINUM

°"inter

= "^exp" °"Drude (ticj p

= 12.8 eV.ti/^ 61.4 meV)

THEORY SZMULOWICZ a SEGALL

2.0 3.0 ENERGY (eV)

The experimental interband conductivity obtained by subtraction of the Drude

contribution is given in Fig. 3. The position and shape of the 1.6 eV

transition are independent of Q and t within the range of the Drude

parameters. The position of thl low-energy peak varies between 0.3 and

0.35 eV, its height is uncertain by ± 20%. The predictions of Szmulowicz and

Segall*- are given in Fig. 3 for comparison. These were made for aluminum at

A K; at higher temperatures broadening and a red shift is expected. Consequently, agreement between theory and experiment is considered quite good.

References

1. F. Szmulowicz and B. Segall, Phys. Rev. B 2U_, 892 (1981).

2. H. Mendlowitz, Proc. Phys. Soc. _75, 664 (1960).

3. H. E. Bennett, M. Silver, and E. J. Ashley, J. Opt. Soc. Am. 53_, 1089

(1963).

4. H. Ehrenreich, H. R. Philipp, and B. Segall, Phys. Rev. 132 , 1918 (1963).

5. C. J. Powell, J. Opt. Soc. Am. _60, 78 (1970).

6. G. Dresselhaus, M. S. Dresselhaus, and D. Beaglehole, in Electronic

Density of States , edited by L. H. Bennett, NBS Special Publication 323,

National Bureau of Standards, Washington, DC (1971).

7. A. G. Mathewson and H. P. Myers, J. Phys. F _2 , 403 (1972).

8. R. L. Benbow and D. W. Lynch, Phys. Rev. B _12 , 5615 (1975).

9. W. H. Harrison, Phys. Rev. 147 , 467 (1966).

10. N. W. Ashcroft and K. Sturm, Phys. Rev. B _3 , 1898 (1971).

11. D. Brust, Phys. Rev. B _2 , 818 (1970).

12. G. P. Mahan, Many Particle Physics (Plenum, New York, 1981).

13. F. Modine and D. Y. Smith, J. Opt. Soc. Am., in press.

14. E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22_, 1612

(1980).

15. Handbook of Chemistry & Physics, R. C. Weast, ed. (CRC, Boca Raton, 1972 & 1983) 52nd and 64th ed.

31
STATUS OF MATERIALS FOR TRANSMISSIVE AND REFLECTIVE INFRARED COMPONENTS

H. E. Bennett

Michelson Laboratory, Physics Division

Naval Weapons Center, China Lake, California 93555

The search for better infrared materials for transraissive and reflective

optics has been ongoing for at least 70 years. Alkali halides were developed

as infrared transmitting materials for spectrometers before 1950, but achieved

very low absorption only in the 1970s. In response to the requirements of the

laser community, alkali halide optics were produced with infrared absorption

coefficients two orders of magnitude lower than had previously been available. For example, at the C0 2 lasing wavelength of 10.6 ym, absorption coefficients of KC1 as low as 8 x 10~ 5 cm

-1 have been reported. In the process

of achieving this low absorption, a better understanding of the absorption

process was achieved. As illustrated in Figure 1, the absorption of a typical

dielectric reaches a maximum in the far and intermediate infrared as a result

of infrared excitation of the molecular vibration or reststrahlen bands. At

shorter wavelengths, the absorption falls off at a rate which in many materials is a nearly exponential function of wavenumber 2 (and hence nearly linear on a semilog plot, as illustrated in Figure 1). This multiphonon absorption

is intrinsic to the material and can only be changed by changing the material

or its crystal structure.

As the wavelength decreases, the absorption levels off and becomes nearly

independent of wavelength. By removing or compensating for impurities, reducing grain boundary absorption, reducing distortion in the crystal lattice,

minimizing lattice defects, and lowering surface absorption, this extrinsic

absorption can be reduced, sometimes dramatically. To obtain a low absorption

infrared material, the technique is then to pick a material (and ideally a crystal structure, although this option is usually not available) which has

low intrinsic absorption in the wavelength region of interest and then through

process control reduce the extrinsic absorption to the desired level.

In addition to optical absorption, various other parameters must be considered

in selecting an infrared transmitting material for a given application. In

many cases, fracture toughness, resistance to thermal shock, and insensitivity

to environmental agents such as water are of great importance. KC1 and many

of the other alkali halides are very soluble in water. To overcome this

difficulty, high-purity ZnSe was developed in a multimillion-dollar program

lasting several years. Eventually, an absorption at 10.6 ym in this material

comparable to purified KC1 was achieved. ZnSe, although hydrophobic, shares

with KC1 and most of the other alkali halides the problem of being extremely

soft with low-fracture toughness. To obtain a stronger, low-absorption material, work began on purifying ZnS. The well-known yellow cast was removed,

leaving a water-clear material, and the infrared absorption coefficient was reduced from about 5 x 10" 2 cm-1 to 2 x 10~ 3

, a factor of 25 times, in the

a extrinsic absorption region.

32
Unfortunately, ZnS has raultiphonon structure in the 10 to 20 ym wavelength

region arising from excitation of the 3ojto phonon. 4 This absorption is

intrinsic and thus cannot be removed. The material, although harder than ZnSe

and surprisingly resistant to thermal shock, is still relatively soft, with

low-fracture toughness. A harder material with lower absorption in the 8 to

12 ym wavelength region would be useful. The ternary sulfides offer promise

here, and Cal^S^, a cubic material with a thorium phosphide structure, has

been under development for several years. The progress made in reducing

extrinsic absorption in this material and a comparison to ZnSe and ZnS are shown in Figure 2.

A compromise must be made between physical properties such as fracture tough- ness and low infrared absorption. Strong, high-melting materials typically

are formed by small, light atoms with low coordination numbers (i.e., number

of nearest neighbors) and covalent (directional) bonding. The atoms are thus

tightly bound, have high vibrational frequencies, and hence have significant

intrinsic multiphonon absorption even in the short wavelength infrared.

Transparent infrared materials typically contain large, heavy atoms with high

coordination numbers and ionic (nondirectional) bonding. They thus have low

vibrational frequencies but also tend to be soft with low melting temperatures.

As one proceeds from longer to shorter infrared wavelengths, vibrational frequencies can increase and harder, tougher materials should become available.

Sapphire, a very hard infrared transmitting material with high fracture toughness and good thermal shock properties, is still intrinsic at a wavelength of

3.5 ym. It also is hexagonal and hence slightly birefringent. A cubic crystal structure can be obtained by substituting a nitrogen atom for one of the

oxygen atoms. Techniques of growing this crystal, 5 which has physical properties approaching sapphire and is commonly called ALON or "cubic sapphire,"

have now been developed. Its absorption spectrum is shown in Figure 3. Other

novel infrared transmitting materials in Figure 3 of interest in the 3 to 5 ym

wavelength range, where an atmospheric window exists, are hot-pressed spinel, 6 and sintered yttrium oxide. 7 Their absorption may be compared to IRTRAN 1 (hot-pressed magnesium fluoride), a more traditional material for this

wavelength region, and to water-clear CVD zinc sulfide. Another interesting

material is zirconium oxide, 7 which is exceedingly hard and durable. Unlike

Y 2 0 3

, its absorption cannot be reduced further in the 4 to 5 ym band since it

does not become extrinsic until about 4 ym. The fluoride glasses, one of

which, zirconium barium lanthanum aluminum fluoride cr ZBLA, is shown in

Figure 3, are also of interest in this region, 8 particularly in waveguide

applications

Mirrors as well as windows are often used as infrared components. Recently,

interest has centered on the insensitivity of the mirror substrates to heating

or cooling and to creep. Low-expansion glasses such as ULE or Zerodur are frequently used as substrate materials. Their low-expansion coefficients over

a range of temperatures near ambient and the excellent optical figure and low

microroughness which can be produced by optically polishing these materials

make them very attractive. It has been shown that ULE and Zerodur are among

the most stable materials known, 9 provided they are maintained at ambient

temperature. However, if they are thermally shocked, Zerodur may not return

33
to its initial shape upon cooling. The optical figure of the mirror is

thus degraded, and in critical applications this small effect can become

important. Reasons for this behavior are currently under study.

References

1. J. W. Davisson et _al .

, Third Conference on High Power Infrared Laser

Window Materials-1973 , Air Force Cambridge Research Laboratory, Report

No. AFCRL-TR-0085, Vol. I, pp. 31-42.

2. T. F. Deutsch, J. Phys. Chem. Solid 34_, 2091 (1973).

3. C. A. Klein and C. Willinghara, Raytheon Research Division, Lexington,

Mass. (to be published).

4. C. A. Klein and R. N. Donadio, J. Appl. Phys. _51, 797 (1980).

5. J. W. McCauley and N. D. Corbin, J. Am. Ceram. Soc. 62, 476 (1979); N. D. Corbin and J. W. McCauley, Proc. SPIE 297 , 19-23 (1981).

6. D. W. Roy, Proc. SPIE 297 , 13-18 (1981).

7. W. H. Rhodes and E. A. Trickett, Proc. SPIE 505 (1984) (in press).

8. B. Bendow and D. Martin, ibid . ; C. T. Moynihan, A. J. Bruce, S. R. Loehr,

S. M. Opalka, R. Mossadegh, and N. Perazzo, ibid . 9. J. W. Berthold III, S. F. Jacobs, and M. A. Norton, Appl. Opt. JL5_, 1898

(1976).

10. J. J. Shaffer and H. E. Bennett, Appl. Opt. 23, 2852 (1984).

11. H. E. Bennett, J. J. Shaffer, and D. K. Burge , ibid . , p. 2734.

12. S. F. Jacobs, S. C. Johnston, and G. A. Hansen, ibid . , p. 3014.

RESTSTRAHLEN INTERBAND

PEAKS ABSORPTION

MICROWAVE FAR IR INFRARED VISIBLE ULTRAVIOLET

WAVENUMBER OR FREQUENCY

FIG. 1. Absorption Spectrum of a Typical Dielectric.

The reststrahlen absorption and its multiphonon tail seen on the left side of the figure and the interband

absorption with its Urbach tail seen on the right side

are intrinsic to the material and can sometimes be

removed

.

34
WAVENUMBER (cm-1

) 400 600 800 1000 1200 1400

i

1 1 1 r-j 1 1 1—i—i

1 r~|

WAVELENGTH (nm)

FIG. 2. Multiphonon Edges of Some Useful 8 to 12 ym Materials.

The absorption of CaLa 2

Sit is extrinsic in this region and has

been reduced by over 100 times in the past three years. At

7 ym the absorption of water-clear raultispectral ZnS has been

reduced by about 25 times. It is now intrinsic in the 8 to

12 ym region, and additional decreases in absorption are not

expected here.

WAVENUMBER (cm'1

) 1000 1500 2000 2500 3000

100

10

1 ABSORPTION

COEFFICIENT , (cm-1) 10" 1

10-2

10"3

10 9 8 7 6 5 4 3 WAVELENGTH (um)

FIG. 3. Absorption of Some Useful 3 to 5 ym Materials.

The absorption of Y 2 0 3 in this region is largly extrinsic

as is that of the fluoride glass ZBLA and of water-clear

multispectral ZnS. These absorption levels can thus, at

least in theory, be further reduced.

35
DIMENSIONAL STABILITY

William Primak

Wolfe Loeb & Co.

735 S. Quincy St., Hinsdale, IL 6C521

A few years ago, after I had succeeded in interpreting the large viscoelastic stress relaxation wnich was observed in my laboratory in the 60' s upon

irradiating vitreous silica, a NASA subcontractor contacted me about the

possible dimensional instability in the Space Telescope from the radiation

in the space environment. When I learned that the specification for the mirror was l/60th wave, I asked whether the mirror was that stable even in the

absence of radiation, for this is an interferometrie tolerance. There are

all sorts of precautions which are given in the literature of interferometry

on the proper handling of mirrors, and even a few reports of changes of

this magnitude in their figures. It was not until much later that I learned

the specification was only an rms one, hence a more relaxed one than the absolute specifications I was accustomed to, but, in the meantime I became interested in the literature of the subject. Except for a few investigations

of grinding and polishing, annealing, and thermal cycling, I was unfamiliar

with any scientific investigations of the dimensional stability, which I attributed to optical specialists feeling constrained to handling their optics

very gently. I have learned since about a few attempts to assess the temporal

stability of a few candidate materials for the telescope application. While

the results lend some assurances for -that project, apart from any questions

about precision, tne major criticism of the investigations is that they were not directed toward determining the effects of specific conditions or treatments, hence they are of little value in guiding the manufacture of the materials or the fabrication of components made from them.

The observations which are available are of the alteration of the figures of

plates, changes in internal stress measured photoelastically, alterations in

surface composition measured by refractive index and other means, cnanges in

the lengths of blocks or rods, and surface scattering measurements. Additional information about surfaces nas been obtained by etching.

Emerson(l) reported a l/60th wave alteration in the figure of an optical

flat subjected to a small stress (resulting from its own weignt), but Primak

(2) considered the change to be too large to attribute it to a bulk viscoelastic deformation, and suspected another cause or an error of measurement.

Dew(3) found that hard crown glass flats were not dimensionally stable. He

hypothesized a stress relaxation was occurring, but he was unable to measure

any stresses. Primak (2) suggested that alkali mobility might have been the cause of the instability. Dew did not find this instability in vitreous silica.

Justice (h) measured length changes of two glass ceramics, ULE, and vitreous

silica with a Zeiss gauge block interferometer; and Jacobs and co-workers (5)

employed a stabilized laser cavity to study these and some other materials.

Most of the measurements indicated a small shrinkage, but those for the ce36
ramies, Zerodur and Cervit showed expansions. The measurements were not of

the bodies themselves, but of the distance between plates wrung to, or contacted to, the bodies of interest. Some of the changes were shown to be con- tact changes {$), and it is possible that the changes in the ceramics mayhave been caused by surface deterioration. Although the preparation of the

bodies is described, no characterization of them is reported.

Angel(6) informed me that after kO years, the 100 in. Mount Wilson telescope

still has a \ arc second resolution. The precision of this measurement is

rather less than the interferometric studies described above since it could

be achieved with a lAO wave rms surface, and its significance for viscoelastic stress relaxation is questionable since, according to 0ke(7), this mirror was figured in the horizontal position and tested in t he vertical position, the mounting being cleverly designed so that the figure of the mirror

would not be altered significantly by the change in position, hence the

stresses associated with the aging data could be insignificant.

Surface scattering associated with various' treatments of the surface, ultrasonic cleaning, acid treatment, polishing are reported by Stowell and Orazio

(3). Stowell also informed me of a severe temporal instability of polished

Cervit, and in other materials, of the areas surrounding very light scratches

(9). Reversible alterations in the figure of flats caused by thermal changes

have been considered by Dew(3) who placed thermocouples on the front and back

faces of his plates. The author(2) pointed out that the typical thermal distributions in transverse heat flow should not alter the figure of flats ; the

alterations are associated with lateral heat flow. Permanent changes caused

by thermal cycling were studied by Jacobs(lO) and others(ll). Attempts to

measure a bulk viscoelastic deformation in silicate glasses at room temperature have been unsuccessful. This is not suprizing since the viscosity extrapolated from higher temperatures is over 10->0 poise, and the maximum feasible

measurement would be about KH° poise. The highest value in the literature

known to this author, 10 poise, seems suspect.

What is needed to establish a science of dimensional stability is relating

changes to forces and to molecular alterations. A 3tep in this direction oc- curred when this author interpreted the stress relaxation of vitreous silica

during irradiation (12). The stresses were known, for they had been measured

in the course of determining the radiation-induced dilatation, and the molecular processes occurring were known to cause bond cleavage in the glass, and

after irradiation some centers remained. The stress relaxation could be ac- counted for by an apparent viscosity of 10*"* poise during ion bombardment

(13), 1016 poise during electron bombardment (111), and icfi^- poise following

ion bombardment. A further quantification of the process could be obtained

if the number of centers present could be evaluated. To understand this method of investigation, it is necessary to appreciate the distribution of internal stresses in a body associated with a surface strain. This is presented

in numerous of the author's papers (12). The solution is a linear stress distribution balancing the stresses associated with the surface strain. Thus, it

is possible to determine the surface strain and the associated stress from

the surface being held in constraint by the rest of the body. This can be

done either by measuring the strain birefringence (if the material is suitable

for this purpose and in suitable orientation) or by measuring the deformation

of the surface associated with this stress distribution.

3 7
Another step in this direction occurred in the author's investigation of the

grinding and polishing stresses (15). The thickness of the layer affected was determined by etching it away and measuring the residual stress. Grinding was

found to develop surface stresses in excess of ICk psi which seemed too great

to be accounted for by macroscopic fractures, hence it was attributed to

breaking bonds on the a tomic scale. It was pointed out by Twyman(l6) that

these stresses are sufficient to alter the figure of a plate very significantly, in our experience by several fringes. Here are present all of the elements required for stress relaxation to take place: the cleaved bonds and the

high stresses; hence for dimensional instability] but I am not familiar with

any investigation of this possibility. It should be appreciated that any sur- face damage may alter the figure of a plate.

The alkali in the complex silicate glasses becomes very mobile not very far

above room temperature, and it is possible to electrolyze it with quite low

voltage drops. In the author's studies (17), large dimensional changes accompanied the ion depletion in this process, and similar results have been reported by others (18). Elastic aftereffects have been attributed to displacement

of alkali in these glasses. Both leaching and incorporation of foreign ions

occur in the grinding and polishing of glass, and it is possible that dimensional changes may accompany these. The author is unaware of any investigation of dimensional instability which may accompany such processes, but he

has suggested they may be responsible for some of the effects reported by

Dew(3).

In the author's examination of figured marble surfaces, large changes in the

figure were encountered after relatively mild thermal cycling, that associated

with cleaning in hot organic solvents (19) • Additionally, a deterioration of

the surface finish occurred. Even as little as a minute of ultrasonic cleaning was sufficient to cause a noticeable deterioration of the surface finish

of the marble. Marble is a random conglomerate of small calcite crystals.

There is a very large aeolotropy in the thermal expansions of calcite and

also in its elastic constants. The dimensional changes probably were caused

by an intergranular ratcheting mechanism, much as has been described for the

behavior of uranium fuel elements. It seems likely that this kind of process

occurs in Cervit and should be anticipated in all inhomogeneous materials.

The high silica borosilicate glasses such as have been favored for large terrestrial telescope mirrors are inhomogeneous because small compositional variations remain in manufacture because of the high viscosity at the manufacturing temperature. These inhomogeneities are typically present on the millimeter scale and are readily seen in a polarimeter. They are called "cords" in

the trade. The birefringence results from differences in thermal expansion

when cooling below the strain point. Stresses approaching 1000 psi have been

observed for these regions (20). This writer is not familiar with any studies

of dimensional instability which may be associated with these cords.

While surface studies do not typically relate behavior to forces, they are valuable in understanding structure and composition. Notable among these studies are Rawstron' s(21) by etching in which he showed that the structure seen in etching of polished hard crown glass is not associated with the prior

grinding, but rather with the action of the polisher in dragging polishing

particles across the surface. Evidence of a special polish layer was found by

Stowell and 0razio(8) in studies of light scattering from the surface.

38
Many of the studies which have been reported here were funded in other con- nections. They could be extended to provide valuable insights into the dimensional instabilities of optical materials and yield the kind of information

which would be helpful in improving the materials in manufacture and in their

performance when fabricated, but no funding for such investigations has yet

been forthcoming. I have not mentioned the dimensional changes caused by radiation, a subject which should be of concern for space applications, because

this could provide a whole talk by itself, but I should mention it appears

that an important component will be the low energy flux about which there is

only limited information (22). It would be very desirable therefore to place

a material like vitreous silica (whose radiation behavior has been explored

extensively) into the space environment and examine it afterward. There is a great deal of information about radiation effects at high fluxes, but tnere

is little for the low fluxes and low fluences which would apply in these applications. Although there is considerable information about the radiation

behavior of vitreous silica, to the best of my knowledge, the behavior of

the low expansion materials (22) has not been investigated.

REFERENCES

1. W. B. Emerson, J. Res. (NBS), 1*9(1952)21*1

2. W. Primak, Opt. Eng., 23(1981*)306

3. G. D. Dew, Opt. Acta, 21(1971*) 609

k. B. Justice, J. Res. (NBS), 79A(1975)51*5

5. J. W. Berthold III, S. F. Jacobs. M. H. Norton, Appl. Opt., 15(1976)1398

6. J. R. P. Angel, Priv. Comm. (193U)

7. B. Oke, Priv. Comm. (1931*)

3. W. K. Stowell, F. D. Orazio, SPIE paper no. 1*06-01* (1931*)

9. W. K. Stowell, Priv. Comm., (198k)

10. S. F. Jacobs, S. C. Johnston, G. A. Hansen, Appl. Opt., 23(193103011*

11. J. J. Shaffer, H. E. Bennett, Appl. Opt., 23(1981*)2352

12. W. Primak, J. Appl. Phys., 53(1932)7331

13. W. Primak, J. Appl. Phys., 55(1931*) 352

ll*. W. Primak, J. Appl. Phys., 55( 1931*) 3315

15. W. Primak, Phys. Chem. Glasses, 1*3(1931)1*3

16. F. N. Twyman, "Prism and Lens Making", Hilger & Watts, 2nd Ed. (1952)p3l8

17. W. Primak, E. Monahan, J. Electrochem. Soc, 126(1979)2196

18. D. E. Carlson, K. W. Hang, G. F. Stockdale, J. Am. Ceram. Soc,

57(197l*)295

19. W. Primak, Report submitted by C. A. Youngdahl to NAPAP Group G Stone

Subcommittee (10/22/1931*)

20. H. Hagy, Priv. Comm. (1931*)

21. G. 0. Rawstron, Trans. Soc. Glass Techn., 1*2(1958)253

22. W. Primak to J. Osantowski, (3/19/1931*), (l*/2/1931*)

23. S. Pearson, J. Soc. Glass Technol.. 36(1952)105T

21*. F. W. Preston, Glass Technology, li*(1973)20

ADDENDUM

Hagy (20) informed me of pertinent investigations (23, 21*) of stress deformation of high alkali silicate glass bodies (non-optical) having high aspect

ratios. Surface affects were shown by effects of humidity; elastic aftereffects were seen.

39
NONLINEAR OPTICAL PROPERTIES OF ORGANIC POLYMER MATERIALS

G.M. Carter, Y.J. Chen, M.F. Rubner, M.K. Thakur, S.K. Tripathy,

J. P. Georger, and J.V. Hryniewicz \

GTE Laboratories, Inc.

40 Sylvan Road, Waltham, Mass. 02254

Research into the nonlinear optical properties of organic polymers includes

such phemonena as harmonic generation, Raman scattering, difference frequency generation, and the Kerr effect as well as including a wide variety of

materials (available through organic synthesis) in various forms (e.g. solu1 tion, liquid crystal, and solid). In order to realize practical applications

from such research an interdisciplinary approach is necessary. As an example, optical signal processing schemes require materials that have large nonli- near optical coefficients combined with desirable linear optical properties (e.g.

low loss, low scatter) as well as being processible in desired forms (e.g.

waveguides). In order to examine the interdisciplinary nature of the re- search, we will restrict our discussion to a class of polymers, the polydiacety lenes (PDA's), ^C-CiC-C^. The PDA's have the potential to be such a material system when their third order optical nonlinearity is suitably em2 ployed. In the solid state, the PDA's have the largest measured nonresonant

f 3 ) - 1 0 2 third order nonlinear susceptibility x ( = 10 esu). In addition, they are

obtainable for a large number of side groups (molecules) R and R' which determine the structural properties of the PDA's, and in many examples can be

grown in single crystalline form. The large nonlinear coefficient is attributed

to the one-dimensional delocalized (pi) electronic states of the carbon back3 bone, and as such has lead to the prediction of subpicosecond response

2 times for these nonlinear coefficients. However, to assess the usefulness of

these materials for signal processing more research is needed. All of the

measurements in the solid state have been on the nanosecond time scale with no time resolution ,

' ^' ^ and recent theoretical research has indicated that

the strong coupling between the electronic and vibrational states in the PDA's

Q may increase the response time of the optical nonlinearity to > picosecond.

Further it is not clear what effect material form has on the results. Two of

4 5 the measurements were in bulk crystals, ' and two of them were in thin

6 7 (3

)

films ' one of which yielded a much smaller value for x than the other

6 three. In the following we present some recent research results from our

laboratory that are aimed at providing information to help assess the PDA's as

a nonlinear optical materials system.

To obtain high optical quality PDA thin films in the form of planar waveguides

used in our nonlinear optical measuements, we use the Langmuir Blodgett

40
(LB) technique to form a diacetylene monomer

[f^CHg-CCh^)-^; R' = (CH2)g-COOH] monolayer on an inert gas-water interface

to polymerize the material while still at the interface and to subsequently deposit the polymer monolayer onto the substrate. Recently we have been able

to "grow" mono-phase high optical density films with either the "blue" or

9

"red" spectrum as shown in Fig.1. The "blue" form was prepared by polymerizing the monomer monolayer for 90 sec at 12.5°C at the gas-water interface followed by transfer of the partially polymerized monolayer to the substrate. After the multilayer of the desired thickness was formed, the film

was further polymerized for 150 sec. at 12.5°C (optical density per monolayer

of 0.004 at 630nm) . The "red" form was prepared by polymerizing the monomer monolayer 9 min. at the gas-water interface followed by the transfer

of the polymer monolayer to the substrate. The final multilayer assembly was

heat annealed at 70° C for 2 min. to insure a completely "red" form (optical

density per monolayer of 0.008 at 500nm.). The nonlinear coefficient re- ported in our earlier work was a mixture of the two phases, and since on

theoretical grounds one would expect the red phase (a more localized PDA

phase) to have a significantly smaller optical nonlinearity , the "blue" phase

films prepared by the technique described above should yield larger optical

nonlinearities

.

To study the LB multilayer growth process we have carried out surface en- hanced and resonant Raman scattering (SERS and RRS) on mono- and multilayers of our LB "grown" films. Fig. 2 shows Raman spectra using a 6328A"

HeNe laser line for one, two, and three bilayers of a PDA film grown on a roughened silver substrate. The Raman spectrum of a single monolayer (attributed to the SERS mechanism ) is the same as that for one bilayer, and

matches that obtained from a bulk "red" phase material while the subsequent

multilayer spectrum matches that of the "blue" phase. RRS data is consistent

with this phase assignment of the first two layers relative to the subsequent

layers. Our experiments show that: 1. The preparation of the monolayer film

is important in obtaining high optical quality "blue" phase films; 2. A lot

more defects were present for the first bilayer than for the subsequent bilayers; 3. To obtain phase matched interfaces two or more bilayer growth is needed for the LB process.

Since no dynamical information exists of the PDA excited states for optical excitations near their absorption maximum (typically 600-650nm), we have initiated pump-probe (saturated transmission) experiments in thin film PDA's to

help understand the excited state processes in these materials and to examine

the limitations imposed on the optical nonlinearity by these processes. These

experiments used an intense (>1 kW peak power), transform limited ( 6 psec

duration) optical pulse from a tunable synchronously pumped cavity dumped

dye laser system. In the LB films we obtained data from 6200- 6700A\ As

shoWn ^"n Fig. 3 for wavelengths shorter than the "blue" absorption maximum

( S 6300A), we observed that the pump beam did not change the transmission

of the weaker probe beam (derived from the same laser pulse) when the two

beams did not overlap in time. However when the incident wavelength was

changed to 6400^ (and other wavelengths longer than the absorption maximum) the probe transmission was affected by the pump when the probe arrival time at the sample was delayed relative to the pump. This "memory" effect

41
had =1 nsec time constant. We have observed a similar time constant for thin

samples of the PDA, TCDU. Note that the spike near zero relative time delay

in Fig. 3 is a coherence (self-scattering) effect, and only lasts for the pulse

duration. Thus in this spectral region the excited state processes observable

by this technique have wavelength dependent decay times which are either

long (=1 nsec) or short compared to our pulse duration, 6 psec (and thus not

resolved). We are now experimentally and theoretically concentrating on re-

(3) lating these excited state time constants to the response time of x for the

PDA's.

To summarize, the polydiacetylenes are an interesting nonlinear optical materials system, and current research is addressing the interrelation between their

structural and the time dependent excited state properties to provide a knowledge base for potential applications. Yet the polydiacetylenes are just

one interesting class of organic nonlinear optical materials. The present investigaton of the nonlinearities in the PDA's can clearly set the broad direction

for the investigation of other molecularly engineered organic systems for practical exploitation.

References

1 . A good general reference is the book Nonlinear Optical Properties of

Organic and Polymeric Materials , ed . by David J. Williams , Published

by The American Chemical Society, Washington, D.C. (1983).

2. P. W. Smith, Bell Sys. Tech. J. 61, 1975(1982).

3. G. P. Agrawal, C. Cojan, and C. Flytzanis, Phys. Rev. B17 , 776(1978).

4. C. Sauteret, J. P. Hermann, R. Frey, F. Pradere, J. Ducuing, R. H.

Baughman, and R. R. Chance, Phys. Rev. Lett. 36, 956(1976).

5. J. P. Hermann and P. W. Smith, Digest of Technical Papers from XI

International Quantum Electronics Conference, Boston, Massachusetts,

June 23-26 (1980) (IEEE, New York, 1980), Paper T6, pp. 656-657.

6. F. Kajzar, J. Messier, J. Zyss, and I. Ledoux, Opt. Commun. 45,

133 (1983).

7. G. M. Carter, Y. J. Chen, and S. K. Tripathy, Appl. Phys. Lett.

43, 891(1983).

8. C. Flytzanis, Chapter 8, Nonlinear Optical Properties of Organic and

Polymeric Materials , Ed. by D. J. Williams, American Chemical Society,

Wash., D.C. (1983).

9. B. Tieke, G. Lieser, and G. Wegner, J. Polym. Sci., Polym. Chem.

Ed. 17, 1631(1979).

42
OD/mon. = 0.0039

I i i i i i i 1 400 450 500 550 600 650 700 750

WAVELENGTH (nm)

Figure 1 Absorbance vs wavelength for high optical quality

"blue" phase (curve A) and "red" phase (curve B)

polydiacetylene films "grown" by the Langmuir

Blodgett technique described in the text.

43
Figure 2 Raman spectra of a two-bi layer (A), a threebilayer (B), and a one-bilayer (C) polydi acetyl ene film that were deposited on a rough silver island

film. Note that the peaks near 1500 cm-1 and

2100 cm-1 are shifted in the one bilayer film

relative to the other bilayers. The frequency shift

in cm-1 i s measured^relati ve to the incident HeNe

laser line at 6328 A.

44
10 -

%

X = 6200

A

• a

***** _^ r±_* •A

- 60 12 84 156 228 30C

<

DELAY (ps)

10

• 1

X = 6400

A

- 60 12 84 156

DELAY (ps)

228 300

Fiqure 3 The signal is the difference between the values of

the transmitted probe power when the pump is present

and when absent. The delay is the difference between

probe and the pump beam arrival time (in picoseconds)

The two curves were obtained at different incident

laser wavelengths.

45
PREPARATION OF ORGANIC NONLINEAR OPTICAL MATERIALS

FOR SECOND HARMONIC GENERATION

Carl W. Dirk,* Robert J. Twieg,* Georges Wagniere

IBM Research Laboratory*

K42/282

5600 Cottle Road

San Jose, California 95123

Institute of Physical Chemistry**

University of Zurich

Winterhurerstrasse 190

CH 8057 Zurich, Switzerland

The proliferation of lasers has permitted, by way of their large optical electric

fields, the observation and investigation of optical nonlinearities in many materials.

Applied and basic research in lasers has necessitated the use of optically nonlinear

materials as component tools, as well as being problems of primary study. Examination

of the vector equation of the microscopic polarizability permits some insight as to the source of the nonlinearities:

P = aE + j3E

2 + yE3 + ... The first term, aE, linear in the optical electric field, is responsible for the familiar

processes of reflection, refraction, and Raman scattering. The second term, jSE2

, is the

lowest order nonlinear term. Fields of the same or different frequency can mix by way of

this term, giving rise to parametric generation, d.c. rectification, the linear electo-optic

effect, and sum and difference frequency mixing, second harmonic generation (SHG)

being a special case of the latter. The second nonlinear term, yE3

, is responsible for

CARS, third harmonic generation (THG), two photon absorption, and the quadratic

electo-optic effect. The tensors a,j8,y typically differ by six to ten orders of magnitude,

decreasing in the order given. Obviously, only the large optical electric fields of lasers can permit observation of nonlinear effects.

Second harmonic generation is mediated by the tensor. This tensor is a 27 component third rank polar tensor which possesses the property that it must be zero under centrosymmetry. This places a severe symmetry requirement upon systems

potentially useful for SHG since most compounds tend to crystallize

centrosymmetrically. Early investigation of SHG focused on inorganic compounds, such

as lithium niobate and KDP (potassium hydrogen phosphate), which are the best

recognized examples and are the two crystals most often employed as practical frequency

doubling components.

46
The ever increasing use of lasers in communications, energy related (e.g., laser

fusion) fields and others requires the fabrication of a variety of frequency doubling

components with a wide range of physical sizes, efficiencies, and phase matching

characteristics dependent on the specific application. Cost, ease of fabrication (i.e y crystal growth), poor conversion effeciency, and stringency of phase matching conditions

tend to restrict further use of the common inorganics. Organic materials can offer higher

conversion efficiencies, and more importantly, device configurations other than single

crystals (e.g., thin films are envisioned). In addition, the diversity of structures and

synthetic methodology available make organic systems especially attractive for the

purposes of iterative modification.

There has been much recent interest in the nonlinear optical properties of organics. 1 Compounds such as urea, 2-methyl-4-nitroaniline (MNA),

3-methyl-4-nitropyridine-l-oxide (POM), and methyl-(2,4-dinitrophenyl)-

aminopropanoate (MAP) have been extensively investigated. 1 From these studies, a general understanding has emerged with respect to the factors concerned with maximizing

the hyperpolarizability tensor and thus optimizing the resulting SHG. The j8 tensor is defined by excited state processes and thus the largest components of the j3 tensor are roughly proportional to the change in dipole moment upon going from the ground to first

excited state. 2 Generally, compounds with large ground state dipoles experience large

dipole changes upon excitation. Therefore, one strategy is to concentrate on molecules

with large ground state dipole moments. Zyss and Oudar3 have further determined an

orientational dependence to j3 with respect to its projection on the macroscopic tensor d,

and have also arrived at a dependence by j3 on crystal point symmetry. These complex

geometry and symmetry requirements are further aggravated by the aforementioned need

for noncentrosymmetry. The severe structural restrictions have little effect on the

chemists optimization of a molecule's intrinsic hyperpolarizability, but take hold due to

the uncontrollable orientations and symmetries brought about by crystallization. Many a compound possessing the correct electronic structure has failed because it crystallized

inappropriately.

Our effort in producing SHG from organic systems began with efforts to optimize

the molecular hyperpolarizability by use of chemical intuition, but recognition of the

supra-molecular structural factors has caused us to assume three different strategies:

First, an exhaustive search of the Cambridge Crystallographic File (CCF) has been

undertaken to sort out all compounds which crystallize noncentrosymmetrically. Many

of these compounds are to be prepared and tested for SHG. Hopefully, new SHG active

moieties can be found and perhaps more importantly, classes of noncentrosymmetrically

crystallizing compounds can be identified and rendered SHG active by suitable synthetic

modification. Second, in conjunction with the above investigation as well as an aid to

intuitive synthesis, a calculational method for jS has been prepared. 4 Use of a PPP-SCF-CI routine permits calculation of the eigenstates and transition moments

necessary for use of Flytzanis'5 perturbational derivation for /^j^:

4 7
i <0 I lexel/iile'xe* |pk |0>

1Jk 2

p Z

} [(E

e " Eo> " 2^H(Ee

, - E0) - M ' - s

Calculational procedures of this type are valuable in saving time in synthetic efforts.

Many compounds from the Cambridge File search can thus be 'tested' without actual

synthesis. Obviously, molecules — as yet unknown — can also be tested, thus obviating

needless synthesis. In addition, the procedure has been configured such that collections

of molecules can be calculated and the tensor components vector summed to give a net j8 for a crystal fragment. Third, since crystal growth is difficult in its own right,

investigations into SHG active thin films have been initiated.

Results

Of the 29052 compounds present in the Cambridge File as of ca. 1980-81, 8004 in

noncentrosymmetric space groups have been sorted out. Of these, 3828 or 48%

crystallize in the optimal^ space groups. From the total of 8004, ~60 compounds have

been tested to date with the result that ~60-70% show some activity and seven possess

powder SHG of the order or greater than urea:

Compound SHG (x urea) Spacegroup

p-aminobenzamide 3 P2j

sulfisomidine 2 Pca2^

0-nitrobenzaldehyde ~urea P2 1 2,4-bis(phenylthio)nitrobenzene 4 P2j

5-iodouracil ~urea P2j

triethylphosphine sulfide ~urea P63 mc

1- N-acetylcysteine ~urea PI

Some of the compounds above are quite unique or represent new variations on the

typical 1 donor-acceptor theme. The most intriguing is the triethylphosphine sulfide. The

SHG active moiety is extremely compact and considering the short dipole length, the

change in charge distribution must be fairly large upon excitation. This compound grows

large crystals relatively easily and is colorless. Examination of other phosphine sulfides,

oxides, and selenides has not revealed any other compounds with analogous activity. The

compound 5-iodouracil is, formally, a urea derivative, and represents the second uracil to

display significant activity. The 5-nitro derivative has been known to be strongly SHG

active. 6 Calculations {vide infra) indicate that 5-fluorouracil should be comparably

active. The Cambridge File holds 267 uracils, ~25% of which are noncentrosymmmetric. Many of these compounds are being tested.

Of primary interest are classes of compounds which tend to crystallize

noncentrosymmetrically. Compounds with large dipoles (suitable to maximize jS) tend to

crystallize with dipoles opposed often promoting a center of symmetry; any steric

influence which can generally reverse this behavior would be a valuable moiety to add to

many SHG active molecules. Chiral centers represent one approach. 1 One small class of

48
noncentrosymmetric compounds uncovered in the Cambridge Search are the

2,6-di-t-butylphenols. The attraction of this class is the presence of the hydroxy donor

and the extremely bulky sterically dominating t-butyls. Addition of a strong acceptor

should produce a large dipole moment but might not offset the action of the t-butyls,

which presumably will cause the molecule to crystallize noncentrosymmetrically. When

either a nitro or formyl acceptor are placed in the 4-position the resulting crystalline

solids display strong SHG. More compounds of this type are being investigated as well as related classes of compounds.

Calculational procedures for the determination of j3 have been employed

previously. 1 Results from the PPP-SCF-CI method used here are shown below:

Compound j3 calca - c

j3 calcb,c

ft expc>1

urea -7.0 1.44 2.3

p-nitroaniline 35.3 26.8 34.3

m-nitroaniline 12.9 8.1 6

o-nitroaniline 26.4 9.2 10.2

5-nitrouracil 5.6

5-fluorouracil -7.0

aRef. 4, crystallographic data used for urea, nitroanilines were calculated using uniform

benzene rings and all other bond lengths invariant from compound to compound,

resonance integrals unchanged throughout.

^Crystallographic data used for all compounds, resonance integrals scaled using

Linderberg's procedure.^

cAverage j8's,units= 10"^ esu.

Examination of these results indicate good agreement with experiment. As stated

earlier, 5-fluorouracil is calcualted to be not significantly different from 5-nitrouracil.

The fluorouracil result indicates the utility of these calculations in that it crystallizes

centrosymmetrically thus preventing an actual powder determination. The calculation

suggests, along with the 5-iodouracil measurement (vide supra), that the uracils may be a generally good class for SHG.

References

1. (a) D. J. Williams, ed., "Nonlinear Optical Properties of Organic and Polymeric

Materials" ACS Symposium Series, No. 233 (American Chemical Society, Washington,

D.C. 1983); (b) D. J. Williams, Angew. Chem. Int. Ed. Eng. 23, 690-703 (1984).

2. J. L. Oudar and D. S. Chemla, /. Chem. Phys. 66, 2664-2668 (1977).

3. J. Zyss, J. and J. L. Oudar, Phys. Rev. .4 26,2028-2048 (1982).

4. G. Wagniere, manuscript in preparation.

5. C. Flytzanis, "Nonlinear Optics, Part A", in Quantum Electronics: A Treatise, Vol. I H. Rabin and C. L. Tang, eds. (Academic Press 1975), pp. 9-207

6. J. Jerphagnon, IEEE J. Quant. Chem. 7, 42-43 (1971).

7. J. Linderberg, Chem. Phys. Lett. 1, 39-41 (1967).

49
OPTICAL PHASE TRANSITIONS IN ORGANO- METALLIC COMPOUNDS

T. 0. Poehler and R. S. Potember

Johns Hopkins University, Applied Physics Laboratory

Johns Hopkins Road

Laurel, Maryland 20707

We have recently reported optical and optoelectronic switching between two

states in polycrystalline organo -metal lie semiconductor films1 -1+ using the

488.0 and 457.9 nm lines of an argon ion laser5

. Although the optical meas- urements have largely concerned films of copper or silver complexed with the

electronic acceptor tetracyanoquinodime thane (TCNQ) , results on other acceptors indicate similar effects. It has been demonstrated that the effect of

the applied electric field on the Initial charge- transfer salt (e.g., CuTCNQ)

is to induce a phase transition resulting in the formation of a non-stoichiometric complex salt containing neutral TCNQ:

hv

[Cu (TCNQ*] ; * Cu° + [ Cu (TCNQ

T

) ] + ( TCNQ° ) . ( 1) n , x n—x x

A

The reaction shown in Eq . (1) is reversible and the initial phase can be

easily reformed by heating the film. The reaction proceeds readily because

simple Cu"*"(TCNQT

) has been shown to be thermodynamically more stable than the

complex salt containing neutral TCNQ (TCNQ 0 ). 6

The previous results on optical switching in the class of semiconducting

organo-me tallic films such as copper and silver te tracyanoquinodime thane

(CuTCNQ and AgTCNQ) have been extended to show that switching can be erased

using CO2 laser radiation. The effect can be observed by Raman spectroscopy

and direct observation. Results on the wavelength and irradiance dependence

of the optical switching threshold show the optical switching occurs over a wide spectral range and can be interpreted in light of proposed switching

mechanisms in these organic materials.

Two switching effects in the organo-me tallic films can be induced by optical

radiation, depending on the irradiance (W/cm2

) of the incident laser beam. At

low irradiance levels, optoelectronic switching from a high to a low electri-

•cal impedance state can be induced, while at higher irradiance levels, highcontrast patterns can be generated by forming macroscopic amounts of TCNQ 0

. Both these effects remain stable until the film is heated, which causes TCNQ0 molecules and the corresponding metal atoms to undergo a solid-state reaction,

Eq. (1), and form the original metal-TCNQ charge- transfer complex.

We have now demonstrated that defocused laser radiation can be used as a source of thermal energy to reverse or erase switched regions of the film.

Shown in Figure 1 are the results on reversing the optical switching using a CO2 laser as a source of thermal energy. The high and low impedance states

exhibit marked differences in the Raman spectrum, especially in the 1300 to

1500 cm" 1 region due to the band (C=C stretching). 5 ' 7 In this spectral

region, the initial charge- transfer complex in the high impedance (insulating)

state has only one strong Raman band at 1375 cm

-1 corresponding to the TCNQ

anion species (Fig. la). In all cases, the laser power of the probe beam was

50
la

Initial

1b Switched to low impedance state by argon laser

1c Reversed to high impedance

state by C0 2 laser high impedance

stata

1375 1450 Wavenumber (cm"'

I

1375 1450 Wavenumber (cm~M

1375 1450 Wavenumber (cm" 1

)

FIGURE 1. Raman spectra in the 1300-1500 cm" 1 region demonstrating the use of

CO2 laser radiation to reverse the optoelectronic switching.

sufficiently low that the equilibrium state of the film was not perturbed.

After irradiation with an argon laser, the film is switched to the low imped- ance (conducting) state, and an additional band is observed at 1450 cm

-1 cor- responding to TCNQ 0 (Fig. lb). The film in the conducting state can be driven

back to the original insulating state using defocused CO2 laser radiation as shown in Figure lc. For thin CuTCNQ films on a copper substrate, the CO2

laser irradiance required to reverse the film state was approximately

200 W/cm2. It should be emphasized that this exposure was necessary because

of the efficient heat dissipation from the film to the metal substrate. Much

lower exposures, however, can be used when the films are on thermally insulating substrates. Other defocused laser sources can also be used as a source of

thermal energy to reverse the reaction [Eq. (1)]. C02 laser radiation can also be used to erase high-contrast patterns which contain macroscopic amounts

of TCNQ 0

.

The wavelength dependence of the optical switching threshold for CuTCNQ and

AgTCNQ was studied to obtain information about the switching mechanism. Wavelengths from three different CW lasers were used: 457.9, 488.0, and 514.5 nm

from an argon ion laser; 632.8 nm from a helium-neon laser and 10,600 nm from

a carbon dioxide laser. At each wavelength, the metal-organic films were irradiated at various laser powers and at several locations on the film. The

switching threshold (i.e., the laser irradiance at which neutral TCNQ was produced) was measured by Raman spectroscopy. By varying the laser spot size, it was determined that the threshold was dependent on the irradiance and not on

the laser power. The results are presented in Table I. Variations in the

observed thresholds are due largely to spatial inhomogeneities in the film,

with the exception of the value at 10,600 nm for CuTCNQ. It is evident that

the optical switching threshold for AgTCNQ is approximately one-half the value

for CuTCNQ. The threshold for AgTCNQ is essentially independent of wavelength, while the threshold for CuTCNQ is relatively constant in the visible

spectral region, but is approximately four times higher in the infrared.

Work in progress has also involved a variety of thin films of semiconducting

charge- transfer complexes different from the typical AgTCNQ and CuTCNQ for

which many of the previous results have been reported. Other salts which are members of the class are those formed of metal donor atoms and the organic

acceptor molecule such as TCNE, TCNQ, methyl TCNQ, and TNAP.

51
TABLE I. Optical switching threshold at various wavelengths.

Wavelength Photon Energy Laser Irradiance Threshold (W/cm2

) Laser Source nm eV AgTCNQ CuTCNQ

Argon Ion

457.9

488.0

514.5

2.71

2.54

2.41

800

600

1000

1500

1500

1500

Helium Neon 632.8 1.96 2000

Carbon Dioxide 10600.0 0.12 600 8000

Many copper complexes are observed to exhibit switching behavior with thresholds varying over almost two orders of magnitude (Table II). Complexes such

as CuTNAP and CuTCNQ (0Me ) (0-ipr) switch at irradiances similar to that

required for CuTCNQ. On the other hand, CuTCNQ (0Et>2 exhibits a switching

threshold at least one order of magnitude lower than CuTCNQ.

TABLE II. Optical switching thresholds of various copper complexes. Beam

area approximately 2x 10~b cm2

.

Compound Wavelength (nm) Incident Power (mW) Irradiance (W/cm2

)

CuTCNQ(0Et)2 458 3 150

CuTCNQ(0Et)2 458 15 750

CuTNAP 488 30 1500

CuTCNQ(0Me)(0- ipr) 488 30 1500

CuDTF 458 15 750

CuTCNQ(i-pr)2 488 40 2000

CuTCNQFi* 488 150 7500

An area of significant interest is the change in macroscopic optical properties of the CuTCNQ films in a radiation field. The potential for large

changes in transmission and reflection in CuTCNQ and other members of this

family under intense radiation fields are of significant practical interest.

We have begun to investigate the transmission spectra of irradiated thin films

formed on glass substrates. As shown in Figure 2, a typical CuTCNQ film

formed by solid state diffusion is rather poorly transmitting from the midvisible into the near infrared in the vicinity of 1100 nm, and there is a substantial increase in transmission extending into the infrared. Upon irradiating the CuTCNQ film with a Nd:YAG laser at 532 nm scanned over a sufficient

region to perform simple transmission measurements, one observes a large

change in the transmission as also shown on Figure 2. A significant increase

in transmission throughout the spectrum from the mid-visible to the IR is

observed. Extremely dramatic increases are observed in the red end of the

spectrum and the near IR, particularly those regions which are of interest

with respect to many of the principal laser sources. These preliminary transmission measurements demonstrate a very large change in the optical transmission which is clearly of practical interest.

52
co

'm

C

03

400 500 600 8001000 1600 2000

Wavelength (nmi)

2600

FIGURE 2. CuTCNQ transmission switch

Nd : YAG laser (532 nm)

.

30 mj pulses from frequency doubled

The transmission properties of an AgTCNQ film are shown in Figure 3. In con- trast to the changes observed in CuTCNQ, the switched and unswitched films are

quite similar in the infrared portion of the spectrum. However, large changes

in transmission are noted in the visible part of the spectrum between 400 and

600 nm. The switched AgTCNQ becomes strongly transmitting in a band centered

at 500 nm while the unirradiated film is poorly transmiting in the same region.

E

c

I-

_ I I II II I II 1 1 1 1 1 1 1 1 I I II

Switchedy^/^

y^00^ 1 Unswitched

\ i —i/ 1

i inn nil 1 1

1

i i i i 400 550 600 800 12001600 2200 2600

Wavelength (nmi)

FIGURE 3. AgTCNQ transmission switch - 45 mJ laser pulses at 532 nm. References

0. Cowan, and A. N. Bloch,

A. N. Bloch, P. Brant, and

1. R. S. Potember, T. 0. Poehler, and D. 0. Cowan, Appl. Phys. Lett. 34 , 405

(1979).

2. R. S. Potember, T. 0. Poehler, A. Rappa, D.

J. Am. Chem. Soc. 103 , 3659 (1980).

3. R., S. Potember, T. 0. Poehler, D. 0. Cowan,

F. L. Carter, Chemica Scripta _17_, 219 (1981).

4. R. S. Potember, T. 0. Poehler, D. 0. Cowan, and A. N. Bloch, Proc. of NATO

Conf. on Chemistry and Physics of One -Dimensional Materials , L. Alca"cer,

ed. (D. Reidel Publishing Co., Boston 1980), pp. 419-428.

5. R. S. Potember, T. 0. Poehler, and R. C. Benson, Appl. Phys. Lett. 41 , 548

(1982).

6. S. Aronson and J. S. Mittelman, J. Solid-State Chem. 36 , 221 (1981).

7. E. I. Kamitos, C. H. Tzinis, and W. M. Risen, Solid State Commun. 42_, 561

( 1982).

53
A REVIEW OF THE OPTICAL DATA ANALYSIS FOR PHTHALOCYANINE CONDUCTING

POLYMER AND MOLECULAR-METAL SYSTEMS*

W.J. McCarthy and C.R. Kannewurf

Department of Electrical Engineering and Computer Science

and the Materials Research Center

Northwestern University, Evanston, Illinois 60201

T. Inabe and T.J. Marks

Department of Chemistry and the Materials Research Center

Northwestern University, Evanston, Illinois 60201

R.L. Burton

Electro-Optics Division, IIT Research Institute

Chicago, Illinois 60616

During the past decade a number of interesting low-dimensional materials

have been prepared which have been found to exhibit a combination of

unusual properties that are not generally observed in the conventional

inorganic semiconductor and metallic systems. Optical diagnostics have

provided a key method for obtaining important information about both

molecular-metal and conducting polymer systems. For many of these systems

the optical measurements and the methods of analysis have been carried out

by D.B. Tanner, | 1

| C.S. Jacobsen|2| and their respective co-workers.

At this laboratory the principal effort in this area has been devoted to

the development of phthalocyanine based systems with various doping

agents|3|. It has been found that the phthalocyanine polymers possess a rather unique blend of properties that show considerable promise for applications. Optical reflectance studies have also provided valuable

information about the phthalocyanine systems, but for many compounds single

crystal samples have not been successfully prepared as yet. Thus the majority of the optical measurements have been performed on polycrystalline

pressed powder compactions. Such specimens also have been used to provide

information in other systems that could not be obtained from single crystal

data alone | 4

|

In previous work with other systems the analysis of polycrystalline compositions generally has been developed on the assumption that the principal

contribution to the specular reflectance, where the metallic-like features

dominate, comes from the high conduction direction parallel to the stacking

axis. Therefore, if 6 is the angle between this direction and the electric

field vector of the optical radiation, then a total metallic reflection

would correspond to <cos

2 9>=l/3; the average is performed over all orientations of the stacking axis in the sample. However, it has been found in

the various phthalocyanine samples that the <cos 9> can actually vary from

0.28 to 0.5. The purpose of the present paper is to examine some alternative

methods for the data processing of polycrystalline samples with a comparison

to the results obtained from single crystal samples of the same compound.

* This research was supported by the NSF-MRL Program through the Materials

Research Center of Northwestern University (Grant DMR82-16972) and by

the Office of Naval Research.

54
The data presented here was obtained for the metal-free molecular metal

H2(Pc)I. This is a system for which samples are available in the form of

single crystals, fibers and thin ribbons; and it is a system which can be

used as a model for many other phthalocyanine compounds. It is also the

system for which the most extensive single crystal optical data is cur- rently available .

| 5

In Figure 1 a computer generated plot is shown of the polarized reflectance

both parallel and perpendicular to the conducting axis. This plot is developed from the actual single crystal data for H2(Pc)I after the data has

been fit to a model for the variation of the dielectric function with

frequency. | 5

| A principal feature of the reflectance data parallel to the

conducting axis is the plasma-like edge for frequencies less than 4400cm . In this region the dielectric function can be fit to a simple Drude

model, 1 6 1 /N 2 / / 2 . / \ /i\

£(<*>)« £«, ~ w

p

/ (oj z + xto/i), (1)

where is the high frequency dielectric constant, Wp is the plasma frequency and T is the electronic relaxation time. At frequencies above

10,000cm 1 the dielectric function for both polarizations can be fit to a Lorentz oscillator model, with a single oscillator in the R (

| data and a sum of two oscillators in the Rj_ data. The identification of these

oscillators for phthalocyanine systems is well known. |3|

Since most of the low-dimensional phthalocyanine systems of interest have a tetragonal crystal structure, the dielectric function can be described by a term e \\ for the conducting (or stacking) axis and a term £j_ f° r tne direction normal to this axis. In processing polycrystalline samples these

terms cannot be directly extracted from the reflectance data. The upper

curve in Figure 2 shows the actual reflectance data obtained from a pressed

pellet of H2(Pc)I. The plasma edge and the possibility of several Lorentz

oscillators at higher frequencies are readily observable, but the data does

not really fit either curve of Figure 1 very closely. It should be pointed

out that for frequencies less than approximately 1300cm 1 a large number of

molecular oscillators appear in the polycrystalline data. These are absent

in Figure 1 since the single crystal data is currently available only

above 1200cm l

, and therefore the computer generated curves show no such

features in the low frequency region.

One of the major reasons for a relatively poor fit of the polycrystalline

data to the single crystal curve in various regions is that from x-ray

diffraction studies the <cos

2 6> for H2(Pc)I powder compactions was determined to be as large as 0.5. Since this factor can be independently

determined, it is possible to use the following expression for the average

dielectric function, that has been employed by Tanner et al.|4| for the

analysis of polycrystalline films.

<£(u»> - ej» +

CfE-L «,)[£„ ftO -SJ»] . (2)

ejlCo)) + G (1-Cf)[e|| (o))-e L

(o))]

Here C = <cos 2 0>, f is the filling factor of the compaction, and G is the

depolarization factor of the crystallites. Eq. (2) has been developed

through effective-medium theory based on the original Maxwell- Garnet t Model

of isotropic spheres imbedded in an insulating matrix. |7|

55
3.0 FREQUENCE

Figure 1 Computer generated curves for the polarized reflectance versus frequency which are calculated from the optical parameters determined from the single crystal reflectance data for H2(Pc)I.

1.2

i.o

0 9 h

UJ (a) o

z<

(b)

1- 0,

6

o (c)

«d) 0.4

(e)

"(f)

0.2

0 1 2.0 LOG

3 0

FREQUENCY

4.0 5.0

I i /cm]

Figure 2 Upper Curve: Reflectance data versus frequency for a polycrystalline compaction of H2 (Pc)I, this curve is displaced +0.3

reflection units vertically from the origin for the lower

curves. Curves (a) through (f): Computer generated plots of

reflectance versus frequency for polycrystalline material with

the depolarization factor selected as follows: (a), G=0.01;

(b), G=0.05; (c), G=0.1; (d), G=0.3; (e), G=0.5; (f), G=0.7.

56
To show that from Eq . (2) a reflectance spectrum can be developed which is

similar to the polycrystalline data of Figure 2, the £ || (w) and £j.(w)

values were directly obtainable from the single crystal spectra of

Figure 1. The set of curves (a) through (f) in Figure 2 are computer

generated from Eq. (2). The depolarization factor is the parameter

starting with G = 0.01 for curve (a) and increasing to G = 0.7 for curve

(f ) . Work now in progress is being carried out to determine typical crystalline dimensions so that an independent G factor can be used in the

analysis. For all curves C = 0.5, and f was assumed to be unity. At high

frequencies the three oscillators generated from Eq. (2) now show a close

similarity to their appearance in the polycrystalline data; in this region

the variation in G has little effect.

Two noticeable differences between the polycrystalline and single crystal

data are the slope of the plasma edge and the value of the reflectance at

the minimum of the plasma edge. One important parameter of the fit that can influence both of these changes is the relaxation time defined in

Eq. (1). It has been found that the relaxation time for polycrystalline

phthalocyanine samples is approximately one-third of the single crystal

value. | 8| This is attributed to the stress produced by the mechanical

force used to prepare the powder compactions. Thus the computer generated

curves of Figure 2 are calculated using the lower relaxation time. The

low frequency behavior of the depolarization factor and the obvious shift

of the plasma edge with a change in depolarization factor will be discussed in conjunction with the influence of other parameters on these same

features

.

The set of curves in Figure 2 is typical of a large number of such plots

that can be generated for the various terms of Eq. (2). Particular

attention has been given to the influence of all these terms on the

parameters of the plasma edge since these parameters yield important information about the electronic carriers and energy band structure of low

dimensional systems. For phthalocyanine materials a superior fit to the

polycrystalline optical data is possible through the use of Eq. (2) in

conjunction with additional parameter measurements.

REFERENCES

1. D.B. Tanner in Extended Linear Chain Compounds , Vol. 2, edited by

J.S. Miller (Plenum, New York, 1982), p. 205 and references therein.

2. For example: C.S. Jacobsen, D.B. Tanner, and K. Bechgaard, Phys. Rev.

B28, 7019 (1983).

3. B.N. Diel, T. Inabe, J.W. Lyding, K.F. Schoch, Jr., C.R. Kannewurf,

and T.J. Marks, J. Am. Chem. Soc . 105 , 1551 (1983).

4. D.B. Tanner, C.S. Jacobsen, A.F. Garito, and A.J. Heeger, Phys. Rev.

Bl^, 3381 (1976).

5. R.L. Burton, T. Inabe, J.W. Lyding, W.J. McCarthy, G.M. Reisner, F.H.

Herbstein, C.R. Kannewurf, and T.J. Marks, (submitted for publication).

6. F. Wooten, Optical Properties of Solids (Academic, New York, 1972) Ch.3.

7. D.B. Tanner, A.J. Sievers, and R.A. Buhrman, Phys. Rev. Bll, 1330 (1975)

and references therein.

8. R.L. Burton, M.S. Thesis (Northwestern U., 1984); R.L. Burton, W.J.

McCarthy, T. Inabe, T.J. Marks, and C.R. Kannewurf, (manuscript in

preparation)

.

5 7
OPTICAL PROPERTIES OF PBS*

+

M. W. Williams, D. W. Young, J. C. Ashley, and E. T. Arakawa

Health and Safety Research Division

Oak Ridge National Laboratory

Oak Ridge, Tennessee 37831

PBS, or poly(butene-l-sulfone) with a formula of -^C 4HgS02

}-n

, is a fast

electron-resist used in microlithography . To understand, and to be able to

predict, the resolution attainable with this system, it is necessary to know

the optical properties of the resist material over the range of photon

energies associated with the oscillator strength of the valence electrons

.

Electron mean free paths in the material can be calculated from these data

as a function of incident electron energy. Energy deposition and details

of track structure can then be calculated for incident electron beams.

Predictions of the sharpness and resolution in the resulting microstructures

can be compared with those obtained experimentally.

