Introduction to the Physics of Electron EmissionISBN: 9781119051893
712 pages
November 2017

Description
A practical, indepth description of the physics behind electron emission physics and its usage in science and technology
Electron emission is both a fundamental phenomenon and an enabling component that lies at the very heart of modern science and technology. Written by a recognized authority in the field, with expertise in both electron emission physics and electron beam physics, An Introduction to Electron Emission provides an indepth look at the physics behind thermal, field, photo, and secondary electron emission mechanisms, how that physics affects the beams that result through space charge and emittance growth, and explores the physics behind their utilization in an array of applications.
The book addresses mathematical and numerical methods underlying electron emission, describing where the equations originated, how they are related, and how they may be correctly used to model actual sources for devices using electron beams. Writing for the beam physics and solid state communities, the author explores applications of electron emission methodology to solid state, statistical, and quantum mechanical ideas and concepts related to simulations of electron beams to condensed matter, solid state and fabrication communities.
 Provides an extensive description of the physics behind four electron emission mechanisms—field, photo, and secondary, and how that physics relates to factors such as space charge and emittance that affect electron beams.
 Introduces readers to mathematical and numerical methods, their origins, and how they may be correctly used to model actual sources for devices using electron beams
 Demonstrates applications of electron methodology as well as quantum mechanical concepts related to simulations of electron beams to solid state design and manufacture
 Designed to function as both a graduatelevel text and a reference for research professionals
Introduction to the Physics of Electron Emission is a valuable learning tool for postgraduates studying quantum mechanics, statistical mechanics, solid state physics, electron transport, and beam physics. It is also an indispensable resource for academic researchers and professionals who use electron sources, model electron emission, develop cathode technologies, or utilize electron beams.
Table of Contents
Acknowledgements 2
Part I Foundations 5
1 Prelude 7
2 Units and Evaluation 11
2.1 Numerical Accuracy 11
2.2 Atomicsized Units 13
2.3 Units Based on Emission 18
3 PreQuantum Models 21
3.1 Discovery of Electron Emission 21
3.2 The Drude Model and MaxwellBoltzmann Statistics 22
3.3 The Challenge of Photoemission 31
4 Statistics 37
4.1 Distinguishable Particles 37
4.2 Probability and States 43
4.3 Probability and Entropy 45
4.4 Combinatorics and Products of Probability 50
5 MaxwellBoltzmann Distribution 55
5.1 Classical Phase Space 55
5.2 Most Probable Distribution 59
5.3 Energy and Entropy 62
5.4 The Gibbs Paradox 63
5.5 Ideal Gas in a Potential Gradient 65
5.6 The Grand Partition Function 67
5.7 A Nascent Model of Electron Emission 69
6 Quantum Distributions 73
6.1 BoseEinstein Distribution 73
6.2 FermiDirac Distribution 74
6.3 The Riemann Zeta Function 75
6.4 Chemical Potential 78
6.5 Classical to Quantum Statistics 84
6.6 Electrons and White Dwarf Stars 85
7 A Box of Electrons 91
7.1 Scattering 91
7.2 From Classical to Quantum Mechanics 92
7.3 Moments and Distributions 94
7.4 Boltzmann’s Transport Equation 96
8 Quantum Mechanics Methods 107
8.1 A Simple Model: The Prisoner’s Dilemma 107
8.2 Matrices and Wave Functions 115
9 Quintessential Problems 133
9.1 The Hydrogen Atom 134
9.2 Transport Past Barriers 151
9.3 The Harmonic Oscillator 162
Part II The Canonical Equations 175
