Table Of ContentS E M I C O N D U C T O R S
A N D S E M I M E T A L S
Edited by R. K. WILLARDSON
BELL AND HOWELL ELECTRONIC MATERIALS DIVISION
PASADENA, CALIFORNIA
ALBERT C. BEER
BATTELLE MEMORIAL INSTITUTE
COLUMBUS LABORATORIES
COLUMBUS. OHIO
VOLUME 9
Modulation Techniques
1972
@
ACADEMIC PRESS New York and London
COPYRIGHT 1972, BY ACADEMPIRCES S, mC.
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IN THE OF
List of Contributors
Numbers in parentheses indicate the pages on which the authors’ contributions begin.
R. L. AGGARWALN,a tional Magnet Laboratory, Massachusetts institute of
Technology, Cambridge, Massachusetts (15 1)
D. E. ASPNESB,e ll Telephone Laboratories, Znc., Murray Hill, New Jersey
(457)
IVAR BALSLEVP,h ysics institute, Odense University, Odense, Denmark (403)
BRUNO BATZ, Semiconductor Laboratories, Free University of Brussels,
Brussels, Belgium (315 )
DANIEFL. BLOSSEYX,e rox Research Laboratories, Rochester, New York (257)
N. BOTTKAM, ichelson Laboratory, China Lake, California (457)
PAULH ANDLERU, niversity of Illinois, Urbana, Illinois (257)
B. 0. SERAPHINO, ptical Sciences Center, University of Arizona, Tucson,
Arizona (1)
vii
Preface
The extensive research that has been devoted to the physics of semiconduc-
tors and semimetals has been very effective in increasing our understanding
of the physics of solids in general. This progress was made possible by
significant advances in material preparation techniques. The availability of
a large number of semiconductors with a wide variety of different and often
unique properties enabled the investigators not only to discover new pheno-
mena but to select optimum materials for definitive experimental and
theoretical work.
In a field growing at such a rapid rate, a sequence of books which provide
an integral treatment of the experimental techniques and theoretical
developments is a necessity. The books must contain not only the essence of
the published literature, but also a considerable amount of new material.
The highly specialized nature of each topic makes it imperative that each
chapter be written by an authority. For this reason the editors have obtained
contributions from a number of such specialists to provide each volume with
the required detail and completeness. Much of the information presented
relates to basic contributions in the solid state field which will be ofpermanent
value. While this sequence of volumes is primarily a reference work covering
related major topics, certain chapters will also be useful in graduate study.
In addition, a number of the articles concerned with applications of specific
phenomena will be of value to workers in various specialized areas of device
development.
Because of the important contributions which have resulted from studies
of the 111-V compounds, the first few volumes of this series have been devoted
to the physics of these materials : Volume 1 reviews key features of the 111-V
compounds, with special emphasis on band structure, magnetic field
phenomena, and plasma effects. Volume 2 emphasizes physical properties,
thermal phenomena, magnetic resonances, and photoelectric effects, as
well as radiative recombination and stimulated emission. Volume 3 is
concerned with optical properties, including lattice effects, intrinsic absorp-
tion, free carrier phenomena, and photoelectronic effects. Volume 4 includes
thermodynamic properties, phase diagrams, diffusion, hardness, and
phenomena in solid solutions as well as the effects of strong electric fields,
ix
x PREFACE
hydrostatic pressure, nuclear irradiation, and nonuniformity of impurity
distributions on the electrical and other properties of 111-V compounds.
Volume 5, which is devoted to infrared detectors, is the first of a number of
volumes to deal specifically with applications of semiconductor properties.
Volume 6 is concerned with injection phenomena in solids, including
current injection and filament formation, double injection, internal photo-
emission, and photoconductor-metal contacts. The next volume is again
devoted to devices (issued in two parts, 7A and 7B) and includes applications
of bulk negative resistance phenomena as well as effects due to barriers and
junctions. Volume 8, concerned with transport and optical properties,
consists of two chapters on photoluminescence, as well as articles on Faraday
rotation, thermal emf, and galvanomagnetic effects in compounds
111-V
with indirect gaps. The present volume is devoted to modulation techniques
such as electroreflectance, interband magnetooptical effects, electro-
absorption, derivative spectroscopy by thermal and wavelength modulation,
piezooptical effects, and electric field effects on the dielectric function.
