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Introduction to the electronic properties of materials
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GHANPtS A
Introduction to the
Electronic Properties
of Materials
David Jiles
A meS Laboratory
US OePartrnent of Energy
and
Department of Materials Science
and Engineering
r ■ 1
Department of Electrical
and C°mputer Engineering
Iowa State University, USA
CHAPMAN & HALL
London Glasgow • Weinheim • New York • Tokyo • Melbourne • Madras
Introduction to the
Electronic Properties
of Materials
David Jiles
Ames Laboratory
US Department of Energy
and
Department of Materials Science *
and Engineering
and
Department of Electrical
and Computer Engineering
Iowa State University, USA
i
508623
CHAPMAN & HALL
London • Glasgow • Weinheim • New York • Tokyo Melbourne •
To Helen, Sarah, Elizabeth and Andrew,
from whom so many hours have been taken...
How soon hath Time, the subtle thief of youth,
stolen on his wing.
Milton
Contents
Preface xiii
Acknowledgements xiv
Glossary of symbols xv
SI units, symbols and dimensions xxi
Values of selected physical constants xxii
Foreword for the student xxiii
Part One Fundamentals of Electrons in Materials 1
1 Properties of a material continuum 3
1.1 Relationships between macroscopic properties of materials 3
1.2 Mechanical properties 5
1.3 Electrical properties 7
1.4 Optical properties 11
1.5 Thermal properties 14
1.6 Magnetic properties 17
1.7 Relationships between various bulk properties 20
1.8 Conclusions 20
References 20
Further Reading 21
Exercises 21
2 Properties of atoms in materials 22
2.1 The role of atoms within a material 22
2.2 The harmonic potential model 25
2.3 Specific heat capacity 32
2.4 Conclusions 39
References 39
Further Reading 39
Exercises 39
viii Contents
3 Conduction electrons in materials - classical approach
3.1 Electrons as classical particles in materials
3.2 Electrical properties and the classical free-electron model
3.3 Thermal properties and the classical free-electron model
3.4 Optical properties of metals
3.5 Conclusions
References
Further Reading
Exercises
41
41
43
46
49
57
58
59
59
4 Conduction electrons in materials - quantum corrections
4.1 Electronic contribution to specific heat
4.2 Wave equation for free electrons
4.3 Boundary conditions: the Sommerfeld model
4.4 Distribution of electrons among allowed energy levels
4.5 Material properties predicted by the quantum freeelectron model
4.6 Conclusions
References
Further Reading
Exercises
/
5 Bound electrons and the periodic potential
5.1 Models for describing electrons in materials
5.2 Solution of the wave equation in a one-dimensional,
periodic square-well potential
5.3 The origin of energy bands in solids: the tight-binding
approximation
5.4 Energy bands in a solid
5.5 Reciprocal or wave vector k-space
5.6 Examples of band structure diagrams
5.7 Conclusions
References
Further Reading
Exercises
Part Two Properties of Materials
60
60
61
63
69
76
79
80
80
81
82
82
85
91
94
99
105
106
106
106
107
109
6 Electror ic properties of metals
6.1 Electrical conductivity of metals
6.2 Reflectance and absorption
6 3 The Fermi surface
References
Further Reading
Exercises
111
111
112
114
126
127
127
Contents ix
7 Electronic properties of semiconductors 129
7.1 Electron band structures of semiconductors 129
7.2 Intrinsic semiconductors 134
7.3 Extrinsic (or impurity) semiconductors 138
7.4 Optical properties of semiconductors 141
7.5 Photoconductivity 142
7.6 The Hall effect 143
7.7 Effective mass and mobility of charge carriers 145
7.8 Semiconductor junctions 146
References 154
Further Reading 155
Exercises 155
8 Electrical and thermal properties of materials 156
8.1 Macroscopic electrical properties - 156
8.2 Quantum mechanical description of conduction electron
behaviour 160
8.3 Dielectric properties 163
8.4 Other effects caused by electric fields, magnetic fields
and. thermal gradients 166
8.5 Thermal properties of materials 168
8.6 Other thermal properties 172
References 178
Further Reading 179
Exercises 179
9 Optical properties of materials 180
9.1 Optical properties 180
9.2 Interpretation of optical properties in terms of simplified
electron band structure 183
9.3 Band structure determination from optical spectra 190
9.4 Photoluminescence and electroluminesence 193
References 196
Further Reading 196
Exercises 196
