Transmission Electron Microscopy: C. Barry Carter David B. Williams [PDF]

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C. Barry Carter · David B. Williams Editors

Transmission Electron Microscopy Diffraction, Imaging, and Spectrometry

Foreword by Sir John Meurig Thomas

Transmission Electron Microscopy

C. Barry Carter  ·  David B. Williams (Eds.)

Transmission Electron Microscopy Diffraction, Imaging, and Spectrometry

Editors C. Barry Carter University of Connecticut Storrs, USA

David B. Williams The Ohio State University Columbus, USA

ISBN 978-3-319-26649-7              ISBN 978-3-319-26651-0 (eBook) DOI 10.1007/978-3-319-26651-0 Library of Congress Control Number: 2016945257 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer International Publishing Switzerland imprint is published by Springer Nature The registered company is Springer-Verlag GmbH Berlin Heidelberg



Dedicated to Bryony Carter and Margie Williams

Foreword by Sir John Thomas of the Companion to Williams and Carter’s book on TEM

Ever since 1996, when the first edition of Transmission Electron Microscopy: A Textbook for Materials Science (by David Williams and Barry Carter) appeared, this became the favoured and standard text for all those interested in mastering the electron microscopic examination of materials. It was, and remains, the vade mecum of choice. With its massive repository of highly relevant information and advice, teeming with attractive pedagogical accoutrements, this text gained almost instant, worldwide popularity. The second edition, published in 2009, contained many new features, prompted primarily by the growth of the subject and the arrival of a range of powerful additional variants of transmission electron microscopy (TEM). It had become fully apparent at that time that TEM is not just a widely useful investigative tool, but also, in its most modern form, a near complete chemical and structural laboratory, from which a multitude of properties pertaining to condensed matter may be extracted. In the intervening years it has become possible to add yet further, powerful variants for identification and characterization of both solids and, increasingly of liquids and surfaces, at evermore impressive resolutions – spatial, spectral and temporal. For example, modern scanning transmission electron microscopes (STEM), used principally for the retrieval of energy-dispersive X-rays (EDX) and electron energy loss (EEL), as may be gleaned from Chap. 11 of this Companion, can routinely generate spectra of images in which behind every image pixel lies a complete (EDX or EEL) spectrum. Moreover, by recording a tilt series of such spectrum images, 4D ‘spectrum tomograms’ produce spectral (and have chemical) information at every real space voxel. One of the most dramatic advances made since the second edition of W&C appeared is the vast improvement (by nearly ten orders of magnitude) in temporal resolution that has been accomplished, largely through the innovative work of Zewail and colleagues in California. Up until less than a decade ago, electron microscopists recorded dynamic changes of specimens in TEMs at around millisecond resolution. Nowadays, sub-picosecond resolutions can be attained, thereby uncovering a whole host of new condensed-matter phenomena. The emergence of major new advances such as this, along with those in tomography, holography, EELS and in ‘aberration corrected’ imaging, has, inter alia, persuaded W&C to enlist a collection of world-renowned experts to expatiate their knowledge following the same admirable pedagogic approach of the progenitor text. Nowadays, thanks to modern versions of electron microscopes, the structure and composition of matter in all realms can be elucidated at unprecedented resolution in both space and time; one can ‘see’ individual atoms, and follow the acts of bond formation and rupture. All this opens up ways, outlined by contributors to this admirable Companion, to even greater insights and information in the years to come. It is reassuring to learn that W&C intend to produce further editions of this Companion when the time is ripe to do so. When I decided to turn to TEM as an investigative tool, more than fifty years ago, other chemists regarded my decision with incredulity and perplexity. ‘Of what possible use could TEM be to the chemist?’ was the refrain I heard. That was in the era when chemists believed that only X-ray crystallography could enlighten chemists about the nature of solids. It was fondly believed by most chemists of that generation that all crystals were, in effect, a paradise of faultless regularity. But I had already discovered that the reactivity of solids, as well as their electronic and excitonic behaviour, is intimately associated with crystalline defects, and TEM, in its numerous variants, could answer most of my questions. These vii

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Foreword by Sir John Thomas of the Companion to Williams and Carter’s book on TEM

days, no self-respecting Department of Chemistry anywhere in the world can function properly without an electron microscope. Indeed, nanoscience and nanotechnology, which are of importance to all physical and biological sciences, are impossible to pursue without a TEM. Today, such is the power of direct-detection cameras (described in Chap. 2), that many X-ray crystallographers have now turned to the TEM to solve very complicated biologically significant structures like large ribosomal subunits from human mitochondria. It is most gratifying that this Companion text is likely to satisfy the scientific appetites of all complexions of investigators of condensed matter. I warmly commend this Companion and, in particular, the way in which it follows the ethos of the original W&C volumes by posing two different levels of questions (Q and T), and the use “traffic light” boxes. Sir John Meurig Thomas Hon. Professor at the Department of Materials Science and Metallurgy, University of Cambridge, and Former Director of the Royal Institution of G.B., London

Transmission Electron Microscopy: Diffraction, Imaging, and Spectrometry

Preface In the prefaces to the first and second editions of Williams & Carter, we asked the same question: “How is this book different from the many other TEM books on the market?” Our answer was, in essence, that these volumes are true textbooks, written to be studied by undergraduates and graduates, constructed in lecture-size segments and (in the softbound versions) able to be used at the console of the microscope. Perhaps the most distinguishing feature of the books was that, unlike all previous TEM texts, we wrote them as we taught in the classroom: in an informal style, interspersed with side comments and the occasional attempted joke – which rendered translation into other languages too challenging. Around 20,000 hard copies have been printed to date, and hundreds of thousands of chapters have been downloaded. So why do we need a Companion Volume, and why do we refer to it as the Companion Volume? The answer requires recounting a little history, which, as we’ve indicated in prior prefaces, is something we enjoy. We see this book as filling a need that is really a reflection on what has happened to the TEM field in the decades since Williams first suggested the need for such a book to Carter in the living room of the Carter home in Ithaca, NY, one cold spring morning in 1985, and which is why Carter proposed that it should be W&C. Buoyed by excess coffee (see Section 34.2 of the second edition) we decided to go ahead and write. At first, we decided that a group of four complementary experts could cover the principal aspects of the TEM field at that time (hence the division of the book into four parts). Such a team was assembled. However, we found that textbook writing was not for the faint of heart. Soon after we started putting fingers to the keyboards of our $2,500(!) Apple Macintoshes and mailing floppy disks to each other containing our initial attempts, we were reduced to just W&C. Despite our lack of expertise in certain key areas of the TEM field, we managed, by 1996, to complete W&CI. Then, no doubt due to the same excesses of caffeine, we decided in 2003 to rewrite the text, and so W&CII was born in 2009. When starting W&CII we recognized that there was not much in W&CI that we could omit! But it was already a macrotome. We also realized that writing another full book on all the new things that were happening in TEM was not what we had time to do – it would take another 10 years at least. (It did.) So we invited a few of our long-time friends and colleagues who were wonderfully qualified to write particular chapters; the ones whose photos you see in these pages are still our friends, we hope. So the Companion Volume was conceived as a collection of chapters that would be written by world experts on topics that are either perennially important or really new and fascinating, and that we could keep current without sacrificing material in W&C. It may not all be conventional wisdom but we decided that this volume would be CW, or C&W for consistency. Our own careers have mirrored the rapid evolution of TEM. If you have nothing better to do than read the previous prefaces to our texts, you’ll know that W&C have both evolved from our professorial positions at Lehigh and Cornell back in 1985. We have both taken on roles that required us (like all TEM operators) to broaden our skills and face more challenging responsibilities. We have each moved on to (two) different universities. Our children of the 1970 s and 80 s are now independent adults with their own twenty-first-century families. Our parents (to whom W&C is dedicated) have all passed on. Yet, particularly important to us, our wives remain with us. Without them, none of this would ever have happened. Thousands of successful TEM students owe their thanks to Bryony and Margie, as do we. So, taking a leaf out of previous prefaces, we ask anew, why is this Companion Volume different from the many multi-author TEM review texts that are published at regular intervals? First, it builds directly ix

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Preface

on W&C, which is extensively referenced throughout. Second, we have taken the high-quality writing of our friends and attempted to give it a W&C flavor, by changing it into informal script where possible. We apologize to all of them when, in doing so, we have destroyed some of their brilliant phraseology. Nevertheless, we believe that, compared to similar texts, we have managed to bring a greater degree of homogeneity to the writings of multiple authors from many different countries. We apologize that a few of the chapters require two or three (or four) lectures and that the 17 chapters will take a full semester to cover. A consequence of this approach is that, except in the About the Authors pages, rather than ascribe individual chapters to individual author(s), we simply acknowledge all our friends up front. If, or when, you are well versed in the TEM field, it should not be difficult to work out who wrote what! Perhaps a good exercise for all you students who are relatively new to TEM would be to search the literature and come to your own conclusions. We’ll mention a few idiosyncrasies that you’ll find in the text. One of us has a thing about hyphens and loves Lynne Truss’s book about the panda. In spite of this, we have tried to omit all punctuation when writing equations: punctuation is supposed to help, not confuse. We’ve used our traffic-light boxes again: if it’s red, be sure to stop for a moment; if it’s amber – you’ve been warned; if it’s green, take note but move on. While we may not have succeeded in making this Companion Volume as comprehensive and uniform as we made the original W&C editions, we do hope that all you students who enjoyed those first volumes will find this one to be equally valuable. It has been one heck of a ride, and this text is the technical apex of both our professional careers, opening doors that we never dreamed of 30 years ago. TEM continues to grow as a discipline and as an instrument: it is the essential tool for studying nanomaterials. What happens on the nanoscale determines what happens, period, and only the TEM can tell us about structure and composition with accuracy and precision at the nanoscale. Finally, we thank our friend Sir John Thomas for writing the Foreword to this volume and remember our friend the late Gareth Thomas who wrote the Foreword to W&C. Albuquerque, Storrs and Columbus, September 2015

Thanks to Our Friends

Most of the authors have discussed their chapters with colleagues, received suggestions and criticisms, and then updated and improved their chapters. As you will appreciate from our ‘People’ sections, we also recognize that we are all building on the contributions of earlier writers and researchers. The editors and authors have been privileged to know many of them personally – this is still a young field. Here we recognize those who specifically helped us in writing these chapters.

Alwyn Eades thanks Jean-Paul Morniroli, Mike Kaufman, and John Spence, who read an early version of his chapter; each of them made suggestions that resulted in important improvements.

Pieter Kruit chapter is based on knowledge that was acquired when he and his then PhD student Merijn Bronsgeest worked closely with Greg Schwind and Lyn Swanson of FEI Beamtech.

Katie Jungjohann and CBC acknowledge the Center for Integrated Nanotechnologies (CINT), a DOE-BES supported national user facility located at both Sandia and Los Alamos National Laboratories. Sandia, where KJ is personally located, is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s (DOE) National Nuclear Security Administration (NNSA) under contract DE-AC0494AL85000. They thank Matt Janish, Yang Liu, Jiangwei Wang, Joseph Grogan, Madeline Dukes, Paul Kotula, Joe Michael, Bill Mook, Khalid Hattar, Blythe Clark, Katie Harrison, Andrew Leenheer, Eric Stach, Dave Mitlin, Grant Norton, Jessica Vanderburg, Kevin Zavadil, Neal Shinn, Sean Hearne, and Charles Barbour for their support and their help in so many ways.

Grace Burke would like to thank her many colleagues and collaborators over the years, especially Tom Nuhfer (Carnegie-Mellon University) and Ram Bajaj (Bettis) for their long-time collaborations and friendship, and to Joven Lim (University of Manchester). The examples used in this chapter relied on the excellent TEM specimens prepared by Jim Haugh (retired) of Westinghouse, whose expertise and friendship have been so important over the years. She would also like to thank Mike for his patience and proof-reading. xi

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Thanks to Our Friends

Stephen J. Pennycook is very grateful to all his collaborators in the work described in his chapter: E. Abe, B. Alen, L. J. Allen, H. S. Baik, B. Beaumont, P. F. Becher, A. Y. Borisevich, N. D. Browning, M. F. Chisholm, A. J. D’Alfonso, N. Dellby, S. Doh, G. Duscher, M. M. Erwin, J. P. Faurie, L. C. Feldman, A. G. Ferridge, S. D. Findlay, D. Fuster, P. L. Galindo, P. Gibart, M. V. Glazoff, L. Gonzalez, Y. Gonzalez, T. R. Gosnell, J.-C. Idrobo, D. E. Jesson, A. V. Kadavanich, M. Kim, T. C. Kippeny, O. L. Krivanek, J. H. Lee, J. T. Luck, A. R. Lupini, J. R. McBride, A. J. McGibbon, M. M. McGibbon, S. I. Molina, M. F. Murfitt, P. D. Nellist, P. D. Nellist, F. Omnes, M. P. Oxley, G. S. Painter, S. T. Pantelides, Y. Peng, R. C. Puetter, S. N. Rashkeev, K. G. Roberts, S. J. Rosenthal, D. L. Sales, M. J. Seddon, W. A. Shelton, N. Shibata, W. H. Sides, S. Sivananthan, K. Sohlberg, Z. S. Szilagyi, M. Tanaka, M. Terauchi, J. Treadway, A. P. Tsai, K. van Benthem, M. Varela, L. G. Wang, S. W. Wang, Y. Xin, A. Yahil, Y. F. Yan.

Paul Midgley thanks all his collaborators, past and present, for their contributions to the work described in the chapters.

Matthew Weyland thanks Chris Boothroyd, Owen Saxton, Ron Broom, Rafal Dunin-Borkowski, and Sir John Meurig Thomas for their critical input to the early development of electron tomography in materials science.

Paul Kotula thanks Peter Duncumb for pioneering X-ray mapping, Legge and Hammond for developing true spectral imaging, and Rick Mott and the late John Friel for bringing modern spectral imaging to the microanalysis community. He would like to thank Michael Rye of Sandia for the preparation of most of the FIB specimens presented here. As we all know, the specimen preparation can be the most critical part of any materials analysis. He would also like to thank Michael Keenan (retired) and Mark van Benthem from Sandia National Laboratories for critical insight and helpful discussions about MSA over the years. Thanks also to Chad Parish (Oak Ridge National Laboratory), Josh Sugar (Sandia), Katie Jungjohann (Sandia), Yang Liu (North Carolina State University), Shreyas Rajasekhara (Intel) for insightful comments that improved this chapter. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States National Nuclear Security Administration, part of the Department of Energy (DOE), under contract DE-AC04 94AL85000.

Masashi Watanabe wishes to thank Prof. David Williams for his thoughtful supervision for many years. In collaboration with Prof. Williams, the ζ-factor method and MSA plug-ins were developed. In addition, the author would like to thank Prof. Christopher Kiely, Mr. David Ackland, Mr. Bill Mushock, Dr. Rob Keyse and colleagues at Lehigh, Prof. Zenji Horita at Kyushu University, Prof. Ray Egerton at University of Alberta, Dr. Kazuo Ishizuka at HREM Research Inc., Dr. Hidetaka Sawada, Mr. Eiji Okunishi and Mr. Masahiko Kanno at JEOL, Mr. Shintaro Yazuka, Mr. Toshihiro Aoki, Mr. Toshihiro Nomura, Dr. Masahiro Kawasaki and Dr. Tom Isabell at JEOL USA, Dr. Toshie Yaguchi at Hitachi Hitechnologies, and Dr. Nestor Zaluzec at Algonne National Laboratory for their collaboration.

List of Contributors

C. Barry Carter

Editor and Chapter 2

University of Connecticut [email protected]

C. Barry Carter is the Editor-in-Chief of the Journal of Materials Science and a CINT Distinguished Affiliate Scientist. He ist the Past President of the International Federation of Societies for Microscopy. He teaches at UConn.

David B. Williams

Editor

The Ohio State University, College of Engineering [email protected]

David B. Williams is the Monte Ahuja Endowed Dean’s Chair, Executive Dean of The Professional Colleges and Dean of the College of Engineering at The Ohio State University.

Pieter Kruit

Chapter 1

Delft University of Technology, Faculty of Applied Sciences [email protected]

Pieter Kruit is Professor of Physics at Delft University of Technology in the Netherlands and has 30 years of experience in developing novel electron- and ion-optical instruments for microscopy and lithography.

Katie Jungjohann

Chapter 2

CINT, Sandia National Laboratories [email protected]

Katie Jungjohann is the TEM Research Leader at CINT, Sandia/LANL. Her research is focused on the development and use of operando TEM techniques to understand the structural/chemical changes to nanomaterials, especially in the electrochemical cell discovery platform.

Grace Burke

Chapter 3

University of Manchester, School of Materials [email protected]

Grace Burke is a Professor in the School of Materials at the University of Manchester, having spent many years in industry, where her research involved microstructural characterization applied to understanding materials behavior. She is Director of both the Materials Performance Centre and the Electron Microscopy Centre.

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List of Contributors

Alwyn Eades

Chapter 4

Lehigh University, Department of Materials Science & Engineering [email protected]

Alwyn Eades worked on electron microscopy and, especially, electron diffraction for more than half a century and now enjoys retirement.

John Spence

Chapter 5

Arizona State University, Department of Physics [email protected]

John Spence FRS (ForMem) is the Richard Snell Professor of Physics at Arizona State University, author of ‘High Resolution Electron Microscopy’, recipient of the Cowley and Buerger Medals, and Director of Science for the NSF BioXFEL Science and Technology Center.

Bernhard Schaffer

Chapter 6

Gatan Inc. [email protected]

Bernhard Schaffer did his PhD in developing EFTEM SI techniques at FELMI/ZFE Graz before working with Cs corrected STEM at SuperSTEM Daresbury/UK. He is currently working as application developer at Gatan Inc.

Michael Lehmann

Chapters 7 and 8

TU Berlin, Institute for Optics and Atomic Physics lehmann@physik. tu-­berlin.de

Michael Lehmann studied physics in Tübingen, was Postdoc at the Triebenberg Lab, and is now full professor at TU Berlin.

Hannes Lichte

Chapters 7 and 8

TU Dresden, Triebenberg Laboratory [email protected]

Hannes Lichte studied physics at Kiel and Tübingen universities, where he finished the Dr.rer.nat. in 1977 under supervision of Gottfried Möllenstedt. He pioneered holographic imaging mainly of atomic structures. Since 1994 he has been professor at the Technische Universität Dresden and founder and director of the Triebenberg Laboratory.

Andreas Thust

Chapter 9

Forschungszentrum Jülich GmbH, Ernst Ruska-Centre [email protected]

Andreas Thust is an Austrian physicist working at Forschungszentrum Jülich, Germany. In 2005 he was awarded together with Wim Coene the internationally prestigious Ernst Ruska Price for their outstanding achievements in the field of focal-series reconstruction.

List of Contributors

Sandra Van Aert

Chapter 10

University of Antwerp, Electron Microscopy for Materials Science (EMAT) [email protected]

Sandra Van Aert is a Senior Lecturer at the University of Antwerp (Belgium). Within the Electron Microscopy for Materials Research (EMAT) group, her research focuses on new developments in the field of model-based electron microscopy aiming at quantitative measurements of atomic positions, atomic types, and chemical concentrations with the highest possible precision.

Dirk Van Dyck

Chapter 10

University of Antwerp, Electron Microscopy for Materials Science (EMAT) dirk.vandyck@ uantwerpen.be

Dirk Van Dyck is Emeritus Professor in Physics of the University of Antwerp. He is known for his pioneering work in dynamical electron diffraction, exit wave reconstruction, electron channeling, and electron tomography.

Stephen J. Pennycook

Chapter 11

National University of Singapore, Department of Materials Science & Engineering [email protected]

Stephen J. Pennycook is a Professor in the Materials Science and Engineering Department, National University of Singapore, an adjunct Professor at the University of Tennessee, USA, and an adjoint Professor at Vanderbilt University, USA.

Paul Midgley

Chapters 12 and 13

University of Cambridge, Department of Materials Science and Metallurgy [email protected]

Paul Midgley is Professor of Materials Science at the Department of Materials Science and Metallurgy at the University of Cambridge and a Professorial Fellow at Peterhouse.

Matthew Weyland

Chapter 12

Monash University, Department of Materials Science and Engineering [email protected]

Matthew Weyland is an Associate Professor at the Monash Centre for Electron Microscopy and in the Department of Materials Science and Engineering at Monash University, Melbourne.

Paul Thomas

Chapter 13

Gatan Inc. [email protected]

Paul Thomas graduated with a PhD in EFTEM Technique Development from the University of Cambridge in 2000. Ever since he has worked for Gatan, where he is passionate about software for analytical EM.

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List of Contributors

Vicki Keast

Chapter 14

The University of Newcastle, School of Mathematical and Physical Science [email protected]

Vicki Keast is currently Associate Professor in the School of Mathematical and Physical Science at The University of Newcastle, Australia.

Ian Jones

Chapter 15

University of Birmingham, School of Metallurgy and Materials [email protected]

Ian Jones is an electron microscopist and Professor of Physical Metallurgy at the University of Birmingham, UK.

Paul Kotula

Chapter 16

Sandia National Laboratories, Materials Characterization Department [email protected]

Paul Kotula is a staff member in the Materials Characterization Department at Sandia National Laboratories on the Albuquerque, NM campus. His research involves analytical electron microscopy, and in particular acquisition and statistical analysis of X-ray and electron energy-loss spectral images.

Masashi Watanabe

Chapter 17

Lehigh University, Materials Science and Engineering masashi.watanabe@ lehigh.edu

Masashi Watanabe is an Associate Professor of Materials Science and Engineering at Lehigh University. Masashi’s research emphasizes materials characterization using AEMs.

List of Initials and Acronyms

The field of TEM is a rich source of initials and acronyms (these are words formed by the initials), behind which we hide both simple and esoteric concepts. While the generation of new initials and acronyms can be a source of original thinking (e.g., see ALCHEMl), it undoubtedly makes for easier communication in many cases and certainly reduces the length of voluminous textbooks. You have to master this strange language before being accepted into the community of microscopists, so we present a comprehensive listing that you should memorize. ABF ABLAD ACF ACT ACTF A/D ADF AEM AES AFF AFM ALCHEMI ALS ANL AOs APB APFIM APW ART ASW ATW AWG AXSIA BF BFP BGPL BSE BZB C1,2 CASTEP CAT CB CBED CBIM CCD CCF CCM CDF CF CFE

annular bright field all-beam large-angle diffraction absorption-correction factor automated crystallography for TEM amplitude contrast transfer function analog to digital (converter) annular dark field analytical electron microscope/microscopy Auger electron spectrometer/spectroscopy aberration-free focus atomic force microscope/microscopy atom location by channeling-enhanced microanalysis alternating least squares Argonne National Laboratory atomic-like orbitals anti-phase (domain) boundary atom-probe field ion microscope/microscopy augmented plane wave algebraic reconstruction technique augmented spherical wave atmospheric thin window arbitrary waveform generator automated expert spectral image analysis bright field back-focal plane beam-gas path length backscattered electron Brillouin-zone boundary condenser 1,2, etc., lens Cambridge Serial Total Energy Package computerized axial tomography coherent bremsstrahlung convergent-beam electron diffraction convergent-beam imaging charged-coupled device cross-correlation function charge-collection microscopy centered dark field coherent Fresnel/Foucault cold field emission xvii

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List of Initials and Acronyms

CL CNTs cps CRT CS CSET CSL CSTEM CV CVD DADF DART DC DDF DF DFT DOS DP DQE DSTEM DTEM DTSA EBD EBIC EBSD EDS EDX EELS EFI EFTEM ELNES ELP™ EMMA EMS (E)MSA EPMA ESCA ESI EST ETEM EXAFS EXELFS FEFF FEG FET FFP FFT FIB FIM FLAPW FOLZ FTP FTs FWHM FWTM GB GGA GIF GIGO

cathodoluminescence carbon nanotubes counts per second cathode-ray tube crystallographic shear compressed sensing electron tomography coincident-site lattice confocal scanning transmission electron microscopy cyclic voltammetry chemical vapor deposition displaced-aperture dark field discrete algebraic reconstruction technique direct current diffuse dark field dark field density-functional theory density of states diffraction pattern detection quantum efficiency dedicated scanning transmission electron microscope/microscopy dynamical TEM desktop spectrum analyzer electron beam deposition electron beam-induced current/conductivity electron-backscatter diffraction energy dispersive spectroscopy energy dispersive X-ray electron energy-loss spectrometry energy-filtered imaging energy filtered transmission electron microscopy energy-loss near-edge structure energy-loss program (Gatan) electron microscope microanalyzer electron microscope image simulation (Electron) Microscopy Society of America electron-probe microanalyzer electron spectroscopy for chemical analysis electron-spectroscopic imaging equally-sloped tomography controlled environment TEM extended X-ray-absorption fine structure extended energy-loss fine structure ab-initio multiple scattering software field-emission gun field-effect transistor front-focal plane fast Fourier transform focused-ion beam field ion microscopy full-potential linearized augmented plane wave first-order Laue zone file-transfer protocol Fourier transformations full width at half maximum full width at tenth maximum grain boundary generalized gradient approximation Gatan Image Filter™ garbage in garbage out

List of Initials and Acronyms

GM Lines GMS GOS GS lines HAADF HOLZ HPGe HREELS HRTEM HV HVEM IBD IBF ICC ICDD ICP ID IDB IEEE IG IHC ITRS IVEM K-M KKR LACBED LCAO LCD LDA LEED LKKR LSDA MAC MAS MBE MC MCA MCDF MCR MDA MDM MEMS MLLS MMF MO MRS MS MSA MT MTF MV NCEMSS NIH NIST NPL OIM OR OTL PARODI

Gjonnes–Moodie lines Gatan Microscopy Suite™ generalized oscillator strength “glide and screw” lines high-angle annular dark-field higher-order Laue zone high-purity germanium high-resolution electron energy-loss spectrometer/spectrometry high resolution transmission electron microscopy high vacuum high-voltage electron microscope/microscopy ion-beam deposition incoherent bright field incomplete charge collection International Center for Diffraction Data incoherent channeling patterns identification (of peaks in spectrum) inversion domain boundary International Electronics and Electrical Engineering intrinsic Ge inverse hole-count International Technology Roadmap for Semiconductors intermediate-voltage electron microscope/microscopy Kossel–Möllenstedt Korringa–Kohn–Rostoker large-angle convergent-beam electron diffraction linear combination of atomic orbitals liquid-crystal display local-density approximation low-energy electron diffraction layered Korringa–Kohn–Rostoker local spin density approximation mass absorption coefficient Microanalysis Society molecular-beam epitaxy minimum contrast multichannel analyzer multi-configuration Dirac–Fock multivariate curve resolution minimum detectable atoms minimum detectable mass microelectromechanical systems multiple linear least squares minimum mass fraction molecular orbital Materials Research Society multiple scattering multivariate statistical analysis muffin tin modulation transfer function megavolt National Center for Electron Microscopy simulation system National Institutes of Health National Institute of Standards and Technology National Physical Laboratory orientation-imaging microscopy orientation relationship ordering tie line parallel recording of dark-field images

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List of Initials and Acronyms

PAW PB P/B PCA PCTF PDA PEELS PIPS PIXE PM POA ppb/m PSF PTS QCBED QHRTEM RB RDF REM RGA RHEED ROI RPA SACT SAD(P) SCF SDD SDK SE SEELS SEM SESAMe SF SHRLI SI SI SIGMAK SIGMAL SIMS SIRT S/N SOLZ SRM STEM STM TB TCC TED TEM TFE UEM UHV URL UTW V/F VLM VUV WB WBDF

projector augmented wave phase boundary peak to background ratio principal component analysis phase contrast transfer function photo-diode array parallel electron energy-loss spectrometer/spectrometry Precision Ion-Polishing System™ proton-induced X-ray emission photomultiplier phase-object approximation parts per billion/million point spread function position-tagged spectrometry quantitative convergent-beam method quantitative high-resolution transmission electron microscopy translation boundary (yes, it does!) radial distribution function reflection electron microscope/microscopy residual gas analyzer reflection high-energy electron diffraction region of interest random phase approximation small-angle cleaving technique selected area diffraction (pattern) self-consistent field silicon-drift detector software development kit secondary electron serial electron energy-loss spectrometer/spectrometry scanning electron microscope/microscopy sub-eV sub-Å microscope stacking fault simulated high-resolution lattice images spectrum imaging Système Internationale K-edge quantification software L-edge quantification software secondary ion mass spectroscopy simultaneous iterative reconstructive techniques signal-to-noise ratio second-order Laue zone standard reference material scanning transmission electron microscope scanning tunneling microscope/microscopy twin boundary transmission-cross coefficient transmission electron diffraction transmission electron microscope/microscopy thermal field emission ultrafast electron microscopes ultra high vacuum uniform resource locator ultra-thin window voltage to frequency (converter) visible-light microscope/microscopy vacuum ultra violet weak beam weak-beam dark field

List of Initials and Acronyms

WDS WP WPOA XANES XEDS XPS XRD/F YAG YBCO YSZ ZAF ZAP ZLP ZOLZ

wavelength-dispersive spectrometer/spectrometry whole pattern weak phase-object approximation X-ray absorption near-edge structure X-ray energy-dispersive spectrometer/spectrometry X-ray photoelectron spectrometer/spectrometry X-ray diffraction/fluorescence yttrium-aluminum garnet yttrium-barium-copper oxide yttria-stabilized zirconia atomic number/absorption/fluorescence correction zone-axis pattern zero-loss peak zero-order Laue zone

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Contents

1

Electron Sources  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1 1.1

Introduction and Definitions of Parameters  . . . . . . . . . . . . . . . .  2

1.2

Schottky Sources  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  4

1.3

1.2.1

Emission Theory  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   4

1.2.2

Coulomb Interactions  . . . . . . . . . . . . . . . . . . . . . . . . .  6

1.2.3

Practical Aspects  . . . . . . . . . . . . . . . . . . . . . . . . . . . .  7

Field Emission Sources  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   8 1.3.1

Emission Theory  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   8

1.3.2

Practical Aspects  . . . . . . . . . . . . . . . . . . . . . . . . . . .   10

1.4

Photo-Emission Sources  . . . . . . . . . . . . . . . . . . . . . . . . . . .   10