10 A Brief History 177
10.1 Thermal Emission 178
10.2 Field Emission 180
10.3 Photoemission 181
10.4 Secondary Emission 181
10.5 Space Charge Limited Emission 182
10.6 Resources and Further Reading 183
11 Anatomy of Current Density 187
11.1 Supply Function 188
11.2 Gamow Factor 189
11.3 Image Charge Potential 194
12 RichardsonLaueDushman Equation 197
12.1 Approximations 197
12.2 Analysis of Thermal Emission Data 199
13 FowlerNordheim Equation 201
13.1 Triangular Barrier Approximation 203
13.2 Image Charge Approximation 205
13.3 Analysis of Field Emission Data 211
13.4 The MillikanLauritsen Hypothesis 213
14 FowlerDubridge Equation 217
14.1 Approximations 217
14.2 Analysis of Photoemission Data 221
15 Baroody Equation 225
15.1 Approximations 225
15.2 Analysis of Secondary Emission Data 232
15.3 Subsequent Approximations 234
16 ChildLangmuir Law 237
16.1 Constant Density Approximation 238
16.2 Constant Current Approximation 241
16.3 Transit Time Approximation 245
17 A General ThermalFieldPhotoemission Equation 251
17.1 Experimental ThermalField Energy Distributions 253
17.2 Theoretical ThermalField Energy Distributions 255
17.3 The N(n; s; u) Function 264
17.4 Brute Force Evaluation 275
17.5 A Computationally Kind Model 282
17.6 General Thermal Field Emission Code 288
Part III Exact Tunneling and Transmission Evaluation 297
18 Simple Barriers 299
18.1 Rectangular Barrier 300
18.2 Triangular Barrier  General Method 306
18.3 Triangular Barrier  Numerical 318
19 Transfer Matrix Approach 325
19.1 Plane Wave Transfer Matrix 326
19.2 Airy Function Transfer Matrix 335
20 Ion Enhanced Emission and Breakdown 353
20.1 Paschen’s Curve 353
20.2 Modified Paschen’s Curve 357
20.3 Ions and the Emission Barrier 360
Part IV The Complexity of Materials 367
21 Metals 369
21.1 Density of States, Again 370
21.2 Spheres in d��Dimensions 372
21.3 The Kronig Penny Model 375
21.4 Atomic Orbitals 381
21.5 Electronegativity 383
21.6 Sinusoidal Potential and Band Gap 388
21.7 Ion Potentials and Screening 391
22 Semiconductors 397
22.1 Resistivity 397
22.2 Electrons and Holes 400
22.3 Band Gap and Temperature 403
22.4 Doping of Semiconductors 406
22.5 Semiconductor Image Charge Potential 411
22.6 Dielectric Constant and Screening 414
23 Effective Mass 417
23.1 Dispersion Relations 417
23.2 The k _ p Method 420
23.3 Hyperbolic Relations 424
23.4 The Alpha Semiconductor Model 428
23.5 Current and Effective Mass 433
24 Interfaces 435
24.1 MetalInsulatorMetal Current Density 435
24.2 Band Bending 445
24.3 Accumulation Layers 447
24.4 Depletion Layers 458
24.5 Modifications Due to NonLinear Potential Barriers 466
25 Contacts, Conduction, and Current 471
25.1 Zener Breakdown 471
25.2 PooleFrenkel Transport 472
25.3 Tunneling Conduction 477
25.4 Resonant Tunneling in Field Emission 483
26 Electron Density Near Barriers 489
26.1 An Infinite Barrier 489
26.2 Two Infinite Barriers 493
26.3 A Triangular Well 495
26.4 Density and Dipole Component 499
27 Many Body Effects and Image Charge 507
27.1 Kinetic Energy 508
27.2 Exchange Energy 509
27.3 Correlation Term 511
27.4 Core Term 512
27.5 ExchangeCorrelation and a Barrier Model 518
28 An Analytic Image Charge Potential 523
28.1 Work Function and Temperature 523
28.2 Work Function and Field 526
28.3 Changes to Current Density 528
Part V Application Physics 531
29 Dispenser Cathodes 533
29.1 Miram Curves and the Longo Equation 534
29.2 Diffusion of Coatings 539
29.3 Evaporation of Coatings 564
29.4 Knudsen Flow Through Pores 568
29.5 Lifetime of a Sintered Wire Controlled Porosity Dispenser Cathode 577
30 Field Emitters 581
30.1 Field Enhancement 582
30.2 Hemispheres and Notional Emission Area 586
30.3 Point Charge Model 590
30.4 Schottky’s Conjecture 594
30.5 Assessment of the Tip Current Models 601
