Introduction to the Physics of Electron Emission

A practical, in-depth 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 in-depth 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 graduate-level 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.

Autorentext

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.

Inhalt

Acknowledgements xiii

Part I: Foundations

1 Prelude 3

2 Units and evaluation 7

2.1 Numerical accuracy 7

2.2 Atomic-sized units 8

2.3 Units based on emission 11

3 Pre-quantum models 13

3.1 Discovery of electron emission 13

3.2 The Drude model and MaxwellBoltzmann statistics 13

3.3 The challenge of photoemission 19

4 Statistics 25

4.1 Distinguishable particles 25

4.2 Probability and states 28

4.3 Probability and entropy 30

4.4 Combinatorics and products of probability 33

5 MaxwellBoltzmann distribution 37

5.1 Classical phase space 37

5.2 Most probable distribution 39

5.3 Energy and entropy 41

5.4 The Gibbs paradox 42

5.5 Ideal Gas in a potential gradient 44

5.6 The grand partition function 45

5.7 A nascent model of electron emission 46

6 Quantum distributions 49

6.1 BoseEinstein distribution 49

6.2 FermiDirac distribution 50

6.3 The Riemann zeta function 50

6.4 Chemical potential 52

6.5 Classical to quantum statistics 56

6.6 Electrons and white dwarf stars 57

7 A box of electrons 61

7.1 Scattering 61

7.2 From classical to quantum mechanics 61

7.3 Moments and distributions 63

7.4 Boltzmann's transport equation 64

8 Quantum mechanics methods 73

8.1 A simple model: the prisoner's dilemma 73

8.2 Matrices and wave functions 78

9 Quintessential problems 91

9.1 The hydrogen atom 92

9.2 Transport past barriers 102

9.3 The harmonic oscillator 110

Part II: The canonical equations

10 A brief history 121

10.1 Thermal emission 121

10.2 Field emission 122

10.3 Photoemission 123

10.4 Secondary emission 124

10.5 Space-charge limited emission 124

10.6 Resources and further reading 124

11 Anatomy of current density 127

11.1 Supply function 128

11.2 Gamow factor 128

11.3 Image charge potential 131

12 RichardsonLaueDushman equation 135

12.1 Approximations 135

12.2 Analysis of thermal emission data 136

13 FowlerNordheim equation 139

13.1 Triangular barrier approximation 140

13.2 Image charge approximation 141

13.3 Analysis of field emission data 145

13.4 The MillikanLauritsen hypothesis 146

14 FowlerDubridge equation 149

14.1 Approximations 149

14.2 Analysis of photoemission data 153

15 Baroody equation 155

15.1 Approximations 155

15.2 Analysis of secondary emission data 160

15.3 Subsequent approximations 161

16 ChildLangmuir law 163

16.1 Constant density approximation 164

16.2 Constant current approximation 165

16.3 Transit time approximation 168

17 A General thermalfieldphotoemission equation 173

17.1 Experimental thermalfield energy distributions 175

17.2 Theoretical thermalfield energy distributions 176

17.3 The N(n,s,u) function 181

17.4 Brute force evaluation 189

17.5 A computationally kind model 193

17.6 General thermalfield emission code 198

Part III: Exact tunneling and transmission evaluation

18 Simple barriers 209

18.1 Rectangular barrier 209

18.2 Triangular barrier: general method 213

18.3 Triangular barrier: numerical 222 19 Transfer matrix approach 227</...