1.5

Effect of the Electron Source Parameters on Resolution in STEM  . .   11 1.5.1

Contributions to the Probe Size  . . . . . . . . . . . . . . . . .   11

1.5.2

Current in a Probe  . . . . . . . . . . . . . . . . . . . . . . . . . .   12

Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   14 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   15 2

In situ and Operando   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   17 2.1

General Principles   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   18

2.2

Some history  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   18

2.3

The Possibilities  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   19 2.3.1

Post-Mortem Characterization  . . . . . . . . . . . . . . . . . .   20

2.3.2 Statistics  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   20 2.4 Time  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   22

2.5

2.4.1

Recording the Data  . . . . . . . . . . . . . . . . . . . . . . . . .   22

2.4.2

The CCD Camera  . . . . . . . . . . . . . . . . . . . . . . . . . . .   22

2.4.3

Direct-Detection Cameras  . . . . . . . . . . . . . . . . . . . . .   22

2.4.4

Software and Data Handling  . . . . . . . . . . . . . . . . . . .   23

2.4.5

Drift Correction  . . . . . . . . . . . . . . . . . . . . . . . . . . .   24

2.4.6

Ultrafast Electron Microscopy  . . . . . . . . . . . . . . . . . . .   25

The Environment  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   29

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2.6

2.5.1

Ultrahigh Vacuum  . . . . . . . . . . . . . . . . . . . . . . . . . .   36

2.5.2

Working in a Gas Cell  . . . . . . . . . . . . . . . . . . . . . . . .   37

2.5.3

Working in a Liquid Cell  . . . . . . . . . . . . . . . . . . . . . .   39

The Temperature  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   41 2.6.1

Temperature Measurement  . . . . . . . . . . . . . . . . . . . .   41

2.6.2 Heating  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   42 2.6.3 Cooling  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   46 2.7

Other Stimuli  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   48 2.7.1 Deformation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   48 2.7.2

Magnetic Fields  . . . . . . . . . . . . . . . . . . . . . . . . . . .   55

2.7.3

Electric Fields  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   56

2.7.4 Photons  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   64 2.8

2.9

Adding or Removing Material  . . . . . . . . . . . . . . . . . . . . . . .   67 2.8.1

Depositing Layers/Particles  . . . . . . . . . . . . . . . . . . . . .   67

2.8.2

Deposition Energy: Electron and Ion Irradiation  . . . . . . .   68

The Future  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   73

Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   75 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   76 3 Electron Diffraction and Phase Identification   . . . . . . . . . . . . . . . . . .   81 3.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   82 3.2

Spinodal Alloys  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   83 3.2.1

3.3

Example: Ordered FeBe Phases and A2 Matrix  . . . . . . . . .   83

Superalloys with Ordered Precipitates  . . . . . . . . . . . . . . . . . .   85 3.3.1 Example: γ″ and γ′ Precipitation in Alloy 718  . . . . . . . . .   87 3.3.2

3.4

3.5

3.6

Example: D0a-Ordered δ Precipitation in Alloy 718  . . . . . .   89

Carbide Precipitation in fcc Alloys  . . . . . . . . . . . . . . . . . . . . .   93 3.4.1

Example: M23C6 Precipitation in a Ni–Base Alloy  . . . . . . . .   93

3.4.2

Example: MC Carbides in a Ni–Base Alloy  . . . . . . . . . . . .   94

Ferritic Steels  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   96 3.5.1

Relationships Between Austenite and Ferrite, Austenite and Martensite (fcc/bcc)  . . . . . . . . . . . . . . . . . . . . . . . . .   96

3.5.2

Relationship Between Cementite (Orthorhombic Fe3C or M3C) and Ferrite/Tempered Martensite  . . . . . . . . . . . . .   97

3.5.3

Relationships Between Alloy Carbides and Ferrite  . . . . . .   97

3.5.4

Precipitation in Ferritic Structures  . . . . . . . . . . . . . . . .   98

Epitaxial Oxide on Metal: Presence of Fe3O4 on Steel Foils  . . . . . .   99

Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   101 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   102

Contents

4 Convergent-Beam Electron Diffraction: Symmetry and Large-Angle Patterns   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   103 4.1 Symmetry  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   104 4.2

Point-Group Determination  . . . . . . . . . . . . . . . . . . . . . . . .   104

4.3

Space-Group Determination  . . . . . . . . . . . . . . . . . . . . . . .   109 4.3.1

Forbidden Reflections  . . . . . . . . . . . . . . . . . . . . . . .   109

4.3.2

Black Crosses  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   111

4.3.3

Complete Procedure for Space-Group Determination  . . .   113

4.4 Ni3Mo – A Worked Example  . . . . . . . . . . . . . . . . . . . . . . . .   114 4.4.1 Ni3Mo – a Worked Example, Part I: Point Group  . . . . . . .   114 4.4.2 Qualifications  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   118 4.4.3 Ni3Mo – a Worked Example, Part II: Space Group  . . . . . .   119 4.5

4.6

4.7

Additional and Alternative Symmetry Methods  . . . . . . . . . . . .   120 4.5.1

Symmetry Determination from Off-Axis Patterns  . . . . . .   120

4.5.2

Symmetry from Precession Patterns  . . . . . . . . . . . . . .   122

More on Glide Planes  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   123 4.6.1

GM Lines in HOLZ Reflections  . . . . . . . . . . . . . . . . . .   124

4.6.2

Glide Planes Normal to the Beam  . . . . . . . . . . . . . . .   124

Beyond Symmetry  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   124 4.7.1

Enantiomorphous Pairs: Handedness  . . . . . . . . . . . . .   126

4.7.2 Polarity  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   126 4.7.3 4.8

Coherent Convergent-Beam Diffraction  . . . . . . . . . . .   127

Tanaka Methods  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   127

4.9 LACBED  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   127 4.9.1

The Nature of LACBED Patterns  . . . . . . . . . . . . . . . . .   129

4.9.2

Obtaining LACBED Patterns in Practice  . . . . . . . . . . . .   130

4.9.3

Choosing the Parameters  . . . . . . . . . . . . . . . . . . . . .   131

4.10 Spherical Aberration and LACBED  . . . . . . . . . . . . . . . . . . . .   132 4.11 Crystal Defects in LACBED Patterns: Dislocations  . . . . . . . . . . .   132 4.12 Crystal Defects in LACBED Patterns: Stacking Faults and Antiphase Boundaries  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   134 4.13 Other Tanaka Methods  . . . . . . . . . . . . . . . . . . . . . . . . . . .   134 4.13.1 Bright- and Dark-Field LACBED  . . . . . . . . . . . . . . . . .   134 4.13.2 Convergent-Beam Imaging (CBIM)  . . . . . . . . . . . . . . .   136 4.13.3 Rastering Techniques  . . . . . . . . . . . . . . . . . . . . . . .   137 Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   141 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   142

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5 Electron Crystallography, Charge-Density Mapping, and Nanodiffraction   145 5.1

Can We Quantify Electron Diffraction Data?  . . . . . . . . . . . . .   146

5.2

Quantitative CBED for Charge-Density Mapping  . . . . . . . . . . .   147

5.3

Strain Mapping, High Voltage, Lattice Parameters Measured by QCBED  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   153

5.4

Spot Patterns – Solving Crystal Structures  . . . . . . . . . . . . . . .   155

5.5

The Precession Method  . . . . . . . . . . . . . . . . . . . . . . . . . . .   157

5.6

Diffuse Scattering, Defects, Phonons, and Phase Transitions  . . . .   158

5.7

Diffractive Imaging, Ptychography, STEM Holography, Ronchigrams, and All That  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   159

5.8

Equipment for Quantitative Electron Diffraction  . . . . . . . . . . .   162

Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   163 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   164 6 DigitalMicrograph  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   167 6.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   168

6.2

6.3

6.4

6.1.1

What Is DigitalMicrograph?  . . . . . . . . . . . . . . . . . . .   168

6.1.2

Installing DigitalMicrograph Offline  . . . . . . . . . . . . . .   168

6.1.3

A (Very) Quick Overview  . . . . . . . . . . . . . . . . . . . . .   168

Understanding Data  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   170 6.2.1

What is an Image?  . . . . . . . . . . . . . . . . . . . . . . . . .   170

6.2.2

Image Display  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   171

6.2.3

Number Formats  . . . . . . . . . . . . . . . . . . . . . . . . . .   173

6.2.4

Image Calibration and Image Tags  . . . . . . . . . . . . . . .   178

6.2.5

Some Simple Tools  . . . . . . . . . . . . . . . . . . . . . . . . .   180

6.2.6

Extracting Subsets of Data  . . . . . . . . . . . . . . . . . . . .   181

Digital Image Processing  . . . . . . . . . . . . . . . . . . . . . . . . . .   183 6.3.1

Image ‘Filters’  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   185

6.3.2

Fourier Transformation in Images  . . . . . . . . . . . . . . .   187

6.3.3

Fourier Filtering  . . . . . . . . . . . . . . . . . . . . . . . . . .   189

6.3.4

Coordinate Transformations  . . . . . . . . . . . . . . . . . . .   192

Scripting and Plugins  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   193

Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   195 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   195 7  Electron Waves, Interference, and Coherence  . . . . . . . . . . . . . . . . .   197 7.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   198 7.2

Description of Waves  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   198 7.2.1

Plane Wave  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   199

Contents

7.2.2

Spherical Wave  . . . . . . . . . . . . . . . . . . . . . . . . . . .   199

7.2.3

Modulated Wave  . . . . . . . . . . . . . . . . . . . . . . . . .   199

7.3 Interference  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   200 7.4

Modulation of a Wave by an Object  . . . . . . . . . . . . . . . . . . .   201

7.5

Propagation of Waves  . . . . . . . . . . . . . . . . . . . . . . . . . . .   201

7.6

7.5.1

Fresnel Approximation in the Near-Field of the Object  . .   202

7.5.2

Fraunhofer Approximation in the Far-Field of the Object  .   202

Imaging: Formation of the Image Wave  . . . . . . . . . . . . . . . .   203 7.6.1

Fourier Transform of the Object Exit Wave  . . . . . . . . . .   203

7.6.2

Building the Image Wave by Inverse Fourier Transform of the Fourier Spectrum  . . . . . . . . . . . . . . . . . . . . . . .   203

7.7

Electron Wave Function  . . . . . . . . . . . . . . . . . . . . . . . . . .   204

7.8

Electron Interference  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   205

7.9 Findings  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   206 7.10 Interpretation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   207 7.11 Coherence  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   207 7.11.1 Spatial Coherence  . . . . . . . . . . . . . . . . . . . . . . . . .   208 7.11.2 Coherent Current  . . . . . . . . . . . . . . . . . . . . . . . . .   210 7.11.3 Temporal Coherence  . . . . . . . . . . . . . . . . . . . . . . .   211 7.11.4 Total Degree of Coherence  . . . . . . . . . . . . . . . . . . .   211 7.11.5 A Generalization  . . . . . . . . . . . . . . . . . . . . . . . . . .   211 7.11.6 Coherence at Inelastic Interaction  . . . . . . . . . . . . . . .   211 Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   213 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   213 8

Electron Holography  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   215 8.1

Big Problem with TEM: Phase Contrast  . . . . . . . . . . . . . . . . .   216

8.2

Wave Modulation and Conventional Imaging  . . . . . . . . . . . . .   216

8.3

8.2.1

Amplitude Modulation  . . . . . . . . . . . . . . . . . . . . . .   216

8.2.2

Phase Modulation  . . . . . . . . . . . . . . . . . . . . . . . . .   217

8.2.3

What Do We See in an Electron Image?  . . . . . . . . . . . .   218

Principle of Image-Plane Off-Axis Holography  . . . . . . . . . . . .   219 8.3.1

Recording a Hologram  . . . . . . . . . . . . . . . . . . . . . .   219

8.3.2

Reconstructing the Object Exit-Wave  . . . . . . . . . . . . .   220

8.3.3

What Have We Achieved so Far?  . . . . . . . . . . . . . . . .   223

8.4

Properties of the Reconstructed Object Exit-Wave  . . . . . . . . . .   223

8.5

Requirements of Holography  . . . . . . . . . . . . . . . . . . . . . . .   224

8.6

Quality Criteria  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   224

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8.7

8.8

Application to Electric Potentials on Nanometer Scale  . . . . . . .   225 8.7.1

Phase Shift Due to Electrostatic Potentials  . . . . . . . . . .   225

8.7.2

Experimental Considerations  . . . . . . . . . . . . . . . . . .   226

8.7.3

Application Example: p–n Junctions  . . . . . . . . . . . . . .   227

Further Derivatives of Electron Holography  . . . . . . . . . . . . . .   227 8.8.1

Holographic Tomography  . . . . . . . . . . . . . . . . . . . .   227

8.8.2

Dark-Field Holography  . . . . . . . . . . . . . . . . . . . . . .   228

Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   230 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   230 9

Focal-Series Reconstruction  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   233 9.1

Motivation: Why the Effort?  . . . . . . . . . . . . . . . . . . . . . . .   234

9.2

Quick Walk Through Electron Diffraction  . . . . . . . . . . . . . . .   235

9.3

From the Wavefunction to the Image  . . . . . . . . . . . . . . . . . .   237

9.4

9.5

9.3.1

Imaging with a ‘Neutral’ Microscope  . . . . . . . . . . . . .   238

9.3.2

Linear Imaging with a Constant-Phase-Shift Microscope  .   240

9.3.3

Linear Imaging with a Real Microscope  . . . . . . . . . . . .   241

9.3.4

From Oscillations to Windings: an Integral View on Linear Imaging  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   247

From the Images to the Wavefunction  . . . . . . . . . . . . . . . . .   249 9.4.1

Tomographic Interpretation of Focal Series  . . . . . . . . .   249

9.4.2

Fundamental Properties of Focal Series  . . . . . . . . . . . .   250

9.4.3

An Explicit Solution to the Linear Inversion Problem  . . . .   253

9.4.4

Nonlinear Reconstruction  . . . . . . . . . . . . . . . . . . . .   255

9.4.5

Numerical Correction of Residual Aberrations  . . . . . . . .   256

Application Examples  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   257 9.5.1

Twin Boundaries in BaTiO3  . . . . . . . . . . . . . . . . . . . .   258

9.5.2

Stacking Fault in GaAs  . . . . . . . . . . . . . . . . . . . . . .   260

Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   263 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   264 10  Direct Methods for Image Interpretation  . . . . . . . . . . . . . . . . . . .   267 10.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   268 10.2 Basics of Image Formation  . . . . . . . . . . . . . . . . . . . . . . . . .   268 10.2.1 Real imaging  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   268 10.2.2 Successive Imaging Steps  . . . . . . . . . . . . . . . . . . . . .   269 10.2.3 Coherent Imaging  . . . . . . . . . . . . . . . . . . . . . . . . .   269 10.2.4 High-Resolution Imaging in the TEM  . . . . . . . . . . . . .   270 10.3 Focal-Series Reconstruction of the Exit Wave  . . . . . . . . . . . . .   271

Contents

10.4 Interpretation of the Reconstructed Exit Wave  . . . . . . . . . . . .   271 10.4.1 Electron Channeling  . . . . . . . . . . . . . . . . . . . . . . . .   272 10.4.2 Argand Plot  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   273 10.5 Quantitative Structure Refinement  . . . . . . . . . . . . . . . . . . .   274 10.5.1 Precision Versus Resolution  . . . . . . . . . . . . . . . . . . .   276 10.5.2 Quantitative Model-Based Structure Determination  . . . .   276 Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   280 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   280 11  Imaging in STEM  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   283 11.1 Z-Contrast STEM: an Introduction  . . . . . . . . . . . . . . . . . . . .   284 11.1.1 Independent Scatterers  . . . . . . . . . . . . . . . . . . . . . .   284 11.1.2 An Array of Scatterers  . . . . . . . . . . . . . . . . . . . . . .   284 11.1.3 As the Crystal Thickens  . . . . . . . . . . . . . . . . . . . . . .   284 11.1.4 Inside and Outside  . . . . . . . . . . . . . . . . . . . . . . . . .   286 11.1.5 The Effect of Defects  . . . . . . . . . . . . . . . . . . . . . . .   287 11.1.6 Quasicrystals  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   288 11.2 An Electron’s Eye View of STEM  . . . . . . . . . . . . . . . . . . . . .   288 11.2.1 Plane Waves and Probes  . . . . . . . . . . . . . . . . . . . . .   291 11.2.2 Rayleigh, Airy and Resolution  . . . . . . . . . . . . . . . . . .   292 11.3 Lens Aberrations for STEM  . . . . . . . . . . . . . . . . . . . . . . . .   293 11.3.1 The Benefits of Aberration Correction  . . . . . . . . . . . .   295 11.3.2 Resolution in the Third Dimension – Depth Resolution  . .   300 11.4 Spatial and Temporal Incoherence  . . . . . . . . . . . . . . . . . . . .   305 11.4.1 Spatial Incoherence  . . . . . . . . . . . . . . . . . . . . . . . .   305 11.4.2 Temporal Incoherence  . . . . . . . . . . . . . . . . . . . . . .   306 11.4.3 “How Do I Know if I Have a Coherent Probe?” The Ronchigram  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   306 11.5 Coherent or Incoherent Imaging  . . . . . . . . . . . . . . . . . . . . .   310 11.5.1 A Point Detector; Coherent Imaging  . . . . . . . . . . . . . .   311 11.5.2 An Infinite Detector: Incoherent Imaging  . . . . . . . . . .   312 11.5.3 An Annular Detector: Incoherent Dark-Field or Bright-Field Imaging  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   314 11.5.4 Atoms Are Smaller in HAADF STEM  . . . . . . . . . . . . . .   315 11.5.5 Transverse Coherence  . . . . . . . . . . . . . . . . . . . . . . .   316 11.5.6 The Origin of Contrast in the Scanned Image  . . . . . . . .   317 11.5.7 Transfer Function and Damping Function  . . . . . . . . . . .   318 11.5.8 Longitudinal Coherence  . . . . . . . . . . . . . . . . . . . . .   319

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11.6 Dynamical Diffraction  . . . . . . . . . . . . . . . . . . . . . . . . . . .   323 11.7 Other Sources of Image Contrast  . . . . . . . . . . . . . . . . . . . . .   326 11.8 Image Processing  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   329 11.9 Image Simulation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   332 11.9.1 Bloch Waves  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   333 11.9.2 Multislice  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   333 11.9.3 Bloch Waves with Absorption  . . . . . . . . . . . . . . . . . .   333 11.9.4 There Is No Stobb’s Factor in HAADF  . . . . . . . . . . . . .   334 11.10 Future Directions  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   335 Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   337 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   338 12 Electron Tomography  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   343 12.1 Theory of Projection  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   344 12.2 Back-Projection  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   346 12.3 Constrained Reconstruction  . . . . . . . . . . . . . . . . . . . . . . . .   347 12.3.1 Constraint by Projection Consistency  . . . . . . . . . . . . .   347 12.3.2 Constraint by Discrete Methods  . . . . . . . . . . . . . . . . .   348 12.3.3 Constraint by Symmetry   . . . . . . . . . . . . . . . . . . . . .   348 12.3.4 Metric-Based Constraint  . . . . . . . . . . . . . . . . . . . . .   348 12.4 Other Reconstruction Approaches  . . . . . . . . . . . . . . . . . . . .   350 12.5 Meeting the Projection Requirement  . . . . . . . . . . . . . . . . . .   350 12.6 STEM Tomography  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   351 12.7 Element-Selected Tomography  . . . . . . . . . . . . . . . . . . . . . .   354 12.8 Dark-Field TEM Tomography  . . . . . . . . . . . . . . . . . . . . . . .   356 12.9 Holographic Tomography  . . . . . . . . . . . . . . . . . . . . . . . . .   358 12.10 Atomistic Tomography  . . . . . . . . . . . . . . . . . . . . . . . . . . .   359 12.11 Experimental Limitations  . . . . . . . . . . . . . . . . . . . . . . . . .   360 12.12 Beam Damage and Contamination  . . . . . . . . . . . . . . . . . . .   364 12.13 Automated Acquisition  . . . . . . . . . . . . . . . . . . . . . . . . . .   365 12.14 Tilt-Series Alignment  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   366 12.15 Visualization of Three-Dimensional Datasets  . . . . . . . . . . . . .   368 12.16 Segmentation  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   369 12.17 Quantitative Analysis of Volumetric Data  . . . . . . . . . . . . . . .   371 Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   373 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   373 13 EFTEM  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   377 13.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   378 13.2 Why Use EFTEM?  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   378

Contents

13.3 Instrumentation for EFTEM  . . . . . . . . . . . . . . . . . . . . . . . .   379 13.3.1 General TEM Considerations  . . . . . . . . . . . . . . . . . .   379 13.3.2 The Imaging Filter  . . . . . . . . . . . . . . . . . . . . . . . . .   379 13.3.3 Detector Considerations  . . . . . . . . . . . . . . . . . . . . .   380 13.4 Limitations and Artefacts  . . . . . . . . . . . . . . . . . . . . . . . . .   381 13.4.1 Spatial Resolution in EFTEM Images  . . . . . . . . . . . . . .   381 13.4.2 Non-Isochromaticity  . . . . . . . . . . . . . . . . . . . . . . . .   383 13.4.3 Sample Drift  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   383 13.4.4 Diffraction Contrast  . . . . . . . . . . . . . . . . . . . . . . . .   384 13.4.5 Illumination Convergence  . . . . . . . . . . . . . . . . . . . .   384 13.5 Application of EFTEM  . . . . . . . . . . . . . . . . . . . . . . . . . . .   385 13.5.1 Zero-Loss Imaging and Diffraction  . . . . . . . . . . . . . . .   385 13.5.2 Measuring Relative Thickness (t/λ Mapping)  . . . . . . . . .   386 13.6 Core-Loss Elemental Mapping  . . . . . . . . . . . . . . . . . . . . . .   387 13.6.1 Elemental Mapping (Three-Window Method)  . . . . . . . .   387 13.6.2 Jump-Ratio Mapping (Two-Window Method)  . . . . . . . .   388 13.7 EFTEM Spectrum-Imaging  . . . . . . . . . . . . . . . . . . . . . . . . .   389 13.8 Low-Loss Imaging  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   392 13.9 Alternative Imaging Techniques for Biological Specimens  . . . . .   393 13.10 Quantitative Elemental Mapping  . . . . . . . . . . . . . . . . . . . .   394 13.11 Chemical State Mapping Using ELNES  . . . . . . . . . . . . . . . . . .   396 13.12 Hybrid EFTEM Modes(ω-q, Line Spectrum EFTEM)  . . . . . . . . . .   397 13.13 EFTEM Tomography  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   398 Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   401 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   401 14 Calculating EELS  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   405 14.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   406 14.2 Density Functional Theory (DFT)  . . . . . . . . . . . . . . . . . . . . .   407 14.2.1 Introduction to DFT  . . . . . . . . . . . . . . . . . . . . . . . .   407 14.2.2 The Exchange Correlation Potential  . . . . . . . . . . . . . .   409 14.2.3 Approximations to the Potential  . . . . . . . . . . . . . . . .   409 14.2.4 Basis Sets  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   410 14.2.5 The Korringa–Kohn–Rostoker (KKR) Method  . . . . . . . .   412 14.3 Calculations of the ELNES  . . . . . . . . . . . . . . . . . . . . . . . . .   412 14.3.1 ELNES Theory  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   412 14.3.2 The Core Hole  . . . . . . . . . . . . . . . . . . . . . . . . . . .   414 14.3.3 Multiplet Theory  . . . . . . . . . . . . . . . . . . . . . . . . . .   415 14.3.4 Multiple Scattering (MS) Methods  . . . . . . . . . . . . . . .   416

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14.4 Calculating Low-Loss EELS  . . . . . . . . . . . . . . . . . . . . . . . . .   417 Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   421 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   422 15 Diffraction & X-ray Excitation  . . . . . . . . . . . . . . . . . . . . . . . . . .   425 15.1 Introduction  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   426 15.2 ALCHEMI  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   426 15.3 Gedanken ALCHEMI  . . . . . . . . . . . . . . . . . . . . . . . . . . . .   426 15.4 Two Examples  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   428 15.4.1 Dilute Solution/Partition Coefficient Analysis  . . . . . . . .   428 15.4.2 Concentrated Solution/OTL Analysis  . . . . . . . . . . . . . .   430 15.5 Delocalization and Axial Channeling  . . . . . . . . . . . . . . . . . .   431 15.6 Optimizing ALCHEMI: ‘Statistical’ ALCHEMI  . . . . . . . . . . . . . .   432 15.7 Incoherent Channeling Patterns  . . . . . . . . . . . . . . . . . . . . .   432 15.8 Vacancies and Interstitials  . . . . . . . . . . . . . . . . . . . . . . . . .   432 15.9 Chemistry  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   434 Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   435 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   436 16 X-ray and EELS Imaging  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   439 16.1 What Are Spectral Images and Why Should We Collect Them?  . .   440 16.2 Some History  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   441 16.3 Acquisition and Analysis of Spectral Images  . . . . . . . . . . . . . .   442 16.3.1 Sampling and the Effect of Probe Versus Pixel Size (STEMXEDS/EELS) or Magnification (EFTEM)  . . . . . . . . . . . . .   442 16.3.2 Signal: Count Rate, Dwell Time, Spectral Image Size, and Acquisition Time  . . . . . . . . . . . . . . . . . . . . . . . . . .   443 16.3.3 Drift Correction and Beam Damage  . . . . . . . . . . . . . .   446 16.3.4 Conventional Data Analysis Methods  . . . . . . . . . . . . .   446 16.4 Multivariate Statistical Analysis Methods  . . . . . . . . . . . . . . . .   451 16.4.1 Principal Components Analysis (PCA)  . . . . . . . . . . . . .   454 16.4.2 Factor Rotations  . . . . . . . . . . . . . . . . . . . . . . . . . .   455 16.4.3 Multivariate Curve Resolution (MCR)  . . . . . . . . . . . . .   456 16.4.4 Quantification  . . . . . . . . . . . . . . . . . . . . . . . . . . .   457 16.5 Example of X-ray and Electron Energy-Loss Spectral Image Acquisition and Analysis  . . . . . . . . . . . . . . . . . . . . . . . . . .   458 16.5.1 Fe-Ni Spectral Image Acquisition and Quantification  . . . .   458 16.5.2 Mn-Doped SrTiO3 Grain Boundary Spectral Image Acquisition and Quantification  . . . . . . . . . . . . . . . . .   459 16.5.3 Plasmon Mapping of AG Nanorods: EELS Spectral Image Analysis  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   462

Contents

Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   464 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   464 17  Practical Aspects and Advanced Applications of XEDS  . . . . . . . . . . .   467 17.1 Performance Parameters of XEDS Detectors  . . . . . . . . . . . . . .   468 17.1.1 Detector, Fundamental Parameters  . . . . . . . . . . . . . .   468 17.1.2 Monitoring Detector Contamination  . . . . . . . . . . . . .   470 17.1.3 Software to Determine Detector Parameters  . . . . . . . .   471 17.2 X-ray Spectrum Simulation – a Tutorial and Applications of DTSA    472 17.2.1 What Is DTSA?  . . . . . . . . . . . . . . . . . . . . . . . . . . .   473 17.2.2 A Brief Tutorial of X-ray Spectrum Simulation for a Thin Specimen Using DTSA  . . . . . . . . . . . . . . . . . . . . . . .   475 17.2.3 Details of X-ray Simulation in DTSA  . . . . . . . . . . . . . .   477 17.2.4 Application 1: Confirmation of Peak Overlap  . . . . . . . .   481 17.2.5 Application 2: Evaluation of X-ray Absorption into a Thin Specimen  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   482 17.2.6 Application 3: Evaluation of the AEM-XEDS Interface  . . .   483 17.2.7 Application 4: Estimation of the Detectability Limits  . . . .   483 17.3 The ζ-factor Method: a New Approach for Quantitative X-ray Analysis of Thin Specimens  . . . . . . . . . . . . . . . . . . . . . . . .   486 17.3.1 Why Bother with Quantification?  . . . . . . . . . . . . . . .   486 17.3.2 What Is the ζ-factor?  . . . . . . . . . . . . . . . . . . . . . . .   487 17.3.3 Quantification Procedure in the ζ-factor Method  . . . . . .   488 17.3.4 Determination of ζ factors  . . . . . . . . . . . . . . . . . . . .   489 17.3.5 Applications of ζ-factor Method  . . . . . . . . . . . . . . . .   490 17.4 Contemporary Aplications of X-ray Analysis  . . . . . . . . . . . . . .   492 17.4.1 Renaissance of X-ray Analysis  . . . . . . . . . . . . . . . . . .   493 17.4.2 XEDS Tomography for 3D Elemental Distribution  . . . . . .   494 17.4.3 Atomic Resolution X-ray Mapping  . . . . . . . . . . . . . . .   495 Appendix  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   500 References  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   501 Figure and Table Credits  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   505 Index  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   515

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1

Electron Sources

Chapter 1



Chapter Preview Without an electron source there is no electron microscope, that’s obvious. For the electron microscopist there are several reasons to know something about the source. Someone knowledgeable decides which microscope to buy; someone equally knowledgeable has to use it when it has been purchased. How is the choice of source reflected in the quality of the images? Being able to use the microscope with a specific source to its optimal performance is another reason. How to operate the microscope without destroying the source? How to recognize that a source does not live up to specification anymore? This chapter starts by introducing the parameters used for describing the quality of electron sources and links these directly to their effect on imaging. The description of

the two most important source types (Schottky sources and cold field emission sources) starts with the physics theory of electron emission that is behind their properties. This involves a bit of mathematics that some readers may enjoy and others may want to skip to go directly to practical aspects of the sources. The last part contains a discussion on the relation between source parameters and resolution in STEM that will allow the reader to find the optimum balance between current in the probe and resolution in the image. We introduced the topic in Chap. 5 of W&C. The present chapter looks at the topic in much more depth, emphasizing why you should know about the source.

© Springer International Publishing Switzerland 2016 C. B. Carter, D. B. Williams (Eds.), Transmission Electron Microscopy, DOI 10.1007/978-3-319-26651-0_1

1

2

1  Electron Sources

Chapter 1

1.1 Introduction and Definitions of Parameters

and thus the emittance is constant. However, in electron microscopes there are many apertures and there is acceleration, so the emittance is not a constant.

