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Contents

1 Introduction

2 The binary collision

2.1 Fundamentals

2.1.1 Scattering by a central force field

2.1.2 Inelastic scattering

2.1.3 The two-body scattering problem

2.1.4 Velocity components and energy transfer

2.1.5 Determination of the scattering angle and the time integrals

2.1.6 Cross-sections

2.1.7 Potentials used in binary collision calculations

2.2 Applications

2.2.1 Rutherford scattering

2.2.2 Surface spectroscopy using shadow cones

2.2.3 Projectile stopping

2.3 Conclusion

3 Interatomic potentials

3.1 General principles

3.1.1 Ab initio potentials

3.2 The repulsive wall potential

3.2.1 The screened Coulomb potential for the isolated atom

3.2.2 Two-body screened Coulomb potentials

3.3 The attractive well potential

3.3.1 The Lennard-Jones potential

3.3.2 The Morse potential

3.3.3 Ionic potentials

3.3.4 Lattice sums for ionic potentials

3.3.5 Many-body empirical potentials

3.3.6 Fitting procedures

3.3.7 The Finnis-Sinclair method and the embedded atom method for metals

3.3.8 Covalent materials

3.4 The overlap potential

3.5 Conclusion

4 Electronic energy loss models

4.2 Electronic stopping for low energies

4.2.1 Firsov's semi-classical model (local)

4.2.2 Lindhard and Scharff electronic stopping (non-local)

4.2.3 Oen and Robinson electronic stopping

4.3 Z\ oscillations in the electronic stopping

4.4 Z2 oscillations in the electronic stopping

4.5 Electronic stopping for high-energy ions

4.6 Ion-electron interaction with regard to MD simulations

4.7 Summary

4.1 Introduction

5 Transport models

5.1 The Boltzmann transport equation

5.1.1 Introduction

5.1.2 The forward transport equation

5.1.3 The backward transport equation

5.1.4 The time-independent Boltzmann equation

5.1.5 Remarks

5.2 Ion penetration

5.2.1 The energy loss distribution

5.2.2 Range distribution: small deflections

5.2.3 Range distribution: the general case

5.2.4 High energy

5.2.5 Numerical solution

5.3 Effects upon the target

5.3.1 Introduction

5.3.2 The transport equation: the recoil term

5.3.3 Deposited energy distribution: equal mass cases

5.3.4 Deposited energy distribution: non-equal mass cases

5.3.5 The distribution of displaced atoms

5.4 Sputtering

5.5 Mixing

5.5.1 Introduction

5.5.2 Modelling ion-beam atomic mixing

5.5.3 The diffusion approximation

5.5.4 A mixing example

5.6 Conclusion

6 The rest distribution of primary ions in amorphous targets

6.1 Introduction

6.2 Ion-solid interaction

6.3 A random solid

6.4 MC simulation

6.4.1 Non-uniform random variables

6.4.2 Algorithms

6.5 Transport equations

6.5.1 Derivation of a Lindhard-type TE

6.5.2 Moments solution of a plane source TE

6.5.3 TEs using the gas and liquid target models

6.5.4 Numerical solution of Lindhard-type TEs

6.5.5 Coupling relations

6.5.6 Implementation

6.6 Spatial moments of implantation profiles

6.6.1 Projections

6.6.2 Moments about the origin

6.6.3 Vertical moments about (z)

6.6.4 Lateral moments

6.6.5 Mixed moments

6.7 Generating profiles in one and two dimensions

6.7.1 The Pearson family of frequency curves

6.8 Models for depth-dependent lateral moments

6.9 Comparison of TE and MC computer codes

6.9.1 Moments

6.9.2 1-D profiles

6.9.3 2-D profiles

6.10 Additional remarks

7 Binary collision algorithms

7.1 Introduction

7.2 Collisions

7.3 Event store models

7.4 The genealogy of a binary collision program

7.4.1 Next event algorithms

7.4.2 Event ordering

7.4.3 Non-linear events

7.4.4 Multiple collisions

7.4.5 Incident ion distributions

7.4.6 Full cascade models

7.4.7 Random materials - Monte Carlo models

7.4.8 Input parameters

7.4.9 Single-crystal materials - deterministic models

7.5 Dynamic models

7.5.1 Dose effects

7.5.2 Annealing effects

7.6 Applications

7.6.1 Ion scattering spectroscopy

7.6.2 Sputtering

7.6.3 Trajectories and displaced particles

7.7 Conclusions

8 Molecular dynamics

8.1 Equations of motion

8.2 Numerical integration algorithms

8.2.1 Hamiltonian systems

8.2.2 Constraint dynamics

8.2.3 Numerical integration algorithms for non-Hamiltonian systems

8.3 Neighbour lists for short-ranged potentials

8.4 Construction of the neighbour lists

8.5 The cell index method

8.6 Timestep control

8.7 The moving atom approximation

8.8 Boundary conditions

8.8.1 Constant temperature-constant pressure molecular dynamics

8.9 Electronic energy losses in MD

8.10 Lattice generation

8.11 Lattice vibrations

8.12 Ensembles of trajectories

8.13 Applications of molecular dynamics to surface phenomena

8.13.1 Angular distributions of ejected particles

8.13.2 The depth of origin of ejected particles

8.13.3 Ejected atom energy distributions

8.13.4 Atoms per single ion (ASI) distributions

8.13.5 Yield variation with incidence angle: impact collision SIMS

8.13.6 Cluster ejection

8.13.7 Cluster beams

8.13.8 Radiation damage in metals

8.13.9 Radiation damage in semiconductors

8.13.10 Ion implantation

8.13.11 Ion scattering and surface skipping motion

8.13.12 Crystal growth

8.14 Conclusion

9 Surface topography

9.1 Introduction

9.2 Cellular models of deposition and erosion

9.3 Continuum models of deposition and erosion

9.3.1 Isotropic erosion and deposition

9.3.2 Non-isotropic erosion

9.4 Re-deposition

9.5 Other secondary effects

9.6 Conclusion

Index