Details

Introduction to the Physics of Electron Emission


Introduction to the Physics of Electron Emission


1. Aufl.

von: Kevin L. Jensen

118,99 €

Verlag: Wiley
Format: PDF
Veröffentl.: 15.09.2017
ISBN/EAN: 9781119051756
Sprache: englisch
Anzahl Seiten: 712

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Beschreibungen

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.
  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 Maxwell–Boltzmann 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 Maxwell–Boltzmann 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 Bose–Einstein distribution 49 6.2 Fermi–Dirac 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 Richardson–Laue–Dushman equation 135 12.1 Approximations 135 12.2 Analysis of thermal emission data 136 13 Fowler–Nordheim 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 Millikan–Lauritsen hypothesis 146 14 Fowler–Dubridge 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 Child–Langmuir law 163 16.1 Constant density approximation 164 16.2 Constant current approximation 165 16.3 Transit time approximation 168 17 A General thermal–field–photoemission equation 173 17.1 Experimental thermal–field energy distributions 175 17.2 Theoretical thermal–field 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 thermal–field 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 19.1 Plane wave transfer matrix 227 19.2 Airy function transfer matrix 233 20 Ion enhanced emission and breakdown 245 20.1 Paschen’s curve 245 20.2 Modified Paschen’s curve 247 20.3 Ions and the emission barrier 250 Part IV: The complexity of materials 21 Metals 257 21.1 Density of states, again 257 21.2 Spheres in d dimensions 259 21.3 The Kronig Penny model 261 21.4 Atomic orbitals 264 21.5 Electronegativity 266 21.6 Sinusoidal potential and band gap 269 21.7 Ion potentials and screening 272 22 Semiconductors 277 22.1 Resistivity 277 22.2 Electrons and holes 279 22.3 Band gap and temperature 281 22.4 Doping of semiconductors 281 22.5 Semiconductor image charge potential 286 22.6 Dielectric constant and screening 287 23 Effective mass 291 23.1 Dispersion relations 291 23.2 The k ? p method 293 23.3 Hyperbolic relations 296 23.4 The alpha semiconductor model 299 23.5 Current and effective mass 301 24 Interfaces 303 24.1 Metal–insulator–metal current density 303 24.2 Band bending 310 24.3 Accumulation layers 311 24.4 Depletion layers 319 24.5 Modifications due to non-linear potential barriers 324 25 Contacts, conduction, and current 329 25.1 Zener breakdown 329 25.2 Poole–Frenkel transport 329 25.3 Tunneling conduction 333 25.4 Resonant tunneling in field emission 336 26 Electron density near barriers 341 26.1 An infinite barrier 341 26.2 Two infinite barriers 344 26.3 A triangular well 346 26.4 Density and dipole component 348 27 Many-body effects and image charge 353 27.1 Kinetic energy 353 27.2 Exchange energy 354 27.3 Correlation term 356 27.4 Core term 357 27.5 Exchange-correlation and a barrier model 360 28 An analytic image charge potential 363 28.1 Work function and temperature 363 28.2 Work function and field 363 28.3 Changes to current density 366 Part V: Application physics 29 Dispenser cathodes 371 29.1 Miram curves and the longo equation 371 29.2 Diffusion of coatings 375 29.3 Evaporation of coatings 391 29.4 Knudsen flow through pores 393 29.5 Lifetime of a sintered wire controlled porosity dispenser cathode 399 30 Field emitters 403 30.1 Field enhancement 403 30.2 Hemispheres and notional emission area 406 30.3 Point charge model 408 30.4 Schottky’s conjecture 412 30.5 Assessment of the tip current models 415 30.6 Line charge models 417 30.7 Prolate spheroidal representation 420 30.8 A hybrid analytic-numerical model 425 30.9 Shielding 433 30.10 Statistical variation 438 31 Photoemitters 443 31.1 Scattering consequences 446 31.2 Basic theory 448 31.3 Three-step model 449 31.4 Moments model 451 31.5 Reflectivity and penetration factors 457 31.6 Lorentz–Drude model of the dielectric constant 458 31.7 Scattering contributions 466 31.8 Low work function coatings 478 31.9 Quantum efficiency of a cesiated surface 485 32 Secondary emission cathodes 487 32.1 Diamond amplifier concept 487 32.2 Monte Carlo methods 494 32.3 Relaxation time 499 32.4 Monte Carlo and diamond amplifier response time 516 33 Electron beam physics 525 33.1 Electron orbits and cathode area 526 33.2 Beam envelope equation 528 33.3 Emittance for flat and uniform surfaces 533 33.4 Emittance for a bump 545 33.5 Emittance and realistic surfaces 563 Part VI: Appendices Appendix 1 Summation, integration, and differentiation 569 A1.1 Series 569 A1.2 Integration 569 A1.3 Differentiation 577 A1.4 Numerical solution of an ordinary differential equation 582 Appendix 2 Functions 585 A2.1 Trigonometric functions 585 A2.2 Gamma function 585 A2.3 Riemann zeta function 585 A2.4 Error function 587 A2.5 Legendre polynomials 587 A2.6 Airy functions 588 A2.7 Lorentzian functions 590 Appendix 3 Algorithms 591 A3.1 Permutation algorithm 591 A3.2 Birthday algorithm 592 A3.3 Least squares fitting of data 593 A3.4 Monty Hall algorithm 595 A3.5 Wave function and density algorithm 596 A3.6 Hydrogen atom algorithms 598 A3.7 Root-finding Methods 601 A3.8 Thermal–field algorithm 604 A3.9 Gamow factor algorithm 606 A3.10 Triangular barrier D(E) 607 A3.11 Evaluation of Hc(u) 608 A3.12 Transfer matrix algorithm 610 A3.13 Semiconductors and doping density 616 A3.14 Band bending: accumulation layer 618 A3.15 Simple ODE solvers 619 A3.16 Current through a metal–insulator–metal diode 622 A3.17 Field emission from semiconductors 624 A3.18 Roots of the quadratic image charge barrier 626 A3.19 Zeros of the airy function 627 A3.20 Atomic sphere radius rs 629 A3.21 Sodium exchange-correlation potential 631 A3.22 Field-dependent work function 632 A3.23 Digitizing an image file 632 A3.24 Lattice gas algorithm 633 A3.25 Evaluation of the point charge model functions 636 A3.26 Modeling of field emitter I(V) data 638 A3.27 Modeling a log-normal distribution of field emitters 640 A3.28 Simple shell and sphere algorithm 643 A3.29 Gyftopoulos–Levine work function algorithm 645 A3.30 Poisson distributions 648 A3.31 Electron–electron relaxation time 650 A3.32 Resistivity and the Debye temperature 651 A3.33 Orbits in a magnetic field 655 A3.34 Trajectory of a harmonic oscillator 657 A3.35 Trajectories for emission from a hemisphere 658 A3.36 Monte Carlo and integration 660 References 663 Index 683
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.
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.

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