Electron microscopy starts with the electron beam, a stream of particles that travels at incredible speed through an almost perfect vacuum to impact and scatter on the object in its path. Or should we say it is a wave that moves smoothly towards the sample to change its phase ever so slightly before traveling on, creating intricate interference patterns on a screen? Whatever this beam is, it needs to be created in the electron source. For the best microscope we obviously want the best electron source, but how to describe the quality of an electron source, and what is the exact relation between the properties of the source and the performance of the microscope?

There is one parameter that does not change at a beam-limiting aperture: it is the differential brightness of a beam. The differential brightness of an electron beam is defined as Bdiff =

dI dAd˝

(1.1)

where dI is the current passing through a surface dA within a solid angle dΩ. Clearly, when an aperture is placed in the beam, either the area or the angle is reduced, but the current is reduced proportionally, so the brightness remains constant. Acceleration or deceleration, however, does not keep the brightness constant: usually the beam angle changes – it reduces with acceleration and increases with deceleration. By defining a reduced brightness of the beam as

Electron sources supply the electrons to the system, so the main property of a source seems to be the number of electrons per second, or current, it supplies. However, we need to distinguish dI between the total current that the emitter emits, the beam current Br = (1.2) dAd˝  V that passes through the extractor aperture, and the probe current or specimen current that arrives at the sample through the beam-­ limiting apertures of the microscope. that problem is solved. Reduced brightness in SI units is expressed in A/(m2 · sr · V). Because this beam parameter is constant After the initial acceleration, the beam seems to come from an in the whole system, we can also use this as a parameter of the area with a diameter that we call virtual source size or just source source. In fact, for microscopic applications of electron sources, it diameter dv. It is called a ‘virtual source’ because it is different is the single most important parameter of a source. We’ll see later from the surface that is actually emitting electrons. If a cathode that there are very few physical phenomena that can change the has a spherical shape, all electrons that come out of the surface beam brightness: stochastic Coulomb interactions between the perpendicular to the surface, seem to come from a single point at individual electrons is one, energy filtering is another. The conthe center of the sphere. Electrons are emitted with a slight lateral cept of brightness is easiest understood in the plane of a source velocity: in Schottky and thermal emitters this is a result of the image, where the area is the size of the source image and the thermal energy kT; in field emission it is considerably larger. These angle is the aperture angle. However, we need to be careful here. electrons seem to come from a circle around the center of the sphere The definition given above for the differential brightness intrinand are thus responsible for the finite size of the virtual source. The sically assumes a homogeneous current density in the area dA. In electric field that causes the acceleration may also partly act like a source image, there is a current distribution with a maximum a lens effect that magnifies and shifts the virtual source position density in the center and often long tails. Although this is not along the optical axis. The convention is to define the virtual source a formal definition, we then often use the concept of practical size looking back from the plane of the extractor. Thus, the virtual brightness B = I/AΩ, which makes it necessary to define the size source size depends on the extractor voltage. Interactions between of the source image. We shall show later that the best definition is the full width that contains 50 % of the current: FW50. Because the electrons may increase the effective size of the source. we still use the full current, practical brightness is larger than The virtual source size is usually small compared to the size of differential brightness (Bronsgeest et al. 2008): the extractor aperture, so we can speak of ‘the’ emission angle of I the beam and thus of the angular current density, I’ which is deBpract =  2 = 1:44 Bdiff (1.3) d  ˛2 fined as the current divided by the emission solid angle, or better: 4 FW50 the beam current divided by the solid angle that is accepted by the extraction aperture. We shall encounter many more current Brightness in an electron microscope can best be measured in densities, such as the emission current density j, which is the spot mode, at relatively large spots. It is important to find a mode emitted current per unit area at the emitter surface. in which the size of the probe is dominated by the size of the source image, so at relatively small aperture angle to avoid abIn the general literature on electron emitters, you will often en- erration contributions to the probe size and at sufficient current counter the parameter emittance, which is defined as the prod- to avoid a diffraction contribution to the spot size. In TEM, the uct of the source size and the emission angle. If there are no spot at the sample plane is magnified with a known magnification beam-limiting apertures and no acceleration, this is a useful pa- to the CCD camera. The angle at the sample can be measured in rameter, because it stays constant from one crossover to the next: diffraction mode, and the current is measured in a Faraday cup, if the crossover size is magnified, the beam angle is demagnified, or on the microscope screen.

The last parameter that is used to describe an electron source is the energy spread ∆E in the beam. Electrons can be emitted with slightly different energies. Whatever the acceleration is afterwards, the energy conservation law tells us that this original energy difference will stay. In fact there is a whole distribution of different energies, the energy distribution. Usually the distribution is asymmetric and it is a little difficult to characterize it with a single number. Some use full width at half maximum FWHM, others use full width that contains 50 % of the current FW50. Even for a nice distribution such as a Gaussian, the FW50 is different from the FWHM (FWHM = 1.75 × FW50), so we have to be careful regarding what to use in calculations of, e.g., the chromatic aberration. It turns out that the FW50 value is less sensitive to the exact energy distribution than the FWHM and thus gives a more consistent result in calculations (Barth and Nykerk 1999). The energy spread can only be increased by stochastic interactions between individual electrons, where a collision may accelerate one electron and decelerate the other. That effect is called the Boersch effect. In practice, we also add the variations in accelerator voltage to the energy spread, because they have the same effect when averaged over time, but strictly this is not a parameter of the electron source. The energy spread may be reduced by an electron monochromator – also called an energy filter. In the filtering process, some electrons are stopped, so the act of filtering decreases the beam current and also the brightness. What is constant is the brightness per electron volt energy spread. So when a monochromator is present, the single parameter that we need to know about the source is Br/∆E. So far, we have been able to limit our view of an electron gun as a source of charged particles, little balls that fly through space! However, electrons have wave properties and these wave properties are crucial for electron microscopy, both in TEM, where we measure phase contrast, and in STEM, where diffraction ultimately limits resolution. The electron wavelength is r 1 h −9  = = 1:226  10 (1.4) p V when λ is given in m and V*, the relativity-corrected acceleration voltage of the beam, is given in volt, V  = V.1 + 10−6 V/. For TEM, we are often interested in the coherence of the beam. If there is coherence between two points in the beam, it means that there is a constant phase relation between the electron waves at the two points: the amplitudes move as two pendulums in perfect unison. Only when there is coherence can interference occur between the waves coming from these points. If only part of the amplitude moves in that unison, we speak of partial coherence. This is mathematically expressed by the degree of coherence, which is the correlation between the wave amplitudes ψ at points r1 and r2 (at a distance x1,2). ˇ ˇ ˇ ˇ Z ˇ Imax − Imin ˇ   .r1 ; t/ .r2 ; t/dtˇˇ = .x1;2 / = ˇˇ lim (1.5) ˇ Imax + Imin ˇ !1 −

Remember that electrons are fermions, and fermions, unlike bosons such as photons, cannot interfere with each other. This means that different electrons are never mutually coherent, so coherence is a phenomenon that plays within individual electrons. When there is coherence between two points in a beam, it means that the electron wave of an individual electron has spread out over those two points. 9 Imax and Imin are the maximum and minimum intensities in the interference pattern. The distance over which an electron wave is coherent is inversely proportional to the internal angle in the beam, that is, the angle towards the nearest source image. For a large coherence length, this source image must be small. In the full Van Cittert–Zernike theory, it is found that the degree of coherence γ(x1,2) is directly proportional to the Fourier transform of the source image intensity function. For instance, when the source image is a homogeneously filled disk, the Fourier transform is the Airy function. In a target plane illuminated from that crossover, the function γ has fallen by 12 % when x1;2 =

 = Xc 2c

(1.6)

where θc is the semi-angle from the target to the crossover disk. Xc is usually called the coherence width. At a distance x1;2 =

 c

(1.7)

the illumination is generally considered fully incoherent. At a distance x1;2 =

 = Xpc 2c

(1.8)

there is still some coherence left and this is often taken as a practical coherence width, although the definition is somewhat arbitrary. The exact degree of coherence obtained between points at this distance will depend on the current density distribution in the source image and on the definition of the diameter of the source image. Probably it is best to define the crossover diameter as the FW50 value. There is a simple relationship between coherence and brightness: the current within the coherent area is    2 2  2 Icoh = Br V Xpc c2 = Br  V = 0:93  10−18 Br (1.9) 4 4 2 This is a surprisingly simple relation that tells us we have a coherent beam as soon as we limit the current to smaller than 10−18 Br. This is important to realize: if the current is smaller than 10−18 Br the beam is coherent: it is a necessary and sufficient con-

3

Chapter 1

1.1  Introduction and Definitions of Parameters

4

1  Electron Sources

Chapter 1

dition! In TEM, there is coherence over an area that contains this current. Thus, spatial coherence is not related to the size of the source, but rather to the size of the last source image before the target and the distance between that source image and the target. Note that lenses between that crossover and the target change the effective size and distance, but we do not need to know these exact relations: in practice, simply reducing the current density on the target increases the coherence. This implies that every beam can be made coherent by sufficient aperturing of the beam. 9 To talk about electron sources as being either coherent or not is generally wrong. The difference between sources is the amount of current that can be put in a coherent beam, but that is just a different way, and not a bad way either, of expressing the reduced brightness of a source. Note that this analysis is limited to sources that have an emitting area larger than the coherent area on the emitting surface itself. For single-atom emitters and carbon nanotubes, this may not be true, in which case the brightness goes effectively to infinity, as it does in laser beams (Kruit et al. 2006). The temporal coherence length or longitudinal coherence is the distance along the z-axis over which the wave is coherent. It can be imagined as the length of the wave package that represents the electron. 9 A perfectly monochromatic beam has a very long temporal coherence length. Different energies, however, have different wavelengths which interfere destructively, so a beam with energy spread has limited temporal coherence. From the uncertainty principle: E  t =

h ; 2

so zcoh =   t =

h 2  E

(1.10)

It is not directly obvious what the definition of this energy spread should be; it must be related to something intrinsic in the emission process and not contain contributions such as the high-voltage instability. Typical coherence length values are in the order of 1 µm (Niklaus and Hasselbach 1993). If two parts of the beam follow very different paths, it may occur that at the point of interference, the different parts of the wave function do not arrive simultaneously, which will affect the interference contrast. In principle, this may even happen in a lens: although the optical path lengths for all paths are equal, the lengths traveled by the wave packages on the different paths may be different. For most practical purposes we assume that the beam has sufficient long­ itudinal coherence.

1.2 Schottky Sources Most high-resolution (S)TEMs now have either a Schottky electron source or a cold field emission source. The reason for that is mostly the superior brightness of these sources. At the highest resolution they easily deliver a factor of a 1,000 more current in a probe or in a coherent area than a simple thermionic source. In other words, at the same current they give a 30-fold larger coherent width. Basically, these are the sources that have enabled routine atomic-resolution microscopy. Tungsten hairpin sources and LaB6 or CeB6 thermionic sources do exist, but for a description we refer to the original W&C where they have been described in sufficient detail.

1.2.1 Emission Theory Although often erroneously labeled as such, a Schottky source is not a field emission source, nor is it even a ‘thermal field emission’ source. A Schottky source in normal operation is a purely thermionic source where the effective work function of the material has been lowered by the Schottky effect. To understand the emission properties we first need to summarize the theory of electron emission. Figure 1.1 gives an illustration of the theory by showing the energy diagram (energy in eV versus distance in nm) for electrons near the boundary between a conductor and vacuum while there is an electric field on the surface. Simply to exit a conductor electrons must overcome an energy barrier called the work function. To find out the emission current density we need to determine the occupation of the states in 3D momentum space (left in the energy diagram) and then calculate the quantum-mechanical probability of their escaping from each state into vacuum, either over the potential barrier, or tunneling through the barrier. Thermionic emission occurs when, by heating, the energies of some of the conductance electrons become higher than the work function. When the work function is denoted by φ, the current density at the surface is expressed by the Richardson equation  '  j = A.1 − r/T 2 exp − (1.11) kT where A is the emission constant, 1 − r is the transmission coefficient of the surface barrier for electrons, T is the temperature, and k is the Boltzmann constant (1.38 · 10−23 J/K = 86 μeV/K). φ and kT are both in eV. The quantum-statistical derivation of this equation leads to A=

4mek2 = 1:204  106 A=.m2 K2 / h3

(1.12)

In general, 1 − r is close to one. Furthermore, there is a slight temperature dependence of φ, so the work function will have the general form ' = '0 + cT

(1.13)

1.2  Schottky Sources

5

Schottky plot

Chapter 1

98

1600K 1700K 1800K

log (l )

96 94 92 90 88

0

Fig. 1.1  Energy diagram (energy in eV versus distance in nm) illustrating the basics of emission theory

Actually, the work function also varies with crystal orientation. In practice, a simpler equation is often used for the current density  '  j = AT 2 exp − (1.14) kT in which the values of A and φ are then adapted for the measured current densities. At the surface of the emitter, the mean energy in the plane of the surface is kT and as long as the acceleration is perpendicular to the surface, this is conserved, so ˛ 2  e  V = kT (α is the half aperture angle in the beam). The intrinsic reduced differential brightness can then be expressed as (where dA is the emission surface) Br =

dI ej = dAd˝  V kT

(1.15)

if we take the FW50 value (diameter that contains 50 % of the current) for the source size. The energy distribution of pure thermionic emission is given by   A E+' dj.E/ = 2  E exp − dE (1.16) k kT The Schottky effect is the effective decrease of the work function when an external field F is applied at the metal surface (see Fig. 1.1). The necessary fields are very high and can only be obtained by sharpening a tip to submicron size, so that the field in front of the tip is enhanced by a large factor. The field-enhancement factor β is defined through F = βVE, where VE is the extractor potential.

10

20

30

√ VE

40

50

60

70

Fig. 1.2  Schottky plot

The magnitude of the Schottky effect can be analyzed by calculating the potential curve based on the image-force potential resulting from the attraction between an electron outside the surface and its image behind the surface. The net potential is now the sum of the zero-field image-force potential and the potential due to the field. For the lowering of the potential barrier we find (in eV) s eF ' = − (1.17) 4"0 This increases the thermi onic emission to ! p ' − eF=4"0 2 j = AT exp − kT

(1.18)

Experimental plots of ln I´ (the angular current density) versus p VE are called ‘Schottky plots,’ see Fig. 1.2. Since F = βVE and I´ = j(r/Mα)2 (Mα is the angular magnification from the emission surface to the measurement plane), the slopes of these plots yield the value of the field-enhancement factor β: ˇ=

4"0 .kB T/2 slope2 = 5:157.T  slope/2 e3

(1.19)

Since r is the tip radius and Mα is the angular magnification of the extraction field, with estimates for Mα and φ, the Schottky plot also yields the tip radius r. The Schottky plot can also give the work function   4em r 2  = kB T ln .k T/ + 2 ln − axis intercept B (1.20) h3 M˛

6

1  Electron Sources 12

Chapter 1

0.3 V/nm 0.5 V/nm 0.7 V/nm

10

0.5

1600 K 1700 K 1800 K

0.4

8

6

0.3

4

2

1

1.5

2

2.5

3

3.5

0.2 7 10

10 8 Br (A/m2eV)

10 9

Fig. 1.3  Energy distributions of electrons emitted from a Schottky emitter

Fig.  1.4 Intrinsic energy spread (FW50 values) versus intrinsic brightness for Schottky emitters

Note that there are several assumptions in the model used to produce the Schottky plot. There is no tunneling through the barrier, the work function is independent of the field, and the tip is a sphere, not a flat facet. Even with approximate equations, the Schottky plot is still useful (Swanson et al. 2008; Bahm et al. 2008). For example, we take into account that Mα is itself a func­ tion of β and r as in Mα = 0.525(βr)0.42. In order to keep the Mα constant, we should scale the voltage of the suppressor with the changing extractor voltage. It is also possible to fit the Schottky plot to a more complete model and extract the parameters from the fit (Swanson et al. 2012).

The energy distribution broadens to:     djES .E/ = A p 1 + exp E + ' − eF=4"0 =kT

The energy distribution for pure Schottky emission is the same as for pure thermionic emitters with the lower work function. The position of the energy spectrum shifts with increasing field to lower energies (Fransen et  al. 1999b). When the field on the emitter surface is sufficiently increased, electron tunneling through the top of the potential barrier occurs. The emission is then in the ‘extended Schottky regime.’ In order to find analytical equations for the emission current and energy distribution, the form of the energy barrier is approximated by a parabolic function. The emission current density is then found from ! p ' − eF=4"0 q 2 jES = AT exp −  (1.21) kT sin q with q=

3=4 h.4"0 e/1=4 F 3=4  −3 F = = 0:118  10 2 2 m1=2 kT kT T

(1.22)

ln Œ1 + exp.E=/ dE   djS .E/  ln Œ1 + exp.E=/ E

(1.23)

with djs(E) the energy distribution for pure Schottky emission. These approximations are valid up to a value of q of about 0.7 when extracting the energy spectrum, but only up to q = 0.25 for the current density jES. For stronger fields, only numerical solutions are available. Figure 1.3 shows how the energy distribution broadens and shifts as the field on the surface increases. Figure 1.4 plots the full width containing 50 % of the current value of the energy spread distribution as a function of brightness for different temperatures. As in thermionic emitters, the practical brightness is Br = 1:44

ejES kT

(1.24)

1.2.2 Coulomb Interactions Schottky emitters yield particle densities that are sufficiently high for stochastic electron–electron interactions to occur. It is customary to distinguish between effects that increase the virtual source size (trajectory displacements) and effects that increase the energy spread (the Boersch effect). Monte Carlo simulations can give reasonably accurate estimates of these effects, but are cumbersome. The effects can also be approximated by analytical equations, but these are strictly speaking only valid for sections in the optics column where the beam has a constant energy. Es-

1.2  Schottky Sources

Which equations we use will depend on the local beam parameters such as the current density. For the typical parameters in a TEM we distinguish between the Holtsmark regime and the pencil-beam regime. In the pencil-beam regime, the electrons have a nearest-neighbor distance that is larger than the diameter of the beam, so this regime is appropriate after the beam has been apertured. In the absence of apertures, and before the first ex­ traction aperture, the crossover size is blurred by a point spread function with a Holtsmark distribution of FW50: FW50H = 0:172

m1=3 I 2=3 L2=3  "0 V 4=3 ˛ 4=3

(1.25)

Here L is the length of the segment under consideration between the crossover where the blur is calculated and a lens or aperture at the other end of the segment. V is the acceleration potential, α the half angle of the beam, m is the electron mass, and ε0 the dielectric constant. If the aperture angle is sufficiently small, the section is in the pencil-beam regime, with a FW50 FW50PB

m3=2 I 3 ˛L3 = 0:145 7=2  5=2 e "0 V

(1.26)

As a rule of thumb, when the regime may be either Holtsmark or pencil-beam, the contribution to the crossover size can be found from " 6=7  6=7 #−7=6 1 1 + FW50T = (1.27) FW50H FW50PB

EFW50H = 0:891

I 2=3 m1=3 1=3 "0 rc ˛V 1=3

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 7 10

108

109

Fig. 1.5  Full energy spread versus intrinsic brightness for Schottky emitters with various tip radii

fectively travels only through one side of the ‘crossover,’ the prefactors for the energy spread should be divided by 2. As a rule of thumb, when the regime may be either Holtsmark or Lorentzian, the contribution to the energy spread can be found from " 4  4 #1=4 E E E = + (1.30) EFW50T EFW50L EFW50H

(1.28)

(1.29)

1.2.3 Practical Aspects

The energy spread resulting from Coulomb interactions occurs mainly in the crossovers, or in the source very close to the tip. For the Boersch effect, the Lorentzian and the Holtsmark regime are most appropriate, with equations for the contribution to the energy spread (in eV) in one beam crossover I m1=2 1=2 "0 e ˛V 1=2

Energy spread including Boersch effect versus brightness

To get a first estimate for the contribution of the Coulomb interactions to the virtual-source size and energy spread of the source, we simply take the values for the parameters in the equations (V, α, rc) as they are at the extraction electrode and compare the FW50 with the virtual source size as seen in that plane. A more sophisticated approach can take the acceleration into account. For brightness values up to a few times 108 A/(m2 sr V), the trajectory displacement in the source region is still small compared to the virtual source size. The main danger of a virtual-source size increase and brightness loss lies in the section between the extractor and the accelerator. However, the energy broadening near the tip is important. Figure 1.5 shows how the energy spread can increase from intrinsic values of about 0.3 eV up to a value close to 1 eV, especially for large tip radii because these emit large total currents.

In Schottky sources and cold field emitters, the trajectory displace­ment reaches values comparable to the virtual-source image more easily than it does in thermionic emitters. The result is effectively a lower brightness of the source.

EFW50L = 1:41

1.8

Chapter 1

pecially in the source region this is not the case, and we should use better approximations. The whole analytical theory is fairly involved, and here we will only touch on it.

where rc is the size of the crossover. When the energy spread comes from the segment that includes the emitter, rc must be interpreted as the size of the emission surface. For Schottky emitters, this is the size of the low work-function facet, usually about one third of the tip diameter. Because the beam from the emitter ef-

7

Schottky emission may occur from any heated material in a strong field. Nevertheless, we shall limit the rest of our discussion to the most commonly used materials: single-crystal tungsten with a (100) surface at the tip end, which is coated with zirconium oxide (referred to as ZrO), see Fig. 1.6.

8

1  Electron Sources

Chapter 1

especially detrimental in this respect. Another ‘contamination’ effect that sometimes occurs is a hindering of the flow of ZrO towards the facet, making the emission unstable. After a vacuum ‘accident,’ the continuous renewal of the ZrO layer may restore the original properties of the source. A serious complication in operating a Schottky source comes from the fact that the shape of the tungsten tip depends strongly on its history: the shape depends on the temperatures and fields that the tip has experienced (Fujita and Shimoyama 2007; Bronsgeest and Kruit 2008; Bronsgeest and Kruit 2009, 2010; Liu et  al. 2010; Bahm et al. 2011). Figure 1.7 shows some different shapes that a tip can have. The creation of a flat facet on an etched, round tip, is a natural result of the thermodynamics of the surface: at elevated temperatures, tungsten surface atoms are mobile and diffuse over the surface. They attach and detach to surface steps such that terraces grow or shrink. At installation, the manufacturer has pretreated the tip to have a certain shape, but this shape may change during operation. To keep this ‘ideal’ shape as long as possible, the extraction voltage should be kept within a narrow range while the tip is hot. At high fields, the end facet shrinks and becomes more square-­ shaped. The sensitivity of the shape to the extraction field is also the intrinsic limitation to the brightness of Schottky sources. A higher brightness, measured up to 2 × 108 A/(m2 sr V), can be obtained by increasing the extraction field, but this results in further faceting, including faceting of the sides of the tip, and ultimately in unstable operation (van Veen et al. 2001). Fig. 1.6  a Schottky emitter with the blob of ZrO clearly visible on the shank. b Tip end of the emitter with the (100) facet. (From Bronsgeest PhD thesis TU Delft 2009)

At a temperature above 1,500 K, the ZrO forms an electric dipole layer at the tungsten surface that lowers the work function from about 4.5 eV to about 2.9 eV. The tip radius ranges from 0.3 to 2 μm. The front face forms a flat-facet surface, which ideally has a diameter of about one third of the tip diameter. The operating temperature is about 1,850 K. A typical suppressor voltage is −300 V and a typical extractor voltage is 5 kV. For a 1-μm-diameter tip with a 300-nm-diameter facet, a typical angular current density is 0.7 mA/sr, total emission from the facet 40 μA, emission from the shank 100 μA, virtual source size 30 nm. In the early years of the Schottky emitter the brightness was limited to about 2 × 107 A/(m2 sr V). Nowadays, brightness values of 5 × 107 A/(m2 sr V) (Maunders et al. 2011) and even above 108 are commercially available with energy spreads as given above. The lifetime of a well-treated Schottky tip can be several years, limited mainly by the supply of ZrO. The rate of evaporation is of course a steep function of temperature: if a tip has a lifetime of 10,000 h at 1,750 K, this reduces to 1,000 h at 1,900 K. The ZrO-coated tungsten must be operated in pressures below 10−7 Pa. If the pressure is too high, this may influence the work function and thus reduce the emission current. O2 and H2O are

At low fields, the atoms tend to move away from terraces of smaller radius towards steps of larger radius. Thus the center terraces on the tip disappear until a flat facet is obtained. In operation, this effect may continue when the extraction voltage is too low. When a number of these terraces pile up and shrink together, this is recognizable as a moving ring in the angular emission pattern. The effect is known as ‘ring collapse.’ This phenomenon is important, because you may be tempted to operate the Schottky source at low extraction field in order to minimize the energy spread. This only works for a short time, until the ring collapse sets in with its accompanying change of current and brightness. At intermediate fields, the facet is reasonably stable, although in the course of many months, the tip head always grows in diameter. This dependence of the tip shape on temperature and field makes it important to follow the correct start-up procedures for a tip and not operate it at temperatures or fields far away from the recommended values.

1.3 Field Emission Sources 1.3.1 Emission Theory By applying an electric field of very high field strength at the surface of a metal, electrons are emitted even without heating the

9

Chapter 1

1.3  Field Emission Sources

Fig. 1.7  Shapes of the W(100) facet in a Schottky emitter after different operating conditions. Magnification markers: a, b 500 nm; c, d 1 µm. (From Bronsgeest PhD thesis TU Delft 2009)

metal: this is known as cold field emission. In cold field emission, electrons tunnel straight from the Fermi level through the potential barrier into free space. Just as in Schottky emission, the high field strength is realized by using a nanometer-size pointed emitter facing an extraction electrode. For these sharp tips, the field-enhancement factor β is assumed inversely proportional to the tip radius: VE F = ˇVE = kr

(1.31)

where k is a factor depending on the exact configuration: it’s typically between 1 and 5. The current-density equation is derived in what is known as the ‘Fowler–Nordheim theory,’ for a model cathode that is flat. For extremely sharp tips, deviations occur which we shall not treat here. ! p "3 k 2 F 2 8' 3=2 2m p jCF = exp − .y/  8h't2 .y/ 3ehF sin p (1.32) with y = '='

and .y/ = 1 − y1:69

(1.34)

The parameter p is a measure for the current emitted above the Fermi level because T is above zero: p = kT=d

(1.35)

The parameter d is a kind of measure for internal energy, when φ and d are given in eV: d=

The energy distribution, shown in Fig. 1.9, is given by: djCF .E/ =

  4me3 2 2.y/' exp.E=d/ d exp −  dE h3 3t.y/d 1 + exp.E=kT/ (1.37)

The practical brightness is given by: Br = 1:44

jCF d

(1.38)

Coulomb interactions do not deteriorate the energy spread as they do in Schottky emitters because the total emission current is much smaller. However, limitations to the brightness occur sooner because of the small intrinsic size of the virtual source (Cook et al. 2010).

(1.33)

the relative decrease of the work function by the field, and t(y) and υ(y) slowly varying functions: t.y/ = 1 + 0:11y1:33

A plot of ln(I/VE2) as a function of 1/VE, called the Fowler–Nordheim plot, yields approximately a straight line in the zero-temperature equation, see Fig. 1.8. For a given work function, it yields the size of the emitting area A = I/j and the field-enhancement factor β = F/VE.

hF F p  9:76  10−11 3=2 ' 4t.y/ 2me' 3

(1.36)

–12

–14

–16

–18

–20

0

0.005

Fig. 1.8  Fowler–Nordheim plot

0.01

0.015

0.02

0.025

10

1  Electron Sources 15

Chapter 1

larger and thus require us to use a larger demagnification, which in turn has the same effect as lowering the brightness. When more than a few nanoamperes are drawn from a field emission tip, there is a danger that gun-lens aberrations will dominate the performance of the source, which can be minimized by careful design of the gun lens (Kasuya et al. 2014).

4.0 V/nm 4.1 V/nm 4.2 V/nm 4.3 V/nm 4.4 V/nm 4.5 V/nm

10

5

0

–0.6

–0.4

–0.2

0

0.2

Fig. 1.9  Energy spectra for a cold field emitter for various extraction fields

1.3.2 Practical Aspects Although tungsten has a high work function (approximately 4.5 eV), it is chosen for its rigidity, high melting point (3,655 K), and good etching characteristics. The high melting temperature is important for the cleaning procedure, which consists of heating the tip to ~2,500 K for a short period to vaporize all contaminants. This is known as flashing the tip. Since the tip of the field emission source (FEG) is spot-welded to a standard microscope filament, this temperature is simply achieved by passing a heating current through the filament. A typical cold field emission tip in a TEM may have a diameter of 10–20 nm and give an angular current density 5 μA/sr, total emission 20–40 μA, virtual source size about 2 nm. There aren’t very many measured brightness values for FEGs, but a representative one is 1.8 × 1010 A/(cm2 sr) at 1 MV (Kawasaki et al. 2000), so a generally accepted value for Br is 2 × 108 to 4 × 108 A/(m2 sr V). An advantage of field emission sources is the intrinsic low energy spread with a FW50 value smaller than 0.3 eV. The presence of even single-molecule contaminants may critically affect the shape and the work function of the tip, so the FEG must operate in a very clean high vacuum, in the range 10−8 Pa, but preferably lower. The general rule is that the emitter is more stable if the vacuum is better. Contaminants diffuse along the surface of the tip towards the emission surface, so it is important to keep the whole tip clean. Traditionally, a tip needed to be cleaned at least once per day, because the emission showed a continuous decrease of 10–20 %/h, but recent advances seem to find an operational mode that is stable for longer times (Cho et al. 2013). The small source size makes the FEG quite sensitive to stray fields and vibration. These may cause the effective diameter to be

Besides pure tungsten emitters in different orientations, many other FEG cathodes have been tested such as: oxygen-processed tungsten tips, carbon and carbon-coated tips, tantalum carbide tips, and semiconductor tips. Soon after the discovery of carbon nanotubes (CNTs), work started on using these as electron sources (de Heer et al. 1995; Fransen et al. 1999a). The main advantage expected of the CNT is that the surface is very stable and rather insensitive to contamination. At slightly elevated temperatures they emit in the order of 200 nA with only about 1 % variations (De Jonge 2004). Metal tips with protrusions of only 3 or even 1 atom were pioneered in the early nineties, but efforts to create such ‘single-atom tips’ have recently increased. The intrinsic brightness of these tips for all practical purposes is infinity because the virtual source size is always smaller than other contributions to the probe size (diffraction, trajectory displacement, gun-lens aberrations). For TEM, the beams from such sources are fully coherent. Efforts to use these innovations in a commercial machine continue (Houdellier et al. 2015) at the time of writing, but have failed in the past either due to insufficient current for analytical applications, or fabrication issues, or unexpected instabilities, or limited lifetime, or any other practical aspect.

