Table Of ContentLeonid V. Azaroff
PROFESSOR OF METALLURGICAL ENGINEERING
ILLINOIS INSTITUTE OF TECHNOLOGY
James J. Brophy
DIRECTOR OF TECHNICAL DEVELOPMENT
IIT RESEARCH INSTITUTE
McGraw-Hill Book Company, Inc.
New York San Francisco Toronto London
electronic
processes
in
materials
WVs'c*
A 97
ELECTRONIC PROCESSES IN MATERIALS
Copyright © 1963 by the McGraw-Hill Book Company, Inc. All Rights
Reserved. Printed in the United States of America. This book, or
parts thereof, may not be reproduced in any form without permission of
the publishers. Library of Congress Catalog Card Number 62-21566
02669
Dedicated to
Carmen and Muriel
Preface
In recent years, there has been a growing awareness of the need to
study the relation between the structure and properties of materials.
This has led to the gradual adoption of the term materials science to
describe such a study and has given the impression that such an approach
to materials is of very recent vintage. Nothing could be further from
the truth.
As a matter of fact, materials science properly begins when man first
seeks to understand what makes one material behave differently from
another. It is a matter of record that Empedocles, Democritus, and
other Greek philosophers speculated over two thousand years ago that
certain materials are composed of atoms that have "hooks" on them that
enable them to stick to each other firmly, while others are composed of
more slippery atoms that can easily move past each other. A more
scientific approach was adopted by metallurgists and mineralogists in
the nineteenth century to relate many distinguishable properties of crys
talline metals and minerals either to chemical composition or to structural
features visible with the aid of a microscope. The discovery of x-ray
diffraction in 1913 and its confirmation of the periodic nature of crystals
made it possible to evolve the much later theoretical concepts of materials
and to establish the completely new sciences of solid-state chemistry and
physics. Historically, metallurgists assimilated these twentieth-century
developments into their field whereas mineralogists were slower to do
this, so that the science of ceramics, fostered jointly by metallurgy and
mineralogy, was born. As the amount of activity in these areas kept
increasing, it became abundantly clear that the same processes were
operative in all materials, including, for example, plastics, and that a
vii
viii
Preface
great deal could be gained by attempting a more unified approach to
their study. This is the modern-day version of materials science, which
does not include, but does make use of, recent developments in solid-
state chemistry and physics in order to relate the properties of materials
to their structure on a submicroscopic as well as a macroscopic scale.
Concurrently, it is concerned with applying any newly gained perspectives
to the improvement of the specific properties that materials can possess
and to their wiser utilization.
In writing this book, the authors have been motivated by this growing
interest in a unified approach to materials. Since the properties of mate
rials are chiefly determined by their atomic composition and the nature
of the atomic aggregation, it is reasonable to say that they are controlled
by the crystal structure in crystalline materials. The interplay of struc
ture and properties, however, can be expressed in essentially two ways.
One is to relate the structural features to the observed properties in a
phenomenological way. The other is to make use of mathematical
theories developed mainly with the aid of statistical mechanics and
quantum mechanics to describe the behavior of materials under the
influence of various forces. This book attempts to combine both
approaches to discuss those properties of materials that are chiefly deter
mined by electronic processes in materials. A companion volume is in
preparation in which the properties of materials best described by ther-
modynamic processes will be considered. Until this second volume is
completed, the reader is urged to consult Introduction to solids,^ which,
in a necessarily brief account, discusses most of the properties of materials
not considered in this volume.
This textbook presupposes a familiarity with the elements of chemistry,
physics, and calculus. Although some discussions make use of differen
tial equations, their manipulation is clearly indicated, so that the mathe
matics serve primarily to decrease the number of words required to
transmit a specific idea. After an introductory discussion of geometrical
and x-ray crystallography, the fundamental concepts of quantum mechan
ics and statistical mechanics are explained and their application to bond
ing and other phenomena is illustrated. The rest of the book is con
cerned with the theoretical developments in our understanding of solids
and their application to the elucidation of the electric, magnetic, optic,
and thermal processes in materials. The relation of these properties to
crystal structure is pointed out, and the interplay between theory and
practice is often illustrated by a discussion of some of the more note
worthy devices that have been developed. In view of the dominant
role that semiconductor technology has played in the evolution of mate
t Leonid V. Azaroff, Introduction to solids (McGraw-Hill Book Company, Inc.,
New York, 1960).
