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. INDICE: Acknowledgements 2 .Part I Foundations 5 .1 Prelude 7 .2 Units and Evaluation 11 .2.1 Numerical Accuracy 11 .2.2 Atomic–sized Units 13 .2.3 Units Based on Emission 18 .3 Pre–Quantum Models 21 .3.1 Discovery of Electron Emission 21 .3.2 The Drude Model and Maxwell–Boltzmann 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 Maxwell–Boltzmann 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 Bose–Einstein Distribution 73 .6.2 Fermi–Dirac 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 Richardson–Laue–Dushman Equation 197 .12.1 Approximations 197 .12.2 Analysis of Thermal Emission Data 199 .13 Fowler–Nordheim 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 Millikan–Lauritsen Hypothesis 213 .14 Fowler–Dubridge 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 Child–Langmuir Law 237 .16.1 Constant Density Approximation 238 .16.2 Constant Current Approximation 241 .16.3 Transit Time Approximation 245 .17 A General Thermal–Field–Photoemission Equation 251 .17.1 Experimental Thermal–Field Energy Distributions 253 .17.2 Theoretical Thermal–Field 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 Metal–Insulator–Metal Current Density 435 .24.2 Band Bending 445 .24.3 Accumulation Layers 447 .24.4 Depletion Layers 458 .24.5 Modifications Due to Non–Linear Potential Barriers 466 .25 Contacts, Conduction, and Current 471 .25.1 Zener Breakdown 471 .25.2 Poole–Frenkel 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 Exchange–Correlation 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 Analytic–Numerical 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 Lorentz–Drude 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 Thermal–Field 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 Metal–Insulator–Metal 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 Exchange–Correlation 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 Log–Normal Distribution of Field Emitters 915 .C.28 Simple Shell and Sphere Algorithm 919 .C.29 Gyftopoulos–Levine Work function Algorithm 921 .C.30 Poisson Distributions 924 .C.31 Electron–Electron 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
- ISBN: 978-1-119-05189-3
- Editorial: Wiley–Blackwell
- Encuadernacion: Cartoné
- Páginas: 712
- Fecha Publicación: 17/11/2017
- Nº Volúmenes: 1
- Idioma: Inglés