Advanced Computing in Electron Microscopy

249 Pages·1998·7.214 MB·English

by  Earl J. Kirkland (auth.)

Advanced Computing
in Electron Microscopy
Advanced Computing
in Electron Microscopy
Earl J. Kirkland
Cornell University
Ithaca, New York
Springer Science+Business Media, LLC
Llbrary of Congress Саtаlоg1пg-lп-РubJlсаtlоп Data
Klrkland. Earl J.
Advanced computlng 1п electron mlcroscopy I Earl J. Klrkland.
р. ст.
Includes bIbllographlcal references and Index.
ISBN 978-1-4757-4408-8 ISBN 978-1-4757-4406-4 (eBook)
DOI 10.1007/978-1-4757-4406-4
1. Electron mlcroscopy--Computer simulatlon. 1. T1tle.
ОН212.Е4К535 1998 98-36299
CIP
Additional material to this book сап Ье downloaded from http://extras.springer.com
AII files оп this CD-ROM аге covered Ьу the following statement:
Copyright © 1998 Ьу Еагl J. Кirkland.
The computer code and ог data in this filе is pгovided for demonstration purposes only with по guarantee
ог warranty of апу kind that it is correct ог pгoduces correct results. Ву using the code and ог data in
this fjle the user agrees to accept all risks and liabilities associated with the code and ог data. The
computer code and ог data in this file тау Ье copied (and used) for noncommercial academic ог research
purposes only, pгovided that this notice is included. This file ог апу portion of it тау not Ье resold,
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The files аге organized into the following directories: [1 J win32exe; [2] тасРРС; [3] mfiles; [4] csource.
For details оп using the CD-ROM, please refer to Chapter 8.
For further information, contact the author via e-mail at [email protected].
ISBN 978-1-4757-4408-8
© Springer Science+Business Media New York 1998
Originally published Ьу Plenum Press, New York 1998
http://www.plenum.com
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Preface
Image simulation has become a common tool in HREM (High Resolution Electron
Microscopy) in recent years. However, the literature on the subject is scattered among
many different journals and conference proceedings that have occurred in the last two
or three decades. It is difficult for beginners to get started in this field. The principle
method of image simulation has come to be known as simply the multislice method.
This book attempts to bring the diverse information on image simulation together
into one place and to provide a background on how to use the multislice method
to simulate high resolution images in both conventional and scanning transmission
electron microscopy. The main goals of image simulation include understanding the
microscope and interpreting high resolution information in the recorded micrographs.
This book contains sections on the theory of image formation and simulation as well as
a more practical introduction on how to use the multislice method on real specimens.
Also included with this book is a CD-ROM with working programs to perform image
simulation. The source code as well as the executable code for IBM-PC and Apple
Macintosh computers is included. Although the programs may not have a very elegant
user interface by today's standards (simple command line dialog), the source code
should be very portable to a variety of different computers. It has been compiled and
run on Mac's, PC's and several different types of UNIX computers.
This book is intended to be at the level of first year graduate students or advanced
undergraduates in physics or engineering with an interest in electron microscopy. It
assumes a familiarity with quantum mechanics, Fourier transforms and diffraction,
some simple optics and basic computer skills (although not necessarily programming
skills) at the advanced undergraduate level. Prior experience with electron microscopy
is also helpful. The material covered should be useful to students learning the material
for the first time as well as to experienced researchers in the field. The programs
provided on the CD can be used as a black-box without understanding the underlying
programs (with a primary goal of understanding the transmission electron microscope
image) or the source code can be used to understand how to write your own version
of the simulation programs.
Although an effort was made to include references to most of the appropriate pub
lications on this subject, there are undoubtedly some that were omitted. I apologize
in advance for leaving out some undoubtedly outstanding references. I also apologize
for the as yet undiscovered errors that remain in the text.
I wish to acknowledge the support of various funding agencies (principly DOE, NSF
and NIH) that have supported my research efforts over the past several decades. My
v
PREFACE
VI
research experience has substantially contributed to my understanding of the material
covered in this book.
I also wish to thank Dr. David A. Muller and Dr. Richard R. Vanfleet for providing
many helpful suggestions and help in proof reading the manuscript and to thank Dr.
M. A. O'Keefe for providing helpful comments on electron microscopy and image
simulation.
