[eBook Code] Electron Beam-Specimen Interactions and Simulation Methods in Microscopy (eBook Code, 1st)

Preface ix

1 Introduction 1

1.1 Organisation and Scope of the Book 3

References 8

2 The Monte Carlo Method 9

2.1 Physical Background and Implementation 11

2.1.1 Elastic Scattering By an Atomic Nucleus 11

2.1.2 Inelastic Scattering by Atomic Electrons 18

2.1.3 Implementation of the Monte Carlo Algorithm 23

2.2 Some Applications of the Monte Carlo Method 27

2.2.1 Spatial Resolution and Backscattered Imaging 27

2.2.2 Characteristic X-Ray Generation 34

2.2.3 Cathodoluminescence and Electron Beam Induced Current Microscopy 37

2.3 Further Topics in Monte Carlo Simulations 40

2.3.1 Classical or Quantum Physics? 40

2.3.2 Spin–Orbit Coupling and the Mott Cross-Section 43

2.3.3 Dielectric Model of Stopping Power and Secondary Electron Emission 46

2.4 Summary 49

References 50

3 Multislice Method 53

3.1 Mathematical Treatment of the Multislice Method 56

3.1.1 Specimen Transmission Function 59

3.1.2 Fresnel Propagator Function 66

3.1.3 Objective Lens Contrast Transfer Function and Partial Coherence 71

3.1.4 Implementation of the Multislice Algorithm 76

3.2 Applications of Multislice Simulations 78

3.2.1 HREM Imaging and Electron Crystallography 78

3.2.2 CBED and STEM Applications: Frozen Phonon Model 87

3.3 Further Topics in Multislice Simulation 93

3.3.1 Accuracy of Multislice Algorithms 93

3.3.2 Is the Frozen Phonon Model Physically Realistic? 97

3.4 Summary 102

References 102

4 Bloch Waves 105

4.1 Basic Principles 106

4.1.1 Mathematical Background 106

4.1.2 Application to Two-Beam Theory 111

4.1.3 Phenomenological Modelling of Thermal Diffuse Scattering 116

4.1.4 Bloch States in Zone-Axis Orientations 124

4.2 Applications of Bloch Wave Theory 132

4.2.1 HREM Imaging 132

4.2.2 HAADF Imaging 134

4.2.3 Bloch Wave Scattering By Elastic Strain Fields 144

4.3 Further Topics in Bloch Waves 149

4.3.1 Dopant Atom Imaging in STEM 149

4.3.2 Electron Channelling and Its Uses 156

4.4 Summary 160

References 161

5 Single Electron Inelastic Scattering 165

5.1 Fundamentals of Inelastic Scattering 166

5.1.1 Electron Excitation in a Single Atom by a Plane Wave 166

5.1.2 Mixed Dynamic Form Factor 180

5.1.3 Yoshioka Equations and Inelastic Scattering within a Crystal 189

5.1.4 Coherence in Inelastic Scattering 195

5.2 Fine Structure of The Electron Energy Loss Signal 201

5.2.1 Origin of Fine Structure 201

5.2.2 Core Hole Effects 206

5.2.3 Magnetic Circular Dichroism 209

5.3 Summary 211

References 212

6 Electrodynamic Theory of Inelastic Scattering 215

6.1 Bulk and Surface Energy Loss 216

6.1.1 Energy Loss in an ‘Infinite‘ Solid 216

6.1.2 Phonon Spectroscopy 226

6.1.3 Interface and Surface Contributions 232

6.2 Radiative Phenomena 244

6.2.1 Cerenkov Radiation and Band Gap Measurement 244

6.2.2 Transition Radiation 249

6.3 Simulating Low Energy Loss EELS Spectra 253

6.3.1 Discrete Dipole Approximation (DDA) 253

6.3.2 Boundary Element Method (BEM) 254

6.4 Summary 259

References 259

Appendix A The First Born Approximation and Atom Scattering Factor 263

Appendix B Potential for an ‘Infinite’ Perfect Crystal 267

Appendix C The Transition Matrix Element in the One Electron Approximation 269

Appendix D Bulk Energy Loss in the Retarded Regime 271

Index 275