1.4 Photo-Emission Sources The photo-emission effect can be used to create an electron source. However, the photons should have sufficient energy: it should be at least as high as the work function, and preferably a little higher, in order to have any efficiency. For unprepared surfaces this means that the light must be far into the ultraviolet, for which there are no good direct-current (DC) sources. So usually people go to low work-function surfaces or to pulsed emission. We can produce low work-function surfaces by, e.g., covering a semiconductor with a few monolayers of cesium, but it is very hard to keep the surface under the right conditions so this has not yet led to a source for TEM. Using high-intensity pulsed lasers, a single electron may absorb the energy from several photons so that photo-emission can occur at visible wavelengths without having to lower the work function of the surface. For TEM, the interest in pulsed emission has recently increased in order to create ‘ultrafast electron microscopes’ (UEMs – see Chap.  2) for the study of effects at the nanoscale and at the sub-picosecond time scale (Zewail 2006). As for normal TEM sources, it is necessary to go to pointed cathodes for obtaining high brightness. When hitting a cold field emission tip with a femtosecond laser, all kinds of interesting processes occur: field

enhancement from the E-field of the laser light, multiphoton absorption, combined photon absorption and field emission, etc. (Hommelhoff et al. 2006). The characteristics of these sources while in operation in a TEM are not yet well established.

1.5 Effect of the Electron Source Parameters on Resolution in STEM The resolution in STEM is determined predominantly by the size of the electron probe, with subtle influences from the coherence in the probe. Of course, there are also effects from the interaction between the beam and the specimen. Before continuing, we must define what we mean by ‘probe size.’ One parameter, the size, cannot, of course, define every aspect of a focused beam. Even for a perfectly round beam, what we would like to know is the full intensity distribution – the current density as a function of the distance to the center of the probe. That distribution is also called the point spread function (PSF – more on this too in later chapters). If the distribution is Gaussian, it is all fairly simple and any measure of size can be used. The full width at half maximum (FWHM) for a Gaussian is the same as the diameter that contains 50 % of the total current (FW50) and the same as the distance between the 12 % point and the 88 % point of the current that is measured when scanning over a knife edge – known as edge resolution d12-88. Many distributions, however, are not Gaussian. One example is the distribution in a spherical-aberration-dominated probe: at underfocus, this distribution has a very bright central spot on a broad background and at overfocus, the highest intensity is at the edge of the probe. The FWHM may then be small, but it contains hardly any current so it’s not a good measure for probe size! We have found that the FW50 is the most consistent measure to characterize a probe, also when it is non-Gaussian. One of the reasons is that the conversion between 25 and 75 % edge resolution and probe size, FW50 = 1.76d25-75, is practically independent of the current density distribution in the probe. There are situations, however, where it is useful to optimize for a minimum FW20 (size of the probe that contains 20 % of the current), which leads to a higher resolution at the cost of a lower contrast. Fundamentally, the correct way to calculate the distribution function in an electron probe is to start with the wave-optical calculation of the diffraction distribution as modified by the spherical aberration of the lens. It is necessary to do this for a range of defocus values, since we do not yet know which defocus will give the smallest probe size. Subsequently, these distributions must be convoluted with the distribution of the (defocused) source image. Finally, we can take account of the chromatic aberration effects by convoluting the distributions in the defocus direction with the energy-spread function. The minimum size of the probe is not found in the Gaussian image plane, but, due to the spherical aberration, at a small defocus. This procedure is worthwhile for a single calculation, but not

practical for optimizing the probe size. So what we usually do is to calculate the different contributions to the probe size separately. These contributions include, e.g., diffraction, spherical aberration, and source image. Now if all these contributions were independent and had a Gaussian intensity distribution, it would be simple to add them and find the full probe size: we could add them in quadrature. However, when the distributions are non-Gaussian this does not work. For some specific analytical forms of the distribution, an addition rule can be derived; for other distributions only a numerical approach can give an approximate addition rule. The equation that yields the best fit to the minimum FW50 results of the fundamentally correct procedure is (Barth and Kruit 1996): 00 1 12 1  1:3 ! 1:31 2 1   B A + dc2 C dP = @@ dI1:3 + dA4 + ds4 4 A

(1.39)

where dI, dA, ds, and dc are the FW50 values of the contributions from the source image, the diffraction disk, the spherical aberration, and the chromatic aberration, respectively. So we first add the diffraction to the spherical aberration with a fourth-power rule, then add the source size contribution with a 1.3-power rule, and finally add the chromatic aberration effect with a simple square-power rule. For spherical-aberration-corrected systems we do not have such an equation yet, but a slight adaptation to the ds term should yield a useful equivalent. Optimization of the probe size consists of finding the aperture angle and source-to-probe magnification that gives the smallest probe size, or the largest current in a specific probe size.

1.5.1 Contributions to the Probe Size To form a probe, the virtual source is imaged on the target with magnification M to an FW50 size Mdv. Since Br is a conserved quantity through the whole system, the current in the probe is calculated from IP = Br

 .Mdv /2  ˛ 2 V 4

(1.40)

where α is the half-aperture angle at the probe, V is the accelerating voltage at the target, and Br the practical brightness as discussed earlier. From this, the contribution to the probe size can be expressed as: s IP 1 2 d1 = Mdv = (1.41)  Br V ˛ 2

11

Chapter 1

1.5  Effect of the Electron Source Parameters on Resolution in STEM

1  Electron Sources

  1 dA = 0:54 = 0:54 1=2 ˛ V ˛

(1.42)

with Λ = 1.226 × 10  m V . −9

1/2

Spherical aberration causes the outer rays in the beam to be defocused by an amount dz = Csα2, so at the Gaussian image plane, they have a distance Csα3 from the axis. This leads to a ‘disk of least confusion’ or minimum width of the total beam (FW100) of 0.5Csα3. However, the FW50 value has a much smaller minimum: ds = 0:18Cs ˛ 3

Chromatic aberration causes the electrons with lower energy to be focused closer to the lens than electrons with higher energy. This leads to a blurring contribution for FW50: ıU ˛ V

dp dp

for I

dI f or I 10

for I

=5

x10 – 18. B

=0

r

.5x1

=0

0 18

.5x1

–1

–

. Br dA

0 –18

. Br

dc

(1.43)

In probe-size calculations, we can often only use the aberration coefficients of the last probe-forming lens for the analysis. This is because usually the last lens demagnifies all aberration contributions of the other lenses in the system. However, for emitters with a very small virtual source size, such as the CNT emitter, we must also explicitly take account of the aberration coefficients of the gun lens. In a microscope with an aberration corrector for the probe lens, this equation should be replaced by a different one that also contains a term increasing with aperture angle. The problem is that we cannot give a general equation valid for each microscope or even for one particular microscope. The reason is that once the third-order aberration (and nowadays sometimes even the fifth-order aberration) is corrected, the remaining aberrations depend on the settings of the corrector and the alignment of the beam. Often the latter are no longer rota­ tionally symmetric.

dc = 0:6Cc

10 0

ds

Chapter 1

The size of the diffraction spot is often given as 1.22λ/α; however, this is not the FW50 size, but the size of the first zero in the ring pattern. The FW50 value is

d [nm]

12

0.005

0.01

0.02

alpha [rad] Fig.  1.10 Optimization of aperture angle (Br = 108, V = 200 keV, dU = 0.8 eV, Cs = 0.7 mm, Cc = 2 mm)

1.5.2 Current in a Probe At very small currents, the size of the source image is negligible. If we assume that the spherical-aberration contribution is much smaller than the chromatic-aberration contribution, the probe size is   !1=2   ıU 2  1 2 dP = 0:54 1=2  + 0:6Cc ˛ (1.45) V ˛ V For optimized α this is 1=2

(1.44)

with Cc the chromatic aberration coefficient of the system and δU the FW50 of the energy distribution of the source. If the energy distribution is Gaussian, the FWHM of the distribution is very different from the FW50 (in contrast with a 2D Gaussian distribution, where FW50 = FWHM). If you were to use that FWHM value, the prefactor in the chromatic aberration contribution would be 0.34 instead of 0.6. Figure 1.10 shows all these contributions as a function of the aperture angle α and the addition according to Eq. 1.39.

.dP /min = dAC = 2:81  10−5 s 0:54V 12 ˛= 0:6Cc ıU

Cc ıU 1=2 V 3=4

at

(1.46)

Thus, the minimum probe size is not dependent on the brightness or the coherence of the emitter; the only emitter property that enters the equation is the energy spread! If we assume the chromatic aberration contribution to be much smaller than the spherical aberration contribution, the probe size is ! 41    1 4 3 4 0:54 1=2  dP = + .0:18Cs ˛ / V ˛



(1.47)

For optimized α this is 1=4

.dP /min = dAS = 1:03  10−8

Cs V 3=8

at

˛ = 1:23



 Cs V 1=2

1=4

(1.48)



Thus, the minimum probe size is not dependent on the brightness or the coherence of the emitter; here it does not depend on any emitter property. For aberration-corrected systems the minimum probe size will depend on the remaining aberrations and the defocus.

where KΛ = 1.08 × 10−18 m2 sr V. This is a very useful equation, because it gives a simple estimate of how much current there is in a probe which is close to the minimum size, whatever causes the minimum size: chromatic aberration, spherical aberration, or any other remaining aberration in a corrected system. When the FW50 of the virtual-source image equals the FW50 of the diffraction spot (dI = dA) we call the current IΛ, with IΛ = KΛBr. For example, for a Schottky emitter at Br =  108 A/(m2 sr V), this current is 100 pA, independent of the beam energy or the lens aberrations! Of course, beam energy and lens aberrations do determine the size of the probe that contains this current.

However, a probe without current is of no use, so we have to allow a contribution to the probe size that is related to the current in the probe. By expressing the probe-size contribution in terms of the diffraction contribution, the probe current can be rewritten as    2   2 2 dI  2 dI 2 IP = Br dI  ˛ V = Br 0:54  = Br K 4 2 dA dA 

(1.49)

Chapter Summary The single most important parameter of an electron source is its brightness: the current that is emitted into a certain solid angle (i.e., the extraction aperture) divided by the virtual size of the source, normalized for the acceleration voltage. We have seen that the brightness is directly related to the current that can be obtained in a coherent beam in TEM, and in a probe in STEM. The second most important parameter is the energy spread, related to the effects of chromatic aberration and to energy resolution in EELS.

field emitters operate at an even higher field than Schottky emitters, which enables field emission, the tunneling of the electrons through the potential barrier of the work function. The differences in how emission occurs cause all kinds of differences in source parameters and practical issues during operation. We included a short ‘excursion’ on the theory of stochastic Coulomb interactions because this effect can be of influence both on the energy spread and the brightness of a source.

The core of this chapter is the description of Schottky electron sources and cold field emission sources. Schottky emitters are really thermionic emitters, where the emission is enhanced by the Schottky effect, which is simply a lowering of the work function by the strong field at the surface. Cold

We ended the chapter with an analysis of the relation between source properties and resolution in STEM, which of course is the same as an analysis of how small we can focus the beam and how much current we can get in the probe. A few useful rules of thumb are explained.

13

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1.5  Effect of the Electron Source Parameters on Resolution in STEM

14

Appendix  Effect of the Electron Source Parameters on Resolution in STEM

Chapter 1

Appendix People Walter Schottky was born in Zurich on 23 July 1886 and died in Pretzfeld, Germany, on 4 March 1976. He contributed to many technological inventions and discoveries, including the Schottky defect, Schottky barrier and Schottky diode.

Self-Assessment Questions Q1.1

Why is the total emission current not a good parameter to characterize a source? Q1.2 What is the difference between the virtual source size and the physical size of the emitting area of an electron source? Q1.3 Why can we assume that the angular current density in a microscope is uniform, while the spatial density in the virtual source is approximately Gaussian? Q1.4 Explain the difference between differential brightness, reduced brightness, and practical brightness. Q1.5 Compute the electron wavelength for acceleration voltage 1 kV, 30 kV, 100 kV, 300 kV. Q1.6 Use the interdependencies of the parameters in the equation for reduced brightness to show that the reduced brightness is not affected by: a. the choice of the magnification from source to probe b. the size of the beam-limiting aperture c. acceleration or deceleration (for ease of explanation assume the acceleration in the plane of a lens) from energy V1 to V2. Q1.7 Why are there three different spatial coherence lengths defined? Q1.8 Derive the relation between current within a coherent area Icoh and the reduced brightness. Q1.9 Explain how electrons are forced to leave the emitter in respectively a Schottky emitter and a cold field emitter. Q1.10 What is the relation between brightness and temperature in respectively a Schottky emitter and a field emitter? Q1.11 (Advanced) Use your favorite math program to perform a simulation that gives you practical brightness and the full-width-50 value of the energy spread of a thermionic electron source as a function of temperature. Q1.12 If a Schottky source in the electron microscope seems not to deliver the expected brightness, how can a Schottky plot show whether this is a result of a blunt tip or an increased work function or neither?

Q1.13 Give two reasons why the energy spread of a beam from a Schottky source increases when more current is extracted from the tip. Q1.14 What limits the lifetime of a Schottky source if all goes well? Q1.15 Give at least three incidents that can end the life of a Schottky source prematurely. Q1.16 What is a Fowler–Nordheim plot and which information on a field emission source can be obtained from it? Q1.17 Why is the short-term current stability of a cold field emission source intrinsically less than that of a Schottky source? Q1.18 Why is the energy spread of a cold field emission source intrinsically smaller than that of a Schottky source? Q1.19 What is the difference between a FWHM and a FW50 of an electron probe, in definition, and in practice? Q1.20 What is the numerical difference between the FWHM, the FW50 of a probe and the 25–75 edge resolution for a Gaussian current density distribution in the probe? Q1.21 Compute the difference in total probe size after adding two equal distributions either linearly or by the twopower rule or by the four-power rule. Q1.22 Consider a lens system that images a Schottky electron source (effective dsource = 30 nm, Br,pract =  108 A/(m2. sr. V), FW50dE = 1 V) onto a sample at electron energy 80 kV. Assume aberration coefficients Cs = 1 mm, Cc = 2 mm. Calculate all contributions to the probe size for an aperture angle of 10 mrad and a source to probe magnification of M = 1/150. Also calculate the total probe size and the current in the probe. Q1.23 (Advanced) Use your favorite math program to calculate and plot all contributions to the probe size as a function of half angle α and determine the optimum angle. Use realistic estimates for all parameters. Q1.24 How does the current in a probe at the highest resolution setting in STEM depend on the aberrations of the microscope? Q1.25 (Advanced) Construct the (I, d) function for parameters of your choice, optimizing both M and α. If applicable for your parameters, show where the dominant aberration changes from Cc to Cs.

References General References Bronsgeest MS (2014) Physics of Schottky Electron Sources, Theory and Optimum Operation. Pan Stanford Publishing Pte, Singapore Fursey G (2005) Field Emission in Vacuum Microelectronics. Kluwer Academic, New York Jansen GH (1990) Coulomb Interactions in Particle Beams. Advances in Imaging and Electron Physics, Supplement 21, Academic Press, Inc, San Diego Jensen KL (2007) Electron Emission Physics. Advances in Imaging and Electron Physics 149 Academic Press Inc, San Diego Kruit P, Jansen GH (1997 and 2008). Space Charge and Statistical Coulomb Effects. Handbook of Charged Particle Optics, edited by Orloff, J., CRC press. Swanson LW, Schwind GA (1997 and 2008). Review of ZrO/W Schottky Cathode. Handbook of Charged Particle Optics, edited by Orloff, J., CRC press. Swanson LW, Schwind GA (2009) A Review of the Cold-Field Electron cathode. Advances in Imaging and Electron Physics 159:63–101 (Elsevier Academic Press)

Specific References Bahm A, Schwind G, Swanson L (2008) Range of validity of field emission equations. J Vac Sci Technol B26(6):2080–2084 Bahm A, Schwind G, Swanson L (2011) The ZrO/W(100) Schottky cathode: Morphological modification and its effect on long term operation. J Appl Phys 110 054322 Barth JE, Kruit P (1996) Addition of different contributions to the charged particle probe size. Optik 101(3):101–109 Barth JE, Nykerk MD (1999) Dependence of the chromatic aberration spot size on the form of the energy distribution of the charged particles. Nuclear Instr Methods Phys Res A 427(1–2):86–90 Bronsgeest M, Kruit P (2008) Effect of the electric field on the form stability of a Schottky electron emitter: A step model. J Vac Sci Technol B26(6):2073–2079 Bronsgeest M, Barth J, Swanson L, Kruit P (2008) Probe current, probe size, and the practical brightness for probe forming systems. J Vac Sci Technol B26(3):949–955 Bronsgeest M, Kruit P (2009) Reversible shape changes of the end facet on Schottky electron emitters. J Vac Sci Technol B27(6):2524–2531 Bronsgeest M, Kruit P (2010) ‘Collapsing rings’ on Schottky electron emitters. Ultramicroscopy 110(9):1243–1254 Cho B, Shigeru K, Oshima C (2013) W(310) cold-field emission characteristics reflecting the vacuum states of an extreme high vacuum electron gun. Review of Scientific Instruments 84, 013305

Cook B, Verduin T, Hagen C, Kruit P (2010) Brightness limitations of cold field emitters caused by Coulomb interactions. J Vac Sci Technol B28(6):C6C74–C6C79 Fransen MJ, van Rooy TL, Kruit P (1999a) Field emission energy distributions from individual multiwalled carbon nanotubes. Appl Surf Sci 146:312–327 Fransen MJ, van Rooy TL, Tiemeijer PC, Overwijk MHF, Faber JS, Kruit P (1999b) On the Electron-Optical Properties of the ZrO/W Schottky Electron Emitter. Adv Imaging Electron Phys 111:91–166 Fujita S, Shimoyama H (2007) Mechanism of surface-tension reduction by electric-field application: Shape changes in single-crystal field emitters under thermal-field treatment. Phys Rev B75(23):75, 235431 de Heer WA, Chatelein A, Ugarte D (1995) A Carbon nanotube Field Emission Electron Source. Science 270:1179–1180 Hommelhoff P, Sortais Y, Aghajani-Talesh A, Kasevich MA (2006) Field Emission Tip as a Nanometer Source of Free Electron Femtosecond Pulses. Phys Rev Lett 96:077401 Houdellier F, de Knoop L, Gatel C, Masseboeuf A, Mamishin S, Taniguchi Y, Delmas M, Monthioux M, Hytch MJ, Snoeck E (2015) Development of TEM and SEM high brightness electron guns using cold-field emission from a carbon nanotip. Ultramicroscopy 151:107–115 De Jonge N (2004) Brightness of carbon nanotube electron sources. J Appl Phys 95(2):673–681 Kawasaki T, Matsui I, Yoshida T, Katsuta T, Hayashi S, Onai T, Furutsu T, Myochin K, Numata M, Mogaki H, Gorai M, Akashi T, Kamimura O, Matsuda T, Osakabe N, Tonomura AA, Kitazawa K (2000) Development of a 1 MV field emission transmission electron microscope. J Electron Microsc 49(6):711–718 Kasuya K, Kawasaki T, Moriya N, Arai M, Furutsu T (2014) Magnetic field superimposed cold field emission gun under extreme-high vacuum. J Vac Sci Technol B 031802 Kruit P, Bezuijen M, Barth JE (2006) Source brightness and useful beam current of carbon nanotubes and other very small emitters. J Appl Phys 99, 024315 Liu K, Schwind G, Swanson L, Campbell J (2010) Field induced shape and work function modification for the ZrO/W(100) Schottky cathode. J Vac Sci Technol B28(6):C6C2–C6C33 Maunders C, Dwyer C, Tiemeijer P, Etheridge J (2011) Practical methods for the measurement of spatial coherence-A comparative study. Ultramicroscopy 111(8):1437–1446 Niklaus M, Hasselbach F (1993) Wien filter: A wave-packet-shifting device for restoring longitudinal coherence in charged-matter-wave interferometers. Phys Rev A 48:152– 160 Swanson LW, Schwind GA, Kellogg SM, Liu K (2012) Computer modeling of the Schottky electron source. J Vac Sci Technol B30 06F603 van Veen AHV, Hagen CW, Barth JE, Kruit P (2001) Reduced brightness of the ZrO/W Schottky electron emitter. J Vac Sci Technol B19:2038–2044 Zewail AH (2006) 4D Ultrafast Electron Diffraction, Crystallography and Microscopy. Annual Rev Phys Chem 57:65–103

15

Chapter 1

Appendix  References

2

Chapter 1

In situ and Operando

Chapter Preview This topic is a very broad one since it involves everything that has been covered in W&C and then allows the specimen to change while you image it, record the spectra, and/or measure what changes are taking place. We are combining two topics that could be treated separately, namely in-situ experimentation and controlled-environment TEM (which we’ll call an ETEM, but you’ll also see E-TEM or eTEM). The reason for combining the two is that changes in the environment about the sample can change the material as we examine it in the TEM. With TEM, it’s always an in-situ study! We’re also including operando with in situ; operando implies that the material is behaving as it would do in “real life”; the translation is “working.” For example, if a catalyst particle is actually acting as a catalyst when we observe it, it’s an operando study; in general such a particle can’t act as a catalyst unless there is something to catalyze! You are often measuring something (there is a metric) that relates to the performance of the materials – so that you know it’s performing! In the traditional TEM, the environment is always very reducing – traditionally we use the highest vacuum we can; historically we deposit a layer of carbon on the sample too (whether we wanted to or not). The reason for the clean vac-

Chapter 2



uum is to prevent contamination of the sample and to avoid gases streaming up the column and degrading the vacuum of the electron gun or depositing on the window of the XEDS detector. Now we have two ways of changing the environment: we can use special holders, or we can actually modify the column around the specimen using extra apertures and differential pumping. The field of in-situ TEM is changing rapidly for two reasons: nanotechnology is being used to build better, more flexible holders, and we have better, faster ways of collecting and recording the information from the changing specimen. Of course, the TEMs are also better and more stable, but that is not what is presently driving the progress. So in this chapter we will outline what the holders can, and maybe can’t, do. We’ll discuss how the environment can be controlled, how we can record the changes, and how we can correct for drift when it is occurring. We’ll also mention the cost of holders, why you might not have the one you want, and what you can do about it. There is no difference between an in situ experiment and an in-situ one – it’s just grammar and both are correct.

© Springer International Publishing Switzerland 2016 C. B. Carter, D. B. Williams (Eds.), Transmission Electron Microscopy, DOI 10.1007/978-3-319-26651-0_2

17

18

2  In situ and Operando

2.1 General Principles Chapter 1 Chapter 2

If you are asking ‘why do we want to do in-situ microscopy?’ you should probably skip this chapter for now. The purpose of the chapter is to show you the potential of this type of microscopy and to give you an idea of how you can apply the techniques. For example, if you are processing nanoparticles, you might want to understand how they change during processing. Similarly, if you study catalysis, you know that the environment is a critical factor in determining and controlling the processes that take place; most catalysis does not take place in a vacuum, especially not in an ultrahigh vacuum (UHV). So we need to be able to change the environment around the specimen, but the atmosphere in a regular TEM is very reducing. Old TEMs tend to deposit carbon on the sample as the electron beam cracks oil vapor in the column. Of course, the vacuum can be an advantage if we want to study film growth in situ, e.g., for molecular beam epitaxy (MBE), because we are already close to the actual growth conditions. So the question then becomes, can you controllably change the environment if you must? The realization that nanomaterials are important and that they often have properties differing from bulk materials has led to enormous interest in TEM characterization. Gradually, we have realized that it is not enough to be able to image these small particles because they change: nanoparticles of ‘inert’ materials can be very reactive. We want to understand how and why they change. Now, it is not enough to synthesize a novel material, we must understand the origin of novelty. In order to understand the origin of novelty, it is important to understand how the atoms come together to form a cluster of atoms, and at a later stage, how they combine together to form the final novel material. This is where in-situ microscopy can play a unique role, using careful experimental design of the process in the TEM: in-situ TEM provides the link between structure, processing, and performance. Traditionally, in materials science and biology, a series of samples are synthesized by varying the processing parameters and then they are characterized under the microscope. What we want to do now is avoid this post-mortem approach by using in-situ studies and continuously vary the processing parameters while the material is still inside the microscope. This can allow us to analyze transition states that we wouldn’t otherwise see! We say that in-situ experiments allow us to study the full parameter space. We will only give examples as illustrations, not as an end in themselves – we’ll give references for you to pursue the applications. Operando

You can read about the origin of the term operando. It is the ablative form of the gerund of the Latin verb operari so we italicize it and do not add ‘in’! It has same meaning in Spanish and Italian. The other rule is that we stop using italics when the word or phrase is in common use. 9

Fig. 2.1  The power of in-situ TEM: controlled manipulation of nanosized objects, and seeing what you are doing! Carbon nanotubes are being used to relocate iron nanoparticles

Materials change as they are used, often due to exposure to corrosive environments. The changes take place at the surface of the sample and propagate into the bulk material. If the material is a nanoparticle, there is no bulk! Atomistic mechanisms are involved whenever a material interacts with the environment. In-situ TEM can directly reveal how these processes occur – especially if you can obtain the necessary resolution (temporal and spatial). In-situ manipulation of a nanoparticle is illustrated in Fig. 2.1; this figure really shows the power of in-situ experimentation – we can see what we are doing to a nanoparticle! Many other components of the TEM will be close to the in-situ holder, including the objective lenses, the objective aperture, the cold-finger, and possibly the XEDS detector(s). When designing a new holder, the proximity and interaction with these microscope components must be considered. The effect of the magnetic field (~ 2 T) of the pole-piece on the specimen has always created a challenge for imaging magnetic samples even if they are fixed tightly in the holder; many older TEMs have such samples decorating the interior of the column. It takes time and effort to learn an in-situ technique; attention to detail and persistence is the key to success.

2.2 Some history The history of in-situ TEM studies is relevant, because you will read and use reports that are in the literature. The in-situ specimen holders used to be top-entry and side-entry. Now they are nearly all side-entry. We often have two competing ‘motivations’: i) improve the vacuum so that there is less contamination, and ii) find ways to envelop the specimen in a liquid or a gas. A FEG source has to be in the best vacuum possible to maximize its stability and lifetime. Remember: the gun may

2.3  The Possibilities

The main emphasis in W&C was often to optimize all the components of the microscope to maximize the spatial resolution. We usually worked hard to obtain a high vacuum (aka a low pressure) and a contamination-free environment. But now our philosophy is going to be slightly different. We now want to observe changes in the specimen/thin foil as some external stimulus is changed. The emphasis here is to be able to see things as they happen, and so, we may compromise on the resolution to be able to achieve this. While in a conventional TEM, we take elaborate steps to minimize thermal gradients (to minimize drift), we actually heat the specimen (often to fairly high temperatures) when we want to study thermal transformations in situ. Since the thermally induced transitions often depend upon the environment, we may also decide to deliberately contaminate the TEM by passing gases into the sample chamber. Of course, we try to do this in a controlled fashion such that this contamination is restricted to a region very close to the specimen. The Stimulus

This stimulus could be chemical, the environment, a temperature change, stress or staining, laser illumination, an applied external electric or magnetic field, etc. 9 The big challenge is how do we fit in-situ capabilities within the pole-piece gap of the TEM? In the future, we will see that one solution is to use aberration correction to increase the polepiece gap without forfeiting the obtainable resolution. That’s the future, but in many labs it is already here.

Fig. 2.2  Schematic summarizing the different sections of in-situ TEM

2.3 The Possibilities Since this topic can take up several books itself, let’s look at the scope of the topic first. The schematic in Fig. 2.2 summarizes the possibilities we are discussing. We may want to combine these topics. We may want to strain the sample while heating it. We may want to apply the strain locally (indentation) rather than globally (compress the specimen). We may even want to strain the specimen while heating it in a gas and irradiating it. We must also think about how fast or slow we want the stimulus to be, and for how long. How quickly do we need to record the specimen’s reaction after stimulation? TEM as a Lab

The basic idea is to use the TEM as an in-situ experimental laboratory with atomic resolution. 9 Some points to keep in mind as we discuss this topic: zz Always keep safety in mind – both your own and that of the TEM and specimen holder. zz You will certainly be able to extract data from an in-situ experiment; the challenge becomes understanding the data and its relevance. zz Before you begin an experiment, think about what the sample will ‘see’ during the experiment; that includes the environment (chemical, pressure, temperature, stress, magnetic and electric fields), any grids, the holder, or anything else that might influence the reaction/mechanism. zz What accelerating voltage should we use in the experiments? For thicker samples, a higher accelerating voltage is preferable. For liquid-cell studies or indentation on bulk-like structures, a medium voltage is preferred. If we want to minimize the effect of the beam, a low voltage may be necessary. In any

Chapter 2

The traditional problems for in-situ TEM studies have always been specimen drift, contamination and alterations caused by the electron beam; and they still are! We can minimize the first two, but the third is unavoidable. Historically, we had three types of in-situ holders: straining, heating, and cooling, but we could generally only have one of these at any one time. Some in-situ studies were carried out in high-voltage (1 to 3 MV) machines so as to see through thicker specimens at high resolution, which more closely represent bulk material. Often these high-kV machines were used to simulate the effect of ion irradiation, which could be carried out in combination with straining, heating, or cooling. With the development of nanotechnology, new holders have become available; this allows us to be more quantitative and to combine stimuli.

Chapter 1

have to go back to the factory if the tip is destroyed. To minimize contamination and back-streaming to the gun, the vacuum within the column for a modern TEM is ~ 1 × 10−7 torr.

