Advances in Imaging and Electron Physics (eBook)

Front Cover 1
Advances in Imaging and Electron Physics 4
Copyright Page 5
Contents 8
Dedication 6
Preface 10
Future Contributions 12
Foreword 18
Chapter 1: Electron Emission Physics 21
I. Field and Thermionic Emission Fundamentals 24
A. A Note on Units 24
B. Free Electron Gas 25
1. Quantum Statistical Mechanics 25
2. The Fermi–Dirac Integral 28
3. The Chemical Potential 29
4. A Phase Space Description 31
C. Nearly Free Electron Gas 31
1. The Hydrogen Atom 31
2. Band Structure and the Kronig–Penney Model 33
3. Semiconductors 40
4. Band Bending 40
D. The Surface Barrier to Electron Emission 42
1. Surface Effects and Origins of the Work Function 42
2. Ion Core Effects. 51
3. Dipole Effects Due to Surface Barriers 53
E. The Image Charge Approximation 60
1. Classical Treatment 60
2. Quantum Mechanical Treatment 62
3. An ‘‘Analytical’’ Image Charge Potential 63
II. Thermal and Field Emission 67
A. Current Density 67
1. Current Density in the Classical Distribution Function Approach 67
2. Current Density in the Schroumldinger and Heisenberg Representations 69
3. Current Density in the Wigner Distribution Function Approach 72
4. Current Density in the Bohm Approach 82
B. Exactly Solvable Models 85
1. Wave Function Methodology for Constant Potential Segments 85
2. The Square Barrier 87
3. Multiple Square Barriers 89
4. The Airy Function Approach 91
5. The Triangular Barrier 100
C. Wentzel-Kramers-Brillouin WKB Area Under the Curve Models 105
1. The Quadratic Barrier 105
2. The Image Charge Barrier 107
D. Numerical Methods 114
1. Numerical Treatment of Quadratic Potential 115
2. Numerical Treatment of Image Charge Potential 115
3. Resonant Tunneling: A Numerical Example 119
E. The Thermal and Field Emission Equation 122
1. The Fowler-Nordheim and Richardson-Laue-Dushman Equations 124
2. The Emission Equation Integrals and Their Approximation 126
3. The Revised FN and RLD Equations 130
F. The Revised FN-RLD Equation and the Inference of Work Function From Experimental Data 138
1. Field Emission 138
2. Thermionic Emission 141
3. Mixed Thermal-Field Conditions 143
4. Slope-Intercept Methods Applied to Field Emission 147
G. Recent Revisions of the Standard Thermal and Field Models 151
1. The Forbes Approach to the Evaluation of the Elliptical Integrals 151
2. Emission in the Thermal-Field Transition Region Revisited 156
H. The General Thermal-Field Equation 159
I. Thermal Emittance 163
III. Photoemission 167
A. Background 167
B. Quantum Efficiency 168
C. The Probability of Emission 171
1. The Escape Cone 171
2. The Fowler–Dubridge Model 172
D. Reflection and Penetration Depth 174
1. Dielectric Constant, Index of Refraction, and Reflectivity 174
2. Drude Model: Classical Approach 176
3. Drude Model: Distribution Function Approach 178
4. Quantum Extension and Resonance Frequencies 182
E. Conductivity 185
1. Electrical Conductivity 185
2. Thermal Conductivity 187
3. Wiedemann–Franz Law 190
4. Specific Heat of Solids 191
F. Scattering Rates 194
1. Fermi’s Golden Rule 194
2. Charged Impurity Relaxation Time 197
3. Electron-Electron Scattering 200
4. A Sinusoidal Potential 206
5. Monatomic Linear Chain of Atoms 206
6. Electron-Phonon Scattering 215
7. Matthiesen’s Rule and the Specification of Scattering Terms 233
G. Scattering Factor 240
H. Temperature of a Laser-Illuminated Surface 243
1. Photocathodes and Drive Lasers 243
2. A Simple Model of Temperature Increase Due to a Laser Pulse 244
3. Diffusion of Heat and Corresponding Temperature Rise 246
4. Multiple Pulses and Temperature Rise 248
5. Temperature Rise in a Single Pulse: The Coupled Heat Equations 255
6. The Electron-Phonon Coupling Factor g: A Simple Model 256
I. Numerical Solution of the Coupled Thermal Equations 260
1. Nature of the Problem. 260
2. Explicit and Implicit Solutions of Ordinary Differential Equations 261
3. Numerically Solving the Coupled Temperature Equations With Temperature-Dependent Coefficients 268
J. Revisions to the Modified Fowler-Dubridge Model: Quantum Effects 274
K. Quantum Efficiency Revisited: A Moments-Based Approach 277
L. The Quantum Efficiency of Bare Metals 282
1. Variation of Work Function With Crystal Face 284
2. The Density of States With Respect to the Nearly Free Electron Gas Model 288
3. Surface Structure, Multiple Reflections, and Field Enhancement 289
4. Contamination and Effective Emission Area 293
M. The Emittance and Brightness of Photocathodes 295
IV. Low-Work Function Coatings and Enhanced Emission 300
A. Historical Perspective 300
B. A Simple Model of a Low-Work Function Coating 301
C. A Less Simple Model of the Low-Work Function Coating 302
D. The (Modified) Gyftopoulos-Levine Model of Work Function Reduction 306
E. Comparison of the Modified Gyftopoulos-Levine Model to Thermionic Data 312
F. Comparison of the Modified Gyftopoulos-Levine Model to Photoemission Data 316
V. Appendices 324
A. Integrals Related to Fermi-Dirac and Bose-Einstein Statistics 324
B. The Riemann Zeta Function 325
VI. Conclusion 326
References 329
Index 345