Details

Introduction to the Physics of Electron Emission


Introduction to the Physics of Electron Emission


1. Aufl.

von: Kevin L. Jensen

116,99 €

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

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Beschreibungen

<p><b>A practical, in-depth description of the physics behind electron emission physics and its usage in science and technology</b></p> <p>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, <i>An Introduction to Electron Emission </i>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.</p> <p>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.</p> <ul> <li>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.</li> <li>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</li> <li>Demonstrates applications of electron methodology as well as quantum mechanical concepts related to simulations of electron beams to solid state design and manufacture</li> <li>Designed to function as both a graduate-level text and a reference for research professionals</li> </ul> <p><i>Introduction to the Physics of Electron Emission</i> 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.</p>
<p> </p> <p>Acknowledgements xiii</p> <p><b>Part I: Foundations</b></p> <p><b>1 Prelude 3</b></p> <p><b>2 Units and evaluation 7</b></p> <p>2.1 Numerical accuracy 7</p> <p>2.2 Atomic-sized units 8</p> <p>2.3 Units based on emission 11</p> <p><b>3 Pre-quantum models 13</b></p> <p>3.1 Discovery of electron emission 13</p> <p>3.2 The Drude model and Maxwell–Boltzmann statistics 13</p> <p>3.3 The challenge of photoemission 19</p> <p><b>4 Statistics 25</b></p> <p>4.1 Distinguishable particles 25</p> <p>4.2 Probability and states 28</p> <p>4.3 Probability and entropy 30</p> <p>4.4 Combinatorics and products of probability 33</p> <p><b>5 Maxwell–Boltzmann distribution 37</b></p> <p>5.1 Classical phase space 37</p> <p>5.2 Most probable distribution 39</p> <p>5.3 Energy and entropy 41</p> <p>5.4 The Gibbs paradox 42</p> <p>5.5 Ideal Gas in a potential gradient 44</p> <p>5.6 The grand partition function 45</p> <p>5.7 A nascent model of electron emission 46</p> <p><b>6 Quantum distributions 49</b></p> <p>6.1 Bose–Einstein distribution 49</p> <p>6.2 Fermi–Dirac distribution 50</p> <p>6.3 The Riemann zeta function 50</p> <p>6.4 Chemical potential 52</p> <p>6.5 Classical to quantum statistics 56</p> <p>6.6 Electrons and white dwarf stars 57</p> <p><b>7 A box of electrons 61</b></p> <p>7.1 Scattering 61</p> <p>7.2 From classical to quantum mechanics 61</p> <p>7.3 Moments and distributions 63</p> <p>7.4 Boltzmann’s transport equation 64</p> <p><b>8 Quantum mechanics methods 73</b></p> <p>8.1 A simple model: the prisoner’s dilemma 73</p> <p>8.2 Matrices and wave functions 78</p> <p><b>9 Quintessential problems 91</b></p> <p>9.1 The hydrogen atom 92</p> <p>9.2 Transport past barriers 102</p> <p>9.3 The harmonic oscillator 110</p> <p><b>Part II: The canonical equations</b></p> <p><b>10 A brief history 121</b></p> <p>10.1 Thermal emission 121</p> <p>10.2 Field emission 122</p> <p>10.3 Photoemission 123</p> <p>10.4 Secondary emission 124</p> <p>10.5 Space-charge limited emission 124</p> <p>10.6 Resources and further reading 124</p> <p><b>11 Anatomy of current density 127</b></p> <p>11.1 Supply function 128</p> <p>11.2 Gamow factor 128</p> <p>11.3 Image charge potential 131</p> <p><b>12 Richardson–Laue–Dushman equation 135</b></p> <p>12.1 Approximations 135</p> <p>12.2 Analysis of thermal emission data 136</p> <p><b>13 Fowler–Nordheim equation 139</b></p> <p>13.1 Triangular barrier approximation 140</p> <p>13.2 Image charge approximation 141</p> <p>13.3 Analysis of field emission data 145</p> <p>13.4 The Millikan–Lauritsen hypothesis 146</p> <p><b>14 Fowler–Dubridge equation 149</b></p> <p>14.1 Approximations 149</p> <p>14.2 Analysis of photoemission data 153</p> <p><b>15 Baroody equation 155</b></p> <p>15.1 Approximations 155</p> <p>15.2 Analysis of secondary emission data 160</p> <p>15.3 Subsequent approximations 161</p> <p><b>16 Child–Langmuir law 