19

20

2  In situ and Operando

Chapter 1

Fig.  2.3 A grain boundary in α-Ti building up dislocations during in-situ loading, followed by the eventual ejection of dislocations with several slip systems shown as B,  C  and D, where C was dominant. The initial (a) and final (c) states would not give a clear understanding of intermediate (b) state without in-situ observation

Chapter 2

zz

zz zz zz

zz

zz

case, how long the beam irradiates the samples may well be critical. Beam control can be automated in STEM. Of course, you always want to know what the beam current is. Use a Faraday cup to check it. It almost goes without saying that we are always interested in the kinetics of processes; some changes, like the phase changes in phase-change materials (PCMs) are very fast, but we can now be quite quick too. What environment do we want or need? The environment will be critical for catalysis, but also the in-situ growth of thin films. What temperature will we need? We like room temperature because that is where the sample is generally most stable. We are often most concerned about how materials respond to stimuli – to applied fields – this is the basis of the electronics industry, the memory industry, etc. We’d like to be able to see directly the impact from an applied field. Whether we are growing thin films, simply depositing particles, or implanting atoms, we are often adding material. Of course, material will also be removed from a structure by sputtering or by displacement, such as bubble formation in a liquid cell. There is always an advantage to using energy-filtered imaging to decrease the effect of chromatic aberration.

We are not going to list every variant of every experiment, but we want to help you see the possibilities. The general question is ‘how does the material change over time? Keep in mind that we should always carry out the corresponding ex-situ analysis to be sure that beam effects have not completely changed the experimental response. Results from the ex-situ experiment will help us know whether or not the study can be completed in situ within the TEM. The experimental study on a microelectromechanical system (MEMS) heating stage could be carried out ex situ in an external vacuum chamber to reproduce the experimental conditions in the microscope without the electron beam. Overall, it might be easier to leave part of the specimen unexposed to the electron beam until the end of the test, to compare characterization with the exposed region.

2.3.1 Post-Mortem Characterization Post-mortem analysis of deformation only provides the end result from a nanoindentation experiment. In-situ observation provides real-time imaging for a complete story of transition states that can be related to the stress-strain measurements. This can be seen in Fig. 2.3, where dislocation accumulation at a random grain boundary in α-Ti produced elastic distortion, until slip systems were activated to minimize the accumulated strain energy. This is why in-situ microscopy is so powerful. You see what happens and the order in which it happens, instead of trying to interpret what has happened during a reaction or process by comparing the initial and final states. We can view the processes as they occur within the microscope with nanoscale resolution (or better). Real-time imaging of dynamic processes enables us to view the effect that defects have on processes and structures. In a post-mortem analysis, you may overlook many factors. You could simulate the process, but hopefully you would remember to check what really happened. However, post mortem analysis is essential for many in-situ studies; e.g., a reactive environment might not allow you to analyze the specimen completely – you hope to stop the reaction and then probe it in a stable state. This is especially important when chemical analysis is not possible in the configuration you may be working with, such as older designs of liquid-cell holders.

2.3.2 Statistics Before you perform in-situ TEM experiments, consider the statistical significance of the experiment and its reproducibility. Questions you should be asked at every presentation of your work will concern the set-up and control of your in-situ TEM experiment: the imaging conditions, beam effects, the defects in the material, especially when caused by specimen preparation, and how these considerations influenced your findings. It is so important to spend time with your experimental design so that you don’t end up repeating all your hard work in an effort to confirm your interpretation, but you need to be able to when necessary for the scientific process! Reporting the complete characterization of the parameters defining your experiment will leave a legacy for

2.3  The Possibilities

Chapter 2

Chapter 1

Fig. 2.4  Measurement of hundreds of inter-nanoparticle spacings of DNA-assembled Au nanoparticles, where the samples dried configured to spacing far below that which was predicted by the DNA attachment in solution. Rows show the time that particles were allowed for attachment. a Hybridized Au nanoparticles imaged on a dry surface in vacuum. b Hybridized Au nanoparticles imaged in a continuous liquid

21

your published results, even if your printed interpretation turns out to be incorrect. Give some thought to the relevance of the properties observed within the TEM to the bulk materials that we are trying to characterize. The electrical, mechanical, magnetic, optical, and reaction properties of materials measured in situ will all be affected by the free surfaces available, particularly when in contact with gas/ liquid. This is especially important when you consider the substrates used to support small catalyst particles or reactive species. In TEM, we cannot avoid having relatively large surface areas (especially of heavy elements like metals), since the samples are thinned to electron transparency or are nanoscale to begin with. The advantage TEM provides is location-specific detail. Specific test cases could be set up to determine the effect of defects, grain boundary orientations, doping, and crack dependence on the nanostructure in comparison to an averaged response in bulk studies. As an example, many researchers have used conventional TEM analysis on carbon grids to study nanostructured assemblies, though it has been shown through controlled experiments that during drying, the free surfaces cause these assemblies to have

smaller inter-nanoparticle spacing than those you would observe if the arrays were in solution, Fig. 2.4. This systematic approach provided enough statistical evidence to prove the conclusion, though reproducibility in the experimental design was required. We do not want to introduce artifacts that will affect our in-situ measurements; otherwise we are only studying sample-preparation artifacts. Pay attention to the preparation of the specimen – it’s at least as important for in-situ analysis as it is in conventional characterization. An example is in preparation of a semiconductor specimen for characterizing the electrical properties of the material: if you use an ion mill to thin the sample, you will implant ions into the material. You may not see these dopants in the image or detect them in a spectrum, but they will highly influence the electrical behavior of the material. Therefore, once again, the success of the TEM experiment for in-situ analysis will be based on how well the specimens are prepared before you put them in the TEM. We have to apply statistics to in-situ studies so that we can compare them to other measurements; you may find the article by Spitzer et al. (2014) interesting. (Remember the meaning of ‘typical image’.)

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2  In situ and Operando

2.4 Time Chapter 1

The experiment defines the temporal resolution required to capture the events of interest happening in a material. For example, atom migration and transient states during phase transitions require sub-microsecond timeframes to capture those events, whereas corrosion and radioactive decay occur on much longer timescales of hours to months. So, when approaching the characterization of a material process or mechanism within the TEM, we should first define the process duration and then choose the instrumentation.

Chapter 2

2.4.1 Recording the Data The first in-situ experiments were captured by pointing a video camera directly at the phosphor screen in the viewing chamber. The first videos of dislocations moving were recorded in this way. There could well be a situation where this will still be the best approach! In this case, you will be limited by how fast your phosphor can respond to changes in the intensity of the electron beam and what resolution it can give. You record changes in your specimen as they take place to prove to others that you understand how the changes occurred. Recording technologies have changed, along with the development of microscopy instrumentation. Of course, you have to record useful and correct data while actually doing the in-situ experiment. You will often be looking at one particular region of a sample while the most interesting things are happening at the other end of the specimen. This could be due to a beam effect, non-uniformities in the environment across your specimen, or just luck. So you need to keep your eyes open for anything that you are not seeing! We can use several different approaches. One comes with experience. You can switch from the CCD camera to the microscope screen for a wider field of view, but this may interrupt the video recording. During insitu microscopy, the sample and the environment may be changing continuously; the focus condition also keeps on changing. You need to keep adjusting the focus while recording the images. The ideal recording media would have a detector quantum efficiency (DQE) of 1, with a large number of pixels and rapid readout rate. As more data is recorded, storing and processing the data becomes challenging; TEM is now a producer of ‘big data’. With the new high-speed 2k-by-2k cameras, 60 seconds of images acquired at 400 frames per second (FPS) produces ~ 160 gigabytes of data. To convert this data from DM format to individual tiffs would require a full day using the DM batch convert software. (See Chap. 6 for more on DM – digital micrograph.) With the new direct detection cameras, described in Sect. 2.4.3, 15 minutes of recording can produce up to 5 terabytes of data. Do the calculation: even 30 FPS at 1k by 1k per frame for 15 minutes produces around 27 GB of data. Researchers and companies are addressing this issue of too much data (big, but redundant, data).

The goal is to use computers to identify the data that you are looking for without manually searching through thousands of images. Still, it is important to plan the experiment well before you start recording it, as you can quickly create more data than a person is able to examine. While doing the experiments, you store data directly onto the TEM’s computer and then transfer it to a removable drive; many managers don’t want their TEM directly connected to the internet. You may even just want to use video to allow you to correct for drift of the sample. To do this you’ll need to find the software that is compatible with your TEM. But remember, our repeated warning: having the beam on so that you can see the specimen may be enough to change what happens to your specimen! So, blank the beam for various intervals upon repeating the experiment to check how bad the beam effects are.

2.4.2 The CCD Camera CCD cameras are now attached to all research-grade TEMs. The CCD cameras may be side-entry or bottom-entry. With a side-entry camera, we do not compromise on the field of view. The bottom-entry camera does compromise on the field of view, but the magnification is ~ 10× larger. In either case the data is stored digitally. The parameters you should know for in-situ microscopy imaging are the digital size of the camera, the sensitivity of the pixels, the threshold electron dose that a pixel can tolerate, and the lifetime electron dose per pixel of the camera. Cameras traditionally use an optical-fiber-based stack technology with multiple read-out ports for high-contrast resolution. While doing the in-situ microscopy, you will always work to optimize the camera parameters. Better image quality usually means poorer time resolution. Of course, the exposure time depends on the quality of the sample, conditions of the experiment, etc.

2.4.3 Direct-Detection Cameras Direct-detection cameras are quite new and currently very expensive. The principle is rather like the operation of a secondary-electron detector in SEM. CCD cameras work by converting an electron signal into photons using a scintillator; direct electron detectors detect each electron that reaches each pixel, so the DQE is much higher. Examples (2015) are the DE-series (up to 67.1 megapixels) from Direct Electron, Falcon II (16 megapixels) from FEI, and the K2 (57 megapixels) from Gatan. Since the DQE is higher (in principle, it is 1, but in practice between 0.35 and 0.8), the ‘exposure time’ can be much shorter. The first users were those in the biosciences, where low dose is recognized as being critical and money is more plentiful. Now these cameras are being applied to materials science questions, such as understanding the interface structure between silicon and a NiSi2

23

Chapter 2

Chapter 1

2.4  Time

Fig. 2.5  Si nanowire growth at an interface with NiSi2 nanocrystal at 400 ˚C, images acquired at 400 frames per second. Angle between crystals is indicated, where rotation for epitaxial alignment is achieved over the 37.1-s period. These high-speed cameras can resolve atomic-scale information when using ‘enough’ electrons

nanocrystal during Si nanowire growth, Fig. 2.5. These cameras generally will cost over 500,000 (2015) US dollars. For our insitu studies, the video frame rate of 1,600 FPS is the enormous improvement, but the amount of data that you must store and transfer is correspondingly large. (Think about this challenge!) A recent advance using these high-speed cameras is the ability to collect full tomographic data from a structure within seconds, though stability of the holder and focus conditions are the key factor in the quality of images obtained.

2.4.4 Software and Data Handling The most important part of in-situ TEM is often considered as an afterthought! You know you will use an electronic device to record the image, but what software will you use? We list some of the manufacturers at the end of the chapter. (Notice we are already no longer saying CCD camera.) One important aspect that we have to discuss is the computer and its processing

24

2  In situ and Operando

Chapter 1

time. Image recording, processing, and saving, depends on the computer that you are using. The computers that are generally interfaced with the microscope should be state-of-the-art and fit the hardware configuration when the instrument is purchased. Shortly after it’s purchased, it will no longer be state-of-the-art; it will still be adequate for running the microscope – but not for doing state-of-the-art image processing, etc.

Chapter 2

Many in-situ experiments require the use of multiple computers to operate the TEM separately from the holder or external stimulus controller. Currently, there are ways to use both hardware (master clock) and plotting software (LabVIEW, Python, Matlab, Mathematica, Igor, Origin, and Excel) to synchronize the quantitative property measurement from the holder with the video/ images collected on the TEM. To correctly overlay the video onto the plot, it becomes necessary to input the exact moments each image/data point was acquired at. If you are working on this analysis, you should refer to the website spacetime.uithetblauw. nl (08/2015) to synchronize your external data with your image. Camera software can usually place a timestamp directly on the image, so that this information cannot be separated from the data during the time it takes between collecting the results and publishing them. At present, we usually use LabVIEW to control laser beams and ion beams incident on the specimen. Many use Comsol® software to model the various in-situ systems, processes, and environments. The camera you use will have its own image-grabbing software package, but you’ll find that different users have different philosophies. In practice, you’ll optimize the camera parameters and then start the auto image-grabbing software: record images continuously. The negative part of this is that you can only see the images while they are being recorded! If your microscope does not have software to record videos, you can load software onto the microscope control computer (with consent of the instrument manager) to collect screen captures of the search screen or scanning frames. Examples include VirtualDub and CamStudio, which allow you to select a region of the monitor to collect a screen shot with a predetermined capture rate (usually synched with the frame rate while searching). Post-processing of the videos and images can be completed using the same software you use for conventional TEM images. ImageJ, Fiji, Python and DM are free; Matlab, Mathematica, Camtasia Corel are not. (Check out youtube.com for instructional videos on using the software, especially for ImageJ.) For example, you can use image registration to correct for drift in an image series or group of video frames. Scripts can also be found through various sources; there are collections for DM or for Matlab such as Smart Align (lewysjones.com (08/2015)). Some image-processing techniques may be tricky for in-situ experiments when the background is not constant, such as with bowed membranes in liquid-cell experiments. In such images, it may be useful to apply more specialized algorithms to gain information from the experimental data, such as adaptive threshholding. Images recorded on high-frame-rate cameras may require their own software to be able to convert the bulk data into a format that is compatible with more conventional image-analysis software.

Processing Data

You must report any changes that are not just correcting levels (brightness/contrast) or cropping the image, even in video. Be sure to record and report any modification done to the video data just as you would for images. 9

2.4.5 Drift Correction Depending on the task at hand, you have to set the working range of magnification. If you’re working in nanoscience and technology, the magnification is generally high. This worsens the drift problem for in-situ microscopy. General methods to reduce drift in a series of images include using different support grids, piezo-controlled goniometers, drift-corrected holders, and automated drift-correction software. Hardware may use electronic drift compensation with piezo-driven stage control or image-shift deflection coils to correct for drift in the images (Banhart 2012), though the drift-correction software and drift-corrected holders on the market are not really drift-corrected for in-situ microscopy. The sources of drift for in-situ microscopy are expansion or contraction of the sample, specimen charging, temperature variations induced by the beam, reaction of the samples with the environment, flowing water inside the holder for cooling, and occasional bubble burst inside the cooling channels; or the sample may change and thus move in most in-situ experiments. The drift thus caused can only be corrected manually by observing the images while they are being recorded, Fig. 2.6. Automated image-drift correction works by keeping a pre-selected reference region (fiducial) in the field of view. The amount of

Fig. 2.6  Tracking of the thermal-drift velocity, as the displacement rate between consecutive images (dark blue), of a heating experiment from room temperature to 501 ˚C (red). Light-blue points show the manual drift corrections during the series of images. Displacement spikes observed at each step increase in temperature, larger displacement values for larger steps

2.4  Time

pulse, but the temporal resolution is determined by the duration of the acquired pulse. Fast vs Ultrafast

This high-speed electron microscopy has come to be known as ultrafast electron microscopy. (1,600 FPS is fast but not ultrafast!) 9

Chapter 1

drift in an image may be related to the electrical conductivity of the specimen/grid and the beam dose on the specimen (related to beam-induced heating). Remember, when only a small region of the sample is exposed at one time, charge build-up is limited and beam-induced movement is reduced. Drift performance for in-situ holders should have been tested and recorded for your instrument when they were installed, but that might have been 10 (or 30) years ago!

25

For all TEM, in situ or not, keep the o-ring on the specimen rod properly lubricated. Tap the base of the holder to seat the o-ring and improve contact between the holder and goniometer, but be aware of when you shouldn’t!9 Note: be careful when tapping to seat the o-ring! Don’t tap the holder if doing so will move your carefully aligned specimen or probe tip (e.g., if you’re using an STM-TEM holder). Drift or mechanical vibrations may be caused by the cabling connected to the base of the holder (common for in-situ and double-tilt holders). Pay careful attention to stabilizing this cabling and avoid moving cables during the experiment. Electrical experiments can be destroyed if static discharge from moving the cables causes a sharp pulse to flow through a nanomaterial sample.

2.4.6 Ultrafast Electron Microscopy What happens when we want to observe dynamic events in materials that occur in very short times? For example, phase transformations, transient states, or nanostructure nucleation can happen in millisecond or shorter times. We need to be able to acquire images in series that are representative of the timescale upon which the dynamic events are taking place. During TEM imaging, images can be acquired at standard video frame rates of 33 ms per frame (30 FPS), or with an advanced high-speed camera down to 625 µs per frame (1,600 FPS as we saw in Sect. 2.4.3). Even the fastest cameras still limit the kinds of dynamic processes in materials that we can study using nanometer-resolution real-space imaging, and we always need to consider the electron beam dose necessary to collect enough information from the sample with the high-frame-rate cameras. A change in electronic states and atomic-scale fluctuations in materials can occur within a femtosecond (1 fs is 10−15 s), which is much too fast for standard TEM imaging. Ultrafast electron microscopy (UEM) has set out to overcome these barriers and to increase the temporal (time) resolution for TEM imaging/diffraction down below the nanosecond time regime. The key development in UEM is that the camera speed no longer defines the temporal resolution; instead the beam is limited to emit electrons for a very short defined pulse. The camera records the data over a much longer timescale by leaving the shutter open to wait for the

The development first targeted imaging and diffraction at high temporal resolution by Bostanjoglo in 2000, framed in the use of laser pump-probe measurements. In this design, an external stimulus induced a modification to the specimen; the imaging signal, has a predetermined timed delay, allowing us to collect the information of the sample’s response. In this experimental design, the temporal resolution is only limited by the pulse duration. Based on this pump-probe approach, two methods have been developed where repeated diffraction or imaging compiles single-electron pulse events for reversible processes – this is the stroboscopic UEM, or an individual packet of electrons is used to produce a single image or diffraction pattern for irreversible processes – this is single-shot UEM (commonly known as dynamic TEM (DTEM)). The single-electron pulse actually consists of 1–10 electrons, whereas the packet of electrons is generally ~ 109 electrons. Although the DTEM is a single-shot process, we can record a series of such images with a defined time delay to make a short video! Using the stroboscopic approach, a femtosecond pulse continuously collects information from events that occur on an ultrafast ( 800 ˚C. Most MEMS heating holders use a disposable MEMS heating chip: the device acts as both the sample support and the heating element. The window region is a conducting ceramic film: typical window dimensions would be 150 nm × 500 µm × 500 µm, supported on a ~ 4 × 6-mm Si chip. In the Protochips version, 2-µm-diameter holes are patterned onto the ceramic membrane and carbon (~ 20 nm), SiN (~ 50 nm), or empty space covers the holes (Fig. 2.29). You place your specimen inside a ‘hole’, or at the edge. Each chip is calibrated by the supplier (using an optical pyrometer) and provided with a chip-specific calibration file. Then you use this current-vs-temperature curve to determine or set the temperature. Just remember that the temperature is calibrated under vacuum, and you have to consider the spatial resolution of the optical pyrometer. There will always be an initial thermal drift when the temperature changes. For the MEMS holders, when the temperature only changes over a small region, high-resolution imaging is obtainable, Fig. 2.30. At 800 ˚C, the sample drift rate has been measured at  3 times the inner angle, which can usually be achieved. The black integral in Eq. 11.53 is the FT of the detector function, given by the difference between the FT of the infinite detector (a delta function) and that of the central hole (an Airy disc), i.e., it represents the detector function in real space Z 0 D.R/ = e2iKf .R −R/ D.Kf /dK f = ı.R − R0 / −

2J1 .K i ; R − R0 / K i .R − R0 /

(11.54)

11.5  Coherent or Incoherent Imaging b

Condenser or collector aperture

a

b

Annular detector

Intensity

2

Part I

a

317

2

0

Fig. 11.35  Schematic illustrating the concept of a transverse coherence length imposed by the detector geometry. a In bright field imaging a small condenser or collector aperture is used such that the coherence length in the specimen is greater than atomic spacings, resulting in a coherent, phase contrast image. b An incoherent image is formed with an annular detector with a hole sufficiently large such that the coherence length in the specimen is less than the atomic spacings

Here J1 is a Bessel function, the mathematical form of the Airy disc for an inner angle of K f . Now we make the inner radius of the detector large on the scale of the Bragg reflections, then the real-space width of the detector function will be correspondingly much smaller than interatomic spacings. In this case one atom will not be able to coherently interfere with a neighboring atom. So although we cannot show strict mathematical incoherence, when we look at a crystal along a major zone axis, atomic spacings are always in the range of a few Å and we can have independent image contributions from adjacent atoms. This is the concept of transverse incoherence as controlled by the width of the detector function in real space. Note in the case of bright-field imaging, the FT of a point detector is infinite, so all atoms contribute via their amplitudes. This is coherent imaging. In reality we do not use an infinitely small detector, we just make the collector angle sufficiently small that the coherence envelope covers several adjacent columns. The concept of a transverse coherence envelope is illustrated in Fig. 11.35. We have not explicitly included thermal vibrations in this discussion, and in fact, thermal vibrations are not required to destroy coherence in the transverse direction, although they do assist to a small degree. The dominant effect is due to the geometry of the detector. This can be easily appreciated with reference to a test specimen consisting of two closely spaced point scatterers, i.e., infinitely sharp potentials. In this case the scattering factor of each ‘atom’ is uniform in reciprocal space, and cosine fringes are formed in the detector plane for a probe located centrally between them, see Fig. 11.36. With real atoms of finite size there is a strong angular decrease in scattered intensity, and the total detected intensity becomes dominated by the region near to the hole. As the inner hole of the detector is enlarged, there is an increasing number of fringes around its perimeter, so the integrated intensity averages over more fringes and approaches the result that would be expected for independently contributing atoms.

100

Fig. 11.36  a Intensity distribution in the detector plane for two point scatterers 1.5 Å apart, illuminated by a probe centrally located between them. Inner and outer detector angles correspond to 10.3 and 150 mrad, respectively. The circle marks 50 mrad radius, and samples many fringes around its perimeter. b Ratio of the detected intensity to the incoherent scattering prediction replacing the point scatterers by Si atoms, as a function of inner detector angle. Probe is optimum for an uncorrected 100 kV STEM with CS = 1.3 mm

A useful criterion for the minimum detector angle i that is required for incoherent imaging of lattice spacing a is  i = 1:22 a

(11.55)

Then a corresponds to a separation in real space that is twice the distance from the peak to the first zero of the Airy disc of the hole in the detector in Fig. 11.35. Figure 11.36b shows that in this case the deviation of the detected intensity from the incoherent signal is less than 5 %.

11.5.6 The Origin of Contrast in the Scanned Image We now examine what happens in the detector plane as the probe is scanned. We will see that despite the incoherent nature of the image the origin of image contrast is coherent interference. Returning to Eq. 11.45, inserting P.K/ from Eq. 11.44 and taking the square gives the intensity at any one point K f in the detector plane Z I.K f ; R0 / = A.K/e−i Z A .K 0 /ei

K/ 2 iK R0

e

'.K − K f /dK

K 0 / −2 iK 0 R0

e

(11.56a)

' .K0 − K f /dK 0



We retain the complex conjugate notation on A .K 0 / for completeness, but since A.K/ is real A .K 0 / = A.K 0 / is also real. Collecting terms gives I.K f ; R0 / =

Z Z

A.K/A .K 0 /ei

.K0 /− K// 2 i.K−K 0 / R0

'.K − K f /' .K 0 − K f /dKdK 0

e



(11.56b)

Chapter 11

0.61

25 50 75 Inner detector angle (mrad)

318

11  Imaging in STEM a

to intersect the overlap regions at the edges of the probe-forming aperture, for example, the ADF detector shown in Fig. 11.37b. To obtain overlaps on the optic axis the maximum spatial frequency is not the diameter of the aperture but the radius, and we need to increase the probe-forming aperture to achieve overlaps on axis and a bright-field image.

b

Part I Bright field collector aperture

Annular detector

Fig. 11.37  Schematic diffraction pattern for a cubic crystal projection with lattice spacings such that neighboring discs are slightly overlapping. A detector placed in an overlap region will show an image as the probe is scanned. For this situation, the axial bright field detector (a) will therefore show no image, whereas the ADF detector (b) shows a lattice image

We can now see how contrast arises in the STEM image. The intensity at this point on the detector results from the interference of all possible pairs of beams within the incident probe with wave vectors K and K′ which are scattered by the sample into the same final direction K f . Since the probe is coherent all the scattered beams are coherent and they all interfere to give the amplitude of the final state K f . Now what happens as we move the probe? Just one term contains the probe position R0: it is the 0 interference term e2i.K−K /R0. This term oscillates as the probe scans, with spatial frequency K − K0, which is the image contrast we want.

Chapter 11

One very important point is already clear. The period of the oscillation is determined by the wave vector difference between the pair of incident beams K and K′. The only possible pairs of beams that can interfere are those contained within the probe-forming aperture because if either A.K/ or A.K 0 / is zero then the entire expression becomes zero. We arrive at the important result that the maximum periodicity (highest spatial frequency) K − K0 that can appear in the image is given by the diameter of the probe-forming aperture. Then beams from the edge of one disc interfere with beams from the opposite edge of the other. Let us take the example of a thin cubic crystal, which gives a diffraction pattern as shown in Fig. 11.37. Only those regions where the discs intersect will show oscillating contrast as the probe scans, so only those regions contribute to image contrast. This is the reason that the enhanced transfer in Fig. 11.14d with an overfocused lens also required a larger aperture. The aperture cutoff is an absolute cutoff for image contrast. If spots are seen in the FT of the image that lie outside the aperture cutoff then they are spurious, due to clipping or instabilities of some sort, as discussed before. We also appreciate immediately from Fig. 11.37a that these regions of overlap may not extend to the optic axis. The usual bright-field detector is a relatively small detector to minimize the damping factor due to beam divergence, and is located on the optic axis, so it does not see such overlaps. We need a large detector

We have the same result as we have in TEM: the radius of the objective aperture limits the bright-field resolution. This is another example of the reciprocal nature of STEM and TEM (see W&C Sect. 22.6). We also see that the resolution limit in ADF STEM is, in theory, a factor of two higher than in bright-field imaging. We say ‘in theory’ because the small overlap regions at the limit of resolution mean that there is little actual image contrast and noise may become limiting in practice. 9 The overlap regions in Fig. 11.37 are shaded schematically, but in reality they contain complex contrast features that depend on the microscope settings and lens aberrations. In Fig. 11.38 we see some simulated Ronchigrams for a model crystal consisting again of point scatterers; the Ronchigram shows the interference pattern without the angular decrease in intensity. As the size of the probe-forming aperture increases, the overlap region increases and reaches to the optic axis, allowing us to obtain a bright-field image. The figure also shows how the optimum conditions lead to a large region of the overlap having a uniform intensity, i.e., being in phase. The optimum conditions chosen in this case are those appropriate for a bright-field image, but differ from those for the dark-field image by only a small amount. Also shown is the effect of ‘turning off’ the spherical aberration, leaving only the defocus term which now leads to vertical fringes because the optimum defocus for zero CS is zero. In the absence of lens aberrations these fringes are straight. Figure 11.39 shows the oscillation of the overlap region as the probe is moved across the unit cell from one ‘atom’ to the next. This is the fundamental origin of STEM image contrast. If the conditions are changed from optimum then the overlap region does not show large areas of uniform phase, as seen in the case of zero CS, in the out of focus condition shown on the right-hand side of Fig. 11.38. The fringes simply translate across the overlap region, integrating to negligible change in total detected intensity, and thus resulting in negligible image contrast.

11.5.7 Transfer Function and Damping Function Now let us return to the basic equations for incoherent imaging, Eq. 11.42 and transform into reciprocal space. We find I.Q/ = j'.Q/j2  jP.Q/j2

(11.57)

a

Fig.  11.38  Simulated Ronchigrams for a rectangular lattice of delta function atoms, with spacings 1.54 Å horizontally and 3.08 Å vertically, for aperture sizes of (a) 8 mrad, (b) 12 mrad, (c) 14 mrad and (d) 18 mrad semiangle at 300 kV. Only in (c) and (d) do the overlaps extend to the center (aperture radius exceeds the lattice spacing). It is clear that for a good contrast bright field image the collector aperture would need to be very small on the scale of the probe-forming aperture to avoid averaging over the fringes in the center of the pattern. The patterns on the left are for the uncorrected case, with CS = 1 mm, defocus – 51.5 nm, when large patches of almost uniform contrast are present. The patterns on the right are for the same defocus but zero CS, and a set of straight fringes is seen. Returning the defocus to zero, all overlaps become uniformly bright

319

Part I

11.5  Coherent or Incoherent Imaging

b

c

d

The figure also illustrates the effect of a finite energy spread due to fluctuations in beam energy or in lens current. In the brightfield case, the damping envelope takes the form of an exponential at the high spatial frequencies, as discussed in Chap. 28 of W&C. The origin of this strong damping factor is the rapid oscillation in the phase CTF at high angles. The oscillations express the phase difference between the beam scattered at K and the zero-order beam, and become progressively more rapid with increasing angle. A spread of defocus shifts the peaks and troughs of the oscillations so that at a high enough angle they will average to zero. The effect on a STEM ADF image is very different. The STEM contrast at the highest resolution comes from the interference of beams across the aperture diameter, +K and –K, which are at equal angles to the optic axis. They, therefore, have exactly the same phase changes for a fluctuation in defocus, and the center line between overlapping discs is achromatic; therefore the presence of fluctuations does not reduce the highest spatial frequencies in the image. There is no loss of resolution to first order, which is the reason that STEM ADF imaging is regarded as being robust to chromatic aberration effects. Regions of overlap away from the achromatic line will suffer changes in relative phase, and so it is the midrange spatial frequencies that are damped, as seen in Fig. 11.40.

