Advanced Computing Electron Microscopy电子显微镜中的高级计算 英文版.pdf

Advanced Computing in Electron MicroscopySecond EditionEarl J.KirklandAdvanced Computingin Electron MicroscopySecond Edition123Earl J.KirklandSchool of Applied and Engineering PhysicsCornell University212 Clark HallIthaca,NY 14853USAejk14cornell.eduISBN 978-1-4419-6532-5e-ISBN 978-1-4419-6533-2DOI 10.1007/978-1-4419-6533-2Springer New York Dordrecht Heidelberg LondonLibrary of Congress Control Number:2010931437c?Springer Science+Business Media,LLC 2010All rights reserved.This work may not be translated or copied in whole or in part without the writtenpermission of the publisher(Springer Science+Business Media,LLC,233 Spring Street,New York,NY 10013,USA),except for brief excerpts in connection with reviews or scholarly analysis.Use inconnection with any form of information storage and retrieval,electronic adaptation,computer software,or by similar or dissimilar methodology now known or hereafter developed is forbidden.The use in this publication of trade names,trademarks,service marks,and similar terms,even if they arenot identified as such,is not to be taken as an expression of opinion as to whether or not they are subjectto proprietary rights.Printed on acid-free paperSpringer is part of Springer Science+Business Media()PrefacePreface to Second EditionSeveral new topics have been added,some small errors have been correctedand some new references have been added in this edition.New topics includeaberration corrected instruments,scanning confocal mode of operations,Blochwave eigenvalue methods and parallel computing techniques.The first edition in-cluded a CD with computer programs,which is not included in this edition.In-stead the associated programs will be available on an associated web site(currentlypeople.ccmr.cornell.edu/kirkland,but may move as time goes on).I wish to thank Mick Thomas for preparing the specimen used to record theimage in Fig.5.26 and to thank Stephen P.Meisburger for suggesting an interestingbiological specimen to use in Fig.7.24.Again,I apologize in advance for leaving out some undoubtedlyoutstanding ref-erences.I also apologize for the as yet undiscovered errors that remain in the text.Earl J.Kirkland,December 2009Preface to First EditionImage simulation has become a common tool in HREM(High Resolution Elec-tron Microscopy)in recent years.However,the literature on the subject is scatteredamong many different journals and conference proceedings that have occurred inthe 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 themultislice method.This book attempts to bring the diverse information on imagesimulation together into one place and to provide a background on how to use themultislice methodto simulate high resolutionimages in bothconventionaland scan-ning transmission electron microscopy.The main goals of image simulation includeunderstanding the microscope and interpreting high resolution information in thevviPrefacerecorded micrographs.This book contains sections on the theory of image forma-tion and simulation as well as a more practical introduction on how to use the mul-tislice method on real specimens.Also included with this book is a CD-ROM withworkingprograms to performimage simulation.The source code as well as the exe-cutablecodeforIBM-PC andAppleMacintoshcomputersis included.Althoughtheprograms may not have a very elegant user interface by todays standards(simplecommand line dialog),the source code should be very portable to a variety of dif-ferent computers.It has been compiled and run on Macs,PCs and several differenttypes of UNIX computers.This bookis intendedto be at the level of first year graduatestudents or advancedundergraduatesin physics or engineering with an interest in electron microscopy.Itassumes a familiarity with quantum mechanics,Fourier transforms and diffraction,some simple optics and basic computer skills(although not necessarily program-ming skills)at the advanced undergraduate level.Prior experience with electronmicroscopy is also helpful.The material covered should be useful to students learn-ing 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 understand-ing the underlyingprograms(with a primary goal of understandingthe transmissionelectron microscope image)or the source code can be used to understand how towrite your own version of the simulation programs.Although an effort was made to include references to most of the appropriatepublications on this subject,there are undoubtedly some that were omitted.I apol-ogize in advance for leaving out some undoubtedly outstanding references.I alsoapologize for the as yet undiscovered errors that remain in the text.I wish to acknowledge the support of various funding agencies(principly DOE,NSF andNIH)thathavesupportedmyresearcheffortsoverthepast severaldecades.My research experience has substantially contributed to my understanding of thematerial covered in this book.I also wish to thank