Electronic Materials Science Eugene A. Irene
University of North Carolina
Chapel Hill, North Carolina
1 Introduction to Electronic Materials Science 1
1.1 Introduction / 1
1.2 Structure and Diffraction / 3
1.3 Defects / 4
1.4 Diffusion / 5
1.5 Phase Equilibria / 5
1.6 Mechanical Properties / 6
1.7 Electronic Structure / 6
1.8 Electronic Properties and Devices / 7
1.9 Electronic Materials Science / 8
2 Structure of Solids 9
2.1 Introduction / 9
2.2 Order / 10
2.3 The Lattice / 12
2.4 Crystal Structure / 16
2.5 Notation / 17
2.5.1 Naming Planes / 17
2.5.2 Lattice Directions / 19
2.6 Lattice Geometry / 21
2.6.1 Planar Spacing Formulas / 21
2.6.2 Close Packing / 22
2.7 The Wigner-Seitz Cell / 24
2.8 Crystal Structures / 25
2.8.1 Structures for Elements / 25
2.8.2 Structures for Compounds / 26
2.8.3 Solid Solutions / 28
Related Reading / 29
3 Diffraction 31
3.1 Introduction / 31
3.2 Phase Difference and Bragg’s Law / 33
3.3 The Scattering Problem / 37
3.3.1 Coherent Scattering from an Electron / 38
3.3.2 Coherent Scattering from an Atom / 40
3.3.3 Coherent Scattering from a Unit Cell / 40
3.3.4 Structure Factor Calculations / 43
3.4 Reciprocal Space, RESP / 45
3.4.1 Why Reciprocal Space? / 45
3.4.2 Definition of RESP / 46
3.4.3 Definition of Reciprocal Lattice Vector / 48
3.4.4 The Ewald Construction / 50
3.5 Diffraction Techniques / 53
3.5.1 Rotating Crystal Method / 53
3.5.2 Powder Method / 53
3.5.3 Laue Method / 55
3.6 Wave Vector Representation / 55
Related Reading / 58
Exercises / 58
4 Defects in Solids 61
4.1 Introduction / 61
4.2 Why Do Defects Form? / 62
4.2.1 Review of Some Thermodynamics Ideas / 62
4.3 Point Defects / 66
4.4 The Statistics of Point Defects / 67
4.5 Line Defects—Dislocations / 71
4.5.1 Edge Dislocations / 73
4.5.2 Screw Dislocations / 74
4.5.3 Burger’s Vector and the Burger Circuit / 76
4.5.4 Dislocation Motion / 77
4.6 Planar Defects / 77
4.6.1 Grain Boundaries / 77
4.6.2 Twin Boundaries / 78
4.7 Three-Dimensional Defects / 79
Related Reading / 79
Exercises / 80
5 Diffusion in Solids 81
5.1 Introduction to Diffusion Equations / 81
5.2 Atomistic Theory of Diffusion: Fick’s Laws and a Theory
for the
Diffussion Construct D / 83
5.3 Random Walk Problem / 87
5.3.1 Random Walk Calculations / 89
5.3.2 Relation of D to Random Walk / 89
5.3.3 Self-Diffusion Vacancy Mechanism in a FCC Crystal / 90
5.3.4 Activation Energy for Diffusion / 91
5.4 Other Mass Transport Mechanisms / 91
5.4.1 Permeability versus Diffusion / 91
5.4.2 Convection versus Diffusion / 94
5.5 Mathematics of Diffusion / 94
5.5.1 Steady State Diffusion—Fick’s First Law / 95
5.5.2 Non–Steady State Diffusion—Fick’s Second Law / 97
Related Reading / 108
Exercises / 108
6 Phase Equilibria 111
6.1 Introduction / 111
6.2 The Gibbs Phase Rule / 111
6.2.1 Definitions / 111
6.2.2 Equilibrium Among Phases—The Phase Rule / 113
6.2.3 Applications of the Phase Rule / 115
6.2.4 Construction of Phase Diagrams: Theory and Experiment
/ 116
6.2.5 The Tie Line Principle / 120