We have obtained the optical properties of PBS over the range of incident

photon energies, -hu), from 2.5 to 41.0 eV. Liquid resist (1) was spin-coated

onto glass substrates and the films obtained were then heat treated at 80°C

for 30 mins to evaporate the solvent. Above ~5.9 eV these films were essentially opaque and normal incidence reflectance, R

n

, was obtained over the

range of energies from 5.9 to 10.3 eV using a Seya-Namioka monochromator and

from 8.0 to 41.0 eV using a grazing-incidence monochromator (McPherson, Model

247). Below V5.9 eV PBS becomes transparent and the real and imaginary parts,

n and k respectively, of the complex refractive index were obtained from

separate observations. The refractive index, n, was obtained from critical

angle measurements. A thick film of PBS was formed on the plane surface of a

^Research sponsored jointly by the Solid State Sciences Division, Rome Air

Development Center, under Interagency Agreement DOE No. 40-226-70 and the

Office of Health and Environmental Research, U.S. Department of Energy,

under contract DE-AC05-840R21400 with Martin Marietta Energy Systems, Inc.

+0ak Ridge Science Semester student participating in the Great Lakes Colleges

Association/Associated Colleges of the Midwest from DePauw University,

Greencastle, Indiana.

58
sapphire semicylinder . Reflectance at the sapphire-PBS interface was measured as a function of angle of incidence and n was then calculated from

the observed value of the critical angle. The extinction coefficient, k, for

a given photon energy was obtained from observations of the transmittance as

a function of film thickness. For these observations liquid PBS was allowed

to flow down a quartz microscope slide which was held at an angle of M5°

from the vertical. The resulting film increased in thickness towards the

bottom. After all transmittance measurements had been obtained, the variation

of thickness along the film was determined interferometrically . For each

incident photon energy, a least squares fit to Fresnel's equations for

transmittance as a function of film thickness yielded values of n and k.

This method gave reliable values of k but not of n. In the energy range from

2.5 to 5.9 eV, the values of n from critical angle measurements and the

values of k from transmittance vs film thickness were used to calculate values

of R . These values were then combined with the measured values of R from

n n 5.9 to 41.0 eV. A Kramers-Kronig analysis, over all photon energies, was then

performed r using6 the R values from 2.5 to 41.0 eV. Below 2.5 eV, the R

n ' n values were smoothly extrapolated to R

q

= 0.04 at zero energy. Above 41.0 eV,

a smooth extrapolation of the data in the vicinity of 41.0 eV was achieved by

a (ftuj)" 4 variation to infinite photon energy. This analysis yielded n and

k values over the range of photon energies from 2.5 to 41.0 eV. The density

of the PBS films was found by the sink-float method to be (1.39 ± 0.02) g.cnf*3

. As expected this density is greater than that of the liquid resist.

The values obtained for R^, n and k, over the experimental range of photon

energies, will be presented. It will be shown how sum rule calculations, of

the effective number of valence electrons participating in excitations, using

these data agree with theoretical predictions for PBS. In these calculations

core-valence electron coupling will be taken into consideration. Values of

electron inelastic mean free path, A, as a function of incident electron

energy, E, will be derived using the experimental values of n and k.

(1) We gratefully acknowledge Mead Technologies, Inc., Rolla, Missouri 65401

for making the liquid PBS available to us.

59
OPTICAL CONSTANTS AND HARMONIC GENERATION

BY SURFACE PLASMONS

H. J. Simon

Department of Physics and Astronomy

The University of Toledo

Toledo, OH 43606

Over fifteen years ago the first demonstration of the prism method of

surface plasmon (SP) excitation for studying the linear optical properties

of metal films was reported. 1 Today there exists a large literature on the

application of SP's in linear optics. 2 A sophisticated example of the

sensitivity that may be obtained with SP's is demonstrated in the use of the

modulated SP resonance for adsorption studies. 3 The SP resonance on highreflectivity metals is very sensitive to changes in the optical properties

of the surface region, in particular, to the effects of adsorbed molecules.

The SP resonance on noble metal films is excited using the Kretschmann

configuration and detected via the surface-roughness scattered light. By

modulating the angle of incidence of the exciting laser beam and using the

electronically differentiated signals to track and monitor the resonance,

the complex dielectric constant of the film and the strength of the surfaceroughness scattering may be measured as a function of time. A schematic

drawing of the apparatus is shown in Fig. 1. This technique was used to

study the chemisorption of 0 2 on Cu and Ag. A compilation of the SP

response for various 0 2 exposures on Cu is shown in Fig. 2. The straight

line is the extrapolation of the linear dependence associated with the oxide

growth back into the linear regime. Values of adsorbed film thickness and

optical constants are determined from a self-consistent fit to the

Lorentzian SP profile. From these data it is estimated that about 0.6% of

a monolayer of 0 atoms on a Cu surface may be determined.

The resonant SP mode may be used to drive the nonlinear polarization sources

at the interface between a metal and a dielectric thereby producing enhanced

optical second-harmonic generation (SH6). In the first experiment, reported

ten years ago, a pulse of light from a ruby laser was incident through a prism on a 500 & silver film in air (the Kretschmann configuration and

enhanced reflected SHG was observed at the angle for laser excitation on the SP.

1* An example of recent data taken with a Nd glass laser is shown

in Fig. 3a where the experimental nonlinear SHG reflectance is plotted on an absolute scale and the theoretical curve is calculated from Sipe's hydrodynamical model for the harmonic nonlinearity of a free electron gas.

5 From such experiments the harmonic normal surface current parameters, which

cannot be easily calculated, may be determined. If the SP is excited at the

interface between a metal film and a nonlinear dielectric then even larger

SHG resonances due to SP excitation may be observed. The experimental

results obtained with a quartz crystal which are shown in Fig. 3b agree well

with the theoretical curve. When a similar experiment is repeated with a polished hygroscopic crystal such as KDP, however, the resonance is

broadened and reduced by an order of magnitude, thus demonstrating the

sensitivity of this technique to crystal surface quality. 6

60
The recent prediction of the properties of a new long range surface plasmon

(LRSP) mode on the two surfaces of a thin metal film bounded by indexmatched dielectrics has stimulated theoretical and experimental interest

in this new mode. 7 When the fundamental mode of this plasmon is excited

on both surfaces of a thin silver film bounded by a nonlinear quartz

crystal and an index-matched liquid, the SHG is over two orders of

magnitude larger than that due to the single-boundary SP as illustrated

in Fig. 4a. The first observation of nonlinear coupling to a harmonic

LRSP mode is demonstrated by the middle peak of the angular scan data

displayed in Fig. 4b. SHG with simultaneously phase-matched fundamental

short-range and harmonic long-range SP modes has also been observed. Since

the frequency-dispersion curve for the LRSP mode falls close to the light

line, the SHG is produced in the radiative region of the curve. This

feature has been exploited to observe transmitted SHG with fundamental

LRSP excitation. 8 By using a crystal with a larger nonlinear susceptibility,

one can predict SHG conversion efficiencies of 1%. In conclusion, the

highly resonant and localized nature of the LRSP mode will make this mode a useful new probe for studying linear and nonlinear optical properties of

metal-dielectric interfaces.

REFERENCES

1. A. Otto, Z. Phys. 216, 398 (1968); E. Kretschmann and H. Raether,

Z. Naturforsch. Teil A23, 2135 (1968).

2. Surface Polaritons, edited by V. M. Agranovich and A. A. Maradudin

(North-Holland, Amsterdam, 1982); Electromagnetic Surface Modes,

edited by A. D. Boardman (John Wiley and Sons, Chichester, 1982).

3. C. F. Eagan, and W. H. Weber, Phys. Rev. B19, 5068 (1979).

4. H. J.Simon, D. E. Mitchell, and J. G. Watson, Phys. Rev. Lett. 33,

1531 (1974).

5. J. E. Sipe, V.C.Y. So, M. Fukui, and G. I. Stegeman, Phys. Rev. B2J_,

4389 (1980).

6. H. J. Simon, R. E. Benner, and J. G. Rako, Opt. Commun. 23, 245 (1977);

J. G. Rako, J. C. Quail, and H. J. Simon, Phys. Rev. B30, 5552 (1984).

7. D. Sarid, Phys. Rev. Lett. 47, 1927 (1981); J. C. Quail, J. G. Rako,

and H. J. Simon, Opt. Lett. 8, 377 (1983); A. E. Craig, G. A. Olson,

and D. Sarid, Opt. Lett. 8, 380 (1983); Y. Kuwamura, M. Fukui, and

0. Tado, J. Phys. Soc. Jpn 52, 2350 (1983).

8. J. C. Quail, J. G. Rako, H. J. Simon, and R. T. Deck, Phys. Rev. Lett.

50, 1987 (1983); J. C. Quail, and H. J. Simon, J. Appl . Phys. 56,

2589 (1984); J. C. Quail and H. J. Simon, J. Opt. Soc. Am. B]_, 319

(1984).

61
1. Schematic drawing of electronic, optical, and vacuum systems employed in angle-modulated SP studies. (Courtesy of Dr. W. H. Weber, Ford Motor Co.)
10

10

10

•17

18

19

10 20

10 21 r

d=510A

42 43 44

ANGLE OF INCIDENCE |deg]

3a. Nonlinear SHG reflectance versus internal angle of incidence from a silver film (d=510 A) on a BK-7 prism. Solid curve is calculated from hydrodynamic theory for free electron gas with a=0.9.

10"

AN6LE OF INCIDENCE (deg)

o 3b. Nonlinear SHG reflectance vs. interior angle of incidence for rutile prism/550 A Ag film/X-cut quartz crystal substrate.

63
ANGLE OF INCIDENCE

4a. Nonlinear SHG reflectance vs. interior angle of incidence from SF-59 prism/3ju index-matching liquid layer/135 A

Ag film/X-cut quartz crystal substrate illustrating optimal excitation of the fundamental LRSP mode. The dotted

curve displays the case for a single-boundary SP for comparison purposes only.

ANGLE OF INCIDENCE

4b. Reflected SHG demonstrating excitation of the fundamental LRSP, the nonlinearly excited harmonic LRSP, and

the fundamental SRSP modes vs. the interior angle of incidence. Inset shows prism geometry.

64
LOW LOSS THIN FIIM MATERIALS FOR INTEGRATED OPTICS

Howard E. Jackson and J. T. Boyd

Department of Physics and Solid State Electronics

Laboratory, Department of Electrical and Computer Engineering

University of Cincinnati, Cincinnati, Ohio 45221

In this paper we review our recent efforts to obtain low loss planar optical

waveguides using both novel fabrication and laser annealing techniques.

Scattering of light which occurs in thin-film optical waveguides represents

a loss mechanism and, more importantly, such scattering can limit the

performance obtainable in integrated optical signal processing and sensing

devices. Reduction of scattering is thus desirable, allowing higher levels

of performance and making optical signal and sensing processing devices

more competitive with other approaches. The possibility of an integrated

version of an optical fiber interferometer would require extremely low

loss channel waveguides. To obtain low loss thin film optical waveguides,

we have utilized the technique of laser annealing to obtain optical attenuation

values below 1 dB/cm for a number of materials with potential for use

in integrated optics. In addition, we have fabricated several types of

graded-index waveguides which display low scattering characteristics.

For each of the thin-film waveguide materials discussed here, the substrate

material is silicon. Silicon as a substrate provides an excellent surface

for formation of a variety of waveguide structures. In addition, the

use of silicon allows the integration of guided wave structures and electronic

devices on the same substrate. In what follows we shall discuss first

the use of laser annealing to achieve low loss waveguides and then several

graded-index structures.

Laser Annealing of Optical Thin-Film Waveguides

We have achieved considerable success in using the technique of laser

annealing to reduce scattering in a variety of thin-film waveguides deposited

onto thermally oxidized silicon substrates. We associate a reduction

in waveguide scattering with an improvement in quality of either the bulk

film, the film surface, the film-Si02 interface, or combinations of these.

In each case values of optical attenuation less than 1 dB/cm were achieved,

and in two cases the low value of 0.01 dB/cm was obtained. After briefly

describing the experimental set-up for the laser annealing and for the

measurement of low values of optical attenuation, we present results which

show improvement in waveguide loss for five different waveguide films:

Corning 7059 glass, ZnO, Si3N4 , Nb205 and Ta2 05

.

Each of the waveguides was annealed by scanning a focused C02 laser beam

of wavelength 10.6 ym horizontally across the waveguide surface at a rate

of 1 cm/sec. Typical vertical translation increments varied from 100

to 150 put. A 6.4 cm focal length lens provided power densities from 9

x 102 W/cm2 to 3 x 105 W/cm2

, with the lower power densities obtained

by moving the sample away from the focal point.

The waveguide loss or the optical attenuation was determined for each

of the waveguides by careful measurement of the out-of-plane scattering

65
before and after laser annealing. HeNe laser light was prism coupled

into the waveguide, and the intensity of light scattered out of the waveguide

was measured as a function of distance along the axis of propagation.

The measurements were performed using a scanning photometric microscope

incorporating a 50 ym aperature optical fiber probe within the microscope

and a lOx microscope objective. This allowed precise positioning of the

probe with respect to the waveguide surface. To obtain an individual

data point for the out-scattered light, the microscope was defocussed

Fig. 1. Schematic of the experimental arrangement for measurement

of out-of-plane waveguide scattering loss.

by 3mm, the fiber probe was scanned a distance of liran transverse to the

propagation axis at a rate of Imm/min, and an integrating digital voltmeter

was used to integrate the signal over the scan. A schematic of the experimental arrangement is given in Fig. 1. In addition, for the very low

loss measurements, the laser power was monitored with a precision of +0.05%,

and the data normalized accordingly. Using these averaging techniques

has allowed consistent measurement of waveguide attenuation values as

low as 0.01 dB/cm.

Corning 7059 glass has been the most widely used thin-film waveguide,

and is advantageous for many applications because of its value of refractive

index and its ease of fabrication. C02 laser annealing of Corning 7059

glass waveguides fabricated on thermally oxidized substrates has been

shown to significantly reduce scattering losses in these waveguides1 . The initial laser experiments reduced the waveguide attenuation from 17.4

dB/cm before laser annealing to 0.6 dB/cm afterwards. More recent laser

annealing experiments carried out at optimized power densities of 3-4

x 103 W/cm2 have resulted in improvements from initial values of 3 to

8 dB/cm to values as low as .05 dB/cm after laser annealing.

Dark field photomicrographs taken before and after laser annealing indicate

clearly that surface, and possibly bulk, defects in these wavesguides

have been reduced substantially after laser annealing. To substantiate

these observations, we have carried out a series of experiments using

index-matched liquid surface coatings to quantify changes in both surface

and bulk contributions to waveguide attenuation after laser annealing.

Table 1 summarizes the results. By comparing the bulk ( ajj) and surface

( a s) attenuation coefficients shown in Table 1 before and after laser

annealing, we conclude that both bulk and surface contributions to the

INTEGRATING

VOLTMETER

]t- WAVEGUIDE

+r- SILICON DIOXIDE

SILICON

66
Table 1. Effect of laser annealing on surface and bulk scattering in

waveguides.

Sample No. a without film a with film a b , a s , Unannealed "1 1.8 an

-1 0.6 cm"1 0.6 cm x 1.2 cm 1

waveguides 2 0.9 cm"1 0.1 cm"1 0.1 cm"1 0.8 cm"1

Laser-annealed 3 0.3 cm"1 0.1 cm"1 0.1 cm"1 0.2 cm"1

waveguides 4 0.05 cm"1 0.002 cm"1 -0 cm"1 ~0 . 05cm"1

waveguide scattering are significantly reduced. To achieve permanently

the extremely low attenuation values obtained with the liquid index-matching

film, we have substituted a spin-on liquid film on the laser annealing

waveguide which can be solidified upon baking. In one waveguide, the

attenuation coefficient was reduced from 4.0 dB/cm to 0.05 dB/cm after

laser annealing, and finally to the extremely low value of 0.01 dB/cm

after adding the solid film. 2

Thin films of ZnO are important for their current use in both bulk and

surface acoustic wave (SAW) devices and for their potential use in integrated

optical devices. Use of ZnO in integrated optical devices allows excitation

of surface acoustic waves and thus allows implementation of the guided

wave acousto-optic effect on substrates either lacking or having a very

weak piezoelectric effect, such as Si or GaAs. Use of Si as a substrate

material is desirable, as it allows integration of photodetector arrays

and utilization of the very low-loss thin-film waveguides. We have laser

annealed ZnO thin-film optical waveguides deposited on an amorphous Si02

layer thermally grown on Si. Previously, values of waveguide attenuation

as low as 0.5 dB/cm for ZnO films deposited on crystalline sapphire substrates

and 1.0 dB/cm for ZnO films deposited on amorphous oxidized silicon substrates

have been observed. We have obtained improvement in loss from several

dB/cm before laser annealing to values as low as 0.01 dB/cm after laser

annealing for ZnO films deposited on amorphous oxidized silicon substrates. 3

The ZnO waveguides were annealed in a similar manner to the Corning 7059

glass waveguides, with the C02 laser scanned at 1 cm/s with power densities

of 2.0 - 2.3 x 105 W/cm2 . ZnO is nearly transparent to the 002 laser

wavelength (10.6 ym), while the Si02 layer absorbs strongly. Thus, we

expect that heating of the ZnO film will occur primarily at the Zn0-Si02

interface, a region characterized by a relatively large defect density.

Waveguide attenuation measurements are presented in Table 2 for two different

waveguide thicknesses and for the first three TE waveguide modes. The

data for the TE1 waveguide mode for one sample is displayed before and

after laser annealing in Fig. 2. Laser annealing of sample #1 reduced

the waveguide attenuation coefficient from 4.6 dB/cm before laser annealing

to the low value of 0.02 dB/cm. In sample #2 the significant reduction

measured in the TE1 and TE2 mode losses following laser annealing supports

the suggestion of substantial improvements in the Zn0-Si02 interfacial

region. A possible decrease in the surface acoustic wave attenuation

after laser annealing is being investigated.

67
55 10 z

H

S 0.5

Q111 e

<o

CO2

§

Ui

0:

0.2 0.8 dB/cm

l l l I I I I I I—I—

00 02 04 0.6 08 1.0 1.2 DISTANCE (cm)

Fig. 2. Logarithm of relative scattered intensity is plotted vs distance

along the ZnO waveguide for the TE1 mode before (upper line) and

after (lower line) laser annealing.

Table 2. Effect of laser annealing on ZnO waveguide attenuation.

Sample ZnO film Waveguide attenuation coefficient Annealing

number thickness (dB/cm) power density

(um) TEq TEt_ TE2 (W/cm2

)

1 0.93 Before anneal 4.6 10.0 16.0 2.0 X 105

After anneal 0.02 8.7 6.5

2 0.93 Before anneal 2.5 7.0 9.3 2.3 X 105

After anneal 0.01 12.4 13.9

3 0.71 Before anneal 1.0 5.4 7.1 2.3 X 105

After anneal 0.03 0.8 1.6

Rutherford backscattering (RES) measurements were used in the case of

both Corning 7059 glass and ZnO waveguides to help elucidate the mechanisms

responsible for the reductions in scattering loss observed after laser

annealing. RBS measurements indicate that no redistribution of implanted

impurities takes place during laser annealing. Thus no melting occurs

and the annealing occurs in the solid phase. 4

We have also used C02 laser annealing to significantly reduce waveguide

scattering losses in waveguides composed of several other materials of

potential use in integrated optics including Si3N4 , Nb205 , and Ta205

. The lowest values of optical attenauation achieved were 0.1 dB/cm for

Si3N4 , 0.6 dB/cm for Nb205, and 0.4 dB/cm for Ta205

.

Graded Index Waveguides

Graded-index planar Si02 optical waveguides might be expected to have

many of the advantages associated with graded-index fibers including low

loss. We have observed extremely low scattering in planar graded-index

Si02 waveguides formed by thermally oxidizing silicon wafers for periods

up to several weeks resulting in waveguide thicknesses of up to 15 microns. 6

The graded refractive index results from some unknown combination of composition, impurity, density, and stress distributions in the Si02 layer.

68
The losses in these optical waveguides were characterized in several ways,

but perhaps the most telling was the attempt to measure scattering losses

in a manner similar to that described above. The amount of out-of-plane

scattering observed using an input power of 160 mW to excite a TE mode

was consistent with the observation of inelastic scattering from phonons

(<2 cps) , i.e. with the observation of no elastic scattering from defects

or inhomogeneities in the waveguide. Waveguide attenuation, of course,

can also be determined by measuring the transmitted intensity as a function

of distance along the waveguide. Such measurements yielded the lew, but

not extraordinarily low, values of 0.3-0.6 dB/cm. Since the out-of-plane

scattering was demonstrably exceedingly low, the loss of 0.3-0.6 dB/cm

is ascribed to substrate absorbtion. Thus we expect that if we can provide

stronger field confinement for these graded-index waveguides, the waveguide

attenuation would indeed be exceedingly small.

We have attempted to provide stronger field confinement in two different

ways. First, phosphorous doping was used, as the presence of phosphorus

increases the refractive index of Si02 . Stronger field confinement was

observed, along with losses of 1 dB/cm, for total oxide thicknesses of

about 6 microns. Second, we have formed graded-index waveguides in Si02

by oxidizing silicon wafers under time-varying conditions. The index

of refraction of a layer of Si02 is dependent on the growth temperature

and the water content of the ambient oxygen. In a variety of experimental

circumstances, all resulting in strong enough field confinement so that

calculated substrate absorbtion loss was <0.1 dB/cm, the lowest value

of waveguide attenuation was still about 0.6 dB/cm. The loss values were

thus much larger than expected.

A second kind of graded .index guide has recently been investigated by

Naik. 7 Nitrogen implantation of a thermally grown Si02 layer on Si was

followed by annealing yielded waveguides with the very low waveguide attenuation of 0.1 dB/cm. Very preliminary results are reported here for three

] ] I I ! I |

I I ! !

]

1 I I I ]

I I I L

~o o ©-

i i i i I i i i i 1 i i i i I i i i i I i i i rl

.5 I 1.5 2 RELATIVE DISPLACEMENT (CM)

Fig. 3. The logarithm of the relative outcoupled intensity is plotted

vs distance along the waveguide for three waveguides. Loss decreases

for increasing thermal nitridation times.

69
graded-index guides formed losing a thermal nitridation process. 8 The

waveguide attenuation values for these samples were obtained by outcoupling

the guided wave for various distances along the waveguide, in contrast

to the out-of-plane scattering measurements discussed above. Waveguide

attenuation measurements for the three waveguides are displayed in Fig. 3.

Values of the optical attenuation range from 0.29 dB/cm (uppermost line)

to 0.08 dB/cm (lowest line). For longer thermal nitridation times, which

might reasonably correspond to stronger field confinement and lower substrate

absorbtion loss, we observe lower values of loss. Clearly much remains

to be done here.

Summary

We have reviewed our recent efforts to obtain low loss planar waveguides

for potential use in integrated optics. Employing both novel fabrication

and laser annealing techniques, we have achieved values of waveguide attenuation substantially below 1 dB/^ for a variety of waveguide materials.

In several cases values below 0*1 dB/^ were achieved, with efforts to

achieve even lower values of waveguides attenuation continuing.

This research was supported in part by the Air Force Office of Scientific

Research and the National Science Foundation.

References.

1. S. Dutta, H. E. Jackson, and J. T. Boyd, Appl. Fhys. Lett. 37, 512

(1980) .

2. S. Dutta, H. E. Jackson, and J. T. Boyd, J. Appl. Fhys. 52, 3873

(1981) .

3. S. Dutta, H. E. Jackson, J. T. Boyd, F. S. Hickernell and R. L. Davis,

Appl. Fhys. Lett. 39, 206 (1981).

4. S. Dutta, H. E. Jackson, J. T. Boyd, and C. W. White, J. Appl. Fhys. 54,

2125 (1983).

5. S. Dutta, H. E. Jackson, J. T. Boyd, R. L. Davis and F. S. Hickernell,

IEEE Quant. Electron. QE-18, 800 (1982).

6. D. E. Zelmon, H. E. Jackson, J. T. Boyd, A. Nauman and D. B. Anderson,

Appl. Fhys. Lett. 42, 565 (1983).

7. I. K. Naik, Appl. Fhys. Lett. 43, 519 (1983).

8. D. E. Zelmon, H. E. Jackson and J. T. Boyd (to be published).

70
QUANTITATIVE SAMPLING IN PLANAR WAVEGUIDES

Paul W. Bohn

Department of Chemistry and Materials Research Laboratory, University of

Illinois, 1209 W. California, Urbana, Illinois 61801

Realization of the goal of direct quantitative analysis of molecules bound in

the matrix of a thin film may be approached by using the thin film of interest

as the active waveguiding medium in a three or four layer asymmetric slab dielectric waveguide. In these structures the spatial asymmetry of the electric

field amplitude distribution perpendicular to the film plane and the fact

that these profiles may be calculated exactly from simple knowledge of the

thickness and dielectric constants of the layers mean that fluorescence or Raman scattering, monitored outside the waveguide, will automatically contain

information about the spatial distribution of the molecules being probed

(1,2). In order for this phenomenon to be exploited however it is necessary

that the characteristic signals being recorded be related to the concentration

of the probe species in a simple manner. In solution the signal in a Raman

scattering experiment is linearly proportional to concentration of scatterers

at low irradiances (3). Thus the solid solution thin films under investigation in these experiments should be characterized by scattering signals which

are proportional to the product of the electric field intensity distribution

and the molecular concentration distribution, summed over the thin film

thickness and the area sampled by the collection optics as shown in equation

where 1^ = Raman scattering intensity measured for the ith mode,E£(z) = electric field intensity distribution in the direction perpendicular to the film

plane, and N(z) = molecular concentration profile.

In the simplest case, that of a spatially homogeneous concentration profile,

N(z) is a constant and the integral of equation 1 can be solved analytically

for any layer of either a three or four layer structure (4). The results can

be expressed as a normalized p-matrix, the elements of which are the normalized portions of the total irradiance resident in each layer for each mode.

In the spatially homogeneous case then the scattering intensities for excitation of different modes of the waveguide should just be proportional to the

elements of the p-matrix for that mode. As an example of a spatially homogeneous matrix a three layer structure composed of a 1.96 ym atactic polystyrene) film on glass was investigated at 514.5 nm in a prism coupled con- figuration. The normalized TE p-matrix for this structure is given in Table

I. In the table the j values are the modes of the waveguide and the i values

are the layers starting with substrate (i=l) and ending with superstrate

(i=3). These values should then be proportional to the scattering signals

from any vibration characteristic of the poly (styrene) repeat unit.

1,

o (1)

2

71
Table I

1=1 1=2 1=3

j=o 0.0043 0.9954 0. 0003

j=l 0.0189 0.9800 0. 0011

3=2 0.0511 0.9465 0. 0024

3-3 0.1536 0.8424 0. 0040

The ring breathing mode at 1004 cm was chosen and the results are shown In

Figure 1. Two striking results are observed. First as the observations are made further from the coupling position, the shape of the curve changes, becoming less linear. In addition the plots for different observation points

are displaced downward for each mode observed. These observations are con- sistent with and typical of other organic polymer thin films studied using

both fluorescence (for doped films) and Raman scattering (for undoped films)

probes. Thus the simple model invoked above wherein the signal strength is

proportional to a weighted average of the probe molecule concentration fails

in this most simple test case.

__I

, ,

.—, 1 0-84 0-92 100

P /P

f ' total

Figure 1. Plot of the Raman scattering intensity of the 1004 cm ring

breathing mode in poly (styrene) as a function of the normalized

irradiance within the waveguiding layer.

The reasons for the failure of the simple model are that it leaves out both

elastic scattering contributions to the overall optical loss in transmission

through these thin films and mode dependent coupling efficiency effects in

the prism coupled configuration. Several models have been put forth in the

literature to explain the effects of surface and volume scattering on the

72
optical loss function. Although differing in detail they all agree that the

surface scattering loss pathway should increase dramatically at higher modes.

Thus if observation of a signal is made at a particular distance away from

the coupling prism, this signal should be weaker for higher modes, because

the irradiance is smaller at that point than it is when lower order modes are excited. This then explains the curvature in Figure 1. Higher order modes

are characterized by smaller normalized irradiances in the main waveguiding

film and appear on the left part of the abscissa. The curvature in the plot

roughly parallels the curvature in the total loss vs. mode plot as given by

Tien (5). If these same data are plotted vs. distance from the coupling

prism for each mode, the resulting familiar plot can be used to estimate the

overall optical loss coefficient, Oj., from the slope. When this plot is ex- trapolated to the coupling prism it is seen that the different modes have

different initial intensities, i.e. the coupling efficiency is mode dependent

as predicted by Ulrich (6). Thus this effect will also contribute to a de- crease in the available excitation power for spectroscopic experiments at

higher order modes.

A simple model for quantitative spectroscopic sampling in thin films has been

advanced and compared with experiment for the simple case of spatially homogeneous scatterers. Agreement with theoretical scattering intensities demands a treatment which takes into account both surface and volume elastic

scattering and mode dependent coupling efficiency effects.

References

1) J.N. Polky and G.L. Mitchell, J. Opt. Soc. Am. 64, 274 (1974).

2) J.F. Rabolt, R. Santo, N.E. Schlotter, and J.D. Swalen, IBM J. Res. Devel.

26, 209 (1982).

3) D.A. Long, "Raman Spectroscopy/1 (McGraw-Hill, London, 1977).

4) P.W. Bohn, "Theory of Spectroscopic Sampling in Thin Amorphous Films,"

submitted to Anal. Chem.

5) P.K. Tien, Appl. Opt. 10, 2395 (1971).

6) R. Ulrich, J. Opt. Soc. Am. 60, 1337 (1970).

73
RELATIONSHIP OF MICROSTRUCTURE TO OPTICAL PROPERTIES OF THIN FILMS

H. A. Macleod

Optical Sciences Center

University of Arizona

Tucson, AZ 85721

Introduction

Although the properties of materials in thin-film form are broadly similar

to those of bulk materials, there are often significant differences.

Frequently the level of performance that can be achieved with thin films is

inferior to that predicted from simple bulk properties. Great progress has

been made in closing the gap between real thin-film properties and bulk

properties but a gap still remains and much of it is a direct consequence of

the effects of microstructure on the optical, mechanical and chemical

properties of thin films. Here we are concerned solely with the optical

properties and we limit the discussion to dielectric films.

Microstructure

Thin-film microstructure is complex, and there are different levels of

structure. In order to relate the structure to the film properties we need

a model that retains the essential features of the real structure but which

is more amenable to calculation and easier to visualise. The principal

detail of film microstructure is its columnar form of the grains and the

simple model, shown in figure 1, which was devised originally by H. K.

Pulker (1) and elaborated by Ogura (2) (3), enables us to discuss and

understand a wide range of microstructure-related effects.

The most important parameter relating to the microstructure is the packing

density p given by

_ Volume of the solid part of the film (i.e. columns)

Total volume of film (i.e. columns plus voids)

p is usually in the range of 0.8 to 0.95 for most thin-film material

deposited by thermal evaporation in vacuo.

Measurements

Optical inhomogeneity is a feature of those models with varying columnar

cross section and indeed is a frequent feature of optical thin films.

Cryolite and zinc sulphide films have been measured in situ by Netterfield

(4). Inhomogeneity in titanium oxide and its agreement with the columnar

model has been considered by Harris et al (3). Borgogno et al (5) have made

measurements on a wide range of inhomogeneous films.

Birefringence in thin films is another microstructure-related area. In 1957,

Bousquet (6) published an analytical treatment for the calculation of the

74
optical properties of an anisotropic thin film. In the same year he

reported (7) calcium fluoride films that were uniaxial with optic axis

perpendicular to the surface with (nQ -ne

) = 2.5 x 10

-3

. With Rouard in 1960

he warned (8) of the problems caused by birefringence in measurement of

optical constants involving obliquely incident light. Rouard (9) had already

noted that if he axes of the grains in the films were normal to the

boundaries, then measurements at only normal incidence would not be

perturbed. Recently King and Talim (10) compared various techniques of

optical constant measurement. Guided waves showed a significant difference

between indices for TE modes, 1.9887, from those for TM, 2.0015, at 632. 8nm

in zirconium dioxide.

The columnar nature of the films strongly suggests that they should be

birefringent with the principal axes of the dielectric tensor along the

columnar direction (n,), and normal to the columns both in the plane of

incidence of the vapor (nj), and normal to the plane of vapor incidence (n 2 ). For films that are evaporated at normal incidence we would expect the

birefringence to be uniaxial with optic axis normal to the film surface and

not detectable by purely normal incidence measurements. Normal incidence

measurements would, however, permit us to infer the presence of

birefringence in obliquely deposited films where we would expect biaxial

birefringence with the optic axes in the plane of incidence of the vapor

during the film growth. Because obliquely deposited columns are less

closely spaced in the plane of vapor incidence than normal to the plane, we

would expect the birefringence usually to be characterised by a maximum

index along the columns and by a minimum normal to the columns in the plane

of incidence. The optic axes for a biaxial film would therefore be in the

plane of vapor incidence.

Some measurements of anisotropic behaviour in zirconium dioxide and titanium

dioxide films have recently been made (11) (12). Zirconium dioxide films

evaporated at very high angles of incidence were found to be anisotropic

with an effective An=0.042 for propagation through the film at normal

incidence (16) (17). The measurements assumed that the orientation of the

columns in the films was known through the tangent rule (13) connecting the

angle of vapor incidence, a, and the column orientation angle, 0,

tana = 2tang

Results are given in Table 1 (12) for wavelengths in the region of 630 nm.

TABLE 1

Material

Zirconium oxide

Zirconium oxide

Titanium oxide

Calculation of optical constants

Since the film is made up of solid parts and voids, we can expect that the

refractive index will be reduced below that for a film made up entirely of

a 0 n n n

30° 16.1° 1.948 1.96*6 2.03*3

65° 47.0° 1.502 1.575 1.788

30° 16.1° 2.437 2.452 2.552

75
solid material. Many attempts have been made at deriving a relationship

between packing density and refractive index. An early attempt by J.C.

Maxwell-Garnet t (14) (15) based on the Lorentz-Lorenz polarization theory, can be written (3)

(l-p)(n2+2)n2+p(n2+2)nl

rif = ^ = (1)

(l-p)(n2+2)+p(n2+2)

where nf is the index of the composite film, n g is the index of the solid

material of the film, and ny

is the index of the voids in the film, usually

unity. The possibility that the particles of the film might depart from the

spherical form assumed in the Maxwell-Garnett theory has been included in an analysis by Bragg and Pippard (16). Assuming cylindrical particles and

manipulating the expressions somewhat, we arrive at the expression (3)

(l-p)n2+(l-p)n2n|

nf = _ _ — (2)

(l+p)n2+(i-p)n

2

where the same symbols have been used. An alternative expression for the

index of a composite film based on an interpolation between two limits, is

that of Kino shit a and Nishibori (17)

nf = (l-p)n

v+pns (3)

The accuracy of these expressions has been investigated by Harris et al (3)

using a finite difference approach to calculate the dielectric permittivity

of a hexagonal array of columns. The linear interpolation is surprisingly

good for low index films but poor for high index films. For intermediate

values of packing density it was found that the Bragg and Pippard expression

gave better agreement than the Maxwell-Garnett. An alternative approach by

McPhedran and McKenzie (18) (19) used a computer to permit the inclusion of

terms of very high order in series expansions based on work by Raleigh.

For packing densities in the region from around 0.75 to 1.0 finite elements

are more suitable. In this region, Harris (20) obtained results of which

those in figure 2 are typical showing a transition from the Bragg and

Pippard law to the linear interpolation at around p=0.8, the details of this

behaviour depending on the precise columnar shape. This result could

explain the difficulty of controlling materials like titanium oxide and

zirconium oxide both of which have packing densities in the critical region.

Recently some experimental evidence of such an effect was obtained by

Martin et al (21) for zirconium dioxide films produced by ion-assisted

deposition with packing densities varying from around 0.7. to 1.0 (Figure 3).

Conclusion

This has been a necessarily short and incomplete survey of some of the

relationships between microstructure and the optical properties of

dielectric thin films. Work to date has been almost entirely from the point

of view of adverse effects, that is a reduction of the performance of

76
coatings below what we could expect from bulk materials and major research

effort is now being devoted to attempts to modify the microstructure so that the films are more like bulk material. Little attention appears to

have been devoted to the opposite question of using some of the special

properties of thin films to our advantage.

References

1. H.K. Pulker and E. Jung, "Correlation between film structure and

sorption behaviour of vapor deposited ZnS, cryolite and MgF2 films," Thin

Solid Films, Vol.9, pp 57-66, 1971

2. S. Ogura, "Some features of the behaviour of optical thin films," PhD

Thesis, Newcastle-Upon-Tyne Polytechnic, 1975

3. M. Harris, H.A. Macleod, S. Ogura, E. Pelletier and B. Vidal, "The

relationship between optical inhomogeneity and film structure," Thin Solid

Films, Vol.57, pp 173-178, 1979

4. R.P. Netter field, "Refractive indices of zinc sulphide and cryolite in

multilayer stacks," Applied Optics, Vol.15, pp 1969-1973, 1976

5. J. P. Borgogno, B. Lazarides and E. Pelletier, "Automatic determination

of the optical constants of inhomogeneous thin films," Applied Optics,

Vol.21, pp 4020-4029, 1982

6. P. Bousquet, "Theoretical study of the optical properties of thin

transparent films," Ann Phys (Paris), Vol.2, pp 5-15, 1957

7. P. Bousquet and Y. Delacourt, "Evidence of the birefringence of calcium

fluoride thin layers obtained by vacuum evaporation", J. Phys. Rad., Vol.18,

pp 447-452, 1957

8. P. Bousquet and P. Rouard, "Constantes optiques et structure des

couches minces," J. Phy. Rad., Vol.21, pp 873-892, 1960

9. P. Rouard, "Determination of the optical constants of thin films." J. Opt. Soc. Am., Vol.46, p 370, 1956 (Abstract)

10. R.J. King and S.P. Talim, "A comparison of thin film measurement by

guided waves, ellipsometry and ref lectometry", Optica Acta, Vol.28, pp

1107-1123, 1981

11. F. Horowitz and H.A. Macleod, "Form birefringence in thin films," Proc.

SPIE, Vol.380, pp 83-87, 1983

12. F. Horowitz, "Structure-induced optical anisotropy in thin films," PhD

Dissertation, University of Arizona, Optical Sciences Center, 1983

13. A.G. Dirks and H.J. Leamy, "Columnar microstructure in vapor-deposited

thin films," Thin Solid Films, Vol.47, pp 219-233, 1977

14. J.C. Maxwell-Garnet, "Colours in metal glasses and in metallic films,"

77
Roy. Soc. Phil. Trans., Vol.203, pp 385-420, 1904

15. J.C. Maxwell-Garnett, "Colours in metal glasses, in metallic films and

in metallic solutions," Roy. Soc. Phil. Trans., 205, pp 237-288, 1906

16. W.L. Bragg and A.B. Pippard, "The form birefringence of macromolecules."

Acta Cryst., Vol.6, pp 865-867, 1953

17. K. Kinosita and M. Nishibori, "Porosity of MgF2 films - evaluation based

on changes in refractive index due to adsorption of vapors," J. Vac.Sci.

Technol., Vol.6, pp 730-733, 1969

18. R.C. McPhedran and D.R. McKenzie, "The conductivity of lattices of

spheres. I. The simple cubic lattice," Proc. Roy,. Soc. London, A, Vol.359, pp

45-63, 1978

19. D.R. McKenzie, R.C. McPhedran and G.H. Derrick, "The conductivity of

lattices of spheres. II. The body centred and face centred cubic lattices,"

Proc. Roy. Soc. London, A, Vol.362, pp 211-232, 1978

20. M. Harris, M. Bowden and H.A. Macleod, "Refractive index calculations

for a thin film with columnar structure," Optics Comm., Vol.51, pp 29-32,

1984

21. P.J. Martin, R.P. Netterfield and W.G. Sainty, "The modification of the

optical and structural properties of dielectric Zr0 2 films by ion-assisted

deposition", J. Appl. Phys., Vol.55, pp 235-241, 1984

Figures

(ai (b) ici

Fig I The three principal variations of the model of the columnar structure of thin films: la' the cylindrical model, p = 0.9069: (bi contracting columns, p < 0.9069 |c| expanding columns, p > 0.9069.

(After Oguravi

78
0.30 048 0.S0 04)S 140

PACKING DENSITY Fig. 3 The refractive index of Zr02 films produced by ionassisted deposition as a function of packing density.

A-linear relationship (3) ,B-(1) , C-(3). After Martin et al (21)

79
THE MICROSTRUCTURE AND OPTICAL PROPERTIES OF THIN FILMS

PREPARED BY MOLECULAR BEAM TECHNIQUES

K. L. Lewis, A. M. Pitt, J. A. Savage,

A. G. Cullis, N. G. Chew and L. Charlwood

Royal Signals and Radar Establishment

Malvern, Worcestershire

England WR14 3PS

Introduction

A common factor in the failure of optical coatings under laser irradiation

has been the lack of perfection and the relatively low purity of the coating

material. Optical absorption levels are frequently too high and the

refractive index uniformity of the film difficult to control. This is a consequence of several contributing factors. In the first instance, the film

may contain a high concentration of impurity species arising from its

fabrication in conventional evaporators at background pressures in the region

of 10~^mbar, where the dominant species present is H2O due to outgassing of

the coating chamber walls and substrate assembly. Even for a partial

pressure of H2O of 4.5 x I0~ 9 mbar, which is some way below that achievable

in conventional equipment, a film of ZnSe produced at a growth rate of 2ym/hr

would contain approximately 0.05% H2O which implies an absorption

coefficient of about 0.5cm~^. The problem is not restricted to H2O - other

molecular species, e.g., CO3 , SO^ , SOg , C0£ f CHn are commonly produced as a result of reactions during deposition and give rise to significant absorption

at 10.6ym.

A second contributory factor may be associated with a degree of

nonstoichiometry in the film which can result in the generation of free

charge carriers which interact strongly with radiation at long wavelengths.

Walsh and Bertke (1) have found that significant variations in the Zn:Se

ratio of ZnSe can occur during RF sputtering, paralleling the results of

O'Brien (2) who suggests that the Zn/Se ratio increases at higher deposition

rates resulting in higher IR absorption.

The presence of further impurity species at the substrate/film or film/film

interfaces contributes to poor adhesion of films and may also act as nucleation sites for the formation of pores and other undesirable

morphological features. At short laser pulses OOOnsec or less) coatings

fail either as a result of heating microscopic coating defects or by electron

avalanche processes in the coating material itself. It may be argued that

the most serious coating defects are voids, from the point of view that they

cannot be controlled by attention to cleanliness, dust control, etc. The

presence of open porosity results in a high susceptibility to water ingress

and inevitably a lower laser damage threshold.

80
The morphology of thin films plays an important part in determining

resistance to laser induced damage. Films prepared by conventional

evaporation techniques exhibit a polycrystalline morphology with a characteristic columnar structure (3). It has long been asserted that void

formation is enhanced at grain boundaries in thin films and that diffusion of

impurities especially water readily proceeds along such paths. The

segregation of heterogeneous impurities at such grain boundaries also results

in the generation of compressive stresses in the film (4,5). An immediate

solution would appear to avoid producing films with polycrystalline columnar

morphology, and to deposit films with an epitaxial relationship to the

substrate. Unfortunately this requires a close match of the crystallographic

parameters of the film and substrate and it may be too much to hope that this can be achieved with simultaneous satisfaction of refractive index criteria

in any one film/substrate combination. The requirements of high interface

perfection to ensure good epitaxy cannot be met in other than a UHV system

employing ion beam cleaning and annealing/surface reconstruction techniques,

or in chemical vapour deposition equipment where high substrate

temperatures/gaseous etchants can be employed. The alternative solution, the

adoption of pseudo amorphous morphologies may offer some potential since the

coating need not be lattice matched to the substrate.

Experimental

The present work assesses the potential of molecular beam techniques for the

deposition of improved optical coatings. This growth technique allows a high

degree of control over the deposition process and in situ assessment

techniques such as Auger and XPS allow the characterization of the surfaces

produced. By combining Knudsen evaporation with RF sputtering processes in a dedicated UHV facility, it is possible to fabricate coating structures

containing a wide range of different materials including sulphides,

selenides, tellurides, arsenides, phosphides, fluorides, chlorides, oxides

and nitrides without necessarily having to break vacuum and risk the creation

of contaminated interfaces. The coatings discussed in this paper were fabricated in a 3 chambered UHV facility incorporating Knudsen sources, a small RF plasma source, a molecular beam sampling spectrometer, Auger

spectrometer and ion guns for substrate cleaning. Details are presented in

previous publications (6,7). The morphology of the coatings was examined in

detail by cross-sectional transmission electron microscopy (XTEM) at 1 20KV

using specimens prepared by sequential mechanical polishing/low voltage AR+ ion milling. Laser damage thresholds were determined using a short cavity

TEA laser (33nsec FWHM with tail extending to 1700nsec) and a grating tuned

hybrid laser (340nsec FWHM) as described previously at 10.6ym.

Morphology

The MBE produced coatings were mirror smooth and replicated the topography of

the substrates used. Some inclusions were evident in ZnS films deposited on

Ge substrates, but these were also present in uncoated regions of the

substrates and were attributed to polishing debris. XTEM micrographs of

0.7pm thick ZnSe films grown on GaAs at 50°C clearly reveal columnar grains

some 250A in diameter running throughout the thickness of the film. The

crystalline structure within the material is highly defective with a high

density of stacking faults each running perpendicular to the direction of

81
growth. X-ray diffraction measurements show that the material is highly

ordered with cubic (111) planes lying parallel to the surface. Careful

examination of the grain boundary regions reveals the complete absence of any

voids within the scale of resolution available (20A). A transition region

some 1 500A in height above the substrate is also evident where growth of the

columnar grains is clearly unstable and new grains are being nucleated. Also

evident is a narrow 60A amorphous region at the surface of the substrate

resulting from ion beam damage during substrate cleaning. The morphology of

ZnSe produced at 192°C is essentially similar to that of the films deposited

at 50°C with the exception of a greatly increased grain size of 1000A. The

grain boundaries are, however, less well defined in the 192°C film and

stacking faults in neighbouring grains tend to merge into one another. No

voids are detected.

XTEM micrographs of SiOx films produced by RF sputtering under ultra-clean

conditions at ambient temperatures are essentially featureless with faint

contrast barely discernable due to ion beam thinning artifacts. The films are amorphous and contain no voids.

Optical Properties and Discussion

A direct comparison has been carried out of film deposition in conventional

vacuum environments (p(H 20) 2.5 x I0" 6 mbar) and UHV (p(H 2 0) 2 x 10" lo mbar)

using the same equipment under otherwise identical conditions. Infra-red

spectral analysis of the resulting films clearly shows the presence of OH

species in ZnS films produced in poor vacuum whilst UHV grown ZnS is

essentially free from such impurities. There are also significant

differences in the adhesion of such films with the UHV produced films

adhering to the substrate more strongly especially during laser pulse

irradiation.

The laser induced damage thresholds (LIDT) of UHV produced ZnSe films on ZnSe

substrates for 33nsec pulses were in the range 60-73J/cm2 (1/e 2 radius

102ym). This was in excess of the value of 50-60J/cm2 measured on uncoated

regions of the same samples, with the uncoated region always damaging at a lower incident energy. This was attributed to the presence of residual

surface impurities on the substrate which had been removed by pre -deposition

ion cleaning. At longer pulse length (340nsec) the LIDT value for such a film was 31-38J/cm2 (1/e 2 radius 180ym) with damage initiated at discrete

microscopic inclusions resulting in craters some lOym in diameter. The

uncoated rear surface of the substrate always damaged at these energy

densities. Refractive indices of such films are in the range 2.39 to 2.40 in

the IR demonstrating the near theoretical density of the film material. The

damage thresholds are significantly in excess of values of the order of

20J/cm2 reported for sputtered ZnSe on KC1 (8), and are attributed largely to

the pore-free nature of the films.

Films of ZnS have been deposited on ZnS, ZnSe and Ge. In these cases, film

stoichiometry was considered to be an additional problem since the sticking

coefficient of sulphur from an S 2 flux is likely to be less than that of

Zn. Experiments have therefore been carried out to assess the importance of

this effect by supplying additional sulphur (specifically S 2) from a second

source. This was conveniently provided by a Knudsen source containing silver

82
sulphide which dissociates to produce S2 and Ag fluxes in the ratio of

about 101* . Provided that this source is purely used as a 'top-up' measure,

significant contamination of the ZnS with Ag is likely to be negligible.

ZnS films deposited in UHV at temperatures of 50°C without the supply of

additional sulphur are slightly colored demonstrating a degree of

nonstoichiometry in the material. However, laser damage thresholds are high

- 70J/cm2 (33nsec, 1/e 2 radius 70ym) when deposited on multispectral ZnS

substrates and 79J/cm2 when deposited on ZnSe. Comparative LIDT values for

the uncoated substrates for these spot widths were 193J/cm 2 (ZnS) and 66J/cm

(ZnSe), respectively. The enhancement in LIDT observed for ZnS windows

compared with that of ZnSe has been reported by others (9) and appears to be

real despite the fact that the absorption coefficient of the ZnS at 10.6nm

(0.2cm~M is significantly greater than that of the ZnSe (0.003cm~ l ).

When deposited at 50°C from fluxes containing an excess of S2/ ZnS films

are no longer colored, demonstrating achievement of the correct

stoichiometry. However the laser damage thresholds of such films so far

examined are very similar to those produced without the sulphur excess,

suggesting that the damage mechanism is dependent on factors other than the

degree of optical absorption in the film.

References

1. D. A. Walsh and R. S. Bertke: Proc. Boulder Laser Damage Symposium 271

(1977).

2. D. F. O'Brien: Proc. Boulder Laser Damage Sympsoium 276 (1977).

3. K. H. Guenther and H. K. Pulker: Appl. Optics J_5, 2992 (1976).

4. H. K. Pulker: Thin Solid Films 58, 371 (1979).

5. H. K. Pulker: Proc. SPIE 325 , 84 (1982).

6. K. L. Lewis and J. A. Savage: Proc. Boulder Laser Damage Symposium

(1983).

7. K. L. Lewis, J. A. Savage, A. G. Cullis, N. G. Chew, L. Charlwood and

D. W. Craig: Proc. Boulder Laser Damage Symposium (1984).

8. A. Golubovic, J. Fitzgerald, I. Berman, J. Bruce, R. Bradbury, J. J.

Comer, W. S. Ewing and H. G. Lipson: Proc. Boulder Laser Damage

Symposium 271 (1976).

9. R. M. Wood, P. Waite and S. K. Sharma: Proc. Boulder Laser Damage

Symposium (1983).

83
A SIMPLE MODEL OF INHOMOGENEITY IN OPTICAL THIN FILMS

G. Deniau, F. Flory, and E. Pelletier

Ecole Nationale Superieure de Physique de Marseille

Laboratoire Associe' au C.N.R.S.

13397 Marseille Cedex 13 - France

Most materials used in thin-film optical coatings exhibit optical

inhomogeneity that is frequently so large that it cannot be neglected. The

inhomogeneity is directly related to the layer microstructure that can be

observed in electron micrographs. This leads directly to the consideration

of a layer model that can be used to represent this inhomogeneity and can be

used in calculations. Its usefulness decreases with its complexity and it

should therefore be as simple as possible but nevertheless it should also

reflect the real behavior of the films. The unprecedented precision with

which multilayer deposition can now be controlled coupled with the

possibility of accurate in situ property measurement makes the time ripe for

a reexamination of this problem.

The simplest possible model, at first sight, would be a layer with a linear

variation of index with optical thickness throughout the layer from rear to

front surface, the front surface being identified as corresponding to the

material deposited at the termination of the layer. A single extra parameter

An/n can then be added to the other layer parameters usually used in

calculations such as n and d. An represents the change in index from the

initial to the final, or rear to front, surface and therefore a negative

value of An/n implies an index that decreases as the layer thickness

increases. While such a model appears simple, it leads to calculation

difficulties and to ease these we modify the model so that it becomes a combination of ten sublayers of equal thickness, each being homogeneous and

having indices that form a regular progression such that their indices are exactly that given by the intercepts of their center lines and the linear

variation through the optical thickness of the layers. The parameter An/n

can therefore still be used to represent this model.

To the refractive index we add a single value of extinction coefficient that

remains constant throughout the ten sublayers.

We have already examined the validity of this model for normal incidence

calculations. The calculation method developed by BORGOGNO et al. [1] is

used for the extraction of the various model parameters from experimental

measurements of R and T. Measurements on complete films can be well

reproduced by the model [2]. Further, in situ measurements during

deposition, which yield actual profiles of the index as a function of layer

thickness, show that a linear variation of index is a reasonable assumption

[3]. It is important that this study should be continued so that layers with

as large a variation of index as possible might be studied and the validity

of the model tested in such cases.

84
All this so far has dealt with near normal incidence. We have recently

examined layers of Ti02 in both polarizations at 45° and been able to

reproduce accurately the results using model parameters derived at normal

incidence. Guided wave techniques give us another opportunity of testing the

validity of the model at oblique incidence.

We used a method based on the measurement of the coupling angles or m-lines

[4] [5]. The principle is simple. A prism coupler permits accurate

measurement of the coupling angles of the various modes of the film and hence

their propagation constants. If the inhomogeneous model is used for the

layer then n, An/n and the geometrical thickness can be extracted from these

constants. The calculations are fairly complicated and involve successive

approximations and it is not always possible to find a unique solution. Most

of our work so far has been with TE waves. Provided we have used fairly

thick layers (nd - 6 to 8 A/4), the values of index gradient that have been

obtained show very satisfactory agreement with measurements made by the other

techniques

.

There can sometimes be an ambiguity in the sign of An/n but this can very

readily be resolved by the use of classical spectroscopy. When the layers

are rather thinner (nd = 4 to 6 A/4), two modes only can be observed,

insufficient to determine n and An/n simultaneously. It is possible to use

the value of An/n obtained by spectrometry and calculate n and d when

excellent agreement with the other measurements of these parameters is

obtained. When TM measurements are added to the TE, the interpretation

becomes still further complicated and an anisotropy of the index as well as inhomogeneity becomes detectable in some materials such as titanium oxide.

It should be stressed that the guided wave measurements are effectively at

very high angles of incidence. We conclude that the layer model works well.

The next step is to consider the inclusion of anisotropy.

[1] J. P. Borgogno, B. Lazarides, E. Pelletier, Applied Optics, 21 , 4020-

4029, (1982).

[2] J. P. Borgogno, F. Flory, P. Roche, B. Schmitt, G. Albrand, E.

Pelletier, H. A. MacLeod, Applied Optics, 22_, 3567-3570, (1984).

[3] F. Flory, B. Schmitt, E. Pelletier, H. A. Macleod, Proc. SPIE, vol 401 , 109-116, (1983).

[4] P. K. Tien, Applied Optics, J_0, 2385-2389, ( 1971 ).

[5] M. Olivier, J. C. Peuzin, Applied Phys. Lett. 32^, 386-388, ( 1978).

85
OPTICAL PROPERTIES OF DIAMONDLIKE

CARBON FILMS ON SEMICONDUCTORS

George M. Bu-Abbud, 1 * L Joel D. Lamb, 1

, and J. E. Ota 1 Department of Electrical Engineering, University of Nebraska

Lincoln, NE 68588-0511

dnd

1 ? 3 John A. Woollam 1 '^

Universal Energy Systems

Dayton, OH 45432

Diamondlike carbon (DLC) films have been described by various authors as being hard, resistant to various chemicals, highly insulating, and

adherent to a wide variety of materials (1). We have recently been

investigating the usefulness of these materials in various applications

including dielectrics for integrated circuits and coatings for optical

(especially infrared) materials (2-4). The purpose of the present paper

is to describe the optical properties of DLC films deposited on several

technologically important semiconductors. Specifically, we have used

spectroscopic ellipsometry and absorption spectroscopy to determine the

index of refraction and extinction coefficient over the wavelength range

from 220 nm to 3.39 microns. Substrate materials include flat,

polished, oriented single crystals of silicon, indium phosphide, cadmium

telluride, mercury cadmium telluride, germanium, and quartz.

All substrate materials are cleaned in triclorethylene, acetone,

methanol, deionized water, and blow dryed with nitrogen gas, prior to

insertion in the DLC deposition system. The deposition chamber is a small diffusion pumped (base pressure <2x-10~ torr) bell jar which

contains the parallel plate, capacitor coupled rf plasma system. The rf

generator operates at a frequency of 136 MHz which is tuned such as to

deliver up to 100 watts to the plasma. The electrode on which the

sample is placed can be electrically biased up to several hundred volts,

and can be heated to several hundred degrees C, as well.

The plasma is a mixture of hydrocarbon and argon gases operating in the

mill torr pressure range. Usually the hydrocarbon is methane but

methane, propane, and ethane were used as well. Deposition rates are on the order of 50 Angstroms per minutes, and thicknesses are usually in

the range from 300 Angstroms to 2000 Angstroms.

Routine measurements of absorption vs wavelength are made, using quartz

substrates and a uv-vis spectrometer. From these data we find that the

optical bandgap is in the 2 to 3 electron volt range, depending on deposition parameters and hydrocarbon gas. The highest bandgap is 2.8

electron volts.

1. Supported by Grant NAG-3-154 from NASA Lewis Research Center.

2. Supported by Contract DAAG-46-84-C-0057 from the Army Materials and

Mechanics Research Center.

3. Also: Department of Electrical Engineering, University of Nebraska.

86
A rotating analyzer automated spectroscopic ellipsometry is used to

determine the index of refraction and extinction coefficient as a function of wavelength (5). Data from a typical sample are shown in

Figure 1. Note that the index of refraction is near 2.0, and the

extinction coefficient shows a rapid rise starting in the range of 550

to 600 nm. A plot of the square root of absorption coefficient times

photon energy vs photon energy yields a straight line with an intercept

of 2 ev (equal to the optical gap) for this sample.

The Bruggeman effective medium approximation is used to analyze the

spectra. Constituent media are assumed to be diamond, graphite,

polyethelene, and voids. The general conclusion is that, DLC films are

not mixtures of constituents, rather that DLC is a unique material with

a unique band structure and optical properties. Data in the ultraviolet

are needed to gain further information on interband transitions in these

interesting materials.

References

1. Workshop on Diamond-Like Carbon Coatings, BDM Corporation Technical

Report BDM/A-82-242-TR under DARPA Contract MDA OP 3-81-C-013.

2. J. A. Woollam, V. Natarajan, J. Lamb, A. .A. Khan, G.H. Bu-Abbud, D. Mathine, D. Rubin, and R.O. Dillon, Thin Solid Films, 119 , 121

(1984).

3. R.O. Dillon, J. A. Woollam, and V. Katkamant, Phys. Rev. B15, 7229

(1983) .

4. A. A. Khan, J. A. Woollam, and Y. Chung, J. Appl . Phys. _55, 4299

(1984) .

5. D.E. Aspnes, and A. A Studna, Applied Optics 14, 220 (1975).

87
21

o o

£o 2.0

uj 1.9

*-

0.25

^ 0.20

«?S 0.15

ht 0.10 X UJ

uj o

0 0.05

0.0 J

DLC ON SILICON

SI13, t

f = 343 A

o O o o

I! 400 500 600

WAVELENGTH, nm

700

Index of refraction and extinction coefficient vs. wavelength

for methane rf plasma deposited DLC on silicon.

88
TEMPERATURE DEPENDENT OPTICAL PROPERTIES OF SILVER SULFIDE THIN FILMS

R.L. Burton, H. Buhay, M. Nisar, J.L. Grieser, N.P. Murarka

I IT Research Institute

Microwave and Electro-Optics Department

Chicago, Illinois 60616

The silver chalcogem'de, Ag

2 S, exhibits a crystallographic phase transition at

T

c = 180°C which affects its optical properties. The stable phase below T

c

, 3-Ag 2 S, has an ordered monoclinic structure with the sulfur ions arranged in a body centered cubic lattice. The stable phase above T

c , a-Ag

2 S, is cubic with

the B.C.C. arrangement of sulfur ions; however, the silver ions are randomly

distributed on the interstices occupying 4 of 42 available point sites of the

unit cell [1,2]. As the temperature increases the electrical conductivity

increases by three orders of magnitude [3,4] due to the phase change. In the

high temperature phase, excess silver atoms act as electron donors.

The infrared properties of the 3-phase can be accounted [5] for by a fundamental absorption edge with a band gap energy Eg = 0.6-0.9 eV [5], In this phase

it transmits through much of the infrared (200 cm"-'- to 6000 cm"*). In the

a-phase, a well-defined plasma absorption edge forms [5] with a plasma frequency of approximately 3300 cm" 1

. In view of these bulk properties, thin

films of silver sulfide may be useful for specialized applications.

Flash evaporation techniques for synthesizing Ag

2

S thin films have been re- ported [1,2,6]. In this work results are presented for films prepared by a triode D.C. sputtering process which has been found to provide greater control

and produced superior films. Sputtering targets used were made by hot

pressing Ag

2

S powder. Typical deposition rates were 0.5 ym/hr. Several films were prepared in this manner on GaAs substrates.