Contents
Preface v
1 Introduction 1
2 The Transmission Electron Microscope 5
2.1 Introduction ........... . 5
2.2 Modeling the Electron Microscope 7
2.3 Relativistic Electrons. 9
2.4 Aberrations .. . 12
2.5 Reciprocity .. . 14
2.6 Further Reading 17
3 Linear Image Approximations 19
3.1 The Weak Phase Object in Bright Field 20
3.2 Partial Coherence in BF-CTEM ..... 24
3.3 Incoherent Imaging of Thin Specimens (CTEM) . 29
3.4 Annular Dark Field STEM ........ . 33
4 Sampling and the Fast Fourier Transform 41
4.1 Sampling .............. . 41
4.2 Discrete Fourier Transform ...... . 45
4.3 The Fast Fourier Transform or FFT .. 46
4.4 Wrap Around Error and Rearrangement 48
4.5 Fourier Transforming Real Valued Data 50
4.6 Displaying Diffraction Patterns 51
4.7 Further Reading ......... . 51
4.8 An FFT Subroutine in C .... . 53
4.9 An FFT Subroutine in FORTRAN 56
5 Simulating Images of Thin Specimens 63
5.1 The Weak Phase Object ..... . 63
5.2 Single Atom Properties ..... . 66
5.2.1 Radial Charge Distribution 67
5.2.2 Potential ...... . 67
VB
viii CONTENTS
5.2.3 Atomic Size . . . . 70
5.2.4 Scattering Factors 70
5.3 Total Specimen Potential 73
5.4 BF Phase Contrast Image Calculation 76
5.4.1 Single Atom Images . . . . . . 78
5.4.2 Thin Specimen Images. . . . . 81
5.4.3 Partial Coherence and the Transmission Cross Coefficient 84
5.5 ADF STEM Images of Thin Specimens. 89
5.5.1 Single Atom Images . . . . 92
5.5.2 Thin Specimen Images. . . 94
5.6 Summary of Sampling Suggestions 94
6 Simulating Images of Thick Specimens 99
6.1 The Wave Equation for Fast Electrons 101
6.2 A Bloch Wave Solution ...... . 104
6.3 The Multislice Solution ...... . 106
6.3.1 A Formal Operator Solution. 106
6.3.2 A Finite Difference Solution . 109
6.3.3 Free Space Propagation . . 110
6.4 Multislice Interpretation . . . . . . 111
6.5 The Multislice Method and FFT's 113
6.6 Slicing the Specimen . . 114
6.7 Aliasing and Bandwidth . 118
6.8 Interfaces and Defects . . 121
6.9 Multislice Implementation 122
6.9.1 The Propagator Function and Specimen Tilt 123
6.9.2 Convergence Tests ....... . 125
6.9.3 Partial Coherence in BF-CTEM 127
6.10 More Accurate Slice Methods .. . 128
6.10.1 Operator Solutions .... . 128
6.10.2 Finite Difference Solutions. 129
7 Multislice Applications and Examples 133
7.1 Gallium Arsenide ....... . 133
7.1.1 BF-CTEM Simulation. 134
7.1.2 ADF-STEM Simulation 138
7.2 Silicon Nitride ......... . 140
7.3 CBED Simulations ...... . 144
7.4 Thermal Vibrations of the Atoms in the Specimen 150
7.5 Quantitative Image Matching ........... . 153
8 The Programs on the CD-ROM 157
8.1 Program Organization . 157
8.2 Image Display ..... . 158
8.3 Programming Language 159
8.3.1 Disk File Format 160
CONTENTS ix
8.4 BF-CTEM Sample Calculations. 162
8.4.1 Atomic Potentials 162
8.4.2 Multislice ..... 166
8.4.3 Image Formation . 168
8.4.4 Partial Coherence 169
8.5 ADF-STEM Sample Calculations. 171
8.6 Non-Periodic Specimens .. 175
8.7 Using the display Program. 181
8.8 Using the Program slicview 183
A Plotting CTEM/STEM Transfer Functions 185
B Files on the CD-ROM 195
C The Fourier Projection Theorem 197
0 Atomic Potentials and Scattering Factors 199
D.1 Atomic Charge Distribution . 200
D.2 X-Ray Scattering Factors 202
D.3 Electron Scattering Factors 202
D.4 Parameterization . . 203
E Bilinear Interpolation 221
F 3D Perspective View 223
Index 249
Chapter 1
Introduction
Electron microscopy continues to push the limits of resolution. At high resolution,
image artifacts due to instrumental or specimen limitations can greatly complicate
image interpretation. The computer is finding an every increasing role in interpreting
high resolution transmission electron micrographs as well as extracting additional
information from the recorded images. Computer technology has been progressing at
a very rapid pace over the past several decades. The rate of improvement in computing
is certainly much faster than the rate of improvement of the electron microscope. A
very powerful computer is now much less than one percent of the cost of a respectable
electron microscope even though this level of computer hardware used to cost much
more than a high performance electron microscope. It is very worthwhile to try to
exploit the computer in electron microscopy in any way possible to extract more
information about the specimen or to reduce the cost or effort required to obtain
this information. Various applications of computing to electron microscopy may be
arranged in the following categories.
