Preface ........................................................ xi
1. Introduction ................................................ 1
2. Historical survey ........................................... 3
2.1. Early experiments ..................................... 3
2.2. Molecular beam epitaxy ................................ 4
2.3. Surface studies ....................................... 7
2.4. Theories of surface-structure determination .......... 10
3. Instrumentation ............................................ 12
3.1. Introduction ......................................... 12
3.2. Design of apparatus .................................. 13
3.3. Electron gun design .................................. 16
3.4. Energy filtering ..................................... 17
4. Wave properties of electrons ............................... 19
4.1. Introduction .......................................... 19
4.2. Wavelength and wave vector ............................ 19
4.3. Tangential continuity of the wave vector:
refraction ............................................ 20
4.4. Plane-wave boundary conditions ........................ 23
4.5. Absorption of the electron beam ....................... 25
5. The diffraction conditions ................................. 28
5.1. Crystal lattices ..................................... 28
5.2. Key idea of the diffraction .......................... 29
5.3. Miller indices and reciprocal lattices ............... 31
5.4. Surface lattices ..................................... 33
5.5. The Ewald construction ............................... 37
5.6. The zeroth Laue zone: diffraction from rows .......... 40
5.7. Lattice with a basis ................................. 41
6. Geometrical features of the pattern ........................ 43
6.1. Finite two-dimensional sheet: RHEED streaks ........... 43
6.2. Incoherent scattering ................................. 45
6.3. Lattice parameter ..................................... 46
6.4. Vicinal surfaces ...................................... 49
6.5. Preferred island size ................................. 58
7. Kikuchi and resonance patterns ............................. 62
7.1. Kikuchi lines ........................................ 62
7.2. Surface-wave resonances (Kikuchi envelopes) .......... 66
8. Real diffraction patterns .................................. 77
8.1. Perfect low-index surfaces ............................ 77
8.2. Streak patterns ....................................... 84
8.3. Ordered islands ....................................... 88
8.4. Transmission patterns ................................. 89
8.5. Rotationally disordered surfaces ...................... 97
8.6. Pseudo-one-dimensional crystals ...................... 103
8.7. The role of the instrument ........................... 107
9. Electron scattering by atoms .............................. 113
9.1. Introduction ........................................ 113
9.2. Elastic scattering: adiabatic approximation ......... 113
9.3. Elastic scattering: Born approximation .............. 114
9.4. Inelastic scattering by atoms ....................... 122
10. Kinematic electron diffraction ............................ 130
10.1. Introduction ........................................ 130
10.2. Born approximation .................................. 131
10.3. The effect of temperature ........................... 148
10.4. Kinematic predictions ............................... 150
10.5. Crystal structure factor of a three-dimensional
periodic lattice .................................... 151
11. Fourier components of the crystal potential ............... 154
11.1. Introduction ........................................ 154
11.2. Doyle-Turner parametrization ........................ 154
11.3. Effect of thermal vibrations ........................ 156
11.4. Scattering factors for ionic materials .............. 159
12. Dynamical theory - transfer matrix method ................. 161
12.1. Plan of Chapters 12-14 .............................. 161
12.2. Introduction ........................................ 161
12.3. General theory ...................................... 162
12.4. The transfer matrix ................................. 163
12.5. The transfer matrix for a single slice .............. 165
12.6. Multi-slice method .................................. 168
12.7. The recursion ....................................... 169
12.8. Effect of absorption ................................ 170
12.9. Relativistic correction ............................. 172
13. Dynamical theory - embedded R-matrix method ............... 173
13.1. Introduction ........................................ 173
13.2. Fourier expansion ................................... 174
13.3. The wave functions .................................. 174
13.4. Multislice method ................................... 175
13.5. The recursion ....................................... 177
13.6. The RHEED intensity ................................. 178
13.7. Inelastic damping ................................... 179
13.8. Examples ............................................ 180
14. Dynamical theory - integral method ........................ 192
15. Structural analysis of crystal surfaces ................... 195
15.1. Introduction ........................................ 195
15.2. One-beam condition .................................. 196
15.3. Examples of structural analysis ..................... 201
16. Inelastic scattering in a crystal ......................... 211
16.1. Introduction ........................................ 211
16.2. One-electron excitation: Yoshioka's theory .......... 211
16.3. Evaluation of the imaginary potential ............... 215
16.4. Plasmon scattering .................................. 218
16.5. Thermal diffuse scattering .......................... 221
16.6. Absorption coefficients ............................. 223
16.7. Analytical form of the imaginary potential .......... 224
16.8. Summary ............................................. 230
17. Weakly disordered surfaces ................................ 234
17.1. Introduction ........................................ 234
17.2. The main result ..................................... 238
17.3. A surface with only two layers ...................... 240
17.4. Markovian distribution of steps ..................... 244
17.5. General Markov results .............................. 248
17.6. Vicinal surfaces .................................... 248
17.7. Antiphase disorder .................................. 253
17.8. Column approximation ................................ 257
18. Strongly disordered surfaces .............................. 260
18.1. Introduction ........................................ 260
18.2. Height-difference correlation function .............. 260
18.3. The diffraction profile ............................. 262
18.4. Gaussian disorder ................................... 266
19. RHEED intensity oscillations .............................. 270
19.1. Experimental observations ........................... 270
19.2. Kinematic theory .................................... 284
19.3. Phenomenological step-density models ................ 290
19.4. Step density with shadowing ......................... 293
19.5. Rate-equation models of epitaxy ..................... 297
19.6. Phase shift and frequency doubling .................. 301
19.7. Sinusoidal oscillations ............................. 305
19.8. Comparisons with scanning probe measurements ........ 308
19.9. Complex oxides ...................................... 309
19.10.Conclusion .......................................... 312
Appendix A. Fourier representations ........................... 314
Appendix В. Green's functions ................................. 318
Appendix С. Kirchhoff's diffraction theory .................... 320
Appendix D. A simple eigenvalue problem ....................... 323
Appendix E. Waller and Hartree equation ....................... 326
Appendix F. Optimization of dynamical calculation ............. 328
Appendix G. Scattering factor ................................. 333
References .................................................... 335
Index ......................................................... 350
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