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Electron-Beam Interactions with Solids : Application of the Monte Carlo Method to Electron Scattering Problems - Maurizio Dapor

Electron-Beam Interactions with Solids

Application of the Monte Carlo Method to Electron Scattering Problems

Hardcover

Published: 23rd April 2003
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The interaction of an electron beam with a solid target has been studied since the early part of the past century. Since 1960, the electron-solid interaction hasbecomethesubjectofanumberofinvestigators'workowingtoitsfun- mental role in scanning electron microscopy, in electron-probe microanalysis, in Auger electron spectroscopy, in electron-beam lithography and in radiation damage. The interaction of an electron beam with a solid target has often been investigated theoretically by using the Monte Carlo method, a nume- cal procedure involving random numbers that is able to solve mathematical problems. This method is very useful for the study of electron penetration in matter. The probabilistic laws of the interaction of an individual electron with the atoms constituting the target are well known. Consequently, it is possible to compute the macroscopic characteristics of interaction processes by simulating a large number of real trajectories, and then averaging them. The aim of this book is to study the probabilistic laws of the interaction of individual electrons with atoms (elastic and inelastic cross-sections); to - vestigate selected aspects of electron interaction with matter (backscattering coe?cients for bulk targets, absorption, backscattering and transmission for both supported and unsupported thin ?lms, implantation pro?les, seconda- electron emission, and so on); and to introduce the Monte Carlo method and its applications to compute the macroscopic characteristics of the inter- tion processes mentioned above. The book compares theory, computational simulations and experimental data in order to o?er a more global vision.

Introductionp. 1
Motivationp. 1
Backscattered Particlesp. 2
Secondary Electronsp. 2
Depth Distribution of Trapped Particlesp. 2
From the Dirac Equation to the Monte Carlo Simulationp. 3
Referencesp. 4
The Spin of the Electronp. 5
The Spectrum of Angular Momentump. 5
The Spin of the Electronp. 7
The Dirac Equationp. 9
The Solution for Free Particlesp. 11
The Dirac Equation in a Central Potentialp. 13
Referencesp. 16
Elastic Scatteringp. 17
The First Born Approximationp. 17
The Density Matrix and Spin Polarisationp. 22
Relativistic Partial-Wave Expansionp. 25
Calculation of the Phase Shiftsp. 34
Exchange and Solid State Effectsp. 37
Comparing Theory and Experimental Datap. 37
Referencesp. 41
Inelastic Scatteringp. 43
The Classical Theoryp. 43
Dielectric Function and Stopping Powerp. 45
Inelastic Mean Free Pathp. 46
Positronsp. 47
Plasma Oscillationsp. 47
Comparing Theory and Experimental Datap. 48
Referencesp. 52
Electrons Impinging on Solid Targetsp. 53
Backscattered Electronsp. 53
Electrons in thin filmsp. 56
Definitions, Symbols, Propertiesp. 56
Unsupported thin filmsp. 58
Supported thin filmsp. 59
Secondary Electronsp. 61
Comparing Theory and Experimental Datap. 65
Referencesp. 68
Monte Carlo Simulationsp. 69
The Monte Carlo Methodp. 69
Random Variablesp. 70
Random Variable Uniformly Distributed in the Interval (0, 1)p. 71
Random Variable Distributed in a Given Interval with a Given Probabilityp. 71
Random Variable Uniformly Distributed in the Interval (a, b)p. 72
Random Variable with Poisson Distributionp. 72
Pseudo-Random-Number Generatorsp. 73
A Simple Monte Carlo Schemep. 73
A More Sophisticated Simulationp. 76
Surface Filmsp. 77
Another Monte Carlo Schemep. 78
Angular Deflection in Electron-Electron Collisionsp. 79
Secondary Electronsp. 80
Comparing Theory and Experimental Datap. 81
Referencesp. 90
Matrices and Operatorsp. 91
Representation of Linear Operatorsp. 91
Matrix Transformationsp. 91
Commuting Operatorsp. 93
The Dirac Notationp. 95
Ket and Bra Vectorsp. 95
Continuous Spectrump. 96
The Schrodinger Equation in the Dirac Notationp. 98
Special Functionsp. 99
Legendre Polynomials and Associated Legendre Functionsp. 99
Bessel Functionsp. 100
The Spherical Harmonicsp. 102
Indexp. 105
Table of Contents provided by Rittenhouse. All Rights Reserved.

ISBN: 9783540006527
ISBN-10: 3540006524
Series: Springer Tracts in Modern Physics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 110
Published: 23rd April 2003
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.6 x 15.6  x 0.76
Weight (kg): 0.78