Dr.David A.Muller and Dr.Richard R.Vanfleet for pro-viding many helpful suggestions and help in proof reading the manuscript and tothank Dr.M.A.OKeefe for providing helpful comments on electron microscopyand image simulation.Earl J.Kirkland March,1998MATLAB(R)is a registered trademark of The Mathworks,Inc.The Matlab and other programs listed in this book are supplied for instruc-tional purposes,AS-IS WITHOUT ANY WARRANTY,WITHOUT EVEN THEIMPLIEDWARRANTY OF MERCHANTABILITYorFITNESSFOR APARTIC-ULAR PURPOSE to the extent permitted by law.Efforthas been made to insure theprogramsarecorrect,butneithertheauthororthepublishershallbeheldresponsibleor liable for any damage resulting from the use or failure to use these programs.Contents1Introduction.11.1Computing in Electron Microscopy.11.2Organization of this Book.32The Transmission Electron Microscope.52.1Introduction.52.2Modeling the Electron Microscope.92.3Relativistic Electrons.102.4Reciprocity.132.5Confocal Mode.152.6Aberrations.152.7Aberration Correction.192.8More Aberrations.242.9Further Reading.263Linear Image Approximations.293.1The Weak Phase Object in Bright Field.303.2Partial Coherence in BF-CTEM.353.2.1Aberration Correctors and Partial Coherence.413.3Detector Influence(CTEM).423.4Incoherent Imaging of Thin Specimens(CTEM).433.5Annular Dark Field STEM.473.5.1Minimum Probe Conditions.533.5.2Source Size.543.5.3Defocus Spread.563.6Confocal Mode for Weak Phase Objects.563.7Phase and Amplitude Contrast Revisited.594Sampling and the Fast Fourier Transform.614.1Sampling.624.2Discrete Fourier Transform.66viiviiiContents4.3The Fast Fourier Transform or FFT.664.4Wrap Around Error and Rearrangement.694.5Fourier Transforming Real Valued Data.704.6Displaying Diffraction Patterns.714.7An FFT Subroutine in C.724.8Further Reading.765Calculation of Images of Thin Specimens.775.1The Weak Phase Object.785.2Single Atom Properties.805.2.1Radial Charge Distribution.815.2.2Potential.815.2.3Atomic Size.845.2.4Scattering Factors.865.3Total Specimen Potential.885.4BF Phase Contrast Image Calculation.915.4.1Single Atom Images.935.4.2Thin Specimen Images.955.4.3Partial Coherence and the Transmission Cross Coefficient.995.5ADF STEM Images of Thin Specimens.1045.5.1Single Atom Images.1065.5.2Thin Specimen Images.1085.6Summary of Sampling Suggestions.1126Theory of Calculation of Images of Thick Specimens.1156.1Bloch Wave Eigenvalue Solution.1186.1.1Bloch Waves.1186.1.2Periodic Potential.1206.1.3Matrix Equation.1216.1.4Initial Conditions and the Exit Wave.1246.1.5Bloch Wave Eigenvalue Summary.1266.2The Wave Equation for Fast Electrons.1276.3A Bloch Wave Differential Equation Solution.1306.4The Multislice Solution.1326.4.1A Formal Operator Solution.1326.4.2A Finite Difference Solution.1366.4.3Free Space Propagation.1376.5Multislice Interpretation.1376.6The Multislice Method and FFTs.1406.7Slicing the Specimen.1416.8Aliasing and Bandwidth.1456.9Interfaces and Defects.1486.10 Multislice Implementation.1496.10.1 The Propagator Function and Specimen Tilt.1516.10.2 Convergence Tests.152Contentsix6.10.3 Partial Coherence in BF-CTEM.1536.10.4 Parallel Computing.1546.11 More Accurate Slice Methods.1566.11.1 Operator Solutions.1566.11.2 Finite Difference Solutions.1577Multislice Applications and Examples.1637.1Gallium Arsenide.1637.1.1BF-CTEM Simulation.1657.1.2ADF-STEM Simulation.1697.1.3Channeling.1717.2Silicon Nitride.1747.3CBED Simulations.1787.4Thermal Vibrations of the Atoms in the Specimen.1837.4.1Silicon 111 CBED with TDS.1857.4.2Silicon 110 ADF-STEM with TDS.1857.5Specimen Edges or Interfaces.1887.6Biological Specimens.1907.7Quantitative Image Matching.1947.8Troubleshooting(What Can Go Wrong).1968The Programs.1998.1Program Organization.1998.2Image Display.2008.3Programming Language.2018.3.1Disk File Format.2028.4BF-CTEM Sample Calculations for Periodic Specimens.2048.4.1Atomic Potentials.2058.4.2Multislice.2088.4.3Image Formation.2108.4.4Partial Coherence.2118.5ADF-STEM Sample Calculations for Periodic Specimens.2148.6NonPeriodic Specimens.2178.6.1Fixed Beam Calculation.2208.6.2Scanned Beam Calculation.2248.7Program Display.2298.8Program Slicview.230APlotting Transfer Functions.233A.1 CTEM.234A.2 STEM.236BThe Fourier Projection Theorem.241xContentsCAtomic Potentials and Scattering Factors.243C.1Atomic Charge Distribution.244C.2X-ray Scattering Factors.246C.3Electron Scattering Factors.247C.4Parameterization.249DBilinear Interpolation.261E3D Perspective View.265References.271Index.287Chapter 1IntroductionAbstract This chapter has a brief summary of various ways that a computer andcomputation can be used in electron microscopy.There is also a short summary ofthe organization of this book and a list of symbols.1.1 Computing in Electron MicroscopyElectron microscopy continues to push the limits of resolution.At high-resolution,image artifacts due to instrumental or specimen limitations can greatly complicateimageinterpretation.Thecomputeris