Multiple scattering theory for fast electrons in single crystals and Kikuchi patterns

Dudarev, S. L.; Ryazanov, M. I.

doi:10.1107/s0108767387008389

Cited by 10 publications

(2 citation statements)

References 23 publications

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“…In the case of non-crystalline targets this equation can be reduced to a Boltzmann type equation. Until recently no solution has been found to these equations except for the high energy limit [16].…”

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New developments in theory of fast electron scattering in solids: Applications to microbeam analysis

Tilinin

Werner

1994

Mikrochim Acta

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Abstract. The study of fast electron interaction with solids in the energy range from 100 eV to several tens of keV is prompted by quickly developing microbeam analysis techniques such as electron probe microanalysis, scanning electron microscopy, electron energy loss spectroscopy and so on. It turned out that for random solids the electron transport problem might be solved on the basis of the generalized radiative field similarity principle. The latter states that the exact differential elastic cross section in the kinetic equation may be replaced by an approximate one provided the conditions of radiative field similarity are fulfilled. Application of the generalized similarity principle to electron scattering in solids has revealed many interesting features of electron transport. Easy to use and effective formulae have been obtained for the angular and energy distribution of electrons leaving a target, total yields of characteristic photons and slow electrons escaping from a sample bombarded by fast primaries, escape probability of Auger electrons as a function of depth etc. The analytical results have been compared with Monte Carlo calculations and experiments in a broad range of electron energies and scattering properties of solids and good agreement has been observed.Key words: quantitative electron microbeam analysis, Boltzmann equation, transport approximation, electron scattering.The study of fast electron interaction with solids in the energy range from about 100 eV to several tens of keV is important from both fundamental and practical points of view. The practical relevance is prompted, in particular, by quickly developing microbeam analysis techniques based on electron bombardment of a target and subsequent measurement of angular and energy distributions of secondary electrons or photons. For example the inelastic backscattering of electrons plays a crucial role in the interpretation of contrast in scanning electron microscopy

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New developments in theory of fast electron scattering in solids: Applications to microbeam analysis

Tilinin

Werner

1994

Mikrochim Acta

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“…The fundamental characteristics of the density matrix were described by Blum (1981). The one-particle density matrix was first applied by Dudarev and Ryazanov (1988) to describe multiple inelastic electron scattering. We now outline the basis scheme of this theory.…”

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Elastic and Inelastic Scattering in Electron Diffraction and Imaging

Wang

1995

143

101

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All rights reservedNo part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher Preface Elastic and inelastic scattering in transmission electron microscopy (TEM) are important research subjects. For a long time, I have wished to systematically summarize various dynamic theories associated with quantitative electron microscopy and their applications in simulations of electron diffraction patterns and images. This wish now becomes reality. The aim of this book is to explore the physics in electron diffraction and imaging and related applications for materials characterizations. Particular emphasis is placed on diffraction and imaging of inelastically scattered electrons, which, I believe, have not been discussed extensively in existing books. This book assumes that readers have some preknowledge of electron microscopy, electron diffraction, and quantum mechanics. I anticipate that this book will be a guide to approaching phenomena observed in electron microscopy from the prospects of diffraction physics.The SI units are employed throughout the book except for angstrom (A), which is used occasionally for convenience. To reduce the number of symbols used, the Fourier transform of a real-space function P'(r), for example, is denoted by the same symbol P'(u) in reciprocal space except that r is replaced by u. Upper and lower limits of an integral in the book are (-co, co) unless otherwise specified. The (-co, co) integral limits are usually omitted in a mathematical expression for simplification. I very much appreciate opportunity of working with Drs. J. M. Cowley and J. , who have kindly allowed me to use their illustrations and results in the text. v vi Preface This book was written in my spare time after working hours. I am heartily grateful to my wife, Cui Xia Yuan, for her encouragement and understanding. This book would have been impossible without her support.Zhong Lin Wang • New imaging techniques using inelastically scattered electrons: In recent years, great interest has developed in structural determination using inelastically scattered electrons. High-angle annular dark-field imaging in STEM, for example, is based on the signal of high-angle phonon-scattered electrons. This imaging technique may provide atomic-number-sensitive structural information with a resolution superior to conventional bright-field imaging.operator Volume of an atom Dynamic scattering operator xxvi <> <>E J(z,Eo -Lili) LT IE fs(u) e p(r, r', E) s(r, r, flw) Symbols and Definitions Time average Average over system energy Energy distribution function of plural inelastically scattered electrons Laplace transform Energy distribution function of single-loss electrons Angular distribution function of single-loss electrons Three-dimensional solid angle One-particle density matrix Energy-dependent mixed dynamic form factor Sign Conventions Free-space plane wave exp (2n...

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Incident beam diffraction effects in Auger electron emission from crystal surfaces

1990

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Multiple scattering theory for fast electrons in single crystals and Kikuchi patterns

Cited by 10 publications

References 23 publications

New developments in theory of fast electron scattering in solids: Applications to microbeam analysis

New developments in theory of fast electron scattering in solids: Applications to microbeam analysis

Elastic and Inelastic Scattering in Electron Diffraction and Imaging

Incident beam diffraction effects in Auger electron emission from crystal surfaces

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