The Story of Semiconductors

John Orton

OXFORD UNIVERSITY PRESS


The Story of Semiconductors


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The Story of Semiconductors
John Orton
Emeritus Professor, University of Nottingham, UK

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978 0 19 853083 1

10 9 8 7 6 5 4 3 2


Al Cho of Bell Labs receiving the US National Medal of Science
from President Clinton and Vice President Gore in 1993. Courtesy
of Al Cho.

Enrico Capasso (left front) with the Bell Labs team which developed
the quantum cascade laser using energy states in conduction band
quantum wells in the AlInAs/GaInAs material system. Courtesy of
Lucent Technologies Inc.

Just to prove that even the most dedicated scientists do not spend all their time
in the laboratory – Hiroyuki Sakaki on the golf course at St Andrews in 1991.
Courtesy of Hiroyuki Sakaki.

Leo Esaki (left) and Hiroyuki Sakaki (right) deep in discussion of the properties of
advanced quantum well structures in 1976. Esaki won the Nobel Physics Prize in
1973. Courtesy of Hiroyuki Sakaki.


Preface

My wife and I bought our first television set in 1966, a major family
decision, which just happened to coincide with England’s soccer World
Cup success at Wembley Stadium. It cost us about £100 out of my then
salary of £2000 a year. Thirty years later, when I retired on a salary
some twenty times greater, the purchase of an infinitely superior

colour set priced at little more than £500 could be contemplated with
considerably less heart-searching. Indeed, the financial outlay involved
in watching England’s rugby World Cup success in 2003 gave us
scarcely a qualm, one measure, perhaps, of the quite remarkable trend
in consumer friendliness inherent in the modern electronics industry. In
this we see one of the great successes of capitalist philosophy—a highly
competitive business environment yielding previously unimaginable
value for the consumer, while providing relatively comfortable employment for a very large workforce and (in spite of recent setbacks, exemplified by the misfortunes of the Marconi company) a satisfactory
return on invested capital for its shareholders. But, more significantly
from the viewpoint of this book, we also see a business based fairly and
squarely on investment in scientific research. With the possible exception of the pharmaceutical industry, there has never been such a
commitment to organized R&D and never before has the marriage
between science and industry been so prolific in its progeny.
More specifically, this remarkable commercial success owes its existence largely to discoveries in semiconductor physics, which blossomed
during the first half of the twentieth century and to developments in
semiconductor technology and device concept, which followed the
exciting events of Christmas 1947 when Bell scientists realized the
World’s first successful solid-state amplifier. Here was vindication for
Bell’s commitment to basic solid-state research in an industrial laboratory, which set the pattern for a rapidly expanding commercial activity,
an activity which has continued to grow at a remarkably consistent rate
into the present, truly worldwide industry we know today. It began
with germanium, which was immediately replaced by silicon, then
gradually drew in an amazing cohort of compound semiconductor
materials required to meet the rapidly diversifying range of device
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Preface

demands, based on an equally diverse range of applications. Today, we

take for granted the involvement of visible light and both infrared and
ultraviolet radiation as well as that of electrons. This expansive industry
is concerned with lighting, display, thermal imaging, solar electricity
generation, optical communications, compact disc audio systems, DVD
video systems, and a quite remarkable array of other uses for semiconductor lasers, as well as the more conventional electronic applications
typified by the personal computer. All in all, this omnipresent electronics
industry represents an annual turnover of about 5 ϫ 1011 US$, a figure
that compares not unfavourably with the $2 ϫ 1012 of the trend-setting
automobile industry.
It is little more than 50 years since the inception of transistor
electronics, a period which has seen quite dramatic developments in
semiconductor devices, an activity with which I was personally involved
for over 30 years. Having, during this time, written a number of books
and specialist review articles, I felt it worthwhile, on reaching retirement, to attempt some kind of summary of the field in which I had
worked. It had seemed to me for some time that, in spite of the numerous excellent texts which describe the physics and technology of semiconductor devices, there was a distinct lack of any coherent account of
just how these devices came into being. What were the driving forces,
what the difficulties to be overcome, what determined why a particular
development occurred when it did, where was the work undertaken
and by whom—in other words, how did the history of the subject
develop. As I became more and more interested in such questions, it
occurred to me that other workers in the field might appreciate a
reasonably concise account of its history, as background to their current
endeavours, also that there might be a wider audience of scientists who
would find a non-specialist account of this epoch-making activity of
general interest and, finally, that undergraduate students should be
encouraged to understand not only semiconductor physics and device
technology but also the background story of their advent. It is a human
story and, as such, may surely illuminate the technical aspects of the
subject to advantage. It is also a rapidly moving story and much of what
I have written will very soon be superseded, so I have made no attempt