findinganeveryincreasingroleininterpretinghigh resolution transmission electron micrographs as well as extracting additionalinformation from the recorded images.Computer technology has been progress-ing at a very rapid pace over the past several decades.The rate of improvementin computing is certainly much faster than the rate of improvement of the electronmicroscope.A very powerful computer is now much less than 1%of the cost of arespectable electron microscope even though this level of computer hardware usedto cost much more than a high-performance electron microscope.It is very worth-while to try to exploit the computer in electron microscopy in any way possible toextract more information about the specimen or to reduce the cost or effort requiredtoobtainthisinformation.Variousapplicationsofcomputingtoelectronmicroscopymay be arranged in the following categories.image simulation:Numerically,calculate electron microscope images from firstprinciples and a detailed description of the specimen and the instrument.Usuallyinvolving various nonlinear imaging modes and dynamical scattering in thickspecimens.image processing:The inverse of image simulation.Try to extract additionalinformation from the experimentally recorded electron micrographs by applyingnumerical computation to the digitized micrographs.E.J.Kirkland,Advanced Computing in Electron Microscopy,1DOI 10.1007/978-1-4419-6533-2 1,c?Springer Science+Business Media,LLC 201021 Introductioninstrument design:computer aided design(CAD)in electron optics.Numericalcalculation of electron optical properties(i.e.,aberration,etc.)of magnetic andelectrostatic lens and deflectors in the electron microscope to optimize theperformance of the instrument.on-line control:Directly control the operation of the microscope and recordimages and spectra directly from the instrument.The computer is directly wiredinto the electron microscope electronics.data archiving:Save the recorded data.Manage the large volume of data gener-ated when recording a series of images.Image simulation of electron micrographs has a long history and is the princi-ple topic of this book.There are two general types of image simulation.One groupof methods involves Bloch wave eigenstates and a matrix formulation in reciprocalspace(Bethe 24,Howie and Whelan 163)and the other group involves mathe-maticallyslicingthespecimenalongthebeamdirection(themultislicemethod).Themultislice method(Cowley and Moodie 63,Lynch and OKeefe 231,Goodmanand Moodie127,Ishizukaand Uyeda179,Van Dyck 357)is usually more flex-ible for a computer simulation of crystalline specimens with defects or interfaces aswell as completely amorphous materials.Bloch wave solution are more amenableto analytical calculations with pencil and paper for small unit cells and can providevaluable insight into the scattering process.Attempts to analytically derive the theory of image formation in the electronmicroscope for specimen with large unit cells(and defects and interfaces)quicklyarrive at equations that do not have a closed form analytical solution or are too diffi-cult to easily interpret.The only recourse is a numerical solution.Image simulationnumerically computes the electron micrographfrom first principles.Starting from abasic quantum mechanical description of the interaction between the imaging elec-trons in the microscope and the atoms in the specimen the wave function of theimaging electrons may be calculated at any position in the microscope.If the opti-cal properties of the lenses in the microscope are known,then the two dimensionalintensity distribution in the final electron micrograph can be calculated with a rel-atively high precision.Image simulation can provide several sources of additionalinformation about the specimen.First,it can reveal which features of the image aredueto artifacts producedbyaberrationsin the electronmicroscopeandwhich imagefeatures are due to the specimen itself(and possibly relate features in the image tounsuspected properties of the specimen).Image simulation is an aid in interpretingthe image recorded in the electron microscope.Second,it is relatively simple tochange instrumental parameters in the simulation that would be difficult if not im-possible to change in practice.For example it is easy to change the beam energy orspherical aberration to an arbitrary value to see what happens.It is much easier touse image simulation to determine what type of instrument is requiredto investigatea particularspecimen than it would be to build each type of electronmicroscopeandsee what happens.Image simulation can be used as both an aid in image interpreta-tion and a means of exploring new types of imaging in the microscope.Image processing is the inverse of image simulation.Starting from recordedexperimental images the computer can process the micrographs to improve their1.2 Organization of this Book3interpretabilityor to try to recoveradditional informationin the micrographs