Optical transmi ttance and reflectance measurements were made using a PerkinElmer Model 580B spectrophotometer. For these measurements the films were mounted in a vacuum furnace and the temperature varied using an Omega Model

CN2010 programmable controller. The typical transmi ttance for a 0.94 urn film

at 26, 160, 165, 170 and 190°C are shown in Figure 1. Absorption due to C0 2 appears in the spectra at ~2350 cm" 1 since the instrument was not purged.

Because Ag

2

S transmits infrared radiation, interference fringes can be seen in

89
the spectra. Absorption due to free carriers is the dominant feature above

T

c

. Figure 2 shows the front surface reflectance at the same five temperatures. The most important feature of these curves is the metal-like plasma

edge at low frequencies. As the temperature increases, a greater number of

silver atoms become ionized into electron donors. This raises the electron

concentration and causes the plasma edge to shift to higher frequencies.

Absorption due to free carriers is lower at higher energies and all of the curves approach similar values for frequencies above 4000 cm"*.

From the optical data, the frequency dependence of the refractive index n and

extinction coefficient k were computed by two methods. The first method involved a nonlinear regression analysis which compared the R and T spectra of

the films to calculated values based on a Drude dispersion model T7]. The

second method makes use of a technique of bivariate optimization adapted from

the literature [8], This method uses the transmittance, reflectance and back

surface reflectance to find values of n and k that directly satisfy these

measurements at every data point. The results of the two methods agreed ex- cellently, except for small regions of the spectra where the bivariate method

fails to find a solution.

The results for n and k are shown in Figures 3 and 4 respectively. The

figures can be interpreted as describing the refractive index and extinction

coefficient due to free carrier absorption at low frequencies and converging

asymptotically toward n = 3.00 and k = 0.0 at 4000 cm~*. Of course the

fundamental absorption edge starts to exhibit influence on n and k at frequencies above 4000 cm

-1

.

By assuming an effective mass value equal to the bulk value [9], m* = 0.24 m

e

, the electron concentration, N, and mobility, u, can be computed from the Drude

parameters w

p

, t, and t^. The results for N and v are given in Table 1. The

film electron mobility is fairly constant with respect to temperature except

for 160°C at which the observed plasma edge was difficult to fit with accuracy.

Bulk values for electron mobility are in the range 160-190 cm

2 /(V-sec) [1],

The thin film mobilities were lower, typically u = 130 cm^/(V-sec), and varied

for different films of Ag2$. The electron concentration versus temperature is

shown in Figure 5. This data agrees well with the bulk value [9] of 3.6 x 10^

90
1300 2000 2500 FREQUENCY (cm"1 )

3000 900 1000 1500 2000 2500 FREQUENCY! cm-1

) 3000 3500

Figure 1. Transmi fiance of a silver sulfide film on a GaAs

substrate at several

temperatures

.

Figure 2. Reflectance of a silver sulfide film on a GaAs

substrate at several

temperatures.

1500 2000 2500 FREQUENCY (cm' 1 ) 3000 3500

2.0

U I 5 8

10

0.5

- 190'Ct

I70*C \

_ 165 *C \ \

[ x io

I60"C u\

26*C 1

I . 1 1 1500 2000 2500 3000 3300 FREOUENCY(cm-' I

Figure 3. Refractive index of a silver sulfide film at several

temperatures

.

Figure 4. Extinction coefficient

of a silver sulfide film at

several temperatures.

91
(cm~J

) at 185°C for silver rich Ag2

S. Thus, it is concluded that the films are silver rich, although the target was initially stoichiometric. The latter

may be accounted for by sublimation of sulfur at the surface of the target

during the sputtering process.

150 160 170 180 190 200

TEMPERATURE (°C)

Figure 5. Electron concentration, N, as

a function of temperature.

References

1. H.P. Geserich and W. Suppanz, Phys. Status Solidi 35, 381-387 (1969).

2. T.Y. Hsu, H. Buhay, N.P. Murarka, Proc. SPIE 259,~T8 (1980).

3. C. Wagner, J. Chem. Phys. 21, 1819-1827 (1953).

4. M.H. Hebb, J. Chem. Phys. "2H, 185-190 (1952).

5. P. Bruesch, and J. WullschTeger, S.S.Comm. _13_, 9-12, (1973).

6. T. Fleisch and R. Abermann, Thin Solid Films 42, 255-263 (1977).

7. F. Wooten, Optical Properties of Solids (Academic Press, Mew York, 1972).

8. R.C. McPhedran, L.C. Botten, D.R. McKenzie and R.P. Netterfield, Appl

Opt. 23, 1197-1205 (1984).

9. H.H. TJorner, H.P. Geserich, and H. Rickert, Phys. Status Solidi 37, K85

(1970).

92
MOLECULAR BONDING IN OPTICAL FILMS DEPOSITED BY

ION-BEAM SPUTTERING*

C. Y. She+

Physics Department, Colorado State University

Ft. Collins, Colorado 80523

Introduction

Recent demands in low-loss and low-scatter optical coatings have stimulated

considerable activities in the investigation of dielectric films with high

refractive index and low absorption. Of particular interest are new deposition methods on the one hand and novel diagnostic techniques on the other,

which could be employed to elucidate the nature and property of the film at

molecular levels. Over the past two or three years, work on ion-beam-sputter

deposition has yielded dense dielectric films, such as titanium oxide, which

are thought to be amorphous having desirable optical and mechanical properties. 1 More recently, the conventional technique of Raman spectroscopy has

been modified and demonstrated to be a simple and effective method, satisfying the apparent need for evaluation of submicron-thick optical coatings.

Despite the great success in crystalline solids, Raman spectroscopy has been

applied only a few times, for example, to interrogate a semiconductor silicon

f ilm^ via a very strong Raman line at 520 cm

- -'- and an interfacial composition of an M-GaAs structure;^ encapsulated nonabsorbing films were, however,

regarded as too weak for Raman study. Up to this point, x-ray diffraction,

which works well only for thick films, * was used for structural characterization; its required long measurement time, typically hours, however, leaves

much to be desired. Using a 180° backscattering geometry, Pawlewicz et al.

recently were able to use Raman spectroscopy to characterize crystalline

single-layer dielectric coatings with a measurement time a factor of 100

times less than that required for the x-ray diffraction method. ^ Very

recently, we recognized that a major limiting factor in Raman study of thin

films is the interference resulting from the Raman signal of the substrate.

Using an oblique-incident technique, we were able to suppress this substrate

interference by a factor of 50, making Raman spectroscopy a simple but effective nonintrusive method for structural characterization of submicron-thick

films. ^ An amorphous coating was then characterized for the first time with

a measurement time of only 500 sec.

Using Raman spectroscopy, we have studied the microscopic structure and

molecular bonding of ion-beam sputtered optical films by the method of thermal and laser annealing. Transformation of amorphous titania coatings to

crystalline anatase and/or rutile structures has been observed. We report

these results and discuss their implications in this paper.

Sample Preparation

Titania (Ti02) films are fabricated by sputtering a metallic Ti target with

O2 and Ar ions from a Kaufman-type ion source. * The deposition chamber is

93
shown in Fig. 1. The secondary ion source is used for pre-sputtering and

cleaning of the substrate. The sample (substrate) holder is rotating during

the deposition process for film uniformity. Although the sample holder may

be cooled or heated in principle, it was not controlled for the coatings used

in this study. The temperatures were monitored during depositipn, typically

from 20°C to 170°C, resulting in amorphous titania films.

Laser Annealing

For laser annealing study, ^ a 240-nm-thick T102 film was deposited on a 2-indiameter COO Si wafer by ion-sputtering, as described above. The coating was then laser annealed with a scanned Ar + laser beam 50 um in diameter over

5 mm x 5 mm squares at different laser powers and scan speeds. Raman spectra

of the laser annealed squares were recorded. Evidences of structural transformation became clear when these spectra are compared.

A typical Raman spectrum of Ti02 as deposited on a Si wafer is shown in Fig.

2(a). Besides the strong Si peak at 520 cm" * and a weak feature at 300 cm~^,

Raman spectra of the coating before annealing or of the areas between

annealed squares are rather featureless indicative of amorphous structure.

Raman spectra of the annealed titania with 6 W of laser power at different scan rates, 50 cm/s, 30 cm/s, and 15 cm/s are shown in Figs. 2(b)-2(d), res- pectively. Anatase peaks at 144 cm~l, 400 cm~l, and 635 cm

-

* can be seen clearly. As the laser annealing time at a given spot is increased by reducing the scan rate, crystalline anatase structure is more fully developed.

Raman spectra of annealed titania coating on a Si wafer for shifts between

300 cm~l to 700 cm

-

*, at different laser powers, are shown in Fig. 3. It is

quite evident from this figure that the amorphous coating has partially

transformed into microcrystals of anatase structure after annealing. At

higher annealing laser intensity, Raman spectra reveal the presence of rutile

microcrystals in the coating as well. Qualitatively, this laser annealed

amorphous-anatase-rutile transformation is consistent with the structure

dependence of films on deposition substrate temperature.-*

Compared to the as-deposited film of Fig. 2(a), these annealed samples show

much higher background scattering which appears to be dependent on annealing

laser intensity, but not on the scan rate. Visual inspection of annealed

areas with a Nomarsky microscope indicates that with this beam diameter, the

laser damages occur at 6 W and get worse at higher powers. As the annealing

power is increased from 5 to 8 W at a constant scan rate, the anatase 144

cm

-

* peak intensity first grows and then decreases as rutile microcrystals

begin to develop in the coating. With high annealing laser power, the film

gets damaged and the background signal increases. This background is a measure of the surface scattering of the film. Even under these high scattering conditions, Raman spectroscopy is evidently still an effective probe

for structural characterization of submicron-thick optical coatings.

Thermal Annealing

Amorphous titania films used for thermal annealing were deposited on Corning

7059 glass under different conditions. Type A films were obtained with lower

ion beam current (0.4-0.8 mA/cm^) while type B films were made with beam

94
current greater than 1 mA/cm^. The thicknesses are 2233 A and 3117 A, res- pectively, for type A and B films. As to be shown below, these films,

although optically identical as deposited, crystallize differently upon thermal annealing. The as-deposited coating was annealed in an air furnace

sequentially at 200, 300, 350, 400, 450, 500, and 600°C. At each temperature,

the coating was annealed for 20 min in the furnace. It is then cooled slowly

to room temperature for Raman scattering and other experimentation before the

film is annealed to the next higher temperature.

Figure 4 shows the Raman spectra of these films subjected to annealing at

various temperatures. Due to the lack of thickness, Raman spectra of the as- deposited films (20°C) are obscured by the broad features of the substrate at

480 cm

-1 and 790 cm

-

*; its broad scattering shoulder is indicative of the

amorphous nature of the film.^ The spectra of annealed films at 200°C (not

shown) and 300°C appear to be identical. For Type A films, upon reaching

350°C, there is a small bump at 612 cm

-

* without any hint of the 144 cm" 1 feature. This indicates crystallization with some rutile mi crocrystals , but no anatase. At 400°C, evidence of anatase is quite clear by the appearance of

the peaks at 144 cm" 1 and 635 cm

- -'- and additional shoulders at 400 cm" 1 and

515 cm" 1

. The concurrent presence of rutile growth is evident by the weak

peaks at 400 cm" 1 and 612 cm" 1

. Subsequent annealing at 450°C, 500°C (not

shown), and 600°C shows that the anatase peaks become more prominent while the

rutile peaks remain constant. At 600°C and higher temperatures, the Raman

intensity tends to be unchanged signifying the completion of the crystallization process. As shown in Fig. 4(b), a Type B film retains its as-deposited

amorphous features up to 350°C, where it crystallizes into rutile structure

without any anatase. Such evidence again comes from the appearance of the 440

cm" 1 and 612 cm" 1 rutile peaks. When the annealing temperature is increased

further to 400 and 600°C, the rutile signal intensity increases along with the

two-photon Raman modes of rutile at 250 cm" 1 and 690 cm" 1

.

If a similar Type A film is heated directly to 600°C, bypassing the lower

temperature steps, it results in anatase crystallization without any detectable rutile, as illustrated in Fig. 5(a). If these Type A anatase films were

further heated to 900°C or above, where rutile structure is thermodynamically

more favorable, ^ the anatase films transform into anatase-rutile structure

with rutile dominance, as shown in Fig. 5(b). The high background above

500 cm" 1 is due to partial melting of the glass substrate.

The elastic light scattering of both types of films at various annealing temperatures has also been recorded simultaneously with the Raman spectra of

Fig. 4. Using the scattering from MgO as a calibration, the percentage scattering can be determined. A dramatic two-order of magnitude increase in

elastic scattering accompanying the film crystallization near 400°C has been

found;^ it suggests degradation upon heating and has obvious implications

for use of these films as coatings for high-power laser mirrors.

Macroscopic optical transmission measurements of these coatings have also

been made at each annealing temperature. An abrupt rise in refractive index

and extinction coefficient has been found at a temperature between 300°C to

400°C for both types of films, ° indicating crystallization at around 350°C.

However, the microscopic differences between the two types of the films can

be deduced only from the Raman data.

95
Conclusions

Raman spectroscopy has been applied to probe the molecular structure of submicron-thick titania films deposited by ion-beam sputtering. Low-scattered

amorphous optical coatings of different types have been characterized by

Raman scattering for the first time. Under laser or thermal annealing, thes

amorphous coatings crystallize into mi crocrystals of anatase or rutile

depending upon conditions of film deposition and subsequent annealing.

Because it is a microscopic probe, Raman spectroscopy is capable of distinguishing different types of coatings with similar optical properties.

*This work is supported by the Air Force Weapons Laboratory under Contract

F29601-83-K-0079. +0n sabbatical at the University of Maryland and Laboratory for Physical

Sciences, College Park, MD.

Acknowl edgeme nt

The author acknowledges the contributions of L. S. Hsu, R. Rujkorakarn, and

R. Solanki, who perform the experiment presented here.

References

1. J. R. Sites, P. Gilstrap, R. Rujkorakarn, Opt. Engr. 22, 477 (1983).

2. L. S. Hsu, C. Y. She and G. J. Exarhos, Appl. Opt. _2_3» 3°49 (1984).

3. S. R. Brueck, B-Y Tsaur, J. C. C. Fan, D. V. Murphy, T. F. Duetsch and

P. J. Silversmith, Appl. Phys. Lett. 40_, 895 (1982).

4. G. P. Schwartz and A. Y. Cho, J. Vac. Sci. Technol. _19_, 607 (1981).

5. L. M. Williams and D. W. Hess, J. Vac. Sci. Technol. Al_, 1810 (1983).

6. W. T. Pawlewicz, G. J. Exarhos and W. E. Conaway, Appl. Opt. 22 , 1837

(1983).

7. L. S. Hsu, R. Solanki, R. Collins and C. Y. She, Appl. Phys. Lett. _4_5, 1065 (1984).

8. R. Rujkorakarn, L. S. Hsu and C. Y. She, 16th Boulder Damage Symposium,

NBS special publication (to be published).

Ar

Shutter f Secondary

ion source

Fixed Target

( Ti)

Primary

ion source

Rotating

sample holder

Cryogenic

vacuum

system

Fig. 1. Chamber for ion-beam sputtering of films.

96
7.0

100 400 WAVENUMBERS

700

(b)6W 50CM/SEC

i

1 1 h-

<d)6W 15CM/SEC

—

>

La

100 400 WAVENUMBERS

700

Fig. 2. Raman spectra of

titania coatings on a Si

wafer. (a) As deposited by

ion sputtering showing amorphous structure, (b) , (c)

,

and (d) are results after

annealing with a 6 W beam at

different scan rates. Peaks

at 300 and 520 cm

- -'- are due

to Si and peaks at 144, 400,

and 635 cm

- -'- are due to

in anatase phase.

2.0r Si UPPER

:

6W 15CM/SEC

..LOWER: 5W 15CM/SEC

A —1—1—1—t-—u1—1—1

3.0n Si UPPER

:

8W 30CM/SEC

..LOWER: 7W 15CM/SEC

R A

1 1 1 H

in

—1—1—1

300 500 WAVENUMBERS

700 300 500 WAVENUMBERS

700

Fig. 3. Raman spectra of

laser annealed Ti02 coatings

on a Si substrate. Besides

the strong Si peak at 520 cm

-

-'-, Raman spectrum of the

coating before annealing is

featureless (not shown) in

this intensity scale. After

annealing at different power

levels, Raman peaks indicative of crystalline anatase

(labeled A) and rutile

(labeled R) structures are clearly evident.

97
100

TYPE A

soo WAVENUMBERS

<20C

900 100 500

WAVENUMBERS

<20C

900

Fig. 4. Raman spectra for coatings annealed at various temperatures,

(a) type A/glass and (b) type B/glass.

500

WAVENUMBERS

SOO 100 500

WAVENUMBERS

900

Fig. 5. Raman spectrum for type A/glass coatings annealed directly at

(a) 600°C to form anatase and (b) 950°C to form anatase-rutile

mixture.

98
HIGHLY TRANSPARENT METAL FILMS: Pt ON InP

D. E. Aspnes

Bell Communications Research, Inc., Murray Hill, New Jersey 07974

Adam Heller, J. D. Porter, T. T. Sheng, and R. G. Vadimsky

AT&T Bell Laboratories, Murray Hill, New Jersey 07974

Highly transparent metal films are of potential interest in a number of areas of science

and technology including light detection, photovoltaic energy conversion, catalysis, and

photoelectrochemistry. In studies of light-activated hydrogen evolution on platinized

semiconducting photocathodes,* it was discovered that the quantum yield of hydrogenevolving semiconducting electrodes did not decline significantly with increasing platinum

coverages, even for metric thicknesses as much as 50 nm where 99.9% of the transmitted

light should have been absorbed. The observation of this anomalous transparency

stimulated further investigation, and in a recent preliminary report we described the

preparation and characterization of the first substantially transparent supported metal

films of significant thicknesses. We found that the essential characteristics giving rise to substantial transparency in metal films were porosity and microstructure, and that by

controlling these properties, absorption and reflection losses could almost be eliminated.

Here, we discuss in more detail the physical principles involved and present further results on Pt film/p-InP system.

The obvious reason that porosity reduces absorption losses in metal films is that porous

films have less absorbing material per unit volume than dense films of the same thickness.

Front-surface reflection losses also decrease because the refractive index of a film

decreases along with its metal packing fraction, fm. But the major factor in reducing

absorption losses is microstructure, that is, spatial inhomogeneities on the scale of

approximately 1 to 25 nm, or small compared to the wavelength of light in the medium.

Losses can be reduced most effectively if the films are constructed of networks of small

metal particles electrically isolated from each other. In physical terms, isolating the

particles with insulating boundaries allows screening charge to develop at their surfaces.

This screening charge excludes the photon fields from the metal particles and forces the

fields into the spaces between the particles. To the extent that the fields do not penetrate

the particles, absorption losses are reduced and transmittances correspondingly increased.

The operation of wire-grid polarizers is based on the same principle. But in addition, the

compression of photon fields into interstitial spaces between the metal particles causes a corresponding increase in the effective refractive index of the interstitial medium,

permitting the metal films to perform simultaneously an antireflection function.

To illustrate these principles theoretically in simple terms, we consider a microscopically

inhomogeneous two-phase composite in the Maxwell Garnett and Bruggeman

approximations in the limit where the dielectric function of the metal, €m, is much larger

in magnitude than that, ea

, of the ambient. The ambient phase is assumed to fill the

interstitial regions between particles. In this case it is straightforward to show from the

99
•5 general two-phase effective medium expression that the macroscopic dielectric function, c, of the composite is given by

€ = ca(l + kfm)/(l - fm) (Maxwell Garnett); (la)

c = ea (l/(l - fm/q)) , fm/q < 1 (Bruggeman); \ (lb)

where q = 1/(1 + k) is the depolarization factor. The depolarization factor assumes the

values 0, 1/3, 1/2, and 1 for no, isotropic 3-dimensional (spherical), isotropic

2-dimensional (cylindrical), and maximum screening, respectively. Minimum and

maximum screening correspond to all boundaries parallel and perpendicular, respectively,

to the applied field, and can be realized with laminar configurations. Note that em does

not appear in either Eq. (la) or (lb), and that e is increased over €a by an amount

depending on q and fm up to the percolation thresholds of the respective microstructures.

Thus to the extent that the magnitude of €m is large compared to that of €a

, losses can be

reduced to small fractions of those expected on the basis of bulk metal dielectric functions

alone, and by controlling the metal packing fraction the refractive index of the film can be

varied independently.

To establish the conditions under which transmittance of light into the substrate is optimized, it is necessary to work with the complete three-phase (semiconductor

substrate-composite film-transparent ambient) model. The optical properties of this

configuration can be expressed analytically'* in terms of e

s , e, ca

, and d, where e

s is the

substrate dielectric function, but the equations are cumbersome and better suited for

numerical analysis. We therefore expand these equations to terms linear in dA, where X

is the wavelength of light in vacuo. Films encountered in practice are typically far too

thick for this approximation to apply, but the expression nonetheless gives insight into the

relative importance of screening and the ratio of metal to ambient dielectric functions. To

first order in dA, the efficiency, r/, of transmission through the film and all interfaces is given by

4naRe(ns) [ 4^ Im(ns)[Re(e)-ea

] - Im(e)[Re(ns) + na]

l ns + nal I A |n

s + na |

(2)

where n,

2 = €a

, etc. The first term in the numerator approximately describes the

impedance-matching effect and the second absorption losses in the film. The first is always positive but vanishes if the dielectric function of the substrate is real; indexmatching in this case becomes a quadratic function of d. The second is always negative,

since absorption always represents a loss. Since na and ns are essentially outside direct

experimental control, the optimization strategy is to minimize film absorption by

minimizing Im(e).

If fm is small enough to allow the Maxwell Garnett or Bruggeman expressions to be

expanded to first order, then

4na Re(ns) 47rd€a fm

ns + na | 2I Xq|ns + na |

: Im(ns) p— Im |em(ns + na)

j (3)

100
The efficiency is now optimized by maximizing both |€m | and q. Since q = 1 represents

maximum screening, the importance of microstructure is immediately apparent.

We now consider a specific example that shows that the ideal conditions can be

approached. A Pt film was electrochemically deposited on a previously prepared p-InP

substrate in strong illumination under diffusion-limited conditions from a highly purified

1 M HCIO4 solution containing lxlO-5 M Pt(IV) as K2PtCl6

. Quantum efficiency

measurements, performed using the sample as an actinometer to reduce protons in acid

solution to neutral hydrogen, showed that the Pt film passed 92% of the incident light.

Spectroellipsometric data for the dielectric response of the film, determined by solving the

three-phase model implicitly, yielded d = 33.7 ± 0.5 nm and showed that the dielectric

function of the deposited film was greatly reduced from that of the reference Pt spectrum

(see Fig. 1). An independent analysis applied directly to the pseudoelectric function data

yielded d = 32.6 ± 0.8 nm, fm = 0.50 ± 0.02, and q = 0.55 ± 0.05. Scanning electron

micrographs indicated that the surface was approximately 85% covered with spherical Pt

particles about 50 nm in diameter. No fine structure was observable to the 20 nm

resolution limit of the SEM, suggesting that the optical value of fm was too small.

To resolve this discrepancy, we also examined the film by cross-sectional transmission

electron microscopy. The results are shown in Fig. 2. These data revealed three levels of

microstructure. The primary microstructure consisted of 2—10 nm microcrystals of dense

Pt. the secondary microstructure consisted of linkages between these microcrystals to form branched chains. The tertiary microstructure consisted of collections of these chains

into approximately spherical clusters of the order of 50 nm in diameter. The overall

macrostructure was homogeneous, showing no detail under optical magnification. While

an accurate quantitative comparison of the metal packing fractions determined

independently by spectroellipsometry and by transmission electron microscopy is not

feasible, the TEM results show that the spherical particles themselves are porous and have

a complex microstructure with characteristic dimensions much smaller than X. This

observation explains why effective medium theory accurately describes the optical data

under conditions where the small-dimensional assumption implicit in the quasistatic model

is apparently violated. We suspect that a similar explanation may apply to many of the

cases where apparent violations of the quasistatic dimensional limit also occur.

In these Pt films the various levels of microstructure are determined by interrelationships

among the various metal nucleation and growth processes. The primary microstructure is principally related to the rate of lattice growth. The secondary microstructure depends on

the rate of formation of viable nuclei on the surfaces of the growing microcrystals. The

tertiary microstructure is determined by the number density and occupation rate of

nucleation sites on the semiconductor substrate and by mass transport conditions in the

ambient fluid established during film growth. The variables that control these growth

processes are surface chemistry through solution composition, ion chemistry through

solution complexes, mass transport rate, temperature, applied potential, and incident light

intensity. We chose chemistries that tended to maximize nucleation and growth rate

constants such as simple aquo coordination of interfaces and metal ions and low-tomoderate rates of mass transport so deposition took place under mass-transport-limited

conditions established by a concentration gradient normal to the surface.

101
A detailed examination of effective medium theory shows that transparency for a given

polarization direction comes at the price of poor dc conductance in that direction. This

follows because nonconducting boundaries are needed for screening charge to develop.

For the system studied here, high transmittance values in unpolarized light were achieved

because electron transport occurred primarily along the surface normal, a consequence of

the growth process involving transport of photoexcited electrons from the space charge

region of the semiconductor to the surface of the growing film.

In many cases it is desirable, or even essential, to maintain a high dc conductance in a

direction parallel to the surface. Here, the optimum configuration consists of parallel

metal lines. The perpendicular polarization component passes virtually unattenuated,

ignoring reflectance losses, while the parallel component is attenuated. Because

transmittance is not improved significantly for non-normal incidence, some compromise

between transmittance and dc conductance is necessary. While details will clearly depend

on the specific situation, the transmittance will obviously be maximized by making the

metal lines as thin as possible and using an overlying dielectric film for antireflection and

protection of the microstructure.

REFERENCES

1. A. Heller, Science 223, 1141 (1984).

2. J. D. Porter, A. Heller, and D. E. Aspnes, Nature (in press).

3. D. E. Aspnes, Thin Solid Films 89, 249 (1982).

4. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (NorthHolland, Amsterdam, 1977).

Fig. 1. Pseudodielectric function data Fig. 2. TEM micrograph for the Pt/InP

for Pt and for Pt/InP. film of Fig. 1.

102
Calculation of the Electronic Structure

of As.S. and As.Se. Molecules

4 4 4 4

Davorin Babic and Sohrab Rabii

Department of Electrical Engineering and

Laboratory for Research on the Structure of Matter

University of Pennsylvania

Philadelphia, PA 19104

The recent developments in preparation of thin amorphous films of the

arsenic chalcogenides by spin-coating from solution [1] have led to renewed

interest in these materials for applications in the field of integrated

optics as waveguides, couplers, or storage media. As part of our theoretical investigation of the electronic structure of these materials, we have

undertaken to calculate the molecular structure for some of their existing

molecules, namely AS4S4, As^Se^, As^S^ and As^Se^. In the present paper we report on our calculations for the first two molecules. Previous theoretical

studies of these molecules include extended Huckel calculation on As^Se^ [2],

CNDO for AS4S4 and As^Se, [3], INDO for AS4S4 and As4Se4 [4], and ab initio

with Gaussian basis set for AS4S4 [5]. We have used the SCF-Xa-scattered

wave technique [6] to calculate the molecular energy levels, charge distributions, ionization potentials and

optical transition energies. Values

of a parameter for the exchange-correlation potential are taken from the

work of Schwarz [7] and are 0.72475,

0.70665 and 0.70638 for S, As and Se

respectively. The structural information for AS4S4 is taken from the

gas-phase x-ray diffraction measurements of Lu and Donohue [8] and for

As4Se4 from the measurements of

Goldstein and Paton on molecular

crystals [9]. These molecules have

the point group symmetry £>2d'

Figures 1 and 2 show the results

of the ground state calculations for

both molecules as well as the atomic

calculations for the constituent

atoms. In addition they show the

ionization potentials for the occupied molecular levels calculated using

the Slater's transition state concept

[10]. The HOMO and LUMO for both

molecules have b£ and e symmetries

respectively. The HOMO is As-As bonding which is in agreement with [3]

and its symmetry agrees with [5]. The

charge distribution for LUMO is more

10 3
As

-5

-10

u -|5

-20

-25

• 4p

of a mixture of As and the chalcogen.

The transition state concept was also

used to calculate the transition

energy for the allowed dipole transition between the HOMO and the LUMO.

The energies are 2.73 and 2.59 eV

respectively for AS4S4 and As4Se4.

These values are consistent with the

optical gaps of ^2.36 and M..76 eV

for the AS2S3 and As2Se3 glasses

[11].

Since the corresponding solid

phases of these compounds (realgar

structure) are molecular crystals it

is expected that a comparison of the

theoretical results for the molecules

are justified with the experimental

measurement on the solid phase. We

obtained a density-of-valence-states

from our calculation by assigning to

each state a Gaussian of width 0.5 eV

and area equal to the degeneracy of

the corresponding state centered at

its ionization potential and adding

the contributions to obtain a continuous curve. The results are compared in Figure 3 and 4 with the

valence band XPS measurement of

Salaneck e_t a_l [3]. As we can see

the agreement with experiment (dashed curve) is very good and also the

agreement with the theoretical density-of-valence-states by the same authors

(not shown in these figures) is very good. Similar studies are now in

progress for AS4S6 and As^Se^.

Fig. 2. Molecular energy levels

and ionization potentials for As4Se4

-28. -6.

ENERGY (eV)

Fig. 3. Comparison of the

calculated density of the

valence states for AS4S4

with measured XPS spectra

[3]. Dashed curve is the

experiment and solid curve the theory.

104
ENERGY (eV)

Fig. 4. Comparison of the calculated density of the valence

states for As4Se^ with measured XPS spectra [3]

Dashed curve is the experiment and solid curve the

theory

* Supported by NSF/MRL DMR 82-16718 and AFOSR-84-0320

1. G.C. Chern and I. Lauks, J. Appl. Phys. , 54, 6979 (1982).

2. I. Chen, Phys. Rev., Bll, 3676 (1975).

3. W.R. Salaneck, K.S. Liang, A. Paton and N.O. Lipari, Phys. Rev., B12 , 725 (1975).

4. K. Tanaka, T. Yamabe, A. Tachibana, H. Kato and K. Fukui, J. Phys. Chem.

82, 2121 (1978).

5. M.M. Palmer and R.H. Findlay, J. Mol. Struct. Theochem., 104 , 327

(1983).

6. K.H. Johnson, Adv. Quantum Chem., 7_, 143 (1973); J. Chem. Phys., 45_,

3085 (1966).

7. K. Schwarz, Phys. Rev., B5, 2466 (1972).

8. C.S. Lu and J. Donohue, J. Am. Chem. Soc, 66, 818 (1944).

9. P. Goldstein and A. Paton, Acta Crystallogr . , B30, 915 (1974).

10. J.C. Slater, J.B. Mann, T.M. Wilson and J.H. Wood, Phys. Rev., 184 , 672 (1969).

11. N.F. Mott and E.A. Davis, Electronic Processes in Non-Crystalline

Materials, (Clarendon Press, Oxford 1979) pp. 500-501.

105
FREE-CARRIER ABSORPTION IN A THIN FILM SILVER SULFIDE GALVANIC CELL

R.L. Burton, H. Buhay, J.L. Grieser, N.P. Murarka

IIT Research Institute

Microwave and Electro-Optics Department

Chicago, Illinois 60616

Ag 2

S undergoes a crystal lographic phase transition at a temperature T

C=180°C.

The electrical conductivity of the high temperature phase, a-Ag

2 S, is three

orders of magnitude greater then the low temperature phase, 3-Ag 2

S [1,2]. As

a result, 3-Ag

2 S transmits through much of the mid-infrared region, whereas

a-Ag 2

S exhibits a distinct plasma absorption edge. Studies of the influence

of the electron concentration on the electrical and optical properties of bulk

Ag2

S have been reported [3-5], Investigations of these properties were

achieved by incorporating an Ag

2 S sample in a galvanic cell structure. The

structure of these bulk material galvanic cells is given by: Ag electrode/Agl/

Ag

2 S/Pt electrode. In a similar manner a thin film galvanic cell, with a design analogous to the bulk cell, has been made and used to vary the electron

concentration in the silver sulfide film of the cell.

With a galvanic cell, an electrical current serves as a mechanism of controlling the a-Ag

2

S electron density and hence its infrared optical properties.

The galvanic cell is in a fully charged state when all Ag

+ ions have been

removed. In this state the cell potential V

c

* 200 mV [1]. Further charging

beyond this point will cause sulfur to plate out at the Pt electrode. Charging

the galvanic cell from 0 to 200 mV shifts the position of the plasma edge [3].

Reversal of the current restores the initial concentrations of Ag

+ and e~ in

the Ag

2 S.

The thin film silver sulfide galvanic cells studied were prepared in the

following manner. Initially an Ag 2S layer was deposited on a GaAs substrate

by D.C. sputtering from a target of hot-pressed Ag2S powder. The Ag 2 S layer was 1.6 ym thick and only its central area was used in the optical measurements. Agl was evaporated over one edge of the Ag 2

S layer to a thickness of

2.0 ym. A Pt layer at a thickness 0.5 ym was evaporated over the opposite

edge. Finally, an Ag layer was evaporated over the Agl layer to a thickness

of 0.5 ym.

Reflectance and transmi ttance measurements were performed on a Perkin-Elmer

Model 580B spectrophotometer over the range from 250 cm"* to 4000 cm~*. The

106
cell was mounted in a vacuum furnace and heated using an Omega Model CN2010

programmable temperature controller. All measurements were made with the cell

at 185°C. In order to charge the cell a D.C. potential, v app » was applied to

the electrodes (Pt electrode positive). Upon application of the charging

voltage, the cell current decayed steadily from a high initial value and

approached zero after approximately 100 seconds. At this point, the voltage

source was removed and the open circuit cell potential, V c

, was measured. For

all cases, it was found that V

c = V ap p. Spectral scans of reflectance and

transmittance were then performed for cell potentials of OmV, 50mV, 80mV,

llOmV, and 150mV.

The transmittance and reflectance data are shown in Figures 1 and 2 respectively. As the cell is charged, the electron concentration within the Ag

2

S layer is decreased. This reduces the degree of free carrier absorption and

results in higher transmittance at lower energies as shown in Figure 1. For

the same reason, the plasma edge in Figure 2 is shifted to lower energy.

In order to quantitatively characterize the measurements at different cell potentials, the reflectance spectra were analyzed by means of a fit to a dispersion formula derived from the classical Drude model of free carrier effects. The parameters of the fit are the asymptotic high frequency dielectric

constant (O, the electron mobility (y[cm2 /vsec]), and the plasma frequency

(o)p 2 = Ne 2 /m* e Q where N [cm~^] is the electron concentration and m* is the

effective mass, assumed equal to the bulk value m* = 0.24m

e

) [3]. Analyses of

the reflectivity spectra were performed by least squares adjustment of these

parameters. The best fit values of electron concentration and mobility appear

in Table 1 along with values for the bulk electron concentration. The corresponding refractive index and extinction coefficient computed from the best fit

parameters are shown in Figure 3 and 4 respectively.

The electron concentrations in Table 1 agree with the bulk values reported by

Dorner [3]. The electron mobility is fairly constant for all cell potentials

and is also less than its bulk value of 160 cm

2 /V-s [3], Figure 5 is a plot

of electron concentration as a function of cell potential. Charging the cell

to V

c = 150mV, reduces electron concentration by a factor of 5 and reduces the

level of free carrier absorption. Repeated chargings and discharging yield

reproducible results.

107
500 1000 1500 2000 2500 3000 3500 FREQUENCY ( cm" 1 )

Figure 1. Silver sulfide film

transmi ttance for five values

of galvanic cell potential.

_ 80m V

0 30 JlOmV

!50mV

ooo' 1 L

T" I85"C

-J I i I i I I I i_ 500 1000 1500 2000 2500 3000 3500 FREQUENCY (cm-l)

Figure 2, Silver sulfide film

reflectance for five values

of galvanic cell potential.

10

T= I85°C

l50mV // /

HOmV / / /

80mV / /

- 50mV /

OmV v^/

1 1 1 1 !_ 1.1,1,1, 1500 2000 2500 FREQUENCY (cm"')

T= I85°C

500 1000 1500 2000 2500 3000 3500 FREQUENCY (cm" 1 )

Figure 3. Silver sulfide film

refractive index for five values

of galvanic cell potential.

Figure 4. Siver sulfide film

extinction coefficient for five

values of galvanic cell

potent i a I .

108
TABLE 1

Cell Electron Electron Concentration (cm

Potential Mobility

(mV) (cm2/v-s) Film Bulk [3]

0 102 4.1 x 10 19 3.6 X 10»

50 99 2.7 x 10 19 2.3 x 10 19

80 100 2.1 x 10 19 1.8 X 10 1 *

110 99 1.5 x 10 19

150 71 0.85 x 10 19 0.59 X 10»

References

1. Carl Wagner, J. Chem. Phys. 21, 1819 (1953).

2. M.H. Hebb, J. Chem. Phys. 20, 185 (1952).

3. H.H. Dorner, H.P. Geserich, and H. Rickert, Phys. Stat. Sol. 37, K85

(1970).

4. G. Bornecuze, A. Lichanot and S. Gromb, J. Phys. Chem. of Sols. 34, 299

(1978).

5. G. Bonnecaze, A. Lichanot and S. Gromb, J. Phys. Chem. Sols. 39, 813

(1978).

109
SYNTHESIS AND CHARACTERIZATION OF

STOICHIOMETRIC CdPS3

J. Covino, P. Dragovich and C. Lowe-Ma

Chemistry Division, Research Department

Naval Weapons Center, China Lake, CA 93555

INTRODUCTION

In recent years, there has been an increasing interest in the layer

transition metal phosphorous trisulfide compounds. Their ability to intercalate such cationic species like alkali, metallocenium and ammonium ions, 1 along with their promising electrical, magnetic and optical properties, 2 make

them an interesting class of compounds to study. Our initial studies focused

on CdPS 3. This material is optically transparent from 4000 cm

-1 to 500 cm-1

(2.5-20 fjm) with a fundamental absorption edge close to 454 cm

-1 (22 pm)

.

Initial studies of CdPS3 suggested that the material could be useful as an infrared transmitting material provided that the material strength could be

increased

.

Transition metal phosphorus trisulfide compounds, which generally

form as thin platelet crystals, were first prepared and characterized by

Klinger et al.

~ 5 Their studies were primarily concerned with preparation

and crystal structure determination. Klinger et al. 5 performed the single

crystal structure determination of FePS3 and found it to have a monoclinic

unit cell o (space group o C2/m) with the lattice parameters a = 5.934 A,

b = 10.28 A, c = 6.722 A, and 0 = 107.16°. The FePS 3 monoclinic structure

is a distortion of the rhombohedral (trigonal space group R3) structure found

for FePSe 3. The structure is related to that of CdCl 2 , with iron ions and

phosphorous-phosphorous (P-P) pairs occupying the cadmium positions and

sulfur or selenium ions occupying the chloride positions. In this structure,

the iron ions and P-P pairs are approximately octahedrally coordinated in a distorted cubic close-packed lattice of anions (S or Se) . The P-P bond lies on the octahedral threefold axis. Complete crystal structure determinations

have been reported only for the layered compounds FePS3 and FePSe 3

. 4 It

should be noted that compounds having the MPX3 (X = S, Se) stoichiometry can also crystalize with other structure types. 6-11

In order to understand the structure of the CdPS 3 more clearly, the

present work was initiated. In this work, single crystals and bulk powder

of the systems CdPS

3 _x Se

x (for x = 0, 1, 2, and 3) and Cd 0. 99Mn0. oip 3 have

been synthesized. Detailed material characterization will be presented.

Special emphasis will be placed on the X-ray diffraction data of this class

of MPX3 compounds and on how the present data, although internally con- sistent, does not agree with literature data. Some conclusions dealing with

the crystal structure of CdPS3 will be made.

RESULTS AND DISCUSSION

The stoichiometry of the CdPS

3 _xSe

x compounds reported in this work is shown

110
TABLE I.

Theoretical stoichiometry Experimental results

Powders Cd

1.00

P

1.02

S2.98

1.00

P

1.02

S 3.00

Cd

1.00

P

.97

S 3.20

Crystals Cd

Literature 13

Cd

Cd

1.00

P

1.05

S

2.32

1.00

P

1.09

S

1.27

Se

Se

1.85

.84

In comparing the analytical data for CdPS 3 obtained in this study with

analytical results on CdPS 3 reported by Francis et al., 12 it can be seen that

the present samples are much nearer to the theoretical stoichiometry. The

samples reported by Francis are either cadmium deficient or phosphorous

deficient and sulfur rich, depending on how the formula is written.

Thermogravimetric analysis (TGA) of CdPS 3 powder was performed. The

TGA curve of the compound, in flowing nitrogen, showed virtually no weight

loss below 500°C. After 500°C, a fairly abrupt decomposition to CdS was observed. This decomposition is consistent with the decomposition of the

MPS3 as reported in the literature. 12

X-ray powder diffraction data were obtained for all samples. CdPSe 3

samples contained some CdSe (black material) which was identified in the

powder patterns. The diffraction lines not due to hexagonal CdSe, definitely

matched the reported powder pattern of CdPSe3 . 13 The Gandolfi film data for

a single flake of the material with the nominal stoichiometry CdPSe2S also

matched the data for CdPSe 3

13 suggesting that both selenium-rich materials

reported in this study were isostructural with CdPSe 3

.

However, despite different synthetic attempts and reannealing, we were unable to prepare any CdPS 3 which had a powder pattern matching the reported

data for CdPS 3

. 13 Our CdPS 3 samples were composed of very pale orange to

nearly colorless flake-like crystals. Table II has representative data of

some 20 powder patterns run on CdPS 3 samples. All of the X-ray diffraction

data in Table II are from Gandolfi films of single flakes. These single

flakes were not necessarily true "single crystals", but visually appeared to

be single-phase. Although most of the reported hkl assignments for CdPS3

13 can be matched to some of the X-ray lines reported in this study, our CdPS 3

samples consistently exhibit far more lines than can be indexed based on

the C2/m structure. Lifshitz and Francis 14 reported a structural phase

transition for Mn(II) -doped CdPS 3 somewhat below room temperature. On the

same film, Gandolfi data were recorded for a flake of Cd0. ggMno. oiPS 3 at

approximately 50°C first and then at approximately 0°C. No differences in

the two powder patterns were observed. This suggests that the observed

anomalies in the X-ray data for the CdPS 3 samples cannot be due to a structural phase transition taking place near room temperature. However, our X-ray data can be consistent with a lower symmetry structure of different

symmetry.

Ill
TABLE II.

CdPS

3

CdPS

3

CdPS

3

CdPS

3

CdPS

3

JC1044-42 JC1044-42 PD1063-17 PD 1063-30 PD1063-52

single flake reannealed reannealed reannealed sinele flake

single flake single flake s ingle flake

d I d I d I d I d I 6.54 80 6.40 60 6.58 80 6.63 80 6.58 60

5.25 20 5.30 20 5.27 20 5.26 20 br 5.22 15 br

4.73 20 4.71 25 4.71 20 4.73 20 br 4.72 20 br

4.16 20 4.17 15 4.16 25 4. 17 20 br 4. 16 20

3.66 20 3.64 15 3.64 20 3.63 20 3.67 15

3. 19 5 3.20 5 3.17 10 3.20 5

3.08 100 3.08 100 3.08 100 3.08 100 br 3.08 100 br

2.96 5 2.96 5 2.96 5 2.96 5 2.96 5

2.80 30 2.80 30 2.79 10 2.79 20 2.81 30

2.63 100 2.63 90 2.63 100 2.63 100 br 2.63 100 br

2.44 30 br 2.44 60 2.46 20 br 2.44 30 2.46 30 br

2.35 5 2.36 5

2.23 10 2.22 20 2.23 10 2.23 10 2.24 20

2.09 10 2.08 40 2.09 15 2.08 20 2.08 10

2.02 15 2.02 15 2.02 20 2.02 20

1.956 5

1.926 60 1.926 80 1.931 80 1 .926 60 1.927 60

1.874 5 weakline(s) 1.873 5

1.843 5

1.795 80 1.796 100 1.795 80 1.797 80 br 1.796 80 br

1.731 40 1.733 80 1.732 60 1 . 734 60 br 1.729 45 br

1.696 5 1.696 5 1.696 10 1.701 5 1.697 10

1.647 5 1.647 10 1.650 10 1.648 5 br 1.645 5 br

1.583 10

1.549 30 1.552 60 1.551 40 1.564 30 br 1 .547 20

1.483 40 1.485 70 . 1.483 40 1.484 40 1.482 25

weaklines (s) 1.449 10 br 1.445 5 1.449 5

1.393 10 br 1.393 10 1.392 10 1.395 5 1.393 5

1.360 15 1.350 10 1.363 15 1.358 5 br 1.358 20

1.344 5

1.316 10 br 1.316 20 1.312 30 1.316 20 1.314 15

1.275 5 1.273 15 1.275 20 1.271 20 1.275 10

weakline(s) 1.231 15 weakline(s) 1.234 5

1.208 20 1.210 60 1.211 30 1.213 60 1.210 40

1.191 5

1.172 20 1.173 30 1.174 20 1.174 40

1.142 40 1.142 40 1.143 30 1.143 30 1.142 60

o d are in A.

I are visually estimated intensities,

br = broad.

112
To check for differences in the local coordination of the Cd(Mn) in

the CdPS 3 structure, the room temperature electron paramagnetic resonance spectrum of Mn(II)-doped CdPS 3 was recorded at 9 GHz. The data obtained

in the present work was identical to that reported by Francis et al. 14 and

is consistent with Mn(II) being in a site of rhombic or lower symmetry.

In order to investigate the number of sites that the Cd occupied in

CdPS 3 , 113Cd NMR was performed. The solid state 113 Cd NMR spectrum of bulk

CdPS 3 powder showed only one cadmium(II) site. However, it is not conclusive

evidence that only one cadmium site is present in CdPS 3

. Because of the

noise to signal level, a second Cd could be present at a concentration of

about 10% or less and, depending on its environment, might not be detectable.

Alternatively, the Cd could be in only one kind of site, but the overall

symmetry of the structure could have changed giving rise to the observed

diffraction data.

There exists some intercalation data in the literature on both CdPS 3

and NiPS3 . These two compounds have been assigned to the C2/m monoclinic

space group, yet their intercalation chemistry is significantly different.

Foot et al. 15 reported that NiPS 3 reacted readily with n-alkylamines , not

at all with ammonia, and only partially with isopropylamine , while CdPS 3

appeared much less selective and reacted more quickly. This suggests a different intercalation process for the two compounds. The authors concluded

that the nickel compound intercalates the amines via an electron transfer

mechanism without any loss of Ni(II) from the structure, while the cadmium

compound showed no sign of a mechanism involving electron transfer. Furthermore, Cd(II) ions were found in the liquid amines after the intercalation

reaction in an amount equivalent to the intercalated amine. The authors

attribute this to the difference in crystal-field stabilization energy

between Cd 2+ (d 10

) and Ni 2+ (d 8

) . Cd 2+ (d 10

) does not possess crystal field

stabilization, whereas Ni 2+ (d 8

) does have a crystal field stabilization.

However, the intercalation data can be better explained if the nickel and

cadmium MPS 3 compounds have different crystal structures. The Cd(II) cations

might be in a more labile site as compared to the Ni(II) cations.

CONCLUSION

CdPS 3 has been synthesized with stoichiometry much closer to the

theoretical value previously reported. 14 The present X-ray data for the

CdPS 3 system, although reproducible from sample to sample, is not consistent

with the C2/m structure assigned to this compound by Brec et al. 13 However,

the presently reported data are consistent with a layer structure in which

cadmium might be in a different environment or in more than one environment.

If cadmium is in a second environment then it must be, as the 113 Cd NMR

shows, only one Cd(II) site. Furthermore, as seen by the EPR data of Mndoped CdPS 3 this cadmium site whether it be interstitial or defect cannot be

substituted by Mn(II). Such structural differences could also explain the

different intercalation chemistries of the cadmium and nickel MPS 3 compounds.

113
ACKNOWLEDGMENT

This work was supported in part by Contract No. N000148WR24182 from the

Office of Naval Research. The authors would like to thank Robin A. Nissan,

and Daniel C. Harris for their technical assistance and profitable

discussions

REFERENCES

1. R. J. Clement, J. Chem. Soc, Chem Commun. 647, (1980).

2. R. Brec, D. M. Schleich, G. Ouvrard, A. Louisy, and J. Rouxel, Inorg.

Chem. , 18, 1814, (1979)

3. H. Hahn, and W. Klinger, Naturwissenschaften, 52, 494 (1965).

4. W. Klinger, R. Ott, and H. Hahn, Z. Anorg. All. Chem., 396, 271 (1983).

5. W. Klinger, G. Eulenberger, and H. Hahn, Z. Anorg. All. Chem., 401,

97 (1973).

6. Y. Mathey, A. Michalowicz, P. Toffoli, and G. Vlaic, Inorg. Chem., 23 , (7), 897 (1984).

7. R. Diehl, C. D. Carpentier, Acta Crystallogr. Sect. B: Struct. Crystallogr. Cryst. Chem., B34, 1097 (1978).

8. C. Lowe-Ma, Final Report for NASA WO-8739 Contract NAS 7-918, December 1983.

9. R. Nitsche, Mat. Res. Bull. 5, 419 (1970).

10. C. D. Carpentier and R. Nitsche, Mat. Res. Bull. 9, 1097 (1974).

11. G. Dittmar and H. Schafer, J. Naturforsh. Teil B29 , B12 (1974).

12. J. Boerio-Goates , E. Lifshitz, and A. H. Francis, Inorg. Chem. 20, 3019

(1981).

13. R. Brec, G. Ouvrard, A. Louisy, and J. Rouxel, Ann. Chim. Fr. , 5, 499

(1980).

14. E. Lifshitz, and A. H. Francis, J. Phys. Chem. 86, 4714 (1982).

15. P. J. S. Foot and G. Shaker, Wat. Res. Bull., 18, 173 (1983).

114
CHARACTERIZATION OF THIN SEMICONDUCTING FILMS

ON TRANSPARENT SUBSTRATES

Bob Edgerton and David Shortt

Energy Conversion Devices, Inc.

1675 West Maple Road

Troy, Michigan 48084

Uniform homogeneous layers of material deposited on a substrate can be

described optically by a thickness and a complex index of refraction,

n(x) - i k ( x ) . Alternately one can describe the absorption coefficient,

a(E), as a function of the photon energy. If the complex index of re- fraction and the thickness are known for both the film and the substrate,

then electromagnetic theory provides a basis for calculating the reflectance and transmi ttance spectra of the film (1). The challenge is to

work this problem backwards. Given the two spectra, can one find a u- nique description of the dispersion in the optical properties as well as

a thickness which satisfy the data?

The first step in our process is to choose a parameterized model to describe the optical properties. For some materials it would be appropriate to describe n and k with a small set of damped harmonic oscillators

and/or free electrons (2). However, we have had success analyzing the

data taken on amorphous silicon films by describing the index of refraction and the absorption coefficient independently. For the index of re- fraction, n(x), a four-term Cauchy power series was found to have a more appropriate shape than a single damped harmonic oscillator. For the absorption coefficient, a(E), a traditional approach for semiconductors is

to match an exponential tail at low energies to some variant of a power

law at higher energies (3). The resulting three-parameter function is

described by the strength of the power law (S), the threshold of the pow- er law which is the bandgap (E r ), and the inverse strength of the tail

(T).

G

0 A f> n(x) = nj + n

2 /x + n 3

/x + n 4

/x

a(E) = S

2

(E-E

Q

) 2 /E for E >= E^

a(E) = exp (TE - TE

M

) S

2 (E^ - Eg)

2 /E^ for E < E^

where E M

=

r + /(i + EqT)

2

2 T

An error function is defined to be the integrated rms deviation of the

calculated spectra from the measured spectra (2). A simplex search algorithm procedes to find a combination of the parameters that minimizes

the error function (4). If there is uncertainty about the order of the

interference, it is appropriate either to make a brief search over the

thickness, holding the other parameters fixed, or to make several trial

115
calculations for different initial parameter choices and to compare them

to the measured data. During a search, if a sufficiently low value of

the error obtains, this first, or parameter, search yields smooth functional descriptions of the index of refraction, the absorption coefficient, and the film's thickness.

The second part of the process determines the values of the optical properties without recourse to a particular choice of parameterized model

for describing the shape of the dispersion. This approach uses the

thickness determined in the parameter search as a known constant. At

each wavelength of interest we search for values of n and k which minimize the deviation between the measured and calculated reflectance and

transmi ttance at that wavelength. For expedience, one chooses an acceptable error and a maximum number of allowed iterations before moving on to

the next wavelength value. The second procedure yields a discrete set of

optical properties rather than the continuous functions of the parameter

search. Since each wavelength is treated separately, this procedure is

model -independent; it gives optical properties consistent with the choice

of thickness, the measured spectra, and the assumption of a uniform homogeneous layer on a known substrate. Plotting the resulting values of

n( a) and k( x) or a(E) in a variety of ways reveals the appropriateness of

the models used in the parameter search. A study of trends in the data

may suggest a different model to be implemented in a new parameter

search.

The film used to illustrate this technique is a glow discharge deposition

of amorphous silicon hydrogen alloy on Corning 7059 glass. The measured

spectra appear in Fig. 1. The quality of the fit resulting from the

search is shown in Fig. 2 by graphing the difference between the calculation and the measurement. The differences are less than 0.5%. The index of refraction and extinction coefficient resulting from the search

are graphed in Fig. 3. Fig. 4 shows the resul ts of the second search.

The arrows indicate the spectral region in which agreement to three significant figures could not be obtained in several hundred iterations.

Several regions of the spectrum show anomalous values that do satisfy

the search criterium. Often the spectral region with no solution lies

between two anomalous values, one high and one low. Different samples

with different thicknesses produce anomalies like these in different re- gions of the spectrum. The index of refraction is most likely a smooth

function, and the anomalies are probably a result of differences between

the actual sample and the model describing it. Further interpretation

of these anomalies will be the subject of future work.

Using the results for the absorption coefficient from the second search, one can plot various algebraic forms of a vs. E and thus evaluate the

appropriateness of the parameterized models. For the absorption model

described above, we should observe a linear relation between the square

root of cxE and E in the power law region. However, for the particular

sample used, Fig. 5 shows slight curvature in this region. A plot of the

square root of a vs. E (Fig. 6) shows linearity over a wider energy re- gion. When the parameter search is repeated using this more appropriate

model, the resulting error is lower. The improved results appear in

Fig. 7 with the new n and k in Fig. 8.

116
Acknowledgments

We appreciate the interest and help of our colleagues, especially Vin

Cannella, Joe Burdick, and finally Ralph Mohr, who expertly prepared a uniform sample.

This work was partially supported by the Standard Oil Company (Ohio) .

References

Ref. 1. 0. S. Heavens, Optical Properties of Thin Solid Films, Butterworth Scientific Publications, London, 1955.

Ref. 2. J. A. Dobrowolski, Applied Optics 22, 3191 (1983).

Ref. 3. G. D. Cody, Hydrogenated Amorphous Silicon, J. Pankove, editor,

Chapter 2, Vol. 21B, Semiconductors and Semimetals, Willardson and Beer,

editors, Academic Press (1984).

Ref. 4. J. A. Nelder, and R. Mead, Computer J. 7, 308-313 (1965).

Figure Captions

Fig. 1. Reflectance and Transmi ttance spectra (0 - 100%) of an amorphous

silicon hydrogen film deposited by glow discharge on a Corning 7059 glass

substrate.

Fig. 2. Difference between the calculated spectra and the measured spectra after the simplex parameter search.

Fig. 3. Values of n and k calculated from the values of the parameters

determined in the search.

Fig. 4. Values of n and k consistent with the thickness 43.88 nm. and

the measured spectra.

Fig. 5. Plot of the square root of aE vs. E.

Fig. 6. Plot of the square root of a vs. E.

Fig. 7. Differences between the calculated and the measured values

after a second simplex search using the more appropriate model.

Fig. 8. Values of n and k described by the parameters determined in the

second parameter search using the new model.

117
118
LASER PROPAGATION THROUGH FIBERS WITH BIQUADRATIC REFRACTIVE INDEX

(CLOSED FORM SOLUTION)

Farag Z. El-Halafawy

Dept. of Electronic Engineering

Menouf, 23951 Egypt

and

Ahmed Y. Rezk and El-Sayed A. Al-Badawy

Dept. of Engineering

Alexandria University

Alexandria, Egypt

In this paper, closed form equations for both trajectories and intensity

profiles of a light beam traveling in a continuous media of biquadratic

graded refractive index are derived avoiding the approximations made by [1]

and [2] .

Graded index fibers employed in optical communication or as sensors are manufactured with biquadratic (or nearly) refractive index of the form

2 2 2 4 n = n^ (l-2a p + 2b p ) (1)

where both the parameters a and b are positive quantities, p = r/R, and R

is the fiber radius.

Without loss of generality, meridional rays profiles are the solution of

[3]

d

2

p _ 1 dn 2

a 2 _ 2 2 d p Ui

dn 2n N

o o

where N is the direction cosine of the incident ray

n = Z/R

and nQ denotes the refractive index at the incident point of r = r Q

.

The use of equation (1) in equation (2) yields

2 n

2

= 4s c- 2ap + 4bp3

)

* (3)

dn n o

N

o

The normalized radial position p n and the normalized propagation distance

n n are defined as

119
p n

= p/2b/a = mp

where m2 = 2b/a (<2) and n n

= n n /2n0

N0a; thus equation (3) reduces

to the form

"

2 p n 3

dr| n

Multiplying equation (4) by p^ and integrating, we obtain

1 2 2 4

1 2 2 4 p + p - l/2p = p + p - 1/2 p = function of r , say A (5) *n ^n H n

K n ^n ^n o

J o o o

where the lower suffix (n D

) denotes the quantities at Z = 0 (launch

conditions)

.

Equation (5) is re-arranged as follows:

'2 4 2 p = 1/2 p - p + A ... ^n ^n K n (6)

where A2 a 2 = 2A and A 2 + A2 = 2, with A > A^, The use of p n= A

2 u and K = h^/h^ in equation (6) yields

u'

2 = 1/2 A (1-u

2

) (1-K

2 u2

) . (7)

The separation of variables and the integration of equation (7) yields

du

or simply

and hence

and finally

Jn Udn

n

=

/

u -

Uo /(1-u

2

) (1-K

2 u

2

)

-1 -1

oon = sn u - sn u n o

u = sn (oin + sn "'"u ) n o

P n

= a

2 sn(wn

n + <|> 0

) (8)

where u amd A //2 and sn denotes the Jacobian periodic elliptic function [4]

of period 4K, *and ^ Qis the solution of sn

qq

= pnQ/A^ . Both A^ and A^

120
and consequently the period 4K are functions of both the launch conditions

and the fiber parameters where

A = 1 + /1-2A = f . (r ,a,b) , 1 1 o

A„ = 1-/I=2A = f (r ,a,b) . 2 2 O

With respect to the intensity profiles and in the same spirit as [2] we have

P 3p

n n

I (p

n ,n) = I (p f 0) —— (—2) (9)

p n

1 9p

n n n

where I (p ,0) is the initial intensity at the entrance of the fiber (i.e.,

at Z = 0) . n°

As the period 4K is a function of the launch radial position for a certain

fiber, thus there is a caustic volume of relatively high harm rather than a single focus. Equation (8) yields the maximum radial position p max as a function of o„ under the form Mn

o

p = A_ . (10) ^max 2

Thus, self-trapping can be achieved by optical fiber if

p = A» < p (at r = a; i.e., = 1) ^max 2 ^n

i.e., if A

2

< m or A < m - m 2/2 and, finally

1 2 2 4 2

pK * + $ - 1/2 p < m - m /2 . (11) n

K n n o o o

This equation couples the launch conditions and the fiber parameter m in

order to achieve self-trapping conditions.

Equation (9) indicates that I(p n / r] n) oscillates along the propagation

path (the fiber axis) and makes a caustic volume of maximum power

concentration which yields concentrated-strain regions acting as damage

centers.

In conclusion, biquadratic-index media yields self-trapping if its parameters

and the launch conditions are adjusted.

References:

[1] P. K. Tien, J. P. Gordan, and J. R. Whinnery, Proc. IEEE, Vol. 43, No.

2, pp. 129-136, Feb. 1965.

[2] P. M. Mejias, Appl. Opt., Vol. 20, No. 24, pp. 4287-4295, 15 Dec. 1981.

[3] T. Okoshi, Optical fiber, Ch. 3, Academic Press, 1982.

[4] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Ch.

16, Dover Publ., NY, 1965.