to include the very latest developments. The account stops roughly
(and perhaps appropriately) at the millennium, my intention all along,
having been to write a history, not an up-to-date text book.
In most academic studies we expect to know something of the
people involved—who painted such and such a picture, who developed
such and such a philosophical idea, who was responsible for certain
political innovations—and it seems no less appropriate in science. The
difficulty here lies in the nature of modern scientific research, which
has become much more of a team activity, rather than that associated
with any one specific individual; so, in many cases, I have found it
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appropriate to refer to laboratories, rather than individuals. In attempting
a broad overview of the subject, it is scarcely possible to give an accurate
account of exactly how each individual scientist contributed to any
particular discovery and I have not even tried to do so. This must be the
task of the professional historian—and I make no pretence of being
one. Perhaps this can be taken as encouragement to serious historians
to become involved in the intricacies of scientific and technological
history. It is a vital part of modern culture and, as such, demands
considerably more attention than it currently receives. I only hope that
the present broad-brush account may serve as a stimulus to further,
more detailed studies.
Having said this, I should acknowledge that one or two detailed studies
do exist. I think, particularly, of the excellent ‘Crystal Fire’ by Michael
Riordan and Lillian Hoddeson, which describes the early work on transistors and integrated circuits, the ‘Electronic Genie’ by Frederick Seitz and
Norman Einspruch, covering somewhat similar ground and the admirable

survey of fibre optics provided by Jeff Hecht in his ‘City of Light’. Charles
Townes has also given us valuable insights into the origins of the laser in
‘How the Laser Happened’, though with rather little reference to semiconductor lasers. All these I have found helpful, as I have acknowledged in
the relevant parts of my own account. There is, though, considerable
scope for other studies, as anyone reading this book will appreciate. At
present, we are far better informed as to the details of Michael Faraday’s
researches in the early years of the nineteenth century than we are to the
development of group III-V semiconductors in the twentieth.
I have already outlined the audience to whom I have addressed this
book, and it covers, I accept, a rather broad spectrum. This has influenced the format of the book in one important respect, the inclusion of
‘Boxes’ which contain the more specialized and mathematical detail
supporting the basic account given in the main text. The book may be
read without reference to these boxes, the text being complete in itself.
Only readers interested in gaining deeper understanding need apply
themselves to the boxes and this they may do either while reading the
text or, if preferred, treat them as appendices to be read separately.
I imagine that most readers interested primarily in the historical aspect
of the subject will be happy with the basic text, while students, in
particular, should find the additional insight provided by these boxes of
value. I should nevertheless emphasize that the book is not, in any
sense, to be seen as a substitute for the various standard texts on semiconductor physics and devices but rather as complementary to them,
serving to provide a human slant to much that is otherwise purely technical. I hope and believe that many students will find this background
information extremely helpful in satisfying their natural curiosity about
how and why things came to pass and help them to appreciate the
nature of the process of device development. Being a human activity, it
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should preferably be understood in that context, complete with all its
human foibles.
The approach I have adopted throughout is essentially an interdisciplinary one. I have tried always to set device development in the context
of relevant applications, providing, for instance, a fairly thorough
account of the development of optical fibres by way of introduction to
long wavelength semiconductor lasers and photodetectors. I have,
similarly, outlined several applications of semiconductor power devices
before describing the relevant devices. In all cases, the technical material is presented in terms of the relevant timescale and I have devoted
considerable attention to the importance of semiconductor materials,
their development in response to device demands and the vital crosslinks with semiconductor physics. All three strands are well represented
and can only be properly understood as a trinity. The book should
therefore be of interest to physicists, electrical engineers, and to materials specialists, alike. Indeed, if I have been able to impart the essential
message that real human activities, such as this, inevitably cross pedagogic boundaries, I shall be well-satisfied. It is clearly apparent that,
without these interdisciplinary interactions, the electronics industry
would not be where it is today and it would be well that its future workforce (i.e., today’s students) should start their careers with an adequate
understanding of this essential truth. While it is common to present
scientific learning, at both School and University levels, in tidy and
coherent packages, the real world shows little respect for such neat
subdivisions—the successful inventor or entrepreneur must frequently
demonstrate powers of imagination that transcend conventional
boundaries.
Anyone familiar with the subject of semiconductor physics or device
development will appreciate that an account of their history, contained
within a book of modest size, must inevitably be highly selective, and
I make no apology for the fact that my own account lays itself wide
open to such criticism. As Norman Davies remarked, in the preface to
his (relatively thick!) work Europe—A History: ‘This volume—is only one
from an almost infinite number of histories of Europe that could be
written. It is the view of one pair of eyes, filtered by one brain and
translated by one pen.’

Apart form the fact that I typed my thoughts directly onto my computer, I could make an identical statement here. This book represents
one person’s view of the semiconductor story. Its emphases are my
own, based on my own involvement and inevitably coloured by my own
experiences—and prejudices. But I certainly believe it to represent one
history and one which I hope can be read with much enjoyment.
Should others wish to write their histories, I shall be delighted to read
them with equal enjoyment, secure in the knowledge that I may possibly
have stimulated them to improve on my prototype.
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Preface

Finally, I am happy to acknowledge the considerable debt which
I owe to many colleagues. My wife, Joyce, suffered patiently the long
hours of separation (even while we existed under the same roof!) and
still found it possible to offer words of encouragement. Specific help
was provided (in no particular order) by Professor Nick Holonyack of
the University of Illinois, Urbana; Dr Frank James of the Royal Institution,
London; Dr Sunao Ishihara of NTT, Kanagawa; Dr Tony Hartland of
the National Physical Laboratory, Teddington; Dr Hirofumi Matsuhata
of the Electrotechnical Laboratory, Tsukuba; Professor Sir Roger Elliott
of Oxford University; Professor Tom Foxon and Dr Richard Campion,
University of Nottingham; Mr Brian Fernley of Siemens, Professor
Rodney Loudon, University of Essex; and Professor Martin Green,
University of New South Wales, Sidney. More generally I must thank
those many colleagues with whom I worked during my years at
the Mullard (later Philips) Research Laboratories, Redhill and their
counterparts in the Philips Nat Lab in Eindhoven. They are far too
numerous for individual mention but I owe them a huge debt of gratitude

for innumerable stimulating interactions as a result of which my imperfect
understanding of semiconductor physics became gradually less blatant.
It is with great affection that I dedicate this book to them—without
their help, I could scarcely even have contemplated writing it. However,
while their contribution made it all possible, the errors and obscurities
that almost certainly remain are, of course, my personal responsibility.
December 2003

