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…mehr
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 and the thermal-field-photoemission model * Practical discussions of mathematical methods, including trigonometric, Gamma, and Riemann Zeta functions * 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.
Kevin Jensen, PhD, is a research physicist in the Materials and Systems Branch, Materials Science and Technology Division at the Naval Research Laboratory in the United States. He is a Fellow of the American Physical Society, which recognized him for his contributions to the theory and modelling of electron emission sources for particle accelerators and microwave tubes.
Inhaltsangabe
1 History 1.1 Discovery of the Electron 1.2 Thermal Emission 1.3 Field Emission 1.4 Photo Emission 1.5 Secondary Emission 1.6 Space Charge Limited Current 1.7 Units and Conventions 1.7.1 Hydrogen Atom Units 1.7.2 Electron Emission Units
2 Methods of Modern Physics 2.1 Electrostatics 2.1.1 Method of Images 2.1.2 Point Charge Models 2.1.3 Line Charge Models 2.2 Statistical Mechanics 2.2.1 Phase Space 2.2.2 Maxwell-Boltzmann Distribution 2.2.3 Quantum Distributions 2.2.4 Energy and Entropy 2.2.5 Richardson Equation 2.2.6 Fermi-Dirac Distribution . 2.2.7 Classical to Quantum Statistics 2.2.8 Electrons and White Dwarf Stars 2.3 Relativity 2.4 Quantum Mechanics 2.4.1 Representations 2.4.2 Schrödinger's Equation 2.4.3 Eigenstates 2.4.4 Wave Packets 2.4.5 Tunneling 2.5 Many Body Physics 2.5.1 Kinetic Energy 2.5.2 Exchange Energy 2.5.3 Correlation Term 2.5.4 Core Term 2.6 Density Matrix 2.7 The Harmonic Oscillator 2.8 The Hydrogen Atom 2.9 The Metal Surface
3 Metals 3.1 Density of States 3.2 Spheres in Multi-dimensions 3.3 The Kronig Penny Model 3.4 Atomic Orbitals 3.5 Electronegativity 3.6 Sinusoidal Potential and Band Gap 3.7 Ion Potentials and Screening 3.7.1 Low Temperature / High Density 3.7.2 High Temperature / Low Density 3.7.3 Many Cores 3.8 Drude Model 3.9 Sommerfeld Model 3.9.1 Chemical Potential 3.9.2 Electron Density 3.10 Boltzmann's Equation 3.11 Wigner Distribution Function 3.12 Continuity Equation 3.13 Exchange-Correlation and an Effective Barrier Model 3.13.1 Infinite Barrier 3.13.2 Infinite Well 3.13.3 A Triangular Well 3.14 An Analytic Image Charge Potential 3.14.1 Work Function and Temperature 3.14.2 Work Function and Field 3.14.3 Changes to Current Density
4 Semiconductors 4.1 Semiconductor Image Charge Potential 4.2 Dielectric Constant and Screening 4.3 Effective Mass 4.3.1 Dispersion Relations 4.3.2 The kp Method 4.3.3 Hyperbolic Relations 4.3.4 Current and Effective Mass 4.4 Resistivity 4.5 Electrons and Holes 4.6 Band Gap and Temperature 4.7 Doping of Semiconductors 4.7.1 Accumulation Layers 4.7.2 Depletion Layers
5 Canonical Emission Models 5.1 An Early Model of Electron Emission 5.2 Supply Function 5.3 Simple WKB Tunneling Model 5.4 Richardson-Laue-Dushman Equation 5.5 Fowler-Nordheim Equation 5.6 Fowler-Dubridge Equation 5.7 Baroody Equation 5.8 Child Langmuir Law 5.9 Contacts 5.9.1 Zener Breakdown 5.9.2 Poole-Frenkel Transport 5.9.3 Tunneling Conduction 5.9.4 Resonant Tunneling in Field Emission
6 Transport 6.1 Conductivity 6.1.1 Electrical Conductivity 6.1.2 Thermal Conductivity 6.1.3 The Lorentz Number for Metals 6.1.4 Deficiencies of the Drude Model 6.2 Scattering 6.2.1 Acoustic Scattering 6.2.2 Electron-Electron Scattering 6.2.3 Impurity Scattering 6.3 Metal-Insulator Transition 6.3.1 Weak Localization 6.3.2 Hall Angle
