Transport of Energetic Electrons in Solids: Computer Simulation With Applications to Materials Analysis and Characterization

Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Acknowledgements
Contents
1 Electron Transport in Solids
	1.1 Motivation: Why Are Electrons Important
	1.2 The Monte Carlo Method
	1.3 The Monte Carlo Ingredients
	1.4 Electron-Beam Interactions with Solids
	1.5 Electron Energy-Loss Peaks
	1.6 Auger Electron Peaks
	1.7 Secondary Electron Peak
	1.8 Characterization of Materials
	1.9 Summary
	References
2 Computational Minimum
	2.1 Numerical Differentiation
	2.2 Numerical Quadrature
		2.2.1 Trapezoidal Rule, Simpson\'s Rule, Bode\'s Rule
		2.2.2 Gaussian Quadrature
	2.3 Ordinary Differential Equations
	2.4 Special Functions of Mathematical Physics
		2.4.1 Legendre Polynomials and Associated Legendre Functions
		2.4.2 Bessel Functions
	2.5 Summary
	References
3 Cross-Sections. Basic Aspects
	3.1 Cross-Section and Probability of Scattering
	3.2 Stopping Power and Inelastic Mean Free Path
	3.3 Range
	3.4 Energy Straggling
	3.5 Summary
	References
4 Scattering Mechanisms
	4.1 Elastic Scattering
		4.1.1 Mott Cross-Section Versus Screened Rutherford Cross-Section
		4.1.2 Polarized Electron Beams Elastically Scattered by Atoms
		4.1.3 Electron-Molecule Elastic Scattering
	4.2 Quasi-elastic Scattering
		4.2.1 Electron-Phonon Interaction
	4.3 Inelastic Scattering
		4.3.1 Stopping: Bethe-Bloch Formula
		4.3.2 Stopping: Semi-empiric Formulas
		4.3.3 Dielectric Theory
		4.3.4 Sum of Drude Functions
		4.3.5 The Mermin Theory
		4.3.6 Exchange Effects
		4.3.7 Polaronic Effect
	4.4 Surface Phenomena
	4.5 Summary
	References
5 Random Numbers
	5.1 Generating Pseudo-random Numbers
	5.2 Testing Pseudo-random Number Generators
	5.3 Pseudo-random Numbers Distributed According  to a Given Probability Density
	5.4 Pseudo-random Numbers Uniformly Distributed  in the Interval [a, b]
	5.5 Pseudo-random Numbers Distributed According  to the Exponential Density of Probability
	5.6 Pseudo-random Numbers Distributed According ...
	5.7 Summary
	References
6 Monte Carlo Strategies
	6.1 The Continuous-Slowing-Down Approximation
		6.1.1 The Step-Length
		6.1.2 Interface Between Over-Layer and Substrate
		6.1.3 The Polar Scattering Angle
		6.1.4 Direction of the Electron After the Last Deflection
		6.1.5 Electron Position in Three Dimensional Cartesian Coordinates
		6.1.6 The Energy Loss
		6.1.7 End of the Trajectory and Number of Trajectories
	6.2 The Energy-Straggling Strategy
		6.2.1 The Step-Length
		6.2.2 Elastic and Inelastic Scattering
		6.2.3 Energy Loss
		6.2.4 Electron-Atom Collisions: Scattering Angle
		6.2.5 Electron–Electron Collisions: Scattering Angle
		6.2.6 Electron-Phonon Collisions: Scattering Angle
		6.2.7 Direction of the Electron After the Last Deflection
		6.2.8 The First Step
		6.2.9 Transmission Coefficient
		6.2.10 How Inelastic Scattering Depends on the Distance from the Surface
		6.2.11 End of the Trajectory and Number of Trajectories
	6.3 Summary
	References
7 Electron Beam Interactions with Solid Targets and Thin Films. Basic Aspects
	7.1 Definitions, Symbols, Properties
	7.2 Unsupported Thin Films
	7.3 Supported Thin Films
	7.4 Summary
	References
8 Backscattering Coefficient
	8.1 Electrons Backscattered from Bulk Targets
		8.1.1 The Backscattering Coefficient: An Analytical Model
		8.1.2 The Backscattering Coefficient: Monte Carlo Simulation
	8.2 Electrons Backscattered from One Layer Deposited  on Semi-infinite Substrates
		8.2.1 Carbon Overlayers
		8.2.2 Gold Overlayers