image simulation: Numerically calculate electron microscope images from a detailed
description of the specimen and the instrument. Usually involving various non
linear imaging modes and dynamical scattering in thick specimens.
image processing: The inverse of image simulation. Try to extract additional in
formation from the experimentally recorded electron micrographs by applying
numerical computation to the digitized micrographs.
instrument design: CAD (computer aided design) in electron optics. Numerical
calculation of electron optical properties (i.e., aberration, etc.) of magnetic
and electrostatic lens and deflectors in the electron microscope to optimize the
performance of the instrument.
on-line control: Directly control the operation of the microscope and record images
and spectra directly from the instrument. The computer is directly wired into
the electron microscope electronics.
1
E. J. Kirkland, Advanced Computing in Electron Microscopy
© Earl J. Kirkland 1998
2 CHAPTER 1. INTRODUCTION
data archiving: Save the recorded data. Manage the large volume of data generated
when recording a series of images.
Image simulation of electron micrographs has a long history and is the principle
topic of this book. There are two general types of image simulation. One group of
methods involves Bloch wave eigenstates and a matrix formulation in reciprocal space
(Bethel, Howie and Whelan2) and the other group involves mathematically slicing the
specimen along the beam direction (the multislice method). The multislice method
o
(Cowley and Moodie3, Lynch and 'Keefe4 , Goodman and Moodie5, Ishizuka and
Uyeda6, Van Dyck7) is usually more flexible for a computer simulation of crystalline
specimens with defects or interfaces as well as completely amorphous materials. Bloch
wave solution are more amenable to analytical calculations with pencil and paper for
small unit cells and can provide valuable incite into the scattering process.
Attempts to analytically derive the theory of image formation in the electron mi
croscope for specimen with large unit cells (and defects and interfaces) quickly arrive
at equations that do not have a closed form analytical solution or are too difficult to
easily interpret. The only recourse is a numerical solution. Image simulation numer
ically computes the electron micrograph from first principles. Starting from a basic
quantum mechanical description of the interaction between the imaging electrons in
the microscope and the atoms in the specimen the wave function of the imaging elec
trons may be calculated at any position in the microscope. If the optical properties of
the lenses in the microscope are known, then the two dimensional intensity distribu
tion in the final electron micrograph can be calculated with a relatively high precision.
Image simulation can provide several sources of additional information about the spec
imen. First, it can reveal which features of the image are due to artifacts produced
by aberrations in the electron microscope and which image features are due to the
specimen itself (and possibly relate features in the image to unsuspected properties of
the specimen). Image simulation is an aid in interpreting the image recorded in the
electron microscope. Second, it is relatively simple to change instrumental parameters
in the simulation that would be difficult if not impossible to change in practice. For
example it is easy to change the beam energy or spherical aberration to an arbitrary
value to see what happens. It is much easier to use image simulation to determine
what type of instrument is required to investigate a particular specimen than it would
be to build each type of electron microscope and see what happens. Image simulation
can be used as both an aid in image interpretation and a means of exploring new types
of imaging in the microscope.
Image processing is the inverse of image simulation. Starting from recorded
experimental images the computer can process the micrographs to improve their in
terpretability or to try to recover additional information in the micrographs. Image
processing includes image enhancement such as simple contrast stretching or noise
cleaning as well as image restoration or image reconstruction. Image restoration at
tempts to deconvolve the transfer function of the instrument from a single image to
improve the apparent resolution of the recorded image. Image reconstruction attempts
to combine several images (such as a defocus series) into one image with more infor
mation. In bright field phase contrast microscopy a series of images taken at different
defocus values (a defocus series) together contain more information than any single