Subsequent volumes of Semiconductors and Semimetals will include
further work on infrared detectors and a variety of fundamental phenomena
such as lattice dynamics, transport properties, tunneling, and nonlinear
optical phenomena.
The editors are indebted to the many contributors and their employers
who made this series possible. They wish to express their appreciation to
the Bell and Howell Company and the Battelle Memorial Institute for
providing the facilities and the environment necessary for such an endeavor.
Thanks are also due to the U.S. Air Force Offices of Scientific Research
and Aerospace Research and the U.S. Navy Office of Naval Research and
the Corona Laboratories, whose support has enabled the editors to study
many features of compound semiconductors. The assistance of Crystal
Phillips, Martha Karl, and Inez Wheldon in handling the numerous details
concerning the manuscripts and proofs is gratefully acknowledged. Finally,
the editors wish to thank their wives for their patience and understanding.
R. K. WILLARDSON
ALBERTC . BEER
Semiconductors and Semimetals
Volume 1 Physics of 111-V Compounds
C. Hilsum, Some Key Features of Compounds
111-V
Franco Bassani, Methods of Band Calculations Applicable to 111-V Compounds
E. 0. Kane, The k -pM ethod
V. L. Bonch-Brueuich, Effect of Heavy Doping on the Semiconductor Band Structure
Donald Long, Energy Band Structures of Mixed Crystals of Compounds
111-V
Laura M. Roth and Petros N. Argyres, Magnetic Quantum Effects
S. M. Puri and T. H. Geballe, Thermomagnetic Effects in the Quantum Region
W. M. Becker, Band Characteristics near Principal Minima from Magnetoresistance
E. H. Putley, Freeze-Out Effects, Hot Electron Effects, and Submillimeter Photoconductivity
in InSb
H. Weiss, Magnetoresistance
Betsy Ancker-Johnson, Plasmas in Semiconductors and Semimetals
Volume 2 Physics of 111-V Compounds
M. Holland, Thermal Conductivity
G.
S. I. Novikova, Thermal Expansion
U. Piesbergen, Heat Capacity and Debye Temperatures
Giesecke, Lattice Constants
G.
J. R. Drabble, Elastic Properties
A. U. Mac Rae and W.G obeli, Low Energy Electron Diffraction Studies
G.
Robert Lee Mieher, Nuclear Magnetic Resonance
Bernard Goldstein, Electron Paramagnetic Resonance
T. S. Moss, Photoconduction in 111-V Compounds
E. Antodik and J. Tauc, Quantum Efficiency of the Internal Photolectric Etrect in InSb
G. W.G obeli and F. Allen, Photoelectric Threshold and Work Function
G.
P. Pershan, Nonlinear Optics in 111-V Compounds
S.
M. Gershenzon, Radiative Recombination in the 111-V Compounds
Frank Stern, Stimulated Emission in Semiconductors
Volume 3 Optical Properties of 111-V Compounds
Marvin Hass, Lattice Reflection
William Spitzer, Multiphonon Lattice Absorption
G.