30.6 Line Charge Models 603
30.7 Prolate Spheroidal Representation 608
30.8 A Hybrid AnalyticNumerical Model 616
30.9 Shielding 627
30.10 Statistical Variation 633
31 Photoemitters 643
31.1 Scattering Consequences 648
31.2 Basic Theory 650
31.3 Three Step Model 652
31.4 Moments Model 656
31.5 Reflectivity and Penetration Factors 664
31.6 LorentzDrude Model of the Dielectric Constant 667
31.7 Scattering Contributions 678
31.8 Low Work Function Coatings 695
31.9 Quantum Efficiency of a Cesiated Surface 706
32 Secondary Emission Cathodes 709
32.1 Diamond Amplifier Concept 710
32.2 Monte Carlo Methods 720
32.3 Relaxation Time 729
32.4 Monte Carlo and Diamond Amplifier Response Time 753
33 Electron Beam Physics 765
33.1 Electron Orbits and Cathode Area 767
33.2 Beam Envelope Equation 769
33.3 Emittance for Flat and Uniform Surfaces 776
33.4 Emittance for A Bump 796
33.5 Emittance and Realistic Surfaces 823
Part VI Appendicies 827
A Summation, Integration, and Differentiation 829
A.1 Series 829
A.2 Integration 830
A.3 Differentiation 840
A.4 Numerical Solution of an Ordinary Differential Equation 847
B Functions 851
B.1 Trigonometric Functions 851
B.2 Gamma Function 851
B.3 Riemann Zeta Function 852
B.4 Error Function 853
B.5 Legendre Polynomials 854
B.6 Airy Functions 855
B.7 Lorentzian Functions 858
C Algorithms 861
C.1 Permutation Algorithm 861
C.2 Birthday Algorithm 862
C.3 Least Squares Fitting of Data 863
C.4 Monty Hall Algorithm 867
C.5 Wave Function and Density Algorithm 868
C.6 Hydrogen Atom Algorithms 870
C.7 Root Finding Methods 873
C.8 ThermalField Algorithm 877
C.9 Gamow Factor Algorithm 879
C.10 Triangular Barrier D(E) 880
C.11 Evaluation of Hc(u) 881
C.12 Transfer Matrix Algorithm 883
C.13 Semiconductors and Doping Density 890
C.14 Band Bending: Accumulation Layer 892
C.15 Simple ODE Solvers 893
C.16 Current through a MetalInsulatorMetal diode 897
C.17 Field Emission From Semiconductors 898
C.18 Roots of the Quadratic Image Charge Barrier 901
C.19 Zeros of the Airy Function 902
C.20 Atomic Sphere Radius rs 904
C.21 Sodium ExchangeCorrelation Potential 906
C.22 Field Dependent Work Function 907
C.23 Digitizing an Image file 907
C.24 Lattice Gas Algorithm 909
C.25 Evaluation of the Point Charge Model Functions 912
C.26 Modeling of Field Emitter I(V ) Data 913
C.27 Modeling a LogNormal Distribution of Field Emitters 915
C.28 Simple Shell and Sphere Algorithm 919
C.29 GyftopoulosLevine Work function Algorithm 921
C.30 Poisson Distributions 924
C.31 ElectronElectron Relaxation Time 927
C.32 Resistivity and the Debye Temperature 928
C.33 Orbits in a Magnetic Field 931
C.34 Trajectory of a Harmonic Oscillator 935
C.35 Trajectories for Emission from a Hemisphere 936
C.36 Monte Carlo and Integration 938
Index
Author Information
Kevin Jensen, PhD is a research physicist in the Materials and Systems Branch, Materials Science and Technology Division, at the Naval Research Laboratory. Since 2001, he has been a visiting senior research scientist at the University of Maryland’s Institute for Research in Electronics and Applied Physics (IREAP). Dr. Jensen joined the theory section of the Vacuum Electronics Branch at NRL in 1990. He earned a doctorate in physics from New York University in 1987. He has been and is Principal Investigator for several research programs investigating the application of electron sources (particularly field and photoemission sources) to microwave devices and Free Electron Lasers. Over the years, he has authored or coauthored over 150 articles and conference proceedings. He became a Fellow of the American Physical Society in 2009 for his contributions to the theory and modeling of electron emission sources for particle accelerators and microwave tubes. He presently serves on the Editorial Board of Journal of Applied Physics.