Advances in Imaging and Electron Physics: Electron Emission Physics
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Table of contents
- Title pageiii
- Copyright Pageiv
- Contentsvii
- Dedicationv
- Prefaceix
- Future Contributionsxi
- Forewordxvii
- Electron Emission Physics1
- I. Field and Thermionic Emission Fundamentals4
- A. A Note on Units4
- B. Free Electron Gas5
- 1. Quantum Statistical Mechanics5
- 2. The Fermi–Dirac Integral8
- 3. The Chemical Potential9
- 4. A Phase Space Description11
- C. Nearly Free Electron Gas11
- 1. The Hydrogen Atom11
- 2. Band Structure and the Kronig–Penney Model13
- 3. Semiconductors20
- 4. Band Bending20
- D. The Surface Barrier to Electron Emission22
- 1. Surface Effects and Origins of the Work Function22
- 2. Ion Core Effects.31
- 3. Dipole Effects Due to Surface Barriers33
- E. The Image Charge Approximation40
- 1. Classical Treatment40
- 2. Quantum Mechanical Treatment42
- 3. An ‘‘Analytical’’ Image Charge Potential43
- II. Thermal and Field Emission47
- A. Current Density47
- 1. Current Density in the Classical Distribution Function Approach47
- 2. Current Density in the Schroumldinger and Heisenberg Representations49
- 3. Current Density in the Wigner Distribution Function Approach52
- 4. Current Density in the Bohm Approach62
- B. Exactly Solvable Models65
- 1. Wave Function Methodology for Constant Potential Segments65
- 2. The Square Barrier67
- 3. Multiple Square Barriers69
- 4. The Airy Function Approach71
- 5. The Triangular Barrier80
- C. Wentzel-Kramers-Brillouin WKB Area Under the Curve Models85
- 1. The Quadratic Barrier85
- 2. The Image Charge Barrier87
- D. Numerical Methods94
- 1. Numerical Treatment of Quadratic Potential95
- 2. Numerical Treatment of Image Charge Potential95
- 3. Resonant Tunneling: A Numerical Example99
- E. The Thermal and Field Emission Equation102
- 1. The Fowler-Nordheim and Richardson-Laue-Dushman Equations104
- 2. The Emission Equation Integrals and Their Approximation106
- 3. The Revised FN and RLD Equations110
- F. The Revised FN-RLD Equation and the Inference of Work Function From Experimental Data118
- 1. Field Emission118
- 2. Thermionic Emission121
- 3. Mixed Thermal-Field Conditions123
- 4. Slope-Intercept Methods Applied to Field Emission127
- G. Recent Revisions of the Standard Thermal and Field Models131
- 1. The Forbes Approach to the Evaluation of the Elliptical Integrals131
- 2. Emission in the Thermal-Field Transition Region Revisited136
- H. The General Thermal-Field Equation139
- I. Thermal Emittance143
- III. Photoemission147
- A. Background147
- B. Quantum Efficiency148
- C. The Probability of Emission151
- 1. The Escape Cone151
- 2. The Fowler–Dubridge Model152
- D. Reflection and Penetration Depth154
- 1. Dielectric Constant, Index of Refraction, and Reflectivity154
- 2. Drude Model: Classical Approach156
- 3. Drude Model: Distribution Function Approach158
- 4. Quantum Extension and Resonance Frequencies162
- E. Conductivity165
- 1. Electrical Conductivity165
- 2. Thermal Conductivity167
- 3. Wiedemann–Franz Law170
- 4. Specific Heat of Solids171
- F. Scattering Rates174
- 1. Fermi’s Golden Rule174
- 2. Charged Impurity Relaxation Time177
- 3. Electron-Electron Scattering180
- 4. A Sinusoidal Potential186
- 5. Monatomic Linear Chain of Atoms186
- 6. Electron-Phonon Scattering195
- 7. Matthiesen’s Rule and the Specification of Scattering Terms213
- G. Scattering Factor220
- H. Temperature of a Laser-Illuminated Surface223
- 1. Photocathodes and Drive Lasers223
- 2. A Simple Model of Temperature Increase Due to a Laser Pulse224
- 3. Diffusion of Heat and Corresponding Temperature Rise226
- 4. Multiple Pulses and Temperature Rise228
- 5. Temperature Rise in a Single Pulse: The Coupled Heat Equations235
- 6. The Electron-Phonon Coupling Factor g: A Simple Model236
- I. Numerical Solution of the Coupled Thermal Equations240
- 1. Nature of the Problem.240
- 2. Explicit and Implicit Solutions of Ordinary Differential Equations241
- 3. Numerically Solving the Coupled Temperature Equations With Temperature-Dependent Coefficients248
- J. Revisions to the Modified Fowler-Dubridge Model: Quantum Effects254
- K. Quantum Efficiency Revisited: A Moments-Based Approach257
- L. The Quantum Efficiency of Bare Metals262
- 1. Variation of Work Function With Crystal Face264
- 2. The Density of States With Respect to the Nearly Free Electron Gas Model268
- 3. Surface Structure, Multiple Reflections, and Field Enhancement269
- 4. Contamination and Effective Emission Area273
- M. The Emittance and Brightness of Photocathodes275
- IV. Low-Work Function Coatings and Enhanced Emission280
- A. Historical Perspective280
- B. A Simple Model of a Low-Work Function Coating281
- C. A Less Simple Model of the Low-Work Function Coating282
- D. The (Modified) Gyftopoulos-Levine Model of Work Function Reduction286
- E. Comparison of the Modified Gyftopoulos-Levine Model to Thermionic Data292
- F. Comparison of the Modified Gyftopoulos-Levine Model to Photoemission Data296
- V. Appendices304
- A. Integrals Related to Fermi-Dirac and Bose-Einstein Statistics304
- B. The Riemann Zeta Function305
- VI. Conclusion306
- References309
- Index325
Advances in Imaging and Electron Physics merges two long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. This series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.
This thematic volume is on the topic of "Field-emission Source Mechanisms" and is authored by Kevin Jensen, Naval Research Laboratory, Washington, DC.
This thematic volume is on the topic of "Field-emission Source Mechanisms" and is authored by Kevin Jensen, Naval Research Laboratory, Washington, DC.