Orchard Cottage
Cotgrave

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CONTENTS

Chapter 1 Perspectives 1
1.1 The ‘Information Age’ 1
1.2 Early materials technology 3
1.3 What makes a semiconductor? 5
1.4 Semiconductor doping 12
1.5 How many semiconductors are there?
Bibliography 18
Chapter 2 The cat’s whiskers 19
2.1 Early days 19
2.2 First applications 21
2.3 Commercial semiconductor rectifiers

2.4 Early semiconductor physics 28
2.5 The cat’s whisker reborn 38
2.6 Postscript—how things happen 42
Bibliography 46

15

23

Chapter 3 Minority rule 47
3.1 The transistor 47
3.2 Ge and Si technology 54
3.3 The physics of Ge and Si 60
3.4 The junction transistor 79
Bibliography 91
Chapter 4 Silicon, silicon, and yet more silicon 93
4.1 Precursor to the revolution 93
4.2 The Metal Oxide Silicon transistor 100
4.3 Semiconductor technology 107
4.4 Wise men from the East 120
4.5 Power and energy—sometimes size is important
4.6 Silicon is good for physics, too 139
Bibliography 147
Chapter 5 The compound challenge
5.1 Why bother? 149
5.2 Gallium arsenide 152
5.3 Crystal growth 158
5.4 Material characterization 171
5.5 Light emitting devices 184
5.6 Microwave devices 195

5.7 Indium-phosphide 207
Bibliography 211

127

149

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Contents

Chapter 6 Low dimensional structures 213
6.1 Small really is beautiful 213
6.2 The two-dimensional electron gas 219
6.3 Mesoscopic systems 229
6.4 Optical properties of quantum wells 237
6.5 Electronic devices 246
6.6 Optical devices 258
Bibliography 275
Chapter 7 Let there be light 277
7.1 Basic principles 277
7.2 Red-emitting alloys 286
7.3 Gallium phosphide 294
7.4 Wide band gap semiconductors 304
7.5 Short wavelength laser diodes 315
Bibliography 328
Chapter 8 Communicating with light
8.1 Fibre optics 331
8.2 Long wavelength sources 343

8.3 Photodetectors 359
8.4 Optical modulators 373
8.5 Recent developments 378
Bibliography 384

331

Chapter 9 Semiconductors in the infrared 385
9.1 The infrared spectral region 385
9.2 Infrared components 391
9.3 Two world wars—and after 398
9.4 Growing sophistication—the 1960s and 1970s
9.5 Quantum wells, superlattices, and other
modern wonders 425
9.6 Long wavelength lasers 436
Bibliography 445
Chapter 10 Polycrystalline and
amorphous semiconductors 447
10.1 Introduction 447
10.2 Polycrystalline semiconductors 448
10.3 Amorphous semiconductors 460
10.4 Solar cells 471
10.5 Liquid crystal displays 486
10.6 Porous silicon 498
Bibliography 501
Index 503

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Perspectives
1.1

The ‘Information Age’

Sitting contemplatively, in front of my computer screen, seeking
inspiration on how best to make a convincing start to the writing of this
book, my mind wandered over the technical changes which had
occurred in my life since I had last been engaged on a similar enterprise.
That was in the 1980s when I collaborated with Peter Blood on, what
turned out (to us) to be, an awesomely lengthy summary of experimental techniques for semiconductor characterization. I reflected that,
between us, we had written all 1026 pages of these two volumes by
hand, delivering countless longhand pages to long-suffering typists who
performed the near impossible task of rendering them comprehensible
to the typesetters of Academic Press. How things have changed! Today,
I compose everything, I write on my own word processor, and submit
it in electronic form (now the errors really are all my own!), the major
problem of filing and collating huge quantities of information being
taken care of more or less automatically. I need do no more than take
care to back up my long-suffering hard disk with an array of carefully
labelled floppies—or, better still, a single CD.
Of course, similar possibilities existed 20 years ago, when Peter and
I began our collaboration but the fact that we could choose to ignore
them then serves to emphasize the change in working practices which
those 20 years have ushered in. It reflects, though, only one incidence of
the influence the ubiquitous silicon chip has had on our lives over the

past few decades—remember, the transistor, itself, was invented as
recently as 1947, little more than 50 years ago—and, then, it was made
from germanium—silicon had not even been heard of (!) (at least, not
outside the laboratory and certain esoteric military applications). It is
hardly an original thought, but the pace of change in our times is
certainly remarkable, if not (to many) actually frightening.
Once launched, then, on my train of thought, I have little difficulty
in following this observation with others in a similar vein. Not only do
I have a facsimile machine as an integral function of my office telephone, but my computer serves me also as basis for e-mail communication with colleagues and friends all round the world. Similarly, I can
obtain technical information (or the times of trains to London) in huge
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The story of semiconductors