7 Tunneling and Transmission 7.1 Schrödinger's Equation 7.1.1 Finite Difference Methods 7.1.2 JWKB Methods 7.1.3 Kemble Approximation 7.2 Shape Factor Method 7.2.1 Rectangular Barrier 7.2.2 Triangular Barrier 7.2.3 Quadratic Barrier 7.2.4 MIM Barrier 7.2.5 Schottky Nordheim Barrier 7.3 Transfer Matrix Approach 7.3.1 Plane Wave Transfer Matrix 7.3.2 Airy Function Transfer Matrix 7.3.3 Fowler Nordheim Equation 7.3.4 Resonance 7.3.5 Revised Gamow 7.3.6 Revised Kemble . 7.3.7 Schottky Deviations 7.3.8 Resonant Transmission 7.4 Tunneling Time 7.4.1 Buttiker-Landauer Model 7.4.2 Delay Time 7.4.3 Hartman Effect 7.4.4 Gaussian Wave Packet 7.4.5 Quantum Carpets 7.4.6 Transmission and Reflection Delay 7.5 Resonant Transmission 7.5.1 Schrödinger Approach 7.5.2 Bohm Approach 7.5.3 Wigner Distribution Function Approach 7.5.4 Time Evolution of Quantum Effects 7.6 Reflectionless Transmission 7.6.1 sech Well 7.6.2 Well-Barrier Model 7.6.3 Effective Barrier Model
8 A Thermal-Field-Photoemission Model 8.1 Experimental Energy Distribution 8.2 Anatomy of Current Density 8.2.1 Rectangular Barrier 8.2.2 Linear Barrier 8.2.3 Schottky-Nordheim Barrier 8.2.4 Gamow and Shape Factors 8.2.5 Transmission Probability 8.3 Current Density Integral 8.3.1 Experimental Thermal-Field Energy Distributions 8.3.2 Theoretical Thermal-Field Energy Distributions 8.3.3 The N-Function 8.4 General TFP Equation 8.4.1 Gamow and Energy Slope Factors 8.4.2 Original Model 8.4.3 Reformulated Model 8.5 Other Barriers 8.5.1 Metal-Insulator-Metal Barriers 8.5.2 Metal-Semiconductor Contacts 8.5.3 Nonlinear: Hemisphere 8.5.4 Nonlinear: Prolate Spheroidal
9 Mathematical Methods 9.1 Trigonometric Functions 9.2 Gamma Function 9.3 Riemann Zeta Function 9.4 Error Function 9.5 Legendre Polynomials 9.6 Lorentzian Functions 9.7 The Riemann Zeta Function 9.8 The Airy Function 9.9 Prolate Spheroidal Coordinates 9.10 Series 9.11 Integration 9.11.1 Series Summation 9.11.2 Series Expansion 9.11.3 Gaussian Quadrature 9.11.4 Sharply Peaked Integrands 9.11.5 Monte Carlo Integration 9.12 Differentiation 9.12.1 Orthogonal Coordinates 9.12.2 Radial Coordinates 9.12.3 Prolate Spheroidal Coordinates 9.12.4 Finite Difference Methods 9.13 Numerical Solution of an Ordinary Differential Equation 9.13.1 First Order 9.13.2 Second Order
1 History 1.1 Discovery of the Electron 1.2 Thermal Emission 1.3 Field Emission 1.4 Photo Emission 1.5 Secondary Emission 1.6 Space Charge Limited Current 1.7 Units and Conventions 1.7.1 Hydrogen Atom Units 1.7.2 Electron Emission Units
2 Methods of Modern Physics 2.1 Electrostatics 2.1.1 Method of Images 2.1.2 Point Charge Models 2.1.3 Line Charge Models 2.2 Statistical Mechanics 2.2.1 Phase Space 2.2.2 Maxwell-Boltzmann Distribution 2.2.3 Quantum Distributions 2.2.4 Energy and Entropy 2.2.5 Richardson Equation 2.2.6 Fermi-Dirac Distribution . 2.2.7 Classical to Quantum Statistics 2.2.8 Electrons and White Dwarf Stars 2.3 Relativity 2.4 Quantum Mechanics 2.4.1 Representations 2.4.2 Schrödinger's Equation 2.4.3 Eigenstates 2.4.4 Wave Packets 2.4.5 Tunneling 2.5 Many Body Physics 2.5.1 Kinetic Energy 2.5.2 Exchange Energy 2.5.3 Correlation Term 2.5.4 Core Term 2.6 Density Matrix 2.7 The Harmonic Oscillator 2.8 The Hydrogen Atom 2.9 The Metal Surface
3 Metals 3.1 Density of States 3.2 Spheres in Multi-dimensions 3.3 The Kronig Penny Model 3.4 Atomic Orbitals 3.5 Electronegativity 3.6 Sinusoidal Potential and Band Gap 3.7 Ion Potentials and Screening 3.7.1 Low Temperature / High Density 3.7.2 High Temperature / Low Density 3.7.3 Many Cores 3.8 Drude Model 3.9 Sommerfeld Model 3.9.1 Chemical Potential 3.9.2 Electron Density 3.10 Boltzmann's Equation 3.11 Wigner Distribution Function 3.12 Continuity Equation 3.13 Exchange-Correlation and an Effective Barrier Model 3.13.1 Infinite Barrier 3.13.2 Infinite Well 3.13.3 A Triangular Well 3.14 An Analytic Image Charge Potential 3.14.1 Work Function and Temperature 3.14.2 Work Function and Field 3.14.3 Changes to Current Density