121
DENSIFICATION OF ZIRCONIA FILMS BY COEVAPORATION WITH SILICA

Albert Feldman and Edward N. Farabaugh

Inorganic Materials Division

National Bureau of Standards

Gaithersburg, Maryland 20899

Optical films of zirconia have been receiving considerable attention because

of their potential use as the high-index layer in multilayer optical coatings

for the ultraviolet portion of the spectrum. Several problems are associated

with electron-beam deposited zirconia films and these include index instability [1] and index inhomogeneity [2]. The index instability is caused by the

adsorption and the desorption of water in the porous columnar structure of

the zirconia films. Index inhomogeneity is due to the inhomogeneous structure in the films. Recent work has shown that the first several tens of

nanometers of a film possess a cubic structure whereas the outmost layers

possess a monoclinic structure [3].

One approach for producing bulk-like zirconia films that is receiving

considerable attention at present is ion-assisted electron-beam deposition.

This is because the method has successfully produced zirconia films having

bulk-like densities and refractive indices that show insignificant sensitivity to water adsorption [1], In this paper we demonstrate a similar effect

when mixed zirconia: silica films are produced by coevaporation from independent electron-beam sources, and, in particular, we show that the admixture of

a small amount of silica with the zirconia produces a film possessing a higher refractive index than a pure zirconia film. This work is based on earlier studies that had shown coevaporated zirconia: silica films to possess

an amorphous structure as determined by x-ray diffraction as opposed to pure

zirconia films which were composed of mixed polycrystalline phases of the

monoclinic and tetragonal structures [4]. In addition, the mixed films had

not shown the columnar structure found in pure zirconia films.

Films in the system (Zr0

2

) x

: (Si02 ) (i- x ) were produced by coevaporation from

two independent electron beam sources onto fused silica substrates at a substrate temperature of 300 °C. Each source was monitored by a separate

quartz-crystal monitor. Six films were produced varying in composition from

pure Zr02 to pure Si02

.

Table 1 lists some of the properties of the films produced. The volume

fractions shown were computed from the thicknesses measured with the quartzcrystal monitors [5]. The results are based on the assumption that the

volume occupied by each molecule is a fixed quantity. The quartz-crystal

monitors were calibrated on the basis of stylus thickness measurements made

on the pure films.

The thicknesses and refractive indices of the films were determined by two

methods. In the first method, thicknesses were measured by means of a diamond-stylus surface profiling instrument. Using the measured thickness

values, we computed the refractive indices from determinations of optic path.

The optic path was computed from thin film channel spectra (CS) measurements

that were analyzed on the basis of a newly developed technique [6].

122
In the second method, known as the method of m-line spectroscopy [7], the

thicknesses and refractive indices of the films were computed by a least

squares fit to measurements of the angles required to couple radiation from

an argon-ion laser ( A=0 • 51^5 ym) , by means of a prism coupler, into the thin

film guided modes. The calculation assumed that the films were homogeneous,

a condition that was not strictly met, as discussed below. Thus, the values

of thickness and refractive index that were computed are to be considered

effective values. These were found to be adequate for the purposes of this

work.

Due to the relatively low refractive index of the prism used (n=1.973), we were not always able to observe the lowest order guided modes; this resulted

in ambiguity in the mode assignment. Observed modes were therefore assigned

to progressively higher mode orders until the computed optic path values

agreed most closely with the optic path values obtained from the channel

spectra measurements. Only computations based on the transverse electric

(TE) modes were used in the comparison, because, in the case of birefringent

films with the optic axis normal to the film surface, TE modes and channel

spectra depend on the same refractive index component. Analysis of the TM

modes indicates that these films are indeed birefringent.

An examination of the shape of the channel spectra and the fit of the m-line

spectra indicate that the films are inhomogeneous as well. This could

account for some of the disagreement between the values in Table 1 obtained

by the two methods. In general, both methods are in reasonably good

agreement.

An examination of the refractive index values in Table 1 indicates that as we

add Si02 to Zr02 the refractive index first increases and then it subsequently decreases. The initial increase is unexpected because Si02 has a lower intrinsic refractive index than Zr02

, and, hence, is expected to lower

the refractive index of the film. The result is explained as follows: a film of electron beam deposited Zr02 has a high porosity, thus, its effective

refractive index is lower than the refractive index of bulk Zr02

. The

admixture of a small amount of Si02 first causes a change in the polycrystalline structure of the film; additional amounts cause the films to

approach a glassy state. These structural changes are accompanied by a decrease in porosity of the films resulting in an increase in refractive

index that more than compensates for the decrease expected from the addition

of Si02

. However, after maximum densif ication occurs, the addition of more Si02 does cause a decrease in the refractive index.

Evidence for densif ication of the films can be seen in the thickness values.

If we sum the thicknesses of the individual components of a particular mixed

film as measured with the quartz crystal monitors and compare this sum with

the thickness as determined by the stylus measurement we find that the stylus

value is always less.

Further evidence for the lower porosity of the mixed films was obtained from

additional channel spectra measurements which are sensitive to the uptake of

water in the films. Channel spectra of the films were measured several

months after deposition and compared to the optical fringe count that was monitored during the film deposition. The spectra of mixed films showed good

123
agreement between the two measurements indicating good index stability

whereas the pure zirconia film showed significant discrepancies. The films were then baked out in vacuum and new channel spectra were taken. Here

again, the pure zirconia film showed the greatest instability. Additional

channel spectra were taken on a fresh film of pure Zr02 just after deposition, after several days of exposure to moist atmosphere, and after vacuum

bakeout. We found a variation in refractive index of as much as 3.5 percent.

Depending on the model used for computing refractive index in a mixed system,

and assuming that index changes due to changes in stochiometry during bakeout

are negligible, the porosity to account for such a variation would fall in

the range 11-33 percent.

This work was supported in part by the Air Force Office of Scientific

Research.

We thank T. Vorburger and C. Giauque of the Micro and Optical Technology

Group for the diamond stylus measurements of specimen thicknesses.

REFERENCES

[1] P. J. Martin, H. A. Macleod, R. P. Netterfield, C. G. Pacey and W. G.

Sainty, Appl. Opt. 22, 178 (1983).

[2] E. E. Khawa and S. G. Tomlin, Thin Solid Films, 30, 361 (1975).

[3] R. E. Klinger and C. K. Carniglia, J. Opt. Soc. Am. A 1 , 1289 ( 1 98-4 )

[4] E. N. Farabaugh and D. M. Sanders, J. Vac. Sci. Technol. A 1, 356

(1983).

[5] R. Jacobsson, in Physics of Thin Films, Vol. 8, G. Hass,

M. H. Francombe, and R. W. Hoffman, editors (Academic Press, New

York, 1975).

[6] A. Feldman, Appl. Opt. 23, 1193 (1984).

[7] P. K. Tien, R. Ulrich, and R. J. Martin, Appl. Phys. Lett. 14, 291,

(1969).

124
TABLE 1. Parameters of Mixed Zr02 :Si02 Thin Films

Volume % Sum Stylus & CS* m-lines

Specimen Monitored

no. Zr02 Si02 t(um) t(um) n t(um) n

428 100 0 1.13 1.13 1 .92 1.13 1 .90

430 86.5 13.5 1 .04 0.95 2.04 0.94 2.05

431 70 30 0.96 0.65 1 .98 0.66 1 .95

438 51 49 0.85 0.69 1 .79 0.69 1 .78

439 32 68 0.80 0.72 1 .65 0.66 1.64

429 0 100 0.70 0.70

channel spectra

125
TEMPERATURE DEPENDENCE OF THE VUV OPTICAL SPECTRA

AND BAND STRUCTURE OF AL 0

R. H. French and R. L. Coble

Mass. Inst, of Tech.

Cambridge, MA 02139

A high temperature vacuum ultraviolet (VUV) spectrophotometer has

been built that is capable of measuring the reflectance and transmittance

of samples from 6 eV to 15 eV (210 nm to 85 nm) in the VUV on samples

heated without contamination from room temperature up to 1100 °C. The

precision (reproducibility) of the measurements is 0.01 eV, the resolution

of the monochromator is 0.1 eV while the spectrophotometer can resolve 0.3

eV wide spectral features of the sample. The temperature dependence of

the electronic structure of single crystal Al^O^ has been studied with

this facility.

Reflectivity Measurements at Room Temperature

At room temperature, the reflectivity shows three main features

(see figure 1): a 9 eV exciton peak, superimposed on a 9 eV absorption

edge, and, at higher energy, a 13 eV peak. The 13 eV peak shows features

that depend on the crystallographic orientation of the sample. A doublet

peak appears for light incident parallel to the c axis, while a peak and a shoulder are observed for light perpendicular to the c axis. The

absorption edge is due to transitions to the Al 3s sub-band of the

conduction band, while the main peak at 13 eV corresponds to transitions

to the Al 3p sub-band of the conduction band. The valence band has a lower lying Al-0 sub-band, with the top of the valence band being of 0 2p

character. Transmission measurements show the absorption edge to lie at

8.8 eV at room temperature. This corresponds to a direct (8.8 eV) optical

band gap at room temperature. This measurement provides no information

about the nature (direct or indirect) of the minimum band^gap of the

material. The^e results are in agreement with band structure and atomic

cluster models of the T = 0 K electronic structure of Al^O^.

Temperature Dependent Reflectivity Measurements

With increasing temperature (see figure 2) the features in the

reflectivity broaden and shift to lower energies. These changes are due

to spreading of the electronic energy level bands and shifts of the band

centers. This may be explained either from the electron-phonon

interaction, or as arising from the superimposed effects of thermal

expansion and atomic vibrations on the instantaneous bond lengths in the

material. It was found that the different sub-bands have different

temperature dependencies. Over the temperature range studied, (25 °C to

1100 °C), the shifts were found to be linear with temperature, second

order terms were negligible. The experimentally determined values of the

linear temperature coefficient B, expressed in eV/K are:

126
ft < A

1

3 s ab s

.

Aeage n ft 1

;

—- 1 1

J. . J. X 1 nJ.U 3 .1/ /ir e v / h. 4- / — 1 -v x x 1 ft ±yj

4

p (9 eV Exc iton Peak) = 1.0 x 10" 3 eV/K +/- 3 x 10~ 5

P (13 eV A13p Peak) 7 x 10" 4 eV/K +/" 4 x 10" 5

High Temperature Optical Properties and Electronic Structure

There have been many studies of the shift of the absorption edge

with temperature for optical materials such as sapphire due to its use as

a window material. Most of these measurements have been over limited

temperature ranges and for energies below the fundamental absorptioij

edge. The values of^jU for the j^>sorption edge reported in the literature

range from 1.5 x 10 to 2 x 10 eV/K. This is the first work to measure

the optical spectra over such a wide temperature range, to such high

temperatures and covering the energy range necessary to observe the basic

optical features of the material. In addition, by measuring the shift of

various features, both peaks and edges, one gains greater confidence in

the reported results.

Th| various theories of the temperature dependence of electronic

structure can not at present theoretically predict the value of the

temperature coefficient for Al^O,, but they all predict a change in the

temperature dependence at the Debye temperature, and at the onset of

anharmonic vibrations associated with melting. We have not been able to

observe a change in the temperature coefficient even though the Debye

temperature lies between 700 and 1000 °C.

The energies reported in this work correspond to optical energies

that create carriers without lattice relaxation. It is this lattice

stabilization energy which determines the difference between the optical

and thermal band gap values. The room temperature band gap extrapolated

to T = 0 K, using the measured temperature coefficients, gives 9.1 eV for

the T = 0 K apparent optical band gap of Al^O^. The optical band gap

energy at 1500 °C is 7.15 eV, as determined by extrapolation from these

measurements

.

Acknowledgements

This work was supported by the U. S. Department of Energy through contract

number DE-AC02-76-ER02390

References

1. R. H. French, H. P. Jenssen, R. L. Coble, Proceedings of the 7th

International Conference on Vacuum Ultraviolet Radiation Physics', August

8-12 1983, Annals of the Israeli Physical Society , 6, p 51.

2. S. Ciraci, I. P. Batra, Phvs Rev B . 28, 2, July 15 1983, p 982.

3. J. A. Tossell, J Phvs Chem Sol , 36, (1975), p. 1273.

4. For a review of the literature see R. H. French, 'Electronic

Structure of Al 0'. VUV Reflectivity Measurements from Room Temperature to

1100°C, Ph.D. Thesis, M. I. T. Cambridge Mass, 1985.

5. M. L. Cohen, D. J. Chadi, Handbook on Semiconductors Vol. 2.

Optical Properties of Solids . North Holland, New York, 1980, p 155.

12 7
.30

.25

Refl.

,20 -

I I I I i i

'

i I I I I I i I i I I i i i i i i I i I I i i i I I I i I I i i I I I I I I l l I I I I i i i i i i i i i i i i i i i i i i i i i i i i

. is * 1 I i n » I i » i

J I I I I I I I I I I I I i t I I I i i I I I I I I I I I I I I I I I I I I I 8R888S85S888R8S8 "j'vrrimsNjfvl-^-IddaicriaiaJr-.'

Energy

FIGUBE la Reflectivity of Al

2°3 : c in P laae » E perpendicular to

the c axis, T equals 21 °C.

30

.25

Refl.

.20

.15 •

1 1 1 1 1 1 1 1 1 1 i 1 1 i 1 1 i 1 1 1 1 1 1

1

1 1 1 i i i 1 1 1 1

1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i 1 1 1 1 1 i 1 1

1

1 1 1 1 i 1 1 1 1 1 1 1

1

A A

1 1 1 1 1 1 1 1 it j , 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 i , 1 1 1 1 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1

in8&?8w?888S8tB8S8fnoS8

M <t? oj oj ~^ c5 d o; a; cd od r-' t~-' ~* w* w+ i—• —

Energy

FIGURE Id Reflectivity of Al^: c in plane, E parallel to the c axis, T equals 21 °C.

128
FIGURE 2 Temperature dependent reflectivities of Al JDl : T (from

bottom to top of figure) equals 21, 300, 500, 100, 900, and noO °C. Each

division on R axis equals 0.01.

129
RAMAN SPECTRA OF Li YFU CRYSTAL

F. Y. Gan and H. Y. Chen

Shanghai Institute of Optics and Fine Mechanics

Academia Sinica, Shanghai, People's Republic of China

Introduction

Rare earth ion doped LiYFlf crystals are well-known laser active materials;

they produce the laser emissions in the range of 0.8-2. 1p wavelength [1].

LiYF(t host structure, a scheelite model, is a body-centre tetragonal with a = 5.175A and c = 10.74A [2]. The polarized fluorescence and absorption,

excitation spectra, life-time, etc. of the crystal doped with Nd^ + have been

studied in detail [3] and the crystal-field parameters have also been

reported [4], but only a few works about its vibrational properties have been

presented so far. The optical phonon spectra are rather important for

development of tunable solid state lasers; for this reason we carried out the

study of Raman spectra of this material, analysed its optical mode vibrations

and finally compared with that of the sample doped with Nd 3+ .

Experiment

The sample we studied is a 10x1 Ox 5mm polished lithium yttrium fluoride

crystal prepared by gradient cooling method. The crystal axes were determined with X-ray diffraction methods. Using a 50mW He-Ne laser at

6328A, we obtained the Raman spectra through a GDM 1000 double grating

monochromator with the resolution of ±5cm~.

The incident beam is a linear polarized laser. When the crystal orientation

was variated for a certain incident beam, the polarized Raman scattering

light with the polarization parallel or vertical to scattering plane was observed. The DPT signs are used to mark the polarization characteristics;

x, y, z indicate the crystal axes a, b, c respectively.

Results and Discussion

Figures 1-3 represent the polarized Raman spectra of the LiYFj^ crystal in

y(zz)x, y(xy)z and z(xz)y direction, and the crystal axes x, y, z correspond

to the a, b, c directions of the scheelite structure unit, respectively.

Four main bands are observed in the spectra. The predominant peaks at

260cm-1 in y(zz)x and 325cm"1 in y(xy)z direction are polarized. Other bands

are at about 375cm" 1 and 440cm" 1 and their polarizations are not very

obvious.

As we know, in ionic crystals cations and anions are systematically arranged

in close proximity to each other, and interactions between them will have a significant effect on the vibrational modes. The site-group and factor-group

analysis are two available methods to study the vibrations of the crystalline

lattice. LiYFl+ belongs to c{j space-group and the site-group of Y3+ is S^

.

In this structure geometry, we consider that the interaction between fluorine

130
ions is small and the vibrations are mainly caused by the interaction of

the Y3 + ion with surrounding fluorine

ions. The site group method can be

used. According to the results of

group theory, only A, Bz, Ex, Ey modes

are Raman active. When the Oz axis is

parallel to the symmetric axis S^, the

Raman matrices can be expressed as follows:

(a 0 0\ /c d 0\

0 a 0

) ( d -c 0) 0 0 b/ , \0 0 0 / , A Bz

) . Gii)

Ey

From electro-magnetic radiation theory

and quantum mechanical treatment, it can be seen that the intensity of

scattered light is proportional to the

modulus of the component product of

the polar izability tensor and the

polarization unit vector of incident

and scattered light [5]. The

polar izability tensor corresponds to

the Raman matrix.

Having analysed the theoretical Raman

intensity, we know that in the y(zz)x

direction only the vibrational

intensity of the A mode is non-zero

and in y(xy)z the Bz mode is nonzero, and the Ex, Ey modes will occur

in the z(xz)y direction. Thus when

these results were compared with the

experimental spectra for each optical

mode, it can be considered that the

predominant peak at 260cm" 1 in y(zz)x

belongs to A mode and 325cm" 1 i n y(xz)^z direction belongs to BZ mode,

corresponding to the theoretical nonzero intensity of A and Bz mode,

respectively. The bands at 375cm~ 1 and 440cm" 1 appearing in the z(xz)y

spectrum reflect the vibrations of Ex

and Ey modes.

+J rlW

C0

P

c

>1

4-) H

HiC

0) +Ja

+j •HW

c

0) p

c

Fig.l 1 y (zz) x

\ . . 200 300 400 500 600

Fig. 2 1 y(xy)z

200 300 400 500 600

Fig. 3 Z (xz)y

200 300 400

1 500

Av (cm ) 600

Fig.l shows the polarized

Raman spectra in y(zz)x

direction.

Fig. 2 shows the polarized

Raman spectra in y(xy)z

direction.

Fig. 3 shows the polarized

Raman spectra in z(xz)y

direction.

131
Comparing the spectra of a LiYF^ crystal doped with Nd J+ ions with that of

the pure host crystal, we have not found any difference; this fact means that

with low doping concentration of Nd3+ ions there is no significant change of

the vibrational states.

Conclusion

The site-group method can be used to study LiYF^ crystals. The vibrational

modes A, Bz, Ex, Ey are determined at 260cm~* , 325cm~*, 375cm~^ and 440cm~^

,

respectively. The vibrational spectra of a crystal doped with Nd 3+ are just

the same as that of the pure one.

Reference

[1] A. A. Kaminskii, "Laser Crystals", p. 170.

[2] G. Keller, J. Inog. Nucl. Chem., 27/ 900 (1965).

[3] A. L. Harmer, A. Linz and D. R. Gabbe, J. Phys. Chem. Solids, 30 , 1483

(1969).

[4] D. Sengupta and J. D. Artman, J. Chem. Phys., 53, 838 (1970).

[5] "Crystal Spectra", ed. by Nankai University.

132
EPR STUDIES OF INFRARED-TRANSMITTING SULFIDE CERAMICS

Daniel C. Harris, Marian E. Hills, Josephine Covino,

Charlotte K. Lowe-Ma and Robert W. Schwartz

Chemistry Division, Research Department

Naval Weapons Center

China Lake, California 93555

Calcium lanthanum sulfide (nominally CaLa 2 S 4 ) and zinc aluminum sulfide

(ZnAl 2 S 4 ) are potentially useful as infrared-transmitting ceramics. The former

is prepared in our laboratory by heating coprecipitated metal carbonates under

flowing H2 S at 1000°C for 1 day and the latter is made by heating the pure elements in a sealed, evacuated quartz ampoule at 800-900°C for 2-3 weeks. In an attempt to, correlate optical properties with the presence of impurities and

defects, we have been studying the electron paramagnetic resonance (EPR)

spectra of powdered samples.

CaLa 2 S 4 and CaS

The EPR spectrum of CaLa 2 S4 1 is dominated by a distinctive six-line signal

that is very similar to the published spectrum2 of 55Mn2+ (I = 5/2, 100%

natural abundance) in CaS. The metal ion environment in CaS is octahedral,

while both metal ion environments in CaLa 2 S 4 have lower symmetry (S 4 ). If Mn2+

is present as a substitutional impurity in CaLa 2 S 4 , the Mn2+ EPR spectrum

should be different from that in CaS. Although our calcium lanthanum sulfide

was made intentionally rich in lanthanum (La/Ca 5: 2.7), it was possible that

CaS was present as an impurity phase. The spectrum of CaS (Fig. 1) prepared

in the same manner as CaLa 2 S 4 had a splitting pattern identical to the pattern observed for Mn2+ in CaLa 2 S 4 , verifying the presence of a CaS phase in the

CaLa 2 S 4 . The spectrum of CaS in Fig. 1 also exhibits signals attributable to

51V

2+ (I = 7/2, 100% natural abundance) and Cr3

t The same V

2+ signals were observed in one sample of CaLa 2 S 4 , but no Cr3+ was found in any samples of

CaLa 2 S 4.

When CaS was irradiated with 366 nm light at 77 K, peak a grew and six new signals appeared at fields ranging from 347 to 5376 G. 3 The new signals

could be explained by photochemical oxidation of iron (Fe 2+ + acceptor -» Fe 3+ + acceptor}, since (1) the behavior was enhanced by Fe2+ doping and (2) nuclear

hyperfine satellites due to 57Fe were observed near the strongest photogenerated signals. The broad peak a (16 G peak-to-trough) at g = 2.017 in Fig. 1 is probably due to the electron acceptor site with its trapped electron.

Powered samples of CaLa 2 S 4 also exhibit a broad band similar to peak a, but at g = 2.022 with a peak-to-trough width of 46 G. The intensity of the

peak increases markedly when the material is irradiated with 366 nm light at

77 K, so we assign the signal to an electron acceptor site in CaLa 2 S 4.

While studying the EPR spectra of CaS samples, another interesting feature

was noted. There is a very weak peak labeled b at g = 2.003 in Fig. 1. In a different preparation of CaS, a peak at the same position was the strongest

133
3000 3100 3200 3300 3400

GAUSS

3500 3600

Fig. 1. EPR spectrum of CaS at 77 K.

The strongest line of Mn2+ near 3266 G

is off scale. Microwave power

- 0.28 mW and modulation amplitude

= 0.32 G. The upper trace is enlarged

by a factor of 10. The broad peak a was recorded with power = 8.8 mW and

modulation amplitude = 2.5 G. The very

weak peak b was the most intense peak

in another sample of CaS whose spectrum

is shown in Fig. 2.

signal in the spectrum. A signal in CaS at this same g value h^s been noted

before and assigned to an electron in a sulfur vacancy (an F center). 4 ' 5 Indicated by asterisks in Fig. 2 are four of the eigljt lines expected for

splitting by 43Ca(I = 7/2). If signal b arises from an F center, the unpaired

electron would interact with six equivalent Ca 2+ ions. Since the natural

abundance of 43Ca is only 0.13%, the intensity of each of the eight satellites

should be 6 x 0.0013/8 = 0.0010 of the total signal. The relative height of

the outermost satellites compared to the central line in Fig. 2 is 0.0004. The

I i I i 1 1 1 3220 3230 3240 3250

GAUSS

Fig. 2. EPR spectrum of defect in CaS

at 77 K. Microwave power = 0.0044 mW

and modulation amplitude = 0.8 G.

Peaks marked by asterisks are part of

the eight-line hyperfine pattern of

43Ca. The central line, whose gain is

reduced by a factor of 200, is at position b in Fig. 1. The 53Cr satellite

is the one at lowest field in Fig. 1.

134
poor agreement with the expected relative height might reflect a difference in

linewidth between the central line and the satellites. The observed coupling

constant is A : 3.2 G = 3.0 x 10-4cm

-1

. This is smaller than the values near

25 x 10~4 cm

-1 for 67 Zn coupling to an F center^ in ZnS 6 ' 7 and values near

40 x 10~ 4 cm

-1 for 135Ba and 137 Ba coupling to an F center in BaS. 8

ZnAl 2 S 4

Two phases of Z11AI2S4 have been characterized. 9 The a phase, formed at

900°C, is reported to have the normal spinel structure. In this structure each

S atom has C3 site symmetry and is 4-coordinate . The sulfur is bonded to one Zn atom and three Al atoms. The Zn atom is surrounded by four S atoms and the

Al atom is attached to six S atoms. In the B phase, prepared at 1050°C, each

S atom is 4-coordinate with two nearest neighbor Al atoms. The other two sites

are occupied by one Zn atom and one vacancy in certain layers and by a random

distribution of Zn atoms and vacancies in other layers. X-ray powder diffraction patterns of our samples showed predominantly Of phase with varying amounts

of other unidentified impurities.

All preparations of ZnAl2S4 exhibited a strong six-line EPR pattern

attributable to Mn2+ in a nearly cubic (tetrahedral or octahedral) environment

with a small axial distortion. Also present in the spectra was a pattern of

at least 29 lines near g = 2.00 with a coupling constant of 3.1 G. This could

arise from one or more types of paramagnetic centers coupled to four to six

equivalent 27A1 nuclei

+

(I = 5/2, 100% natural abundance). The paramagnetic

species might be an F center or an S ion or a cluster of Al atoms with an

odd number of electrons.

A few light yellow chunks of material selected from a typical gray preparation of ZnAl2S 4 proved to be (Y-ZnAl2S 4 within the limits of X-ray powder

diffraction. The EPR spectrum of this light yellow material showed Mn2+

, but not the 29-line pattern. The unidentified paramagnetic species that gives

rise to the 29-line pattern is therefore located in one of the products other

than 0f-ZnAl2S 4

. The method of preparation and identification of the reaction

products are under investigation.

Summary

EPR spectroscopy has established that CaS is an impurity phase in CaLa 2 S 4 and has been used to identify transition metal impurities, paramagnetic defects

and photochemical processes in these materials. Both Mn2+ and a paramagnetic

center with coupling to several 27A1 nuclei were observed in preparations of

ZnAl2S 4. These spectra may be useful in evaluating the quality of ZnAl2S 4 preparations and in the identification of impurity phases that are present.

Acknowledgment

This work was supported, in part, by Contract No. N000148WR24182 from

the Office of Naval Research. Some of the materials used in these studies were

supplied by R. Gentilman and K. Saunders of the Raytheon Company.

135
References

1. Covino, J., Harris, D. C. , Hills, M. E., Loda, R. T., and Schwartz, R. W. , Proc. Soc. Photoptical Instr. Eng. (SPIE) 505 (1984), in press.

2. Nair, P. G. , Lingaro, K. V., and Machwe, V. G. , Proc. Indian Acad. Sci. A,

70, 53 (1969).

3. Harris, D. C, Covino, J., Hills, M. E. , and Schwartz, R. W. , J. Phys.

Chem. Sol . , in press.

4. Auzins, P., Orton, J. W. , and Wertz, J. E., Proc. 1st Intnl. Conf. Paramagnetic Resonance (Jerusalem 1962) , 90 (1963).

5. Shanker, V., Gosh, P. K. , and Reddy, T. R. S., Indian J. Pure Appl. Phys.

14, 193 (1976).

6. Schneider, J., and Rauber, A., Sol. State Commun. 5 , 779 (1967).

1. Shono, Y., J. Phys. Soc. Jap. 47 , 590 (1979).

8. Kolopus, J. L. and Lapeyre, G. , Phys. Rev. 176 , 1025 (1968).

9. Steigmann, G. A., Acta Cryst. 23 , 142 (1967).

136
ELASTIC PROPERTIES OF CHEMICALLY VAPOR-DEPOSITED ZnS AND ZnSe

Claude A. Klein and Charles B. Wiliingham

Raytheon Company, Research Division

Lexington, Massachusetts 02173

Material characteristics such as Young's modulus and Poisson's ratio play an important

role in designing optical windows or assessing their performance from the point of view

of thermally-induced distortion as well as pressure-induced fracture. For single-crystal

cubic material, as in the case of ZnS and ZnSe, a complete description of the elastic

properties requires fourth-rank tensors involving three elastic constantsJ which are

listed in Table 1. Both materials exhibit considerable anisotropy [C44 # 1/2 (C11-C12)],

which implies that the elastic moduli of single crystals may assume a wide range of

values depending on crystalline orientation. With chemically vapor-deposited (CVD)

ZnS and ZnSe, measurements of the elastic properties reveal very little anisotropy, thus

suggesting that these solids are made up of randomly-oriented polycrystalline aggregates.

Various methods exist for deriving the properties of aggregates from the single-crystal

elastic constants; the results of such calculations for polycrystalline ZnS and ZnSe are presented in Tables 2 and 3, in conjunction with a listing of measured property values.

These values are not expected to change much with further development of the CVD

process, albeit small plate-to-plate differences in elastic behavior undoubtedly will

continue to occur. The elastic properties of interest include Young's modulus (E), the shear modulus (G),

the bulk modulus (K), Poisson's ratio (v), the velocity of compressional waves (Vp), and

the velocity of shear waves (V s

). For a single-phase aggregate of cubic material, it is known that the bulk modulus can be derived, unambiguously, from the single-crystal

elastic constants:

K = 1/3 (C n + 2C 12 ) . (1)

Furthermore, the shear modulus,

G = 1/2 (C-|* - C 1 2) , (2)

falls between narrow bounds (the Hashin and Strikman averages2

), which are tabulated

in Ref. 3. Since these two moduli (K and G) suffice to completely characterize the

elastic properties of a macroscopically isotropic solid, it is then a straightforward

matter to obtain Young's modulus and Poisson's ratio in the Hashin or the Strikman

limit:

Efc - 9 KG (3)

G + 3K KS}

and

v

=

Similarly, the two velocities can be obtained from

v

p

=

and

3K - 2G . fa) 2 (G + 3K) W

e obtained from

^K + (4/3)G

j

1/2

(5)

Vs = [G/p] 1 /2 (6)

if p is the density of the aggregate. For polycrystalline ZnS and ZnSe with CVD

densities of 4.09 and 5.26 g/cm 3

, respectively, Eqs. (1-6) in conjunction with the

single-crystal elastic constants of Table 1 yield calculated elastic properties as listed

137
in Tables 2 and 3; note that the Hashin and Strikman limits do not differ significantly

thus providing acceptable averages for randomly oriented aggregates.

Young's modulus and Poisson's ratio of both "standard" and "multispectral" grades of

CVD ZnS have been measured at room temperature by means of strain gauges mounted

on the tensile side of 4-point bend-test specimens. In addition, sound-velocity

measurements were made in the longitudinal mode on specimens oriented paraded and

perpendicular to the growth direction. A summary of this work2* is presented in Table 2 in terms of average values and standard deviations. Compared to calculated

values, these results show that the properties of as-deposited ZnS differ significantly

(and consistently) from those expected on the basis of the Hashin-Strikman averaging

procedure. Post-deposition treated material, however, behaves precisely as predicted

for a randomly-oriented single-phase polycrystalline ZnS aggregate. It is not known

what causes the discrepancy in the case of standard CVD ZnS but it should be pointed

out that this materia! configuration always exhibits a hexagonal second-phase

contribution in addition to a substantial concentration of structural imperfections.

Three teams,**-6

at least, have carried out independent measurements of the elastic

properties of CVD ZnSe (see Table 3). In Ref. 5, the moduli as well as Poisson's ratio

were derived from ultrasonic velocity measurements and thus are indicative of dynamic

conditions; the average value of Young's modulus (75.4 CPa) falls between the two

theoretical bounds but turns out to be appreciably larger than typical values (70.3 CPa)

derived from flexural testing.** Poisson's ratio, however, and the longitudinal velocity

measured at Raytheon are in good agreement with theory. The technique used at the

National Bureau of Standards" involves interferometric measurements on specimens

under static uniaxial stress and provides elastic compliances, which in turn yield

Young's modulus and Poisson's ratio simply from E = Ms-\i and v=-s-| 2/s-\ f since the

material is essentially isotropic. In summary, it appears that the elastic properties of

CVD ZnSe are almost independent of orientation and show no evidence of statistically

significant variances with changes in the deposition process. Furthermore, they are compatible with calculated values derived from single-crystal elastic constants by

means of standard averaging procedures for polycrystalline aggregates.

References

1. J. F. Nye, Physical Properties of Crystals (Oxford U. Press, Oxford, 1957).

2. Z. Hashin and S. Strikman, J. Mech. and Phys. Solids _HL 335 (1962) and_liL 343 (1962).

3. C. Simmons and H. Wang, Single-Crystal Elastic Constants and Calculated Aggregate

Properties (MIT Press, Cambridge, 1971).

4. Unpublished measurements (Raytheon Research Division, Lexington, Massachusetts).

5. S. Kulin, R. Salzbrenner, and H. Posen, in Proc. Fourth Conf. Infrared Laser Window

Materials (ARPA, Arlington/VA, 1974), p. 678.

6. A. Feldman, D. Horowitz, R. Waxier, and M. Dodge, Optical Materials

Characterization: Final Report (NBS-TN-993, Washington, 1979).

138
Table 1. Elastic constants (stiffnesses) of single-crystal ZnS and ZnSe

at room temperature [D. Berlincourt, H. Jaffe, and L. Shiozawa,

Phys. Kev.J29, 1009 (1963)].

Constant ZnS ZnSe

C n (GPa) 104.62 80.96

C 12 (GPa) 65.34 48.81

C44 (GPa) 46.13 44.05

Table 2. Elastic properties of CVD ZnS at room temperature.

Property Calculated Measured

"Hashin" "Strikman" "Standard" "Multispectral

Bulk modulus (GPa) 78.4 78.4

Shear modulus (GPa) 33.4 32.4

Young's modulus (GPa) 87.7 85.5 74.5±3.5 87.61.7

Poisson' s ratio ( 1

)

0.314 0.318 0.29±.01 0.3181.001

Longitudinal velocity (km/sec) 5.484 5.455 5.351.03 5.471.01

Transverse velocity (km/sec) 2.858 2.816

Table 3. Elastic properties of CVD ZnSe at room temperature.

Property Calculated

"Hashin" "Strikman"

Measured

ManLabs^) NBS^

Bulk modulus (GPa) 59.5 59.5 65.31.5

Shear modulus (GPa) 30.2 28.8 28.81.3

Young's modulus (GPa) 77.6 74.5 75.41.7 72.113.1

Poisson' s ratio ( 1

)

0.283 0.291 0.3081.003 0.321.03

Longitudinal velocity (km/sec) 4.356 4.315

Transverse velocity (km/sec) 2.397 2.341

Raytheon

70.312.8

0.281.01

4.381.04

(a) Ultrasonic velocities (Ref. 5)

(b) Interferometric technique (Ref. 6)

(c) Flexural testing (Ref. 4)

139
Additional Note

It has come to our attention that comprehensive measurements of the

elastic properties of Raytran® ZnSe were also performed at General Electric

Company and are documented in a Government Report dated August 1979.*

Ultrasonic measurements that were carried out in the longitudinal mode,

at a frequency of 10 MHz, confirmed that the material is essentially isotropic,

with Vp = 4.39 ± .01 km/sec, in accord with the result listed in Table 3. In-plane

flexure tests at room temperature gave E = 10.1 ± .15 Mpsi (69.7 ± 1.0 GPa) and

v = .29 ± .01, whereas tensile tests, parallel and perpendicular to the deposition

plane, yielded E= 10.3 ± .3 Mpsi (71.0 ± 2.0 GPa) and v = .28 ± .01. These

results are in good agreement with measurements that were carried out in our

laboratory (see Table 3) and, thus, substantiate our observation that the "static"

modulus of elasticity of chemically vapor-deposited ZnSe is lower than

anticipated on the basis of standard averaging procedures.

*J. Brazel, R. Fenton, J. Roetling, and R. Tanzilli, Millimeter Ware Hardened

Antenna Window Materials Development (AD-A076769/9, NTIS, Springfield/VA).

140
RADIATION EFFECTS IN A GLASS-CERAMIC (ZERODUR)

N. Koumvakalis

Litton Systems, Inc.

Guidance & Control Systems Division

5500 Canoga Avenue

Woodland Hills, California 91365 U.S.A.

M. G. Jani and L. E. Halliburton

Department of Physics

Oklahoma State University

Stillwater, Oklahoma 74074 U.S.A.

Zerodur [1 ] is a low-expansion glass-ceramic with important

applications in laser-gyro guidance systems. The material

contains by weight 10-75% crystalline quartz in the form of

crystallites approximately 50 nm in diameter which are embedded

in a glass matrix. The glass-crystal ratio is adjusted so that

the resultant expansion coefficient at room temperature is near

zero

.

Ionizing radiation causes numerous effects in Zerodur. The most

obvious is a change in the optical absorption, and this will have

possible consequences in the thermal expansion behavior.. Thus,

characterization of radiation- induced defects will help solve

problems affecting Zerodur's performance in guidance systems and

will provide an understanding of the basic properties of this

unique class of materials.

Our Zerodur samples were optically polished at Litton. Dimensions were (2x3x7)mm^ for the electron-spin-resonance (ESR) and

(15x15x3)mm^ for the optical samples. Radiation sources were a Van de Graaff accelerator (1 .5-MeV electrons, 10 5 rads/min) and

an x-ray tube (Machlett 0EG-60, tungsten target). During the

77 K irradiation, the ESR sample was immersed directly in liquid

nitrogen. Further details of the experimental technique and the

apparatus are given in reference [2], Optical absorption data

were obtained using a Perkin-Elmer Model 330 spectrophotometer.

For optical measurements at 77 K, a Sulfrian cryostat was used.

Figure 1 shows the ESR spectra of a Zerodur sample after electron

irradiation at 77 K (trace a) and after subsequent warming-up to

room temperature. Both spectra were measured at 77 K.

A number of spectral features are present after the 77 K irradiation. The sharp central line (g value = 1.9983) displays the

line shape and long spin-lattice relaxation times (causing severe

microwave power saturation effects) characteristic of the E«i • center in crystalline quartz [3].

141
The large negative g shift of the high-field broad band, centered

at g = 1.9, indicates the presence of an electron trap. Results

from recent studies of heavyrmetal fluoride glasses [4] suggest

that the electron trap is Zr or Ti^ +. Both of these ions are

present in Zerodur as nucleating agents in the form of Ti02 or

Zr0 2

. In trace b of Figure 1 , the same spectral features are

present although the intensity is reduced significantly. An ESR

spectrum almost identical to trace b is produced after room

temperature electron irradiation.

Figure 2 shows the optical absorption of Zerodur after electron

irradiation at 77 K. The absorption increases with irradiation;

each curve represents a different total dose. After 300 krads no

indication of saturation was observed. The absorption band is

peaked at -565 nm.

Figure 3 shows the optical absorption of Zerodur after electron

irradiation at room temperature. In addition to the absorption

band centered at -565 nm which grows in first, there is a second

absorption band centered at 740 nm , growing at a slower rate.

The highest absorption curve corresponds to a dose of 16 Mrads.

Both bands display saturation at this dose. Thermal anneal and

optical bleaching data suggest that the 565 nm band and the ' ESR spectrum are correlated and that the 740 nm band (or a portion thereof) and the g = 1.9 ESR spectrum are correlated.

Figure 4 shows the x-ray- induced luminescence of a Zerodur sample

at 17 K. Its temperature dependence, depicted in the inset,

indicates that unlike quartz [5] the observed emission is composed of only one band. At this stage the origin of the x-rayinduced luminescence is an open question.

In summary, a first look at the radiation-induced defects in

Zerodur has been very informative. However, further work is

necessary for a complete characterization of the material.

References

[ 1 ] Zerodur (glass ceramic) manufactured by Schott Glass Works,

Mainz, Germany

[2] M. G. Jani and L. E. Halliburton, J. Appl . Phys . _56_ , 942

(1 984)

[3] M. G. Jani, R. B. Bossoli and L. E. Halliburton, Phys. Rev.

B 27_, 2285 (1 983)

[4] P. E. Fisanich et al .

, to be published in the J. Non-Cryst.

Solids

[5] P. J. Alonso et al .

, J. Appl. Phys. 54_, 5369 (1 983)

142
FIG. 1 ESR spectra of

Zerodur. In part

a, the sample was

electron- irradiated

at 77 K; in part b,

the sample was

warmed up to room

temperature and

measured at 77 K.

g VALUE

FIG. 2 Optical absorption of a sample electron-irradiated at 77

K. The label by each curve represents the accumulated

dose

.

143
T

-I I I I I 500 1000 1500 2000 2500

WAVELENGTH (nm)

Optical absorption of a sample electron-irradiated at

room temperature. The label by each curve represents

the accumulative dose.

I

1 1

' 1 -*T- _ 1

WAVELENGTH (nm)

X-ray- induced luminescence spectrum from an as-received

sample taken at 17 K. The inset shows the temperature

dependence

.

144
Infrared Characterization of Defect Centers in Quartz

Herbert G. Lipson

Solid State Sciences Division

Rome Air Development Center

Hanscom AFB, Bedford, MA 01731

The radiation hardness and ageing properties of quartz oscillator

devices depend strongly on the impurity and defect content of the

synthetic quartz material. Low temperature infrared Fourier spectroscopy

is a powerful tool for characterizing changes in quartz defect centers

introduced by ionizing radiation and processing techniques such as electrodi f fusion (sweeping). The technique of scanning large crystals

normal to the growth or sweeping axis reported in this paper has

revealed localized changes in defect center distribution produced by

irradiation and the effect of impurity concentration on vacuum sweeping.

Transient and steady state radiation induced frequency shifts in

quartz oscillator devices are partially attributed to radiation induced

redistribution of point defect centers in the quartz used for the

resonator disk. These disks are fabricated from pure z-growth bars

and incorporate material produced during the entire growth cycle. The

quality and impurity content of the nutrient used for crystal growth

varies. In addition, during the growth period of several months,

thermodynamic conditions change and introduce variations in quartz

quality, aluminum impurity and hydroxyl concentrations between the

seed and z-growth surfaces.

Specific point defect models for synthetic high quality quartz

are well established and are reviewed in several publications.

The major defects are substitutional aluminum impurities in silicon

sites, compensated with interstitial alkali metals to form Al-M+ (M= Li +

, Na + or K

+

), and water molecules adjacent to oxygen sites

to form as-grown OH" centers. Room temperature ionizing radiation

dissociates both Al-M+ and 0H~ and two new centers are formed, A1-0H"

and aluminum holes, Al-h + . 0H~ in the crystal is the hydrogen

source for A1-0H-

. The point defect structure of quartz is also

modified by sweeping. Sweeping a crystal in an air atmosphere, at

elevated temperatures, dissociates Al-M+

, saturates OH defects,

and forms A1-0H-

. In this process, external water vapor provides

hydrogen ions for A1-0H~ and at the same time, most of the alkali

metal ions are physically "swept" out of the crystal. Sweeping a crystal in a vacuum atmosphere^ also dissociates Al-M+ and forms

A1-0H". but similar to irradiation, the hydrogen source is the

145
as-grown OH", which is reduced or depleted as the alkali metals are swept toward the cathode. Longer term vacuum sweeping also removes the A1-0H", leaving large regions of the crystal completely free

of alkali and hydrogen defects. A completely vacuum swept material

should contain Al-h+ as the basic defect and resonators fabricated

from this material should have improved radiation hardness.

Infrared transmissions were measured between 3100 and 3700 cm" 1 with the focused beam of a Nicolet 170SX Fourier Spectrophotometer.

The normal beam size was 3mm in diameter, but 1.5 mm beams were also

used to scan more localized regions. The sample mounted inside a dewar cooled to 85K, was moved across the spectrophotometer beam

axis. Measurements were made normal to the z-growth or sweeping

direction, that is, the incident unpolarized infrared beam is proagated parallel to the crystal y-axis. Beam positions are designated

by the distance of the beam center from the +z face of the crystal.

At 85K, the four principal bands associated with as-grown OH" in

synthetic quartz have vibration peaks at 3348, 3396, 3438 and 3581

cm" 1 and are usually designated Sj, S3 and S4, respectively.

The 3581 cm" 1 S4 band has a strong narrow peak and easily determined

background absorption and is used to monitor as-grown OH-. A1-0H"

has peaks at 3306 and 3366 cm" 1

, designated ei and respectively.

The stronger &2 P ea ^ 1S used to monitor A1-0FT. We are interested

in evaluating only relative changes in as-grown 0H~ and A1-0H",

and for this purpose it is sufficient to compare absorption peak

heights instead of integrated changes in band areas. Both the

&2 and S4 bands have large dichroic rations with maximum strengths

when the electric vector is normal to the optic c~, or z- axis.

With the beam aligned along y-axis maximum strength is obtained only

with a properly oriented polarizer. The measurements reported in

this investigation were made with unpolarized radiation, since the

normally used wire grid type polarizer introduces large transmission

losses in this spectral region.

The quartz samples were rectangular in shape and between 1 and

2 cm in size with parallel x-, y- and z-faces. The quartz material

was Premium-Q grade grown at SARP to which lithium salt was added to

the nutrient and the Na2C03 mineral izer. The effects of radiation

and vacuum sweeping are compared on samples of two different autoclaves, BH-A containing high aluminum and high 0H~ impurity and

D14-45 with relatively low aluminum and OH". The aluminum

concentrations as determined from electron spin resonance (ESR)

measurements are 11 ppm for BH-A and 1 ppm for D14-45.

Variations in the 3581 and 3366 cnr 1 peak heights obtained by

scanning across samples of BH-A and D14-45 normal to the z-growth

axis before and after irradiation are shown^ in Figure 1 and 2.

From Figure 1 for BH-A, the as-grown OH" can be seen to vary from

0.25 to 0.37 cm" 1 with the highest concentration found in the

center of the sample. Even though a 0.8 Mrad irradiation reduced

the as-grown OH" uniformly across the crystal, a large variation in

A1-0H" is observed between the +z and -z faces. Further irradiation

to the estimated saturation level of 1.6 Mrad produces essentially

146
no change in 0H~ or A1-0H" between the center and -z face, and

only small changes between the +z face and center. The differences

in A1-0H produced in different sections of the crystal for the

same OH" decrease can be interpreted in terms of radiation induced

hydrogen migration to compensate nonuniformly distributed Al^+ sites. An alternate explanation is that a second hydrogen source is

present in addition to the as-grown OH". With no further change is

as-grown OH" over most of the crystal, the 1.6 Mrad A1-0R"

distribution reflects the Al 3+ profile.

As- Grown OH" Band

358 1 cm

0 . 8 M r a d

1 .6Mr ad -

"

_l l i l_

0.60 r

Al - OH" Band 3366 en

1 ,6Mrad ~

. 0.8Mrad

PREMIUM-Q

QUARTZ

8 H - A

Unirradiated

-Z Face

. t

As— Grown OH" Band

PREMIUM-Q

QUARTZ

D 1 4-4S

Unirradiated

__^0.8Mrad — x 6 4Mrad

Al- OH" Band 3366 cm 1

0.10- V * _

+ Z Face

n nnt

6.4Mrad

O.SMrad

Z Face

Distance Along Z-Axis (mm) Dis;ance Along Z-Axis (mm)

Figure 1. Peak absorption

coefficient values for 3581cm~l

and 3366cm~l bands before

irradiation and after 0.8 and

1.6 Mrad 60co irradiation

doses for Premium-Q crystal

BH-A. Beam normal to crystal

z-axis

Figure 2. Peak absorption

coefficient values for 3581cm~l

and 3366cm"l bands before

irradiation and after 0.8 and

6.4 Mrad 60r,o irradiation doses

for Premium-Q crystal D14-45.

Beam normal to crystal z-axis

From Figure 2 for D 14-4 5. it can be seen that the average OH"

level is about one-fourth of that of sample BH-A with the highest

concentration toward the -z face of the crystal. A 0.8 Mrad

irradiation depletes the as-grown 0H~ close to the +z end and

reduces it over the remaining part of the crystal. The relatively

uniform A1-0H" distribution produced by the 0.8 Mrad dose initially

appears to indicate a uniform Al^+ distribution. Additional irradiation

147
up to the estimated saturation level of 6.4 Mrad further depletes or reduces the as-grown OH". A surprising feature is the increase in

Al-OH" toward the z-face of the crystal in OH" depleted regions.

As with sample BH-A, this implies either radiation induced migration

to Al 3+ sites or the presence of a second source of hydrogen. The

situation for this sample may be further complicated by the presence

of Al-h + which has been observed in OH" depleted regions of vacuum

swept samples.

6

The effect of impurity concentration on the progress of vacuum sweeping is demonstrated in Figures 3 and 4. Figure 3 shows

the as-grown OH" distribution and the movement of Al-OH" through

the crystal as alkali ions are replaced by hydrogen at Al 3+ sites

for sample BH-A after various total sweeping times. No significant

changes in as-grown 0H~ occur for short sweeping times up to 3.5

days. During this same sweeping period Al-OH" forms across the

crystal extending to about one third the distance between the anode

and cathode. After 17.5 days of sweeping, OH" is considerably

reduced near the anode and is increased in other sections of the

crystal. The Al-OH" distribution follows a similar pattern, with a reduction near the anode and a strong increase toward the center of

the crystal where the initial 0H~ concentration was the largest.

For this material with high aluminum and OH" content vacuum sweeping

proceeds slowly and formation of Al-OH" across the entire crystal

which indicates complete removal of alkali ions, does not occur

during the 17.5 day time period.

Vacuum sweeping of sample D14-45 with low aluminum and 0H~

content proceeds much more rapidly? as demonstrated in Figure 4.

After 12 hours of total sweeping time as-grown OH" is depleted near

the anode and Al-OH" is formed across the entire crystal. Sweeping

1 day eliminates OH" over a section 4 mm from the anode and produces

a significant decrease in Al-OH" in this same region. After 4 days

of sweeping 0H~ is depleted over the half of the crystal closest to

anode and A10H" is further reduced. Al-h+

is found in the OH"

depleted regions from ESR measurements. The possibility for complete

vacuum sweeping is demonstrated in this sample where removal of

alkali and hydrogen defects and replacement with aluminum-holes has

been effected for a large section of the crystal.

References

1. A. Kats, Philips Res. Reports, 17_ (1962).

2. D. B. Fraser; Physical Acoustics , Vol 5, W. P. Mason, editor,

Academic Press, New York 59, (1968).

3. L. E. Halliburton, N. Koumuakalis, M. E. Markers, and J.

X J.

Martin, J. Appl. Phys., 52, 3565 (1981).

4. J. C. King, Vacuum Electrolysis of Quartz, U.S. Patent 3, 932,777,

January 13, 1976.

148
5. H. G. Lipson and A. Kahan (submitted for publication in Journal

of Appl ied Physics)

.

6. H. G. Lipson and A. Kahan and J. O'Connor, Proc. 37th Annual

Frequency Control Symposium (AFSC) 169 (1983).

7. H. G. Lipson and A. Kahan, IEEE Transactions on Nuclear Science,

NS-31 . 1223 (1984).

Figure 3. Peak absorption

coefficient values for 3581cm-l

and 3366cm-l bands between

anode and cathode for 6 hrs,

12 hrs, 3.5 days and 17.5 days

vacuum sweeping times measured

normal to the sweeping axis.

Premium-Q crystal BH-A

Figure 4. Peak absorption

coefficient values for

3581cm"l and 3366cm_ l bands

between anode and cathode for

3 hrs, 12 hrs 1 day and

4 days sweeping times measured

normal to the sweeping axis.

Premium-Q crystal D14-45.

149
THE IMPORTANCE OF ELECTRON-ELECTRON CORRELATION IN THE CALCULATION OF SECONDORDER NONLINEAR OPTICAL PROPERTIES OF ORGANIC MOLECULES. THE CASE OF UREA.

Brian M. Pierce

Hughes Aircraft Company

Bldg. A-l, M/S 3C923

P. 0. Box 9399

Long Beach, CA 90810

In studies of nonlinear optical organic molecules, the theoretical understanding of the relation between the electronic structure of the molecule and

the molecular electronic component of the second-order nonlinear optical

susceptibility (the hyperpolarizability tensor, 3-jjk) has been an important

objective (1). The theoretical description of molecular electronic structure

improves with the theoretical treatment of electron-electron correlation

(EEC) in the molecule. Three general quantum mechanical molecular orbital

(MO) formalisms (2) used to study molecular electronic structure, and

ordered according to an improving treatment of EEC, are 1) the selfconsistent-field (SCF)-MO method, 2) the SCF-MO method with single excitation

configuration interaction (SCF-MO-SCI), and 3) the SCF-MO method with single

and double excitation configuration interaction (SCF-MO-SDCI )

.

In published calculations of 3ij|< for organic materials utilizing the results

of molecular orbital calculations (1), the treatment of EEC was never extended beyond that of the SCF-MO and SCF-MO-SCI methods. It has been shown that

EEC at the level of SCF-MO-SDCI is required to calculate with greater accuracy the third-order nonlinear optical property of molecular two-photon

absorption for the ir-electron singlet excited states in linear conjugated

polyenes and related organic molecules (3,4). Therefore, it is necessary to assess the importance of EEC at the level of SCF-MO-SDCI in the calculation

of 3-jjk for organic molecules.

The organic molecule selected for our initial theoretical study was urea,

(NH2)2C = 0, because its nonlinear optical response has been the subject of

extensive theoretical (5,6) and experimental (5,7-9) investigations.

The method of direct summation over singlet electronic states in a perturbation theory based expression was used to calculate 3-jjk (10). The terms

needed to evaluate this expression were calculated using CND0- and IND0-SCFM0 procedures (4,11) combined with SCI and SDCI methods. The CND0-SCF-M0-SCI

(CND0-SCI) and IND0-SCF-M0-SCI (IND0-SCI) calculations used the empirical

Mataga electron-electron repulsion integral (4), whereas the CND0-SCF-M0-SDCI

(CND0-SDCI) and IND0-SCF-M0-SDCI (IND0-SDCI) calculations employed both the

empirical Mataga and Ohno (4) electron-electron repulsion integrals. Thus,

six calculations of 3-jjk for urea were performed that varied in the treatment

of EEC in the molecule: CND0-SCI, CND0-SDCI with Mataga and Ohno integrals,

IND0-SCI, and IND0-SDCI with Mataga and Ohno integrals. All six calculations

were for an isolated urea molecule unperturbed by a solvent or crystalline

150
envi ronment.

The parameterization of the CNDO and INDO formalisms is given in Ref. 4. All

96 singly excited configurations that can be generated from the valence

electron molecular orbitals were used in calculations employing SCI. In

calculations employing SDCI, all 96 singly excited configurations and the

200 lowest energy doubly excited configurations were used. Seventy-five

singlet excited states were calculated for all six calculations of 3-jjkThis number of states has been shown to ensure the convergence of the sum- over-states expression for the 3

-j j ^ of urea (5). The internal coordinates

of urea used in the calculations were the samp as those in Fig. 1(b) of

Ref. 5. The molecule-fixed coordinate axes were such that urea lies in a z-x plane with the z-axis directed from the carbon atom to the oxygen atom.

The calculated values of B-jjk were used to compute several second-order non- linear optical properties of urea: 1) the two linear electro-optic

coefficients for a single crystal, ^3 = rxyz (co-j, 0) and r^i = r, Xy

(co] , 0) =

ryzx 0) for co] = 632. 8nm: 2) the macroscopic susceptibility for

second harmonic generation, d|^, for co-j = 002 = 1060nm; and 3) the term

3 Z * = Z3 z ii for oo-i = ouo = lObunm.

ij J Table I contains second-order nonlinear optical properties of urea measured

experimentally and calculated in the present study and in other ab-initio - SCF-M0 (6) and CND0-SCI (5) studies. The CND0-SCI study by Morrell, et al

(5) is virtually identical to ours, and the small differences between the two

sets of calculations are attributed to differences in parameterization. All

calculated results in Table I are for an isolated urea molecule; whereas the

experimental results are for single crystals of urea or for the molecule

dissolved in a given solvent. Consequently, there are differences between

the calculated and experimental results. The discrepancy between theory and

experiment can be resolved by incorporating local field corrections (5) and

the influence of hydrogen bonding (6) into the theoretical formalisms.

The salient conclusions concerning the comparison of our calculated results

for urea against those of experiment and the sophisticated ab - ini tio -SCF-MO

calculation (6) are as follows. 1) The IND0-SCI and IND0-SDCI formalisms

describe the second-order nonlinear optical properties of urea better than

the CND0-SCI and CND0-SDCI formalisms. The principal reason is that, unlike

CNDO theory, INDO theory accounts for the difference in electrostatic interaction between two electrons in different orbitals on the same atom (11).

2) The CND0-SDCI and IND0-SDCI calculations with the Ohno integral are better than those with the Mataga integral because the Ohno integral combined

with an extensive SDCI treatment of EEC results in more accurate calculations

of the ground state dipole moment and singlet excited state transition

energies and oscillator strengths for urea (not shown). This finding is

consistent with that of other theoretical studies of EEC at the level of

SCF-M0-SDCI (12). 3) Although the ground state dipole moment and singlet

excited state transition energies and oscillator strengths of urea calculated

by the IND0-SCI method and the IND0-SDCI method with the Ohno integral are similar (not shown), the second-order nonlinear optical properties of urea

in Table I calculated by the two methods are different. The magnitudes of

these calculated second-order nonlinear optical properties decrease as the

151
treatment of EEC improves from the INDO-SCI method to the INDO-SDCI method

with the Ohno integral. Thus, the treatment of EEC at the level of SCF-MOSDCI has a significant impact on the calculation of second-order nonlinear

optical properties for urea. This impact is expected to be greater for

organic molecules with more extensive ir-electron systems.

Dr. David B. Chang is thanked for interesting and helpful discussions.

1. The chapters by Garito, et. aj_ and Badan, et. aj_ and the references

therein in Nonlinear Optical Properties of Organic and Polymeric

Materials , D. J. Williams, Ed., American Chem. Soc, Washington, D.C., TM

2. H. F. Schaefer III, The Electronic Structure of Atoms and Molecules

A Survey of Rigorous Quantum Mechanical Results , Addi son-Wesley, Reading

MA, 1972.

3. R. R. Birge and B. M. Pierce, J. Chem. Phys., 70, 165 (1979).

4. R. R. Birge, J. A. Bennett, L. M. Hubbard, H. L. Fang, B. M. Pierce,

D. S. Kliger, and G. E. Leroi, J.A.C.S., 104, 2519 (1982).

5. J. A. Morrell, A. C. Albrecht, K. H. Levin, and C. L. Tang, J. Chem.

Phys., 71_, 5063 (1979).

6. J. Zyss and G. Berthier, J. Chem. Phys., 77_, 3635 (1982).

7. C. Cassidy, J. M. Halbout, W. Donaldson, and C. L. Tang, Opt. Commun.,

29, 243 (1979).

8. J. M. Halbout, S. B 1 it, W. Donaldson, and C. L. Tang, IEEE J. Quantum

Electron., QE-15 , 1176 (1979).

9. I. Ledoux and J. Zyss, Chem. Phys., 73, 203 (1982).

10. C. Flytzanis, in Treatise of Quantum Electronics , Vol. Ia, H. Rabin

and C. L. Tang, Eds., Academic, New York, 1975.

11. J. A. Pople and B. L. Beveridge, Approximate Molecular Orbital Theory , McGraw-Hill, New York, 1970.

12. K. Schulten, I. Ohmine, and M. Karplus, J. Chem. Phys., 64, 4422 (1976).

152
Table I. Calculated and Experimentally Measured Second-Order Nonlinear

Optical Properties of Urea.

Expt. Theory

Present Study Other . CNDO- CNDO- SDCI INDO- INDO- SDCI ab- a CND0- D SCI Mataga Ohno SCI Ma tag a Ohno initio SCI

r

41

5.6

b 1.63 1.36 1.04 2.05 2.13 1.45 -- 1.51

(108esu)

rco 2.5

b 1.73 1.48 1.14 2.18 2.41 1.66 -- 1.55

63

(108esu)

d

SHG 3.4+1.0c 3.42 2.92 2.23 4.30 4.68 3.21 4.4 3.0

z (109 esu)

3* + 2.3

d -0.97-0.71 -0.76-1.60-1.45 -1.30-0.55 -0.92

,30„..x 0.3 + 0.1 e (10-esu)

S:^5-

±

Ojf

0.3 + 0.039

3 zxx

h — -0.53 -0.45 -0.34 -0.68 -0.70 -0.50 0.6

(1030esu)

3

h

zyy

(1030esu)

6

h

(1030esu)

3

h 0.04 0.02 0.01 0.03 0.02 -0.01 -0.08

3zz

h — -0.49 -0.27 -0.43 -0.94 -0.77 -0.79 -1.15

(a

(b

(c

(d

(e

(f

(9

(h

Ref. 6

Ref. 5

Absolute value, Ref. 8

In DMF solvent, Ref. 7 In DMF solvent, Ref. 9

In H2O solvent, Ref. 9

In DMSO solvent, Ref. 9

Nonzero 3 components with a)j = = 1060nm

153
DIFFUSE MULTILAYER ANALYSIS USING A MULTIFLUX METHOD

S.O. Sari

Rockwell International Science Center

Thousand Oaks, CA 91360

The use of uniform material layers to form multilayer films forms the

basis for an extensive coating technology. The transmissive and reflective

properties of such structures are dominated by optical interference occurring among the layers. Comparatively less attention seems to have been

given to treating stratified media consisting of random rather than uniform

material layers. Within such structures, the optical scattering properties

of each sublayer dominate the optical properties.