variety from the latest wonder of the modern world, the Internet. On
a more mundane level, the central heating system which is even now
keeping me in bodily comfort against the external chill is controlled by
a microprocessor, the family washing machine in an adjacent room
makes available to us a wide range of washing programmes under the
supervision of a similar tiny piece of suitably processed silicon. While
my wife and I would never claim to be in the vanguard of the electronic
revolution, we routinely use either of two audio systems based on the
wonders of optoelectronics, not to mention the inevitable television
set, with its accompanying video recorder which graces a corner of our
living room, where it can, of course, be remotely controlled. The 1990s
vacuum cleaner we use without much serious thought has a motor
with electronic control, so too does the food mixer which relieves us of
much of the physical hard work in our kitchen, not to mention several
power tools which languish unused in my workshop while I am otherwise engaged in writing. We even have a mobile phone, though it

stays firmly closeted in the car glove box for emergency use only. Our
mass-produced car, in common with most of its competitors, boasts an
engine monitoring system and electronic ignition, the stop lights are
augmented by bright-red light emitting diodes (which everyone, nowadays, refers to as LEDs, such is their comonplace nature!), the instrument panel display is also based largely on LEDs and we are able to
control the central locking with an infrared device buried conveniently
within the ignition key. There is nothing remarkable in any of this, of
course. Out of the house, one of my favourite pastimes is hill walking
and my daughters recently bought me a wonderful satellite navigation
sytem which tells me exactly where I am at any moment and where
I need to aim in order to reach my next way point. I find it truly amazing but, no doubt, by the time this book reaches the market, everyone
will have one and it will be seen as just another of those modern aids to
civilized existence which we all tend to take for granted.
I could extend this line of thought considerably but I have probably
said more than enough already—we are all aware of the information
technology (IT) revolution—the press is full of the latest possibilities for
home working, life on the Internet Waves, electronic home buying, etc.
and we are rapidly becoming accustomed to the virtues (?) of smart
telephones and smart cards which seem able to do most things without
human intervention, these days. However, most people are, perhaps,
less familiar with the origins of their new-found information skills—
how is it all possible?, what depth of technical expertise has been
employed in order to produce the necessary hardware and software?,
what are the limitations to further progress?, etc. One reason for our
relative ignorance is the enormous size of the subject and its daunting
technical complexity, not made easier by the difficulty many scientists
have in writing for the non-specialist. What follows here, therefore, is
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an attempt to describe just one aspect of this exciting story in narrative
form so that the efforts of countless scientists and technologists may be
more widely appreciated, while furthering better understanding on the
part of non-specialists and specialists alike. For, what is more, it makes
a wonderful story, every bit as fascinating as the sagas of earlier technological breakthroughs (of which we actually know far less) such as
copper, bronze, and iron.

1.2

Early materials technology

All hardware aspects of mankind’s many technologies are based on, and
are limited by materials, so obvious a truism that we are prone to overlook it. Early man made use of stone for millennia, before discovering the
wider possibilities of copper. It took a mere thousand years to acquire
the greater capability of bronze and perhaps a further thousand for
iron to make its entry into the evolutionary stream. However, things
move at a greater pace nowadays—semiconductors, the materials of the
information age, took just a hundred years to develop from the status of
ill-understood and totally uncontrolled materials with certain mysterious
properties, to their present position as some of the most thoroughly
explored and well understood of all mankind’s conquests. It represents a
success story of which we should be proud, ranking alongside impressionism, Concord, mediaeval cathedrals, Burgundy wines, the Beethoven symphonies, and modern medicine, to name but a few (largely European!)
highlights. No fewer than fourteen semiconductor scientists have been
honoured by the Nobel Committee since the inception of the Prize
in 1901 (when the discovery of X-rays by Wilhelm Conrad Rontgen was
formally acknowledged). In 1909 Carl Braun shared the prize with
Marconi for the development of wireless telegraphy (Braun’s contribution included the discovery of semiconductor rectification), there was
then a considerable gap until 1956, when John Bardeen, Walter Brattain,
and William Shockley were recognized for their world-shaking invention

of the transistor, followed much more briskly by awards to Leo Esaki
(1973) for his discovery of tunnelling in semiconductors, Sir Nevill Mott
and Philip Anderson (1977) for discoveries in amorphous semiconductors, Klaus von Klitzing (1985) for discovering the quantum Hall effect in
a metal oxide silicon structure, Robert Laughlin, Horst Stormer, and
Daniel Tsui (1998) for their work on the fractional quantum Hall effect
in a gallium arsenide ‘low dimensional structure’ and, finally in 2000,
Zhores Alferov, Herb Kroemer, and Jack Kilby for various contributions
to the fields of electronics and optoelectronics. Clearly, my eulogistic
statement can be supported with some sound references!
The history of mankind’s discovery and taming of materials is a long
one, stretching back to the stone age, some 5000 years before the birth
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The story of semiconductors