163</b></p> <p>16.1 Constant density approximation 164</p> <p>16.2 Constant current approximation 165</p> <p>16.3 Transit time approximation 168</p> <p><b>17 A General thermal–field–photoemission equation 173</b></p> <p>17.1 Experimental thermal–field energy distributions 175</p> <p>17.2 Theoretical thermal–field energy distributions 176</p> <p>17.3 The N(n,s,u) function 181</p> <p>17.4 Brute force evaluation 189</p> <p>17.5 A computationally kind model 193</p> <p>17.6 General thermal–field emission code 198</p> <p><b>Part III: Exact tunneling and transmission evaluation</b></p> <p><b>18 Simple barriers 209</b></p> <p>18.1 Rectangular barrier 209</p> <p>18.2 Triangular barrier: general method 213</p> <p>18.3 Triangular barrier: numerical 222</p> <p><b>19 Transfer matrix approach 227</b></p> <p>19.1 Plane wave transfer matrix 227</p> <p>19.2 Airy function transfer matrix 233</p> <p><b>20 Ion enhanced emission and breakdown 245</b></p> <p>20.1 Paschen’s curve 245</p> <p>20.2 Modified Paschen’s curve 247</p> <p>20.3 Ions and the emission barrier 250</p> <p><b>Part IV: The complexity of materials</b></p> <p><b>21 Metals 257</b></p> <p>21.1 Density of states, again 257</p> <p>21.2 Spheres in d dimensions 259</p> <p>21.3 The Kronig Penny model 261</p> <p>21.4 Atomic orbitals 264</p> <p>21.5 Electronegativity 266</p> <p>21.6 Sinusoidal potential and band gap 269</p> <p>21.7 Ion potentials and screening 272</p> <p><b>22 Semiconductors 277</b></p> <p>22.1 Resistivity 277</p> <p>22.2 Electrons and holes 279</p> <p>22.3 Band gap and temperature 281</p> <p>22.4 Doping of semiconductors 281</p> <p>22.5 Semiconductor image charge potential 286</p> <p>22.6 Dielectric constant and screening 287</p> <p><b>23 Effective mass 291</b></p> <p>23.1 Dispersion relations 291</p> <p>23.2 The k ⋅ p method 293</p> <p>23.3 Hyperbolic relations 296</p> <p>23.4 The alpha semiconductor model 299</p> <p>23.5 Current and effective mass 301</p> <p><b>24 Interfaces 303</b></p> <p>24.1 Metal–insulator–metal current density 303</p> <p>24.2 Band bending 310</p> <p>24.3 Accumulation layers 311</p> <p>24.4 Depletion layers 319</p> <p>24.5 Modifications due to non-linear potential barriers 324</p> <p><b>25 Contacts, conduction, and current 329</b></p> <p>25.1 Zener breakdown 329</p> <p>25.2 Poole–Frenkel transport 329</p> <p>25.3 Tunneling conduction 333</p> <p>25.4 Resonant tunneling in field emission 336</p> <p><b>26 Electron density near barriers 341</b></p> <p>26.1 An infinite barrier 341</p> <p>26.2 Two infinite barriers 344</p> <p>26.3 A triangular well 346</p> <p>26.4 Density and dipole component 348</p> <p><b>27 Many-body effects and image charge 353</b></p> <p>27.1 Kinetic energy 353</p> <p>27.2 Exchange energy 354</p> <p>27.3 Correlation term 356</p> <p>27.4 Core term 357</p> <p>27.5 Exchange-correlation and a barrier model 360</p> <p><b>28 An analytic image charge potential 363</b></p> <p>28.1 Work function and temperature 363</p> <p>28.2 Work function and field 363</p> <p>28.3 Changes to current density 366</p> <p><b>Part V: Application physics</b></p> <p><b>29 Dispenser cathodes 371</b></p> <p>29.1 Miram curves and the longo equation 371</p> <p>29.2 Diffusion of coatings 375</p> <p>29.3 Evaporation of coatings 391</p> <p>29.4 Knudsen flow through pores 393</p> <p>29.5 Lifetime of a sintered wire controlled porosity dispenser cathode 399</p> <p><b>30 Field emitters 403</b></p> <p>30.1 Field enhancement 403</p> <p>30.2 Hemispheres and notional emission area 406</p> <p>30.3 Point charge model 408</p> <p>30.4 Schottky’s conjecture 412</p> <p>30.5 Assessment of the tip current models 415</p> <p>30.6 Line charge models 417</p> <p>30.7 Prolate spheroidal representation 420</p> <p>30.8 A hybrid analytic-numerical model 425</p> <p>30.9 Shielding 433</p> <p>30.10 Statistical variation 438</p> <p><b>31 Photoemitters 443</b></p> <p>31.1 Scattering consequences 446</p> <p>31.2 Basic theory 448</p> <p>31.3 Three-step model 449</p> <p>31.4 Moments model 451</p> <p>31.5 Reflectivity and penetration factors 457</p> <p>31.6 Lorentz–Drude