	8.3 Electrons Backscattered from Two Layers Deposited  on Semi-infinite Substrates
	8.4 A Comparative Study of Electron and Positron Backscattering Coefficients
	8.5 Summary
	References
9 Secondary Electron Yield
	9.1 Secondary Electron Emission
	9.2 Monte Carlo Approaches to the Study of Secondary Electron Emission
	9.3 Specific MC Methodologies for SE Studies
		9.3.1 Continuous-Slowing-Down Approximation  (CSDA Scheme)
		9.3.2 Energy-Straggling (ES Scheme)
	9.4 Secondary Electron Yield: PMMA and Al2O3
		9.4.1 Secondary Electron Emission Yield as a Function  of the Energy
		9.4.2 Comparison Between ES Scheme and Experiment
		9.4.3 Comparison Between CSDA Scheme and Experiment
		9.4.4 CPU Time
	9.5 Summary
	References
10 Electron Energy Distributions
	10.1 Monte Carlo Simulation of the Spectrum
	10.2 Plasmon Losses and Electron Energy Loss Spectroscopy
		10.2.1 Plasmon Losses in Graphite
		10.2.2 Plasmon Losses in Silicon Dioxide
	10.3 Energy Losses of Auger Electrons
	10.4 Elastic Peak Electron Spectroscopy (EPES)
	10.5 Spectrum of Secondary Electrons
		10.5.1 Wolff Theory
		10.5.2 Other Formulas Describing the Spectrum  of the Secondary Electrons
		10.5.3 Initial Polar and Azimuth Angle of the Secondary Electrons
		10.5.4 Comparison with Theoretical and Experimental Data
	10.6 Summary
	References
11 Applications
	11.1 Linewidth Measurement in Critical Dimension SEM
		11.1.1 Critical Dimension SEM
		11.1.2 Lateral and Depth Distributions
		11.1.3 Linescan of a Silicon Step
		11.1.4 Linescan of PMMA Lines on a Silicon Substrate
	11.2 Application to Energy Selective Scanning Electron Microscopy
		11.2.1 Doping Contrast
		11.2.2 Energy Selective Scanning Electron Microscopy
	11.3 Energy Density Radially Deposited Along Ion Tracks
		11.3.1 Ion Track Simulation and Bragg Peak
		11.3.2 Damage in the Biomolecules by Dissociative  Electron Attachment
		11.3.3 Simulation of Electron Transport and Further Generation
		11.3.4 Radial Distribution of the Energy Deposited in PMMA by Secondary Electrons Generated by Energetic Proton Beams
	11.4 Summary
	References
Appendix A The First Born Approximation and the Rutherford Cross-Section
A.1 The Elastic Scattering Cross-Section
A.2 The First Born Approximation
A.3 Integral-Equation Approach
A.4 The Rutherford Formula
A.5 Summary
Appendix B The Mott Theory
B.1 The Dirac Equation in a Central Potential
B.2 Relativistic Partial Wave Expansion Method
B.3 Phase Shift Calculations
B.4 Analytic Approximation of the Mott Cross-Section
B.5 The Atomic Potential
B.5.1 Electron Exchange
B.5.2 Charge Cloud Polarization Effects
B.5.3 Solid-State Effects
B.6 Positron Differential Elastic Scattering Cross-Section
B.7 Summary
Appendix C The Fröhlich Theory
C.1 Electrons in Lattice Fields. Interaction Hamiltonian
C.2 Electron-Phonon Scattering Cross-Section
C.3 Summary
Appendix D The Ritchie Theory
D.1 Energy Loss and Dielectric Function
D.2 Homogeneous and Isotropic Solids
D.3 Summary
Appendix E The Chen and Kwei and the Li et al. Theory
E.1 Outgoing and Incoming Electrons
E.2 Probability of Inelastic Scattering
E.3 Summary
Appendix F The Mermin Theory and the Generalized Oscillator Strength Method
F.1 The Mermin Theory
F.2 The Mermin Energy Loss Function-Generalized Oscillator Strength Method (MELF-GOS)
F.3 Summary
Appendix G The Kramers–Kronig Relations and the Sum Rules
G.1 Linear Response to External Perturbations
G.2 The Kramers–Kronig Relations
G.3 Sum Rules
G.4 Summary
Appendix H From the Electron Energy Loss Spectrum to the Dielectric Function
H.1 From the Single-Scattering Spectrum to the Energy Loss Function
H.2 Summary
Index