10 Magnetic properties of materials 198
10.1 Magnetism in materials 198
10.2 Types of magnetic material 201
10.3 Microscopic classification of magnetic materials 203
10.4 Band electron theory of magnetism 207
10.5 The localized electron model of magnetism 215
10.6 Applications of magnetic materials 218
References 218
x Contents
Further Reading 219
Exercises 219
Part Three Applications of Electronic Materials 221
11 Microelectronics - semiconductor technology 223
11.1 Use of materials for specific electronic functions 223
11.2 Semiconductor materials 225
11.3 Typical semiconductor devices 226
11.4 Microelectronic semiconductor devices 234
11.5 Future improvements in semiconductors 238
References 241
Further Reading 241
12 Optoelectronics - solid-state optical devices 242
12.1 Electronic materials with optical functions 242
12.2 Materials for optoelectronic devices 245
12.3 Lasers 249
12.4 Fibre optics and telecommunications 255
12.5 Liquid-crystal displays 256
/ References 257
Further Reading 257
13 Quantum electronics - superconducting materials 259
13.1 Quantum effects in electrical conductivity 259
13.2 Theories of superconductivity 262
13.3 Recent developments in high-temperature superconductors 268
13.4 Applications of superconductors 269
References 278
Further Reading 278
14 Magnetic materials - magnetic recording technology 279
14.1 Magnetic recording cf information 279
14.2 Magnetic recording materials 282
14.3 Conventional magnetic recording using particulate media 284
14.4 Magneto-optic recording 290
References 293
Further Reading 293
15 Electronic materials for transducers - sensors and actuators 294
15.1 Transducers 294
15.2 Transducer performance parameters 296
15.3 Transducer materials considerations 299
15.4 Ferroelectric materials 304
Contents xi
15.5 Ferroelectrics as transducers- 307
References 311
Further Reading 312
16 Electronic materials for radiation detection 313
16.1 Radiation sensors 313
16.2 Gas-filled detectors 314
16.3 Semiconductor detectors 315
16.4 Scintillation detectors 321
16.5 Thermoluminescent detectors 322
16.6 Pyroelectric sensors 323
References 323
Further Reading 324
Solutions - 325
Subject Index 359
Author Index 369
Preface
The subject of electronics, and in particular the electronic properties of materials,
is one which has experienced unprecedented growth in the last thirty years. The
discovery of the transistor and the subsequent development of integrated circuits
has enabled us to manipulate and control the electronic properties of materials
to such an extent that the entire telecommunications and computer industries
are dependent on the electronic properties of a few semiconducting materials.
The subject area is now so important that no modern physics, materials science
or electrical engineering degree programme can be considered complete without
a significant lecture course in electronic materials. Ultimately the course
requirements of these three groups of students may be quite different, but at
the initial stages of the discussion of electronic properties of materials, the course
requirements are broadly identical for each of these groups. Furthermore, as
the subject continues to grow in importance, the initial teaching of this vital
subject needs to occur earlier in the curriculum in order to give the students
sufficient time later to cover the increasing amount of material.
It is with these objectives in mind that the present book has been written. It
is aimed at undergraduates who have only an introductory knowledge of
quantum mechanics. The simplified approach used here enables the subject to
be introduced earlier in the curriculum. The goal at each stage has been to
present the principles of the behaviour of electrons in materials and to develop
a basic understanding with a minimum of technical detail. This has resulted in
a discussion in breadth rather than depth, which touches all of the key issues
and which provides a secure foundation for further development in more
specialized courses at a later stage. The presentation here should be of interest
to two groups of students: those who have a primary interest in electronic
materials and who need an introductory text as a stepping-stone to more
advanced texts; and those whose primary interest lies elsewhere but who would
nevertheless benefit from a broad, passing knowledge of the subject.