Some previous work on diffuse coatings has been concerned with investigations of surface-roughened layers and the form of diffuse scattering from

one or more roughened interfaces. 1 Such analytical investigations have been

based on lowest-order solutions to Maxwell's equations at a perturbed roughened interface, a calculational procedure which has been carried out by several different authors in recent years. 2 Our present objective is to point

toward a possible alternative method for treating diffuse scattering from

inhomogeneous materials. This procedure may be helpful for analyzing specialized coatings which are diffusely scattering. Examples would include

aggregate suspensions, artificial dielectrics, solids containing scattering

defects, paint layers or inhomogeneous recording materials.

The approach which we presently follow is the extended Kubelka-Munk

theory developed some years ago by Mudgett and Richards. 3 In this framework, we assume a layer of scattering material having parallel interfaces to

be oriented normal to the x-axis. Orthogonal (y,z) axes are assumed to lie

in the plane of the interfaces. Diffuse flux pencils F(£2) propagating in

the angular directions Q = (9,<t>) defined with respect to these axes are taken to be scattered among themselves through diffuse scattering or to ex- ternal channels by optical absorption. A convenient approximation is to assume four distinct integrated fluxes propagating either along the positive

or negative x-directions through the layer. These are taken as collimated

specular fluxes F$+ and F$~, and as integrated diffuse fluxes F D+ and Fq",

where FD * = /.dQFiJQ) is understood to be integrated over either the forward

or reverse cone of diffuse radiation. Mudgett and Richards show 3 (their Eq.

(51)) that the flux propagation can be written as

(1)

154
where the and are cross-channel scattering and absorption coefficients, respectively, within the layer. We write this compactly as

<JF/dx = S *JF. F^r a layer of thickness L, we obtain the formal solution

F(L) = exp(SL) • F(0) = a(L) • F(0), where a(L) = exp (SL).

We now consider a stack of

nected by smooth interfaces for

nel coupling. In this case, we left (ith medium) to the medjum

transfer matrix % such that F

i

such stochastically scattering layers, con- which there is no specular-to-diffuse chancan relate the fluxes for the medium on the

on th<| right (i+lth medium) by defining a = i i+1* Because of the absence of crosschannel coupling, the form of x is block diagonal and can be written as

/l/T

0

0

\R/T

0

!/T

a R a/Ta 0

" R a/T

a (l-2R

a )/-T

0

-R/T \

0

0

(1-2R)/T/

(2)

The interfacial Fresnel reflectance and transmission coefficients R and T

satisfy the condition R+T = 1. Also,R

a and T.a are a solid angle and polarization averaged reflectance and transmission such that we again have R

a +

T

a = 1. As an example, R

a

= /dQR(£2)F

D (Q)/ /dQFg(Q) , where Fq(q) is the incoming diffuse flux from either side of the interface. This procedure is

approximately self -consistent when both of these averages are about the

same. This will occur either when the distribution Fn(Q) is relatively narrow or when the interfacial index mismatch is not too large.

-> ->• In the present model, incident and exiting fluxes F and F through an N-layer diffuse scattering stack can be written as

> *

F

n (0) = Y;i (-L1 )y*o2

(L

1 -L2

).....;

N (LN . 1 -LN )nN+1

.F x

(L

N

) (3)

where 0 < Li < L2...< L^. Each coordinate along the x-axis determines

the location of the ith interface between diffuse layers. We assume that

the nonzero components of F are F

x $ + and F xn+

so that no flux is incident

from the exiting side. Let

x us also assume that a collimated impinging beam

F

n

c + strikes the incident side. Then we may define a specular-to-diffuse

integrated hemispherical reflectance and transmission as RSD

= F

n Q-/Fn 5+ and

T SD

= fr xD

+

/ F nS

+ and collimatecl specular components as R sp = F

n $"/'r nS

+ and

Tr P = F r +

/Fn c+. If we define a total diffuse multilayer reflectance and

155
transmission by R^. = R sp

+ R<j D and = T

sp

+ T$q, then R

t + T

t

= 1 in the

absence of absorption. This will hold because all component matrices in Eq.

(3) are flux conserving, assuming that Ki = K2 = 0 for each layer. If positive absorption coefficients K.,- occur for one or more layers,- we will have

Rj. + Tj. + A

§ = 1. Here, the absorptivity depends in lowest order only on those coefficients which are nonzero. It is also possible to have a diffuse cone of radiation F

n Q incident on the multilayer rather than F

n $ +

. Then we will have a diffuse-to-diffuse channel coupling such that Rqq =

— "4* R nD / p nD and TDD

= F xD / F nD

+

. Because of solid angle restrictions, no diffuse-to-specular coupling ordinarily occurs. Moreover, excluding absorption, we again have Rqq + Tqq = 1. In the case of absorption, we again define an absorptivity Aq which depends to lowest order on nonzero such

that RDD

+ Tqq + Aq = 1.

In the present discussion, we will restrict our application of the

foregoing multiflux approach to a single weakly scattering layer having

S-j L « 1 and K^L << 1. Suppose the density of individual particulate scatterers within the layer to be N

p and the particulate scattering cross sec- tion to be C(Q). Then, we define

S

x = N

p /+dQC(Q) and S

2 = N

p /_dSC(Q)

where integrations are over forward and reverse cones. Particularly interesting in this model are the hemispherical backscattering or hemispherical

forward scattering. We may state these as

(1-R

l)(

l-R

la ) L{Sl(

R

2 + R 2a ) + S

2 (l+R 2R 2a )} K SD ~ (l-R

1 R2

)(l-R

la

R

2a )

[ * ]

and

x (l-RjHl-FW L jS

1 (l + R la

R

2

) +S

2

(R

2 + R la )}

'SD (l-R^^d-R^R^) * ^

Since all interfacial reflectances are < 1, we may show that 1 + Ri

aR2 > R2 + Ri

a and 1 + R2R2. > R2 + R2

a

. Thus, if the individual particulate

scattering coefficient S2 > Si, the diffuse reflectance R5Q will be > Tcq.

On the other hand, if Si > S2, then the diffuse transmittance Tcq will be

> Rcq instead. Thus, simultaneous integrated hemispherical back and forward

scattering measurements can yield some microparti cul ate defect scattering

information through determination of the coefficients Si and S2.

This analysis may have applications to optical material studies such as ensemble microparticle drop sizing 4 or other related topics of current interest. It may serve as an adjunct to scattering models based on direct

solutions to Maxwell's equations for various scattering geometries.

156
REFERENCES

1. J.M. Elson,' Kirtland Weapons Laboratory, Technical Report No. AFWL-TR75-210, Kirtland AFB, NM (1976).

2. See e.g., J.M. Elson and J.M Bennett, Opt. Eng. 18, 116 (1979); E.

Kretschmann and E. Kroger, J. Opt. Soc. Am. j>5_, 150 (1975).

3. P.S. Mudgett and L.W. Richards, Appl. Opt. JLO, 1485 (1971).

4. See e.g., D.J. Holve and K.D. Annen, Opt. Eng. 23, 591 (1984).

157
OPTICAL ABSORPTION IN THE BAND GAP IN HIGH PURITY SILICON

Randall T. Swimm

Center for Laser Studies

University of Southern California

Los Angeles, CA 90089-1112

Calorimetric measurement of weak optical absorption of laser illumination

by solid samples is a well established method. The possibility of applying

such methods to the study of deep level impurities has been discussed in

the literature (1,2), but little data has been published. In this paper, some of the many difficulties and constraints in applying calorimetry to

the study of deep level impurities will be discussed.

The goal of the present study was to determine the energy of a deep level

with respect to either the valence or conduction band edge. In order to

do this it is necessary to measure the photoionization or photoneutral ization cross section as a function of photon energy. In order to accurately

determine the energy of the level, it is essential that the photo cross section be measured in the very low absorption limit near the threshold

energy for transitions. This is because the absorption near the threshold

is strongly influenced by coupling to the lattice, as shown by Ridley (3)

using photoconductivity, and Monemar and Samuel son (4) using photoluminescence. The effect of this coupling must be included in the lineshape model

used to analyze the data, and determine the level energy. Measurements of

only the upper portion of the photo cross section cannot be relied upon to

yield an accurate energy determination.

Extremely high sensitivities for calorimetry and closely related photoacoustic measurements have been reported - absorption coefficient capabilities of 10~ 7 cm"l. However, such sensitivities are useless if background

absorption levels are greater than the signal being sought. Calorimetric

measurements of optical absorption in high purity silicon single crystals

were carried out at room temperature in order to determine limiting background absorption levels.

Samples were cut from a boron-doped float-zone ingot grown by WacherSiltronic. Sample restivity was 10%2-cm, and minority carrier lifetime was

5 x 10" 3

s. Absorption measurements were carried out at two wavelengths.

One set of data was measured at a wavelength of 1.9 ym, obtained by Raman

shifting in hydrogen the 1.06 ym radiation from a Q-switched Nd:YAG laser.

An apparent absorption coefficient of 1 x lO^cm" 1 was measured at an incident intensity of 3 MW/cm^. Subsequent measurements showed the absorption to be intensity dependent, consistent with multiple photon absorption.

A second set of data was measured at a wavelength of 1.32 ym. obtained from

a CW Nd:YAG laser. An absorption coefficient of 1 x 10" 3 cm~l resulted. It

is suspected that this absorption may be due to an indirect band-to-band

process involving three phonons. This process has been shown to exist at

photon energies above 0.991eV by Anagnostopoulos and Sadasiv (5).

158
The relatively high background absorption found in these measurements, and

the requirement of measuring the lowest possible absorption limit of the

photo cross section imply that heavy doping will be required if the energies

of deep level impurities in silicon are to be measured by calorimetric

methods (including photoacoustic) . The high background absorption suggests

that it may not be possible to fully utilize the extremely high sensitivity

of which calorimetric methods are capable.

This research was sponsored by the California Institute of Technology Jet

Propulsion Laboratory.

1. D. Bimberg and A. Bubenzer, Appl . Phys. Lett. 38, 803 (1981)

2. G. Wetsel and F.A. McDonald, 1st Topical Meeting on Photoacoustic

Spectroscopy, held Aug. 1979 at Ames Iowa, paper ThA5.

3. B.K. Ridley, J. Phys. C. Solid St. Phys., U, 2015 (1980).

4. B. Monemar and L. Samuelson, Phys. Rev. B 18, 809 (1978).

5. C. Anagnostopoulos and G. Sadasiv, Phys. Rev. B7^, 733 (1973).

159
PROPERTIES OF GUIDED MODES IN BIDIRECTIONAL ANISOTROPIC MEDIA

0. Schwelb

Department of Electrical Engineering

Concordia University v 1455 de Maisonneuve Blvd. West

Montreal, Quebec, H3G 1M8

Guidance has been investigated in layered anisotropic media characterized by

a permittivity or permeability tensor that is Hermitian and has one pair of

off-diagonal elements, but is otherwise arbitrary. Depending on the

location of the off-diagonal elements one distinguishes between polar,

longitudinal and equatorial orientation. In polar orientation the nonzero

off-diagonal element pair: e yz - £ Zy> corresponds to the plane of the

interface, in our case the y-z plane. In longitudinal orientation £Xy~£yX

is the non-vanishing pair, corresponding to the plane perpendicular to the

direction of propagation (x-y plane). Finally the equatorial configuration

is associated with an optic axis in the plane of incidence (x-z plane).

Assuming exp( jwt) time dependence and a wave vector k" = k

0 [<(n)ax

+{3a

z

]

,

where k

0

=u)vV 0

e 0

, P is taken to be real and <(n) is a transverse guide index

in region n, the polar and longitudinal orientations admit bidirectional

wave propagation, i.e. the normalized wave members of the four partial waves

satisfy the constraints (n)*-^ (n) and (n)=-<^ (n) . The equatorial

orientation is quasi-isotropic in the sense that TE and TM modes are separate, but the TM mode exhibits peculiarities of which more will be said

later.

The layer transfer matrix G(x) is defined by

i(x) = G(x)I(o) (1)

where the state vector is g(x)=col[T)~^E

y

(x) , ti^H z (x), ti~^E

z (x), -T^jH (x)]

and ti 0 = /y 0/e 0

, and the normalized characteristic impedance of a medium is

computed from

^

gXi = ^0 5

Ti < 2 > where a =

[j| ~q] and ETi (^xi^ is the incident electric (magnetic) field

vector component in the plane of the interface.

It can be shown [1] that in a polar medium

G(x) - G, (x) - G.(x)

where

(3)

Gi(x) =

L-jw\Vi s

i

jh

3 <7

i s

j h C

6 1

-c.

jk1 hjKl s

x -hlCl

J whiS s

i

-1 _1

jw <

L S

L

jh

i wi <

i - i Si -h

l c

l

(4)

160
h

i = e zy

(e xx"^ )/ L e xx

K i^*e

z Z

( e xx-^)J' i=1 ' 3 > w = exx

/(exx"P2) ' = cos K^Xy = sin k and (x) obtains from G^(x) by interchanging

indices 1 and 3. Note that e^^ is the ij-th element of the Hermit ian

relative permittivity tensor, and x is normalized with respect to k

Q

. From

(3) it can be seen that H

z=0 and dEy/dx=0 occur in the same x=xQ plane.

Conversely, Hy=0 and dE

z /dx=0 also occur simultaneously in the same x=const.

plane. The values of the normalized transverse wave numbers can be

calculated from

2k z = (e +e We +e )-&--+ {[(e -e We -e ) ^ ] 2 ZZ V XX ZZ' ^ lV VV 7.7.' V VTf 7.7.' XX

yy zz xx zz XX

+4|e

yz |^(l-_§i)}^ • e xx

(5)

The forward characteristic impedance matrix of a polar layer is given by

Z

f =

WK

i K

c (hrhi )

(6)

and the backward characteristic impedance is simply the negative of this

expression.

In a longitudinal medium the transfer matrix is also given by (3) but now

G

A (x) =

Jis k S

i i -c

1 -38

3 k

1 s

i -s CL j<i S

i jS

gi

K iSi

(7)

jSg

i g^Ki Si gA gd c

A -jg

i gd K;

i s

i jgi s-Vi

-i S

i -

g l C

l where B ±=^ zz

e xy / [e zz(e xx~^ Wxx< ±

z

) , i-1,3 and s=l/e

zz

. The turning

points in longitudinal configuration are such that either H z=0 and dEy/dx=0,

or E

z=0 and dHy/dx=0 occur simultaneously in the same transverse plane. The

values of the normalized transverse wavenumbers can be obtained from

2k 2 = (ev +e )-

yy zz'

XX

e —e — e yy zz | xy

2 /e' ) xx '

~ ( £ xx-

£ zz^2 + 4

| £ xy

E xx

2 z B

2 /e 2 \% • ZZ K XX > (8)

The forward charactersitic impedance matrix of a longitudinal layer is

Z

f =

K ~K

1 i Sg.g^K^K^) SK^Cg^)

but now the backward characteristic impedance is related to via

(9)

"1 0' "l 0

" zb

= -

. 0 -1

m

Z

f

. 0 -1

.

(10)

161
The TE mode in an equatorial medium is equivalent to that in an isotropic

medium. The TM mode however "walks off" the z axis at an angle 6 given by

[2]

tan 6 = Re(e

xz

)/e xx» (11)

The TM mode wave admittance in the forward direction is

Y , = {jpime X2+[A

yy

(e xx-^)-p^(Imexz)^]^}/(e xx-^) (12)

where A

yy

= £ xx

£ zz ~

| e Xz|^*

^en Ree

xz=0 wave propagation is

bidirectional, but the backward and forward wave admittances are not simply

of opposite signature. When Ime xz

=0 forward and backward wave admittances

have opposite signature, but the guide does not support bidirectional wave

propagation.

Bounds of 8 refer to those values of the real axial wavenumber, or effective

guide index, at which either an external region attenuation coefficient (oc^)

vanishes (cutoff), or an internal region transverse wave number (k^)

approaches zero (high frequency limit). In a lossless waveguide change

from real to imaginary at cutoff, as the effective guide index decreases.

This limit marks the frequency below which the guide becomes leaky. Since

there is more than one limit condition, the highest 8 is critical. As the

frequency increases, the rays approach the axial direction, the axial

wavenumber approaches the free space wavenumber and vanishes.

In polar orientation, when 8

2 =8 !=£-___ and e ..__>€____ , then k

2 =e„„-£„„ and k

2 =0. d aa yy aa j_ yy *»x j

On the other hand, at the same value of 8, when e <e , and

yy xx i k

2 =£,-£„„. Therefore 8 Q is a high frequency limit condition. The other

j yy xx a

| high frequency limit is at P 2=

Pb=e yy~

|

e yz

|

2

^ e zz* At tnis val ue if

(l/e xx+l/e zz

)|e yz | 2 >(e

yy

/e xx

-l)e

zz , then ^= d/e xx+l/e zz )

|

e

yz \ 2 -(e /e -l)e and <

2 =0 t whereas if the inequality points in the other

yy aa £*c* .i direction, then and exchange roles. The same conditions apply to

cutoff if primed quantities, referring to an external region, are used in

the above expressions, and if the Kj^-ja^ substitution is made.

In longitudinal orientation one of the high frequency limits is at

P 2=

Pa

= ^e xx^yy)+ [^ e xx-

£ yv)H e xyJ^ ' " V^"*"6 "" e xyf ^

"^xx^zz^a^xx'0 ' then a* P =Pa *I"6 a and whereas if'o

a<0,

6=8 k

2 =0 and k?=6 0

. The other high frequency limit is at B

2 =8£=^(e,+e„„) a i o a ^ d xx yy

-[\(e-eY2 +\e\ 2

] . If 6 K

=e +e 7 ~\e\ 2 /e -(e v +e^)B£/evv > 0, then

xx

then at

xx yy' | xy|., J * b yy zz | xy,

at 8=8^ <^ =o^ and k^ =0> whereas if 6^<0, then at the same value of 8 k^=0

and k^o^. The cutoff conditions are given by the same expressions provided

primed quantities are used and is interpreted as -ja^.

In conclusion explicit expression have been presented for the layer transfer

matrix, for the characteristic impedance and for the bounds of the effective

guide index for uniaxial media in polar and longitudinal orientation. Some

properties distinguishing the equatorial orientation have also been

mentioned.

162
0. Schwelb: Anistropic stratified waveguides for electromagnetic

waves: a matrix analysis, Internal Report, Dept. Electrical Eng.,

Concordia University, Montreal, Quebec, 1984.

D. Marcuse: IEEE J. QE-14, 736 (1978).

163
CALORIMETRIC MEASUREMENT OF OPTICAL ABSORPTION IN SAPPHIRE

AT VISIBLE, NEAR IR, AND NEAR UV WAVELENGTHS

Antonio Balbin Villaverde* Randall T. Swinun, and Michael Bass

Center for Laser Studies

University of Southern California

Los Angeles, CA 90089-1112

In this paper calorimetric measurements of optical absorption

in sapphire at visible, near IR and near UV wavelengths are

reported. Single-crystal sapphire grown by Union Carbide was

fabricated into rectangular prism samples and polished on all

faces. Sample cross section was 1 cm square, and samples of

thickness 0.5, 1.0, and 2.0 cm were measured. CW-laser irradion from krypton ion, dye, Nd : YAG and NdtYAlO lasers was

used, over a wavelength interval from 1.32 ym to 0.35 ym.

Measurements were carried out at room temperature using a

calorimeter which was been described previously [1]

Chromium is a ubiquitous impurity in sapphire, and was apparently present even though the samples were not intentionally

doped. Fluorescence was observed when samples were pumped at

wavelengths in the Cr+ 3 bands. The weak peaks in the absorption

data at these absorption band wavelengths are due to the combined effect of nonradiative recombination, and indirect heating

of calorimeter components by the radiated fluorescence. For this

reason, it is difficult to estimate the chromium concentration.

A plot of In a vs wavelength A, where a is the absorption coefficient in cm"-'- yields a surprisingly linear behavior over the

wavelength interval from 0.75 ym to 0.35 ym. However, this may

be fortuitous, considering the presence of chromium absorption.

A plot of In a vs photon energy -fioa yields a reasonably linear

behavior over a wider wavelength range, extending from 1.08 ym

to 0.35 ym (1.15 eV to 3.50 eV) . This result is consistent

with an exponential absorption edge described by Urbach's rule,

with some additional absorption in the chromium absorption bands.

An Urbach tail may be modelled [2] by the relationship

a = A exp [a (-fioj-fioj ) /k_ T]

o a

where h is Plack's constant, kB is Boltzmann's constant, T is

temperature and A, a, and oj q

are fitting parameters. "tf^0

is

is usually approximately equal to the lowest exciton energy,

9.5eV is the case of sapphire [3]. If the data are assumed to

follow the behavior of Urbach's rule, then the slope of the

measured data plotted in the figure results in a value for

the parameter a of 0.065. This is rather small, considering

164
that the value is usually of order unity.

In summary, the optical absorption of sapphire was measured

calorimetrically in the wavelength interval from 1.32 ym to 0.35

ym. The data show reasonably linear behavior in a plot of the

natural logarithm of the absorption coefficient versus photon

energy, with some additional absorption due to residual chromium ions.

This research was sponsored by Lawrence Livermore National

Laboratory.

1. R. T. Swimm, Y. Xiao and M. Bass, "A Calorimetric Study

of Optical Absorption of Suprasil W-l Fused Quartz at

Visible Near IR and Near UV Wavelengths", accepted for

publication in early 1985 in Applied Optics.

2. John D. Dow and David Redfield, Phys . Rev. B 5, 594 (1972)

and references therein.

3. E. T. Arakawa and M. W. Williams, J. Phys. Chem. Solids

29, 735 (1968)

.

*Antonio Balbin Villaverde, Instituto de Fisica, Depto Eletronica

Quantica, Universidade Estual de Campinas CP. 6166, 13100 - Campinas - S.P. Brazil

Figure. Plot of Absorption Coefficient for Sapphire vs Photon

Energy. Indicated lines show Cr^+ absorption bands. (Note that

there is a data point in the upper right corner)

.

165
Sapphire Absorption vs

Photon Energy

-2

1x10 i I

i ii i i I

i i » i I

i » i i I i i i i i

-3

1x10 U E

z

uy

-4

1x10

O

u

z

o

o

un<

lxlO

5

Cr

3 V

O

o o

oo

J , 1

I

' I I I I I I ' 1

I I ' I

1

I I t 1.0 1.5 2.0 2.5

PHOTON ENERGY [eV]

3.0 3.5

166
OPTICAL PROPERTIES OF ION

BEAM IRRADIATED MOLYBDENUM

LASER MIRRORS AS STUDIED

BY ELLIPSOMETRY+

John A. Wool lam, George H. Bu-Abbud,

and David L. Mathine

Department of Electrical Engineering

University of Nebraska, Lincoln, NE 68588-0511

David Poker

Solid State Division

Oak Ridge National Laboratory

Oak Ridge, TN 37830

David Ingram and Peter Pronko

Universal Energy Systems

Dayton, OH 45432

Molybdenum mirrors are widely used in high energy lasers because of

their desirable high temperature thermal properties such as high thermal

diffusivity, low thermal expansion coefficient, and high laser damage

threshold (1). It is also stiff so it can be attached to water cooled

backs. However it is nearly impossible to diamond-turn the surface, and

mechanical polishing is mainly used. Ion beam processing of materials

is of considerable interest, and sizable literature in this field is

developing (2). Heavy ion implantation into metal surfaces can radically change surface properties, as a result of chemical changes and

enhanced atomic kinetics.

In this paper we report on implantation of Mo ions into polished

molybdenum surfaces to investigate the effects of implantation of

surface roughness, and optical reflectivity. The motivation is to

develop ion beam techniques for improving the reflectivity and (surface

smoothness) over a wide spectral range. Information on the index of

refraction, and extinction coefficient as functions of wavelength are also obtained.

Three sets of mirrors were prepared from rolled sheet stock of

molybdenum, and polished with a series of grits down to a final cloth

lap using 1 micron diamond paste.

Samples were irradiated with 150 kv Mo ions with fluences of 0, 2, 4,8,

and, 16 x 10 15 ions 1 cm

2 directed at separate sections of the sample.

Thus the starting surfaces for the various fluences were identical.

Each sample was held at a separate temperature: 25°C, 250°C, and 500°C

respectively.

+Research supported by the College of Engineering, University of

Nebraska, The Department of Energy, and the National Science Foundation.

167
El 1 i psometric data were taken with both null and automated rotating

analyzer systems for angles of incidence near the principle angle for

each wavelength. Data were analyzed by comparing the measured

el 1 ipsometric parameters i> and a with those calculated assuming several

possible geometrical models. The Marquardt algorithm was used to find

the minimum of the sum of squares between measured and calculated

ip's and A's (3).

The results are as follows: the reflectivity is found to increase as a function of fluence, but most of the increase is in the range up to 4 x 10 15 ions/cm2

. This statement is true no matter what wavelength is used

in the 365 to 800 nm range, although the absolute value of reflectivity

depends on wavelength of course. The fluence for maximum reflectivity

is reached earlier for higher temperatures and shorter wavelengths.

We used the index of refraction and extinction coefficient data, along

with the Bruggeman effective medium theory (EMA) to analysis what is

happening physically at the surface (4). The following models were

assumed:

1. A bare surface of unknown refractive index.

2. A bare surface consisting of molybdenum metal which is

microscopically rough. (In the EMA, voids plus Mo are the assumed

constitutents)

.

3. A bare substrate including a mixture of voids, Mo, and MoOo. (ESCA

measurements were used to identify the presence of small amounts of

Mo0

2 ).

Several other models were tried by the sum of the squares of differences

of experimental and calculated ij/s and A's were unreasonably high.

The best fit to the data came by using Model 3, when the fraction of

void was 0.2, Fraction Mo was 0.8, and fraction Mo0

2 was less than

0. 01. This fraction void is consistent with a mi crostructure of

hemicyl inders. As a function of fluence the fraction Mo reaches a maxjmum (fraction void reaches a minimum) for fluences in the 2 to 4 x 10 15 ions/cm2 range, consistent with the reflectivity reaching a maximum

in the same range.

References

1. J.M. Bennett, S.M. Wong, and G. Kraus, Applied Optics _19, 35662

(1980)

2. Metastable Materials Formation by Ion Implantation , Materials

Research Society Proceedings, Vol. 7, S.T. Picroux, and W.J. Choyke,

Editors, 1982.

3. G.H. Bu-Abbud, N.M. Bashara, and J. A. Wool lam, "Sensitivity

Correlation Test of Variable Wavelength Variable Angle El 1 ipsometric

Solutions", accepted for publication in Thin Solid Films, 1985.

4. D.E. Aspnes, J.B. Theeton, and F. Hottier, Phys. Rev. 320 , 3292

(1979).

168
CRYSTAL FIELD ENERGY LEVELS AND OPTICAL ABSORPTION

INTENSITIES OF Ni 2+ :MgF

Bing Zhang, Ji-Kang Zhu and Song-Hao Liu

Anhui Institute of Optics and Fine Mechanics, Academia Sinica

P.O. Box 25, Hefei, Anhui, People's Republic of China

One-electron energy levels and wave functions of laser crystal Ni 2+ :MgF

2 with

lower symmetric crystal fields D^ are calculated by use of the spinunrestricted MS-Xa method. The calculated value of lODq is in much better

agreement with the experimental result than another theoretical value which

was based on higher symmetric crystal field consideration^ ^ . By

analyzing 3 T

2 g and 3 T^g energy levels related with laser operation the

splitting values of 3 T

2 g and 3 T^g in lower symmetric crystal field have

been derived. MS-Xa calculation of magnetic dipole intensity by means of

Karplus electronic charge partition method has been reported for the first

time. The oscillator strengths of electric dipole coupled with vibration

between ground state and 3 T g state have been estimated. It is shown

theoretically that ^A^-^T^ is magnetic dipole transition and 3 A

2 g- 3T^g

is electric dipole transition coupled with vibration. Comparisons between

the calculated and experimental results of 10D

q

and oscillator strengths

are shown in Tables 1 and 2.

[1] S. Larsson, J. W. D. Connolly, Chem. Phys. Lett., 20, 323 (1973).

169
Table 1. One--Electron Eigenvalues and lODg for Crystal Ni 2+ :MgF

2

Energy Levels Eigenvalues 10D

q

(cm"l)

Oh °2h (cm *) This work Expt. Calc. 1 1

J

3B n

39

7594

3T

29

3B

29

3A

7780

8011

7795 7407 9500

9835

3T

19

3B

S9

3B

!9

11105

11360

Table 2. Magnetic Dipole Oscillator Strengths f of 3T

2g

Energy Levels f (xl0"6) f (xlO" 6

)

Oh D2h This Work Expt.

3B „

39

4.4

3tX 29

3 B „

29

3A

4.5 5.0

4.6

170
STATUS OF OPTICAL CONSTANTS OF SOLIDS FROM X-RAY TO MM-WAVE REGION

E.D. Palik

Naval Research Laboratory

Washington, DC 20375

INTRODUCTION

As editor of the Handbook of Optical Constants of Solids (1), I have obtained a bird's-eye view of the quantity and quality of optical constants for 37 solids

of technological and physics interest. These include 11 metals - Al , Cu, Au,

Ir, Mo, Ni, 0s, Pt, Rh, Ag, W; 14 semiconductors - CdTe, GaAs, GaP, Ge, InAs,

InSb, InP, PbSe, PbS, PbTe, Si, a-Si, SiC, ZnS; 12 insulators - As2Se3, AS2S3

C (diamond), LiF, LiNK>3, KC1, Si02, a-Si02 , SiO, Si3N4, NaCl, Ti0£. Twenty one critiquers have examined the existing literature for these materials and have

tabulated a single set of refractive index n and extinction coefficient k for as wide a spectral region as possible. Examples of a metal Ag, a semiconductor

Si and an insulator a-Si02 (silica) are given in Fig. 1. Some effort is made

to discuss the measurement techniques and the quality of the data. The problems encountered here with measurements and data are representative of all the

solids studied. The Handbook also contains 11 chapters on how to determine n and k in various spectral regions.

EXPERIMENTAL TECHNIQUES

The experimental techniques are numerous and change as the spectral region

changes. In the x-ray region 1-500 A (12500-25 eV) samples are generally

evaporated thin films removed from backings, so that transmission/reflection

measurements can be made with x-ray or synchrotron sources and spectrometers.

For any material but especially for metals, external total reflection is done

to determine n where it is only slightly less than unity, and n»k holds true.

In the UV region 25-6 eV (500-2000 A) reflectance of bulk samples is made,

followed by Kramers-Kronig analysis with due consideration of frequency limits.

For opaque solids ellipsometry or variable angle-of-incidence reflectivity are dominant over normal-incidence unpolarized reflectivity. In the near infrared

generally near or below the fundamental band gap, a thin slab sample or a film

on a substrate are used for transmittance and reflectance measurements. In the

transparent region below the band gap thick samples can be used to determine k

from a transmittance or a caloriraetry measurement. Interestingly, the prism

minimum-deviation technique is still the best for determining n to 5 significant figures. In fact, Ruben's data for NaCl of nearly 90 years ago (2) is in

agreement with todays data (3) to 4 figures, usually. Measurement of

interference-fringe spacing is the next best technique for determining n. As

the optical-phonon region is approached in the far infrared, it is necessary to

go to reststrahlen reflectivity measurements fitting with a Lorentz-oscillator

model or Kramers-Kronig analysis if no thin films are available. Fortunately,

asymmetric Fourier transform spectroscopy gives both phase and amplitude of R

directly with no model or analysis assumptions (4). Techniques like

ellipsometry and variable angle-of-incidence reflectance have not found general

use in the infrared.

There are a number of special-purpose measurement techniques such as emittance

(5), internal reflection critical-angle determination (6), launching and

retrival of guided modes for thin transparent films (7), interference effects

to determine both n and k in thin films (8). Many of us have forgotten the

171
measurement of capacity of dielectrics well beyond the ram-wave region to

determine the low-frequency real and imaginary parts of the dielectric

function. While the mass absorption constant was measured for many elements

in the x-ray region early in the century (9), it now proves to be convenient to

use a model of Henke et al. (10) to calculate this quantity to obtain k. This

model for chemical elements as well as compounds is based on the atomic

scattering cross-section of the elements and allows calculation of the

absorption edges in the x-ray to UV region before chemical bonding begins to

perturb the valence electron states.

In addition to the chapters in the Handbook, there are a number of other

reviews of the many ways to determine n and k (11-15).

SAMPLE PROBLEMS

While different experiments in different spectral regions give rise to a myriad

of accuracy and precision problems, samples also vary from lab to lab. Problems include: 1) Bulk samples are mechanically polished with grit rather than

chemically polished. This can affect the reflectivity minimum and maximum in

the reststrahlen region and becomes more important as the wavelength gets

shorter; 2) Bulk sample surfaces grow native oxides when polishing or cleaving

is done in air. This problem is most important where the absorption edge of

the dielectric layer 10-20 A thick occurs (generally > 4 eV). It also affects

the ellipsometric determination of e \ and e 2 , the real and imaginary parts of

the dielectric function (16), and should be included in the modeling used to

obtain the dielectric function or native-oxide-free surfaces should be measured

in the first place (such as in laboratory UHV apparatus; 3) Roughness is also a layer which can be treated as an effective medium and if not considered, gives

"psuedo" optical constants; 4) An especially bad actor is the deposited,

evaporated or CVD grown film on a substrate. Authors invariably do not

characterize films several different ways to determine stoichiometry

,

roughness, void fraction, crystallinity , etc., so the optical constants vary

from lab to lab. This has been especially true of deposited metals (17). Any

film grown on a substrate will be strained, so that the refractive index is

affected (for example, Si02 on Si (18)), or the band gap is shifted (19).

MODELS

Models are especially useful in accounting for a) refractive index in the

transparent region (Sellmeier equation), b) dielectric function in the

reststrahlen region (Lorentz oscillator), and c) dielectric function in the

free-carrier plasma region (Drude model).

An ultimate Sellmeier equation which includes contributions of several higherfrequency interband transitions represented as classical oscillators as well as low-frequency lattice oscillators is

A E X 2 - (hu)) 2 Gi G2 03 n2 = 1 H In 5 T + — ? + —? ? + —5 5 ,

tt E0

Z - (hu) Ei - (hw) E 2 - (hw) E 3 - (hw)

where EQ is the fundamental band gap and E\ and E2 are the next higher-lying

band gaps, and E3 is the transverse optical phonon frequency. This formula has

been used to fit a wide variety of semiconductors over a wide range of

frequency from the fundamental band gap to the first reststrahlen band,

generally reproducing the experimental data to 2-4 figures (20).

The Lorentz-oscillator model gives

172
= ei + ie2 = (n + ik)2 = et 1 +

2 2

oj-j^ _ 03^ - irw

where co-p and wl are the transverse and longitudinal optical photon frequencies,

respectively, T is the damping constant and £«, is the high-frequency dielectric

constant. The corresponding values of k are probably good to one significant

figure near the peak and poorer in the wings as measurements on thin films

indicate (21). There are few examples of measurement of reflectivity R with

both oscillator and Kramers-Kronig fits (22). For CdTe the results agree to

±30%. The dc dielectric constant can be estimated by letting w+0.

Free-carrier absorption is often analyzed with the Drude model with

2 1

£ = £c

(I) 1 - P_

to(w + iy)

For metals it is useful for extrapolating to longer infrared wavelengths where

R>0.95. The plasma reflection edge is fitted for semiconductors to obtain the

plasma frequency = 4jrNe2/m*e00 and damping constant y (23). Here, N is the

free-carrier density and m* is the effective mass. Then n and k can be

calculated. This k is invariably too small as transmittance measurements show,

because n generally dominates the reflectivity. Thus, measurement of R is a good way to get n; measurement of transmission absorption is a good way to get

k. Data near 1 ym for Ag in Fig. 1(a) do not agree between two labs probably

because of differences in sample preparation. Polarimetric measurements were

used in each case (24,25). Generally, Si of high resistivity > 1000 ftcm is

used to minimize free-carrier effects. However, some absorption shows up near

100 ym in Fig. 1(b).

The Henke model does not include x-ray fine structure seen in experiments for

Si near 10~2 ym in Fig. 1(b). Note that M absorption edges of atomic Si are smeared into interband transitions as are 0 edges of Ag and M and L edges of Si

and 0 for Si02« Absorption edges of c- and a-Si02 would be similar since

chemical bonding does not affect core levels very much. It is just these

differences, however, which are exploited in core-level spectroscopies.

SOME OBSERVATIONS

We find that room temperature in the literature is anything from 292 to 300 K.

It is surprising how many authors neglected to report this number; it is

usually important when you are measuring n to more than 4 significant figures

or are measuring the band-edge absorption of a semiconductor.

In Fig. 1 we show values of n and k for Ag, Si and a-Si02, plotted from

detailed numerical tables. I had never seen k displayed over such a wide

spectral region before. Since a = 4rrk/X, and I/I 0 = (l-R)^exp (-ax) for the

simple case of no multiple reflections, it is easy to see how thickness x must

vary over such a wide range to do a transmission experiment. For example, a Si

sample thin enough for I/I 0 = 0.2 at 10 ym (k = 10~5, n = 3.4, r = o.3) is 0.71

cm thick, while at 10"3 ym (k = 10~ 5

, n«l, R«0), the sample must be 0.013

cm thick. Note that a film 130 ym thick for x-ray measurements can be handled

unsupported, whereas a film used to measure band-edge absorption (k=10~l) in

the near infrared must be ~ 1 ym thick and is generally mounted on a substrate.

Also, a film -1 ym thick (k=l) is needed to measure transmission at the TO

frequency of GaAs, for example.

173
A collection of data from several labs over a wide spectral range cannot be

easily massaged to give uniformity in accuracy. Most measurements were made to

locate optical phonons or interband transitions rather than to determine n and

k. Therefore, experimenters paid more attention to precision to resolve peaks

in a. Some general observations are; 1) Al, Si, GaAs, NaCl, Sit>2, a-S102, LiF

have been worked upon over the widest spectral range by the largest number of

workers; 2) Where minimum-deviation or interference-fringe techniques have been

used, the values of n are good to 3-5 figures with a caution about temperature.

Where transmission measurements have been performed, values of k are usually

good to 1-2 figures, i.e., two measurements in two labs agree to 1-2 figures;

3) Kramers-Kronig analysis of near-normal incidence reflectivity of NaCl in the

6-15 eV region in two laboratories (26,27) disagree in n and k to ±20% because

the uncertainty in R is ±3%; k is generally too small in the ends of spectral

regions especially if n>>k; 4) We feel that spectroscopic ellipsometry provides

the most consistent numbers in the 1.5-6 eV region, especially when native

oxides and roughness are accounted for and transmission data are used when

k<<n. We expect n and k are reliable to 2-3 figures; 5) In transparent regions

where calorimetry is done (visible and near infrared), k is found to be ~10~^,

but numbers vary by factors of two from sample to sample. This absorption is

probably due to impurities and structural defects, once surface effects are properly accounted for; 6) One of the main errors in the accuracy of the data

quoted in the tables is in reading the graphs given in the literature. Authors

often omit the fiduciary marks 2-9 on log scales. Some researchers kindly

provided original numerical tables; 7) The least studied materials as far as workers and spectral range are concerned are Ir, Os , Rh, InP, InAs, LiNb03,

Si3N4; 8) Conspicuous by their absence in the Handbook are Cr, Fe, Zn, Sn, CdS,

Se, Te, GaSb, KBr, MgF2 , C (graphite), AI2O3. While data exist, no collection

was made due to lack of critiquers.

While tables of n and k from x-ray to mm-wave region with n and k accurate to

3-4 figures are desirable, this is not the real experimental world. Throughout

the tables, n in transparent regions is probably good to 3-4 figures, while in

opaque regions it is good to 1-2 figures, k is good to 1-2 figures throughout

(I have not found measurements of k from two laboratories in agreement to 3

figures)

.

OTHER COLLECTIONS OF n AND k

Several reports on optical properties have proved useful during the preparation

of the Handbook. They include; a) "The Refractive Index of Alkali Halides" by

Li (3) in which the refractive index is fitted with a Sellmeier equation; b)

"Optical Properties of Some Insulators in the Vacuum Ultraviolet Region" by

Haelbich et al. (28) in which all the x-ray UV work of a number of insulators

are listed; c) "Refractive Index of Optial Materials for the Infrared Region"

by Moses (29) and d) "Optical Materials for Infrared Instrumentation" by

Ballard et al. (30) give refractive index and other physical properties of many

window materials; e) "Properties of Optical Materials" by Wolfe (31) cites may

optical properties in numerous figures; f) "Optical Properties of Metals" by

Hass and Hadley (32) is an old reliable source, while g) "Optical Properties of

Metals" by Weaver et al. (33) is more up-to-date.

REFERENCES

1. Handbook of Optical Constants of Solids, (E.D. Palik, ed.), (Academic

Press, New York, 1985).

174
2. H. Rubens and E.F. Nichols, Ann. Phys. Chem. j>0, 418 (1897); H. Rubens

and A. Trowbridge, Ann. Phys. Chem. 60_, 724 (1897).

3. H.H. Li, J. Phys. Chem. Ref. Data _5> 329 (1976).

4. J.E. Eldridge and P.R. Staal, Phys. Rev. B16, 4608 (1977).

5. D.L. Stierwalt and R.F. Potter, in "Semiconductors and Semimetals", Vol.

3, p. 171, (R.K. Willardson and A.C. Beer, eds.), (Academic Press, New

York, 1967).

6. D.C. Gupta, Solid State Electr. L3, 543 (1970).

7. E.D. Palik and R.T. Holm, Opt. Eng. L7, 512 (1978).

8. J. Shamir and P. Graff, Appl. Opt. 14, 3053 (1975); J. Shamir, Appl Opt.

1_5, 120 (1976).

9. E.P. Bertin, "Principles and Practices of X-Ray Spectrometric Analysis",

Chap. 2, (Plenum, New York, 1970).

10. B.L. Henke, P. Lee, T.J. Tanaka, R.L. Shimabukuro and B.K. Fujikawa, Low

Energy X-Ray Diagnostics-1981 , AIP Conference Proc. No .75, (D.T. Attwood

and B.L. Henke, eds.), (American Institute of Physics, New York, 1981).

11. E.E. Bell, in "Handbuch der Physik", Vol. 25, Part 2a, p. 1, (S. Flugge,

ed. ), (Springer-Verlag, Berlin, 1963).

12. F. Abeles, in "Progress in Optics", Vol. 11, p. 251, (E. Wolf, ed.)

(North-Holland, Amsterdam, 1963).

13. H.E. Bennett and J.M. Bennett, in "Physics of Thin Films", Vol. 4, p. 1,

(G. Hass and R.E. Thun, eds.), (Academic Press, New York, 1967).

14. O.S. Heavens, "Optical Properties of Thin Solid Films", (Dover, New York,

1965).

15. P.H. Berning, in "Physics of Thin Films", Vol. 1, p. 69, (G. Hass, ed.),

(Academic Press, New York, 1963).

16. D.E. Aspnes, J. Phys. (Paris), C10 , 3 (1983).

17. E. Shiles, T. Sasaki, M. Inokuti and D.Y. Smith, Phys. Rev. B22 , 1612

(1980).

18. E. Taft and L. Cordes, J. Electrochem. Soc. 126 , 131 (1979).

19. G.G. Macfarlane, T.P. McLean, J.E. Quarrington and V. Roberts, Phys. Rev.

Lett. 2, 252 (1959).

20. A.N. Pikhtin and A.D. Yas'kov, Sov. Phys. Semicond. _12, 622 (1978); Fiz

Tekh. Poluprovodn. 12_, 1047 (1978).

21. S. Iwasa, I. Balslev and E. Burstein, in Seventh Intern. Conf . Phys.

Semicond., Paris 1964, (Dunod, Paris and Academic Press, New York, 1964),

p. 1077.

22. A. Manabe, A. Mitsuishi and H. Yoshinaga, Japan. J. Appl. Phys. 4_, 581

(1965).

23. R.T. Holm, J.W. Gibson and E.D. Palik, J. Appl. Phys. 48^, 212 (1977).

24. B. Dold and R. Mecke, Optik 22_, 435 (1965).

25. P. Winsemius, F.F. van Kampen, H.P. Lengkeek and C.G. van Went, J. Phys.

F 6, 1583 (1976).

26. D.M. Roessler and W.C. Walker, J. Opt. Soc. Am. _57, 835 (1967); Phys.

Rev. 166 599 (1968).

27. T. Miyata and T. Tomiki, J. Phys. Soc. Japan 24_, 1286 (1968); 22_, 209

(1967).

28. R.P. Haelbich $ M. Iwan and E.E. Koch, "Physik Daten, Phyics Data",

(Fach-Information Zentrum, Karlsruhe, 1977).

29. A.J. Moses, "Refractive Index of Optical Materials in the Infrared

Region", Report on Contract F33615-68-C-1225, Air Force Systems Command,

Hughes Aircraft Company, Culver City, CA, 1970).

175
30. S.S. Ballard, K.A. McCarthy and W.L. Wolfe", Optical Materials for

Infrared Instrumentation", Report from Infrared Information and Analysis

Center, University, of Michigan, Willow Run, Laboratories, Ann Arbor, MI

1959.

31. W.L. Wolfe, in "Handbook of Optics OSA", Section 7, (McGraw-Hill, New

York, 1978).

32. G. Hass and L. Hadley, in "AIP Handbook", Section 6, (McGraw-Hill, New

York, 1972).

33. J.H. Weaver, C. Krafka, D.W. Lynch and E.E. Koch, "Physik Daten, Physics

Data", "Optical Properties of Metals," Vol. 18-1, (Fach-Information

Zentrum, Karlsruhe, 1981).

Fig. 1 Log-log plot of n ( ) and k ( ) vs. wavelength in urn for Ag(a), Si(b) and a-Si02(c).

icr4

io- hi

XT I

'

'

, L 2.3

/ , I N l N2.3

/ I "2.3 /

M,

i I mil i i i I mil i itl mil i i i 1 1 1 ill i i i 1

1

l0

x

10"' !0

U 10' 10 100 WAVELENGTH (fim)

ICT

1 10° WAVELENGTH (|im)

176
OPTICAL CONSTANTS AT X-RAY WAVELENGTHS*

D. Y. Smith, A. E. Williamson*, and T. I. Morrison

Argonne National Laboratory

Argonne, IL 60439

The present paper is a preliminary report on optical properties of selected

elements at x-ray wavelengths as derived from measured absorption spectra.

Need for such data is an outgrowth of the world-wide development*" of synchrotron radiation sources: the reflectance is of interest for designing

grazing-incidence mirrors,^ and knowledge of optical constants is required

to calculate the properties of multilayer elements,^ as well as to analyze

differential absorption and anomalous scattering experiments.^

Generally, the only optical data available at x-ray wavelengths are for bulk

absorption. In principle the other optical properties may be derived from

these using the Kramers-Kronig relation"*

i \ . 2 r « a)'k(a)')doj"

n<u>) - 1-Pl0 — r , (1)

a) - a) that connects the real and imaginary parts of the complex refractive index,

N(u) = n(w) + ik(w).

The x-ray photoelectric mass absorption cross section u(w), the quantity

usually tabulated, is related to the extinction coefficient k(w) by

k(u>) = cpu(o>)/2u), (2)

where c in the speed of light in vacuum and p is the density of the material.

The primary difficulty in applying Eq. (1) is that knowledge of k(co) for all

a) is required. While good absorption data are generally available for hard

x-ray energies, UV and soft x-ray data are often uncertain or fragmentary.

This uncertainty at low energies would seem of minor importance for hard x- ray processes. However, we have found that systematic underestimates of

oscillator strength in the low-energy portion of the data^ we analyzed, gave errors in n(u)-l exceeding 30-35% at "fito > 5 keV for roughly half the elements,

An important point evident from Eq. (1) is that the low-energy absorption

contributes a smoothly varying component to n(w) at high energies. This

contribution is proportional to the integrated oscillator strength at low

energies, but is insensitive to its distribution. Thus, if the net absorption strength in the region of uncertainty can be estimated, a KramersKronig analysis can be made despite the lack of reliable low-energy spectra.

A major guide for estimating the unknown or uncertain oscillator strength is

This work supported by the U.S. Department of Energy.

Present address: Department of Physics, University of California, Berkeley,

California 94720.

177
the Thomas- Re iche-Kuhn f-sum rule 7,8

.00 2 2

J wk(a))da) = tt e /m, (3)

o where «yr, e, and m are the electron number density, charge, and mass, re- spectively. Provided reliable x-ray absorption data at high energies are available, their contribution to the f sum may be calculated and the remaining oscillator strength assigned to the low-energy region so that Eq. 3 is

satisfied. In the cases in which the absorption of individual electron

shells (or groups of shells) can be identified separately, an even more powerful guide is provided by partial f sums^. An example of this

procedure is given by Shiles etal.^

In the present study, the photoelectric cross sections above 10 eV as compiled by Biggs and Lighthill^ from experimental and theoretical sources were used. These consist of piece-wise continuous four-term polynomial fits

to the absorption in regions bounded by the various absorption edges, a form

particularly convenient for analytic integration of Eq. 1. To estimate the

net absorption strength S below 10 eV we have used the f-sum rule, assuming

the absorption to be concentrated at a single frequency os^,;

k(u>) = S 6(u>-u> ), 0 < -fiu) < 10 eV, (4)

where -fiw < 10 eV. By Eq. (1) v

2 2 ,oo

id S = i e J^/m - f,„ „ u)k(o))do). (5) v

; 10 eV

The properties at x-ray wavelengths are virtually independent of wv

, but

experience with materials for which UV refractive index data are available

indicates that 1iw ~ 9.5 eV is a reasonable choice,

v The absorption below 10 eV is dominated by the most loosely bound electrons;

hence, S is expected to be roughly equal to the number of valence electrons. In approximately half of the elements this expectation held for

Biggs and Lighthill's cross sections. ^ In these cases the refractive index

was calculated directly from Eq. 1 using S determined via Eq. 5. In the

remaining half of the elements — particularly the transition elements — S was significantly greater than the number of outer-shell electrons. From a study of partial f sums it became clear that this arose from a deficiency in

absorption strength between 10 and 1000 eV. In most cases this deficiency

could be ascribed to an underestimate of absorption by weakly bound d or f

electrons. For these elements the low-energy data were scaled to make their

integrated oscillator strength approximately equal to the occupation number

of the shells involved in the absorption. This reduced S to approximately

the number of valence electrons as expected. The optical constants were

then calculated using the modified data. The results are best presented in

terms of the complex atomic scattering factor for forward scattering:

2 2 2 2 f^O) = (mw Mnpe )[l - e (w)], and f

2 (0) = (mw /4irpe )e

2

(oj), (6)

where e(o)) = e^(w) + ie (w) denotes the complex dielectric function.

Representative results tor metallic platinum are given in Fig. 1.

178
Platinum Z=78

Pig. 1 The real and imaginary parts of the atomic scattering factor for forward

scattering by metallic platinum. The solid curve was calculated from the cross- section data of Biggs and Lighthill, Ref. 6, in which the region below ~1 keV was treated approximately. The results of Henke et al . , Ref. 1

1

, who studied the lowenergy region in detail are shown for comparison.

The optical properties relevant to reflecting optical elements are the

reflectance, critical angle for total external reflection, Brewster's angle,

etc. Experience^ indicates that, at the energies of interest here,

continuum electrodynamic theory holds approximately even though the x-ray

wavelengths approach atomic dimensions. In particular, the reflectance as a function of angle may be calculated using the Fresnel equations. ^ The

results for the reflectance of a smooth platinum surface for unpolarized

light are given in Fig. 2. (In practical mirrors these results must be

reduced by a factor accounting for surface roughness, see Ref. 13.)

1t

Fig. 2 The reflectance for

unpolarized x-rays of a smooth

surface of metallic platinum as calculated from the forward

scattering factors given in Fig. 1 via the Fresnel equations. Angles

are" measured relative to the

surface.

0

u

c

CO *»u

©

DC

Legend

5 MIIMridlani

10 Ml l llradlans 15 Mllllndlini

20 Mllll ra dlans

25 MJIJUadjans 30 MJIHradlans. 35 Mllllradlans 40 Mjmrjdjani 45 MIMIradlana 50 Mllllradla ni

100 Mllllradlana 200 MJIIJridlan* 300 Mllllradlans 400 Mllll radlans 500 Mllllradlans

Energy in eV

179
The critical angle for total external reflection 9 (as measured relative to

the surface) is given by

8 (a)) = cos

1 n(w), (7)

c *

in the absence of absorption. Values of 9 C( W ) for our exemplary substance

platinum are given in Fig. 3. For k ^ 0 the reflectance, while not total,

approaches unity for grazing angles less than 9 c provided the photon energy

is not near an absorption edge, cf. Fig. 2.

m

C

Fig. 3 The critical angle

(measured relative to the surface)

for total external reflection for

a smooth metallic platinum surface

calculated via Eq. 7 from the

forward scattering factors given

in Pig. 1

.

Energy in eV

References and Footnotes

1 . Current Status of Facilities Dedicated to the Production of Synchrotron Radiation , National Research Council (National Academy Press, Washington, 1983).

2. W. Gudat and C. Kunz, in Synchrotron Radiation , C. Kunz ed. (Springer, Berlin, 1 979)

3. E. Spiller, in Low Energy X-Ray Diagnostics-1 981 , D. T. Attwood and B. L. Henke, APS

Conf. Proc. No. 75, (American Institute of Physics, New York, 1981).

4. R. W. James, The Optical Principles of the Diffraction of X-Rays , (Cornell, Ithaca,

1965).

5- J. S. Toll, Phys. Rev. _104, 1760 (1956).

6. F. Biggs and R. Lighthill, Analytical Approximations for X-Ray Cross Sections II , Sandia Report SC-RR-71 0507, (Sandia National Laboratory, Albuquerque, 1971).

7. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms , (Springer-Verlag, Berlin, 1957).

8. For the purposes of this preliminary study the non-relativistic f-sum rule is

sufficient. In more detailed work involving heavy elements, core electrons should be

treated relativistically. The largest relativistic correction to the f sum arises

from the mass-velocity effect. This may be thought of as. reducing the contribution of an electron to the f sum by a factor [l-(5/3mc ) T0

+ 0(v /c )], where T0 is the

expection value of the electron's kinetic energy in the ground state and v is its

velocity; See J. S. Levinger, M. L. Rustig, and K. Okamoto, Phys. Rev. 106 , 1191 (1957). This correction has been discussed independently in connection with anomalous

scattering factors by D. T. Cromer and D. Liberman, J. Chem. Phys. _55, 1891 (1970),

and M. S. Jensen, Phys. Lett. A 74 , 41 (1979).

9. D. Y. Smith and E. Shiles, Phys. Rev. B _1_7 , 4689 (1978).

10. E. Shiles, T. Sasaki, M. Inokuti, and D. Y. Smith, Phys. Rev. B 22, 1612 (1980).

11. B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, and B. K. Fujikawa, Atomic Data

and Nuclear Data Tables 2J_, 1 (1982).

12. F. Stern, in Solid State Physics , edited by F. Seitz and D. Turnbull (Academic, New

York, 1963), Vol. 15-

13. D. H. Bilderback and S. Hubbard, Nucl. Instrum. Methods 195, 91 (1982).

14. For further details, see J. A. Prins, Z. Physik 47, 479 (1928)

.

180
VACUUM ULTRAVIOLET LOSS IN MAGNESIUM FLUORIDE FILMS

0. R. Wood, II and P. J. Maloney

AT&T Bell Laboratories

Holmdel, New Jersey 07733

and

H. G. Craighead and J. E. Sweeney

Bell Communications Research

Holmdel, New Jersey 07733

Because MgF 2 is transparent to wavelengths as short as 1100 A in

the VUV, 1 it finds extensive use for lenses and windows in this

region. Major applications can be found in UV lasers,

spectroscopy and space astronomy. Another important use of MgF 2 is as an evaporated coating onto aluminum, 2 r3 where it greatly

increases the VUV reflectance and also retards oxidation. In

practice the reflectance obtainable by this means is limited to

83 - 85% 4 ' 5 at 1216 A because of the high loss of the evaporated

material, 6 which is 10 4 times that of single crystal MgF?. If

the loss were as low as single crystal material,' a reflectivity

of 94% would be possible, 4 '** exceeding any known value at this

wavelength.

We have investigated the excess loss in evaporated films and

found^ that it is due to scattering from inhomogeneities and

absorption from the low energy tail of an exciton band. Both of

these mechanisms were found to be strongly dependent on the

degree of crystallinity of the film, which is largely determined

by the substrate temperature during deposition. Our study has

allowed us to produce films with extinction coefficients as low

as 0.005, several times better than previously reported. Our

study included a series of measurements from 1050 to 1600 A of

the optical constants of evaporated MgF 2 films deposited on

single crystal LiF substrates. These films were produced over a wide range of deposition rates and substrate temperatures.

Transmission electron microscopy was used to determine the grain

size of the resulting polycrystalline evaporated film.

Our measurements of the optical constants of MgF 2 films (1000 A

thick) at 1216 A deposited on room temperature LiF substrates at

different rates are shown in Table I, together with the optical

constants of a MgF2 crystal. Independent of deposition rate, the

MgF 2 films are characterized by a lower index of refraction and

an extinction coefficient some 10,000 times higher than the

single crystal material. As was found in the earlier work, 6 the

highest deposition rates resulted in the highest losses. In

contrast to the earlier work on MgF 2 _ OVercoated aluminum mirrors,

however, no improvement in the optical properties of these films

181
Table I. Optical Constants of MgF 2 Film Deposited onto Room

Temperature LiF Substrate Vs Deposition Rate

Evaporation Refractive Extinction

rate (A/sec) index cbef f

2 1.69 0.046

5 1.70 0.053

14 1.71 0.041

150 1.69 0.064

Crystalline 1.73 0.000003

with increasing deposition rates was seen for deposition rates in

the 2-45 A/sec range. This dependence suggests that the film

growth process is more important than impurity incorporation.

We have found that when impurities are inconsequential the degree

of crystallinity (i.e., the polycrystall ine grain size)

determines film absorption regardless of how the crystalline

state was obtained. We have further found that the losses

observed in evaporated MgF2 films in the wavelength range from

1050 to 1600 A can be fully accounted for by a simple model that

includes absorption by the low energy tail of an exciton band and

scattering from inhomogeneities at the surface and in the body of

the film. Such a model can account for the wavelength dependence

of the absorption coefficient of the films deposited at various

substrate temperatures and gives a value for the band gap energy,

E„ = 12.3 eV, that agrees with previous measurements. 10

Furthermore, in the region where the absorption coefficient

appears to obey the Urbach relation [k ~ exp(E/Eg)] the model

leads to values for the character istic energy, Es

, that are close

to those of other materials. 11 Previous attempts to explain the

observed wavelength dependence of the absorption coefficient led

to values for Eg that varied from 10.95 (for the most crystalline

films) to 8.8 eV (for amorphous films, gave abnormally large

values of the characteristic energy and led to explanations based

on the presence of impurities. 2

We now see that the attempt by Hutcheson et al.5 to significantly

improve the VUV reflectance of MgF 2 ~overcoated mirrors by varying

the deposition rate and substrate temperature, and that gave

little change in reflectance when the substrate temperature was

increased from 40 to 100 °c, and a decrease in reflectance at

higher substrate temperatures was probably unsuccessful because

of the conflicting growth requirements of the two films. A low

loss MgF2 film can best be produced at high substrate

temperatures, whereas, a high reflectance aluminum film is

destroyed at high temperatures.13 One solution to the problem of

fabricating a high reflectance mirror in the VUV would be to

overcoat a freshly evaporated Al film with a crystalline (i.e.,

low loss) layer of MgF 2 . This might be accomplished through the

use of pulsed laser annealing to neat the film and at the same

182
time minimize heating of the aluminum layer. Another possibility

might be to modify the m icr ost r uctur e by methods other than

heating such as low energy ion bombardment during deposition. On

the other hand, these techniques probably could not be used to

fabricate a low loss Al-MgF 2 interference filter for the VUV.