11.5.8 Longitudinal Coherence We discussed the role of the detector geometry in imposing transverse incoherence to the HAADF image on the scale of atomic spacings, by ensuring neighboring columns contribute

Chapter 11

The intensity of the image spatial frequency Q is that in the object multiplied by that same spatial frequency content of the probe intensity. The FT of the probe-intensity profile acts as the CTF for the incoherent image, or as it is usually referred to, the optical transfer function or modulation transfer function. Figure 11.40 shows transfer functions corresponding to the images shown in Fig. 11.14 for the optimum Scherzer conditions and for the oversized aperture. You can see how the oversized aperture and high defocus boost the high spatial frequencies at the expense of the midrange and lower frequencies.

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11  Imaging in STEM

Part I Fig. 11.39  Simulated Ronchigrams as an uncorrected 300 kV probe is scanned across the artificial crystal of point atoms used for Fig. 11.38, moving in equal steps from above one delta function atom to the next (a–e). The upper set is near optimum dark field conditions (CS = 1 mm, aperture semiangle 10 mrad and defocus −44.4 nm). Overlap regions are bright when the probe is over an atom and dark when in between. This is the source of image contrast. The lower set is for CS = 0, but keeping the defocus as before, which leads to vertical fringes in the overlap region. As the probe is scanned the fringes are displaced. With several fringes inside the overlap region the integrated intensity on the detector barely changes as the probe is scanned. With optimum defocus (zero) the overlaps would be uniformly bright or dark similar to those in the upper row a

 = 0 nm  = 30 nm

P(Q)

(0.136 nm) -1

Coherent

0

1

2

3

b

4

5

6

7

8

spatial frequency (nm -1)

9

P(Q)

 = 0 nm  = 10 nm

10

11

12

13

(0.093 nm) -1

Coherent

0

1

2

3

4

5

6

7

8

spatial frequency (nm -1)

9

10

11

12

13

Chapter 11

Fig. 11.40  Incoherent transfer functions (black lines) corresponding to the images shown in Fig.  11.14 for an uncorrected 300 kV STEM with (a) Scherzer optimum conditions, (b) an oversized aperture and high defocus giving extended transfer into the sub-Ångstrom regime. Shown in red is the transfer including a defocus spread of ∆ in each case. The value of the transfer function at zero spatial frequency is proportional to the square of the objective aperture radius. The corresponding damping envelope for phase contrast imaging under the same conditions is shown as the dotted line

independently to the detected signal. For a 75 mrad inner detector angle in a 300 kV STEM the transverse coherence length is 0:61=  = 0.16 Å, which is much smaller than atomic spacings. Now we consider coherence in the longitudinal direction. Just as in our considerations of resolution, the coherence envelope is a 3D function, with a dimension along the optic axis that is much longer than the transverse coherence length given

by 2= 2 = 7.0 Å. This length along the optic axis exceeds the typical separations of atoms along a column for a crystal in a major zone axis orientation; a second monolayer of atoms will scatter in phase with the first if separated by a distance small on this scale. For typical detector angles used in HAADF imaging the transverse coherence length is much shorter than the atomic spacing whereas the longitudinal coherence length is larger. The intensity from a column of atoms will therefore initially increase as the square of the number of atoms in the column, but as the length exceeds the longitudinal coherence length, scattering from atoms at the top and bottom of the column will go out of phase. We can include the phase factor in the z direction explicitly with a kinematical description of the scattering. The kinematical model includes the thickness effect as a geometric phase factor, but does not include any multiple-scattering (dynamical) effects. Figure 11.41 shows the scattering geometry. The phase difference between atoms at different height z is the same as that for a defocus by f , see Eq. 11.4. For this reason the effect of a finite column length is sometimes referred to as z defocusing. Then the path difference for scattering at an angle  from two atoms a distance z apart is z.1 − cos  /  z 2 =2

(11.58)

in the small-angle approximation, and the total amplitude scattered by a column of length t is Ac. / = f

Zt 0

ei

2z 2 2

dz



(11.59)

11.5  Coherent or Incoherent Imaging a

b

z

k

. . . . . . . .s . c

d

80 120 Thickness (Å)

The quantity s =  2 =2 is the deviation parameter from W&C; in reciprocal space it is the distance from the zero-layer diffraction plane to the Ewald sphere along the propagation direction. As drawn in Fig. 11.41b, s is negative, and the columnar amplitude is

0

e2isz dz

(11.60)

.

Ac . / = f

 i  1 − e2ist 2s .

(11.61)

Ac . / = f

i Œ1 − cos.2st/ − i sin.2st/ 2s .

(11.62)

Ac . / = f

sin.st/ Œcos.st/ + i sin.st/ s .

(11.63)

Ac . / = f

sin.st/ ist e s .

(11.64)

and the columnar intensity is then Ic . / = f 2



sin.st/ s

2

,

(11.65)

which is the shape factor for a crystal of thickness t, as derived in W&C, Chap. 13. The general behavior is clear from the form

160

qz

200

of the function shown in Fig. 11.41b. The first zero occurs for s = 1=t, so as the crystal thickness increases, the shape factor becomes narrower, and moves further away from the Ewald sphere. Therefore, as the thickness increases, the number of atoms contributing to the scattering increases, but the Ewald sphere cuts further out from the central peak of the shape factor, so that the total amplitude does not increase but oscillates. Figure 11.41c shows the detected intensity calculated for a probe located centrally over a dumbbell in Si 〈110〉. The intensity rises rapidly initially, when the column is short compared to the longitudinal coherence length, but then the interference becomes destructive and the intensity goes through several oscillations, never exceeding the intensity scattered by the very thin crystal. This is exactly what we might expect for coherent scattering, but is not the behavior we find experimentally (which increases with thickness for several hundred Å, see Fig. 11.4). This discrepancy highlights the importance of thermal vibrations: they destroy the longitudinal coherence along the column. 9 An illuminating way to visualize the effect of phonons on the columnar interference is to imagine what a single phonon will do to the zero-layer diffraction spots. A periodic modulation by a wave vector qz in the z direction will produce satellite reflections at the positions of ˙qz , see Fig. 11.41d. These satellite reflections will have the same shape factor as the main reflection. Now at high angles, there are many phonons excited with different q, and furthermore, multiphonon scattering is dominant. In multiphonon scattering many phonons are simultaneously created or

Chapter 11

40

Here f is the atomic scattering amplitude (assumed identical for each atom) and we have treated the column as a continuum.

Ac . / = f

k

. . . . . . . .s . 0

Zt

Part I



Intensity

Fig.  11.41 Scattering geometry for a column of atoms in (a) real space and (b) reciprocal space showing the Ewald sphere and the kinematic shape factor. c  Image intensity as a function of thickness for Si 〈110〉 with a 2.2 Å probe centered between the two columns of one dumbbell, collecting coherent scattering over the range of 50–150  mrad. The probe forming aperture is 10.3 mrad, CS = 1.3 mm and the accelerating voltage is 100 kV. d The effect of phonons is to produce sidebands shown in red. With enough phonons, the Ewald sphere effectively integrates over the shape factor

321

322

11  Imaging in STEM

Part I

destroyed by the thermal scattering event with consequently a large distribution of possible final wave vectors. It is at the end point of the total momentum transfer that we place the shape factor, and so, in effect, large-angle phonon scattering places the shape factor at all positions in reciprocal space, in effect, integrating the scattered intensity over the deviation parameter. The diffuse-scattered intensity is therefore given by  Z  sin.st/ 2 2 ITDS . / = f ds (11.66) s . (11.67)

ITDS . / = f 2 t.

Integrating the shape factor produces an intensity that is proportional to the thickness t weighted by the atomic cross section f 2. This is the dependence we would expect for incoherent scattering in a kinematic model; every atom contributes equally throughout the specimen thickness. The destruction of z coherence is achieved by phonons with wave vectors in the z direction, which overcome the curvature of the Ewald sphere. To see how phonons break up the column in a real space picture we can introduce the effect of thermal motion into the columnar scattering amplitude. Because the fast electron moves at around half the speed of light, for specimens of the order of 15 nm thick they spend only 10−16 s in the specimen, which is a small time compared to the phonon vibration period, typically 10−12 s. Therefore, the fast electron sees a ‘frozen’ atomic configuration, and subsequent electrons see a different configuration. This is the basis of the so-called ‘frozen lattice’ or ‘frozen phonon’ method for image simulation. Analytically, we can treat the column using a time average of atomic displacements. Consider each atom to have an instantaneous displacement of u where we now consider not just the transverse component of the scattered electron wave vector, but the total scattered wave vector k by including the z component, i.e., k = .K f ; s/. Then the instantaneous columnar scattering amplitude becomes Z ATDS . / = f 2 e−2iku e2isz dz (11.68)

Chapter 11

and the intensity becomes ITDS

/ = f2

Zt 0

ITDS

/=f

2

he−2

Zt Zt 0 0

ik u

he−2

ie2

isz

Zt

dz he2

ik .u−u0 /

ik u0

0

ie2

is.z−z0 /

ie−2

dzdz0



isz0

dz0 (11.69) .

(11.70)

The angled brackets denote the time average between successive electrons, which see different instantaneous displacements. Note how this expression couples atoms at heights z

and z0 in the column. This will result in the introduction of a longitudinal coherence length. It is essential to use a phonon model for this purpose, since the usual Einstein model approximates the situation by independently vibrating atoms, which by definition is an incoherent scattering model. In the Einstein model every atom is coherent with itself but incoherent with all others. To see how the phonons approach this limit, we can adopt the phonon model developed by Warren (1990) in which phonons are treated with a Debye dispersion relationship and equipartition is assumed between all modes. This model is very convenient because it reduces the time average to a modified Debye–Waller factor,

−2ik.u−u0 /

he

(

) Si.qB ju − u0 j/ −1 i = exp 2M qB ju − u0 j 

(11.71)

Here M = B42 is the usual Debye–Waller factor ( is the scattering angle, twice the Bragg angle), Si.x/ is the sine integral function, qB is the Brillouin zone boundary wave vector in the z direction, and B = 8 2 hu2 i, where hu2 i is the mean-square thermal-vibration amplitude in the transverse direction. Equation 11.71 represents a correlation function for atoms at different heights in the column and is plotted in Fig. 11.42. Closely spaced atoms scatter coherently, but atoms far apart have a coherence that reaches a limiting value of e−2M, which is the value from the Einstein model of independently vibrating atoms. 2

The Warren model shows how near-neighbor atoms are correlated in position because the phonons have finite wave vectors. The situation is reminiscent of the formation of the STEM probe, where a sum of different transverse wave vectors are in phase for some distance before destructive interference sets in. It is the same with the phonon wave vectors here. Near neighbors vibrate in phase, so scattering from them remains in phase as they oscillate. The degree of correlation decreases rapidly with distance, so the model shows that a vibrating column of atoms can be thought of as a column of independently vibrating packets, as shown in Fig. 11.42b. 9 For a column that is short compared to the length of the packet, the scattering is coherent, but for a column of n packets, the intensity is n times the intensity of a single packet, i.e., it increases linearly (again this is a kinematic model with no absorption or multiple scattering effects). The intensity may not increase at the same rate as in the Einstein model; however, the intensity from the packet can be enhanced or reduced compared to the incoherent value depending on whether the correlations within the packet are constructive or destructive. The Warren model conveniently captures the mechanism whereby thermal vibrations destroy long-range correlations between atoms, bridging the gap between a full phonon description of the scattering and the incoherent Einstein model.

b

Degree of coherence

1 0.8

0 1 2 3

0.6 0.4 0.2 0

0

1

2 3 4 Atom separation (n)

The effect of thermal displacements depends strongly on angle because of the appearance of  2 in the exponential.  9

We have already seen that it is phonons with wave vectors in the z direction that are required to break longitudinal coherence. If we expand the thermal displacement into transverse and longitudinal components, as u = .U; uz /, we obtain (11.72)

E D E 0 0 0 e−2ik.u−u / = e−2iKf .U−U / e−2is.uz −uz /

a

Coherent 120

Plots of the thickness dependence for a column of Rh atoms are shown in Fig. 11.43, showing the changeover from coherent behavior to incoherent behavior as the scattering angle increases.

5

Fig. 11.42  a The degree of coherence between one atom in a column of atoms and its neighbors n atoms away, calculated with a phonon model (red) and in an Einstein model (green). The phonon model shows how the degree of correlation falls smoothly with increasing n until it reaches the Einstein value at large n. In the Einstein model all atoms are assigned this degree of correlation except the atom at the origin, which is coherent with itself on both models. b Schematic showing how thermal vibrations break up a column into independently vibrating packets, inside which the scattering is highly correlated. Calculations are for B = 0.45,  = 75 mrad at 100 kV

D

Now K f is the transverse scattering vector, which is large, and s is the longitudinal scattering vector that is much smaller. Therefore the most effective phonons in the destruction of coherence are those propagating in the z direction but with transverse displacements.

11.6 Dynamical Diffraction We are now going to delve into Bloch theory. So if you skipped Chap. 14 in W&C, you’ll either want to step back to it now or jump ahead to the discussion after Eq. 11.92. The kinematical model shows us how the scattering geometry coupled with thermal motion completely changes the dependence of scattered intensity on crystal thickness. However, it does not include any multiple scattering and is not realistic for the imaging of thick crystals in a zone-axis geometry where strong dynamical scattering takes place. From Fig. 11.4 we know that this multiple scattering has no apparent effect on the

b

c

Warren

10

3.5

100

8

3

60

6

Intensity

Intensity

80

Intensity

Einstein 4

4

40

2 1.5 1

2

20

2.5

Chapter 11

a

323

Part I

11.6  Dynamical Diffraction

0.5

0

0 0

10

20

30

Atom

40

50

60

0 0

10

20

30

Atom

40

50

60

0

10

20

30

40

50

60

Atom

Fig. 11.43  Thickness dependence for a column of Rh atoms spaced 2.7 Å apart along the beam direction, for inner detector angles of (a) 15, (b) 30, and (c) 45 mrad, calculated on a kinematic model assuming coherent scattering (black), and with thermal vibrations using a phonon model (red) and the Einstein model (green)

324

11  Imaging in STEM

Part I

nature of the image. We can understand a simple explanation for this if we recognize that the HAADF detector is large on the scale of the diffraction angles. Multiple scattering rearranges intensity as a result of dynamical diffraction; it locally changes the details of the interference pattern seen on the detector plane. Interference does not change the total scattered intensity, it just redistributes it. 9 We might anticipate that the HAADF image would, therefore, be insensitive to dynamical interference. A phase-contrast image using a point detector would naturally be sensitive to local changes in the interference pattern. A convenient way to see the physics of the dynamical diffraction is to incorporate dynamical effects into the expression for the probe intensity, so that it then describes the probe propagating through the crystal. Each plane-wave component incident at wave vector K is expanded into a set of Bloch states inside the crystal,  .R; z/ =

X j

j

j

"j .K/bj .K; R/e2ikz .K/z e− .K/z

(11.73)

Here "j is the excitation amplitude of Bloch state j, denoted bj, with wave vector kzj in the z direction and absorption coefficient j. For simplicity we will ignore absorption. The Bloch states have the periodicity of the lattice and can be expanded in a set of plane waves as X bj .K; R/ = gj .K/e2i.K+g/R (11.74) g j 0 .K/.

We now obtain a reThe excitation amplitude is " .K/ = ciprocal-space expression for the image intensity. Transforming the Bloch states into reciprocal space gives the component at K f in the detector plane Z bj .K f / = bj .K; R/e−2iK f R dR (11.75) j

Chapter 11

bj .K f / =

Z X g

bj .K f / =

X g

The incident probe amplitude in reciprocal space is a set of aberrated plane waves of unity amplitude, given in Eq. 11.44 as (11.79)

P.K/ = A.K/e−i.K/ e−2iKR0.

R0 is again the probe coordinate. Integrating these plane wave components gives the total amplitude scattered to Kf from depth z inside the crystal, Z  .K f ; R0 ; z/ = P.K/ .K f ; z/dK (11.80)  .K f ; R0 ; z/ =

Z

A.K/e−i.K/

X

j

0 .K/

j

X

gj .K/ı.K

j

+ g − Kf /e2ikz .K/z e−2iKR0 dK

(11.81)

g

Comparing Eq.  11.80 with Eq.  11.28 you can see how the Bloch states are acting as a kind of dynamical transmission function for the probe. The Bloch state components contain all the information on the specimen scattering power. If we now perform the integral over K, the delta function forces K = K f − g and we obtain X j  .K f ; R0 ; z/ =A.K f − g/e−i.Kf −g/ 0 .K f − g/ j

X

gj .K f

− g/e

e



g

Now we can find the intensity at K f by squaring, I.K f ; R0 ; z/ =A.K f − g/e−i

K f −g/

X

j 0

.Kf − g/

j

X

j g .K f

− g/e2

j

ikz .Kf −g/z −2 i.Kf −g/ R0

e

(11.83)

g

i Kf −h/

A .K f − h/e

X

k 0 .K f

− h/

k

X

k h

.K f − h/e−2

ikzk .Kf −h/z 2 i.K f −h/ R0

e

h

gj .K/e2i.K+g/R e−2i.Kf R/ dR

gj .K/ı.K + g − Kf /

(11.76)

(11.77)

(11.82)

j

2ikz .K f −g/z −2i.K f −g/R0



which couples pairs of Bloch states j and k. We can rearrange Eq. 11.83 to give Eq. 11.84. I.K f ; R0 ; z/ =

X A.K f − g/A .K f − h/e−i

Kf −g/ i Kf −h/

e

g;h

This delta function couples the incident and final wave vectors via the g component of the Bloch state. The reciprocal space form of Eq. 11.73 becomes  .K f ; z/ =

X j

j

j

0 .K/bj .K f /e2kz .K/z

(11.78)

X

j 0

.K f − g

j g .K f

− g/

j;k

k k 0 .K f − h h .K f − h/ h i j 2 i kz .Kf −g/−kzk .Kf −h/ z −2 i.h−g/ R0

e

e

(11.84)



k .K/ Now the periodicity of the Bloch states means gk .K + h/ = g+h and kzk .K + g/ = kzk .K/ , so we arrive at the general reciprocal space expression for the image intensity from the crystal at depth z, in terms of a single integral over the incident probe, Z X I.Q; z/ = D.K + g/ A.K/A .K + Q/ g

e

−i

K/ i K+Q/

g;h

e−i X

Kf −g/ i K f −h/

e

j 0

j g .K f

.K f − g

− g/

(11.86)

k k 0 .K f − h h .K f − h/ h i j 2 i kz .K f −g/−kzk .K f −h/ z

e Z

e−i2

i.h−g+Q/ R0

X

dR0



Kf −g/

g

e

j 0 .K f

X

j g .K f

−g

− g/

(11.87)

j;k

k k 0 .K f − g + Q g−Q .K f h i j 2 i kz .Kf −g/−kzk .Kf −g+Q/ z

− g + Q/



dKf

e

We now integrate over the detector as before to obtain the image intensity I.Q; z/ =

Z

X D.K f / A.K f − g/A .K f − g + Q/ g

i Kf −g/ i K f −g+Q/

e

e

j 0 .K f

X

− g/

j;k

j k g .K f − g/ 0 .K f − g + Q h i j 2 i kz .K f −g/−kzk .K f −g+Q/ z

k g−Q .K f

− g + Q/

dK f

e

tuting K f − g by K results in Z X I.Q; z/ = D.K + g/ A.K/A .K + Q/e−i

(11.88) Substi-

K/

g

ei

K+Q/

X

j 0 .K

j g .K/

j;k

k k 0 .K + Q/ g−Q .K h i j 2 i kz .K/−kzk .K+Q/ z

e

(11.89)

+ Q/

dK

j g .K/



(11.90)

h i j 2 i kz .K/−kzk .K+Q/ z k dK g .K/e

Notice that the only terms that depend on the detector are the Bloch state components, and we can rewrite Eq. 11.90 as

j;k

A.K f − g/A .K f − g + Q/e−i

i Kf−g+Q/

j 0 .K

I.Q; z/ =A.K/A .K + Q/e−i K/ ei K+Q/ h i X j j 2 i kz .K/−kzk .K+Q/ z k .K .K/C .K/e jk Q 0

Performing the integral over R0 gives the delta function ı.h − g + Q/, which allows us to perform the sum over h, which sets h = g − Q, thus eliminating h to give I.K f ; Q; z/ =

X j;k

k Q .K

j;k

e

(11.91)



The detector sum Cjk .K/ is just a sum of Bloch wave intensity contributions to the image. X  Cjk .K/ = D.K + g gj .K / gk .K/ g (11.92) This expression for Cjk .K/ allows us to evaluate the contribution of different Bloch state pairs to the image intensity. Now we can directly appreciate the physics of the image formation. Exactly as discussed in the context of imaging phase objects, the HAADF detector selects Bloch states that are sharply peaked on the scale of the Airy disc of the hole in the detector. The only such states are the 1s states. The action of the detector is therefore to filter the states that contribute to the dynamical diffraction. The effect can be seen in Fig. 11.44, where the partial images calculated from particular Bloch states are shown for the case of InAs 〈110〉 at 100 kV. The images are shown for the limit of high thickness where the oscillation of the exponential term in Eq. 11.91 destroys all cross terms leaving only those terms with j = k, the independent contributions of the Bloch states. Clearly, the 1s states on the In and As columns are responsible for almost all of the image contrast. This is despite the fact that their excitation coefficients are small (0.19 and 0.24  respectively) compared to an excitation of 0.81 for the In 2s state. The In 2s state would contribute strongly to a bright field image, however, with a 30 mrad inner detector angle the Cjj .0/ for the In 2s state is only 0.02, much smaller than the values of 0.16 and 0.08 for the 1s states of In and As. Thus, the In 2s state contributes only weakly to the Z-contrast image despite its high contribution to the bright-field image. zz Physically, the 2s state is a broader state in real space and so passes mostly through the hole in the detector. The Bloch-



Chapter 11

We now take the FT with respect to R0, the probe position; R0 is the only real-space component remaining in the expression. We again label the spatial frequency with respect to probe position as Q, the spatial frequency in our STEM image, Z I.K f ; Q; z/ = I.K f ; R0 ; z/e−2iQR0 dR0 (11.85) . X I.K f ; Q; z/ = A.K f − g/A .Kf − h/

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corresponding to the atomic columns. In this case, they therefore propagate almost as plane waves. That means that each individual plane wave may not have a significant Cjj .K/ but because all the plane waves are essentially in phase, as they are outside the crystal, then the sum total contribution can be quite significant. It is best to think of the probe as a sum of two components: zz a channeling component represented by the 1s state, and zz a non-channeling component represented by the sum of all other states. The non-channeling component is dominated by the plane waves around the periphery of the aperture, as shown schematically in Fig. 11.45a, b. This latter component will come to a focus at a specific depth inside the crystal, much as it would outside, whereas the 1s component tends to channel and explore more of the column (until it is scattered out to the detector). Therefore, as the probe-forming angle is increased we see a change over from a channeling (projection) behavior to a depth-sectioning behavior, even with a crystal aligned on a zone axis. The effect is shown in Fig. 11.45c, d, where simulations are shown for Bi atoms inside Si 〈110〉, which come into focus at the appropriate focus setting.

11.7 Other Sources of Image Contrast

Fig. 11.44  Contributions of different Bloch states to the HAADF image of InAs. a In 1s state, b As 1s state, c both 1s states, and d all states, calculated from Eq. 11.91 using 311 beams and an inner detector angle of 30 mrad

Chapter 11

state filtering action of the high-angle detector is one key reason why Z-contrast images tend to be intuitive in nature. 1s states are located on the atom columns, and the scattering cross section means they contribute according to their atomic number. zz The second key ingredient for incoherent imaging is again the action of the phonons. As seen in the kinematic description, they introduce incoherence over the thickness of the specimen. The final result is an image that shows incoherent characteristics and Z-contrast. This explains why thickness fringes were seen in the bright-field image of Si, Fig. 11.4a, but little evidence of thickness oscillations was seen in the ADF image, Fig. 11.4b. This picture needs some modification in the era of aberration correction because probe angles can increase to where the high-angle components of the incident probe can be at such high angles to the zone axis that they no longer see the deep potential wells

Now we have to discuss sources of image contrast that are not related to the atomic-scattering factor itself: we include contrast due to changes in the thermal vibration amplitude and contrast due to static strains. We have seen how thermal displacements break the coherence of an atomic column in the z direction, and as a result can greatly enhance the intensity reaching the annular detector. The thermal vibration amplitude can therefore be a significant source of image contrast. For a simple picture of how this works we can adopt the Einstein model and split the atomic-scattering factor into coherent and incoherent parts. The coherent scattering is reduced by the Debye–Waller factor giving a cross-section for the total coherent scattering of c = f 2 e−2M

(11.93)

The cross-section for incoherent scattering is the remainder,   TDS = f 2 − c = f 2 1 − e−2M (11.94) Remember that M = B ; then we see that with increasing an42 gle there is a rapid change over from coherent to incoherent scattering. At a sufficiently high angle c tends to zero and TDS becomes the full atomic cross-section, f 2. However, at lower angles, when there is a significant c. Equation 11.94 shows that the incoherent contribution from each atom will be reduced from 2

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Fig. 11.45  Schematic showing the contribution to a HAADF image of (a) the 1s states, which channel down columns until they are scattered, and (b) all other states, which, for a sufficiently large probe-forming aperture, can be focused at different depths inside the crystal. (c) Model crystal of Bi atoms in different columns at different depths. d HAADF intensity profiles with the probe focused at the four depths indicated in (c) show strong peaks at the corresponding Bi atoms

the full f 2. This reduction is not compensated for by the coherent component, because, as we have seen in Fig. 11.41c and 11.43, once the column is longer than the longitudinal coherence length, much of the coherent scattering interferes destructively and we detect only a small fraction of c from each atom. It is in this angular range that the scattered intensity becomes very sensitive to changes in the Debye–Waller factor. An example of this reduction is shown in Fig. 11.46; the images are from an Al-Co-Ni decagonal quasicrystal using two different detector inner-angles. With the high inner-angle a Z-contrast image is formed, similar to those shown in Fig. 11.7, but with the lower inner-angle we see that the central region of each 2 nm ring shows bright. These are exactly the regions showing the broken symmetry in Fig. 11.7, and are quasiperiodically correlated. Raising the temperature can also enhance the contrast of the central ring, proving that the origin of the contrast is an enhanced thermal vibration amplitude from these atomic sites, roughly by a factor of 2. It is not necessary for the atoms to be actually vibrating to show enhanced contrast, static displacements can be sufficient. As we saw earlier, phonon configurations are effectively frozen during

Fig.  11.46 Images of an Al-Co-Ni decagonal quasicrystal using an annular detector with inner angle of (a) 50 mrad, giving a Z-contrast image, and (b) 35 mrad which shows bright contrast in the centers of the quasiperiodically correlated 2 nm clusters due to thermal vibration anomalies. Images recorded using a 100 kV aberration-corrected STEM

the passage of the fast electron; random, static displacements are equally effective as time varying ones. In this case it is usual to define a static Debye–Waller factor contribution by defining a total Debye–Waller factor as BTotal = B + Bs, where Bs = 8 2 hu2s i and hu2s i is the mean square static atomic displacement in the transverse direction. Clearly, random atomic displacements comparable in scale with the thermal vibration amplitude will be significant sources of image contrast, and since the atomic vibration amplitude is a small fraction of 1 Å (e.g., ~ 7.5 pm for Si at room temperature), this is can be a sensitive measure of static displacements. An example of strain contrast at a Si/SiO2 interface is shown in Fig. 11.47. The random displacements that give enhanced scattering at intermediate angles mean that the excitation of the 1s Bloch state is slightly lower, and the intensity scattered to high angles is slightly reduced. This effect is just apparent in Fig. 11.47, but is much clearer in the images of an interface between a LaAlO3 (LAO) substrate and a La0.67Ca0.33MnO3 (LCMO) film (Fig. 11.48). Images obtained at two inner-detector-angles show a contrast reversal between the two. In both regions the image intensity is dominated by the La-containing columns (Z = 57 for La compared to 25 for Mn). For high detector-angles the LCMO film shows weaker intensity than the LAO film, as would be expected for the reduced mean-square atomic number due to the Ca substitution. For lower angles, however, the LCMO shows higher intensity than LAO. The reason is that in LAO the La columns are straight, whereas they become zigzag columns in LCMO (viewed along the Pnma b-axis). The transverse atomic displacements lead to an increased atomic scattering cross-section. We can make a simple estimate of the expected image contrast by calculating the 1s state Bloch wave intensities in the two structures and using Eq. 11.94 for the atomic-scattering cross-section. The calculated Bloch-wave amplitude at the atom sites reduces to 91 % of its value in a straight column, which represents the reduced channeling effect of the zig-zag column

Chapter 11

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Fig. 11.47  Strain contrast at a Si/SiO2 interface is observed by comparing images with (a) a low inner detector angle of 34 mrad and (b) a higher inner angle of 43 mrad. The intensity profiles below each image are taken through the dumbbells outlined in white, and show an increased intensity near the interface in (a) which is absent in (b). It therefore cannot be due to Z-contrast, but indicates some additional random atomic displacements in this region. Images recorded with an uncorrected 300 kV STEM

Chapter 11

Fig. 11.49  a Bright field and (b) ADF images of a Si layer containing 50 nm B-doped layers (3.5 × 1020 B cm−3). The B-doped layers and threading dislocations are visible by strain contrast

ADF Intensity

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Fig. 11.48  Annular dark field images of a La0.67Ca0.33MnO3 film on LaAlO3 obtained with an uncorrected 100 kV STEM with an inner detector angle of (a) 25 mrad (b) 75 mrad showing a contrast reversal. c  Calculated intensity as a function of inner detector angle for the La column (red) and the La0.67Ca0.33 column (blue)

11.8  Image Processing

Defects that show in diffraction contrast such as dislocations and stacking faults will also show contrast changes in the HAADF image, although the contrast mechanism is better termed ‘channeling contrast’ in this case; the changing excitations of the various Bloch states alters the illumination of each atom and hence the intensity scattered to high angles. An example of the imaging of inclined dislocations in a superlattice of Si and B-doped Si layers is shown in Fig. 11.49. Near the beam-entrance surface the dislocations show oscillatory contrast, whereas deeper down, when the 1s states have been absorbed, the dislocation strain field regenerates some 1s state contribution, so the dislocations appear to be bright. The B-doped layers are also seen as bright in the HAADF image because the B introduces random atomic displacements in the surrounding Si atoms, and these displacements lead to strain contrast, as we saw in Fig. 11.47.