As with the earlier textbook, Introduction to Magnetism and Magnetic
Materials (1991) the subject area under discussion here is truly multidisciplinary,
spanning the traditional subject areas of physics, electrical engineering and
materials science. In writing this book I have striven to keep this in mind in
order to maintain the interest of a wider audience. Therefore some of the treatment will seem relatively easy for one group of students while relatively hard
for another. Over the entire book however I think that the general mix of
subject areas leads to a text that is equally difficult for these three groups of
students. Chapters 1-5 could easily be included in a traditional solid-state
physics course and should be very familiar to physicists. However chapters 6-10
will appeal more to materials scientists since they will be more familiar with
dealing with meso- and macroscopic properties. Finally chapters 11-15 discuss
the functional performance of these materials in technological applications
which are likely to be of most interest to electrical engineers. These chapters
provide a rapid introduction to five important applications of electronic
materials, each of which could be further developed in a separate advanced
course.
Also, as in Introduction to Magnetism and Magnetic Materials, the early
chapters of this book contain a number of key exercises for the student to attempt.
Completed worked solutions are given at the back of the book. It has been my
experience that this is much more useful than simply giving a numerical answer
at the back, since if you do not get the problem exactly right under those
conditions, you cannot easily find out where you went wrong!
On completion of the text the reader should have gained an understanding
of the behaviour of electrons within materials, an appreciation of how the
electrons determine the magnetic, thermal, optical and electrical properties of
materials and an awareness of how these electronic properties are controlled
for use in a number of important technological applications. I hope that the
text will provide a useful introduction to more detailed books on the subject
and that it will also provide the background for developing the interest of
students in this fascinating subject at an early stage in their careers.
Finally, I would like to acknowledge the assistance of several friends and
colleagues who have helped me in writing this book. In particular thanks go to
M. F. Berard, F. J Friedlaender, R. D. Greenough, R. L. Gunshor, J. Mallinson,
R. W. McCallum, R. E. Newnham, S. B. Palmer and A. H. Silver.
D J
Ames, Iowa
xiv Preface
ACKNOWLEDGEMENTS
I am grateful to those publishers credited in captions for permission to reproduce
some of the figures in this book.
Glossary of Symbols
A Area
a Distance
a Lattice spacing
a Mean field constant
Optical attenuation coefficient
B Magnetic induction (magnetic flux density)
BR Remanent magnetic induction
B> Saturation magnetic induction
C Capacitance
Curie constant
Specific heat or heat capacity
Cc Electronic specific heat
c ' Lattice specific heat
Cv Specific heat capacity at constant volume
Cp Specific heat capacity at constant pressure
c Velocity of light
X Magnetic susceptibility
Xp Pauli paramagnetic susceptibility
D Electric displacement (electric flux density)
D(a>) Vibrational density of states
Phonon density of states
D (E) Density of available energy states
d Diameter
Distance
S Optical penetration depth
BF Fermi energy
4 Electric field strength
Elastic (bulk) modulus
Binding energy
EY Elastic (Young’s) modulus
Es Elastic (shear) modulus
E Energy
Ec Cohesive energy
e Electronic charge
Strain
£a Anisotropy energy
£ cx Exchange energy
£ h Magnetic field energy (Zeeman energy)
€ h. ii H a l1 fie ld
£ k Kinetic energy
E \oss Energy loss
£P Potential energy
£P(x) Potential energy at location x
Ea Stress energy
c Permittivity (dielectric constant)
Cj Real component of dielectric constant (polarization)
c2 Imaginary component of dielectric constant (absorption)