The large surface roughness of a low loss MgF2 layer,

particularly one with a large grain size, would result in

coupling to the surface plasmon 14 and would severely limit the

performance of an Al-MgF^ multilayer. Even so, it is thought

that the understanding of the important film parameters and loss

mechanisms gained in this study could eventually lead to improved

performance of MgF2 coated optics in the VUV.

References

1. A. Duncanson and R. W. H. Stevenson, Proc. Phys. Soc. London

I2f 1001 (1958)

.

2. G. Hass and R. Tousey, J. Opt. Soc. Am. M, 593 (1959).

3. P. H. Berning, G. Hass and R. P. Madden, J. Opt. Soc. Am. 50 f 586 (1960).

4. L. R. Canfield, G. Hass and J. E. Waylonis, Appl. Opt. 5_, 45

(1966) .

5. E. T. Hutcheson, G. Hass and J. T. Cox, Appl. Opt. H, 2245

(1972)

.

6. G. Hass and J. B. Ramsey, Appl. Opt. £, 1115 (1969).

7. D. L. Steinmetz, W. G. Phillips, M. Wirick and F. F. Forbes,

Appl. Opt. 6_, 1001 (1967).

8. W. R. Hunter, J. Opt. Soc. Am. M, 208 (1964).

9. 0. R. Wood, II, H. G. Craighead, J. E. Sweeney and P. J.

Maloney, Appl. Opt. 21, 3644 (1984).

10. G. Stephan, Y. LeCalvez, J. C. Lemonier and S. Robin, J.

Phys. Chem. Solids 2£, 601 (1969).

11. N. F. Mott and E. A. Davis, Electronic Processes in

Noncrystalline Materials (Clarendon, Oxford, 1979), p. 275.

12. A. S. Barriere and A. Lachter, Appl. Opt. 1£, 2865 (1977).

13. Yu. I. Dymshits, V. A. Korobitsyn and A. A. Metelnikov, Sov.

J. Opt. Technol. i£, 649 (1979).

14. E. Spiller, Appl. Opt. 11, 1209 (1979).

183
SURFACE EROSION INDUCED BY ELECTRONIC TRANSITIONS

Richard F. Haglund, Jr. and Norman H. Tolk

Department of Physics and Astronomy

Vanderbilt University

Nashville, TN 37235

The problem of damage to ultraviolet optical materials has been and continues

to be a major source of concern in the design and operation of high-power

lasers. Little fundamental understanding exists of the atomic-level mechanisms

which operate to produce this damage. However, recent experiments have

shown that irradiation of optical materials by electrons and photons at

energies characteristic of high-power and high-energy laser systems is an efficient cause of surface erosion. The experiments described here

are intended to illuminate the basic mechanisms associated with energy

absorption, distribution and localization leading to electronically induced

desorption, and to determine the role of defects in these processes.

In ultraviolet laser systems currently operating or under design, laser

fluences range up to several J/cm2 . The significance of these flux levels

can be put into context by observing that, for a KrF laser (248 nm), 1 J/cm2 of laser output corresponds to a flux of some 10^ photons per surface

site on the optical components experiencing the laser irradiation. In

electron-beam- pumped lasers, Bremsstrahlung X-rays produced by the deceleration

of submegavolt pump-beam electrons, as well as scattered or diffusing low-energy

electrons, will also irradiate nearby optical surfaces. It is becoming

clear that each of these sources of radiation is efficient in producing

Desorption I_nduced by Electronic Transitions (DIET), and that the most

abundant products of DIET processes are not ions but neutral atoms and

molecules. These kinds of processes may well be the most plausible microscopic

physical mechanisms responsible for the observed macroscopic optical damge.

In our experiments, controlled doses of low-energy electrons or synchrotron

uv photons are delivered to clean surfaces under ultra-high vacuum conditions.

Desorption products are identified by the characteristic line radiation

either from excited states or from fluorescence induced by laser pumping

of ground-state atoms and molecules. Substantial research has been performed

over the past decade on desorbing ionsJ However, our recent work has

shown that the overwhelming majority of desorbed particles are neutral

atoms and molecules, with yields often several orders of magnitude larger

than corresponding ion yields.

In the initial experiments, the excitation source was an electron beam

incident on single-crystal surfaces of NaCl and LiF. 2 By using varying

collection geometries, it was easy to distinguish the atomic emission line

spectra of the desorbed neutrals from the broad-band cathodoluminescence

of the substrate. Results of these experiments on several alkali halide

surfaces are shown in Fig. 1. The characteristic features of the experiments

include a gradually-rising yield of neutral excited-state alkalis as a function of electron energy, with some features corresponding to threshold

energies for various electronic transitions.

184
Fig. 1 Yield of excited-state neutral alkali atoms desorbed from

single-crystal alkali-halide surfaces under electron bombardment,

shown as a function of electron energy.

This same detection method was subsequently extended to photon-stimulated

desorption of excited neutrals. 3 The excitation source for these experiments

was the Tantalus storage ring at the University of Wisconsin Synchrotron

Radiation Center. Experiments were performed with photons in the energy

range from 40-200' eV, using a grazing-incidence "Grasshopper" monochromator .'

Figure 2 shows the optical emission intensity of desorbed excited Li atoms

as a function of the primary-beam photons, compared to the similar curve

for Li + ions and to the LiF photon absorption coefficient. In particular,

the main excitonic structure of the Li K-edge is evident in all three curves. The comparison of the three curves affords important insights into the

nature of the desorption process for this particular crystal. Similar

photon-stimulated desorption experiments have also been undertaken on AI2O3

and Ji02

.

In our most recent experiments the goal has been to detect desorbed groundstate neutral atoms emitted due to electron beam irradiation. ^ This has

been accomplished using a tunable dye laser to excite Na and Li desorbing

from clean alkali halide surfaces. Because typical counting rates in these

laser-induced fluorescence measurements are greater than 10^ Hz, this method

clearly overcomes the signal-level difficulties which have discouraged

the development of neutral-species detection based on quadrupole mass spectro185
metry. The ground-state

yields indicate substantial

efficiencies for stimulated

desorption — of order

1 0

~ 3 for ground-state

Li neutrals desorbing

from LiF crystals, for

example.

5

The mechanisms responsible

for these electronically

induced desorption phenomena

are now believed to be

associated with the production

of excitons and defects

which migrate to the

surface and release energy

during the desorption

process. The resulting

DIET affects the material

by producing (1) macroscopically visible cratering;

(2) microscopic pools

of metal which can act

as optical absorption

sites for subsequent

photon irradiation; and

(3) ejected gas- phase

halide (e.g., fluorine)

atoms which can then

interact chemically with

surrounding gases and

surfaces. All of these

processes can occur in

pure, defect-free crystals

under electron and photon

irradiation.

200

80 100 1 20

PHOTON ENERGY (eV)

140 160

Fig. 2 Excited-state neutral yields

for Li desorbed by photon bombardment

from LiF (upper curve in (a)); 10^xLi

ion yield under the same conditions

(lower curve in (a)); and the photon

absorption curve for LiF (curve (b)).

A number of questions are being addressed in current and planned experiments

in order to obtain a more complete picture of fundamental erosion mechanisms

in optical materials. The yields for neutral atoms desorbed at low electron

and photon energies are being measured to establish threshold mechanisms.

Differing temperature dependences of the yield for excited and ground-state

Li desorbed from LiF have been observed; it may be possible to establish

a relationship to defect mobilities by measuring at very low temperatures.

Significant yields of excited neutral hydrogen have been observed in both

electron- and photon-stimulated desorption experiments, and ways to measure

the ground-state yield are being sought as well. Finally, the intensity

dependence of the photon-stimulated desorption yields at selected wavelengths

needs to be measured.

However, the present work clearly establishes erosion induced by electronic

processes in surfaces as an efficient mechanism for changing surface composition

and probably surface structure in optical materials.

186
ELECTRON

GUN

SAMPLE HOLDER

AND HEATER

ELECTRON

BEAM

MONOCHROMATOR

SLIT

^

REFERENCE

CELL

Fig. 3 Schematic of experimental geometry for detecting neutral

ground-state atoms desorbing from crystal surfaces under electron

bombardment. The tunable dye laser illuminates a portion of the

transparent NaCl surface irradiated by the electron beam; the

de-excitation radiation from neutral atoms excited by the laser is

detected in a monochromator . Movement of the NaCl target manipulator

allows measurement of the fluorescence yield as a function of distance from the target surface.

REFERENCES

For a recent review, see M. L. Knotek, Physics Today 37 (9), 24 (1984).

N. H. Tolk, L. C. Feldman, J. S. Kraus, R. J. Morris, M. M. Traum

and J. C. Tully, Phys. Rev. Letters 46, 134 (1981).

N. H. Tolk, M. M. Traum, J. S. Kraus, T. R. Pian, W. E. Collins, N. G.

Stoffel and G. Margaritondo, Phys. Rev. Letters _49, 812 (1982).

N. H. Tolk, P. Bucksbaum, N. Gershenfeld, J. S. Kraus, R. J. Morris,

D. E. Murnick, J. C. Tully, R. R. Daniels, G. Margaritondo and N. G.

Stoffel, Nucl. Instr. and Meth. in Physics Research B2, 457 (1984).

R. F. Haglund, Jr., N. H. Tolk, D. E. Murnick, R. R. Daniels, P. G. Pappas and N. G. Stoffel, to be submitted to Surface Science.

187
DIELECTRIC FUNCTION AND INTERBAND TRANSITIONS IN SEMICONDUCTORS

M. Cardona

Max-Planck-Institut fiir Festkorperforschung - 7000 Stuttgart 80, Federal Republic of Germany '*

The optical constants (dielectric function) of semiconductors in the region

of interband transitions have been intensively studied during the past 25

years. Nevertheless available data are incomplete and often inaccurate. The

advent of automatic rotating analyzer ellipsometry pioneered by Aspnes and

coworkers [1-3] has changed this situation and made possible the rapid collection of data. The resulting data are so accurate that they allow repeated

differentiation with respect to the frequency. The derivative spectra enhance

the so-called critical point structure which can be directly related to the

band structure of the material. Thus this procedure has partly replaced the

modulation techniques in which the derivatives of the spectral dependence

of some optical parameter (e.g., transmissivity or reflectivity) with respect

to an external modulated agent (e.g., electric field, pressure, strain) are measured [4] . An interesting form of modulation spectroscopy which has been

profusely used in the past 15 years is resonance Raman scattering [5].

The derivative spectra obtained from ellipsometric data are, in principle,

equivalent to those obtained through Kramers-Kronig transformation of wavelength modulated reflectivity spectra [4], They are, however, more accurate

since they avoid errors due to spectral dependence of the light source and

Kramers-Kronig transformation of the data.

The derivative spectra of optical functions are easier to interpret than

those obtained from modulation spectroscopy since they involve only the

theory of the optical functions and not the effect of external perturbations

on these functions. Nevertheless conventional modulation spectra are still

useful. Electroreflectance , for instance, enhances structures due to bands

with small effective masses. Such is the case of the lowest direct gap E of

tetrahedral semiconductors. It is easily seen in electroreflectance while it

is hardly observable because of its low strength, in the derivative spectra.

In a rotating analyzer ellipsometer linearly polarized light is reflected on

a sample at oblique incidence (angle -70 ) . The state of polarization of the

reflected light (ellipticity and orientation of the ellipse) is measured

with an analyzer rotating at the frequency followed by a photomultiplier

.

The signal thus has the form:

I = A + B cos(2ftt +i>) . (1)

Fourier analysis of the signal yields the parameters and B/A which can be

used to determine numerically e^oo) and £

2

(co). Because of the speed of the

instrument one can take measurements for different surface treatments so as to optimize the surface quality following certain criteria (e.g., sharpness

of a given critical point) . Results obtained in this manner for Ge [ 6] are shown in Fig. 1. Typical second derivative spectra of e (oj) and £

?

(oj) are

188
shown in Fig. 2 for gray tin (a-Sn) [ 7] . In this figure the points are experimental while the lines are fits with theoretical critical point (cp) shapes

to the rich structure observed. Typical cp shapes are:

Ae = ce

1^ (w-o) +iT) 1/2

(3d)

ill; g

Ae = -ce

r

ln(w-oo

g

+iT) (2d) (2)

Ae = Ce

1

^(co-o) +iD _1/2

(Id) , g

where we have distinguished between one-, two-, and three-dimensional critical

points. The fits yield for every critical point the parameters C (strength)

,

to (critical energy) , T (Lorentzian broadening due partly to electron-phonon

interaction and partly to interaction with defects such as substitutional

donors and acceptors), and phase angle ip which represents, in a phenomenological way, excitonic effects. This angle is a multiple of tt/2 in the absence

of excitonic effects.

As seen in Fig. 1 the critical points shift to lower energies and broaden

with increasing T. The shift in go vs. t obtained ellipsometrically for the

E^ critical points of Ge and Si ±s shown in Fig. 3 [8] and compared with

calculations of the effect of the electron-phonon interaction on the corresponding conduction and valence band levels (dashed line) . The solid line re- presents this calculation plus the effect of thermal expansion. Excellent

agreement with experiment is found. Similar work has recently been performed

for the broadening parameters T(T) [9]. The electron-phonon interaction effects are composed of two contributions, the so-called Debye-Waller term,

which arises from second-order terms in the electron-phonon Hamiltonian, and

the self-energy which arises from first-order terms taken in second order

perturbation theory. The Debye-Waller terms are real and contribute to the

energy shift of the cp. The self-energy terms are complex: the real part con- tributes to the energy shift while the imaginary part determines the broadening parameter.

Ellipsometry can also be used to study the effect of impurities on the dielectric function and the critical point parameters. Figure 4 shows the spectra of four heavily doped silicon samples compared with those of undoped

Si [10]. Red shifts and broadenings of the E^ and E^ critical points are seen. The impurity induced red shifts of co^ obtained from fits with Eqs. (2) are represented in Fig. 5 and compared with the result of theoretical calculations. These calculations follow similar lines as those for the temperature

shifts [10]. The perturbing potential is taken to be the Coulomb potential

of one impurity screened by the free carriers. The first order perturbation

terms, which would yield opposite shifts for donors and for acceptors, are negligible. Second order perturbation theory expressions, when multiplied by

the carrier concentration, yield the shifts shown by the solid lines in Fig.

5. For a given concentration of either donors or acceptors these shifts are nearly the same, small differences being due to differences in the screening

of electrons and of holes.

Ellipsometry is also being used for the investigation of the effect of alloying on the interband critical points [11,12], Figure 6 shows results for the

189
E. , E +A1 , and E gaps of Hg Cd Te [12]. One of the most interesting aspects

of these data is the so-called bowing or deviation from the linear dependence

of cp-energies on x. Part of this deviation can sometimes he accounted for

with the virtual crystal approximation (VCA) , in which the crystal potential

is taken to contain the average potential of the disordered atoms (Hg and

Cd in this case) . Additional contributions are due to potential fluctuations

related to the chemical and topological disorder [13] (by topological disorder it is meant the variation of bond lengths due to the cation disorder)

The VCA contribution and that of the potential fluctuations have often the same sign and order of magnitude.

Particularly interesting is the study of magnetic semiconductors such as

Cd. Mn Te. As shown in Fig. 7 the E. , E,+A, energies decrease with increas1-x x 1 1 1

ing x while the opposite is true for the E gap. This effect must be attributed to the admixture of Mn 3d states to the valence and conduction bands. In

particular , such admixture is symmetry forbidden for the conduction state of

the E gap. This is no longer the case for the E gap.

Ellipsometry can also be used for the investigation of anisotropic materials

[14]. As an example we show in Fig. 8 data obtained for GeS with polarizations parallel to the two crystal axes which lie in the cleavage plane [15].

Data for the third polarization direction, perpendicular to the cleavage

plane, are also obtained, although less accurately than those of Fig. 8, with

ellipsometry [15]. One notices in Fig. 8 considerable differences in the positions of cp structure for the two polarization directions. These differences, while in principle due to polarization selection rules for the interband transitions, have not been unambiguously explained. We note the strong

sharpening of some of the cp structures of Fig. 8 obtained at low temperatures. This sharpening emphasizes the advantage of performing ellipsometric

measurements at low temperatures in order to resolve cp structure. Such measurements are still lacking for many common semiconducting materials.

REFERENCES

1. D.E. Aspnes, in Optical Properties of Solids: New Developments, ed. by

B.O. Seraphin (North Holland, Amsterdam, 1976) , p. 799.

2. D.E. Aspnes and A. A. Studna, Phys. Rev. B 27_, 985 (1983).

3. P.S. Hauge, Surf. Sci. 96, 80 (1980); 96, 108 (1980).

4. M. Cardona, Modulation Spectroscopy (Academic Press, N.Y. 1969).

5. M. Cardona, in Light Scattering in Solids II (Springer, New York,

1982)

6. L. Vina, S. Logothetidis, and M. Cardona, Phys. Rev. B 30, 1979 (1984) . 7. L. Vina, H. Hochst, and M. Cardona, Phys. Rev., in press.

8. P. Lautenschlager , P.B. Allen, and M. Cardona, Phys. Rev., in press.

9. P. Lautenschlager, to be published.

10. L. Vina and M. Cardona, Phys. Rev. B 29_, 6739 (1984) . 11. S.M. Kelso, D.E. Aspnes, M.A. Pollak, and R.E. Nahory, Phys. Rev. B 29_,

6739 U982) . 12. L. Vina, C. Umbach, M. Cardona, and L. Vodopyanov, Phys. Rev. B 29_,

6752 (1984).

190
13. P. A. Fedders and C. Myles, Phys. Rev. B 29_, 802 (1984); K.C. Haas, R.J.

Lampert, and H. Ehrenreich, Phys. Rev. Letters 52_, 77 (1984) . 14. D.E. Aspnes, J. Opt. Soc. Am. 70, 1275 (1980)

.

15. P. Lautenschlager , S. Logothetidis, L. Vina, and M. Cardona, to be published.

16. S. Logothetidis, L. Vina, and M. Cardona, Phys. Rev. B, in press.

2 3 4 5

E(eV)

Fig. 1. Imaginary part °f tne dielectric function of undoped Ge at several

temperatures showing the , E^+A^, E' , E^ , and Ej critical points. A red

shift and broadening of critical points with increasing temperature is clearly observed.

191
1*10-

-1»103 -

—I

1 1-

e; e

1,^, e3

,)

1

-2*103 - f~E

\ E'0 E^a'q

|

| a-Sn(OOI) — d

2 E,/dw2 —- d

2 e2/du>2

Li 1 J u U 1 l_

B-implantnJ, Inwr anneoltd Si -bulk Si . Ne-W^'crr

3 A E(eV)

Fig. 2: Second derivative of the dielectric function of a-Sn. The points are experimental for z^. The lines are critical point fits.

-0.2

-0.3

Fig. 3: Temperature dependence of

the E critical point energies of

Ge and Si. The dashed line gives

calculated electron-phonon effects,

the solid line includes thermal ex- pansion.

40

30

20

10

0

-K>

-20

bulk Si.boron doped flu'W

—1 i"n -1 4

2 3 H 1

1 5

(•V) f

to

e,.£:

30

20

10

0

-10

-20

- Ai-implanttd.lattf anrwaltd Si •bulkSI , AN^O-lO^cm5 undoped ft

Fig. 4: Dielectric function of pure

and heavily doped Si.

1000

10

17 10

18

10

,19 1020

10

21

10 22

100

AE1 (meV)

10

1

1000

100 AE2 (meV)

'10

CALCULATED

Si- Ei shift AE1 = E 1pure " E L

10

17 1018

10.

,19 10 20

10

21 10 22

o p- type bulk

a n- type bulk

o p-type ion implanted

• n-type ion implanted

Aspnes.Studnaand Kinsbron

FIT SLOPE 0 36 Si-E 2 shift AE 2

= E 2pure - E 2l

10

17 10

18 no

,19 10 20

10

21 no 22 Nj(cm"3

)

Fig. 5: Shift with doping of the

critical point energies of and

E^ of silicon.

192
0.70

At (eV)

0 55

5

0 X 1

1 1 1 I A A—A

'oJ 1 1 ' ' ' oo

"2 —a A o

1 1 1 1 a_o - .iiiii,

E(eV)

"i '

i i—i—i—i—i—i—i—

r

CdxHg^xTe

o<P

Fig. 6: Dependence of critical

point energies E^, E

^ + ^^' E

2

' and of on concentratxon x for Cd Hg„ Te

.

x 1-x

0.2 0.4 0.6

i

i i i ii

i i i

i

i i

i i i

i

i i i

i

i i i I

i ' Cdi- x Mn x Te 4

4.0

3.5

E(eV)

3.0

25

Ei *

-to

6.0

E2(eV)

50

4.0

2.5 E0

(eV)

2.0

?(V

i i i i I i i 1 15 0 0.2 04 0.6 x

T = 84 K

T = 215 K

T = 460K

£,,£2

Fig. 8: Dielectric functions of

GeS for polarizations parallel to

the a and b axes at several temperatures .

Fig. 7: Dependence on x of criti-

•*- * cal point energies E , , E ^+A^

,

and of A, for Cd, Mn Te.

1 1-x x

193
BAND STRUCTURE AND DENSITY OF STATES CHANGES FOR

DOPED GALLIUM ARSENIDE

Herbert S. Bennett

Semiconductor Devices and Circuits Division

National Bureau of Standards

Gaithersburg, MD 20899

Introduction

Lasers, opto-electronic devices, and transistors have high carrier and/or doping concentrations in their active regions during operation. Such high concentrations produce changes in

the band structure, density of states, and optical properties. These changes then influence

considerably the performance of optical materials at 300 K in advanced applications for

optical signal processing, computing, and communications.

This paper contains calculations of the changes in the band structure and density of states

for both n-type and p-type doped GaAs. These band structure changes may be applied to

optical properties such as absorption, luminescence, and refractive index. The application

to absorption is given here.

Past interpretations of optical absorption measurements in heavily doped GaAs to give

the dependence of the direct bandgap, Ec{ezp), on doping density use intrinsic values for

the band structure and density of states. However, in heavily doped GaAs, the dopant

ion-carrier and many-body (majority-carrier exchange and minority-carrier correlation)

interactions greatly distort the band structure and the density of states. These interactions

result in energy shifts of the band edges and distorted bands and density of states. Such

modifications to the band structure have technological implications for the optical and

electronic behavior of GaAs devices.

This paper shows that reducing the uncertainty in how the band structure and density of

states change with carrier and/or doping concentration requires improved optical measure- ments on doped GaAs at 300K. Such measurents are essential for estimating many-body

interactions. These interactions are of the same order of magnitude as the one-body

(dopant ion-carrier) interactions and greatly alter the dependence on doping density, N,

and carrier density of the input parameters used in numerical simulations of optical and

electronic devices.

Optical Absorption

According to the one-electron model, the optical absorption coefficient for transitions between a valence band and a conduction band has the form [1],

2 ft y»+00

a < g> =

, Z~> V \ Pc(Ef)pv {Ei)\M{Es ,Ei)\

2 (h{Ei) - f0 {Ef))dEf , (1)

194
where c is the speed of light, h is Planck's constant divided by 2tt, m0 is the free-electron

mass, 6 0 is the permittivity of free space, E is the photon energy, nr

is the index of refraction, pc and pv are the densities of states per unit volume and unit energy in the conduction

and valence bands, respectively, and M is the effective matrix element of the momentum

operator between valence band states at energy Ej — Ej — E and conduction band states at

energy Ej. The Fermi-Dirac distribution function, fo(Ef) = l/[l+exp ((Ej -Ep)/kBT)] , gives the probability that a state of energy Ej is occupied by an electron. The Fermi energy, Boltzmann constant, and temperature are denoted by Ep, and T. The total

absorption coefficient for GaAs is given by a sum of terms like Eq. (l) for each of the three

valence bands.

Whenever carrier densities or ionized dopant densities, N, exceed 8 X 10 16 cm

-3

for n-type

and 10 19 cm~3 for p-type GaAs at 300K, the above one- and many-body interactions lead

to appreciable changes in the band structure and carrier density of states pc and pv . These

changes must be included in the interpretation of optical measurements. They also affect

greatly the performance of optical materials for the above mentioned applications. The

self-energy formalism of Klauder [2,3] is applied to the dopant ion-carrier interactions in

the effective mass approximation for GaAs. This formalism yields numerical procedures for

computing the distorted bands and density of states. These perturbations and distortions are due to the effects of large dopant densities and/or carrier concentrations. Because theories for the many-body effects of majority-carrier exchange and minority-carrier correlation

do not exist for carrier densities intermediate between the non-degenerate and degenerate

cases in GaAs at 300 K, estimates for these energies are obtained as follows. When optical absorption measurements are available, these estimates are obtained from the relation

Emb — Eoi^xp) — 1.424eV - E{C , where Emb

is the energy shift of the bandgap associated

with many-body interactions and E\c is the energy shift of the bandgap associated with

one-body interactions. The latter are calculated by the Klauder formalism. When optical

absorption measurements are not available, then Emb

is estimated by degenerate theory.

The optical absorption measurements [1,4] are interpreted in terms of the above distorted

bands and density of states from the Klauder self-energy formalism. The latter yield

values for Fermi energies and band edges which differ from those obtained by earlier

interpretations of the experiments. When applied to heavily doped GaAs, this self- energy formalism for dopant ion-carrier interactions and the estimates for the above manybody effects give the modified band structure and the dependences of the Fermi energy,

Ep(N,T), the screening radius, rs (N, T), and the effective intrinsic carrier concentration,

rii e (N,T) = \/np, on the ionized doping density, N, and temperature, T. The equilibrium

electron and hole concentrations are denoted by n and p.

These calculations incorporate the Thomas-Fermi expression for the screening radius and

the charge neutrality condition, N = n — jp, to compute self-consistently Ep and rs , for

given values of N and T. The input parameters for the above calculations are the values

at 300 K of the unperturbed effective masses mc = 0.067mo and mv = 0.572mo, intrinsic

bandgap energy Eg = 1.424eV, and static dielectric constant /c = 12.9.

Ideally, the procedure would be as follows. First, the values of Ep{N, T) and the perturbed

densities of states pc and pv from the Klauder formalism would be inserted in Eq. (1). Then,

the bandgap Eo(N,T;exp) in Eq. (1) would be varied until satisfactory agreement occurs

195
between the calculated and measured absorption coefficients. However, the published data

and our knowledge of the energy dependence of the momentum matrix element, M, are not adequate to accomplish this. Instead, the bandgaps given in references 1 and 4 are

shifted by the differences between the Fermi energies used in these references and the Fermi

energies obtained from the above Klauder formalism. This latter procedure is justified since

the bandgap values interpreted from absorption measurements are much more sensitive to

the value of the Fermi energy than to distortions in the density of states.

The above 300 K formalism is a compromise between two conflicting goals: 1) calculating

the band structure changes as rigorously as possible; and 2) having the 300 K results

incorporated readily and economically into numerical simulations of GaAs devices. The 0

K many-body theories [5,6] do meet the second goal but generally are not correct unless

the device or sample is fully degenerate. In order to meet goal 2, it is necessary to use the

Yukawa potential to describe the screening of carriers at 300 K.

The hole and electron concentrations at thermal equilibrium are given by

/+oo r+oo (l-f0 (E))pv (E)dE and n = I f0 {E)pe (E)dE. (2)

-oo J —oo

The quantities pc and pv are, respectively, the perturbed densities of states for the distorted conduction and valence bands which result from doping the semiconductor. The

calculations of p and n from Eq. (2) require, at the least, the above estimates for the

many-body effects.

Band Structure Changes

Numerically integrating the products in Eq. (2) of the perturbed densities of states and the

appropriate Fermi-Dirac distributions over the distorted bands gives p and n separately

as functions of N. Then, multiplying p and n together yields nfe (N). Tables I and II show the results for the band structure changes as functions of N from this self-energy

approach. The unperturbed intrinsic carrier density, nt , in these tables is the limit of

as N approaches zero.

Table I. Band structure changes for n-type GaAs as a function of donor density, at

300 K. The many-body energy, Emb, is estimated by comparison with optical absorption

measurements which are interpreted in terms of distorted bands and density of states. ND r8 Ep Emb Etc EG (exp) nu/ni

(1018 cm-3

) M (eV) (eV) (eV) (eV)

10.0 65.8 0.28 -0.04 -0.10 1.28 0.16

3.0 82.2 0.13 -0.03 -0.06 1.34 0.75

0.6 127.0 0.03 -0.003 -0.04 1.38 0.96

196
Table II. Band structure changes for p-type GaAs as a function of acceptor density, Na,

at 300 K. The many-body energy, Emb , is estimated from degenerate theory.

NA r8 Ef Eic EG (theory) «<«/

(10

19 cm-a

) M (eV) (eV) (eV) (eV)

12.0 15.0 -0.19 -0.07 -0.06 1.29 0.97

8.0 16.2 -0.14 -0.06 -0.05 1.31 1.36

5.5 17.6 -0.11 -0.05 -0.04 1.33 1.65

The Bohr radius is a0 = 0.529 x 10-8

cm; the Fermi energy Ef is relative to the majoritycarrier distorted band edge; and the bandgap narrowing is AEg = E{C + Emb. The

decreases in riie/rii from the value of unity for large values of N arises because the FermiDirac statistics dominates over the other interactions in this regime. Degeneracy makes

Ef rise more rapidly into the majority band with increasing carrier density. This effect

compensates the effect of bandgap narrowing in the evaluation of integrals such as those in

Eq. (2). When it becomes dominant in GaAs, then the minority-carrier density decreases

more rapidly with increasing N than the majority-carrier density increases. Hence, the

net result is that r^ c decreases for increasing values of N in the highly degenerate regime.

Conclusions

Calculations of optical and electronic device operation, fabrication process parameters,

device performance, and degradation mechanisms for GaAs which is heavily doped or which has high carrier concentrations must consider many-body interactions. Because

computationally efficient theories for these interactions do not exist, comparisons with

correctly interpreted optical measurements are essential for obtaining estimates of these

terms. The example of the optical absorption serves to illustrate the relations among

basic optical properties, carrier densities, band structure, and the performance of optical

materials.

Acknowledgments

The author acknowledges the many contributions of his colleagues at the National Bureau

of Standards to this work.

REFERENCES

1. H. C. Casey, Jr. and F. Stern, J. Appl. Phys. 47, 631(1976).

2. J. R. Klauder, Ann. Phys. 14, 43(1961). The third level approximation is used here.

This approximation provides a medium in which a number of completed scatterings occur

to second order in the scattering potential.

3. J. R. Lowney and H. S. Bennett, J. Appl. Phys. 54, 1369 (1983).

4. H. C. Casey, Jr., D. D. Sell, and K. W. Wecht, J. Appl. Phys. 46, 250 (1975).

5. R. A. Abram, G. N. Childs, and P. A. Sauderson, to be published in J. of Physics C

(London), January 1985.

6. G. D. Mahan, J. Appl. Phys. 51, 2634 (1980).

197
MICRO-RAMAN STUDY OF LASER-INDUCED DAMAGE

Philippe M. Fauchet,(a) Ian H. Campbell(a) and Fran Adar(b) ^'Department of Electrical Engineering and Computer Science, Princeton University,

Princeton , NJ 08544

(^Instruments S.A. Incorporated, Metuchen, NJ 08840

In most laser systems, damage to optical components is the major factor that limits scal- ing towards higher energy density. Although laser-induced damage in solids has been an

active field of research for many years, we do not have a satisfactory understanding of

the physics involved in these processes. This situation is in part due to the lack of nondestructive, quantitative probes that can be used in situ. In this paper, we show that

Raman scattering is such a probe and can be used successfully in a wide range of practical situations.

Raman scattering is a probe of structural properties. In our experiments, incident probe

photons are scattered off lattice vibrations and the backscattered Stokes signal is analyzed with a Ramanor U-1000 double-grating spectrometer. A spatial resolution of 1 /im is achieved by passing the CW Argon laser beam and the scattered light through a microscope objective. All Raman spectra (peak and width) are reproducible to 0.1 cm

-1

. The spectral resolution of the entire apparatus can be as good as 0.2 cm

-1 although it is routinely set at 2 to 3 cm

-1

. The spectra discussed below consist of data spaced by 0.1

cm with 2 or 4 second exposure times.

The damaging beam is produced by a modelocked Nd:YAG laser. The samples discussed

below are irradiated with modelocked trains of 20 1.06 //m pulses. Experiments are in

progress with single picosecond pulses in the gigawatt range at 1.06 /im, 532 nm and 355 nm. To date, we have performed experiments on thin films or bulk samples (single crystal, polycrystal or amorphous). Here, we only discuss our results on silicon, which is a

well-characterized material and thus can be used to calibrate our method. Results

obtained on other materials will be presented later.

In Figure 1, we show a high-resolution Nomarski microphotograph of the surface of a

silicon-on-insulator (SOI) sample after irradiation with 600 identical laser shots having

an energy density that is half the measured single shot threshold. If the illumination

sequence is stopped at 300 shots or less, no damage is visible. Even at 600 shots, a preliminary inspection with 160 X magnification revealed no damage. At 1200 shots, a more

or less uniform surface damage is observed. We took micro-Raman spectra of this

heterogeneously damaged region, as well as of many other areas (either virgin or irradiated with different numbers of shots at various energy densities). Figure 2 shows spectra

taken at different locations in the area shown in Figure 1. The variations in the central

frequency, linewidth and asymmetry of the lineshape clearly indicate that the structure

has been altered. The magnitude of the effects shows the power of Raman spectroscopy.

Similar experiments performed on other materials (including silicon-on-sapphire and

amorphous silicon layers) show changes in the spectra that are also easily detected.

The undoped SOI samples were grown at 625

0 C by low pressure chemical vapor deposition to a thickness of 1 ixm. At room temperature, the silicon is under tensile stress because the film and the substrate have different thermal expansion coefficients. Furthermore, the film is microcrystalline [2]. If laser damage is associated with local melting

and subsequent regrowth, we can expect that the stress and microcrystallite properties

will be affected. For our geometry, the stress will shift the central frequency lo0 and the

198
microcrystallite size will alter ojq as well as the linewidth T and lineshape Ta/r b

. As

shown in Figure 3, we clearly observe changes in these quantities upon laser irradiation.

We estimate the uncertainty on <x>0 and V to be less than ± 0.2 cm

-1 and that on Ta/r b to be ± 0.05.

After laser damage, we observe a reduction in ra/Fb and T, and a reduction in the

Stokes shift. According to Richter et al. [3], the reduction in linewidth and asymmetry

of the lineshape would indicate larger microcrystallites, while from Anastassakis et al.

[4], the smaller Stokes shift would indicate an increased tensile stress. A complete quantitative interpretation of these and other spectra (including the amount of stress and

microcrystallite size) is presently under way. However, it is already clear that Raman

scattering is an excellent probe of the structural changes produced by laser-induced damage. It is more sensitive and quantitative than Nomarski microscopy. Furthermore, we

have preliminary indications, from theory and experiments, that Raman scattering can be sensitive to the subtle subthreshold transformations which occur prior to visible damage in a multipulse exposure sequence [5]. We thank C. Paddock for her help with the laser and Dr. N. Johnson for providing us with the SOI samples.

1. J. Gonzalez-Hernandez, D. Martin and R. Tsu, in Spectroscopic Characterization

Techniques for Semiconductor Technology, F.H. Pollak and R.S. Bauer editors,

SPIE Proceedings Vol. 452, 1984, pp. 44-50.

2. N. Johnson, private communication.

3. H. Richter, Z.P. Wang and L. Ley, Solid State Commun. 39, 625 (1981).

4. E. Anastassakis, A. Pinczuk, E. Burstein, F.H. Pollak and M. Cardona, Solid State

Commun. 8, 133 (1970).

5. P.M. Fauchet, Phys. Lett. A93, 155 (1983).

Fig. 1: High-resolution Nomarski

microphotograph of a 53

/im X 41 [im area at the

center of a spot illuminated

with 600 laser shots at one

half single shot damage

threshold. The light,

worm-like, micron-size

features are localized damage spots that do not

appear even after 300 laser shots.

199
WAVENUMBERS

Fig. 2: Stokes line of a) virgin SOI; b). and c) two different locations in the area of fig.

1. The central frequency oj0 , linewidth T(=ra + Tb ) and asymmetry (as measured by the ratio of the half-width half-maxima T^/T^) change continuously

from the center of one of the worm- like features to a worm-free region. The

spectra are excited at 5145A with a 1 fim spatial resolution.

200
517 -

OJ0

(cm"

1 )

518-

519-

520

r(cm ')

Fig. 3a: Central frequency and linewidth of virgin SOI (o) and at various locations in the area of fig. 1 (•). The data taken in the neighborhood of worm-like

features yield lower Y/ lower ooQ

.

(cm ')

y 1 ' ' 1 ' 0.9 1.0 I.I 1.2 1.3 1.4 1.5 1.6 1.7 1.8 r0 /rb

Fig. 3b: Linewidth versus asymmetry for the same spectra. The full line is the theoretical prediction based on a model where the increase in T and ra/r|, is due to the gradual relaxation of the q-vector selection rule when the microcrystallite

size decreases.

201
Optical Effects in Quantum Well Structures and Superlattices

D. S. Chemla

AT&T Bell Laboratories, Holmdel, N.J., U.S.A.

INTRODUCTION

Recently analog and digital optical processing have attracted much attention. However

the operation of optical devices such as switches or modulators requires very large optical or

electro-optical nonlinearities. These can be found in semiconductors at excitonic transition resonances (1). In bulk semiconductors excitonic resonances are only observed at low temperatures.

It has recently been shown that excitonic effects are enhanced in ultra-thin semiconductor layers due

the quasi two-dimensional carrier confinement (2) . The combination of an increased exciton binding

energy (3) and a slightly reduced overall exciton-phonon interaction result in the observation of

clear and well resolved exciton peaks in the absorption spectra of GaAs/AlGaAs multiple quantum

well structures (MQWS) at room temperature (4). The nonlinear optical effects involving room temperature excitons are extremely

interesting to investigate for practical as well as fundamental reasons. From the point of view of

applications MQWS exhibit at room temperature very large nonlinear optical and electro-optical

effects at wavelengths, power levels and speeds compatible with laser diodes and electronics. In addition MQWS are prepared by advanced semiconductor technology (5), and therefore they have

the potential to be incorporated in integrated systems. From a more fundamental viewpoint,

MQWS form a model system to study the effects of reduced dimensionality on excitonic behavior.

Furthermore, the room temperature excitons found in MQWS, are in the very unusual situation where;

HCIlo > kT > Eb

In this equation, fifl^—36 meV is the GaAs LO-phonon energy, kT—25 meV at room

temperature and Eb — \0 meV is the exciton binding energy. Under these conditions excitons

generated by resonant optical excitation are ionized in a very short time by phonon collisions. This

provides a unique opportunity to study the dynamics of the transformation of excitons into an

electron-hole (e-h) plasma and to investigate the nonlinear optical effects associated with both

species.

/. OPTICAL NONLINEARITIES OF GaAs/AlGaAs MULTIPLE QUANTUM WELL

STRUCTURES

The low temperature linear absorption in MQWS has been reviewed in Ref. (2) and the room temperature linear absorption has been discussed in Ref. (6). The confinement of an e-h pair

in ultra-thin semiconductor layers increases the exciton binding energy (3,7,8) resulting in the

observation of well resolved resonances in the room temperature absorption spectra of MQWS

(4,9,10,11). This is shown in Fig. 1. where the 300 K absorption spectra of a 3.2 nm thick high

quality GaAs sample is compared to that of a MQWS sample. A small bump is seen at the edge of

the GaAs spectrum, it corresponds to the remains of the excitonic resonance. The MQWS spectrum

show two clear resonances for the heavy and the light hole excitons, followed by the flat two- dimensional continuum and the onset of the next subband transitions. This type of absorption

spectrum is very well described by two Gaussian absorption lines corresponding to the two excitons

and a two-dimensional continuum with the appropriate Sommerfeld enhancement factor for the

202
interband transitions (6). In the insert of Fig. 1. is shown the variation as a function of the

temperature of the width of the heavy hole exciton peak, it is well described by a semi-empirical fit, shown by the solid line, involving two terms; a constant inhomogeneous line width, T0~2 meV

(12,13,14) and a term proportional to the density of LO-phonons (9,6). The coefficient giving the temperature-dependent broadening, Tph —5 meV, is smaller than that of bulk GaAs, Tph —1 meV

(15). From this dependence one can deduce a mean time for ionization by thermal LO-phonon

collision of about 400 fs. Since at room temperature kT ~2.5x£fc almost no excitons can reform

from the electrons and holes created by the thermal phonons ionization (6). Therefore, although

excitonic resonances are observed at room temperature the gas of excitons resonantly generated

through photon absorption is very short lived; it transforms into a free e-h plasma in less than 0.5

ps. Under optical excitation, as free e-h are generated they screen the Coulomb interaction

causing the renormalization of the single particle states, with however very little shift of the exciton

energy because of its neutrality (16). Nevertheless, the binding energy of the exciton with respect

to the normalized band gap decreases, the e-h correlation diminishes progressively and the height of

the absorption peak decreases. Eventually the correlation is completely lost and the exciton peak

disappears leaving a step like absorption continuum edge near the exciton original position. This

edge is much more difficult to saturate and can be shifted further to low energy if more carriers are generated. The large optical nonlinearity observed in MQWS with cw and ps sources results from

conjunction of two factors; the concentration of a large oscillator strength in a narrow energy band

and the screening of the Coulomb interaction by a charged plasma that modifies and eventually

destabilizes the excitonic states.

Saturation of excitonic absorption in MQWS has been observed with cw laser excitation

at resonance (4,9) and well above the exciton energy well in the continuum (6). The intensity

dependence of the exciton peaks of the two samples (whose absorption spectra are given in Fig. 1.) are shown in Fig. 2a. and 2b., respectively for the GaAs sample and the MQWS. The solid curves

are semi-empirical fits based on the model discussed in the previous paragraph. For GaAs the

saturation is well described by a constant ( ~ not saturable) background plus a saturable species

with a saturation intensity /j~4.4 kW/cm2. The fit for the MQWS involve two saturable species one with a very small saturation intensity /j—580 W/cm2 and the other one more difficult to saturate, Is —44 kW/cm2 (9). According to our model these results can be interpreted in terms of

the bleaching of the excitonic absorptions for the two samples, followed, in the case of the MQWS,

by the saturation of the renormalized two dimensional continuum as it is shifted down in energy. In the case of GaAs, the interband transitions in the three-dimensional continuum show no saturation,

at least up to the intensities reached in our experiments. This interpretation is well supported by the

shapes of the spectra observed with a low intensity tunable cw dye laser with or without the

excitation of a cw diode laser delivering about 800 W/cm2

, and emitting at 42 meV above the

exciton peak (6). Examples of these spectra are shown in Fig. 3. Under excitation the exciton

peaks have disappeared, and the absorption spectrum observed is a step-like edge which has exactly

the same shape as the two dimensional continuum used to describe the interband transition in the

unexcited spectrum.

The absorptive and dispersive part of the optical nonlinearity at low excitation has been

measured by forward degenerate four wave mixing (DFWM) using a picosecond dye laser (17). In these experiments the nonlinear transmission induced by the pump beam on the probe beam and the

diffraption efficiency of the coherent gratings generated by pump-probe interference can be

simultaneously measured. In addition to the linear transmission the same set-up gives access to the

recombination life time, t—-30ns, and to the diffusion coefficient, D~\3cm 2/s . An example of the

experimental data is shown in Fig. 4a,b,c for the linear transmission, the differential nonlinear

transmission, and the DFWM signal respectively. From the spectra of Fig. 4a and 4b and an

adapted Kramers-Kronig inversion it is possible to obtain the spectra of the changes of absorption

coefficient per e-h pair aef, and of refractive index per e-h pair nef, (6) these are shown in Fig. 5. They determine completely the optical nonlinearity in the fundamental absorption region. A severe

test of the accuracy of this determination is that the two complex spectra of Fig. 5 should reproduce

203
the measured DFWM diffraction efficiency of Fig. 4c. The comparison of the experimental data of

Fig. 4 with the theoretical predictions based on the spectra of Fig. 5 is shown in Fig. 6, the

agreement is excellent (6) . The measured nonlinearities are very large, more than one order of

magnitude iarger than that of GaAs and six order of magnitude that of Si at room temperature.

To demonstrate the potential use of MQWS for nonlinear optics with cw laser diodes;

DFWM experiments were performed in a \.25nm MQWS using a commercial diode laser as the

sole light source (18). Internal diffraction efficiency of about 5xl0-4 was measured with pump

power as low as 2.5 mW (Ip —20 W/cm2

) and probe power of 0.1 mW (/, —0.8 W/cm 2

) . It should

be mentioned that such experiments are usually performed on thick samples with high power lasers.

Optical bistability using MQWS as the nonlinear element in a Fabry-Perot etalon, has

been demonstrated (19).

More recently saturation of excitonic absorption in MQWS has been used to mode-lock

laser diodes. Pulses as short as 1.6 ps and reliable operation have been obtained (20)

.

The dynamics of the exciton ionization by thermal phonons has been studied with the

recently developed femtosecond spectroscopic techniques (21). The changes in the absorption

spectrum of MQWS samples under excitation resonant with the heavy hole exciton or under nonresonant excitation in the continuum, have been measured with a resolution of 150 fs (22,23). In order to avoid any interference with band gap renormalization effects a moderate excitation was

used in both cases. It was found that after a transient evolution which last approximately 0.5 ps, the changes are very similar to those observed with cw or ps lasers. However the transient regime

(t<0.5 ps) is highly dependent on the nature of the excitation. For the non-resonant case a smooth

evolution of the spectrum takes place, from the unpumped spectrum to that observed at long times

(t>l ps). Conversely in the case of resonant pumping one observes a very efficient bleaching of the

exciton absorption that recovers partially in 300 ±100 fs. Typical spectra under resonant pumping

and at various probe delays, are compared to the unexcited spectrum on Fig. 7. The time

dependence of the height of the heavy hole exciton peak for the two excitation conditions is shown in Fig. 8. The smooth variation found for non-resonant pumping follows quite well the integral of the

pump pulse, showing that the effects are proportional to the number of e-h pairs generated in the

continuum. The behavior in the resonant pumping case corresponds to the instantaneous generation

of a species that, in 300 ±100 fs, transforms into free e-h pairs, which have the same effects as in the non-resonant pumping case (22,23) . The experiment is interpreted as the first observation of the

exciton saturation due to the generation of excitons that occupy the lowest lying energy states of the

system, followed by the thermal phonon ionization of these excitons into free e- h pairs. The

saturation induced by the resonantly generated excitons is indeed large, and can be used for applications in ultra-fast optical devices.

//. ELECTRO-ABSORPTION IN GaAslAlGaAs MULTIPLE QUANTUM WELL

STRUCTURES

MQWS absorption is also very sensitive to perturbation by electrostatic fields. The

reason for such sensitivity is that the energies associated with the carrier confinement in the layers or with the Coulomb attraction between electrons and holes are small, typically ~10 meV, and that the corresponding envelope wave functions are large, of the order of —100 A. Therefore the

application of rather small fields, of the order of 10 raK/100 A/.e.,10+4 V/cm, well within the

range that can be applied to semiconductors will cause large changes of the absorption spectra (24-

27). Large changes of the luminescence efficiency with applied field have also been observed at low

temperatures (28,29).

By symmetry it is expected that fields parallel and perpendicular to the layers will produce different effects. For a field parallel to the layers there is no effect on the confinement but

the relative motion of the electron and the hole is perturbed as in the case of the Stark effect, with

however some changes due to the lowered dimensionality of excitons in MQWS (30). For a field perpendicular to the layers the confinement energy of the electron and the hole are affected, and

204
since the two particles are pushed away from one another and squeezed against the walls of the

potential well the exciton binding energy is also changed.

The design of samples to distinguish between the two geometries is quite important. In the case of field parallel to the layers photolithography used to define proper electrode geometry.

The main observed effect is a broadening of the exciton peak which is due to the reduction of the

exciton lifetime by the field ionization. This is shown in Fig. 9. At an applied field of

1.6xl0+4 V/cm the two peaks have substantially broadened, and they are no more resolvable at 5xl0+4 V/cm. The low field ionization rate has been calculated for two dimensional excitons by the same method as in the case of the Hydrogen atom (31). It is smaller than in three dimensions

because of the increased binding energy and because of other effects related to the lowered

dimensionality, the results are in qualitative agreements with the measurements.

To apply fields perpendicular to the layers special samples have been prepared; they

consist of a MQWS in the intrinsic region of a p-i-n diode (25). The p and n regions are made of

AlGaAs transparent at the energy of the fundamental gap of the MQWS. The diode is operated

back-biased to vary the field across the MQWS and yet avoid large currents and thermal effects. The dominant effect is a shift of the whole spectrum with a small broadening of the exciton peaks.

However these remain well resolved at fields as large as 10+5 V/cm, i.e., more than fifty times the

classical ionization field. At such field shifts 2.5 times the binding energy are observed. Typical

spectra under various static fields are shown in Fig. 10. At field larger than 10+5 V/cm the excitons are no longer resolvable. The interpretation of these observations is the following. As the static

field is applied the potential seen by the electrons and the holes in the GaAs layers becomes that of

a skewed well and the energy levels of the individual particles are shifted down. Simultaneously the wave functions are compressed against the walls of the well; the charge distribution is thus modified

resulting in a variation of the binding energy of the excitons. If the field is further increased, the

less-confined particles, i.e., the holes finally tunnel out owing to the finite depth of the well, so that the resonances can no longer be resolved. No adjustable parameters are used and the agreement

with the measured shifts is very good (26). In this calculation the usual discontinuities at the band

edges (i.e., 0.l5*Eg for the valence band and 0.85x£

?

) for the conduction band have been used

(2); an almost perfect agreement is obtained if a larger discontinuity at the valence edge is taken

(~.4QxEg

) as recently suggested (32). The reason why excitons are still observed at field much

larger than the ionization field is that the large potential barriers prevent the particles from escaping

from one another. This remarkable property is specific to MQWS; it allows us to move an abrupt

absorption edge into a region of the spectra where the sample is transparent is the absence of field. The intrinsic speed of the effect is very high since it corresponds to the response of the

electronic envelope functions. In practice the limits are set by the RC constant of the circuit in which the MQWS is incorporated (25). Recently high speed modulation of laser diode has been

achieved using a p-i-n MQWS 0.965 \im thick in form of a 95 \im mesa with a 25 nm optical

window. When the device is driven by electrical pulses of -8V and 125 ps duration, optical pulses — 131 ps are produced (27). A schematic of the device and the optical response compared to the

electrical excitation pulse are shown in Fig. 11. A modulation of 2.3 dB was measured. The overall response time of the device is well accounted for by the characteristics of the electric circuit. Deeper modulation and faster responses should be obtained with thicker MQWS and smaller device

area. A bistable optical switch based on a novel principle, has been demonstrated using the pi-n MQWS devices; it is called Self-Electro-Optic-Effect-Device or SEED (33). It presents several

attractive features: it requires no cavity, it has a very small switching energy, it operates over a broad band of wavelengths and eventually with incoherent light sources. When a reverse bias is applied to the p-i-n MQWS, the structure also acts as an efficient photodetector. The bistable

optical switch consists of a series resistor and a constant voltage supply that are used to bias a p-i-n

MQWS. A light beam at a wavelength close to the peak of the exciton at zero bias is sent through

the sample and the bias is applied. The absorption spectrum is shifted so that the transmission is high. As the intensity of the incident beam is increased, the photocurrent passing through the

205
resistor induces a reduction of the voltage applied to the device, which in turn increases the

absorption by shifting the spectrum thus further increasing the photocurrent and so on. This process provides the feedback mechanism for optical bistability (33). An example of the optical hysteresis

loop obtained with a SEED is shown in Fig. 12. The SEED used in these experiments was rather

large (about 600 \im in diameter), nevertheless the measured switching energy per unit area is remarkably low, Wso —4 fJ/tint

1 for optical incident energy and Wst <18 fJ/iitn 2 for the total switching energy (electrical plus optical) substantially lower than any previously reported bistable

optical device. Even lower switching energy should be possible for smaller devices, the physical limit for a (X/n) 2 device is ~1 fj/nm 2

, comparable to that of electronic switches.

CONCLUSION

We have presented some recent progress made in the investigation and the utilization of

the excitonic resonances observed at room temperature in GaAs/AlGaAs multiple quantum well

structures. Novel nonlinear optical and electro-optical effects are observed which result from the

lowered dimensionality of the electrons in ultra-thin semiconductor layers. Room temperature

excitonic peak are not only interesting for the applications, they also exhibit the most unusual

properties owing to their extremely short life time and their transformation into free e-h pairs.

Finally, we would like to stress that although the GaAs/AlGaAs alloys form a model

system from which extremely high quality MQWS have already been made, MQWS made with

other semiconductors should soon be available with comparable quality. In addition, quantum wells represent only one type of microstructure soon it will be possible to prepare novel microstructures

and investigate their even more exciting physical properties.

ACKNOWLEDGEMENTS

The work that has been reviewed in this article has been performed at the AT&T Bell Laboratories in close collaboration with D. A. B. Miller, A. C. Gossard, P. W. Smith, T. C. Damen,

T. H. Wood, C. A. Burrus, W. H. Knox, R. L. Fork and C. V. Shank.

REFERENCES

[l] D. S. Chemla, A. Maruani, Progress in Quantum Electronics, 8, 1 (1982).

[2] R. Dingle, "Confined Carrier Quantum States in Ultra Thin Semiconductor

Heterostructures," in Festkorperprobleme XV, p. 21, Ed. H. J. Queiser,

Pergamon/Vieweg Braunschweig (1975).

[3] R. C. Miller, D. A. Kleinman, W. T. Tsang, A. C. Gossard, Phys. Rev., B24, 1134 (1981).

[4] D. A. B. Miller, D. S. Chemla, P. W. Smith, A. C. Gossard, W. T. Tsang, Appl. Phys., B28,

96 (1982).

[5] A. C. Gossard, "Molecular Beam Epitaxy of Superlattices in Thin Films" in "Thin Films

Preparation and Properties," ed. K. N. Tu and R. Rosenberg, Academic Press, NY (1983).

[6] D. S. Chemla, D. A. B. Miller, P. W. Smith, A. C. Gossard, W. Wiegmann, IEEE JQE-20,

265 (1984).

[7] G. Bastard, E. E. Mendez, L. L. Chang, L. Ezaki, Phys. Rev., B26, 1974 (1982).

[8] R. L. Greene, K. K. Bajaj, Sol. State Commun., 45, 831 (1983).

[9] D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P. W. Smith, A. C. Gossard,

W. T. Tsang, Appl. Phys. Lett., 41, 679 (1982).

[10] Y. Ishibashi, S. Tarucha, H. Okamoto, Inst. Phys. Conf. Ser. No. 63, Proceeding of Int. Symp. GaAs and Related Compounds, Japan 1981, pp. 587-588 (1982).

[11] S. W. Kirchoefer, N. Holonyak, K. Hess, D. A. Gulino, H. G. Drickamer, J. J. Coleman,

P. D. Dapkus, Appl. Phys. Lett., 40, 821 (1982).

206
[12] C. Wiesbuch, R. C. Miller, R. Dingle, A. C. Gossard, Sol. State Commun., 37, 219 (1981).

[13] R. C. Miller, D. A. Kleinman, W. A. Norland, A. C. Gossard, Phys. Rev., B22, 863 (1980).

[14] C. Weisbuch, R. Dingle, A. C. Gossard, W. Wiegmann, J. Vac. Sci. Technol 17, 1128

(1980).

[15] V. I. Alperowich, V. M. Zalekin, A. F. Kranchinko, A. S. Terekhev, Phys. Stat. Sol., B77,

466 (1976).

[16] H. Haug and S. Schmitt-Rink Progr Quantum Electronics, 9, 3 (1983).

[17] D. A. B. Miller, D. S. Chemla, D. J. Eilenberger, P.W.Smith, A. C. Gossard,

W. Wiegmann, Appl. Phys. Lett., 42, 925 (1983).

[18] D. A. B. Miller, D. S. Chemla, P. W. Smith, A. C. Gossard, W. Wiegmann, Optic Letter, 8, 477 (1983).

[19] See, for example H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai,

A. C. Gossard, S. L. McCall, A. Passner, and W. Wiegmann, Appl. Phys. Lett. 41, 221

(1982).

[20] Y. Silberberg, P. W. Smith, D. J. Eilenberger, D. A. B. Miller, A. C. Gossard,

W. Wiegmann, Optic Letters 9, 507 (1984).

[21] R. L. Fork, C. V. Shank, R. Yen, C. A. Hirlimann, IEEE JQE-19, 500 (1983).

[22] W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, C. V. Shank,

A. C. Gossard, W. Wiegmann, Proceedings of the "Ultrafast Phenomena" Monterey, CA

(1984).

[23] W. H. Knox, R. L. Fork, M. C. Downer, D. A. B. Miller, D. S. Chemla, C. V. Shank,

A. C. Gossard, W. Wiegmann, to be published.

[24] D. S. Chemla, T. C. Damen, D. A. B. Miller, A. C. Gossard and W. Wiegmann, Appl. Phys.

Lett. 42, 864 (1983).

[25] T. H. Wood, C. A. Burrus, D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard and

W. Wiegmann, Appl. Phys. Lett. 44, 16 (1984).

[26] D. A. B. Miller, D. S. Chemla, T. C. Damen, A. G. Gossard, W. Wiegmann, T. H. Wood

and C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).

[27] T. H. Wood, C. A. Burrus, D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, and

W. Wiegmann, to be published.

[28] E. E. Mendez, G. Bastard, L. L. Chang, L. Esaki, H. Morkoc and R. Fisher, Phys. Rev. B26, 7101 (1982).

[29] R. C. Miller and A. C. Gossard, Appl. Phys. Lett. 43, 954 (1983).

[30] J. D. Dow and D. Redfield, Phys. Rev. Bl, 3358 (1970).

[31] D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T.H.Wood

and C. A. Burrus, to be published.

[32] R. C. Miller, A. C. Gossard, D. A. Kleinman, O. Munteanu, Phys. Rev. 529,3740 (1984).

[33] D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Damen, A. C. Gossard, W. Wiegmann,

T. H. Wood, C. A. Burrus, Appl. Phys. Lett. 45, 13 (1984).

207
FIGURE CAPTIONS

Figure 1 Room temperature absorption spectra of a 3.2 urn thick high purity GaAs sample

and of a MQW sample consisting of 77 periods of 102A GaAs layers and

207A Al i%Ga tiAs layers.

Insert: Temperature dependence of the line width of the n — 1 heavy hole exciton. The solid line corresponds to fit discussed in the text.

Figure 2 Intensity dependence of the absorption at the peak of the exciton resonance for the

GaAs (curve (a)) and MQW (curve (b)) samples whose absorption spectra are shown in Figure 1. The solid line corresponds to the empirical fits discussed in the

text.

Figure 3 Absorption spectra of a MQW sample consisting of 65 periods of 96A GaAs layers

and 98A Al^Ga jAs layers with (solid line) and without (dashed line) a pumping

beam from a cw laser diode operating 42 meV above the first exciton resonance. The intensity of the pumping beam is I — 800 W/cm . The fast oscillations in these spectra are Fabry-Perot fringes in a thin glass plate covering the sample.

Figure 4 Raw data obtained by pump-probe experiments on the sample described in Figure 3. (a) linear transmission; (b) nonlinear transmission; diffraction efficiency on the light

induced grating. For (b) and (c) the pump and probe beam powers were ~300 iiW and —60 fiW respectively.

Figure 5 Spectra of the imaginary and real parts of nonlinearity of the MQW sample. aek and neh describe respectively the change of absorption and the change of refractive index induced by one electron-hole pair.

Figure 6 Comparison of the experimental data of Figure (6), corrected for the small

variations of the laser power, with the semi empirical fit for the linear absorption

(a) and nonlinear absorption (b). The sold curve in (c) is obtained by the

Kramers-Kronig inversion discussed in the text.

Figure 7 Comparison of the absorption spectrum of an unexcited MQWS to the spectra after excitation by an ultra short pump pulse at resonance with the heavy hole exciton.

Figure 8 Dynamic of the absorption of the heavy hole exciton peak for resonant and non

resonant femtosecond pumping.

Figure 9 Absorption spectra for electric fields E parallel to the quantum well layers,

(a) E = 0; (b) E = 1.6xl04 V/cm; (c) E = 4.8xl04 V/cm.

The insert shows figuratively the distortion of the electron-hole Coulomb potential

with the applied field.

Figure 10 Absorption spectra for electric fields E perpendicular to the quantum well layers

(a) E =lxl04 V/cm; (b) E =4.7xl04 V/cm; (c) E =7.3xl04 V/cm.

The insert shows figuratively the distortions of the quantum well potentials with the

applied field.