D. L. Stierwalt and R. F. Potter, Emittance Studies
H. R. Philipp and H. Ehrenreich, Ultraviolet Optical Properties
Manuel Cardona, Optical Absorption above the Fundamental Edge
Earnesf J. Johnson, Absorption near the Fundamental Edge
John 0. Dimmock, Introduction to the Theory of Exciton States in Semiconductors
B. Lux and J. G. Mavroides, Interband Magnetooptical Effects
xi
xii CONTENTS OF PREVIOUS VOLUMES
H. Y. Fan, Effects of Free Carriers on the Optical Properties
Edward D. Palik and George B. Wright, Free-Carrier Magnetooptical Effects
Richard H. Bube, Photoelectronic Analysis
B. 0. Seraphin and H. E. Bennett, Optical Constants
Volume 4 Physics of IIEV Compounds
N. A. Goryunova, A. S. Borscheuskii, and D. N. Tretiakov, Hardness
N. N. Sirota, Heats of Formation and Temperatures and Heats of Fusion of Compounds A"'BV
Don L. Kendall, Diffusion
A. G. Chynoweth, Charge Multiplication Phenomena
Robert W. Keyes, The Effects of Hydrostatic Pressure on the Properties of 111-V Semiconductors
L. W. Aukerman, Radiation Effects
N. A. Goryunova, F. P. Kesamanly, and D. N. Nasledov, Phenomena in Solid Solutions
R. T. Bate, Electrical Properties of Nonuniform Crystals
Volume 5 Infrared Detectors
Henry Levinstein. Characterization of Infrared Detectors
Paul W. Kruse, Indium Antimonide Photoconductive and Photoelectromagnetic Detectors
M. B. Prince, Narrowband Self-Filtering Detectors
Ivars Melngailis and T. C. Harman, Single-Crystal Lead-Tin Chalcogenides
Donald Long and Joseph L. Schmit, Mercury-Cadmium Telluride and Closely Related Alloys
E. H. Putley, The Pyroelectric Detector
Norman B. Stevens, Radiation Thermopiles
R. J. Kcyes and T. M. Quisr, Low Level Coherent and Incoherent Detection in the Infrared
M. C. Teich, Coherent Detection in the Infrared
F. R. Arams, E. W. Sard, B. J. Peyton, and F. P. Pace, Infrared Heterodyne Detection with
Gigahertz IF Response
H. S. Sommers, Jr., Microwave-Biased Photoconductive Detector
Robert Sehr and Ruiner Zuleeg, Imaging and Display
Volume 6 Injection Phenomena
Murray A. Lampert and Ronald B. Schilling, Current Injection in Solids: The Regional Approxi-
mation Method
Richard Williams, Injection by Internal Photoemission
Allen M. Burnett, Current Filament Formation
R. Baron and J. W. Mayer, Double Injection in Semiconductors
W.R uppel, The Photoconductor-Metal Contact
Volume 7 Applications and Devices: Part A
John A. Copeland and Stephen Knight, Applications Utilizing Bulk Negative Resistance
F. A. Padovani, The Voltage-Current Characteristic of Metal-Semiconductor Contacts
P. L. Hower, W. W. Hooper, B. R. Cairns, R. D. Fairman, and D. A. Tremere, The GaAs Field-
Effect Transistor
Marvin H. While, MOS Transistors
G. R. Antell, Gallium Arsenide Transistors
T. L. Tansley, Heterojunction Properties
CONTENTS OF PREVIOUS VOLUMES xiii
Volume 7 Applications and Devices: Part B
T. Misawa, IMPATT Diodes
H. C. Ukean. Tunnel Diodes
Robert B. Campbell and Hung-Chi Chang. Silicon Carbide Junction Devices
R. E. Ensrrom, H. Kressel, and L. Krassner, High-Temperature Power Rectifiers of GaAs, -,P,
Volume 8 Transport and Optical Phenomena
Richard J. Stirn, Band Structure and Galvanomagnetic Effects in IIILV Compounds with
Indirect Band Gaps
Roland W. Ure, Jr., Thermoelectric Effects in Ill-V Compounds
Herbert Piller. Faraday Rotation
H. Barry Bebb ond E. W. Williams, Photoluminescence I : Theory
E. W. Williams and H. Barry Bebb, Photoluminescence I1 : Gallium Arsenide
CHAPTER 1
Electroreflectance
B . 0. Seraphin
I . INTRODUCT~ON . . . . . . . . . . . . . . 1
11 . ELECTROREFLECTANINC PEH ENOMENOLOGDICEASLC RIPTION . 7
1 . General Features . . . . . . . . . . . . . . 11
2 . Homogeneous Modulation ofthe Rejecting Medium . . . . 8
3 . Inhomogeneous Modulation of the Reflecting Medium . . . . 16
111 . THEORETICCOANCLE PTS IN ELECTROREFLECTAN.CE. . . . . 22
4 . Electric Field Effects in One-Electron Approximation . . . . 23
5 . Electron-Lattice Interactions and the Dielectric Function . . . 29
6 . Electric Fieid Eflects on Coulomb Interactions . . . . . . 31
Iv . EXPERIMENTMAELT HODSIN ELECTROREFLECTAN.CE. . . . . 32
7 . General Features . . . . . . . . . . . . . . 32
8 . Surface Barrier Electrorejectance . . . . . . . . . . 34
9 . Transverse Electroreflectance . . . . . . . . . . . 44