e0 Permittivity of free space
£inl Internal, or interactive, force
F Force
^app Applied force
/ Fermi function
g Transducer generation coefficient
Spectroscopic splitting factor
Lande splitting factor
y Gyromagnetic ratio
H Magnetic field strength
h Planck’s constant
h Planck’s constant divided by 2n
Hc Coercivity
Critical field
Hcr Remanent coercivity
Hd . Demagnetizing field
Hc W .iss mean field
Hcff Effective magnetic field
/ Magnetic polarization (intensity of magnetization)
/ Intensity of light
Electric current
xvi Glossary of symbols
*^Q Thermal current density
^ Electric current density
Atomic angular momentum
J Total atomic angular momentum quantum number
Exchange constant
J Total electronic angular momentum quantum number
^atom Exchange integral for an electron on an atom with electrons on several
nearest neighbours
4 Exchange integral; exchange interaction between two electrons
K Anisotropy constant
Thermal conductivity
k Optical extinction coefficient
Interatomic force constant
Coupling coefficient of transducer
Wave vector
kB Boltzmann’s constant
K ul First anisotropy constant for uniaxial system
K u2 Second anisotropy constant for uniaxial system
First anisotropy constant for cubic system
K 2 Second anisotropy constant for cubic system
L Inductance
Length
Electronic orbit length
Macroscopic length of lattice chain
Length of side of cubic specimen
L Atomic orbital angular momentum
/ Length
l0 Unstrained length
A/ Change in length
/ Orbital angular momentum quantum number
if(x) Langevin function of x
A Wavelength
Magnetostriction
Penetration depth in superconductor
Ad Penetration depth
A, Transverse magnetostriction
As Saturation magnetostriction
A0 Spontaneous bulk magnetostriction
M Magnetization
m Magnetic moment
Momentum
Glossary of symbols xvii
xviii Glossary of symbols
M Mass
Man Anhysteretic magnetization
mc Electronic mass
m, Orbital magnetic quantum number
m0 Orbital magnetic moment of electron
M r Remanent magnetization
Ai0 Saturation magnetization
(spontaneous magnetization at 0 K)
M s Spontaneous magnetization within a domain
ms Spin magnetic moment of electron
ms Spin magnetic quantum number
mlol Total magnetic moment of atom
m* Effective mass of electrons in bands
/i Permeability
Mobility of charge carriers
fiB Bohr magneton
/j0 Permeability of free space
N{E) Density of occupied energy states (= 2 D (E)f (£)), electron population
density
N Number of atoms per unit volume
Number of electrons per unit volume
N x Number of turns on coil or solenoid
n Refractive index
Principal quantum number
Number of atoms
N 0 Avogadro’s number
N 0(E) Total number of energy states between zero energy and energy E
N* Effective number of conduction electrons
v Frequency (oy/ln)
a> Angular frequency (2nv)
P Pressure
P Polarization
P(E) Probability of occupancy of state with energy E
P(x) Probability of electron being at location x
Angular momentum operator
P0 Orbital angular momentum of electron
Ps S[ in angular momentum of electron
Plot Total angular momentum of electron
p angular momentum
n Peltier coefficient
<1> Magnetic flux
<p Angle
Work function
Spin wave function
C/3 C/}
Glossary of symbols xix
T Total wave function
if/ Electron wave function
q Electric charge
Q Quantity of heat
R Resistance
Reflectance
r Radius vector
r Interatomic separation
Radius
Radius of ionic cores of atoms in lattice
Electronic orbit radius
p Density
Resistivity
Pmag Magnetoresistivity
Atomic spin angular momentum
Entropy
s Electronic spin angular momentum quantum number
(7 Conductivity
Stress
T Temperature
t Time
Thickness
Tc Curie temperature
Critical temperature
tQ Orbital period of electron
0 Angle
r Torque
r Time constant
Relaxation time
rmax Maximum torque
U Internal energy
u Unit vector
u Displacement of an atom from equilibrium
vf Final velocity (terminal velocity) of electrons in Drude model
v Velocity
vr, Velocity of electrons at Fermi surface
V Electrical potential
V Voltage (potential difference)
Volume