Contents
vii
3.3.4 Amplitude in the diffraction plane . . . . . . 208
3.3.5 Optical transformation for a general imaging system with coherent illumination . . . . 210
3.3.6 Optical transformation for a general imaging system with incoherent illumination . . . 217
3.3.7 The wave front aberration function . . . . . 222
3.3.8 Relationship between diffraction and the
Heisenberg uncertainty principle . . . . . . . 229
4 Particle scattering
233
4.1 Classical particle kinematics . . . . . . . . . . . . . 236
4.2 Scattering cross section and classical scattering . . 248
4.3 Integral expression of Schr¨ odinger’s equation . . . . 252
4.4 Green’s function solution for elastic scattering . . . 256
4.5 Perturbation theory . . . . . . . . . . . . . . . . . . 265
4.6 Perturbation solution for elastic scattering . . . . . 270
4.7 Inelastic scattering of a particle by a target atom . 272
4.8 Slowing of a charged particle in a dielectric medium 278
4.9 Small angle plural scattering of fast electrons . . . . 281
5 Electron emission from solids
297
5.1 The image force . . . . . . . . . . . . . . . . . . . . 299
5.2 The incident current density . . . . . . . . . . . . . 300
5.3 Thermionic emission . . . . . . . . . . . . . . . . . 304
5.4 Field emission . . . . . . . . . . . . . . . . . . . . . 309
5.5 Emission with elevated temperature and field . . . 319
5.6 Space charge limited emission . . . . . . . . . . . . 327
Appendix A The Fourier transform
331
Appendix B Linear second-order differential
equation
339
Bibliography
343
Index
353
vii
3.3.4 Amplitude in the diffraction plane . . . . . . 208
3.3.5 Optical transformation for a general imaging system with coherent illumination . . . . 210
3.3.6 Optical transformation for a general imaging system with incoherent illumination . . . 217
3.3.7 The wave front aberration function . . . . . 222
3.3.8 Relationship between diffraction and the
Heisenberg uncertainty principle . . . . . . . 229
4 Particle scattering
233
4.1 Classical particle kinematics . . . . . . . . . . . . . 236
4.2 Scattering cross section and classical scattering . . 248
4.3 Integral expression of Schr¨ odinger’s equation . . . . 252
4.4 Green’s function solution for elastic scattering . . . 256
4.5 Perturbation theory . . . . . . . . . . . . . . . . . . 265
4.6 Perturbation solution for elastic scattering . . . . . 270
4.7 Inelastic scattering of a particle by a target atom . 272
4.8 Slowing of a charged particle in a dielectric medium 278
4.9 Small angle plural scattering of fast electrons . . . . 281
5 Electron emission from solids
297
5.1 The image force . . . . . . . . . . . . . . . . . . . . 299
5.2 The incident current density . . . . . . . . . . . . . 300
5.3 Thermionic emission . . . . . . . . . . . . . . . . . 304
5.4 Field emission . . . . . . . . . . . . . . . . . . . . . 309
5.5 Emission with elevated temperature and field . . . 319
5.6 Space charge limited emission . . . . . . . . . . . . 327
Appendix A The Fourier transform
331
Appendix B Linear second-order differential
equation
339
Bibliography
343
Index
353