of Christ. While this is no place for a detailed analysis of our, generally
slow, progress (even if the present author were competent to undertake
it), there are similarities with the recent development of semiconductors
that make it worthwhile to look briefly at one or two aspects of the
story. In all such material development activity one recognizes certain
common features—first, the discovery of the material in its crude form,
its isolation, perhaps from suitable ores, its initial application to ‘practical’ problems, the realization of limitations, the discovery of means for
modifying the raw material properties, and a gradual struggle to gain
control over and perfect each material in turn. Thus, we see that (very
roughly) about 4000 BC copper was first employed in making small items
of jewellery, possibly as a by-product of attempts to obtain a suitable pigment for making green eye-shadow! (human vanity plays its part in a
multitude of ways). Some small amounts of metallic copper were probably found in proximity to the ores used as pigment and this was followed by the discovery that copper could be hammered into desirable
shapes. However, work-hardening must have been a serious problem
and it is only with the application of heat that our ancestors could begin

to gain satisfactory control over the material. Again, this probably happened as a side-effect of early attempts (c.3000 BC) to make an artificial
form of lapis lazuli for the cheaper end of the jewellery trade, a process
involving copper-blue colour in decorative glass, widely known as
Egyptian faience. This probably represents the first serious attempt to
develop a materials technology based on the application of heat, in this
case to glass formation, and represents a particularly important step,
controlled heating being an essential feature of the majority of technologies which followed, not least the development of semiconductors.
The next major development came with the discovery that copper
could be melted in a crucible by raising the temperature sufficiently
(as we now know to 1083ЊC for the pure metal), a requirement which
implies the use of some form of forced air flow, probably by fanning or
use of a blow-pipe. This led to the use of moulds to form a more sophisticated range of shapes, including tools and (not surprisingly, perhaps!)
weapons. The advantages of technological superiority in warfare were
realized long before our high-tech age and there could be no denying
their political influence, even in 3000 BC (though increasing considerably in value as populations grew and mobility became greater).
Important though this was, there were still problems with obtaining
adequately free flow of molten copper for accurate moulding and, as
we know well, copper is a trifle soft in relation to the need for maintaining sharp cutting edges. The answer to this difficulty emerged,
eventually(!)—round about 2000 BC it was found that the addition of
small amounts of tin to the copper melt resulted in three major
improvements. First, the ‘alloys’ melted at significantly lower temperatures, making the firing process easier to manage, second, the resulting
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   | Perspectives

melt was considerably less viscous, allowing more accurate and finer
moulding, and third, the final material was harder and less prone to
(uncontrolled) work-hardening. (The success of the Assyrian armies in
the period prior to 1000 BC can be attributed in no small degree to these

particular properties.) Thus began the Bronze Age and, over the ensuing centuries, it was established just how the properties of this superior
alloy could be adjusted, by incorporating various controlled proportions of tin (typically between 5 and 15%), to optimize its performance
against specific requirements. Finally, in the period round about 1000 BC,
it was discovered that iron could also be applied to many of the more
demanding tasks, such as the manufacture of weaponry and ‘industrial’
tools. This was not so much the result of iron’s superiority, as of its
greater availability but it brought with it the need for even higher furnace temperatures (iron melts at 1535ЊC) and the application of hot
forging techniques, the invention of the bellows at about this time
being an essential co-requisite.
We shall now skip conveniently past the intermediate centuries in
which mankind gradually gained increasing control over the technology of iron-based materials and simply note the importance of recent
developments in steels based on the addition of small amounts of suitable ‘impurities’ into the molten iron (shades of the early Bronze Age?).
The production of tool steel is just one example of this, demonstrating the importance of obtaining a highly purified basic material which
may then be modified in a number of desirable ways (by the addition of
small amounts of chromium, vanadium, or nickel) to meet wide ranging requirements. We also note the importance of controlling the
atmosphere surrounding the molten charge—it is no longer adequate
merely to heat in air—carefully controlled oxidizing or reducing conditions are frequently essential. We shall see many parallels in semiconductor processing in the following pages.

1.3

What makes a semiconductor?

Semiconductors have been, and are, used in various forms, as mechanically cut slices from a single crystal ‘boule’, as single crystal thin films
deposited on a suitable substrate by a more or less complex chemical or
physical process, as glass-like elements, and as polycrystalline or glassy
thin films deposited on (typically) a glass substrate. In the great majority of applications, an essential part of the process is concerned with
growing a high quality bulk single crystal either to serve directly as the
active material or to act as a substrate for epitaxial film growth (see
Box 1.1). This, therefore, has generally required crystal growth from a
crucible of the molten semiconductor, a technique demanding similar

care and attention to appropriate atmosphere as those encountered in
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The story of semiconductors

