Fundamentals of Electron Emission Physics

Kevin L. Jensen, PhD, was a research physicist in the Materials and Systems Branch, Materials Science and Technology Division at the Naval Research Laboratory in the United States until his retirement in 2023, and is now a Research Physicist at the Institute for Research in Electronics and Applied Physics at the University of Maryland. He is a Fellow of the American Physical Society, which recognized him for his contributions to the theory and modelling of electron emission sources or particle accelerators and microwave tubes, and a recipient of the Sigma Xi Applied Science Award for his work on electron emission.

• Preface xiAcknowledgments xiiiAcronyms xivPart I Foundations 11 Historical Background 32 Basic Methods 72.1 Units 72.2 Elementary Emission Models 132.3 Exercises 23Part II A Review of Methods 253 Electrostatics 273.1 Method of Images 273.2 Point Charge Models 283.3 Constant Line Charge 323.4 Tapered Line Charge 333.5 Orthogonal Polynomials 353.6 Prolate Spheroidal Models 363.7 Exercises 394 Statistical Mechanics 414.1 Maxwell–Boltzmann Distribution 414.2 Entropy 434.3 Phase Space 454.4 Diffusion 464.5 Quantum Distributions 484.6 Temperature 504.7 Exercises 515 Light 535.1 Index of Refraction 535.2 Relativistic Effects 556 Quantum Mechanics 596.1 Wave Mechanics 596.2 Matrix Mechanics 606.3 Representations 636.4 Wave Functions 646.5 Tunneling Through a Delta-Barrier 706.6 Tunneling Through a Rectangular Barrier 736.7 Other Quantum Representations 786.8 Exercises 847 Solid State Physics 877.1 Conductivity 877.2 Metals and Semiconductors 907.3 Alpha Semiconductor Model 987.4 Scattering 997.5 Optical Properties 1057.6 Exercises 114Part III Current and Barriers 1178 Current Density Formalism 1198.1 Master Equation 1198.2 Richardson–Laue–Dushman Equation 1228.3 Fowler–Nordheim Equation 1228.4 Fowler–DuBridge Equation 1238.5 Exercises 1259 Simple Barriers 1279.1 Shape Factor Method 1279.2 Exponential Barrier 1299.3 Trapezoidal Barrier 1309.4 Depletion Barrier 1309.5 Exercises 13210 Schottky–Nordheim Barrier 13310.1 SN Shape Factors 13310.2 Standard Fowler–Nordheim 13410.3 Shape Factor FN Model 14010.4 Exercises 14511 Modified SN Barriers 14711.1 Semiconductor Surface 14711.2 Non-planar Image Charge 15011.3 Polynomial Barriers 15111.4 Metal–Insulator–Metal Barrier 15511.5 Quantum Modifications 15811.6 Exercises 164Part IV Emission 16512 Thermal-field Emission 16712.1 The Thermal-field Regime 16712.2 The N(n,s) Function 17212.3 Original GTF Equation 17812.4 Reformulated GTF Equation 18112.5 Exercises 18613 Photoemission 18913.1 Simple Quantum Efficiency 18913.2 Simple Moments Model 19213.3 Enhanced Moments Model 20313.4 Delayed Emission 20513.4.1 Simple Monte Carlo Model 20813.4.2 Shell and Sphere Model 21113.5 Laser Heating 21513.6 Exercises 22114 Secondary Emission 22514.1 Simple Model Revisited 22514.2 Other Models 22814.3 Bethe Model 23014.4 Exercises 23415 Space Charge 23515.1 Child–Langmuir Law 23515.2 Space Charge and Surface Fields 23915.3 Transit Time Approach 24415.4 The Miram Curve 25415.5 Exercises 26016 Conclusion 263A Methods and Functions 265A.1 Gamma Function 265A.2 Riemann Zeta Function 265A.3 Error Function 267A.4 Legendre Polynomials 267A.5 Hermite Polynomials 268A.6 Prolate Spheroidal Coordinates 269A.7 Polynomial Fitting 271A.8 Local Maximum/Minimum 272A.9 Finite Difference Method 274A.10 Iterative Solutions 275B Algorithms 277B.1 Basic Methods 277B.2 Review of Methods Algorithms 281B.3 Current and Barriers Algorithms 295B.4 Emission Algorithms 304B.5 Appendix Algorithms 341References 343Index 365