Fundamentals of Electron Emission Physics

An authoritative and accurate guide to the physics of research- and technology-relevant phenomena of electron emission In Fundamentals of Electron Emission Physics, distinguished research physicist, Dr. Kevin Jensen, delivers a practice-oriented introduction to the physics of electron emission. The book uses a physical intuition approach based on many years of research instead of heavy-handed mathematical formalism. The author explores and explains the fundamentals of electron emission and the basis for successful performance and interpretation of experiments conducted at lab- and large-scale electron sources. He addresses the most common stumbling blocks that students and researchers who are new to the field often run into when confronted with the intricacies of the physics of electron emission. Thorough introductions to semiconductors, canonical emission models, and modern physics methods Comprehensive explorations of tunneling and transmission, the thermal-field-photoemission model, three-step models of photo- and secondary emission, and space charge Practical discussions of mathematical methods and specialized functions (e.g., Gamma function, Riemann Zeta function, orthogonal polynomials) A mathematical appendix, as well as sample problems and solutions to help explain the topics discussed in the book Perfect for advanced undergraduate and doctoral students in solid state physics, materials science, electron transport, and beam physics, Fundamentals of Electron Emission Physics will also benefit users and developers of electron sources and practicing academics and researchers.

Table of Contents:
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

About the Author :
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.