Box 1.1. Epitaxy
The word ‘epitaxy’ is derived from two Greek words ‘epi’ ϭ ‘on’ and ‘taxis’ ϭ ‘arranged’. It implies that appropriate atoms
or molecules may be placed in some convenient way on a supporting surface or ‘substrate’ so as to produce a thin film of
the desired material. However, in crystal growth lore, it has further been taken to imply that the atomic arrangement
of the deposited material conforms precisely to that of the substrate. The most straightforward case to consider is that of
‘homoepitaxy’ where the substrate and growing film consist of the selfsame material, for example, a single crystal GaAs
film growing on a single crystal GaAs substrate.
This process is very widely utilized in semiconductor technology, in the numerous situations where bulk single crystals
are available but where their electrical quality is inadequate for direct application to device fabrication. A frequent method
of avoiding the difficulty thus created is, then, to grow a high quality epitaxial film on a carefully prepared bulk crystal
slice which serves merely as a mechanical support. This, of course, adds to the complexity (and cost!) of the overall process
but is almost certainly preferable to a direct attack on the almost impossible task of growing sufficiently high grade bulk
crystals. In many cases, the concept has been extended into ‘heteroepitaxy’ where the grown film differs, chemically, from
its substrate but where there is close similarity between their crystal structures. An excellent example of this is the growth
of AlAs films on GaAs substrates. Not only do both materials crystallize in the same form, but their natural lattice parameters (essentially, the separation between neighbouring atoms) are closely similar. The further extension to cases where
the two materials have significantly different lattice parameters often introduces serious difficulties and the extreme case
of growing a film of one structure on a substrate which crystallizes in a different structure can only be justified when no
other substrate is available. It has occasionally been done with remarkable success but is, without doubt, the last resort of
desperate men—for example, those crystal growers whose managers have decreed that compound XYZ3 is the only
answer to the managing director’s urgent request for a solution to his latest marketing problem, bulk crystals of XYZ3
being impossible to grow, except at temperatures of 3500ЊC under hydrogen vapour pressures in excess of 20 kbar!

steel production. However, the purity levels required for semiconductor
preparation turn out to be enormously more stringent—impurities in

steel typically demand control at the percentage level (1 in 102), whereas
a typical semiconductor will be susceptible to impurity levels measured
in parts per billion (1 in 109). Crystal perfection is another critical
parameter which raises demands on the crystal grower to levels
unheard of in most metallurgical applications. So, in summary, we see
that, though there are qualitative similarities between the material
technologies of metals and semiconductors (which will surely act as
helpful guides in many cases), the quantitative differences raise possibly
formidable problems.
This having been said, by way of introduction, it is now time to come
to terms with the nature of these intriguing materials on which so much
of our lives depend. What, exactly, is a semiconductor? The usual dictionary definition that it is a material which conducts electricity with
a facility somewhere between those of metals and insulators (as the
name clearly suggests) certainly provides a convenient starting point but
leaves an awful lot unsaid. However, it is useful first to quantify the above
definition. Most metals are found to be good electrical conductors,



   | Perspectives

Box 1.2. Electrical resistivity
Entertain conjecture (as Shakespeare once put it) of a regular, uniform cube of silicon with sides each 1 m in length and
having metallic electrical contacts covering one pair of opposite faces. (‘Conjecture’ is appropriate here—in spite of the
truly amazing feats off bulk crystal growth demonstrated of late, no such volume of crystalline material has yet been seriously contemplated.) If a small current I (ampere) is passed through this massive block, from one contact to the other and
the voltage drop V (volts) across the sample measured, the resistance R (ohms) obtained, R ϭ V/I is, by definition, the resistivity ␳ of the silicon material. Its units are ohm-metres (⍀ m). Note that, because the geometry of the measurement is
specified, ␳ is a material parameter, that is, a property of the silicon alone. It depends on the density of free carriers within
the silicon and on their ‘mobility’, that is, their ability to move through the crystal, but not on any external features. For
example, if we change the geometry to a slightly more general one of a rectangular brick of length L and cross-sectional
area A, the resistance of this sample is given by R ϭ ␳L/A. Thus, resistance depends on both geometry and material.


having resistivities (see Box 1.2) in the order of 10Ϫ7–10Ϫ8 ⍀ m,
whereas, at the other end of the scale, we encounter insulating materials
such as certain oxide films, mica, glass, plastics, etc. where the corresponding quantity ranges between 1010 ⍀ m and 1014 ⍀ m. This huge
variation of resistivity between metals and insulators is remarkable in
itself but we are more interested at present in where typical semiconductors lie in the scheme of things—they cover quite a range themselves—10Ϫ6–102 ⍀ m being typical resistivities for silicon, for example,
whereas inclusion of the so-called ‘semi-insulating’ gallium arsenide
with resistivity near 107 ⍀ m extends the range upwards by a further five
orders of magnitude. Clearly, the values appropriate to semiconductors
do lie between those of metals and insulators but, perhaps the more
striking observation is that semiconductor resistivities, themselves vary
so much (roughly 13 orders of magnitude!) that it is hard to see this as a
suitable parameter with which to ‘pin them down’. We need an explanation for the origin of the resistivity if we wish to know what these numbers really mean, and this can only be obtained by referring to the band
theory of solids developed during the late 1920s and early 1930s. It was
this which laid the foundation for our present understanding of semiconductors and how they relate to metals and insulators.
The band theory represented an important application of the recently
developed (and highly exciting) quantum theory of atomic structure. The
first major success of quantum theory was its explanation of atomic spectra, particularly that of the simplest atom, hydrogen. An important concept introduced by quantum mechanics was the notion that electrons in
atoms could occupy only certain well-defined energy states (in contrast
to classical mechanics which allows all possible energy values) and, in
single (i.e. isolated) atoms these energy states were extremely sharp. The
resulting spectral emission lines which corresponded to electrons jumping from one ‘allowed’ energy state to another (of lower energy) showed



The story of semiconductors

correspondingly narrow line widths. The rather simple, but very important, equation which defines this emission process was found to be:
h␯ ϭ E2 Ϫ E1,