Figure 1 1 Schematic of the p-i-n MQWS modulator. Comparison of the electric pulse applied

to the modulator and the optical pulse generated by the modulator.

Figure 1 2 Theoretical and measured optical transmission of the optical bistable SEED.

208

210
t—i—i—i—i—i—i—|—i—i—i—

r

1N3I0UJ3OD NOIldaOSflV

211
o o o

NOIldUOSeV 3AUVH3H

NOUdUOSflV

212
213
PHOTOREFLECTANCE IN GaAs/AlGaAs MULTIPLE QUANTUM WELLS

O.J. Glembocki, B.V. Shanabrook, N. Bottka, W.T. Beard and J. Comas

Naval Research Laboratory

Washington, DC 20375

Photoreflectance (PR) is a contactless form of electromodulation spectroscopy

in which the built-in surface field is periodically modulated by the

photoinjection of electron-hole pairs. Photoexcited minority carriers re- combine with surface state charge and thereby reduce the built-in electric

field. 1>2 As in electroreflectance (ER), this modulation produces "third

derivative-like" features in the optical dielectric function, in the vicinity

of critical points. Consequently, even at room temperature, one observes

very sharp differential reflectance lines related to the joint density of

states of the material being studied. ^ Because of this ER and PR have proven

to be sensitive room temperature probes of interband transitions in bulk

semiconductors. However, there have been few ER or PR studies of microstructural systems.

Recently, we demonstrated that photoreflectance is a sensitive probe of

interband transitions in GaAs/AlxGa^_x

As multiple quantum wells (MQW) and

modulation doped hetero junctions exhibiting a two dimensional electron gas.^

In this paper, we describe the photoreflectance technique and review the

results of the MQW work of Ref. (4).

The experimental arrangement for photoreflectance is similar to one used in

ER measurements. Shown in Fig. 1 is a schematic diagram of an ER

spectrometer modified to perform PR measurements. The modulation is

accomplished by mechanically chopping a laser of photon energy greater than

the band gap of the sample. The reflectance measurement is performed with a probe beam of white light dispersed by a monochromator and then reflected

from the sample. The reflected beam is passed through a filter which blocks

the laser light and is detected by a photomultiplier (PMT) or some other

suitable detector. The signal from the PMT is processed by a lockin

amplifier tuned to the modulation frequency of the chopper. A servo mechanism on the high voltage power supply of the PMT is used to maintain a constant DC current in the phototube, allowing us to directly obtain AR/R.

In our system, a quartz halogen lamp and a 1/4 m Jarrell-Ash monochromator

provided the probe beam. The detector was either a PMT with an S-l response

or a Si diode cell. In the later case, the servo mechanism was not used and

AR/R was obtained from independent measurements of AR and R. The modulation

was produced with a 1/2 mW HeNe laser chopped at 150 HZ.

Our samples were made by the molecular beam epitaxy (MBE) technique. The MQW

structures consisted of approximately 30 periods of GaAs/AlxGai_xAs layers

grown on semi-insulating GaAs substrates and clad with either 200 A thick

GaAs or 1000A thick AlxGaj_x

As films. The AlxGai_xAs layers separating the

quantum wells were about 125 A thick. The well width, Lz , was estimated by

several methods including the use of the growth rates of the MBE films,

photoluminescence and resonant Raman scattering measurements.

Shown in Fig. 2 are the 300 K photoreflectance spectra obtained from Ref.

(4). The topmost trace is for a single undoped GaAsMlo.i7Gao.83As

214
hetero junction, covering the spectral range between the direct gaps of the

GaAs and AlxGai_xAs components, i.e., the E Q

(T g v

>

c

) transitions. The

lowest energy line near 1.42 eV results from the GaAs E 0 transition, while

the sharp feature located at 1.65 eV is the E 0 transition from the

Gao.83Alo.i7As thin film. The latter line allows us to obtain x.

The bottom three traces of Fig. 1 are PR spectra of the MQW samples. There

are several general features to note. First, each spectrum contains a weak

GaAs PR line. This line was observed in all of our samples, regardless of

the type of cladding layer (GaAs or AlxGai_xAs) . The GaAs signal originates

from the buffer layer, which is typically grown between the quantum wells and

the substrate material.^ This indicates that the built-in modulating field

reaches across all of the quantum well layers. Second, we see that each

spectrum has a line near 1.70 eV corresponding to the Eq transitions in the

AlxGai_xAs films. From this line we obtain x for each sample.

The quantum well (QW) nature of our samples is evident in the numerous PR

structures observed between the E0 transitions of the GaAs and AlxGai_xAs.

The strongest features increase in number and their energy separations

decrease with increasing quantum well width, a behavior expected from parity

allowed QW interband transitions. ^ There are also weaker structures located

between the strong lines. In Ref. (4) these lines were identified by

comparing their energy positions to predicted results of a finite square well

calculation of the subband structure. The fraction of the band gap difference

between GaAs and AlxGai_xAs taken up in the conduction band was assumed to be

Q e=0.7. In Fig. 2, we have marked the calculated energy positions of parity

allowed interband transitions, from heavy (hi,...hn ) and light (l]_,...ln ,)

hole states to conduction subband states. This shows that the strong

features are due to hn transitions while the weaker ones are due to ln transitions. Shown in Fig. 3 is a comparison of the calculated and

experimental values of the transition energies hn

-

hi for all of our samples.

Values relative to h^ were used to partially account for excitonic effects on the transitions. The agreement between experiment and theory is good.

In Ref. (4) the value of Qe was varied and it was found that the best

agreement between experiment and theory for interband transition energies was obtained using Qe = 0.6. Consistent with recent findings, this value of Qe is smaller than the 0.85 initially suggested by Dingle. ^ Our value of Qe is

in excellent agreement with the 0.57 of Miller et al..^ It is interesting to

note that the values of x used in the experiments of Refs. (7) and (6) were

0.3 and 0.54 respectively, while in our case they were approximately 0.2 and

0.03. The differences among the reported values of Qe suggest that it may be a function of x.

The ln transitions are typically much less in intensity than the hn features,

consistent with previous work.^»^ By using bulk conduction and valence band

wave functions we estimated^ that the ln PR lines should be about a factor of

3 less intense than the hn transition, in reasonable agreement with the

experimental results.

In conclusion, we see that photoref lectance is a powerful, contactless room temperature probe of the optical properties of multiple quantum wells. Its

contactless nature extends modulation spectroscopy to samples prepared on

215
on semi-insulating substrates. In MQW samples we observed the Eq transitions

from the AlGaAs barrier and the allowed hn and ln interband transitions from

the quantum wells. Our experimental results for the transition energies agree

with a square well calculation of the QW states using Qe = 0.60. Therefore,

a single PR spectrum can provide information about the x value of the AlGaAs

layers, the quality of the quantum wells from spectral line widths and (given

Qe ) the well width from the allowed QW transitions.

REFERENCES

1. J.L. Shay, Phys. Rev. B2_, 803(1970).

2. D.E. Aspnes, Solid State Coramun. _8, 267(1976).

3. F.H. Pollak, SPIE Proceedings, 276 , 142 (1981).

4. O.J. Glembocki, B.V. Shanabrook, N. Bottka, W.T. Beard and J. Comas,

submitted to, Appl. Phys. Lett.

5. R. Dingle, W. Wiegmann and C.H. Henry, Phys. Rev. Lett., 33_» 827(1974).

6. D. Arnold, A. Ketterson, T. Henderson, J. Klein and H. Morkoc, Appl.

Phys. Lett., 4_5, 1237(1984).

7. R.C. Miller, D.A. Kleinman and A.C. Gossard, Phys. Rev. B29, 7085(1984).

8. M. Erman, J.B. Theetan, P. Frijlink, S. Gaillard, F.J. Hia and C.

Alibert, J. Appl. Phys. 56, 3241(1984).

Figure 1. A schematic diagram of the photoreflectance apparatus.

216
-*— AIGaAs

1

0

-1

-2

1 k

h

« hs

2

1

0

-1

-2

GaAs

= 460A

AIGaAs Mi h

f f

h, h. J

h7 h8 h9

1.4 1.5 1.6 1.7 PHOTON ENERGY (eV)

iff

300

200

uf 100

MOW - T = 300 K OPEN SYMBOLS = THEORY

SOLID SYMBOLS = EXPERIMENT

(x, LI

(0.33, 340)

(0.24. 460I

(0.22, 150)

(0.19. 90)

3 4 5 6 7 SUBBAND INDEX, n

Figure 3. Theoretical (open) and

experimental (solid) values of the hn transition energies taken relative to

hi . Values of x and Lz for each

sample are in parenthesis The lines are drawn only as a guide to the eye.

Figure 2. Photoreflectance spectra for an undoped GaAs/AlxGai-xAs heterojunction (top trace) and three multiple

quantum well samples with x* 0.2. The arrows labeled hi , . . .hn (li,...^)

correspond to the calculated values of

allowed interband transitions between

heavy (light) hole valence and conduction subbands

217
PICOSECOND CARRIER DYNAMICS IN a-Si

A. I. D'Souza, M. G. Roe, P. E. Wigen

Department of Physics, The Ohio State University

174 West 18th Avenue, Columbus, Ohio 43210

and

R. Messier

Materials Research Laboratory

The Pennsylvania State University

University Park, Pennsylvania 16802

Experiment: A mode locked argon ion laser is used to synchronously pump a cavity dumped dye laser in a picosecond spectrometer. A block diagram of

the spectrometer is shown in Figure 1 . The cavity dumped dye laser is

operated at a wavelength of 600 nm, an average output power of 14 mW, and a repetition rate of 0.4 MHz. The pulses have a FWHM of 15 ps and a peak

power of 2300 W/pulse. The output beam is divided by a beam splitter

with 95% of the power used as a pump beam, incident normally on the sample.

The remainder is again split with one portion monitored by a PMT, giving a real time monitor of any changes in laser power. The balance is used as a probe beam which is passed through a delay line determining the time

interval between arrival of pump and probe pulses at the sample. The pump

and probe beams are focussed on the sample with spot diameters on the order

of 30 ym to 40 pm, resulting in a peak power density of approximately

2.4 x 10** W/cm^. The probe spot is maintained at a smaller diameter

than the pump spot in order to assure proper overlap. The analyzer is

initially set crossed to the reflected beam insuring that the signal PMT

POL X/4

Figure 1. The experimental setup. Stepper motors control the shutters. Box HI and the delay line, Box 112. The symbols are PMT photomul tipl ier detectors, POL polarizers,

L. lenses, IF interference filter, and x/4 quarterwave phase plate.

218
. 01600

. 01400

. 01200

. 01000

<-> . 00800

, 00600

00400

. 00200

0. 00000

o-Si, T-300K

DELAY IN PICOSEC. 2. Change in reflectance as a function of delay time in picoseconds

1. 800

-2. 000

-2. 200

-2. 400 -

-2. 600

-2. 800

a-Sii T-300K

DELAY IN PICOSEC. Fig. 3. Semilog plot of the log (change in reflectance) as a function of delay time in picoseconds.

219
will measure changes in reflectance of the sample due to changes in the

electronic properties induced by the pump beam.

Sample: Films of a-Si of thickness 1 pm were prepared by rf diode

sputtering under fixed Ar pressure of 7 mTorr [1] on substrates of fused

silica. The band gap was determined from optical absorption measurements,

by extrapolation of (ahv) 1 ^ 2 vs. (hv) curves to a = 0. [2]. The band gap EQ was measured to be 1.32 eV.

Discussion: Changes in reflectance as a function of time in the range

-150 ps to +900 ps were measured by using a pump-probe technique. Typical

data is shown in Figure 2. Photons of energy 2.1 eV excite 4.4 x 10^°

carriers/cm3 from the valence band to a point high in the conduction

band. This carrier density was calculated using a reflectance R of .35 and

an absorption coefficient a = 10^ cm

-* . The hot electrons are assumed

to decay down to the localized states near the conduction band edge in 0.7

ps [3]. Since the pulses have a FWHM of 15 ps, this process is too fast to

be observed in this experiment. The initial condition is then assumed to

be that of the excited carriers near the conduction band edge. Figure 3

shows a semi-log plot of the data in Figure 2. The plot is linear,

indicating an exponential decay of the change in reflectance with time. The

decay time constant is determined, from the slope of the semi-log plot, to

be t = 270 ps. Since the change in reflectance is, to first order,

proportional to the conduction band carrier density n, [4] n satisfies an equation of the form:

The decay of carriers from the conduction band is therefore a single body

process

.

A rough sketch of the density of states in the gap for a-Si is shown in

Figure 4 [5] . The large density of states in the gap enhances the

percolation of charge carriers through the defect states in the gap into the

valence band. This is the proposed non-radiative single body process that

dominates the decay in a-Si at T = 300 K as opposed to a radiative two-body

process normal in single crystal materials. The near absence of radiative

recombination [5] is consistent with photoluminescence experiments performed

dn

dt

n

T

Fig 4. Density of states as a function of

energy. (Reference 5) Ec and

define the mobility edges.

hi in in- 1 iii- 10-

Density of states/ (cm liV

220
on sputtered a-Si:H. These experiments indicate that photo-luminescence

intensity tends to zero as the partial pressure of hydrogen during growth

of the samples tends to zero.

Experiments performed on a-Si:H indicate decay processes different from

that observed in a-Si. The decay is no longer exponential, suggesting the

existence of competing processes such as radiative recombination. Other

decay processes are currently being studied.

In conclusion, the observations suggest that the large density of states in

the gap in a-Si provides a fast and easy non-radiative channel for the decay

of charge carriers out of the conduction band. This conclusion is derived

from the exponential decay in the reflectance which is interpreted as indicating the dominance of monomolecular non-radiative recombination, with

bimolecular radiative recombination relatively unimportant in sputtered a-Si

at T = 300 K up to 900 ps.

References

:

[1] . J. S. Lannin, L. J. Pilione, S. T. Kshirsagar, R. Messier and

R. C. Ross; Phys. Rev. B26.3506 (1982).

[2]. R. C. Ross and R. Messier; J. Appl. Phys. 52,5329 (1981).

[3]. J. Tauc, Physica 117B & 118B (1983) 889-893.

[4]. D. 6 . McLean; Ph.D. Dissertation, The Ohio State University (1984).

[5]. S. R. Ovshinsky and D. Adler; Contemp. Phys. 19,109 (1978).

[6]. M. A. Paesler and W. Paul; Phyil. Mag. B, 41,393 (1980).

221
PHOTOREFRACTIVE AND NONLINEAR-OPTICAL PROPERTIES OF NEW ELECTROOPTIC MATERIALS

Peter Giinter

Laboratory of Solid State Physics

Swiss Federal Institute of Technology

ETH Honggerberg

CH-8093 Zurich, Switzerland

In this paper we will present a review of both photorefractive and nonlinearoptical materials for optoelectronic applications. The materials requirements

for nonlinear optical laser frequency conversion using the electronic hyperpolarizabilities and optical signal processing using the photorefractive effect

shall be discussed. Some representative examples of newer photorefractive and

nonlinear optical materials, its properties and applications will be described.

In recent years ferroelectric materials with their large electro-optic coefficients have found new optical applications in the field of phase conjugate optics, image processing and dynamic holography. These applications are based on the photoinduced refractive index changes or photorefractive effect which is

due to the linear electro-optic effect driven by photoinduced space-charge

fields. The light induced changes of refractive indices in electro-optic crystals are based on the spatial modulation of photocurrents by non-uniform illumi

nation. The electrons or holes which are excited from impurity centers by light

of suitable wavelength, are upon migration, retrapped at other locations leaving behind positive or negative charges of ionized trap centers. The resulting

space-charge field between the ionized donor centers and the trapped charges

modulates the refractive indices via the electro-optic effect.

In photoconductive materials the photocurrent along one dimension (z) with elec

trons as carriers is given by:

s e$a

T/ x r ^UxakT dl(x,t) . J (z > t} = — I(z ' t),Ld-— dT~ (1)

where L^ = UtE

q

is the drift length, e the electronic charge, $ the quantum

efficiency for exciting an electron, a the absorption constant, hv the photon

energy, y the electron mobility, T the lifetime of photoexcited electrons,

I(z,t) the light intensity distribution and E

Q the applied electric field. The

space-charge build-up process is mainly affected by yi and a,$. The latter two

quantities being strongly wavelength dependent.

Laser-induced dynamic phase gratings can be recorded by means of this photorefractive effect. The main requirements for photorefractive materials used in

"real-time" recording and processing are:

a) short recording time constants and

b) large refractive index changes.

It has been shown in Refs. 1 and 2 that photoinduced grating recording using

the migration of photoinduced charge carriers by an external electric field is

222
most efficient. The grating recording time constant T for small drift length

can be determined from the relaxation time of charged dielectric layers separated by half a fringe spacing:

hv ££

o 1 , ,. , . T = — — — (.£: dielectric constant) (2)

e $yx aIQ

Therefore short recording times are found in electro-optic materials with

large drift length L<j=]JT E , i.e. in materials with large lifetime of photoinduced carriers. This parameter is mainly determined by the defect concentration (donor- or trapping concentration). (Table 1).

The maximum refractive index changes depend on the value of the photoinduced

space-charge field and the electro-optic coefficient rjj of the material. The

maximum possible space-charge field Eq is limited by the concentration of

trapping centers

e Na A

E = = . (3)

q 2-rree o

For a peak field E =10^ V/cm, a fringe spacing A = 1 ym, and a dielectric

constant £=50, the^required trap density would be Na=1 . 7 • 10^ cm

-

^. This value

is comparable to the ones determined in BaTiC>3, KNbC>3 and Bii2SiC>20^ • In Table 1 the electro-optic coefficients and peak refractive index changes are listed in addition to the photoconductivity parameter yx. Table 1 also shows,

that photoconductive f erroelectrics with large electro-optic coefficients

(e.g. KNbC>3:Fe 2+

, BaTi03 , Ba2NaNb50i5 , Bai_xSrx

Nb2C>6) are extremely interesting for photorefractive applications such as optical phase conjugation and

'real-time" image processing.

The materials requirements for nonlinear optical laser frequency conversion

using the electronic hyperpolarizabilities in inorganic crystals is discussed

in the second part of this contribution. It is shown, that high quality materials with large nonlinear optical coefficients and the possibility of phase

matching between interacting beams have been found, in which low power laser

light (e.g. from Ga^_x

AlxAs laser diodes) can be efficiently converted to the

second-harmonic

.

For the ideal case of second-harmonic generation of plane monochromatic waves,

neglecting pump depletion, the second harmonic intensity is given by:

2 2 2 ton

^ 1

eff

d

eff 2, , / sinAk£/2 \

2

... 1(20)) = — - (w> Ak£/2 (4)

c e

o n \ /

where £, o) and c are the crystal length and the vacuum speed of light respectively andAk = ko - 2k^ is the phase mismatch. As seen from (4), d|ff/n^ can

be used as a figure of merit for frequency doubling (see Fig. 1 for a comparison of materials). Phase matching (Ak=0) is possible e.g. in birefringent materials by a suitable choice of the direction of propagation and polarization

223
of the fundamental wave. For extremely long interaction lengths one would

like to use collinear phase matching (PM) , where the fundamental and second

harmonic beams generally propagate along a main axis of the index ellipsoid.

Adequate birefringence for PM is the most restrictive requirement. Room tempe

rature operating and 90° noncritical phase-matching are particularly important to eliminate the use of temperature controllers for compactness and to

ascertain long effective interaction length without walk-off for high efficiencies. The group symmetry of the doubling crystal must be such, that nonzero tensor elements exist for the proper phase matchable polarizations. Some

nonlinear optical materials which fulfill these requirements for Ga^_x

Alx

As

and InGaAsP/lnP double heterostructure laser radiation will be discussed.

KNbQ3 *- s such a material with large nonlinear optical coefficients ^32 = 21 pm/V, d^i = 16 pm/V and d33 = 33 pm/V) and the possibility of 90° noncriti

cal phase matching for frequency doubling Al xGa^_xAs diode and (Styril-9) dye

laser radiation (840 nm < X^m

< 950 rim) at room temperature 3,4. up to P2W

= 0.35 mW blue light (A = 430 nm) could be generated in a 5.74 mm long crystal

with a Ga^_xAs laser diode Pw

= 155 mW) . Frequency doubling experiments with

dye lasers (e.g. Styril-9) and KNb03 within or out of the laser cavity are described 5.

IOOOO

cv^ 1000

>

q. '00

toc

CMT3

o

m

10

0.1

0.01

0.001

1—1 1 1 1 m i

1—1 1 1 1 1 ill 1—1 1 1 1 in

I I I Mill I I I I I I III I I I I I III

-Te

: ' CdGeAs2 -GaAs

=- MNA

A ZnGeP2 / m-NA

AgGaSe 2 KNbO \ TUAsSe, " CdSe POM

AgGaS2

• KTiOP04

x aq Asc LiNbO, Ag3 AsS3

Li 10,

ADP

BeS04 Si0?

No2 SbF5 KB5 08 -4H20

0.1 I 10 Transparency Range (ftm)

100

FIGURE 1: Figure of merit d^/n-* and transparency range

for nonlinear optical materials (including

organic crystals.

POM: 3-methyl-4-nitropyridine-l-oxide

MNA: 2-methyl-4-nitroaniline

m-NA: metanitroaniline)

224
TABLE 1: Photoconductive electro-optic materials

Material yT

2 (10-7

TM )

EO coefficient

ij V

'

T

(S)

10 3 -An

Bi 12 SiO2 0

1 5 -

Bi 12Ge0

2() 0.8 3.4 30* 0.01

KNb0

3

:Fe 0.3 64, 380+ 0.001-0.1* 0.3

K(NbTa)O3 (T

c=40°C) 0.01 500

BaTi0

3

0.001 80,1640+ 40* 0.1-1

LiNb03 io"5

31 100 1

Ba

.25

Sr

.75

Nb 2°6 0.8 45 0.03

An: Peak steady-state refractive index change

+

: depending on crystal orientation. (A = 600 nm)

References

1. P. Giinter, Physics Reports 93, 199-299 (1982)

2. P. Gunter, Optics Letters 7_, 10 (1982)

3. P. Gunter, SPIE (Proceedings of ECOSA'80) Vol. 236, 8-18 (1981)

4. J.-C. Baumert, P. Gunter and H. Melchior, Optics Commun. 48, 215 (1983)

5. J.-C. Baumert, J. Hoffnagle and P. Gunter, Appl. Optics

(to be published)

225
MEASUREMENT OF DEFECT AND TRANSPORT PROPERTIES OF

ELECTRO-OPTIC MATERIALS USING THE PHOTOREFRACTIVE EFFECT

M. B. Klein and George C. Va I I ey

Hughes Research Laboratories

3011 Ma I i bu Canyon Road

Ma I i bu , CA 90265

In this paper, we use steady state beam coupling as a function of

grating period at 442 nm to obtain data on the sign of the

dominant photoca r r i e r , the concentration of empty traps and the

effective electro-optic coefficient for several samples of

BaTi03 , Ba

2

NaNb

5

0 15 (BNN) and Sr^Ba^b^ (SBN) . We assume an energy level model in which a single species X, in

two valence states X and X , is responsible for the photoactive

energy states in the bandgap of each sample. We denote the

concentration of X as N, and that of X as N . We a I low for the

photo-generation of both electrons and holes, through the

ionization of X or X , respectively.

In our experiments, we used a cw He-Cd laser to measure the

intensity gain T as a function of grating period A for each

sample. The grating normal was aligned parallel to^the c-axis,

and in most BaTiO^ experiments the beams were s-polarized in

order to avoid the comp I i cations of beam fanning [1] . For each

crystal the c-axis direction was set so that the weak probe beam

was amp I i f i ed at the expense of the strong reference beam. By

measuring the sense of the resulting c-axis orientation, and

using the convention developed by Feinberg, et. al. [2], we were

able to determine the sign of the dominant photocarri er in each

c rysta I . We have developed an expression for the beam coup I i ng gain as a function of grating period, taking into account the explicit

contribution from both holes and electrons, and the poss i b i I i ty

of incomplete po I i ng of our crystals. The model contains two

lumped experimental parameters which can be determined for each

sample by fitting our gain expression to the experimental points.

The first parameter is an effective electro-optic coefficient,

defined as

r rr = a F r , etf ang ' where a is the normalized conductivity, F is the fractional

poling and r is the appropriate combination electro-optic

coef f i c i ents angular factors for a f u I ly poled crystal . The

second experimental parameter is an effective trap density,

written as NN

+ / (N+N+

)

.

226
In Fig. 1 we show typical gain data for each of the three

materials studied. Through curve fitting techniques, this data

yields values of effective electro-optic coefficient and

effective trap density for each sample. The sol id curves in each

case represent a best fit to the data. In Table I we present our

results for the sign of the dominant charge carrier, the

effective trap density, the effective electro-optic coefficient,

and the fractional poling times the normalized conductivity for

seven crystals of BaTiO^- Through non-photoref ract i ve

+ measurements [3] on the same crystals, we have shown N<<N , so

that NN

+ /(N+N )ZN, the concentration of level X. Other

measurements of this parameter in BaTiOo [2,4] give values

sj_mi lar to ours. We be I i eve that the reduction in the values of

F<J from unity (as obtained in a perfectly poled crystal with a single dominant charge carrier) is primari ly due to the

comparable contribution of electrons and holes to the

photoconductivity. The results of the same analysis for BNN and

SBN will a I so be presented

Ref e rences

1. J. Feinberg, J. Opt. Soc . Am. 72, 46 (1982).

2. J. Feinberg, D. Heiman, A.R. Tanguay, Jr. and R.W. Hellwarth,

J. Appl. Phys. 52, 1297 (1980).

3. M.B. Klein, S.P.I.E. Conference on Analog Optical Processing

and Computing, Cambridge, MA, 25-26 October, 1984, Paper 519-

22.

4. S. Ducharme and J. Feinberg, J. Appl. Phys. 56, 839 (1984).

227
0 0.4 0.8 12 1.6 2.0 2.4 2.8 GRATING PERIOD Ag

, ^im

Figure 1. Intensity gain vs. grating period for BaTi03

, BNN and

Sr0.75Ba 0.25Nb2°6 at 442 nm '

CRYSTAL

SIGN OF

DOMINANT

PHOTOCARRIER

NN+

N + N

+ cm-"*

EFFECTIVE E-0 COEFFICIENT

reff (PM/VOLT)

F?=reff/r 13

G/L + 4.4 x 10 16

7.3 0.30

R1 + 8.1 9.5 0.40

R2 2.8 -7.9 -0.33

GB3 + 6.1 9.7 0.41

K2 + 8.7 12.0 0.50

SC + 4.2 8.3 0.35

GB4 + 3.0 4.2 0.18

Table I. Sign of the dominant photoca r r i e r , effective trap

density, effective electro-optic coefficient and fractional

poling times the relative conductivity for seven crystals of

BaTi03

.

228
ANALYSIS OF SCATTERING PATTERNS AND DECAY DYNAMICS OF

PHOTOREFRACTIVE GRATINGS IN LiNbO-r CRYSTALS

Jacek K. Tyminski , Richard C. Powell, H.C. Chow,

«nd Michael J. Kiel war

Department of Physics, Oklahoma State University

Stillwater, OK 7407B

One technique for studying the photorefractive effect (PRE) in

crystals is to establish and probe holographic gratings with

crossed laser beams. Generally the gratings are assumed to have

a sinusoidal shape and the measurement which is made is the

scattering efficiency of the probe beam at the Bragg condition.

We report here the development of a new technique for studying

the PRE based on the analysis of small angle scattering

patterns. This technique allows for the inclusion of multiple

Fourier components in the geometric shape of the grating in

interpreting the data. The results of applying this type of

analysis to LiNb03 crystals with several different types of

defect properties show that the measured scattering patterns are

extremely sensitive to the microscopic Properties of the

grating. In addition, the dynamics of charge relocation in the

PRE were investigated by monitoring the decay curve of the scattered probe beam during erasure for a variety of samples and

experimental conditions. The results were interpreted in terms

of the recently proposed hopping model .

The crossed laser beams used to write a holographic grating

produce an electric field pattern in the crystal in the form of

a sine wave. However, the final shape of the photorefractive

pattern established by the laser—induced charge relocation will

generally not have exactly the same shape as the laser pattern

due to the geometric effects of the spatial distributions of the

donor and trap defect sites and possible assymmetric charge

relocation dynamics. This situation is enhanced when more than

one type of defect contributes to either donor or trapping

kinetics. Previous investigations of the PRE in solids have not

addressed the effects of these deviations from Pyre sine wave

gratings either theoretically or experimentally. 2 ' 3 This information is important in developing an understanding of the properties of the chemical and structural defects which contribute

to the PRE characteristics of a material.

The samples used for this investigation were single

crystals of LiNb03 containing different types of defects. One

was a nominally pure crystal which we subjected to a series of

thermal annealing treatments in either air or a vacuum for

oxidation and reduction. The effects of these treatments on the

concentration and valance states of lattice defects and the

valance states of chemical impurities has been determined previously by electron paramagnetic resonance measurements.

229
Another sample was treated with bensoic acid to introduce

deep traps into the crystal. 5 Also a crystal doped with Cu

(which enhances the PRE) and one doped with Mg (which decreases

the PRE) were studied. These samples provide a wide variety of

defect distributions which is necessary -for enhancing our under

standing of the effects these distributions have on the PRE

characteristics.

The 442 nm emission from a 16 mW He-Cd laser was used to write

and erase the photorefractive holograms. Holograms were established using several different crossing angles for the write

beams in order to determine the effect of grating spacing on the

PRE properties. The 632 nm emission from a 6 mU He-Ne laser was

used to probe the grating without damaging the hologram. The

scattered signal beam was detected by a RCA C31034 photomultiplier tube and recorded with the help of a EGG/PAR lock-in

amplifier to improve the signal-to-noise ratio. The charge

relocation associated with the PRE reached steady state conditions in 2 to 5 minutes. The variation of the scattering efficiency of the probe beam as a function of scattering angle was

measured by slightly rotating the sample holder base. The

charge relocation dynamics were determined by monitoring the

time dependence of the grating erasure. The erasure was accomplished by redirecting the He-Cd laser beam to provide uniform

illumination of the crystal. The experiments were performed at

several temperatures to determine the effects of thermal activation on the charge relocation dynamics.

For the simplest case of a single set of donor and acceptor

traps • a sinusoidal grating* and one type of charge relocation

dynamics i the grating erasure gives an exponential signal decay

with the decay rate given by*

K»2Rd2Nq2/ (ee0

k BT)+2Rd2 C4irsin (0/2) /\1 2 (1)

where 0 is the write beam crossing angle* N is the average

concentration of the photocarriers contributing to the photorefractive effect* q is their charge* and R is the rate of

charge relocation over a distance d. After measuring K as a

function of sin2 (0/2) * the slope and intercept of the experimental data can be used to obtain the charge concentration and

relocation rate parameters. The results of our measurements

show the erasure decay patterns to be bi exponential decays with

the two decay rates varying differently for different defect

distributions. This is attributed to the Presence of two types

of charge carriers contributing to the PRE. In addition* the

temperature dependence results show the effective charge

densities to be affected by filling and emptying shallow traps.

The angular scattering patterns were generally found to have

several major scattering maxima which included the Bragg peak*

peaks having positions and erase rates consistent with harmonics

of the Bragg peak* and peaks whose properties could not be

related to those of the Bragg peak. Small angle scattering

patterns were measured around each of these major scattering

230
maxima. These pattern* varried -from intenae t narrow central

peaks with weak, damped side lobes, to weak central peaks with

strong side lobesi to very broad central peaks no visible side

lobe oscillations. The type o-f pattern varried with write beam

crossing angle and with partial erasure conditions. The coupled

wave theory of holographic gratings2 was extended to include

higher order harmonics and subharmonics in the scattering

patterns. The results were used to develop a computer program

•for -Fitting the observed angular scattering patterns. This

procedure provided information concerning the geometric shape

and modulation depth of the gratings.

ACKNOWLEDGMENTS s This work was sponsored by the U.S. Army

Research Office.

REFERENCES

1. J. Feinberg, D. Heiman, A.R. Tanguay, Jr., and R.W.

Hellwarth, J. Appl . Phys. 51, 1279 (1980),

2. H. Kogelnik, Bell Sys. Tech. J. £B, 2909 (1969).

3. P. Bunter, Phys. Repts. 23, 199 (19B2).

4. K.L. Sweeney and L.E. Halliburton, Appl. Phys. Lett. 42i 336

(19S3)

.

5. J. Jackel , A.M. Glass, G.E. Pctereson, C.E. Rice, D.A. Olson

and J.J. Veselka, J. Appl. Phys. 55, 269 (1984).

231
Use of optical phase conjugation for understanding basic material

properties

R.W. Hellwarth

Departments of Electrical Engineering and Physics

University of Southern California

Los Angeles, CA 90089-0484

(213)743-6390

When nearly counter-propagating monochromatic optical beams whose complex field

amplitudes are Gj and H. (i=x,y,z) overlap an image-bearing beam of amplitude E- in a transparent material, the nonlinear polarization density can generate a fourth beam whose

complex amplitude F- in some plane is related to Ej in the same (or a slightly displaced)

plane by

Tk.e

4* 'j , +N i- 0)

J Here is a complex constant matrix and IST is a non-conjugate or noise background

assumed to be small. For ideal phase-conjugation, K

j j=K5j j

# Nj=0 and

F.=KE.* (2)

in one plane, the conjugate "reflectivity" or "gain" being |K| 2

. However, the more general case described in (1) is often referred to as phase-conjugation, as we will here. The

particular geometries of the "four-wave mixing" of beams E, F, G, and H that lead to (1)

produce a signal F. whose dependence on the sixteen possible combinations of beam

polarization, and on beam angles and frequencies, gives much information on the process

mediating beam mixing.

Phase-conjugation by four-wave mixing requires the beam frequencies to obey

u> F=u)G+od H-u>

E

(3)

and the beam wavevectors (or subsets of them when complex images are propagating) to

obey the "phase-matching" condition

|£G

+lT H-lt

E -irF |<L- 1 (4)

where L is the length of the region over which the F beam interacts with the others. A

great advantage of phase-conjugation as a spectroscopic probe is the ease of satisfying

232
(4) for a wide range of input angles and frequencies. When all frequencies are equal

(degenerate four-wave mixing) and G and H are perfectly counter-propagating, then any

direction of input beam E results in a perfectly phase-matched output F.

In the simplest class of phase-conjugation experiments the two beams E and G interfere

to create intensity variations (moving or stationary) which in turn cause a variation in the

refractive index seen by beam H. This variation is often called an index "grating". The H

beam scatters from this grating to generate the F beam. This may be called the (tensor)

volume holographic process for phase-conjugation. The beams can be on simultaneously

or in various time sequences. We will describe how this single-grating process has been

used to obtain the most accurate measurements of impurity density, conduction band

diffusion lengths, and trap excitation cross-sections in photorefractive bismuth silicate

and barium titanate. Results for electron-hole pairs in semiconductors will also be

described. This process gives often the simplest and most accurate method of measuring

thermal conductivities of slightly absorbing transparent media. It is also the basis for

another coherent Raman spectroscopic technique (Raman-induced phase conjugation)

which has advantages and disadvantages relative to coherent anti-Stokes Raman

spectroscopy and other weil-known laser spectroscopic techniques.

In another class of phase-conjugation experiments, there are two gratings formed

simultaneously, one by interference of beams E and G, the other by interference between

beams E and H. The interference of the two beams formed by the scattering of H and G

respectively from these gratings gives a precisely calibrated comparison of the relative

phases, index tensor, and amplitude of the two gratings. We will describe how this

process can be used to measure the diffusion of optically-excited ions in transparent

media, as well as the alteration in optical polarizability of the excited states. We will also describe other forms of phase-conjugation in which optical intensity gratings

play no role. One depends on resonant two-photon absorption by beams G and

H. Another depends on spatial variations in the state of polarization of the optical field. These have yielded accurate spectroscopic data where two-photon induced flourescence

is absent, and also evidence on the nature of atomic collisions in vapor.

233
MEASUREMENT OF DIELECTRIC PROPERTIES OF KTa_ _ Nb 0,

AT MILLIMETER WAVELENGTHS 1 x x *

D. Rytz and M.B. Klein

Hughes Research Laboratories, Ma I i bu , California 90265

B. Bobbs , M. Matloubian and H. Fetterman

Dept. of Electrical Engineering

UCLA

Los Angeles, Ca 90024

Mixed crystals of KTa^^Nb^O.^ or KTN are we I I known

f erroe I ectr i cs whose transition temperatures T can be adjusted

between -273 and 430 C by varying the Nb concentration x. In the

present work, we report on dielectric measurements in the 60-95

GHz range for crystals with x = 0.20, 0.09, 0.025, 0 and T = -103, -183, -238 C respectively (for x=0, i.e. pure KTaO^, there

is no transition) . The crystal growth of these samples is

described by Rytz and Schee I (1982) and the phase transition

properties are reviewed by Kuge I et a I . (1984) . The measurement technique utilizes samples with plane

para I lei faces mounted between the flanges of two standard

rectangular metal waveguides. The sample thus acts as a FabryPerot etalon, yielding a fringe pattern when the phase factor

27rnL/X is varied (n is the microwave refractive index and L is

the sample thickness). The use of free-standing samples

eliminates the mechanical problems associated with mounting the

sample inside the waveguide, and fact I i tates the interchange of

samples. In particular, high values of dielectric constant and/or

loss tangent can be accurately measured by using samples with

sufficiently sma I I thickness. In our experiments, we have varied

the phase factor by two different means, and analyzed the

resulting fringe pattern in transmission to obtain the dielectric

constant and the loss tangent. First, by using a swept frequency

source we varied X, and thus obtained the dielectric properties

as a function of frequency between 60 and 85 GHz. Second, by

varying the temperature (and thus the refractive index) at a fixed frequency of 94 GHz, we obtained data on the temperature

variation of the dielectric constant and the loss tangent between

20 °C and 200 °C

.

The Fabry-Perot fringe pattern (in transmission) is

desc r i bed by :

I trans/I inc = (l-R) 2r/((l-Rr) 2

+ 4Rrsin 2 (27rnL/X)) (1)

where R is the reflection coefficient, r=exp(-aL), and a is the

absorption coefficient. The coefficient R is taken as the Fresnel

reflection from an air-dielectric interface, modified by the

change in phase velocity resulting from the presence of the

metal I ic waveguide wa I I s (Bridges et a I . 1982) . For each sample, we began the experimental sequence by

234
analyzing the transmission fringe pattern at room temperature,

using a swept frequency source. The refractive index (and thus

the dielectric constant) was obtained from the spacing between

fringe peaks, and the absorption coefficient was obtained from

the fringe contrast, or the peak transmission. Finally, the loss

tangent was obtained from the absorption coefficient and the

refractive index using

tan 5 = \a/2nn . (2)

A typical measured fringe pattern is shown in Fig. 1. Note the

excellent fringe visibility and the lack of dispersion over the

measured frequency range. We find that the loss tangent values

obtained from the fringe contrast agree very we I I with those

obtained from the peak transmission, thus giving firm support to

our Fabry-Perot analysis.

After a sample was measured as a function of frequency, the

transmission variation with temperature was recorded by inserting

the waveguides holding the sample into a cylindrical furnace.

Typical transmission plots are displayed in Fig. 2, and the

resulting values of loss tangent are plotted vs. temperature in

Fig. 3. For all the Nb concentrations but one (x=0.025), the data

points have been obtained with more than one sample. The

scattering observed for x=0.20 and 0.09 can be explained by

concentration i nhomogene i t i es

.

Our experimental findings may be related to the phonon

properties of KTN . In a simple harmonic osc i I I ator model

tan 6 = 7s"/(n

s 2

" "

2

) (3)

where w is the angular frequency corresponding to X, fl the soft

mode frequency and 7 the damping of the soft mode. In Table 1,

we give relevant figures for ft and 7 at room temperature and

compare the loss tangent obtained from Eq . (3) to the value

measured at 94 GHz. The agreement is reasonable for x=0.09, 0.025

and 0. For the highest concentration x=0.20, the soft mode is

ove rdamped- at room temperature (Kuge I et a I . 1984) and_^herefore

7 /ft > (2) ' . From Eq . (3), one can estimate 7 >90 cm . The

variation of soft mode properties with temperature and the

comparison of our high frequency measurements with static

measurements wi I I also be discussed.

One of the authors (DR) acknowledges financial support from

the Swiss National Science Foundation.

REFERENCES

Bridges, W.B., Klein, M.B., and Schweig, E., IEEE Trans. MTT-30

(1982) 468.

Kugel, G. , Vogt, H., Kress, W., and Ry tz , D. , Phys. Rev. B30

(1984) 985.

Rytz, D., Fontana, M.D., Servoin, J.L., and Gervais, F., Phys.

Rev. B28 (1983) 6041.

Rytz, D., and Schee I , H.J., J. Cryst. Growth 59 (1982) 468.

Vogt, H., and Uwe , H., Phys. Rev. B29 (1984) 1030.

235
14718-5

0.15 —

0.10 —

o8

inz

<

cr

t0.05 -

60 70 75 FREQUENCY, GHz85

14718-4

0.010 -

FIGURE 1 : Fabry-Perot transmission

pattern recorded at room temperature

as a function of frequency. The

measured dielectric constant is 287

and the measured loss tangent is

0 . 005

.

FIGURE 2 : Fabry-Perot transmission

pattern at 94 GHz as a function of

tempe ratu re

.

200

TEMPERATURE, °C

236
FIGURE 3 : Temperature dependence of the loss tangent in KTN

14718-1

KTa

-x Nbx°3 REFERENCE

(cm' 1

)

ys

(cm

-1

)

tanfi = tan6 AT 94 GHz

x = 0 VOGT AND UWE (1984, 81 20 0.010 0.007

x = 0.018 RYTZ, et al. (1983) 86 32 0.014

X

= 0.02 KUGEL. et al. (1984) 83 24 0.010

x = 0.025 0.007

x = 0.09 KUGEL, et al. (1984) ~55 -30 0.031 0.030

x = 0.20 KUGEL, et al. (1984) OV ER- 0.07 DAMPED

TABLE 1 : Soft phonon frequency fi and damping 7 , calculated

loss tangent (see Eq . (3)) and measured loss tangent at room

tempe ratu re

.

237
REFRACTIVE INDICES AND THERMO-OPTIC COEFFICIENTS

OF NONLINEAR CRYSTALS ISOMORPHIC TO KHoP0.

K. W. Kirby, C. S. Hoefer and L. G. DeShazer

Hughes Research Laboratories

3011 Malibu Canyon Road

Malibu, CA 90265

Crystals of the potassium dihydrogen phosphate (KDP) group are

widely used in laser technology. These tetragonal isomorphs

have the composition M^XO^, where M may be K, Rb , Cs or NH4;

X may be P or As; and H may be replaced by deuterium D, fully

or partly. They encompass sixteen crystals potentially useful

in state-of-the-art optical devices. These devices are second

harmonic generators, sum and difference frequency mixers,

electro-optical switches, and phase modulators. The

refractive indices and their thermal behavior were measured

for eleven of these nonlinear crystals (Table 1) . These

parameters are needed to establish the phase matching geometry

and thermal behavior of a nonlinear crystal in the frequency

upconversion operation in high-power laser systems.

The ordinary and extraordinary indices of refraction were

measured at twelve wavelengths spanning the visible and near

infrared region from 404 to 1064 nm. The measurements were

obtained by the method of minimum deviation using a Zeiss

spectrometer designed for this technique. The overall angular

accuracy of the instrument is ±5 arc seconds, which translates

to a systematic uncertainty in the refractive index of

±3x10 . A small hot stage stabilizes the prism temperature

at about 6 C above room temperature to avoid both water

adsorption on the crystal faces and thermal variation of the

refractive indices during the measurement run. The prism

temperature was measured by a thermocouple attached to the top

of the prism, and showed ±0.5 C stability over an eight hour

day. Crystal prisms having 1 cm" faces and 50° apex angle were

furnished by Interactive Radiation Inc. The measured indices

of refraction were fitted to a two resonance Sellmeier formula

n

2 = A + CB/[CX 2

- 1] + DX 2/[EX 2

- 1]

with deviations between measured and calculated values

consistent with the estimated systematic error.

We observed that the indices of refraction of three KDP

crystals varied with crystal supplier, with index differences

as much as 6 x 10 in the visible spectrum (Table 2) . The

differences correlated to variations in the lattice parameters

of these crystals determined by standard x-ray techniques

(Table 3) . The index of refraction decreased as the lattice

parameters increased, which is expected from dispersion

238
theory. We speculate that the changes in lattice parameters

arise from variations in the inclusion of crystalline defects

during the crystal growth process . We are currently examining

this conjecture with relation to the growth rate.

The thermo-optic coefficients a - n "^dn/dT and the thermal

expansion coefficients ag perpendicular to the optic axis were

measured using a double interf erometr ic technique involving

the stimul taneous use of the Twyman-Green and Fizeau

configurations. Crystal plates 8x11x12 mm were held in a

gimbal mount in a vacuum oven which provided a linear heat

ramp to the crystal from 25 to 40 C. The chamber was

evacuated to 10 torr to eliminate index contributions due to

air. The chamber was placed in one arm of a Twyman-Green

interferometer. Fringe changes from this interferometer are

caused by path length changes in the arm containing the

crystal . The Fizeau interferometer was formed by the front

and rear faces of the sample which was polished to provide 2

or 3 fringes of wedge between the two surfaces. Phase shifts

measured with this interferometer are caused by optical path

length changes in the sample. The coefficients a and a % are

determined from the simultaneous solution of the Swo equations

that describe the phase shifts for the two interferometers

.

The quantites actually determined by the experiment are AT^,

and ATp, the temperature change needed to move one fringe in

the Twyman-Green and Fizeau interf erograms . Each fringe

pattern is magnified and sampled by a pinhole placed in front

of photomul tipl ier detectors. As the sample is heated the

motion of each pattern across its pinhole is recorded on a

chart recorder. AT^, and ATp are then determined from the

record and used to calculate and £*£ using the relations

a z = (X/2L) (ATT

_1

- ATp" 1

) a

n

= (X/2L){ATT

" 1 - [ (n-1) /n] ATp" 1

}

where X is the wavelength of light and L is the length of the

sample. This measurement is made for light polarized parallel

(7r) and perpendicular (a) to the optic axis for three

wavelengths (441.6, 632.8 and 1152 nm) . The signs of the

temperature changes are chosen such that a £ determined from

the above equation does not depend on polarization or

wavelength. The wavelength variation of the a coefficients

was compared to the theoretical formula [1] , and the necessary

constants were determined in order to be able to calculate the

values of in the range from 440 to 1150 nm

.

We acknowledge helpful discussions with David Eimerl , LLNL

,

and Stephen C. Rand, HRL, and the experimental assistance of

James E. Brown, HRL, in performing the interferometer

measurements. This research was partially supported by

Lawrence Livermore National Laboratory.

2 39
REFERENCE

1. Y. Tsay, B. Bednow and S. 3 . Mi tra

,

Phys. Rev. B8, ZOoo

(1973)

.

Table 1. Listing of nonl inear crystals an d refractive indices

at wave 1 engths of Nd : YAG laser h armonics

Acronym Formula Pol Wave 1 ength (Angs troms)

3547 5321 10642

KDP KHoP0

.

Ord 1 . ool 114 1 .512125 1 . 493807

2 4 Ext 1 .485358 1 .470396 1 . 459882

KD*P KD„P0 . Ord 1 con ooo . ozo2o2 1 . 507339 1 . 493102

2 4 Ext I . 483432 1 .468282 1 . 458221

ADP NH.HoPO. Ord 1 . 547578 1 .526734 1

.

505719 4 2 4 Ext 1 . 498635 1 .481351 1 . 467922

AD*P NH.DoP0. Ord 1 . 540189 1 .520750 1 . 504601 4 2 4 Ext 1 .512196 1 .494977 1 . 481440

CDA CsHoAs0. Ord 1 . 602576 1 .573174 1

.

551442

2 4 Ext 1 .578136 1 .551465 1

.

535613

CD*A CsDoAs0. Ord 1 . 597533 1 .569171 1

.

549921

2 4 Ext 1 .576096 ii

i

j.

.

Out J. £t £j ADA NH.HoAs0„ Ord 1 .610849 1 .580123 1 . 555052

4 2 4 i .550872 J .525129 1 . 508105

AD*A NH4D

2

As04 Ord 1 .603119 1 . 573608 1 . 552381

Ext 1 . 546980 1 .521465 1 . 505873

RDP RbHoP0. Ord ] .528293 1 .509970 1 . 492026

2 4 Ext 1 .496667 1 .480662 1 . 469535

RD*P RbDo P0„ Ord ] . 556300 1 .537537 1 . 521639

2 4 Ext

RDA RbHoAs0. Ord 1 .590975 1 .562495 1 . 540502

2 4 Ext 1 .549174 1 .525049 1 . 510470

240
Table 2. Comparison of refractive indices of KDP crystals from

two different suppliers

X (A) Pol Inrad Clev. Cry. An (xlO°)

4799 .91 Cd rd 1 .51570 1 .51598 28

Ext 1 .47314 1 .47325 11

5085 .82 Cd Drd 1 .51365 1 .51392 27

Ext 1 .47150 1 .47183 33

5893 Na Ord 1 . 50897 1 .50955 58

Ext 1 . 46808 1 . 46860 52

6438 .47 Cd Ord 1 .50671 1 . 50702 31

Ext 1 . 46644 1 . 46687 43

Table 3. Lattice parameters of the different KDP crystals

Crystal source Lattice parameters

(Angstroms)

a c

a/c ratio

Inrad 7 .460 6.965 1 .071

Clev. Cry. 7.451 6.950 1 .072

241
BISMUTH SILICON OXIDE: SAMPLE VARIABILITY

STUDIED WITH THERMALLY STIMULATED

CONDUCTIVITY AND THERMOLUMINESCENCE

Brian W. Holmes

Department of Physics

San Jose State University

San Jose, California 95192

Jacques E. Ludman

Charles L. Woods

RADC/ESOP

Hanscom AFB, MA 01730

1 . Introduction

Bismuth silicon oxide (BSO)is widely used in optical data processing,

reversible, real-time holography, and optical phase conjugation. The optical

characteristics (such as wavefront reflectivity) vary significantly, even for

identically prepared crystals./1/ The manufacture of uniform and improved BSO

crystals may well depend on a better understanding of the fundamental

processes responsible for its photosensitivity.

In BSO and other photorefractive materials, absorbed light causes electrons to

diffuse through the crystal or to drift under an applied electric field.

Electrons tend to be trapped in regions of weaker illumination, and the

resulting uneven charge distribution causes variations in the refractive

index, due to the electro-optic effect. However, the centers responsible for

electron trapping in BSO have not been identified. /2/

We studied electron trapping in BSO using thermally stimulated conductivity

(TSC) and thermoluminescence (TL). These techniques/3/ entail irradiating

samples at low temperatures (filling the electron traps), followed by warming.

During warming, electrons are released from the traps, contributing to the

conductivity when they are promoted to the conduction band, and contributing

to luminescence when they lose energy via a luminescent center. In this

study, we survey a number of different BSO crystals, in order to assess sample

variability as revealed in TSC and TL.

2. Experimental details

Of the nine crystals studied, one was from Crystal Technology and the rest

were from Itek. The Itek crystals were from different growth runs. The

crystals were cut in 0.5 x 0.5 cm 2 and 1.0 x 1.0 cm 2 samples. Thicknesses

varied from 0.08 to 0.17 cm. Often several small and large samples of the same crystal were available for comparison. Electrical contact was made using

ultrasonic indium soldering; contacts were ohmic./V

Samples fitted on a copper mount inside an optically accessible dewar. The

copper mount was in thermal contact with a liquid nitrogen reservoir and a heater. A copper-contantan thermocouple monitored the temperature. The BSO

samples were electrically isolated from the copper mount by thin teflon tape;

teflon fittings pressed the samples against the copper mount, ensuring good

thermal contact.

242
Samples were irradiated at liquid nitrogen temperatures using unfiltered light

from a mercury lamp. This produces light near 350nm, corresponding to the

band gap of BS0./5/ All samples were exposed for ten minutes; longer exposure

did not alter the TSC and TL spectra. The heating rate was 0.8 K/sec.

Samples were biased at 10 volts during warming. TSC was measured using a Keithley 103B electrometer. TL was measured using a cooled RCA 7102

phototube, sensitive in the infrared. Data were collected on x-y recorders,

giving TSC and TL as a function of thermocouple voltage.

3. Results

Figure 1 gives TSC and TL for one of the samples. All samples studied showed

three major peaks. Peak 1 has a peak temperature (Tm ) near 1 60 K ; peak 2 has

Tm near 235 K; peak 3 has Tm near 298 K. Peak 2 is always double; peak 1 is

double for some of the samples, making the measurement of Tm uncertain for

this peak; and there is evidence for other minor peaks.

3a. Peak temperatures - Tm values

obtained for TSC and TL show systematic variations. Neglecting Tm

for

peak 1 (since this peak is sometimes

double), we note that TL peaks at

lower temperatures then TSC for all

samples. For peak 2, the average

temperature shift is 1.8 K; for peak

3, the average temperature shift is

6.2 K. These temperature shifts are probably due to the quenching of the

luminescence at higher temperatures

/5/.

b. Peak heights - The peak heights

are not directly comparable. For TSC,

peak heights depend on heating rate,

applied voltage, and sample thickness.

For TL, peak heights depend on heating

rate, sample size, phototube characteristics, and experimental geometry.

However, we note the following

consistent pattern: peak 3 is higher than peak 2 for TSC, and peak 3 is

smaller than peak 2 for TL. This may also be attributed to the quenching of

the luminescence at higher temperatures; however, this feature is not present

in the TSC and TL spectra reported earlier by Lauer./V

300

TEMPERATURE(K)

Fig. 1 - TSC and TL for a BS0

sample. The vertical scales are arbitrary.

3c Thermal activation energies - The thermal activation energies E^ can be

calculated from TSC and TL curves using initial rise techniques. /4, 6/

Expressing these energies as multiples of kTmfor peaks 2 and 3, we obtain

E^ - 26 kTra

, consistent with Lauer's earlier measurement./ 4/ There is no significant difference between TSC and TL. If this relation holds for peak 1 , then the three major peaks represent electron traps with thermal activation

energies of 0.36, 0.53, and 0.67 ev below the conduction band.

243
3d. Sample consistency - Different samples of the same crystals were studied,

In this case, TL results differ for large and small samples, owing to

geometrical factors. For TSC, however, the results for large and small are quite similar, since the large

and small samples had the same thicknesses. Figure 2 gives TSC

spectra for large and small samples

of the same crystal. Typically,

large and small crystals agree on peak positions, and the agreement

on peak heights is within 10%.

3f. Sample variability - Different

crystals, while yielding similar Tm values, show considerable variation

in peak heights. Table 1 gives peak

heights measured for TSC in eight

different samples. It can be seen

that peak 1 heights vary by a factor

of 3.4; peak 2 by a factor of 2.2;

and peak 3 by a factor of 2.5. It can also be seen that the height

variations are not obviously cor- related; that is, a crystal which has

a high peak 1 will not necessarily

have a high peak 2 or 3.

iOO 200 300

TEMPERATURE (K) Fig. 2 - Comparison of TSC for

large and small samples of a BSO

crystal. (Not the same crystal

in Fig. 1 .

)

Sample Peak 1 Peak 2 Peak 3

G-9 3.00 0.73 1 .56

G-21 2.14 1.11 2.03

G-25-1

1.33 1 .41 3.00

G-27-6 0.89 1 .20 1 .90

Q-2-22 1 .09 0.61 1 .46

Q-17-18 2.27 0.63 1 .22

J-2 1 .68 0.77 1 .48

C.Tech. 1 .61 0.98 2.16

Table 1 - Peak heights (in nanoamperes) for TSC

in different BSO crystals.

4. Discussion

Since the TSC and TL spectra results from the release of electrons from traps

in BSO, it would be valuable to learn what the density of these electron traps

is. Our results do not give this information directly. One can integrate

under a TSC curve to obtain the number of electrons passing through the

electrometer; however, the limited drift range for electrons in BS0/5/ means such a calculation will greatly underestimate the trap density. More

important, from the standpoint of applications of BSO, is the fact that the

traps studied in TSC and TL are probably not responsible for the trapping

which produces photorefractivity J2/ These latter traps are likely to be

deeper than the shallow traps studied here, which release electrons at room temperatures or below. However, the variation in peak heights we measure

surely reflects a variation in trap densities by a factor of three or more. A

similar variation in the concentration of photorefractive traps centers has

244
been inferred from studies of wavefront reflectivity; and an even larger range

of variability has been reported in bismuth germanium oxide./1/

In summary, although TSC and TL do not give information regarding the specific

nature of electron trapping in BSO, these studies do provide additional

evidence of the variability of BSO crystals. Supplementary studies, such as

EPR, optical absorption, photoluminescence, and four-wave mixing will be

needed to give more information on the fundamental character of the electron

traps, and to show how the variations in TSC and TL relate to variations in

the centers responsible for photorefractivity

.

5. Acknowledgments

We are pleased to acknowledge the assistance and advice of R. Aldrich of Itek,

and C. Pitha of RADC/ESOP, Hanscom AFB, MA. This work was conducted while BWH was a fellow in the 1984 USAF-SCEEE Summer Faculty Research Program.

/1/ Y. Ja, Opt. Quant Elec. J_6, 355-8 (1984).

/2/ M. Peltier & F. Micheron, J. App. Phys. 48(9), 3683-90 (1 974).

/3/ See P. Brftunlich (ed.), Thermally Stimulated Relaxation in Solids

(Springer-Verlag, New York, 1979).

/4/ R. Lauer, App. Phys. Lett. 42(5), 2147"9 (1971).

/5/ S. Hou, R. Lauer, & R. Aldrich, J. App. Phys. 44(6), 2652-8 (1973).

/6/ R. Chen, J. App. Phys. 40(2), 570-85 (1969).

245
MATERIALS REQUIREMENTS FOR OPTICAL LOGIC AND BISTABLE DEVICES

N. Peyghambarian and H. M. Gibbs

Optical Sciences Center

University of Arizona

Tucson, Arizona 85721

Semiconductors are attractive materials not only because of device

applications but also because of their unique physical properties. 1 They

exhibit large optical nonlinearities near the band edge due to the excitons,

biexcitons, electron-hole plasma, carrier, and thermal effects. They provide

adequate absorption (ctl * 1) in a very short (i = 1 ym) length. As a result,

a large nonlinear phase shift, of the order of ir/2, is obtained for logic

operation, with kW/cm2 intensities in micrometer lengths.

When an optical nonlinear material is sandwiched between two partially

reflecting mirrors, a nonlinear etalon is formed. Nonlinear etalons can perform various optical logic operations such as AND, OR, and NOR. The

principle of such operations is the shifting of the Fabry-Perot transmission

peak in response to input pulses. The nonlinear medium must be such that the

absorption of one input pulse changes the refractive index at the probe

wavelength enough to shift the transmission peak of the etalon by about one instrument width. For example, if the etalon is initially tuned to the probe

wavelength, a NOR gate operation results if the control pulse can detune the

etalon from the probe wavelength. The speed of the gate can be very rapid,

allowing picosecond decision making at a gigahertz repetition rate without

thermal problems. A GaAs-AlGaAs optical NOR gate has recently been

demonstrated to respond in 1 ps with very low switching energy. 2

Individual pixels can be defined by dividing the beam and focusing on different spots on the device or by plasma etching an array of devices.

Already, an array of 1-ym-diameter cylinders spaced 5 ym apart has been

constructed in a GaAs wafer of millimeter dimension by plasma etching, but

switching of pixels in the array has not yet been tried.

Optical bistability, which is referred to as the existence of two stable

output intensities for the same input intensity, has been realized in many

semiconductors. 1 In bulk GaAs and GaAs-AlGaAs multiple-quantum-well

superlattices, the nonlinearity arising from the presence of the free-exciton

resonance has produced room-temperature optical bistability with a few

milliwatts of power. l

» J »* The biexciton resonance in CuCl is responsible for

subnanosecond optical bistability at cryogenic temperatures. 5 ' 6 The index

change caused by thermal effects in ZnS and ZnSe interference filters has

produced bistability at room temperature with a visible light source using

= 50 kW/cm2 intensity and = 10 ys switching times. 7 In this talk, we focus

our attention on these materials because of their greater potential to be

used as practical devices, however, a survey of other materials will be

given. 1

The larger the nonlinear refractive index, n2

, the lower the switching power.

