Electron-beam interactions with solids : application of the Monte Carlo method to electron scattering problems / M. Dapor.

Format:

Book

Author/Creator:

Dapor, Maurizio.

Series:

Springer tracts in modern physics ; 186.

Springer tracts in modern physics, 0081-3869 ; v. 186

Language:

English

Subjects (All):

Electrons--Scattering.

Monte Carlo method.

Physical Description:

x, 106 pages : 27 illustrations ; 25 cm.

Place of Publication:

Berlin ; New York : Springer, 2003.

Summary:

The interaction of electron beams with solid targets has been studied since the early part of the last century. Present interest is spurred on by the fundamental role played by the electron-solid interaction in -- among other areas -- scanning electron microscopy, electron-probe microanalysis and Auger electron spectroscopy. This book aims to investigate selected aspects of the interaction of electrons with matter (backscattering coefficient for bulk targets, absorption, backscattering and transmission for supported and unsupported thin films, implantation profiles, secondary electron emission and so on); to study the probabilistic laws of interaction of the individual electrons with the atoms (elastic and inelastic cross sections); to introduce the Monte Carlo method and its use for computing the macroscopic characteristics of the interaction processes. Each chapter compares theory, simulations and experimental data.

Contents:

1.1 Motivation 1

1.1.1 Backscattered Particles 2

1.1.2 Secondary Electrons 2

1.1.3 Depth Distribution of Trapped Particles 2

1.2 From the Dirac Equation to the Monte Carlo Simulation 3

2. The Spin of the Electron 5

2.1 The Spectrum of Angular Momentum 5

2.2 The Spin of the Electron 7

2.3 The Dirac Equation 9

2.4 The Solution for Free Particles 11

2.5 The Dirac Equation in a Central Potential 13

3. Elastic Scattering 17

3.1 The First Born Approximation 17

3.2 The Density Matrix and Spin Polarisation 22

3.3 Relativistic Partial-Wave Expansion 25

3.4 Calculation of the Phase Shifts 34

3.5 Exchange and Solid State Effects 37

3.6 Comparing Theory and Experimental Data 37

4. Inelastic Scattering 43

4.1 The Classical Theory 43

4.2 Dielectric Function and Stopping Power 45

4.3 Inelastic Mean Free Path 46

4.4 Positrons 47

4.5 Plasma Oscillations 47

4.6 Comparing Theory and Experimental Data 48

5. Electrons Impinging on Solid Targets 53

5.1 Backscattered Electrons 53

5.2 Electrons in thin films 56

5.2.1 Definitions, Symbols, Properties 56

5.2.2 Unsupported thin films 58

5.2.3 Supported thin films 59

5.3 Secondary Electrons 61

5.4 Comparing Theory and Experimental Data 65

6. Monte Carlo Simulations 69

6.1 The Monte Carlo Method 69

6.2 Random Variables 70

6.2.1 Random Variable Uniformly Distributed in the Interval (0, 1) 71

6.2.2 Random Variable Distributed in a Given Interval with a Given Probability 71

6.2.3 Random Variable Uniformly Distributed in the Interval (a, b) 72

6.2.4 Random Variable with Poisson Distribution 72

6.2.5 Pseudo-Random-Number Generators 73

6.3 A Simple Monte Carlo Scheme 73

6.4 A More Sophisticated Simulation 76

6.4.1 Surface Films 77

6.5 Another Monte Carlo Scheme 78

6.5.1 Angular Deflection in Electron-Electron Collisions 79

6.5.2 Secondary Electrons 80

6.6 Comparing Theory and Experimental Data 81

A. Matrices and Operators 91

A.1 Representation of Linear Operators 91

A.2 Matrix Transformations 91

A.3 Commuting Operators 93

B. The Dirac Notation 95

B.1 Ket and Bra Vectors 95

B.2 Continuous Spectrum 96

B.3 The Schrodinger Equation in the Dirac Notation 98

C. Special Functions 99

C.1 Legendre Polynomials and Associated Legendre Functions 99

C.2 Bessel Functions 100

C.3 The Spherical Harmonics 102.

Notes:

Includes bibliographical references and index.

ISBN:

3540006524

OCLC:

51817445