(1.1)

where ␯ is the frequency of the light emitted, E2 is the upper and E1 the
lower of the two energy states and h is the (now) famous Planck’s constant, one of the most important fundamental constants of modern
physics. In semiconductor work, it is customary to refer to energies in
units of ‘electron volts’ (the energy an electron gains when it is accelerated through a voltage drop of 1 V) so we can define the Planck’s constant in terms of the unit ‘electron volts per Hertz’, in which case, it
takes the value 4.136 ϫ 10Ϫ15 eV s—a value of ⌬E ϭ (E2 Ϫ E1) ϭ 1 eV
corresponds to a frequency of 2.418 ϫ 1014 Hz which lies in the nearinfrared region of the spectrum. Another very useful relation which can
be obtained from this connects the emission wavelength ␭ with the
energy difference, as follows:
␭ ϭ 1.240/⌬E

Allowed
electron
states
No
allowed
states

Eg

Allowed
electron
states
E
x

Figure 1.1. Schematic diagram representing
the valence and conduction bands in a
semiconductor. The vertical axis represents

energy, while the horizontal axis represents
a spatial coordinate. Semiconductors are
characterized by the forbidden energy gap
which separates the two allowed bands of
states, the gap being typically 0.5–2.0 eV wide.
No allowed states for electrons exist within
the gap of a pure semiconductor.



(1.2)

in which the wavelength is measured in microns (1 ␮m ϭ 10Ϫ6 m) and
the energy difference in electron volts. In this book, we shall make
much use of these equations (and the corresponding physical concepts)
which is why they have been spelled out in detail here.
In a crystalline solid, the atoms of copper, aluminium, silicon,
germanium, gallium, and arsenic (in GaAs), for example, cannot be
treated as isolated—in fact, they are in close proximity and nearest
neighbours are chemically bonded to one another. This means that an
electron on one atom ‘sees’ the electric field due to electrons on other
atoms and the nature of the chemical bond implies that electrons on
close-neighbour atoms are able to exchange with one another. Two
important results follow: the sharp atomic energy states are broadened
into energy ‘bands’ in the solid and these bands are associated, no
longer with single atoms, but with the crystal as a whole. In other
words, electrons may appear with equal probability on atoms anywhere
in the crystal. This implies that these negatively charged electrons are
able to move through the crystal lattice and we have, at least in principle, the possibility of electrical conduction (which is simply the flow of
electric charge).

Figure 1.1 provides a schematic illustration of the energy bands in a
semiconducting crystal. It is an essential feature of any semiconductor
that these two bands are separated by an ‘energy gap’, that is, there is
a range of energies which is not available to electrons, and this gap is
known variously as ‘the fundamental energy gap’, the ‘band gap’, the
‘energy gap’, or the ‘forbidden gap’. By whichever name, it is the most


   | Perspectives

Empty
state

Time
sequence
1
2
3
4
5
6
Electric field

Figure 1.2. Pictorial representation of a
positive hole current in the valence band of a
semiconductor. Electrons move, under the
influence of an applied electric field, into
available empty states in the valence band,
leaving behind new empty states in the sites
they have abandoned. When negatively

charged electrons move from right to left, the
resulting holes move from left to right.
Positive charge flow is in the direction of
hole flow.

important property of any semiconducting material, as we shall see.
In a perfect, pure semiconductor at the absolute zero of temperature,
the lower band, known as the ‘valence’ band is completely full of
electrons—that is, every available energy state is occupied—while the
upper band, the ‘conduction’ band is entirely empty. At first sight, the
presence of the filled valence band seems to imply that the material
might act as an electrical conductor but deeper insight supports the
opposite conclusion. In order that net charge can flow, there must be
empty states available for electrons to move into, which is not the case
in a completely filled band—the exchange of electrons between any pair
of states does not, of course, change the overall electron distribution,
so such a process (which is possible) does not represent a flow of
charge. Needless to say, the empty conduction band is equally ineffective, but for a more clearly obvious reason. Under these, rather special
circumstances, therefore, our ‘semiconductor’ behaves as a perfect insulator! Its true semiconductor properties only become apparent if we lift
the restriction on its temperature.
At temperatures above absolute zero, thermal energy is freely available in the crystal in the form of ‘lattice vibrations’—that is, the atoms
of the crystal oscillate about their mean lattice positions, the amplitude
of the oscillation increasing in sympathy with the rise in temperature—
and some of this energy may be transferred to the valence band electrons, so as to ‘excite’ a small proportion of them into the empty conduction band. Immediately, it is apparent that these ‘free’ electrons
(they have been liberated from the confines of the valence band) can act
as charge carriers—if we apply an electric field across the sample
(by connecting the terminals of a battery across it) these conduction
electrons will be able to move through the crystal—there being large
numbers of empty states available for them in the conduction band.
Hey presto! a current flows. We call it an ‘electron current’ because it is

carried by free electrons. What may be less immediately obvious, the
empty states created in the valence band can also carry current—their
existence is all that is required to permit a net flow of charge in the
valence band, too. In practice, semiconductor scientists have chosen to
call this current a ‘hole current’—though we must be clear that it is the
electrons which physically move in the valence band, the net effect can
equally well be represented as a flow of ‘positive holes’ in the opposite
direction to the electron flow. Because the number of these holes is
identically equal to that of the free conduction band electrons, it is convenient to think of the holes as the charge carriers. Figure 1.2 will make
clear that, though the hole and electron flows are in opposite directions,
the net charge flows are in the same sense—the two currents add
together. A flow of negative electrons from right to left represents a positive charge flow from left to right, while the positive holes, flowing from
left to right, also constitute a positive current in the same direction.



