Preface xi
Acknowledgments xiii
Acronyms xiv
Part I Foundations 1
1 Historical Background 3
2 Basic Methods 7
2.1 Units 7
2.2 Elementary Emission Models 13
2.3 Exercises 23
Part II A Review of Methods 25
3 Electrostatics 27
3.1 Method of Images 27
3.2 Point Charge Models 28
3.3 Constant Line Charge 32
3.4 Tapered Line Charge 33
3.5 Orthogonal Polynomials 35
3.6 Prolate Spheroidal Models 36
3.7 Exercises 39
4 Statistical Mechanics 41
4.1 Maxwell–Boltzmann Distribution 41
4.2 Entropy 43
4.3 Phase Space 45
4.4 Diffusion 46
4.5 Quantum Distributions 48
4.6 Temperature 50
4.7 Exercises 51
5 Light 53
5.1 Index of Refraction 53
5.2 Relativistic Effects 55
6 Quantum Mechanics 59
6.1 Wave Mechanics 59
6.2 Matrix Mechanics 60
6.3 Representations 63
6.4 Wave Functions 64
6.5 Tunneling Through a Delta-Barrier 70
6.6 Tunneling Through a Rectangular Barrier 73
6.7 Other Quantum Representations 78
6.8 Exercises 84
7 Solid State Physics 87
7.1 Conductivity 87
7.2 Metals and Semiconductors 90
7.3 Alpha Semiconductor Model 98
7.4 Scattering 99
7.5 Optical Properties 105
7.6 Exercises 114
Part III Current and Barriers 117
8 Current Density Formalism 119
8.1 Master Equation 119
8.2 Richardson–Laue–Dushman Equation 122
8.3 Fowler–Nordheim Equation 122
8.4 Fowler–DuBridge Equation 123
8.5 Exercises 125
9 Simple Barriers 127
9.1 Shape Factor Method 127
9.2 Exponential Barrier 129
9.3 Trapezoidal Barrier 130
9.4 Depletion Barrier 130
9.5 Exercises 132
10 Schottky–Nordheim Barrier 133
10.1 SN Shape Factors 133
10.2 Standard Fowler–Nordheim 134
10.3 Shape Factor FN Model 140
10.4 Exercises 145
11 Modified SN Barriers 147
11.1 Semiconductor Surface 147
11.2 Non-planar Image Charge 150
11.3 Polynomial Barriers 151
11.4 Metal–Insulator–Metal Barrier 155
11.5 Quantum Modifications 158
11.6 Exercises 164
Part IV Emission 165
12 Thermal-field Emission 167
12.1 The Thermal-field Regime 167
12.2 The N(n,s) Function 172
12.3 Original GTF Equation 178
12.4 Reformulated GTF Equation 181
12.5 Exercises 186
13 Photoemission 189
13.1 Simple Quantum Efficiency 189
13.2 Simple Moments Model 192
13.3 Enhanced Moments Model 203
13.4 Delayed Emission 205
13.4.1 Simple Monte Carlo Model 208
13.4.2 Shell and Sphere Model 211
13.5 Laser Heating 215
13.6 Exercises 221
14 Secondary Emission 225
14.1 Simple Model Revisited 225
14.2 Other Models 228
14.3 Bethe Model 230
14.4 Exercises 234
15 Space Charge 235
15.1 Child–Langmuir Law 235
15.2 Space Charge and Surface Fields 239
15.3 Transit Time Approach 244
15.4 The Miram Curve 254
15.5 Exercises 260
16 Conclusion 263
A Methods and Functions 265
A.1 Gamma Function 265
A.2 Riemann Zeta Function 265
A.3 Error Function 267
A.4 Legendre Polynomials 267
A.5 Hermite Polynomials 268
A.6 Prolate Spheroidal Coordinates 269
A.7 Polynomial Fitting 271
A.8 Local Maximum/Minimum 272
A.9 Finite Difference Method 274
A.10 Iterative Solutions 275
B Algorithms 277
B.1 Basic Methods 277
B.2 Review of Methods Algorithms 281
B.3 Current and Barriers Algorithms 295
B.4 Emission Algorithms 304
B.5 Appendix Algorithms 341
References 343
Index 365