4 Semiconductors 4.1 Semiconductor Image Charge Potential 4.2 Dielectric Constant and Screening 4.3 Effective Mass 4.3.1 Dispersion Relations 4.3.2 The kp Method 4.3.3 Hyperbolic Relations 4.3.4 Current and Effective Mass 4.4 Resistivity 4.5 Electrons and Holes 4.6 Band Gap and Temperature 4.7 Doping of Semiconductors 4.7.1 Accumulation Layers 4.7.2 Depletion Layers
5 Canonical Emission Models 5.1 An Early Model of Electron Emission 5.2 Supply Function 5.3 Simple WKB Tunneling Model 5.4 Richardson-Laue-Dushman Equation 5.5 Fowler-Nordheim Equation 5.6 Fowler-Dubridge Equation 5.7 Baroody Equation 5.8 Child Langmuir Law 5.9 Contacts 5.9.1 Zener Breakdown 5.9.2 Poole-Frenkel Transport 5.9.3 Tunneling Conduction 5.9.4 Resonant Tunneling in Field Emission
6 Transport 6.1 Conductivity 6.1.1 Electrical Conductivity 6.1.2 Thermal Conductivity 6.1.3 The Lorentz Number for Metals 6.1.4 Deficiencies of the Drude Model 6.2 Scattering 6.2.1 Acoustic Scattering 6.2.2 Electron-Electron Scattering 6.2.3 Impurity Scattering 6.3 Metal-Insulator Transition 6.3.1 Weak Localization 6.3.2 Hall Angle
7 Tunneling and Transmission 7.1 Schrödinger's Equation 7.1.1 Finite Difference Methods 7.1.2 JWKB Methods 7.1.3 Kemble Approximation 7.2 Shape Factor Method 7.2.1 Rectangular Barrier 7.2.2 Triangular Barrier 7.2.3 Quadratic Barrier 7.2.4 MIM Barrier 7.2.5 Schottky Nordheim Barrier 7.3 Transfer Matrix Approach 7.3.1 Plane Wave Transfer Matrix 7.3.2 Airy Function Transfer Matrix 7.3.3 Fowler Nordheim Equation 7.3.4 Resonance 7.3.5 Revised Gamow 7.3.6 Revised Kemble . 7.3.7 Schottky Deviations 7.3.8 Resonant Transmission 7.4 Tunneling Time 7.4.1 Buttiker-Landauer Model 7.4.2 Delay Time 7.4.3 Hartman Effect 7.4.4 Gaussian Wave Packet 7.4.5 Quantum Carpets 7.4.6 Transmission and Reflection Delay 7.5 Resonant Transmission 7.5.1 Schrödinger Approach 7.5.2 Bohm Approach 7.5.3 Wigner Distribution Function Approach 7.5.4 Time Evolution of Quantum Effects 7.6 Reflectionless Transmission 7.6.1 sech Well 7.6.2 Well-Barrier Model 7.6.3 Effective Barrier Model
8 A Thermal-Field-Photoemission Model 8.1 Experimental Energy Distribution 8.2 Anatomy of Current Density 8.2.1 Rectangular Barrier 8.2.2 Linear Barrier 8.2.3 Schottky-Nordheim Barrier 8.2.4 Gamow and Shape Factors 8.2.5 Transmission Probability 8.3 Current Density Integral 8.3.1 Experimental Thermal-Field Energy Distributions 8.3.2 Theoretical Thermal-Field Energy Distributions 8.3.3 The N-Function 8.4 General TFP Equation 8.4.1 Gamow and Energy Slope Factors 8.4.2 Original Model 8.4.3 Reformulated Model 8.5 Other Barriers 8.5.1 Metal-Insulator-Metal Barriers 8.5.2 Metal-Semiconductor Contacts 8.5.3 Nonlinear: Hemisphere 8.5.4 Nonlinear: Prolate Spheroidal
9 Mathematical Methods 9.1 Trigonometric Functions 9.2 Gamma Function 9.3 Riemann Zeta Function 9.4 Error Function 9.5 Legendre Polynomials 9.6 Lorentzian Functions 9.7 The Riemann Zeta Function 9.8 The Airy Function 9.9 Prolate Spheroidal Coordinates 9.10 Series 9.11 Integration 9.11.1 Series Summation 9.11.2 Series Expansion 9.11.3 Gaussian Quadrature 9.11.4 Sharply Peaked Integrands 9.11.5 Monte Carlo Integration 9.12 Differentiation 9.12.1 Orthogonal Coordinates 9.12.2 Radial Coordinates 9.12.3 Prolate Spheroidal Coordinates 9.12.4 Finite Difference Methods 9.13 Numerical Solution of an Ordinary Differential Equation 9.13.1 First Order 9.13.2 Second Order
10 Solutions to Select Problems
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