The story of semiconductors

Following that subtle piece of sleight of hand, we may now begin to
understand the large range of resistivities observed between different
semiconductors. It originates with the fact that different semiconductors are characterized by different band gaps—for example, indium
arsenide has a band gap of 0.354 eV, germanium 0.664 eV, silicon 1.12 eV,
gallium arsenide 1.43 eV, (cubic) zinc sellenide 2.70 eV, GaN 3.43 eV, and
all the way to diamond with a gap of 5.5 eV. What is more, indeed very
much more, the numbers of free carriers in the conduction and valence
bands due to thermal excitation are related to the energy gap by the
following exponential expression:
n ϭ p ϭ ͙{NCNV} exp{ϪEg/2kT}.

(1.3)


In this important equation, n and p are the densities of free electrons
(‘n’egative) and holes (‘p’ositive), Eg is the energy gap, k is Boltzmann’s
constant and T the temperature of the semiconductor sample in
degrees absolute. (Readers familiar with the kinetic theory of gases
will recall the significance of kT in relation to the kinetic energy of gas
molecules—in our case, because of the strong interaction between
atoms in a solid, this energy cannot be associated with single atoms, but,
rather, with their collective motion.) NC and NV are parameters, referred
to as ‘effective densities of states’ for the conduction and valence bands,
respectively. At room temperature, the prefactor ͙{NCNV} has a typical
value of about 1025 mϪ3. Again, at room temperature, the ‘thermal
energy’ kT ϭ 0.026 eV so equation (1.3) may then be written as:
n ϭ p ϭ 1025 exp{ϪEg(eV)/0.052}

(1.4)

and the reader who can lay hands on a pocket calculator will have no
difficulty in confirming the following (approximate) values for n and p
at room temperature:
Germanium 2.85 ϫ 1019 mϪ3, silicon 4.43 ϫ 1015 mϪ3,
GaAs 1.14 ϫ 1013 mϪ3, ZnSe 2.82 ϫ 102 mϪ3.
The range of values for free carrier density is clearly enormous, and, if
we bear in mind that the resistivity ␳ is inversely proportional to n (or p),
we can readily appreciate the likelihood of ␳ varying strongly from one
pure semiconductor to another. Suffice it, for the moment, to say that
the values of resistivity corresponding to these free carrier densities vary (very roughly) between 1 ⍀ m (germanium) and 1017 ⍀ m
(zinc sellenide). In other words, pure zinc sellenide behaves as a very good
insulator, indeed! (Compare the typical values of measured resistivity
quoted above.) We shall see in a moment that this account overlooks




   | Perspectives

another vital aspect of the semiconductor repertoire so we should be
careful not to treat our newly acquired numbers as quite Gospel truth,
but they do, nevertheless, represent a major step forward in our understanding of semiconductor behaviour. It is clear now, that wide band
gap materials tend to behave as insulators—true semiconductors appear
to be those materials which have band gaps in the region of 0.3–2.0 eV—
this is still a very imprecise definition but somewhat more manageable
than our earlier attempt to use resistivity, which varied over some thirteen orders of magnitude!
Before leaving equation (1.3), it would be well to point out another
important feature, namely the form of the temperature-dependence of
free carrier density. Intuitively, it should be obvious that, as more thermal energy becomes available at higher temperatures, the larger will be
the density of free carriers excited. This, indeed, is consistent with
equation (1.3) (see Box 1.3). In turn, it implies that semiconductor resistivities decrease with increasing temperature, that is, the temperature
coefficient of resistivity is negative, a property which can be taken to

Box 1.3. Temperature coefficient of resistivity
The temperature coefficient of resistivity ␣ of a metal or semiconductor is defined as follows:
␳(T) ϭ ␳0{1 ϩ ␣(T Ϫ T0)},

(B1.1)

where ␳(T) is the resistivity at temperature T, ␳0 is the resistivity at the reference temperature T0 (say room temperature). It assumes a linear variation of resistivity with temperature, and, as such, is usually only valid over a very limited
range of temperature. If we now differentiate equation (B1.1) with respect to temperature, we obtain:
␣ ϭ (1/␳0) d␳/dT.

(B1.2)


Referring now to equation (1.3), and bearing in mind that ␳ ∝ 1/n, we can write:
␳ ϭ C exp{Eg/2kT},

(B1.3)

where C is a constant. Differentiating equation (B1.3), d␳/dT ϭ Ϫ(CEg/2kT)(1/T) exp{Eg/2kT} and writing ␳0 ϭ
C exp{Eg/2kT}, it then follows that:
␣ ϭ Ϫ(Eg/2kT)(1/T),

(B1.4)

which demonstrates that ␣ is negative but also that it decreases with increasing temperature. The relationship between
resistivity and temperature is not a linear one so we expect ␣ to depend on T, as it does. Evaluating ␣ at room temperature for a semiconductor with a band gap of 1 eV, we obtain: ␣ ϭ Ϫ(1/0.052) (1/300) ϭ Ϫ6.4 ϫ 10Ϫ2 KϪ1. This is a large
negative coefficient, compared with a value typical for a metal of ϩ4 ϫ 10Ϫ3 KϪ1.

