Current flow in reflection electron microscopy and RHEED

Marks, Laurence D.; Ma, Y.

doi:10.1107/s0108767387011243

Cited by 14 publications

(8 citation statements)

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“…To match waves at the boundary, tangential components of wave vectors satisfy However it has been pointed out by Marks and Ma (1988) that problems are encountered when the absorption effect is considered. In this case, the electron wave vector has an imaginary component, so that the exp[21li(Kz + gz + vi)D] factor damps very quickly, especially for a large slab thickness D. Thus Eqs.…”

Section: Bloch Wave Theorymentioning

confidence: 99%

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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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Section: Bloch Wave Theorymentioning

confidence: 99%

“…The so-called evanescent wave is thus generated, and it propagates in a direction parallel or nearly parallel to the surface. An alternative method for finding a unique solution is to use the energy flow concept (Ma and Marks, 1989;Marks and Ma, 1988), which follows.…”

Section: Bloch Wave Theorymentioning

confidence: 99%

Elastic and Inelastic Scattering in Electron Diffraction and Imaging

Wang

1995

143

101

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“…Provided that the second surface is well separated from the first and that the crystal is absorbing this method will be perfectly valid. The second method, which has been briefly described in an earlier note (Marks & Ma, 1988a), is to use the current flow to obtain n boundary conditions. (We can use current Without absorption Eigenvalues Current flow 1 ( 0.733, 0"000) 0'381 2 (-0'733, 0"000) -0"382 3 ( 0"599, 0"000) 0"264 4 (-0"599, 0"000) -0"275 5 ( 0"354, 0"149) 0"000 6 ( 0"354,-0"149) 0"000 7 (-0"354, 0'149) 0"000 8 ( 0"245, 0"097) 0"000 9 ( 0.245, -0.097) 0.000 10 (-0.354,-0-149) 0"000 11 (-0"245, 0"097) 0"000 12 (-0"245,-0"097) 0"000 13 ( 0"000, 0-149) 0.000 14 ( 0"115, 0"054) 0.000 15 ( 0"000,-0"149) 0"000 16 ( 0'115, -0"054) 0"000 17 (-0"115, 0"054) 0"000 18 (-0"115,-0"054) 0"000 Table 1 The strongly excited evanescent waves outside the surface should be noted.…”

Section: Ke#o)mentioning

confidence: 99%

Bloch-wave solution in the Bragg case

Ma¹,

Marks

1989

Acta Cryst Sect A

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NEW SURFACE PATCHES FOR MINIMAL BALANCE SURFACES. II b ]/ 2, [ a + b ]/ 2, c/2).These four surfaces are mapped onto another, for example, by the symmetry operations listed in Table 1. The genus is 9 for MC6 as well as for MC7 surfaces. Minimal surfaces oMC5 (double catenoids)Rectangular nets 44 of twofold axes (case 26) are defined by orthorhombic group-subgroup pairs of 33 types. Only 12 of them are compatible with catenoidlike surface patches and with the respective minimal balance surfaces oP, a family of orthorhombically distorted P surfaces. Common properties of MC surfacesFor all minimal balance surfaces built up from multiple catenoids two layers of such catenoids exist per c-translation period. AbstractThe Bloch-wave method for reflection diffraction problems, primarily electron diffraction as in reflection high-energy electron diffraction (RHEED) and reflection electron microscopy (REM), is developed.0108-7673/89/020174-09503.00The basic Bloch-wave approach for surfaces is reviewed, introducing the current flow concept which plays a major role both in understanding reflection diffraction and determining the allowed Bloch waves. This is followed by a brief description of the numeri- A number of other Bloch-wave phenomena are also discussed, namely resonance diffraction and its relationship to internal and external reflection and variations in the boundary conditions and Blochwave character, splitting of diffraction spots due to stepped surfaces, which can be completely explained, and the reflection equivalent of thickness fringes.

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“…To avoid the problem of determining excited wave points, they considered the crystal as a slab which had a finite thickness. Very recently, we introduced the argument of current flow for the reflection case (Marks & Ma, 1988;Ma & Marks, 1989) and cleared up the confusion around the wave points in the band gap (evanescent wave) and the wave points which are not excited in the crystal and were able to solve the general n-beam problem.…”

Section: Introductionmentioning

confidence: 99%

Bloch waves and multislice in transmission and reflection diffraction

Ma¹,

Marks²

1990

Acta Cryst Sect A

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The consistency between Bloch-wave and multislice approaches to calculating high-energy electron diffraction is investigated in both transmission and reflection cases, the emphasis being upon the latter. It is first shown, in more detail than previously published, that in transmission the two yield identical results. Next, the Bloch-wave approach for reflection is shown to yield a stationary solution in multislice, except for a small effect from the surface truncation. It is pointed out that the multislice approach can be exploited to solve exactly for the reflected wave for an arbitrary surface potential by using it as a Picard iteration solution of the Schr6dinger equation. The surface potential scattering is not incidence-angle related and is not significant as might be expected. The introduction of absorption improves the consistency between the two methods. Finally, the stationary solutions are compared with solutions obtained using a top-hat incident wave. The latter approach leads to partially stationary solutions, although it is very hard to identify these.

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Current flow in reflection electron microscopy and RHEED

Cited by 14 publications

References 1 publication

Elastic and Inelastic Scattering in Electron Diffraction and Imaging

Elastic and Inelastic Scattering in Electron Diffraction and Imaging

Bloch-wave solution in the Bragg case

Bloch waves and multislice in transmission and reflection diffraction

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