Preface ix
rials science, the fundamental principles underlying the operation of
semiconductor devices are explained and related to commonly used semi
conductor materials. No attempt has been made to discuss all materials
or all conceivable devices; rather, the main classes of each have been
explored at moderate depth. Exercises have been included at the end
of each chapter in order to permit the reader to test his grasp of the
subject matter and to stimulate further development of some of the ideas
mentioned in the text. The answers to some of the problems are also
provided so that the reader can evaluate his own progress. The literature
lists at the end of each chapter have been divided into two groups, one
referring to sources of supplementary information, the other to some
what more advanced discussions of the same topics. References to
individual contributions are not included because it is the objective of
this book to provide a general synthesis rather than a discussion of
specific details.
The units used throughout this book are mks units because these units
are most appropriate for describing electric phenomena. It has become
the practice to use mixed units in semiconductor technology because the
measured quantities are usually quite small. Since this often leads to
confusion, it is hoped that this book will help place the matter of units
on a more consistent basis. Unfortunately, mks units are not the most
natural units possible for the discussion of magnetic phenomena; never
theless, this also can be done as discussed in the text. The equivalences
of mks and cgs designations are given in Appendix 2. Another innova
tion in this book is that the symbols recently recommended by the
American Institute of Physics, in cooperation with the International
Union of Pure and Applied Physics, are used throughout. The most
significant change is that capital letters, usually representing the first
letter of a unit named in honor of its discoverer, are used in place of the
previously used abbreviations. A partial listing of the most commonly
used units and their symbols is given in Appendix 1, and each symbol
is identified in the text when it first appears.
The authors are deeply indebted to many of their colleagues, who,
through their publications, have made most of the information presented
in this book available. In addition, a number of them consented to
have their illustrations reproduced in this book. We gratefully acknowl
edge the permissions granted by the authors and previous publishers of
the following illustrations:
Chapter 8: Fig. 16, J. E. Hill and K. M. van Vliet, J. Appl. Phys.,
vol. 29 (1958), p. 177; Fig. 25, T. H. Geballe, Phys. Rev., vol. 98 (1955),
p. 940.
Chapter 9: Fig. 14, R. F. Brebrick and W. W. Scanlon, Phys. Rev.,
vol. 96 (1954), p. 598.
x Preface
Chapter 10: Fig. 18, M. Keilson (ed.), Electronic Progress (Raytheon
Manufacturing Co., Lexington, Mass., 1957).
Chapter 11: Figs. 7 and 9, G. A. Haas and J. T. Jensen, Jr., J. Appl.
Phys., vol. 31 (1960).
We also express our thanks to those of our colleagues who kindly read
and criticized this manuscript. In particular, we wish to thank Professor
L. I. Grossweiner for carefully reading the entire manuscript. Our
thanks go also to Mrs. Marion Vogt for preparing the final typescript
and to those unsung heroines, our wives, who selflessly encouraged us
throughout its preparation.
Leonid V. Azdroff
J.
James Brophy
Contents
PREFACE vii
Chapter 1. STRUCTURE OF CRYSTALS 1
INTRODUCTION TO CRYSTALLOGRAPHY 1
Periodicity in crystals. Representation of planes. Symmetry elements.
Symmetry groups. Classification of crystals. Equivalent positions in a
unit cell.
THE CLOSEST PACKINGS OF SPHERES 17
Hexagonal and cubic closest packings. Body-centered cubic packing. Voids
in closest packings. Voids in body-centered cubic packing.
ATOMIC PACKINGS IN CRYSTALS 25
Effect of atomic size. Common crystal-structure types. Variations in
atomic packings.
Chapter 2. DIFFRACTION OF X-RAYS 35
ELEMENTARY DIFFRACTION THEORY 36
Bragg law. Diffraction intensities. Determination of unit-cell contents.
Determination of atomic arrays. Reciprocal-lattice concept.
THE POWDER METHOD 47
Experimental arrangement. Determination of unit-cell dimensions. Identi
fication of unknown crystals.
SINGLE-CRYSTAL METHODS 52
Rotating-crystal method. Moving-film methods. The Laue method.
xi