6.2.6 The Lever Rule / 121
6.2.7 Examples of Phase Equilibria / 125
6.3 Nucleation and Growth of Phases / 130
6.3.1 Thermodynamics of Phase Transformations / 130
6.3.2 Nucleation / 133
Related Reading / 137
7 Mechanical Properties of Solids—Elasticity 139
7.1 Introduction / 139
7.2 Elasticity Relationships / 141
7.2.1 True versus Engineering Strain / 143
7.2.2 Nature of Elasticity and Young’s Modulus / 144
7.3 An Analysis of Stress by the Equation of Motion / 147
7.4 Hooke’s Law for Pure Dilatation and Pure Shear / 150
7.5 Poisson’s Ratio / 151
7.6 Relationships Among E, e, and v / 151
7.7 Relationships Among E, G, and n / 153
7.8 Resolving the Normal Forces / 156
Related Reading / 157
Exercises / 158
8 Mechanical Properties of Solids—Plasticity 161
8.1 Introduction / 161
8.2 Plasticity Observations / 161
8.3 Role of Dislocations / 163
8.4 Deformation of Noncrystalline Materials / 175
8.4.1 Thermal Behavior of Amorphous Solids / 175
8.4.2 Time-Dependent Deformation of Amorphous Materials /
177
8.4.3 Models for Network Solids / 179
8.4.4 Elastomers / 183
Related Reading / 186
Exercises / 186
9 Electronic Structure of Solids 187
9.1 Introduction / 187
9.2 Waves, Electrons, and the Wave Function / 187
9.2.1 Representation of Waves / 187
9.2.2 Matter Waves / 189
9.2.3 Superposition / 190
9.2.4 Electron Waves / 195
9.3 Quantum Mechanics / 196
9.3.1 Normalization / 197
9.3.2 Dispersion of Electron Waves and the SE / 197
9.3.3 Classical and QM Wave Equations / 199
9.3.4 Solutions to the SE / 200
9.4 Electron Energy Band Representations / 215
9.4.1 Parallel Band Picture / 215
9.4.2 k Space Representations / 216
9.4.3 Brillouin Zones / 219
9.5 Real Energy Band Structures / 221
9.6 Other Aspects of Electron Energy Band Structure / 224
Related Reading / 226
Exercises / 227
10 Electronic Properties of Materials 229
10.1 Introduction / 229
10.2 Occupation of Electronic States / 230
10.2.1 Density of States Function, DOS / 230
10.2.2 The Fermi-Dirac Distribution Function / 232
10.2.3 Occupancy of Electronic States / 235
10.3 Position of the Fermi Energy / 236
10.4 Electronic Properties of Metals: Conduction and
Superconductivity / 240
10.4.1 Free Electron Theory for Electrical Conduction / 240
10.4.2 Quantum Theory of Electronic Conduction / 244
10.4.3 Superconductivity / 247
10.5 Semiconductors / 253
10.5.1 Intrinsic Semiconductors / 253
10.5.2 Extrinsic Semiconductors / 257
10.5.3 Semiconductor Measurements / 261
10.6 Electrical Behavior of Organic Materials / 264
Related Reading / 266
Exercises / 266
11 Junctions and Devices and the Nanoscale 269
11.1 Introduction / 269
11.2 Junctions / 270
11.2.1 Metal–Metal Junctions / 270
11.2.2 Metal–Semiconductor Junctions / 271
11.2.3 Semiconductor–Semiconductor PN Junctions / 274
11.3 Selected Devices / 275
11.3.1 Passive Devices / 276
11.3.2 Active Devices / 279
11.4 Nanostructures and Nanodevices / 290
11.4.1 Heterojunction Nanostructures / 290
11.4.2 2-D and 3-D Nanostructures / 293
Related Reading / 294
Exercises / 295
Index 297