model of the dielectric constant 458</p> <p>31.7 Scattering contributions 466</p> <p>31.8 Low work function coatings 478</p> <p>31.9 Quantum efficiency of a cesiated surface 485</p> <p><b>32 Secondary emission cathodes 487</b></p> <p>32.1 Diamond amplifier concept 487</p> <p>32.2 Monte Carlo methods 494</p> <p>32.3 Relaxation time 499</p> <p>32.4 Monte Carlo and diamond amplifier response time 516</p> <p><b>33 Electron beam physics 525</b></p> <p>33.1 Electron orbits and cathode area 526</p> <p>33.2 Beam envelope equation 528</p> <p>33.3 Emittance for flat and uniform surfaces 533</p> <p>33.4 Emittance for a bump 545</p> <p>33.5 Emittance and realistic surfaces 563</p> <p><b>Part VI: Appendices</b></p> <p>Appendix 1 Summation, integration, and differentiation 569</p> <p>A1.1 Series 569</p> <p>A1.2 Integration 569</p> <p>A1.3 Differentiation 577</p> <p>A1.4 Numerical solution of an ordinary differential equation 582</p> <p>Appendix 2 Functions 585</p> <p>A2.1 Trigonometric functions 585</p> <p>A2.2 Gamma function 585</p> <p>A2.3 Riemann zeta function 585</p> <p>A2.4 Error function 587</p> <p>A2.5 Legendre polynomials 587</p> <p>A2.6 Airy functions 588</p> <p>A2.7 Lorentzian functions 590</p> <p>Appendix 3 Algorithms 591</p> <p>A3.1 Permutation algorithm 591</p> <p>A3.2 Birthday algorithm 592</p> <p>A3.3 Least squares fitting of data 593</p> <p>A3.4 Monty Hall algorithm 595</p> <p>A3.5 Wave function and density algorithm 596</p> <p>A3.6 Hydrogen atom algorithms 598</p> <p>A3.7 Root-finding Methods 601</p> <p>A3.8 Thermal–field algorithm 604</p> <p>A3.9 Gamow factor algorithm 606</p> <p>A3.10 Triangular barrier D(E) 607</p> <p>A3.11 Evaluation of Hc(u) 608</p> <p>A3.12 Transfer matrix algorithm 610</p> <p>A3.13 Semiconductors and doping density 616</p> <p>A3.14 Band bending: accumulation layer 618</p> <p>A3.15 Simple ODE solvers 619</p> <p>A3.16 Current through a metal–insulator–metal diode 622</p> <p>A3.17 Field emission from semiconductors 624</p> <p>A3.18 Roots of the quadratic image charge barrier 626</p> <p>A3.19 Zeros of the airy function 627</p> <p>A3.20 Atomic sphere radius rs 629</p> <p>A3.21 Sodium exchange-correlation potential 631</p> <p>A3.22 Field-dependent work function 632</p> <p>A3.23 Digitizing an image file 632</p> <p>A3.24 Lattice gas algorithm 633</p> <p>A3.25 Evaluation of the point charge model functions 636</p> <p>A3.26 Modeling of field emitter I(V) data 638</p> <p>A3.27 Modeling a log-normal distribution of field emitters 640</p> <p>A3.28 Simple shell and sphere algorithm 643</p> <p>A3.29 Gyftopoulos–Levine work function algorithm 645</p> <p>A3.30 Poisson distributions 648</p> <p>A3.31 Electron–electron relaxation time 650</p> <p>A3.32 Resistivity and the Debye temperature 651</p> <p>A3.33 Orbits in a magnetic field 655</p> <p>A3.34 Trajectory of a harmonic oscillator 657</p> <p>A3.35 Trajectories for emission from a hemisphere 658</p> <p>A3.36 Monte Carlo and integration 660</p> <p>References 663</p> <p>Index 683</p>
<p><b>Kevin Jensen, PhD </b>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.</p>
<p><b>A practical, in-depth description of the physics behind electron emission physics and its usage in science and technology</b></p> <p>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, <i>An Introduction to Electron Emission </i>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.</p> <p>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.</p> <ul style="text-align: justify;"> <li>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.</li> <li>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</li> <li>Demonstrates applications of electron methodology as well as quantum mechanical concepts related to simulations of electron beams to solid state design and manufacture</li> <li>Designed to function as both a graduate-level text and a reference for research professionals</li> </ul> <p><i>Introduction to the Physics of Electron Emission</i> 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.</p>

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