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compared to a straight column because of the blurred projected potential. However, at low inner-detector-angles, this reduced illumination of the atoms, and their reduced mean square Z, is more than compensated by the effect of static displacements. Figure  11.48c shows the calculated dependence of the scattered intensity on the inner detector angle using these simple approximations for the image contrast and it predicts a contrast reversal as observed. Quantitative analysis is, of course, better when based on accurate simulations, but it is remarkable how the basic form of the image can be understood using simple physical principles.

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Another interesting example of strain contrast is seen in Fig.  11.50a, where surface relaxations around dislocations emerging at the surface of GaN cause sufficient transverse displacements to be visible in the HAADF image. They are visible even if the dislocations, such as the screw dislocation in Fig. 11.50b, are not visible by normal diffraction contrast. The displacements cause a slight blurring of the atomic resolution image. This effect is very useful for locating the dislocation cores to allow study by EELS, for example.

11.8 Image Processing The most common form of image processing is a simple Fourier filter used to reduce the noise present in the image, as shown in the image of a CdSe/CdS/ZnS core/shell nanorod, Fig. 11.51. The raw image shows the dumbbells clearly resolved. Application of a band-pass Fourier filter greatly enhances the contrast of the dumbbells and removes much of the uniform background present in the raw data. In both images the envelope of the peak intensities reveals the nanocrystal thickness, i.e., its shape in the third dimension, as seen in the schematic.

Fig.  11.50  a Low magnification ADF image of GaN viewed along 〈0001〉 showing threading dislocations as bright dots due to their strain field. Approximately 20 % of them are pure screw dislocations, as seen in the high magnification image (b)

Fourier filtering is a direct method in which the frequency content of the data is altered. As a Z-contrast image is an incoherent image, essentially a convolution of the scattering power of the object with the probe, it might be expected that deconvolution of the probe would recover the object. Unfortunately, the convolution loses all information on the high frequencies in the object, and these cannot be restored just by changing the frequency content of the image. 9

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Fig. 11.52  a Z-contrast image of Co-doped anatase TiO2, viewed along the [ 100 ] direction, on a LaO2 substrate, seen on the left. The image is smoothed to reduce noise, except in the inset, which shows the raw data. This region is shown in (b) after maximum entropy processing, using the HREM Research Inc. software package and a probe of 0.071 nm FWHM. Red circles mark O columns while gray circles correspond to Ti/O columns. (c) Intensity traces along the atomic planes marked with red arrows on (b), compared to traces from the raw image before deconvolution. The blue lines represent an average over 5 lateral pixels as indicated by the white box on (b). The red dots represent the intensity traces from the same regions averaged in the same way on the raw data. It is seen that the bright O column actually comprises two peaks: one (red arrow) in the expected position for O and the other (green arrow) displaced away from the O column. This peak is due to preferential segregation of Co interstitials and is exactly at the predicted positions of Co interstitials from density functional theory, and explains the origin of ferromagnetism in this system. Images obtained with an aberration-corrected 300 kV STEM

zz One common indirect approach is maximum entropy. Some assumptions are needed to recover the lost high frequency information, because, in principle, there are an infinite number of structures that can fit any image. The maximum entropy algorithm weights in the direction of the least structure, i.e., maximum disorder, and will only put the least number of atomic columns necessary to account for the peaks in an image. This is therefore very appropriate for Z-contrast imaging, and an example of its application to the detection of Co interstitials in TiO2 is shown in Fig. 11.52. zz Another method that has been very successful is the pixon approach, which is not based on entropy but on seeking correlations between adjacent pixels to distinguish structure (the object) from noise. These patches of correlated pixels are called pixons. An example of this method is shown in Fig. 11.53.

zz Principal component analysis, based on multivariate statistical analysis, has been very useful for EELS images, as we’ll see in Chap. 16. The entire data set is analyzed into independent eigenvalues. Spectral features that are most highly correlated form the principle components, whereas those that are uncorrelated are presumably less significant and are more likely to represent noise. These components can be removed from the data set, and in this way noise reduction is obtained without significant loss of spectral or spatial resolution. You must always be very careful when image processing. A feature at an interface may be very significant but only a minor component because it appears in only a small fraction of the total pixels. Remember the golden rule: you should submit your unprocessed data when you submit your processed image for publication. In practice this is rarely done! Today, the US NSF actually requires that data obtained with their funding remain available for others to use.

Fig. 11.51  Z-contrast images of a CdSe/CdS/ZnS core/shell nanocrystal viewed along the [010] direction recorded with a 300 kV aberration-corrected STEM, (a) raw data, (b) band-pass Fourier filtered. A line trace across the raw image (c) taken across the long axis of the nanocrystal reveals the thickness profile of the core. The sublattice polarity is also directly visible, but is more clearly seen from a line trace across the filtered image (e). This nanocrystal is oriented as shown in the ball and stick model (d), the beam direction being vertical, and the scan direction for the thickness profile being shown by the green arrow. (f) Raw image of a CdSe nanocrystal embedded in polymer recorded with an uncorrected 300 kV STEM. In this case attempts to enhance the resolution by Fourier filtering (g) introduces spurious detail

Chapter 11

Fourier methods can introduce spurious details into the image, as in the filter shown in Fig. 11.51f, g. Indirect methods are the preferred alternative to Fourier deconvolution as they tend to introduce less spurious detail. They involve only forward modeling, that is, the simulation of trial structures with comparison to the experimental data, and are much more robust, although computationally more intensive.

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Part I Fig. 11.53  a Raw Z-contrast image of a disordered intergranular film in polycrystalline β-Si3N4. The grain on the right-hand side is oriented along the [0001] direction and the interface is formed by the prismatic plane, which is seen edge on. The image reveals the attachment sites of La atoms, which are added as a dopant to improve mechanical properties. b Pixon image processing removes the noise very effectively. Observed sites are in reasonable agreement with calculated sites (circled) for La segregation on the bare prismatic surface

11.9 Image Simulation Chapter 11

So far we have been examining the physical mechanisms underlying image formation in the STEM, not attempting to perform an accurate image simulation. When talking about thickness dependence of the image and strain contrast, we have seen the rapid change over from coherent to incoherent scattering with increasing angle. None of the treatments attempted to provide a quantitative simulation that includes both dynamical diffraction and thermal scattering, which is necessary for a full simulation. We get a rough indication of the overall form of a HAADF image by just modeling the HAADF image as a convolution of the incident probe intensity profile with an object function comprising delta functions at the atomic sites weighted by the Z2 Rutherford scattering cross-section. Although neither dynamical nor thermal scattering are explicitly included, it often works surprisingly well, as shown in Fig. 11.54. The presence of nitrogen columns in AlN is predicted to give streaks in the

image, as seen experimentally. Removing those columns gives no such streaks. Bloch vs Multislice

As in simulation of TEM images, two distinct methods are in use, the Bloch wave approach and the multislice method. 9 Several methods have been developed over the years to describe accurately the dynamical diffraction and scattering to the high-angle detector. Here we will summarize the different approaches to HAADF image simulation.

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11.9.1 Bloch Waves

When you’re ready, go to Earl Kirkland’s book, which includes the necessary computer codes.

Early analysis of the HAADF image took the view expressed in Fig. 11.3, that high-angle scattering is diffuse, and therefore generated incoherently by each atom in proportion to the intensity of the probe at its site. We then replace the detector by a scattering cross-section, calculated for the appropriate range of angles, and treat the probe propagation dynamically using Bloch waves. We use an absorptive potential both to reduce the Bloch wave amplitudes with propagation through the crystal and to generate the high-angle incoherent scattering. This model is only appropriate at high scattering-angles where there is negligible coherent component.

The frozen-phonon method simulates the phonon scattering by performing a number of coherent calculations over an ensemble of displaced atoms, which is a semiclassical approximation to the process of excitation and annihilation of phonons. Nevertheless, unlike when we use an absorptive potential, electrons are not now removed from the calculation and continue to propagate through the crystal. They can therefore undergo further scattering events. Frozen-phonon simulations therefore contain Kikuchi line features in the convergent-beam diffraction pattern due to elastic scattering after the phonon scattering event, and with enough configurations an excellent agreement with experiment is obtained. The method has been extended to include phonon-dispersion curves, although, due to the detector integration, the changes are minimal compared to the Einstein model. The disadvantage of the frozen-phonon method is the need for a large number of beams (covering the entire range of the detector) and use of a number of phonon configurations to achieve convergence in the simulation.

11.9.2 Multislice Early multislice simulations made the opposite assumptions! We tracked all the coherent scattering onto the detector and found a depth-dependent contrast, although the transverse form of the image appeared correct. From the discussions of the previous sections we can understand that transverse incoherence as a result of the detector integration would give the approximate transverse form of the image, but the coherence in the longitudinal direction would give thickness oscillations. Introduction of the frozen-phonon technique broke the longitudinal coherence.

11.9.3 Bloch Waves with Absorption The Bloch-wave methods include a phenomenological absorption model by adding an imaginary part to the crystal potential,

Chapter 11

Fig. 11.54  a Z-contrast image of an antiphase boundary in AlN from an uncorrected 300 kV STEM with derived atomic structure (b). Large circles denote Al, small circles N, white and black denote different atomic heights, and upper and lower case letters indicate Al and N planes, respectively. c Simulation using a convolution of the probe intensity profile with a Z2 weighting at the atomic sites. d Simulation without the N columns removes the zig-zag streaks between the Al columns. These features, seen in the raw image, are due to the N columns, which are only 1.09 Å from the Al column and therefore unresolved. The spacing between the first Al plane and the next, labeled d1, is measured to be approximately 0.28 ± 0.02 nm, significantly larger than the AlN (0001) planar spacing of 0.25 nm, denoted by d2. The expansion is due to substitution of O for N in the red locations, as detected by EELS

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Part I Fig. 11.55  a Experimental HAADF images of SrTiO3 along 〈100〉 with intensity variations normalized to the incident beam intensity (see color scale bar (d)). Regions of three different thicknesses are shown. The Sr columns are the brightest and the Ti-O columns are the second brightest features (see unit cell schematic on the left). The image of the 105 nm region has been drift corrected. b frozen phonon image simulations. c Bloch wave image simulations. In each case, simulations are shown without (left pane) and with convolution with a 0.08 nm FWHM Gaussian (right pane)

in which case the electrons are lost to the calculation. The incoherent component to the image is then calculated through a separate absorptive potential, which instead of modeling the rate of loss of electrons, models the rate of generation of high-angle scattering Z 2 I.R0 / = V HA .R/ jP.R − R0 ; z/j2 dRdz (11.95) hv

Chapter 11

Here VHA(R) is the potential for scattering onto the detector, as shown in Fig. 11.34, and P.R − R0 ; z/ is the dynamical probe wave function at depth z. This method can be very efficient as it is only necessary to include sufficient low-order beams to describe the dynamical diffraction of the probe. The high-angle scattering is generated kinematically; i.e., there is negligible probability for a second high-angle scattering event that would return the scattered electron into the dynamical wave field. Therefore, the number of beams may not need to extend even as far as the inner angle of the detector. Of course, if coherent scattering is significant, then the beams must extend onto the detector to allow their interference, and the calculation becomes more involved. This approach fails in thicker and/or higher Z crystals when this single scattering approximation for the high angle intensity breaks down.

11.9.4 There Is No Stobb’s Factor in HAADF Experimental, phase-contrast, TEM-image simulations historically have always significantly overestimated the image contrast compared to experiment by the Stobbs factor. Recently, however, it has been shown that an excellent quantitative fit can be obtained to experimental ADF images using just a Gaussian sourcesize contribution that fits the expected source size. Figure 11.55 shows the results of Bloch wave and frozen-phonon simulations for SrTiO3 compared to experiment. Excellent quantitative agreement is seen with both methods for a thin crystal, but the Bloch wave method fails in thicker crystals for the reasons discussed above. This quantitative agreement with experiment is a very significant result since it shows for the first time that HAADF images can be well simulated using existing descriptions of elastic and thermal diffuse scattering. We now know that STEM bright field images are free of any Stobbs factor, clearly suggesting that our present understanding of imaging is sufficient. So, the Stobbs factor in TEM must be due to something else: the detector response. Quantification can also be done in an empirical manner, even if this sounds like a contradiction in terms! Figure 11.56 shows a compositional profile obtained from a Z-contrast image of an InAsxP1–x wetting layer in between InP barrier layers. In this case, the InP acts as an intensity reference, and the As composition

profile is obtained by comparing intensity ratios measured from group V columns in the wetting layer to those measured in InAsxP1–x thin films, with uniform composition that was calibrated by high resolution  X-ray diffraction. Over a moderate range of specimen thicknesses the intensity ratios are independent of thickness, and the extracted profile is in agreement with the composition deduced from photoluminescence measurements.

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11.10  Future Directions

11.10 Future Directions The success of aberration correction has opened the door to a whole range of new insights into the origin of materials properties using the STEM. zz In ferroelectrics, it is possible to map local displacements on a cell-by-cell basis and image the influence of defects and surfaces on local polarization. zz With EELS it is possible to track O vacancies in oxide thin films, even to map spin states through the O K edge fine structure. zz We have seen the development of theories for near-edge structure that properly take account of the dynamical diffraction of the probe and solid-state bonding. zz Combining microscopy data with DFT calculations, the origins of materials properties are being unraveled at the fundamental atomic level.

Fig.  11.56  Quantification of As composition in InAsxP1-x from the Z-contrast image. a Ratio of columnar intensities for AsxP1–x compared to pure P from experiment and simulation. b Z-contrast image of a wetting layer of InAsxP1–x between InP barriers. c  Deduced composition profile. Note the asymmetric form of the profile along the growth direction

Chapter 11

For example, the origin of the eight orders of magnitude enhanced ionic conductivity in strained epitaxial ZrO2:Y2O3/SrTiO3 heterostructures was shown to be a combination of the expansive strain and the incommensurability of the fluorite and perovskite O sublattices. The origin of white-light emission in sub-2 nm CdSe nanocrystals was shown to be due to a fluxional state induced by photon absorption.

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Chapter Summary We have come a long way, but do we have all the resolution we need? Clearly, we can solve a lot of problems that were unimaginable in 2000. But we still cannot see into amorphous materials and find where every atom lies, and how it is bonded. We cannot yet make movies of point defects diffusing and reacting inside materials. Enhanced resolution would bring these dreams closer to reality, closer to Feynman’s dream in his now-famous lecture “There’s Plenty of Room at the Bottom”. In 1959, he called for resolution to be improved a hundred times, in order to ‘just look at the thing!’ Indeed, another factor of two improvements in lateral resolution would enormously enhance our sensitivity to atomic

displacements, down to the picometer level. And depth resolution would improve fourfold again to the level of a few Ångstroms. Such gains could require the development of a monochromator to overcome chromatic aberrations; then it would be possible to probe electronic structure sub-surface, in 3D, in a manner similar to that done today for the surface by the scanning tunneling microscope. And finally we will be able to make movies of single atoms inside crystals, or on their surfaces, track their bonding and chemical reactions. One thing is quite clear – the future for imaging and spectroscopy in STEM is truly bright.

Chapter 11

Appendix

Albert Crewe was born in Bradford, Yorkshire, on February 18, 1927 and died on November 18, 2009 in Chicago. His thesis advisor at the University of Liverpool was Sir James Chadwick, who discovered the neutron. Crewe demonstrated the first field emission STEM in 1970. Vasco Ronchi was born in Florence on December 19, 1897 and died on October 31, 1988. He completed his Ph.D. in 1919 with Luigi Puccianti; Enrico Fermi started his Ph.D. in the same group in 1920. Ronchi published ‘The History of Light’ in 1939. In 1945 he founded the Giorgi Ronchi Foundation to honor his son. Since Ronchi was Italian, Ronchigram is pronounced Ron-keegram.

Self-Assessment Questions Q11.1 What is the key requirement for incoherent imaging? Q11.2 Explain concisely the difference between coherent and incoherent scattering. Q11.3 What do we really mean by the term ‘diffuse scattering’? Q11.4 Explain what we mean by channeling in this chapter. Q11.5 Explain concisely why channeling is important in HAADF imaging. Q11.6 Can we measure the probe’s intensity distribution inside the crystal? Explain your answer. Q11.7 Can we see defects in HAADF? Justify your answer. Q11.8 Imagine you are Mr. Tompkins in the TEM. What are we talking about? Q11.9 The electron is quantum mechanical and finally hits the detector. Does it know it is there? Q11.10 Discuss the possible confusion over the phrase ‘objective aperture’ in STEM. Q11.11 What is the relationship between Airy and Raleigh? Q11.12 How did Scherzer’s classical approach differ from today’s Cs-correction approach? Q11.13 We noted that ‘the channeling does not make the La atoms appear smaller, only brighter’. Explain this point. Q11.14 What do we mean by the term ‘depth sectioning’? Q11.15 The depth resolution for extended objects is much poorer than for a point object. Explain why this is so. Q11.16 Explain why Z-contrast imaging can tolerate a much lower beam current than spectroscopic imaging. Q11.17 STEM imaging is fundamentally limited by the brightness of the source. Why is this so and what can we do about it?

Q11.18 Q11.19 Q11.20 Q11.21 Q11.22 Q11.23 Q11.24 Q11.25

What is a Ronchigram? Explain two uses of the Ronchigram. We explicitly refer to the year 1993. Why? ‘Atoms are smaller in HAADF STEM’ appears to be a nonsense phrase. Explain why it is not. Explain the difference between ‘longitudinal’ and ‘transverse’ coherence. What is the Warren model? There are two methods for simulating STEM images. Are they both used? What is a fluxional state?

Text-Specific Questions T11.1 Using the literature, discuss the current state of HAADF imaging of quasicrystals. T11.2 Why is the tail a problem in STEM. Be thorough in your answer. T11.3 We can observe light atoms in STEM even though we have Rutherford scattering. Explain why this is such an important result and why it is true. T11.4 We mention ‘density functional calculations’ often. Using the literature, elaborate on why we do so. T11.5 Some people say we can do confocal microscopy in STEM. Explain. T11.6 What application in ‘light’ optics did the Ronchigram derive from? Use the internet. T11.7 Does anyone use a point-projection microscope these days? Explore your resources. T11.8 The Fourier transform of the image intensity can give misleading information. Discuss this statement. T11.9 Can you use ABF, ADF, and HAADF at the same time? Discuss. T11.10 Explain why we have to discuss contrast in a scanned image as a separate topic. T11.11 How do thermal vibrations affect ‘longitudinal’ and ‘transverse’ coherence? T11.12 Is dynamical scattering relevant in STEM? Explain your answer. T11.13 What does the 2s state have to do with channeling? T11.14 Has channeling contrast been used to study defects in crystals? Discuss. T11.15 Frozen appears in this chapter more than once. Discuss its appropriateness.

Chapter 11

People

Part I

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Part I

References General References Born M, Wolf E (1999) Principles of Optics. Cambridge University Press, Cambridge Kirkland EJ (2010) Advanced Computing in Electron Microscopy, 2nd edn. Springer, New York, Dordrecht, Heidelberg, London Pennycook SJ (2011) Scanning Transmission Electron Microscopy. Springer, New York. (Much more detail)

Specific References Bak P (1986) Icosahedral crystals – where are the atoms. Phys Rev Lett 56:861–864 (A key theme in this chapter) Beck V, Crewe AV (1975) High-resolution imaging properties of STEM. Ultramicroscopy 1:137–144 (The Founding Editor, Elmer Zeitler was also in Chicago) Crewe AV, Wall J, Langmore J (1970) Visibility of single atoms. Science 168:1338–1340 (The annular detector) Feynman RP (1992) There’s plenty of room at the bottom. J Microelectromechanical Systems 1:60–66 (Reprinted article of his 1959 talk which was almost ignored at the time. The paper/talk actually began to be noticed in the early 1990s) Howie A (1963) Inelastic scattering of electrons by crystals .1. Theory of small-angle inelastic scattering. Proc R Soc Lond A 271:268–287 (Preservation of contrast under inelastic scattering) Ronchi V (1964) 40 years of history of grating interferometer. Appl Opt 3:437–451 (One of his 900 papers) Rose H (1974) Phase-contrast in scanning-transmission electron-microscopy. Optik 39:416–436 (The ABF detector) Warren BE (1990) X-Ray Diffraction. Dover, New York. (A classic)

Background References Chapter 11

Abe E, Pennycook SJ (2005) Ultrahigh-resolution Scanning Transmission Electron Microscopy with Sub-Ångstrom-Sized Electron Beams. J Cryst Soc Jpn 47:26–31 Abe E, Pennycook SJ, Tsai AP (2003) Direct observation of a local thermal vibration anomaly in a quasicrystal. Nature 421:347–350 (Enhanced thermal vibration amplitude) Abe E, Yan YF, Pennycook SJ (2004) Quasicrystals as cluster aggregates. Nature Mater 3:759–767 (A review paper) Ade G (1977) On the incoherent imaging in the scanning transmission electron microscope (STEM). Optik 49:113–116 (The hole in the detector problem) Allen LJ, Findlay SD, Lupini AR, Oxley MP, Pennycook SJ (2003) Atomic-resolution electron energy loss spectroscopy

imaging in aberration corrected scanning transmission electron microscopy. Phys Rev Lett 91(10):105503 (Examples of full image simulations) Batson PE (1993) Simultaneous STEM imaging and electron energy-loss spectroscopy with atomic-column sensitivity. Nature 366:727–728 (First atomic column EELS data) van Benthem K, Lupini AR, Kim M, Baik HS, Doh S, Lee JH, Oxley MP, Findlay SD, Allen LJ, Luck JT, Pennycook SJ (2005) Three-dimensional imaging of individual hafnium atoms inside a semiconductor device. Appl Phys Lett 87:034104(1–3) Borisevich AY, Lupini AR, Pennycook SJ (2006a) Depth sectioning with the aberration-corrected scanning transmission electron microscope. Proc Natl Acad Sci USA 103:3044 Borisevich AY, Lupini AR, Travaglini S, Pennycook SJ (2006b) Depth Sectioning of Aligned Crystals with the Aberration-Corrected Scanning Transmission Electron Microscope. J Electron Microsc 55:7–12 Borisevich A, Ovchinnikov OS, Chang HJ, Oxley MP, Yu P, Seidel J, Eliseev EA, Morozovska AN, Ramesh R, Pennycook SJ, Kalinin SV (2010a) Mapping octahedral tilts and polarization across a domain wall in BiFeO3 from Z-contrast scanning transmission electron microscopy image atomic column shape analysis. ACS Nano 4:6071–6079 (Influence of defects and surfaces on local polarization) Borisevich AY, Chang HJ, Huijben M, Oxley MP, Okamoto S, Niranjan MK, Burton JD, Tsymbal EY, Chu YH, Yu P, Ramesh R, Kalinin SV, Pennycook SJ (2010b) Suppression of octahedral tilts and associated changes in electronic properties at epitaxial oxide heterostructure interfaces. Phys Rev Lett 105:087204 (Influence of defects and surfaces on local polarization) Bosman M, Watanabe M, Alexander DTL, Keast VJ (2006) Mapping chemical and bonding information using multivariate analysis of electron energy-loss spectrum images. Ultramicroscopy 106:1024–1036 (Using multivariate statistical analysis) Bosman M, Keast VJ, Garcia-Munoz JL, D’Alfonso AJ, Findlay SD, Allen LJ (2007) Two-Dimensional Mapping of Chemical Information at Atomic Resolution. Phys Rev Lett 99:086102 (2D maps. Using multivariate statistical analysis) Browning ND, Chisholm MF, Pennycook SJ (1993) Atomic-resolution chemical analysis using a scanning transmission electron microscope. Nature 366:143–146 (First atomic resolution spectroscopy) Browning ND, Chisholm MF, Pennycook SJ (2006) Atomic-resolution checmical analysis using a scanning electron microscope. Nature 444:235 (Atomic resolution spectroscopy) Cowley JM (1975) Coherent and incoherent imaging in scanning-transmission electron-microscope. J Phys D 8:L77–L79 (The hole in the detector problem) Cowley JM (1976) Scanning-transmission electron-microscopy of thin specimens. Ultramicroscopy 2:3–16 (The hole in the detector problem) Cowley JM (1979) Adjustment of a STEM instrument by use of shadow images. Ultramicroscopy 4:413–418 (Adjusting the astigmatism)

crystal using STEM and EELS. Nature 450:702–704 (2D maps) Kirkland EJ (2010) Advanced Computing in Electron Microscopy, 2nd edn. Springer, New York, Dordrecht, Heidelberg, London Krivanek OL, Nellist, Dellby N, Murfitt MF, Szilagyi Z (2003) Towards sub-0.5 Å electron beams. Ultramicroscopy 96:229 Krivanek OL, Dellby N, Keyse RJ, Murfitt MF, Own CS, Szilagyi ZS (2008) Advances in Aberration-Corrected STEM and EELS. In: Hawkes PW (ed) Aberration-Corrected Electron Microscopy, vol 121. Elsevier, Amsterdam (On the probe size effect in equation 11.19) Krivanek OL, Ursin JP, Bacon NJ, Corbin GJ, Dellby N, Hrncirik P, Murfitt MF, Own CS, Szilagyi ZS (2009) High-energy-resolution monochromator for aberration-corrected scanning transmission electron microscopy/electron energy-loss spectroscopy. Philos Trans A Math Phys Eng Sci 367:3683–3697 (Chromatic aberrations) Krivanek OL, Chisholm MF, Nicolosi V, Pennycook TJ, Corbin GJ, Dellby N, Murfitt MF, Own CS, Szilagyi ZS, Oxley MP, Pantelides ST, Pennycook SJ (2010a) Atom-by-atom structural and chemical analysis by annular dark-field electron microscopy. Nature 464:571–574 Krivanek OL, Dellby N, Murfitt MF, Chisholm MF, Pennycook TJ, Suenaga K, Nicolosi V (2010b) Gentle STEM: ADF imaging and EELS at low primary energies. Ultramicroscopy 110:935–945 LeBeau JM, Stemmer S (2008) Experimental quantification of annular dark-field images in scanning transmission electron microscopy. Ultramicroscopy 108:1653–1658 (Gaussian source size contribution) LeBeau JM, Findlay SD, Allen LJ, Stemmer S (2008) Quantitative Atomic Resolution Scanning Transmission Electron Microscopy. Phys Rev Lett 100:206101 (Gaussian source size contribution) LeBeau JM, D’Alfonso AJ, Findlay SD, Stemmer S, Allen LJ (2009) Quantitative comparisons of contrast in experimental and simulated bright-field scanning transmission electron microscopy images. Phys Rev B 80:174106 (No Stobbs factor) Lee J, Zhou W, Pennycook SJ, Idrobo JC, Pantelides ST (2013) Direct visualization of reversible dynamics in a Si6 cluster embedded in a graphene pore. Nat Commun 4:1650 (Graphene nanopore) Loane RF, Kirkland EJ, Silcox J (1988) Visibility of single heavy atoms on thin crystalline silicon in simulated annular darkfield STEM images. Acta Cryst A44:912–927 Loane RF, Xu PR, Silcox J (1991) Thermal vibrations in convergent-beam electron diffraction. Acta Cryst A47:267–278 (The frozen phonon) Loane RF, Xu P, Silcox J (1992) Incoherent imaging of zone axis crystals with ADF STEM. Ultramicroscopy 40:121–138 (Longitudinal coherence) Lupini AR, Borisevich AY, Idrobo JC, Christen HM, Biegalski M, Pennycook SJ (2009) Characterizing the two- and three-dimensional resolution of an improved aberration-corrected STEM. Microsc Microanal 15:441–453 (Locating Bi atoms in Si [100])

Part I

Findlay SD, Shibata N, Sawada H, Okunishi E, Kondo Y, Yamamoto T, Ikuhara Y (2009) Dynamics of annular bright field imaging in scanning transmission electron microscopy. Appl Phys Lett 95:191913 (Using different contrast transfer functions) Findlay SD, Shibata N, Sawada H, Okunishi E, Kondo Y, Ikuhara Y (2010) Dynamics of annular bright field imaging in scanning transmission electron microscopy. Ultramicroscopy 110:903–923 (Using different contrast transfer functions) Garcia-Barriocanal J, Rivera-Calzada A, Varela M, Sefrioui Z, Iborra E, Leon C, Pennycook SJ, Santamaria J (2008) Colossal ionic conductivity at interfaces of epitaxial ZrO2:Y2O3/ SrTiO3 heterostructures. Science 321:676–680 (Perovskite O sublattices melting) Gazquez J, Luo W, Oxley MP, Prange M, Torija MA, Sharma M, Leighton C, Pantelides ST, Pennycook SJ, Varela M (2011) Atomic-resolution imaging of spin-state superlattices in nanopockets within cobaltite thin films. Nano Lett 11:973 (Map spin states) Haider M, Uhlemann S, Zach J (2000) Upper limits for the residual aberrations of a high-resolution aberration-corrected STEM. Ultramicroscopy 81:163 Hall CR, Hirsch PB (1965) Effect of Thermal Diffuse Scattering on Propagation of High Energy Electrons Through Crystals. Proc Roy Soc A286:158 (The frozen lattice) Hytch MJ, Stobbs WM (1994) Quantitative comparison of high resolution TEM images with image simulations. Ultramicroscopy 53:191 (The Stobbs factor) Ishikawa R, Okunishi E, Sawada H, Kondo Y, Hosokawa F, Abe E (2011) Direct imaging of hydrogen-atom columns in a crystal by annular bright-field electron microscopy. Nature Mater 10:278–281 James EM, Browning ND (1999) Practical aspects of atomic resolution imaging and analysis in STEM. Ultramicroscopy 78:125–139 Jesson DE, Pennycook SJ (1993) Incoherent imaging of thin specimens using coherently scattered electrons. Proc Roy Soc Lond Ser A441:261–281 (Width of the detector function in real space) Jesson DE, Pennycook SJ (1995) Incoherent Imaging of crystals using thermally scattered electrons. Proc Roy Soc Lond Ser A449:273–295 (Independently vibrating packets) Kadavanich AV, Kippeny TC, Erwin MM, Pennycook SJ, Rosenthal SJ (2001) J Phys Chem B 105:361–369 Kim YM, He J, Biegalski MD, Ambaye H, Lauter V, Christen HM, Pantelides ST, Pennycook SJ, Kalinin SV, Borisevich AY (2012) Probing oxygen vacancy concentration and homogeneity in solid-oxide fuel-cell cathode materials on the subunit-cell level. Nature Matt 11:888–894 (Vacancies in oxide thin films) Kim YM, Kumar A, Hatt A, Morozovska AN, Tselev A, Biegalski MD, Ivanov I, Eliseev EA, Pennycook SJ, Rondinelli JM, Kalinin SV, Borisevich AY (2013) Interplay of octahedral tilts and polar order in BiFeO3 films. Adv Mater 25:2497–2504 (Influence of defects, surfaces on local polarization) Kimoto K, Asaka T, Nagai T, Saito M, Matsui Y, Ishizuka K (2007) Element-selective imaging of atomic columns in a