10 . Combination Techniques . . . . . . . . . . . . 45
V . EXPERIMENTRAELSU LTS . . . . . . . . . . . . . 51
1 I . Electrorejectance of Semiconductors . . . . . . . . 51
12 . ElectrorefIectance of Metals . . . . . . . . . . . 99
13 . Electrorejectance of Ferroelecirics . . . . . . . . . 1 00
VI. ANALYSIOSF ELECTROREFLECTASNPCEEC TRA. . . . . . . . 1 02
14 . Scope, Intention, and Problems of the Analysis . . . . . . 102
15 . Fundamentals of a Symmetry Analysis . . . . . . . . 1 07
16 . Signatures of Electrorejecronce Spectra . . . . . . . . 1 21
VI1 . ADDENDUM . . . . . . . . . . . . . . . . . 1 25
17 . Analysis of Electroreflectance Spectra . . . . . . . . 1 26
18 . Experimental Results . . . . . . . . . . . . . 1 39
19 . Experimental Methods . . . . . . . . . . . . . 1 45
20 . Photoreflectance . . . . . . . . . . . . . . 1 47
.
I Introduction
The first chapters of this volume review the various modulated reflectance
techniques developed during the last five years . All techniques modulate
the reflectance of a sample through a periodic change of an external param-
eter such as an electric field. pressure. or temperature. Modulation of the
.
reflected beam is detected synchronously and phase.sensitively separated
from the unmodulated background. and amplified .
1
2 B. 0.S ERAPHIN
Various modulation parameters define a whole family of modulated
reflectance techniques such as electroreflectance, piezoreflectance, and
thermoreflectance. The sample can be “prestressed” by one parameter and
modulated by a second, establishing combinations of the three basic tech-
niques. Modulation by rotation is possible, and a magnetic field can be added
to all techniques.
Under similar conditions, modulated reflectance techniques better define
the spectral contrast of structure than do static reflectance techniques. A
rather featureless reflectance curve is replaced by a modulated trace rich in
structure compressed into narrow regions of photon energy.
A response so sharply localized in energy suggests a correlation to dis-
continuities in parameters of the band structure. Consequently, band struc-
ture analysis in particular has taken an interest in the results of modulated
reflectance techniques. Most of what follows will therefore be reviewed from
this point of view. Other promising aspects, such as the apparent potential
of electroreflectance in surface physics, for example, take second place.
In a considerable effort during the last decade, energy band calculations
have been used to establish the key features of the electronic structure of
solids, to provide a basis for the qualitative interpretation of numerous
experimental results, and to guide further investigations.
As a matter of economy rather than principle, the most successful of these
calculations rely on some input from properly interpreted experimental
results. Although we can solve the Schrodinger equation for such compli-
cated systems as crystals, the definition of a physically realistic crystal poten-
tial is complicated by exchange, correlation, and relativistic effects. Recent
improvements in the computational tools permit us to treat these effects
more rigorously, but the return is hardly worth the increase in effort. We can
improve accuracy more efficiently by adding reliably interpreted experi-
mental features to the procedure. A rough classification of the available
methods can actually be obtained by considering the first principle effort
that enters the initial stage of computation before some parameter of the
computational scheme is adjusted to experiment.
The accuracy of such empirically adjusted calculations depends (to a
varying degree) on the proper interpretation of experimental results. The
collation of existing band models and new experimental evidence, which has
been amazingly successful in the past, must be continued. The better the
general features of a band structure are known, the more successful further
analysis becomes.
Information from a number of experimental methods is available for the
identification of the lowest band extrema. Away from these fundamental
edges, however, the interpretation of reflectance measurements was the main
source of experimental information. A bridge to band structure parameters
