Theory of electron backscattering from crystals

S. L. Dudarev, Peter Rez, M. J. Whelan

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

The contrast in electron channeling patterns is quantitatively treated using a theory in which electrons in Bloch states excited by the incident electron are scattered through large angles by the fluctuation part of the potential (thermal diffuse scattering). The subsequent multiple elastic and inelastic scattering is described by an inhomogeneous transport equation. Formally this is shown to be identical to the solution of the kinetic equation for the one-particle spectral density matrix. Employing the supermatrix algorithm proposed by Fathers and Rez, we develop a computational technique which makes it possible to perform full-scale multiple scattering simulations of electron backscattering from crystals and to provide a consistent quantitative explanation of a number of experimental observations, including the dependence of the contrast on the detector position and on the energy of the backscattered electrons, the origin of which has not previously been fully accounted for. Our computational results show a substantial increase in the channeling contrast and in the signal-to-noise ratio for the conditions of oblique incidence and low takeoff angle of backscattering, which agrees with recent experimental studies. We show that under the conditions of multiple scattering there exists a perturbation expansion which considerably simplifies the problem of evaluation of the contrast and which can be employed for interpretation of channeling images of defects.

Original languageEnglish (US)
Pages (from-to)3397-3412
Number of pages16
JournalPhysical Review B
Volume51
Issue number6
DOIs
StatePublished - 1995

Fingerprint

Backscattering
backscattering
Multiple scattering
Crystals
Electrons
crystals
electrons
scattering
takeoff
Inelastic scattering
Elastic scattering
Spectral density
Takeoff
Excited states
kinetic equations
Signal to noise ratio
elastic scattering
inelastic scattering
signal to noise ratios
incidence

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

Theory of electron backscattering from crystals. / Dudarev, S. L.; Rez, Peter; Whelan, M. J.

In: Physical Review B, Vol. 51, No. 6, 1995, p. 3397-3412.

Research output: Contribution to journalArticle

Dudarev, S. L. ; Rez, Peter ; Whelan, M. J. / Theory of electron backscattering from crystals. In: Physical Review B. 1995 ; Vol. 51, No. 6. pp. 3397-3412.
@article{0259906acf6b42a3827f7d095dcfa973,
title = "Theory of electron backscattering from crystals",
abstract = "The contrast in electron channeling patterns is quantitatively treated using a theory in which electrons in Bloch states excited by the incident electron are scattered through large angles by the fluctuation part of the potential (thermal diffuse scattering). The subsequent multiple elastic and inelastic scattering is described by an inhomogeneous transport equation. Formally this is shown to be identical to the solution of the kinetic equation for the one-particle spectral density matrix. Employing the supermatrix algorithm proposed by Fathers and Rez, we develop a computational technique which makes it possible to perform full-scale multiple scattering simulations of electron backscattering from crystals and to provide a consistent quantitative explanation of a number of experimental observations, including the dependence of the contrast on the detector position and on the energy of the backscattered electrons, the origin of which has not previously been fully accounted for. Our computational results show a substantial increase in the channeling contrast and in the signal-to-noise ratio for the conditions of oblique incidence and low takeoff angle of backscattering, which agrees with recent experimental studies. We show that under the conditions of multiple scattering there exists a perturbation expansion which considerably simplifies the problem of evaluation of the contrast and which can be employed for interpretation of channeling images of defects.",
author = "Dudarev, {S. L.} and Peter Rez and Whelan, {M. J.}",
year = "1995",
doi = "10.1103/PhysRevB.51.3397",
language = "English (US)",
volume = "51",
pages = "3397--3412",
journal = "Physical Review B-Condensed Matter",
issn = "0163-1829",
publisher = "American Institute of Physics Publising LLC",
number = "6",

}

TY - JOUR

T1 - Theory of electron backscattering from crystals

AU - Dudarev, S. L.

AU - Rez, Peter

AU - Whelan, M. J.

PY - 1995

Y1 - 1995

N2 - The contrast in electron channeling patterns is quantitatively treated using a theory in which electrons in Bloch states excited by the incident electron are scattered through large angles by the fluctuation part of the potential (thermal diffuse scattering). The subsequent multiple elastic and inelastic scattering is described by an inhomogeneous transport equation. Formally this is shown to be identical to the solution of the kinetic equation for the one-particle spectral density matrix. Employing the supermatrix algorithm proposed by Fathers and Rez, we develop a computational technique which makes it possible to perform full-scale multiple scattering simulations of electron backscattering from crystals and to provide a consistent quantitative explanation of a number of experimental observations, including the dependence of the contrast on the detector position and on the energy of the backscattered electrons, the origin of which has not previously been fully accounted for. Our computational results show a substantial increase in the channeling contrast and in the signal-to-noise ratio for the conditions of oblique incidence and low takeoff angle of backscattering, which agrees with recent experimental studies. We show that under the conditions of multiple scattering there exists a perturbation expansion which considerably simplifies the problem of evaluation of the contrast and which can be employed for interpretation of channeling images of defects.

AB - The contrast in electron channeling patterns is quantitatively treated using a theory in which electrons in Bloch states excited by the incident electron are scattered through large angles by the fluctuation part of the potential (thermal diffuse scattering). The subsequent multiple elastic and inelastic scattering is described by an inhomogeneous transport equation. Formally this is shown to be identical to the solution of the kinetic equation for the one-particle spectral density matrix. Employing the supermatrix algorithm proposed by Fathers and Rez, we develop a computational technique which makes it possible to perform full-scale multiple scattering simulations of electron backscattering from crystals and to provide a consistent quantitative explanation of a number of experimental observations, including the dependence of the contrast on the detector position and on the energy of the backscattered electrons, the origin of which has not previously been fully accounted for. Our computational results show a substantial increase in the channeling contrast and in the signal-to-noise ratio for the conditions of oblique incidence and low takeoff angle of backscattering, which agrees with recent experimental studies. We show that under the conditions of multiple scattering there exists a perturbation expansion which considerably simplifies the problem of evaluation of the contrast and which can be employed for interpretation of channeling images of defects.

UR - http://www.scopus.com/inward/record.url?scp=0001588123&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001588123&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.51.3397

DO - 10.1103/PhysRevB.51.3397

M3 - Article

VL - 51

SP - 3397

EP - 3412

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 6

ER -