For excitonic nonlinearities, the switching intensity is the intensity required

246
to saturate the exciton resonance. The saturation intensity is smaller for a larger exciton radius or smaller exciton binding energy. Smaller electronphonon interaction reduces the exciton broadening and causes observation of

the exciton feature at higher temperatures close to the ambient. Therefore,

a moderate exciton binding energy with a small electron-phonon interaction is

ideal for low-power switching operation at room temperature. Nonlinear

spectroscopy reveals characteristics of the materials and their suitability

for device applications. We will show nonlinear transmission and

luminescence spectra obtained in a pump-probe technique with femtosecond

pulses' and discuss their use in characterizing some materials.

The switch-on time of a bistable device is limited by how fast the exciton

feature saturates. Since the exciton screening occurs in a fraction of a picosecond8 and the cavity build-up time is also « 1 ps, a switch-on time of

« 1 ps is expected and has been demonstrated in GaAs-AlGaAs devices.*

However, the switch-off time is limited by how fast the exciton feature

recovers, which depends on the carrier lifetime and is usually on the order

of a nanosecond in semiconductors at room temperature.

In conclusion, semiconductor optical bistable etalons lend themselves

naturally to parallel logic operations, taking advantage of parallel

propagation and imaging properties of light. They should be useful for such

applications as multiplexing, encoding, and spatial modulation.

This research is supported by a National Science Foundation grant No. ECS

8020303 and by the Air Force Office of Scientific Research (United States Air

Force) and the Army Research Office (United States Army) under contract No.

F49620-80-C-022.

247
REFERENCES

1. N. Peyghambarian and H. M. Gibbs, invited article for the special issue of

JOSA B on Excitonic Nonlinear Optical Processes in Semiconductors (1985);

also Ne Peyghambarian and H. M. Gibbs, invited paper for the special issue

of Opt. Eng. on Optical Computing (Jan. 1985).

2. A. Migus, A. Antonetti, D. Hulin, A. Mysyrowicz, H. M. Gibbs, N.

Peyghambarian, and J. L. Jewell, Appl. Phys. Lett. Jan. 15, 1985.

3. H. M. Gibbs, S. S. Tarng, J. L. Jewell, D. A. Weinberger, K. Tai, A. C.

Gossard, S. L. McCall, A. Passner, and W. Wiegmann, Appl. Phys. Lett. 41,

221 (1982).

4. S. S. Tarng, H. M. Gibbs, J. L. Jewell, N. Peyghambarian, A. C. Gossard, T. Venkatesan, and W. Wiegmann, Appl. Phys. Lett. 44, 360 (1984).

5. No Peyghambarian, H. M. Gibbs, M. C. Rushford, and D. A. Weinberger, Phys.

Rev. Lett. 51, 1692 (1983); also, R. Levy, J. Y. Bigot, B. Honerlage, F. Tomasini, and J. B. Grun, Solid State Commun. 48, 705 (1983).

6. S. W. Koch and H. Haug, Phys. Rev. Lett. 46, 450 (1981); also E. Hanamura,

Solid State Commun. 38, 939 (1981); and D. Sarid, N. Peyghambarian, and H.

M. Gibbs, Phys. Rev. B., Rapid Commun. 28, 1184 (1983).

7. G. Olbright, N. Peyghambarian, H. M. Gibbs, A. Macleod, and F. Van

Milligan, Appl. Phys. Lett. 45, 1031 (1984); also, S. D. Smith, J. G. H.

Mathew, M. R. Taghizadeh, A. Walker, B. S. Wherrett, and A. Hendry, Opt.

Commun. 51, 357 (1984).

8. C. V. Shank, R. L. Fork, R. F. Leheny, and J. Shah, Phys. Rev. Lett. 42, 112

(1979); also N. Peyghambarian, H. M. Gibbs, J. L. Jewell, A. Antonetti, A.

Migus, D. Hulin, and A. Mysyrowicz, Phys. Rev. Lett. 53, 2433 (1984).

248
Mirrorless Optical Bistability in CdS

J.W. Haus

Physics Dept.

Rensselaer Polytechnic Institute

Troy, NY 12181

C.C. Sung

Physics Dept.

University of Alabama in Huntsville

HUNTSVILLE, AL 35899

CM. Bowden

Research Directorate

US Army Missile Lab

US Army Missile Command

Redstone Arsenal, AL 35898-5248

and

J.M. Cook

Physics Dept.

Middle Tennessee State University

Murfreesboro, TN 37132

Summary

Recently, Dagenais and Sharfin* have reported whole-beam optically bistable

behavior in uncoated platelets of CdS. This phenomenon was observed at

milliwatt power levels when the incident laser frequency was tuned just below

the resonance of the I2 bound-exciton. Using a qualitative model, they

successfully correlated the temperature dependence of the absorption with the

observed bistable behavior.

Our research extends their qualitative model by eliminating several

unnecessary assumptions. 2 The first point to consider, is that the previous

treatment assumed a constant temperature across the sample; this is valid only

for small absorption and small sample lengths. The second point concerns the

heat dissipation outside the active volume; because the large heat conductivity

of CdS at low temperature, we assume in our model that the variation of

temperature over a cross-sectional area normal to the incident laser field is

small and can be neglected. Thus, the heat dissipation through the end faces

determines the temperature variation across the material. The third point is

the inclusion of the boundary conditions for both heat conduction and the

electromagnetic field at each end of the sample.

Our results clearly demonstrate the importance of the temperature

boundary conditions. Even small changes in the boundary thermal resistances

can significantly alter the results. Also we find the existence of a second

optically bistable hysteresis which has not been reported as yet. We show how

such devices can be used as multiplexers and as composite optical logic

elements-* (AND, XOR and negation XOR gates) for use in optical computing and

optical communications.

249
The role of the temperature-induced absorption in CdS which leads to

bistable output intensities is explained as follows. The initial tuning of the

incident laser frequency is below the bound-exciton resonance, as the input

intensity increases, the temperature of the medium rises and the absorption

resonance is shifted toward the laser frequency, thus the absorption

increases. The result is a further increase in the temperature in the medium

due to the extra absorbed energy and this mechanism provides positive

feedback. In our treatment, the temperature is no longer homogeneous,

therefore the exciton resonance frequency is also inhomogeneous and this

yields a more complex behavior. At a certain input intensity, a runaway

behavior is observed where the exciton resonance frequency overshoots the

laser frequency at the input face; this causes a sudden increase in absorption

inside the sample and a resulting low transmission. As the input field is

further increased the resonance frequency distribution in the medium is

shifted to lower values until the highest resonance frequency in the

distribution lies below the laser frequency. Again, the transmission changes

abruptly, but this time to a larger value. As the input intensity is reduced,

the switching points can, depending on the initial detuning between the laser

and exciton resonance frequency, occur at a lower value of the intensity.

1. M. Dagenais and W.F. Sharfin, Appl. Phys. Lett. 45, 210 (1984).

2. J.W. Haus, C.C. Sung, CM. Bowden and J.M. Cook, submitted to J. Opt. Soc.

Amer. B (1984).

3. J.W. Haus, CM. Bowden and C.C. Sung, "Composite Logic Gate Element and

Multiplexer for Optical Computing and Optical Communications" patent

applied November, 1984.

250
NONLINEAR OPTICAL EFFECTS IN LIQUID CRYSTALS

D. Armitage and S. M. Delwart

Lockheed Missiles & Space Company, Inc.

Research and Development Division

3251 Hanover Street

Palo Alto, California 94304

Liquid crystals are birefringent materials with fluidity comparable to water.

Device potential arises from the influence of electric, magnetic or optic

fields on the optic axis orientation. The response time is viscous limited.

However, the more viscous smectic phases have storage properties.

The birefringence is directly related to the order parameter of the fluid and

is therefore sensitive to temperature, particularly near a phase transition.

At the nematic to isotropic phase transition, the refractive index (n)

discontinuity approximates 0.1. This is a weak first order transition with

latent heat approximately 1 J/cm3. These properties make the nematic phase

an interesting solvent in a thermal dye cell. The thermal response is not

viscous limited. It can be shown that when submi 11 i second response is

demanded the thermal process is more efficient than the viscous limited

orientation response.

The value according to mean-field theory is also plotted. The well known

inadequacy of the theory close to the transition point is revealed. The

extraordinary axis value are always greater than the ordinary axis values, in

accordance with theory. These results are representative of nematic s. Although there is some variation in behavior close to the transition, it is

unlikely that substantially higher values will be found.

A further advantage of nematics follows from the use of pleochroic dyes. The

dye is oriented by the nematic and results in a polarization-dependent

absorption, which can be exploited by orthogonally polarized write and read

beams such that minimum absorption of the read beam occurs.

Experiments were performed with 5CB doped with L-dye D81 (EM Chemicals). A

lO-pm period grating was written with a 10-ns doubled YAG pulse. The grating

dynamics were probed with a HeNe readout beam. Figure 2 shows the evolution

of the first-order diffraction intensity. Nematic theory suggests a functional form [l-exp-(t/T) ]2

9 which is verified experimentally. Figure 3

shows the temperature dependence of r. The higher dn/dT of the nematic is

accompanied by a significant delay time approaching 100 ns.

In the isotropic phase the response time is essentially the thermal ization

time of the dye. An improved value for the order parameter response should

result from subtracting the dye thermal ization time. This is shown against

reduced temperature in Fig. 4, and implies the form r =(J^j - T)-°« 7 . The

same behavior is seen in the ultrasonic experiments (Ref. 5).

The order parameter response derived from this experiment is about a factor of

2 greater than that associated with ultrasonic attenuation (Ref. 4). However,

the differing thermodynamic situation could account for the discrepancy.

251
The cell was generally operated at 1 percent diffraction efficiency, which

should require according to Fig. 1 a write energy of 1 mJ/cm2 at

T^si - T = l

e C„ Fluctuation in the write pulse prevented verification of

this prediction to better than a factor of 2.

The thermal grating is accompanied by an acoustic grating, but output

oscillations from this source are beyond the response time of the system

(Ref. 5). The response is much stronger when the grating is modulated across

the nema ti c - i sotrop 1 c transition, where the index discontinuity approaches

0. 1. The grating decay time increases by a factor of 103 to approximately

10 ms. This is due to a quenching of the grating through the

isotropic -nematic transition, which results in a disoriented nema tic with a viscoelastic decay process

The nematic phase is turbid, with a 1/e optical attenuation length approaching

100 mn. This makes it difficult to achieve the high-efficiency thick-phase

grating condition, which is possible in clear liquids. At infrared

wavelength, nematic s are favored since other solvents lose path length

advantage.

REFERENCES

1. F. Rondel ez, W. Urbach, and H. Hervet, Phys. Rev. Lett. 61, 1058 (1978)

2. I. C. Khoo and S. Shepard, J. App. Phys. 54, 5491 (1983)

3. D„ Armitage and S. M„ Delwart, Int. L. Cryst. Conf. (1984), Mol . Cryst

Liq. Cryst. (1985)

4 e S. Candau and S. V. Letcher, Advances in Liquid Crystals V3, ed. G. H. Brown (Academic, 1978)

5. I. C. Khoo and R. Hormandin, J. App, Phys. 55, 1416 (1984)

252
Fig. 1 (A) MBBA n e , (B) 5CB ne , (C) Mean-Field Prediction for "(B)",

(D) MBBA n 0 , (E) 5CB n 0

O ISO 300 150 600 7S0 900

t (n»)

Fig. 2 Oscilloscope Recording of First-Order Diffraction Intensity from 5CB

at TN j . T = 2°C. Circles are calculated from 5.3 [l-exp(-t/T) ] 2

with r = 150 ns

253
Fig. 3 Response Time as Function of Temperature T Through Nematic- Isotropic

Transition J\\i = 35°C

Fig. 4 Nematic Response Time Minus Isotropic Response Time (dye thermal ization

time) Against Reduced Temperature

254
A STUDY OF SECOND HARMONIC GENERATION COEFFICIENTS

AND

ULTRAVIOLET ABSORPTION EDGE OF BARIUM BORATE CRYSTAL

Ji-Kang Zhu, Bing Zhang, and Song-Hao Liu

Anhui Institute of Optics and Fine Mechanics, Academia Sinica

P.O. Box 25, Hefei, Anhui, People's Republic of China

Barium borate ( 6-63820^ ) is a new type of non-linear optical crystal which

was made by China for the first time. Its transparent range 190-3000nm and

SHG coefficient of macroscopic crystal = 4.6 x 10- ^ e.s.u. have been

111

shown by experiments. CNDO/S calculated value of X^W ^ which was in good

agreement with the experimental one was obtained by Chen et al.t^

However, their ultraviolet absorption edge 90nm was far from the experimental

result and unbelievable (the best UV crystal LIF has its ultraviolet

absorption edge 104nm.

In this paper we report one-electron energies and wave functions of barium

borate by use of EHMO theory. Both the calculated values of SHG coefficient

and ultraviolet absorption edge for barium borate crystal are in quantitative

agreement with the experimental results. The comparison between EHMO, CNDO/S

and experimental values is show in table 1

.

Table 1 . Comparison between calculated and experimental values of

SHG coefficient x^

2W ^ an<^ ultraviolet edge Ay

111

EHMO CNDO/S EXPT.

X

(2W) (10-9 e.s.u.) 5.39 3.78 4.60

111

X\i (nm) 188 90 190

Since there has been dispute on the position of ultraviolet absorption edge

we also calculate it by use of more accurate MS-Xa method and the calculated

result supports the EHMO calculation mentioned above. The factors which

determine the positions of ultraviolet absorption edges and the values of SHG

coefficients are discussed briefly.

[1] Chuangtion Chen, et al., a report on International Conference on Quantum Electronics, 1984.

255
SOLITON TRANSMISSION IN INHOMOGENEOUS

MEDIA WITH W-TAIIORED REFRACTIVE INDEX

Farag Z. El-Halafawy

Fac. of Electronic Eng.

Menouf, 23951, Egypt

El-Sayed A. El-Badawy, Mohammed A. El-Gammal,

and Mostafa H. Aly

Fac. of Eng.

Alexandria University

Alexandria, Egypt

In this paper , a method for soliton transmission in inhomogeneous media with W-tailored refractive index is modeled and

pa rametr i ca 1 1 y analyzed. Two kinds of i nhomogenei ti es are simultaneously considered : (a) Biquadratic variation of the refractive index (W-tailored radial profile), and (b) Boundary

conditions of the cladded fiber.

The achievable bit rate of such important transmission was Shown [1J to comfortably match with and could be made an order

of magnitude better than that of the best linear transmission.

The refractive index , n , is W-tailored under the biquadratic

nonl i near form,

n ,E) = n (7i) [l-«f2 + m*/4

] + n

2 |E| 2

(

1 ) where f = r / R and R,^\ , E, and n 2

are respectively fiber radius , carrier wavelength , electric field , and nonlinear coefficient of the refractive index. The parameters <X and m control both the values of minimum and maximum refractive index and the radial position of the first JPm j n wnere : W n < « + * m »• Vn n(*)(1-«/4"0. and/2.

n

= ,/2 .

The wave equation for the electric field, E, is given by [2]

V

2

E . _> . JUlA. £_ (| E |2 F ) ( 2 )

where the electric field in the fiber E (r,z,t) is given by

E (r,z,t) = Re If (z,t) U (/) exp [j (qz - *t ) ] ( 3 ) where U (f) is the solution of the steady state wave equation

for the linear i nhomogeneous medium ,

256
E Vl " ^ + k

0

( 1 " 2

^ + 2o< m J

>4

)^ U (-f) = 0 ( 4 ) where P is the eigenvalue of the propagation constant and

k = ( w + w

o

) n (w + w

c ),w =2t7-c/^, and k a

= lim k

VhfO

the solution of Eq.(4) is assumed under the series form,

U (j>) = exp ( -J

2

II ) ^ a 2i y

2i

( 5 ) with a = 1 . It is found that a~.

3 s ( i >1 ) are functions of

a 2

, o( , and m where a 2

= 0.5 + ( P - k£ ) R /4

2

P Q

was calculated through the perturbation theory to the third

order [3] under the form .

P o

= k o

" 2k

o i 2<K/ R +2m /r2 + 4 * 5m2 /R 3

k

0 Y2<7+79 m

3

/8c(R

2

k

2

( 7 ) The function ^(z,t) =

<f

> ( 1 ) possesses a light solitary solution of the form <- <P( \ ) = ^sech (7 ) ( 8 ) where Cp 2

= Vg

= 2

- Q ( kf + k e k;' )

I °

( n 2 /n

0 ) k o r

2

<f

with a propagation velocity Vg , Vg = P

Q

/ Q k0 kj ( 10 ) where X =(Vg*C- 7 )/ Vg f , T is the pulse durat i on , k^k 0

"' are

the derivatives of k w.r.t. w, Q = 1 - + yoCm , and& is a function of R , c< ,

( and m,

& =y u (/) d^2 (11)

It is not the^same as reported by [2].

The peak power R Q

is given by [1]

where £ is the permittivity of free space and S is the cross

sectional area of the fiber core .

A sample of the calculations based on this model will be discussed. The variations of the peak power po and the group velocity Vg with the parameter^ at different values of m and the

assumed set of parameters are displayed respectively in Figs.

1

and 2. From these figures and the other obtained data, it is

found that both ?0 and Vg possess exponential correlations with the parameter^. The results clarified in Fig. 3, where the

radius R appears as a parameter , assert that, at any assumed set

257
of parameters , there is a threshold value Of., to achieve a stable soliton transmission where 0*, increases as the fiber ra dius increases , Fig. 4.

In conclusion, to design a W-tailored refractive index fiber

for stable soliton transmission of high bit rate , minimum power and high group velocity, the parameter «<must be of minimum

value while the parameter m must be of maximum value .

1*

12

10

as 2,

2 -

R = 2.5

10" ?2 m /v

"2

= 1.2 x

*x = 1.06

1 ps

2.05

0.05 0.10 0.15

THE PARAMETER °<

Fig.1. Variation of P„ without or different values of m and the assumed set of other parameters .

OO

i o

2.04

2.03 ..

2.02

J 2.01

2.00

R = 2.5

"2

= -22

1.2 x 10

2 , m / v \ , 1.06 /im T, = 1 ps

±

0.05 0.10 0.15 0.20 0.25 0.30

THE PARAMETER <X

Fig. 2. Variation of Vg withcyfor different values of m and the assumed set of other parameters .

0.35

258
[1] A. Hasegawa and Y. Kodama, Proc. IEEE, Vol. 69, No 9, PP.

1145 - 1150 , Sep. 1981.

[2] M. Jain and N. Tzoar , J. Appl. Phys.,Vol. 49, No. 9, PP.

4649 - 4654 , Sep. 1978.

[3] G. Jacobsen and J.J.R. Hansen, Appl. Opt., Vol. 18, No. 16,

PP. 2837 - 2842, 15 Aug. 1979 .

0.05 0.10 0.15 o.20 0.25

THE PARAMETER cmL

Fig. 3. Variation of5£ with^for different values of R and the assumed set of

other parameters . 0.3 |

THE FIBER RADIUS , R , /im .k. Variation of*"., with R at the assumed set of parameters . th

259
COMPARISON OF VIBRATIONAL SPECTRA OF HEAVY METAL

FLUORIDE GLASSES WITH THOSE OF "COMMON" GLASSES*

Bernard Bendow

The BDM Corporation

Albuquerque, NM 87106

Heavy metal fluoride (HMF) glasses have generated considerable interest

recently! as potential materials for laser hosts, mid-IR optical fibers, and

multi spectral windows, domes, lenses and filters. A wide variety of HMF

glasses have been synthesized, but only a few, such as f luorozirconate

(FZ)-type glasses (f luorozirconates and fluorohaf nates) , have been investigated in detail. FZ-type glasses are composed primarily of ZrF4 or HfF4,

in combination with BaF£ and a variety of tertiary components such as LaF3,

ThF4 and alkali-fluorides. Rare earth (RE) glasses based on ThF4 and BaF£ in

combination with ZnF£, YbF3, YF3, AIF3 and/or LUF3, have also attracted

considerable interest due to their extended IR transparency and improved

chemical resistance relative to FZ glasses. Another family of glasses which

has generally received less attention than FZ and rare-earth fluoride

glasses, is the transition metal (TM) fluoride glasses. Typical compositions

consist of combinations of the fluorides of bivalent metals such as Mn, Co,

Ni, or Zn; trivalent metals such as Cr, Ga, or In; and other constituents

such as PbF2 and AIF3.

Vibrational spectroscopy, including polarized Raman scattering and fundamental IR reflectivity (Reststrahlen spectra), has been used to study the

structure and bonding of many glasses^, and to determine the origins of

observed IR edge characteristics. In this paper, we review the spectra

obtained to date for heavy metal fluoride glasses, and compare them with the

spectra of simple halide, oxide and chalcogenide glasses.

The fundamental vibrational spectra of single component halide glasses such

as ZnCl2 and BeF2 are quite similar to those of simple oxide and chalcogenide

glasses. An inspection of figures 1-3, which display spectra for Si02, BeF2,

and ZnCl2» reveals two peaks in the IR reflectivity and one dominant, highly

polarized peak in the Raman spectrum. These peaks are smaller in number and

generally much broader than those of their crystalline analogues--an expected

consequence of the breakdown of selection rules in vitreous materials. The

dominant Raman line may be attributed to symmetric stretch vibrations of the

bridging atom (0, F, CI) along the bisector of the angle that it makes with

its two nearest neighbors. The high frequency infrared mode represents

"rigid cage" or sublattice-type motion of (0, F, CI) relative to (Si, Be,

Zn).

The Raman spectra of a few simple glasses containing two different kinds of

bonds have been measured, and they show two highly polarized Raman lines of

roughly equal strength, one at low frequencies and the other at high frequencies; some examples are P2O5 and the alkali oxide glasses, and again the

motions are symmetric stretches. Thus, it appears that the number of dominant, highly-polarized Raman lines gives the number of well-defined but

different bonds in the main framework of the glass structure.

260
0.8

0.6

0.4

0.0

( t f I' -INFRAREDi i—i—i—i—i—i—i—i—i

VITREOUS - REFLECTIVITY A

*°2

Ji i i i i W"l 1 1 l l l V i 600 1000 WAVENUMBER. W. em-1 1M0 500 1000 WAVENUMBER. W, cm-1 1500

Figure 1. Raman and IR Spectra of S1O2 Figure 2. Raman and IR Spectra of BeF2

102 «* SaAWwMM si

so

40

aj*

60

40

20s

5 60

a. Ice

<t

J« 40

20«

60

CO

40

200 job- WoveNumber .em-1

200

- A», cm" 1

Figure 3. Raman and IR Spectra of ZnCl2

261
The fundamental vibrational spectra of f luorozirconate-type glasses indicated

in figures 4-7 are similar to those of "simple" glasses because they display

a small number of relatively broad peaks^. Notably, despite the multiple

components in the glass, only a single highly polarized mode dominates the

Raman spectrum, suggesting a single principal bond in the glass. A major

difference between these and other glasses is that the Raman line falls in

between the high frequency LO-TO mode pair of the glass--a behavior

characteristic of crystalline fluorides such as BaF?. This feature and the

narrowness of the Raman line suggest that the ionic bonding of the individual

constituents may be retained in the vitreous state as well. Other

characteristics worthy of note include a relatively high peak reflectivity of

the f luorozirconates, indicating large coupling to light, and an insensitivity of the spectra to the choice of tertiary components. A more detailed analysis of HfF4 compared to ZrF^based glass spectra (see figure 7)

suggests, among other things, that the lower frequency peak in the

reflectivity is due primarily to Hf/Zr-F bending modes, as opposed to Ba-F

Figure 4. Reflectivity Spectrum and Derived e 2 and "Ime -1 for the Fluorohafnate Glass HBT

1 1 1 1 1 1 1 ' FREQUENCY SHIFT (10 2 cm" 1

) 8 6 4 2 0 FREQUENCY SHIFT HO2 em" 1

)

Figure 5. Raman Spectrum and Depolarization Ratio for HBT Glass

262
stretching modes; that the Hf-F force constant is larger than that of Zr-F;

and that the oscillator strength of the high frequency vibration is higher

for ZrF^based glasses. Comparisons with molten salt spectra imply

coordination numbers for Zr with F in the range of 6 to 8, which is in

agreement with the results of molecular dynamics calculations and X-ray data.

POLARIZED RAMAN SPECTRUM

frequency shift how'i Figure 7. Reflectivity of Fluorohafnate Glass HBT Com- pared to its Fluorozirconate Analogue ZBT

Figure 6. Raman Spectrum ( VV-Polarized)

of Typical Fluorozirconate and Fluorohafnate Glasses

The IR spectra of other glasses based on Th/Ba fluorides display 4 characteristics similar to f luorozirconates, except that peak reflectivities are lower in the compositions investigated to date, indicating smaller coupling

to light (figure 8). When significant amounts of aluminum are incorporated

into the glass, a third distinct peak emerges in the IR reflectivity

(figure 9). Available Raman spectra^ for these glasses display much broader

features than those of f luorozirconates (figures 10 and 11). The results

suggest that these glasses are more highly disordered than f luorozirconates,

and that a multiplicity of bonds exists in the glass. Preliminary data

suggest that Ba/Th fluoride glasses having large amounts of AIF3 are the most

disordered, as evidenced by. a flattening of their depolarization ratios as a function of frequency (figure 12).

The Raman and IR spectra of transition metal fluoride glasses^ are similar to

those of f luorozirconates, displaying essentially two-mode behavior in both

Raman and IR (see figures 13 and 14).

A comparison of the vibrational spectra of the various HMF glasses suggests

that FZ-type glasses, whose spectra are most similar to those of crystalline

fluorides, are the most highly "ordered" of the HMF glasses, and presumably

contain well-defined structural units consisting of Zr or Hf with F. The TM

fluoride glasses are somewhat less ordered than FZ glasses, but also possess

distinct structural units, in this instance based on TM ions with F. The RE

fluoride glasses are the "most disordered" of the HMF glasses, containing the

broadest distribution of local structural configurations. While glasses

without AIF3 appear to possess some distinct structural units comprised of RE

ions with F, glasses containing large amounts of AIF3 display spectra characteristic of highly disordered systems without clearly identifiable local

structural units.

263
bo

I—j

1— i — r

100 300 800 700 900 FREQUENCY (em-')

Figure 8. Comparison of Reflectivity of Fluorozlrconate and Th/Ba Fluoride Glass

w (cm*') 834 709 584 459 334 209 84

.7

Figure 10. Raman Spectrum of BZYbT Glass

1 1 1 ~T

i I i I i lI 200 400 600 800 FREQUENCY SHIFT (cm ')

Figure 12. Depolarization Ratio for Several

Ba/Th Fluoride Glasses

264

10* 1

I I I I I I I I I I I I I I L 200 600 1000 1400 FREQUENCY (cm" 1

)

Figure 9. Fundamental and IR Edge Absorption

of Several Th/Ba Fluoride Glasses

Containing 0 (BZYbT), 14(BZYAT), and

29 (BYAT) mol * A1F 3

o H- 1 i

1 1— 1— * 100 200 300 400 500 600 700

FREQUENCY (cm-1

)

Figure 11. Raman Spectrum of BYAT Glass
0J(crtv 1

)

0

Pb/Mn/Ga FLUORIDE GLASSES

Figure 14. Reflectivity Versus Frequency for Tran- sition Metal Fluoride Glasses

1200 1000 800 600 400 200

GJlcm-')

The position and strength of the peaks in the fundamental spectra correlate

well with observed IR edge behavior of fluoride glasses. For example, as indicated in figure 9, the deleterious effect of aluminum on the IR transmission edge is related directly to the appearance of high-frequency Al-F vibrational modes in the fundamental spectrum.

In summary, HMF glasses display a rich diversity of vibrational characteristics, some similar to highly ordered (nearly-crystalline) solids, others

similar to "common" glasses, and still others similar to highly disordered

solids such as amorphous semiconductors.

*Supported by Air Force Weapons Laboratory under Contract No. F39601-81-0012.

1. D. Tran, G. Sigel and B. Bendow, J. Lightwave Tech. 5, 566 (1984).

2. J. Wong and C. Angel, "Glass Structure by Spectroscopy" (Marcel Dekker,

NY, 1976).

3. B. Bendow, M. Drexhage et al , Sol. State Commun. 37, 485 (1981); and

B. Bendow, P. Banerjee et al , J Amer. Ceram. Soc. 65, C8 (1982).

4. B. Bendow, P. Banerjee et al , J. Amer. Ceram. Soc. 66, C64 (1983).

5. B. Bendow, P. Banerjee et al , to be published.

6. B. Bendow, P. Banerjee et al , J. Amer. Ceram. Soc. 67, C136 (1984).

265
THE VERDET CONSTANT OF OPTICAL GLASSES

Hans J. Hoffmann, Werner W. Jochs , Gudrun Przybilla

Schott Glaswerke, Hattenbergstrasse 10, D-6 500 Mainz,

Fed. Rep. Germany

A magnetic field can rotate the plane of vibration of linearly

polarized electromagnetic waves propagating in an optical medium.

In a standard Faraday configuration, a linearly polarized wave

propagates in a transparent medium parallel to the magnetic

field vector. Then the angle of rotation a is given by

(1) a = V • I • B

with the absolute value B of the magnetic flux density, the

distance I of the wave travelled in the sample and the Verdet

constant V being the factor of proportionality. The sign of the

Verdet constant V - and that of the rotation angle - is positive

(negative) if the rotation is clockwise (counter-clockwise)

looking parallel to the vector B of the magnetic flux density

irrespective of the^propagation vector of the wave being parallel

or antiparallel to B.

A relation for the Verdet constant as a function of wavelength

was first derived by Becquerel [l] . He obtained

2 mc " d X with the charge e and the mass m of the electron, the velocity c of light in vacuum, the wavelength X of the electromagnetic wave

and the dispersion dn/dX of the refractive index. Equation (2)

has been derived on the premise of classical physics that the

rotation frequency of electrons changes by the Larmor frequency

oo^ = eH/2mc in a magnetic field H. In order to obtain a rather

reasonable agreement between experimental results and formula (2),

however, one has to introduce into (2) the correction factor y

( "magnetooptic anomaly").

Unfortunately Becquerel' s equation (2) - even with the factor y

- cannot generally be justified on the basis of quantum mechanics.

L. Rosenfeld [2] calculated a quantum mechanical expression of

the Faraday rotation angle for the monoatomic case. His formula

can be reduced to (2) under rather special conditions, only. A

thorough discussion of the limitations is given by Van Vleck [-3J . Special limiting cases of Rosenfeld 's expression have been

recently discussed with respect to glasses [4-6J . Experimental

results, however, could not be evaluated quantitively , since

there are too many unknown parameters

.

In order to avoid these difficulties , we developed recently a

simple new dispersion formula [7] . We started from the Sellmeier266
type equation for the refractive index n

(3) n*- 1 - A £ f

with just one term representing electronic oscillators with

suitably averaged parameters: the mean density N/v of dispersion

electrons, the mean oscillator strength f , the mean resonance

wavelength X Q

and the constant A.

From (3) one can derive the approximate relation

o with the fitting parameters a and b for the Verdet constant as a

function of wavelength.

To test this equation, we determined experimentally the Verdet

constant V(X) of different glasses in the visible spectral region

by measuring the rotation angle a induced by a magnetic field.

For that purpose, linearly polarized monochromatic light (interference filters with FWHM of about lOnm) propagated along the

axis of cylindrical glass samples (length: 100mm). The axis of

the samples was oriented parallel to the magnetic flux density

vector in the homogeneous field within a solenoid. The maximum

flux density was about 3 • 10" 2 T. The temperature of the samples

was 295 ± 2K.

The rotation angle a of the plane of polarization could be

measured with an accuracy of 5' making use of a half-shade plate.

This corresponds to an absolute error of about 0.5rad/T.m. In

addition, there is a relative uncertainty of 3 to 4% for the

experimental data of V, mainly due to the error of the magnetic

flux density.

Typical results for an arbitrary choice of different glasses are

shown in Fig. la and b by the data points.

The data for different glasses at about 440nm vary between 0 and

70 rad/T'm. The values of V(X) decrease monotonically with

increasing wavelength X in nearly all cases. For SF-glasses the

Verdet constant increases monotonically with the PbO content.

The largest values of V were measured for heavy flint glass SF 59.

This glass has an extremely large content of PbO, namely about

80 weight %. Because of its large Verdet constant, this glass

type is an excellent candidate as Faraday rotator material.

On the other hand, the Verdet constants of the glasses SF 64

and SFL 56 are nearly zero. The plane of polarization of an

electromagnetic wave is nearly unaffected by a magnetic field. To

our knowledge the absolute values for SFL 56 are the smallest data

of V reported for any glass in the literature until now.

Except for glass SFL 56 and for glass-ceramics ZERODUR we fitted

the data by equation (4). The mean resonance wavelengths A Q

of

267
o a)

in Jd o <P

•rl CO o H -P O CO c p

CO rH

<4H CU& CO

rd CU rH Ph CO rd

<d

H cu C

f*J QJ

p P £ Q P O h C

04 0) CU w ft CO

IS]

X CU

a)

u

ft o cu <u • 13 Eh C CO JHi a CU C > w O

0) •H

H o

to bQ

O •H

(X) CD P

rd rH •H bOrH rH cr< fd o (U F & CO c o

CDa 03

p

CD

CD ft P bO

4h CO

C

Mh •v •H H <D rH rd &o

Uh •H CO 0 O CO p 0

•H

G (ti > > •HO CO F 0) ft co

rti +J rd •H P H P

to c fd fd c •H oo ^< CU o

X! rH

-H P rd

CD

H

a

T3 bO >> bO

CU a)C > rH G •H

a)

CU > o P & fd x: •H H CO 4h

rQ

-ac

rd

rd

-rH

bO •H

268
the different glasses were determined from a fit of the known

dispersion curves n(A) by equation (3) in the visible spectral

region. Thus, we had to determine for a fit of V(X) by (4) only

the parameters a and b. This was achieved by a linar regression

of V(X)2n/(n 2 -l) as a function of 1/(A 2 -A 2 ). The full curves in

Fig. la and b show the results of this fitting procedure. In fact

we obtained a good fit within the experimental accuracy of the

Verdet constant for all glasses investigated by us [7]

.

For comparison with (4) we fitted our data also by Becquerel's

formula (2) with the magnetooptic anomaly factor y as fitting

parameter. A fit with suitable factor y is possible within

reasonable deviation of the fitting curve from the experimental

data points. In most cases, however, the experimental data can

be fitted better by our equation (4) than by (2). This is not

surprising since there are two fitting parameters in (4) whereas

there is only one in (2).

In order to understand why a fit of the experimental data by (2)

can be successful irrespective of its theoretical shortcomings,

we estimate the dominant dependence of V upon X according to (2)

and (4). Calculating dn/dX from (3) and inserting into (2)

yields V ~ 1/X 2 ,if one neglects X

2 as compared to X2

. On the

other hand, according to (4) V(X) is given by a superposition of

two terms proportional to 1/X and 1/X 3

, respectively, neglecting

X

2 as compared to X2 as well. Since both terms have the same sign

they can obviously be approximated by only one term proportional

to 1/X 2 in a relatively small interval of wavelength. Thus, in

order to discriminate between the validity of (2) or (4) from the

quality of fitting alone , one needs experimental data of the

Verdet constant in a larger interval of X.

References

[1] H. Becquerel Compt. Rend. 12_5, 679 (189 7 )

[2] L. Rosenfeld Zeits . f. Physik 5J7 , 835 (19 30)

[3] J. H. Van Vleck The Theory of Electric and Magnetic

Susceptibilities , Oxford University Press

(19 32 )

[4] N. F. Borrelli J. Chem. Phys . 41, 3293 (1964)

[5] L. D. Pye, S. C. Cherukuri , J. Mansfield and T. Loretz

J. Non-Crystalline Solids 5_6 , 99 ( 1983 )

[6] M. J. Weber Faraday Rotator Materials Report M-103

Lawrence Livermore National Laboratory, Ca.

,

(1982)

[7] Hans J. Hoffmann, Werner W. Jochs , Gudrun Przybilla

to be published

269
TEMPERATURE DEPENDENCE OF MAGNETOOPTIC EFFECTS

IN MID-INFRARED FIBERS

Heihachi Sato, Yuji Azumai and Mitsunori Saito*

Department of Electrical Engineering, National Defense Academy,

Yokosuka 239, Japan.

^Research and Development Department, Horiba Ltd., Kyoto 601,

Japan

.

Recently, mid-infrared fiber is getting important for its various applicational feasibilities such as power transmission,

sensing, welding, machinary and medicine. Among many candidates

KRS-5 and As-S fibers are very promising because of not only

being flexible but also their low loss characteristics at the

mid-infrared wavelengths covering that of high power CO and CO2

lasers,, So far, many researchers have reported about the propagationproperty and low-loss mechanism, involving fabrication

processes [1] - [3] . The authors have also studied mainly on the

magnetooptic effects of KRS-5 fiber and crystal at room temperature [4], [5]. In the present papar low temperature properties

of KRS-5 and As-S fibers will be emphasizingly described about

their magnetooptic effects such as the Faraday- and Voigt effects

at CO2 10.6 ym and He-Ne 3.39 ym laser lines.

Experimental schematic diagram is typically illustrated in

Fig.l for measuring temperature dependence of IR fibers on the

Faraday effect. A CO2 laser or a He-Ne 3.39 ym laser was used

as an optical source, because these fibers have almost minimum

loss points which just correspond to the operation wavelengths

of the above lasers. The linearly polarized beam was focused

onto the fiber through a ZnSe or CaF2 lens. The fiber placed

inside a hollow solenoid magnet variable up to 2 kilogauss was

cooled down up to about -110 °C through the brass heat-sink by

liquid nitrogen. The temperature was also measured by a thermocouple (not shown in the figure) at the center portion of the

magnet. The transmitted beam was detected through a ZnSe polariDC SOURCE

C02 10.6 pm LASER TjlR FIBER

Or^He-Ne 3.39 LASER^ LENS ^^^^ \^

DtltCTOR

M2

Liq. N2

POLARIZER

Fig. 1 Experimental setup for the Faraday effect.

2 70
zer(II-IV : PAZ-6) by a power meter (Coherent M201) or an InAs

detector (Judson) . For the measurements using a CO2 laser a grating was used instead of the flat mirror Mi. For measuring the

Voigt effect a transverse dc magnetic field was applied instead

of the longitudinal field, variable up to 800 gauss. Because of

using an effective dewar lower temperature was obtained up to

-190 °C in case of the Voigt-effect measurement using KRS-5 fiber.

About 3 0 of the Faraday rotation at room temperature became

10 o - 11 0 for both KRS-5 and AS2S3 fibers under the applied

field 2 kG and the effective length 7.5 cm. From the measurements of the Faraday rotation the temperature dependence of these

fibers upon the Verdet constant V is depicted in Figs. 2 and 3

for KRS-5 and AS2S3 fibers, respectively. It is seen that the

Verdet constant tends to increase rapidly with decrease of temperature, and that both fibers follow A + B/T characteristics

( T : temperature, A and B : constants) . The values of V at

room temperature was well consistent with that obtained theoretically by using known refractive indices [6] as

V = - (e/2mc2) X (dn/dX ) , (1)

where e and m are, respectively, the charge and mass of electron,

c the light velocity in vacuum, n the refractive index and X

the wavelength.

-100 -50 -25

TEMPERATURE T(°C)

Fig 2 Temperature dependence of KRS-5 fiber on the

Verdet constant.

271
57e o

u\

C

•He

Eh

S3

EhcnO

u

EhW

Q

K

W

>

T 1—i 1 1 1 1—i 1 1 r—|—i

1 1—i 1—:

t

1 1 1—i

1 r

As-S FIBER

MAGNETIC FIELD : %= 2 kG

WAVELENGTH : A = 3.39 ym

EFFECTIVE LENGTH: Le ff =7.5 cm.

I_—t—I—1—I—I——I I i_ j l L J L -100 -75 -50 -25

TEMPERATURE T(°C)

25

Fig. 3 Temperature dependence of As2S3 fiber on the Verdet constant.

The temperature dependence of KRS-5 on the Voigt constant C is

shown in Fig. 4 using a CO2 10.6 ym laser line. It can be seen

that the Voigt constant also significantly increases at low

temperature. Almost one order enhance ment was recognized at

-160 °C in comparison with that of room temperature. By cooling

down the birefringent retardation is enhanced with increase of

the applied field, in addition to increase of the natural retardation. However, the natural birefreingence tends to saturate at

about -100 oc and tends to keep constant. The Voigt constant at

room temperature was also compared with the theoretical estimate

using known parameter as

C = -(e2/16Trmc2) \3 (d 2 n/dA2) , (2)

being consistent well each other.

From the obtained temperature dependence of both Verdet- and

Voigt constants it was found that these follow roughly A + B/T

dependence. Especially, the temperature dependent term B is

strongly related to the angular momentum quantum number J and

the Lande splitting factor g[7] as

B = a ( J + l)gy B/3kB , (3)

where kB

is the Boltzman constant, y B the Bohr magneton and

a the constant. Thus, the obtained results gives us some information to analyze the above paramters. On the other hand, since

cooling techniques using liquid nitrogen is, so far, getting

popular without any diffculty, increase of these constants must

be great benefit not only for designing magnetooptic devices and

sensing elements for magnetic field or electric current, but

also gives us fundamental informations to evaluate dispersion

272
0 ' « 1 . 100 150 200 250 300

TEMPERATURE T(K)

Fig. 4 Temperature dependence of KRS-5 fiber on

the Voigt constant.

property at low temperature. As seen from Eqs. (1) and (2)

the temperature dependence of dn/dX and d2n/dx2 can be readily

evaluated in the experiments, so that this allows us to find the

coefficients of a Sellmeier fit. More about this point will be

discussed.

References

[1] J. A. Harrington et al f Adv. Ceram. 2, 94(1981).

[2] S. Sakuragi et al, Opt. Lett. 6., 629(1981).

[3] J. A0 Harrington et al, Opt. Lett. 8, 223(1983).

[4] H. Sato et al, Opt. Lett. 8, 180(1983).

[5] H. Sato et al, Appl. Opt. 23, 2633(1984).

[6] W. G. Driscoll, Ed., Handbook of Optics (McGraw Hill, New York

1978) , p 7 - 108.

[7] C. Kittel, Introduction to Soltid State physics (Wiley, New

York, 1976) , p 438.

273
OPTICAL CHARACTERIZATION OF DEVITRIFICATION FOR Cr-DOPED

Zr-Ba-La-AI FLUORIDE GLASS

W.J. Miniscalco, L.J. Andrews, B.T. Hall, and D.E. Guenther

GTE Laboratories Incorporated

40 Sylvan Road

Waltham, MA 02254

The past decade has seen an enormous increase in activity in the area of

heavy metal fluoride glasses. These glasses contain no oxygen and are distinguished from the f luoroberyllates by the absence of beryllium. In addition

to their scientific interest as a largely unexplored glass-forming system,

heavy metal fluoride glasses are of technological interest because they have

high optical transmission from the UV to the mid-IR (>7 ym) . One potential

application is as optical fiber for both communications and energy transmission

in the mid-IR. Since these glasses can be doped with transition metal and

rare earth ions, other promising applications are as solid state laser hosts

and magneto-optic devices.

An important consideration in all applications is the relatively poor stability of

these glasses compared to oxide glasses as indicated by their extremely nar- row working ranges. Even for the best compositions the crystallization temperature is seldom more than 100 C higher than the glass transition temperature. To further understand the stability of heavy metal fluoride glasses, we

have undertaken an investigation of crystallization using primarily optical

techniques. The work has concentrated on a Zr-Ba-La-AI fluorozirconate

glass (ZBLA) which has been doped with probe ions whose optical spectra are

sensitive to their local environment. The strength and symmetry of the crystal field at the site occupied by these ions affect the positions of their electronic states. The d^d transitions of transition metal ions are particularly

sensitive because their electron-lattice coupling strengths range from intermediate to strong. The peak positions, bandwidths, and oscillator strengths of

the optical transitions for a given transition metal ion vary greatly depending

upon the particular glass or crystalline host. Major spectral changes associated with devitrification have been reported by Andrews et al . for

3+

Cr -doped oxide glasses and ceramics [1]. More recently Tanimura et al

.

have observed that crystallization has a significant effect upon the emission

3+

spectrum of ZBLA.Er [2]. However, Feuerhelm et al . found only minor

2+

changes for Mn in the same glass [3]. The dopants we have investigated

3+ 3+ 2

+ 2+ include the transition metals Cr , Fe , Fe , and Mn , as well as the rare

3

+ 3+ 3

+ earths Nd , Eu , and Ce . We have established that it is possible to determine whether these ions reside at amorphous or crystalline sites on the ba3+

sis of their photoluminescence spectra. For this glass Cr is a particularly

sensitive probe of its environment and not only indicates the presence of

trace amounts of crystalline phase in the glass, but can also be used to identify the types of crystals present.

274
The glass investigated had the composition 58 m/o ZrF^, 34 m/o BaF2, 5 m/o

LaFg, and 3 m/o AIF^. Dopant concentrations ranged from <100 ppm to

1 m/o. High purity commercially available fluoride starting materials were

used and NH4HF2 was added to maintain fluoridation since the glasses were

melted and poured in air. After annealing at 300 C, the samples were cut

and polished for the optical investigations. Absorption spectra were measured

for the more concentrated dopants. Room temperature photoluminescence

spectra were obtained using cw argon and krypton ion lasers as excitation sources. The samples were then subjected to heat treatment and the photoluminescence spectra measured again. To assist in assigning the crystalline

3 + phases corresponding to the different Cr emission spectra, polycrystalline

samples of BaZrFg:Cr were synthesized by slow cooling or quenching in liquid

nitrogen to form the different crystalline phases possible for this compound.

Phases of BaZrFg and BaZ^F^Q are believed to nucleate and grow when ZBLA

is devitrified upon reheating [4,5,6]. Emission spectra were measured for

the polycrystalline samples and correlated with those observed for the glass.

In addition, powder x-ray diffraction patterns were measured for the crystalline phases and compared to those observed for the devitrified glasses.

3 + Figure 1 compares the Cr photoluminescence spectrum of (a) untreated

ZBLA, (b) a sample which has been heated for 2 hr at 375 C, and (c) a sample which has been heated for 30 min at 426 C. The spectral changes are

quite dramatic. We have tentatively assigned curves (a) and (b) to emission

from the phases reported to be dominant in published x-ray diffraction studies of devitrified ZBLA. The heat treatment at 375 C has been observed to

produce primarily (3-BaZrFg for similar compositions [4,5,6] and the emission

band (b) which peaks at -890 nm indicates that this phase provides a very

3 + low crystal-field-strength site for Cr . Although narrower than (a), this

band is still excessively wide on the short wavelength side, most probably as 3 + a result of Cr sites in other crystalline phases. The emission intensity is more than an order of magnitude higher than for the untreated glass, imply3+

ing a significantly larger quantum efficiency for Cr in this phase. After

treatment at 426 C the emission band (c) is narrowed and shifted to shorter

3+

wavelength, peaking at =780 nm. This indicates that Cr has been incorporated into a phase with a higher field site, most likely either a-BaZrFg or fc-BaZ^F-jQ [6]. The narrowing of the band implies that the luminescence is predominately from a single site. Moreover, the emission is >1500 times

brighter than from the untreated glass. The luminescence band for untreated

ZBLA is atypical and extremely broad even for a glass. One explanation is 3+ an unusually broad range of crystal field strengths for a single Cr site in the glass. Another possibility is that of multiple sites, including the presence of trace quantities of crystalline phase in the untreated glass, Neilson

et al. have reported microcrystals of a-BaZrFg in untreated ZBLA [5]. Emission from this phase, curve (c), would broaden the band on the short wavelength edge. The higher quantum efficiency for this phase would make the

glass luminescence spectrum extremely sensitive to minute quantities.

275
WAVELENGTH inm)

Figure 1 3+

Photoluminescence spectra for Cr -doped ZBLA subjected to different heat

treatments. Curve (a) is for the untreated glass; curve (b) — — — is for a sample held for 2 hr at 375 C; curve (c) — is for a sample held for

30 min at 426 C. All samples were excited at 647.1 nm.

Although self-consistent, the above assignment of the emission spectra re- 3+

mains open to question since we cannot exclude the possibility that Cr is preferentially incorporated into phases present in only small amounts. The

luminescence could, in principle, emanate from phases present in such small

quantities as to be undetectable by x-ray diffraction. Accordingly, we have

3+

attempted to synthesize single phase polycrystalline samples of BaZrFgiCr to

verify the above assignments. The emission spectrum for the sample treated

at 426 C corresponds most nearly to that of BaZrFg synthesized by melting at

850 C, holding for 3 days at 512 C, and rapidly cooling to room temperature.

The x-ray pattern for this polycrystalline sample is identical to that published

by Laval et al . and attributed by them to a-BaZrFg [7]. The luminescence

spectrum for ZBLA heat treated at 375 C is most similar to that of a polycrys276
talline sample quenched from 654 C. The x-ray pattern for this latter

crystalline sample corresponds closely to that reported by Mehlhorn and

Hoppe although they synthesized their sample by slow cooling [8]. We have

also synthesized samples by slow cooling (10 days), and find x-ray patterns

very similar to those of the quenched samples although their photoluminescence spectra are quite different. In all cases, the polycrystalline emission

spectra have been broader than expected, implying that we have not yet suc- ceeded in synthesizing single phase material.

In conclusion, we have observed radical changes in the photoluminescence

spectrum of Cr-doped ZBLA. These changes indicate that, depending upon

3+

the heat treatment applied, Cr is being incorporated into different crystalline phases which have sites with significantly different crystal field

strengths and quantum efficiencies. A general correspondence has been

found between emission from these phases and that from polycrystalline samples, but the results are still inconclusive. This ambiguity is probably due

to the presence of multiple phases in both the glass and polycrystalline samples combined with the difference in sensitivity between x-ray diffraction and

optical probe ion spectroscopy. A phase which is present in trace quantities

may not be observable in an x-ray diffraction pattern. However, if the optical probe ion is preferentially incorporated into this phase with a higher

quantum efficiency than in the majority phase, the luminescence spectrum will

reveal cr even be dominated by the trace phase. Since it is not always possible to resolve the emission spectra from different phases under cw excitation, we are now investigating these materials using time-resolved spectroscopy which provides additional discrimination based upon variations in excited

state lifetime. It is a pleasure to acknowledge helpful discussions with R. M.

Klein, R. C. Folweiler, and M. G. Drexhage, who also provided a sample.

[1

[2

[3

[4

[5

[6

[7

[8

L.J. Andrews, A. Lempicki, and B.C. McCollum, Chem. Phys. Lett. 74,

404 (1980); and L.J. Andrews et al . , "Development of Materials for a Luminescent Solar Concentrator," Final Report for DOE Contract No.

DE-AC02-78ER-04996, January 1983.

K. Tanimura, M.D. Shinn, and W.A. Sibley, Phys. Rev. B 30, 2429

(1984).

L.N. Feuerhelm, S.M. Sibley, and W.A. Sibley, J. Solid State Chem. 54,

164 (1984).

M.C. Weinberg, G.F. Neilson, and G.L. Smith, J. Non-Cryst. Solids 55,

45 (1983).

G.F. Neilson, G.L. Smith, and M.C. Weinberg, Mat. Res. Bull. 79, 279

(1984).

N.P. Bansal, R.H. Doremus, A.J. Bruce, and C.T. Moynihan, Mat.

Res. Bull. 79, 577 (1984)

J. -P. Laval, D. Mercurio-Lavaud, and B. Gaudreau, Rev. Chim. Minerale 77, 742 (1974).

Von B. Mehlhorn and R. Hoppe, Z. anorg. allg. Chem. 425, 180 (1976).

277
OPTICAL STUDY OF Ge-P-Te AND Ge-Se-Te CHALCOGENIDE GLASSES

L. Boehm, A. Bornstein, and S. Arie

Solid State Physics Department,

Soreq Nuclear Research Center, Yavne 70600, Israel

1. Introduction

Chalcogenide glasses have been thoroughly investigated, especially in con- nection with their electronic properties and their promise as IR windows in

the 8-12um region [1]. For the purpose of the present study, the major

attraction of chalcogenides lies in their promise as IR materials for

infrared optical fibers. Such fibers are needed in applications using highpower C0 2 laser for surgery as well as in cutting and heat treatment of

metals. These fibers will also play an important role in the development of

many infrared devices in the field of image relaying and remote sensing.

In this study we present the preparation and optical characterization of two

glass systems containing relatively high amounts of Te. Such glasses are expected to be transparent up to 20ym and may serve as preforms for drawing

IR fibers.

2. Experimental Procedure and Results

Starting materials are semiconductor grade germanium, selenium, and tellurium

of 99.9999% purity, subjected to a special process of purification by which

oxides are separated by zone refining. Red phosphorous 99.99% pure (Cerac

Corp.) was used. Melting is conducted in charges of 90g in evacuated, sealed

silica tubes of 8.0mm diameter and 200mm length. Before use, the tubes are carefully cleaned with HNO3-HF solution and fused to 1000*C, under vacuum. The

melting temperature is 950°C, and the melt is homogenized by continuous axial

rotation of the tube for approximately 40 hours. Then the tube is air-cooled

in the vertical position, by which the melt solidifies in the form of a glass

cylinder. The glasses are cut and polished before conducting physical measurements. X-ray diffraction showed that all samples were glassy. Inspection with

a scanning electron microscope showed homogeneity with no particles and phase

separation (detection limit 3u) in contrast to previously reported [2] results

for the Ge-Se-Te system.

2.1 Chemical analysis by EDS and WPS methods

Since we are synthesizing complicated ternary systems, and the properties of

the glasses (mainly the index of refraction) are composition-dependent,

chemical analysis of the prepared samples was performed. Two main techniques

are used, both based on the X-ray spectrum emitted from an excited atom: EDS

(Energy Dispersive Spectrum) and WDS (Wavelength Dispersive Spectrum). The

two techniques differ in the way the X-rays are accumulated and identified.

The EDS technique analyzes all elements simultaneously, but the poor energy

278
resolution of the Si-Li detector used causes errors in the quantitative

analysis of elements adjacent in the periodic table such as Se and Ge. This

is why the WDS technique was used for elements in the system Ge-Se-Te; this

technique has a much better resolution. A more detailed description of the

techniques will be presented in a forthcoming study. In both methods,

standards composed of the investigated elements are used. Table 1 presents

the chemical analysis of the glass Ge-P-Te performed by the EDS method. In

Table 2, the analysis of the glass Ge-Se-Te is presented as measured both by

the EDS and WDS techniques.

The results show that the amount of phosphor present in the Ge-P-Te glass is

much less than weighed, although the glass obtained is homogeneous. Such a low amount of phosphor enabled us to obtain a stable glass phase in the alloy

system Ge-Te, which is known to have the tendency to crystalize [3].

From Table 2 it is obvious that the EDS technique is not accurate enough for

analyzing the glass Ge-Se-Te, as there is an overlap both between the emitted

lines Ge-K and Se-K, and between Ge-L and Se-L. Therefore, the WDS method was

used. As seen, the glass obtained has the same composition as the weighed

starting materials.

Table 1. Chemical Analysis of Ge-P-Te Glass by EDS

Element Composition weighed Composition of

in at% polished glass

Ge 20.0 23.44 ± 1.40

P 10.0 3.04 ± 0.64

Te 70.0 73.52 ± 1.30

Table 2. Chemical Analysis of Ge-Se-Te Glass

Element Composition weighed Composition obtained by

in at%

WDS technique EDS technique

Ge 20.0 19.88 ± 0.6 15.1 ±1.2

Se 50.0 50.19 ± 4.0 59.0 ± 1.3

Te 30.0 30.18 ± 0.6 25.8 ±1.0

279
2.2 Optical measurement

Interferometric mapping of refractive index inhomogeneity was used to

diagnose optical imperfections in components. Such inhomogeneity arises from

the existence of stresses or impurities in the sample. When it exists, it

distorts the wavefront and impairs optical performance. For such measurements

each surface has to be flat within one visible fringe, to separate surface

irregularities from volume inhomegeneities. Picture 1 shows an interferogram

of the glass Ge2QSe,-QTe2Q 12mm in diameter and 10mm thick. It was calculated

that the inhomogeneity in the index of refraction (An) of the sample is

4x10

4 which indicates that the glass has no crystalization or other

imperfections. This result is consistent with those obtained by the SEM

measurements.

The IR spectra were measured on polished samples at room temperature, with a Nicolet 5DX FT-IR Spectrometer having a resolution of 4cm-1

. Figure 1 shows

the IR spectra of 1.5mm thickness of the two glasses, Ge2QSe5QTe3Q and

GJ e23 t-P,, Q^ej2 5* ^s can ^e seen » tne ^e based glass is transparent up to

15ymJ while tne glass based on Ge-Te is transparent up to 20ym.

Picture 1. Interferogram of the Glass Ge9nSe,- nTe

280
100

80 -

Figure 1. Emission Spectra of Ge-P-Te Glass (unbroken line) and Ge-Se-Te

(broken line), 1.5mm thickness

Discussion and Conclusion

We succeeded in preparing a stable glass in the system Ge-Te by adding a small amount of phosphor (around 3 at%). It is known [3] that such alloys

containing high amounts, of Te tend to crystalize. This glass shows to

absorptioiji up to 430cm . The glass Ge2QSe^QTeog shows a weak absorption band

at 780cm , due to Ge-0 stretching vibration [4j. It arises from an oxide

layer or absorbed oxygen formed at the surface layej of the Ge_element used

in this preparation. The absorption bands at 560cm and 475cm presumably

result from Ge-Se and Se-Se stretching, respectively.

We conclude that both glass systems are promising materials for application

in IR systems such as fiberoptics or IR components.

Special care should be taken in fabricating the glasses from high-purity

materials in a controlled atmosphere,.

Acknowledgements

The authors are grateful to Dr. K. Shilo and Dr. Y. Noter for the

interferometric measurements.

(1) J. A. Savage, P. J. Weber, and A. M. Pitt, Infrared Physics, 20 313

(1980).

(2) S. Bordas, M. Geli, Y. Casas-Va'zquez, N. Clavaguera, and M. T. Clavaguera-Mora, Revue Physique Applique _12 677 (1977).

(3) D. Rerewnicka, P. G. Zielinski, and H. Davies, J. Material Science

Letters 1 87 (1982).

(4) S. Maruno and M. Noda, Rep. Asahi Glass Found. Ind. Technol. 3J5 367

(1979).

281
AUTHOR INDEX

Page Page

. 119, 256

El-Halafawy, F. Z. . . . 119, 256

Haglund, R. F., Jr. . . . . 184

Bu-Abbud, G. H. * • • » 86 f 167

Burton, R. L. . . 54, 89, 106

198

Ingram, D. ... 167

Kirby, K. W ... 238

Koumvakalis, N. • • • ... 141

Lieberman, A. G. . . . ... 17

282
Page Page

154

270

80

133

160

28

214

93

99

115

60

, 177

249

181

, 164

40

184

40

46

229

99

226

164

46

218

58

Williamson, A. 177

Willingham, C. 137

Wood, 0. R., II 181

242

, 167

58

, 255

Zhu, J-K. . . • • ... 169 , 255

tf.U.S. GOVERNMENT PRINTING OFFICE. 1985-461*105/20073

283
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SHEET (See instructions) NBS/SP-697 April 1985

4. TITLE AND SUBTITLE

OM85 Basic Properties of Optical Materials, Summaries of Papers (Topical Conference

on Basic Properties of Optical Materials)

5. AUTHOR(S)

Albert Feldman, Chairperson, Editorial Committee

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7. Contract/Grant No.

National Bureau of Standards

Department of Commerce 8. Type of Report & Period Covered

Gaithersburg, Ml) 20899 Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State, ZIP)

National Bureau of Standards Air Force Office of Scientific American Physical Soc.

Department of Commerce Research 335 East 45th Street

Gaithersburg, MD 20899 Boiling Air Force Base New York, NY 10017

Washington, DC 20332

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number 85-600534

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11. ABSTRACT (A 200'Word or less factual summary of most si gnificant information. If document includes a significant

bibliography or literature survey, mention it here)

This Special Publication contains summaries of papers to be presented at the

Topical Conference on Basic Properties of Optical Materials to be held at the National

Bureau of Standards in Gaithersburg, Maryland on May 7-9, 1985. The conference is

sponsored by the National Bureau of Standards, the Air Force Office of Scientific

Research, and the American Physical Society in cooperation with the Optical Society of

America and SPIE-The International Society for Optical Engineering. This publication

contains summaries of 70 papers which include 17 invited papers.

The purpose of the conference is to bring together researchers from industry,

academia, and government to discuss the physical and structural properties of optical

materials as they affect optical performance. The scope of the conference includes the

measurement and theory of basic properties of optical materials in bulk and in thin

film form and the dependence of these properties on atomic structure, morphological

structure, impurity content, and inhomogeneity

.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) Glasses; infrared; modulated structures; nonlinear optics; metals; organics; optical

constants; optical waveguides; photorefractive effect; polymers; semiconductors; thin

films; ultraviolet

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