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Part I Chapter 11

McBride JR, Kippeny TC, Pennycook SJ, Rosenthal SJ (2004) Aberration-Corrected Z-Contrast Scanning Transmission Electron Microscopy of CdSe Nanocrystals. Nano Lett 4:1279–1283 McBride J, Treadway J, Feldman LC, Pennycook SJ, Rosenthal SJ (2006) Structural basis for near unity quantum yield core/ shell nanostructures. Nano Lett 6:1496–1501 McGibbon AJ, Pennycook SJ, Jesson DE (1999) Crystal structure retrieval by maximum entropy analysis of atomic resolution incoherent images. J Microsc 195:44–57 McMullan D, Rodenburg JM, Murooka Y, McGibbon AJ (1990) Parallel EELS CCD detector for a VG HB501 STEM. Inst Phys Conf Ser 98:55–58 Merli PG, Missiroli GF, Pozzi G (1976) On the statistical aspect of electron interference phenomena. Am J Phys 44:306–307 Molina SI, Varela M, Ben T, Sales DL, Pizarro J, Galindo PL, Fuster D, Gonzalez Y, Gonzalez L, Pennycook SJ (2008) A method to determine the strain and nucleation sites of stacked nano-objects. J Nanosci Nanotechnol 8:3422–3426 (Calibrated by high resolution X-ray diffraction) Molina SI, Sales DL, Galindo PL, Fuster D, Gonzalez Y, Alen B, Gonzalez L, Varela M, Pennycook SJ (2009) Column-by-column compositional mapping by Z-contrast imaging. Ultramicroscopy 109:172–176 (Calibrated by high resolution X-ray diffraction) Mory C, Colliex C, Cowley JM (1987) Optimum defocus for stem imaging and microanalysis. Ultramicroscopy 21:171– 177 (Using the integrated current for resolution measurement) Muller DA, Tzou Y, Raj R, Silcox J (1993) Mapping sp2 and sp3 states of carbon at sub-nanometre spatial resolution. Nature 366:725–727 (First maps of bonding configurations) Muller DA, Edwards B, Kirkland EJ, Silcox J (2001) Simulation of thermal diffuse scattering including a detailed phonon dispersion curve. Ultramicroscopy 86:371–380 Muller DA, Kourkoutis LF, Murfitt M, Song JH, Hwang HY, Silcox J, Dellby N, Krivanek OL (2008) Atomic-scale chemical imaging of composition and bonding by aberration-corrected microscopy. Science 319:1073–1076 (2D maps. Using multivariate statistical analysis) Nellist, Chisholm MF, Dellby N, Krivanek OL, Murfitt MF, Szilagyi ZS, Lupini AR, Borisevich A, Sides WH, Pennycook SJ (2004) Direct sub-angstrom imaging of a crystal lattice. Science 305:1741–1741 Nellist, Pennycook SJ (1996) Direct imaging of the atomic configuration of ultradispersed catalysts. Science 274:413–415 Nellist, Pennycook SJ (1998) Accurate structure determination from image reconstruction in ADF STEM. J Microsc-Oxford 190:159–170 Nellist, Pennycook SJ (1998) Subangstrom Resolution by Underfocussed Incoherent Transmission Electron Microscopy. Phys Rev Lett 81:4156–4159 Nellist, Pennycook SJ (1999) Subangstrom resolution imaging using annular dark-field STEM. Inst Phys Conf Ser 161:315– 318 Nellist, Pennycook SJ (1999) Incoherent imaging using dynamically scattered coherent electrons. Ultramicroscopy 78:111–124

Nellist, Pennycook SJ (2000) The Principles and Interpretation of Annular Dark-Field Z-Contrast Imaging. Adv Imag Elect Phys 113:147–203 Nellist PD, Xin Y, Pennycook SJ (1997) Direct structure determination by atomic-resolution incoherent STEM imaging. Inst Phys Conf Ser 153:109–112 (Pt atoms on γ-alumina) Nellist, Behan G, Kirkland AI, Hetherington CJD (2006) Confocal operation of a transmission electron microscope with two aberration correctors. Appl Phys Lett 89:124105 (Two aberration correctors) Nellist, Cosgriff EC, Behan G, Kirkland AI (2008) Imaging modes for scanning confocal electron microscopy in a double aberration-corrected transmission electron microscope. Microsc Microanal 14:82 (Two aberration correctors) Oxley MP, Pennycook SJ (2008) Image simulation for electron energy loss spectroscopy. Micron 39:676–684 (Examples of EELS image simulations) Oxley MP, Varela M, Pennycook TJ, van Benthem K, Findlay SD, D’Alfonso AJ, Allen LJ, Pennycook SJ (2007) Interpreting atomic-resolution spectroscopic images. Phys Rev B 76(064303):1–8 (Examples of EELS image simulations) O’Keefe MA, Allard LF, Blom DA (2005) HRTEM imaging of atoms at sub-Angström resolution. J Electron Microsc 54:169–180 (More on Sparrow and Rayleigh) Peng YP, Nellist, Pennycook SJ (2004) HAADF-STEM imaging with sub-angstrom probes: a full Bloch wave analysis. J Electron Microsc 53:257–266 (Probe propagation) Peng Y, Oxley MP, Lupini AR, Chisholm MF, Pennycook SJ (2008) Spatial resolution and information transfer in scanning transmission electron microscopy. Microsc Microanal 14:36–47 Pennycook SJ (2002) Structure Determination through Z-Contrast Microscopy. Adv Imag Elect Phys 123:173–206 Pennycook SJ, Boatner LA (1988) Chemically sensitive structure imaging with a scanning transmission electron microscope. Nature 336:565–567 (Incoherent characteristics) Pennycook SJ, Jesson DE (1990) High-resolution incoherent imaging of crystals. Phys Rev Lett 64:938–941 (Incoherent characteristics; the probe propagating) Pennycook SJ, Jesson DE (1991) High-resolution Z-contrast imaging of crystals. Ultramicroscopy 37:14–38 (Incoherent characteristics; the probe propagating) Pennycook SJ, Jesson DE (1992) Atomic resolution Z-contrast imaging of interfaces. Acta Metall Mater 40:S149–S159 Pennycook SJ, Nellist PD (1999) Z-Contrast Scanning Transmission Electron Microscopy. In: Rickerby DG, Valdré U, Valdré G (eds) Impact of Electron and Scanning Probe Microscopy on Materials Research. Kluwer Academic Publishers, Dordrecht, the Netherlands, pp 161–207 Pennycook SJ, Jesson DE, Chisholm MF, Ferridge AG, Seddon MJ (1992) Sub-Ångstrom Microscopy through Incoherent Imaging and Image Restoration. In: Hawkes PW (ed) Signal and Image Processing in Microscopy and Microanalysis, Scanning Microscopy Supplement, vol 6. Scanning Microscopy International, SEM Inc., AMF O’Hare, Chicago

Scherzer O (1949) The theoretical resolution limit of the electron microscope. J Appl Phys 20:20–29 Shibata N, Pennycook SJ, Gosnell TR, Painter GS, Shelton WA, Becher PF (2004) Observation of rare-earth segregation in silicon nitride ceramics at subnanometre dimensions. Nature 428:730–733 Sohlberg K, Rashkeev S, Borisevich AY, Pennycook SJ, Pantelides ST (2004) Origin of anomalous Pt-Pt Distances in Pt/ Alumina catalytic system. Chemphyschem 5:1893–1897 Sparrow CM (1916) On spectroscopic resolving power. Astrophys J 44:76–86 (Two-point resolution) Spence JCH, Cowley JM (1978) Lattice imaging in STEM. Optik 50:129–142 (Diameter of the probe-forming aperture) Steinhardt PJ, Jeong HC, Saitoh K, Tanaka M, Abe E, Tsai AP (1998) Experimental verification of the quasi-unit-cell model of quasicrystal structure. Nature 396:55–57 Thust A (2009) High-Resolution Transmission Electron Microscopy on an Absolute Contrast Scale. Phys Rev Lett 102:220801(1–4) (Stobbs factor) Tonomura A, Endo J, Matsuda T, Kawasaki T, Ezawa H (1989) Demonstration of single-electron buildup of an interference pattern. Am J Phys 57:117–120 (The effect of increased detection time at fixed beam current) Urban K (2008) Studying Atomic Structures by Aberration-Corrected Transmission Electron Microscopy. Science 321:506– 510 Varela M, Lupini AR, van Benthem K, Borisevich A, Chisholm MF, Shibata N, Abe E, Pennycook SJ (2005) Materials characterization in the aberration-corrected scanning transmission electron microscope. Annu Rev Mater Res 35:539–569 Varela M, Oxley MP, Luo W, Tao J, Watanabe M, Lupini AR, Pantelides ST, Pennycook SJ (2009) Atomic-resolution imaging of oxidation states in manganites. Phys Rev B 79:085117(1–14) (Using multivariate statistical analysis) Wang ZL (1998) An optical potential approach to incoherent multiple thermal diffuse scattering in quantitative HRTEM. Ultramicroscopy 74:7–26 (Excitation and annihilation of phonons) Wang ZL (2003) Thermal diffuse scattering in sub-angstrom quantitative electron microscopy-phenomenon, effects and approaches. Micron 34:141–155 (Excitation and annihilation of phonons) Wang SW, Borisevich AY, Rashkeev SN, Glazoff MV, Sohlberg K, Pennycook SJ, Pantelides ST (2004) Dopants adsorbed as single atoms prevent degradation of catalysts. Nat Mater 3:143–146 (On an alumina flake) Warren BE (1990) X-Ray Diffraction. Dover, New York Witte C, Findlay SD, Oxley MP, Rehr JJ, Allen LJ (2009) Theory of dynamical scattering in near-edge electron energy loss spectroscopy. Phys Rev B 80:184108-1-15 (Solid state bonding) Xin Y, Pennycook SJ, Browning ND, Nellist, Sivananthan S, Omnes F, Beaumont B, Faurie JP, Gibart P (1998) Direct observation of the core structures of threading dislocations in GaN. Appl Phys Lett 72:2680–2682 (Dislocations emerging at the surface of GaN)

Part I

Pennycook SJ, Jesson DE, Chisholm MF, Browning ND (1993) Atomic-Resolution Imaging and Analysis with the STEM. Inst Phys Conf Ser 130:217–224 Pennycook SJ, Jesson DE, McGibbon AJ, Nellist (1996a) High angle dark field STEM for advanced materials. J Electron Microsc 45:36–43 Pennycook SJ, Browning ND, McGibbon MM, McGibbon AJ, Jesson DE, Chisholm MF (1996b) Direct Determination of Interface Structure and Bonding with the Scanning Transmission Electron Microscope. Philos T Roy Soc A 354:2619– 2634 Pennycook SJ, Lupini AR, Kadavanich A, McBride JR, Rosenthal SJ, Puetter RC, Yahil A, Krivanek OL, Dellby N, Nellist PDL, Duscher G, Wang LG, Pantelides ST (2003) Aberration-corrected scanning transmission electron microscopy: The potential for nano- and interface science. Z Metalkd 94:350–357 Pennycook SJ, Varela M, Lupini AR, Oxley MP, Chisholm MF (2009) Atomic-resolution spectroscopic imaging; past, present and future. J Electron Microsc 58:87–97 (Perovskite O sublattices) Pennycook TJ, Beck MJ, Varga K, Varela M, Pennycook SJ, Pantelides ST (2010) Origin of colossal ionic conductivity in oxide multilayers: interface induced sublattice disorder. Phys Rev Lett 104:115901(1–4) (O sublattice melting) Pennycook TJ, Oxley MP, Garcia-Barriocanal J, Bruno FY, Leon C, Santamaria J, Pantelides ST, Varela M, Pennycook SJ (2011) Seeing oxygen disorder in YSZ/SrTiO3 colossal ionic conductor heterostructures using EELS. Eur Phys J-Appl Phys 54:33507–33517 Pennycook TJ, McBride JR, Rosenthal SJ, Pennycook SJ, Pantelides ST (2012) Dynamic Fluctuations in Ultrasmall Nanocrystals Induce White Light Emission. Nano Lett 12:3038– 3042 (Photon absorption) Perovic DD, Rossouw CJ, Howie A (1993) Imaging inelastic strains in high-angle annular dark field scanning transmission electron microscopy. Ultramicroscopy 52:353–359 Prange MP, Oxley MP, Varela M, Pennycook SJ, Pantelides ST (2012) Simulation of Spatially Resolved Electron Energy Loss Near-Edge Structure for Scanning Transmission Electron Microscopy. Phys Rev Lett 109:246101(1–5) (Solid state bonding for EELS) Puetter RC, Gosnell TR, Yahil A (2005) Digital Image Reconstruction: Deblurring and Denoising. Annu Rev Astron Astr 43:139–194 Rafferty B, Nellist PD, Pennycook SJ (2001) On the Origin of Transverse Incoherence in Z-Contrast STEM. J Electron Microsc 50:227–233 Rayleigh L (1896) On the theory of optical images with special reference to the microscope. Philos Mag 5(42):167–195 (His original paper) Reimer L (1985) Scanning Electron Microscopy. Springer, Berlin (For example, the edge resolution test) Roberts KG, Varela M, Rashkeev S, Pantelides ST, Pennycook SJ, Krishnan KM (2008) Defect-mediated ferromagnetism in insulating Co-doped anatase TiO2 thin films. Phys Rev B 78:014409(1–6)

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Xin Y, James EM, Arslan I, Sivananthan S, Browning ND, Pennycook SJ, Omnes F, Beaumont B, Faurie JP, Gibart P (2000) Direct experimental observation of the local electronic structure at threading dislocations in metalorganic vapor phase epitaxy grown wurtzite GaN thin films. Appl Phys Lett 76:466–468 (Dislocation cores studied by EELS) Yan YF, Pennycook SJ (2000) Alloys: Atomic structure of the quasicrystal Al72 Ni20 Co8. Nature 403:266–267 Yan YF, Pennycook SJ (2001) Chemical Ordering in Al72 Ni20 Co8 Decagonal Quasicrystals. Phys Rev Lett 86:1542–1545) Yan YF, Pennycook SJ, Terauchi M, Tanaka M (1999) Atomic Structures of Oxygen-associated Defects in Sintered Aluminum Nitride Ceramics. Microsc Microanal 5:352–357

Yu ZH, Muller DA, Silcox J (2004) Study of strain fields at a-Si/c-Si interface. J Appl Phys 95:3362–3371 (Accurate simulations) Zhou W, Kapetanakis M, Prange M, Pantelides S, Pennycook S, Idrobo JC (2012a) Direct Determination of the Chemical Bonding of Individual Impurities in Graphene. Phys Rev Lett 109:206803(1–5) Zhou W, Oxley MP, Lupini AR, Krivanek OL, Pennycook SJ, Idrobo JC (2012b) Single atom microscopy. Microsc Microanal 18:1342–1354

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12

Part I

Electron Tomography

Chapter Preview men from a series of 2D micrographs, usually acquired at a range of tilts. Electron tomography was briefly mentioned in Sect. 1.3.B and 29.1 of W&C and specifically in relation to energy loss tomography in Sect. 40.9; this section seeks to expand on this brief introduction. While electron tomography was developed primarily as a tool for the examination of macromolecular assemblies and cellular structure, in this chapter we will explore how this technique can be applied in the physical sciences. This chapter will address some of the most important considerations when applying this technique for materials science. We will cover in some detail the choice of imaging technique, introduce the experimental limitations of the microscopy, cover the processing of the tomography data from tilt series to volume, and discuss the care that you must take in interpreting the results.

© Springer International Publishing Switzerland 2016 C. B. Carter, D. B. Williams (Eds.), Transmission Electron Microscopy, DOI 10.1007/978-3-319-26651-0_12

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It is the nature of ‘transmission’ that we can never overlook the finite thickness of our specimens. We will always lose information about the specimen in the beam direction; this can be both concealing and misleading. However, in some cases in order to successfully characterize the structure of nanoscale materials this information is invaluable. So how do we return the missing information, and resolve three-dimensional (3D) information from what is essentially a two dimensional (2D) technique? The problem of determining higher dimensionality information from lower dimensionality data arises in many technical disciplines; from radio astronomy to medical imaging to geophysics. Tomography, from the Greek ‘tomos’ – to slice, describes a broad class of techniques to solve this problem. Electron tomography, specifically, can be used to restore the 3D structure of a speci-

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12.1 Theory of Projection Part I

As in many other areas of microscopy research, the theory of tomography outpaced its experimental implementation. The theory of projection was first formulated by the Austrian mathematician Johan Radon in 1917 (Radon 1917). However, the first demonstration of a practical application of this theory didn’t occur until 1957 when Ronald Bracewell used Radon’s theory in order to reconstruct 2D radio astronomy data from 1D line integrals (Bracewell 1956). Radon’s theory describes for us how an object D in real space f(x,y) can be described by a line integral through all possible lines L through that object: Z Rf = f .x; y/ds (12.1) L where ds is the unit length of L, see Fig. 12.1. The projection operator R, the Radon transform, is best explored by describing its geometry more explicitly. We can simplify this by defining a new set of coordinates that are perpendicular (l) and parallel (z) to the projection/transform direction defined by the line L. We define the angle θ as that from the horizontal to the line normal of L, usually termed the ‘projection angle’. The geometry of these terms is illustrated in Fig. 12.2a. We can then directly relate the intensity in real and radon space by these two equations; Z1 p Rf .l;  / = f . l2 + z2 + tan−1 .zl//dz −1

Z1  n Rf .0;  / = f z;  + 2 −1

if l = 0



if l ¤ 0

(12.2)

(12.3)

We use the Radon transform R to convert an object in Cartesian co-ordinates (x,y) into an object in Radon co-ordinates; where the object is described in terms of the angle θ of the normal of the projection angle to the x-axis and l the line perpendicular to the projection direction. When we carry out the Radon transform a point in real space (x,y) becomes a line in Radon space (l,θ) linked through the equation l = rcos(θ–φ), such as the one marked in Fig. 12.2b. A model example of this transformation is shown for a 2D test object in Fig. 12.3. In the Radon-transformed object the bright spots have been converted into sine curves; for this reason the Radon space image is often termed a ‘sinogram’. Sometimes it is also known as a ‘tomogram’.

Chapter 12

A complete sampling of Radon space is achieved by recording projections over the continuum of angles. With a sufficient number of projections spread across the entire range of θ, we can achieve a reconstruction of an object can by simply applying the inverse Radon transform.

As we live in an imperfect, experimental world any sampling of Radon space is actually discrete and the numbers of projections acquired always limited by practical considerations. Therefore any reverse transform will be imperfect; as with any finite approximation to an infinite function. The Challenge

Obtaining the most accurate reconstruction from discrete experimental data is the central challenge of tomographic reconstruction. 9 So how does this imperfection in sampling manifest in real systems? We can elegantly describe the effects of limited sampling by using the ‘projection slice theorem’; a projection of an object at an angle is mathematically identical to a section through the Fourier transform of that object at the same angle. This also puts a different spin on the description of how tomographic reconstruction is possible from a tilt series of projections. Each projection at each angle gives us information about the object in Fourier space in a particular direction. By taking projections at many angles we can describe the whole object in Fourier space, and also in real space by a simple inverse Fourier transform. This theorem instantly suggests one potential method of tomographic reconstruction: by simply summing the tableau of projections in Fourier space (at the correct angles) and applying an inverse Fourier transform. While this ‘direct’ Fourier approach can be used for tomographic reconstruction it has largely been superseded, due to ease of implementation, by real-space techniques based on backprojection, which we will discuss at length later in the chapter. Fourier and Radon space

The relationship between Fourier and Radon space is invaluable for both conceptualizing reconstruction and describing the limitations incurred during experimental tomography. 9 We have already discussed how resolution in two dimensions can be expressed as the highest spatial frequency with statistically significant sampling transfer in Fourier space; the same in true in three dimensions. This statement also describes one of the most important limits to tomography, the number of sample points in three dimensions is the square of those in two dimensions; logically therefore it is much harder for us to achieve a particular resolution in 3D than in 2D. While imaging resolution in 2D TEM has passed the 1 Å barrier in a single image, the highest homogeneous resolution achieved in 3D TEM reconstruction is 3.3 Å. However, achieving this resolution in tomography requires approximately 20,000 images of a single repeating structure (Zhang et al. 2010) (for the ‘single particle reconstruction’ method).

12.1  Theory of Projection

Part I

Fig. 12.1  The Radon transform defines the projection of an object D in Cartesian space (x,y) through an infinite number of lines (L)

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Fig. 12.3  Demonstration of the Radon transform, over a full range of tilt ± 180°, applied to a test object. A point object is Cartesian space (a), circled, becomes a sinusoidal line in Radon space (b), indicated by the dashed lines. The amplitude of the line in l is a function of its average distance from the center of the volume

We need a certain sampling, number of projections, in 3D frequency space to reach a particular resolution. By assuming a perfect imaging system, with a complete absence of noise, it is possible to derive a simple equation relating resolution (d) to sampling. d=

D N

(12.4)

where N is the number of projections (N) and (D) is the diameter of the volume to be reconstructed. This simple relationship is known as the Crowther criterion (Crowther et al. 1970), and is regularly used to give a rough estimate of the resolution which can be attained from a particular tilt series. In deriving the Crowther criterion we make the implicit assumption that the projections are evenly spaced throughout Fourier space. However, in electron tomography this is almost exclusively not the case. The need to clamp and support the specimen almost always introduces a range of angles which cannot be sampled, and in practice tilt series rarely extend beyond ± 75°. This results in a ‘missing wedge’ of information in Fourier space, reducing the sampling and hence resolution in the depth (z) direction. A more quantitative description of the effects of both limited tilt and sampling can be made by calculating the pointspread- unction (PSF) in the reconstruction plane (y,z) for a given maximum tilt angle (θmax); h.y; z/ =

1  2 .z2 tan max / − y2 =.tan max /

(12.5)

Fig. 12.4  The effect of the tomographic point spread function has both positive and negative components. Here the PSF for ± 60° has been convolved with a small Gaussian, shown in the inset, to illustrate its effect. The negative component is much weaker, and the above plot has been boosted by 4× to allow comparison with the positive component. a The limited tilt range serves to elongate the point in the z-direction and reduces its intensity in the perpendicular direction, with two negative peaks on either side of the object. b, c The PSF also shows weaker +ve/-ve “fan” artefacts, at the angle of maximum tilt, that are characteristic of tomographic reconstruction

An example of point spread functions is shown in Fig. 12.4. This figure shows the distinctive ‘fan’ artefacts present in all tomographic reconstructions from limited tilts. Probably the most significant feature of this PSF is the vertical elongation, a reflection of the poor sampling in the z direction. An estimation of the degree of this elongation factor (e), as a factor of our maximum tilt angle (α), has been made by Radermacher (1988). r ˛ + sin ˛ cos ˛ e= ˛ − sin ˛ cos ˛  (12.6) For a maximum tilt angle of 70º, not uncommon in electron tomography, our reconstructions are subject to an elongation factor of ~ 30 %. It is worth stressing that e is a convolution, rather than a stretch, so accurate geometry cannot be returned simply by resampling the volume. While the Crowther criterion is based on an equi-axed reconstruction volume, TEM samples are more often extended thin slabs with far larger dimension in plane (x,y) than in depth (z). A valid hypothesis in this situation is that while we have less z direction information in a tilt limited series, for such a reduced

Chapter 12

Fig. 12.2  The Radon transform converts objects in Cartesian space (a) to Radon space, (b) measured in terms of the projection angle (θ) and the distance from the origin (l). A point in real space (x,y) is converted into a line with the equation l = rcos(θ-φ)

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volume we do not need as much information! The effect of this can be estimated by the use of a modified diameter (D), which is a factor of the thickness of the slab (T) and the maximum tilt angle (α) D = T cos ˛

(12.7)

Therefore, fewer projections are required to attain the same overall resolution, leading to a less pessimistic resolution prediction than the basic Crowther equation.

12.2 Back-Projection Whereas the projection slice theorem allows us to explore the possibilities of reconstruction in Fourier space, the theory of backprojection allows us to do the same for reconstruction in real space. If a projection is the act of summing an object along a given line L, a backprojection is what will arise if we sum that projection back through a volume at the projection angle. This leads to a set of rays, of varying intensity, crossing the volume in a single direction. If we then sum two such backprojections from different directions, an increase in total intensity will be observed where the two sets of rays cross, which will coincide at a possible location of the original object. Combine enough of these backprojections and the density distribution of the original object should be restored. This process is illustrated for a test object in Fig. 12.5. What becomes quickly apparent is that the more complex the object, the more projections we require to achieve an adequate reconstruction through backprojection; a practical illustration of the Crowther criterion.

In practice we carry out the backprojection operator by using a real space discrete estimation of the infinite integrais 12.2 and 12.3 to estimate the inverse Radon transform. There are a number of strategies that have evolved for this estimation, and they include brute force rotate and sum, reconstruction by convolutions, orthogonal functions, and using Riemann sums. These real space techniques have largely superseded the Fourier approach for a number of reasons, including mathematical stability, ease of implementation, insensitivity to noise and, perhaps most importantly, they are more suited to the regular grid applied by digital processing. Whilst backprojection avoids using the projection slice theorem for reconstruction, its consequences are used to improve the quality of the reconstruction. Even if each individual image has uniform sampling of spatial frequencies, each projection is a central section through 3D Fourier space, and a tilt series will sample that space unevenly. We will have greater sampling close to the center of Fourier space and less sampling at the extremities; low frequencies will be over-sampled and high-frequencies under-sampled. If uncorrected this will give us a blurred reconstruction. In order to restore the correct object the frequencies of the reconstruction will need to be weighted to take account of this limitation. As the exact geometry of the sampling is known, it is simple to generate a frequency space filter which is weighted to correct the average radial sampling, also known as an r-weighting filter. This can be applied in Fourier space to the original projections, or to the final reconstruction with equivalent effect. This frequency restoration is illustrated for a test object in Fig. 12.6. Weighted backprojection is the standard reconstruction technique used for electron tomography; it is fast, robust, easy to implement and retains the relationship between sampling and resolution. However, by setting the zero frequency data to zero (using a typical ramp filter) we lose information about the overall ‘black level’ of the image.

Chapter 12

Fig. 12.5  Backprojection acts to sum each projection as a single ray through the reconstruction. A single projection becomes a ray, as above, and where rays cross the increase in intensity suggests an object. But as the object becomes more complex, as here from 1 to 6 Gaussians, more projections are required before any certainty about the object can be reached. With just 2 projections the single Gaussian is well described however, for the more complex object it takes 16 projections to reach a similar certainty

A Word of Warning

Regarding constrained reconstructions – as soon as any of these techniques are applied the resultant reconstruction is almost always a non-unique solution. Many of these techniques rely on a subjective choice regarding the nature of the constraints or somewhat ill-defined choices regarding the reconstruction. 9

12.3 Constrained Reconstruction In a real experimental situation the limit on projection numbers is well below that required to give us a reconstruction with the same resolution as the original images. When this is combined with the limited angular sampling of the TEM, with further complications arising due to the type of interpolation used in the reconstruction, the use of a non-optimal weighting filter and by deficiencies in the signal-to-noise (SNR) ratio of the original data, a typical reconstruction will be far from ideal. In carrying out tomographic reconstruction we already make use of the assumption that a discrete estimation is a valid approximation to the infinite Radon transform. However, we can make use of number of other valid assumptions, which can be applied as constraints to improve the overall reconstruction quality. You should always view the final reconstruction from these techniques with healthy skepticism! Consider any conclusions you draw from them very carefully.

12.3.1 Constraint by Projection Consistency We can assume, not unreasonably, that a tomographic reconstruction generated from a series of projections should be entirely consistent with those projections. However, a re-pro-

SIRT and ART

While SIRT and ART do not, theoretically, offer any resolution improvements over weighted backprojection, we can use them to generate reconstructions that show significant reductions in reconstruction artifacts. Such a reduction will simplify any subsequent interpretation and segmentation of the reconstruction volume; and in that way may result in an improvement in the “useful” resolution. 9 There are a large number of other variants on applying the projection constraint, which modify typically how the projection information is utilized, but they typically take the form of a modified ART/SIRT approach. Variations include using multiplicative/additive approaches to determining/applying differences, the number of iteratons used and using a middle ground between single/average comparisons. All these techniques are actually specific examples of the ‘projection onto convex sets’ (POCS) approach to solution. It is worth explaining that while ART and SIRT were developed in the 1970s there has been a resurgence of interest in these approaches, especially in materials science; it appears that an assumption of positivity, implicit in ART/SIRT, can offer us significant gains in reconstruction fidelity when combined with high SNR data available from imaging techniques such as HAADF STEM (Midgley and Weyland 2003). Another advantage of materials science datasets is that often the object to be reconstructed is surrounded by low (or even zero) intensity regions; it is ‘isolated’ much like the test object in Figs. 12.3–12.7. This

Chapter 12

Fig. 12.6  Weighted backprojection. Here a test object, left, has been sampled by 141 projections with a 1° increment over ± 70°. This is fairly typical for real tilt series. A raw backprojection, center, of this data leads to a hazy and indistinct reconstruction. However, when we r-weight the reconstruction, right, to take account of the uneven spatial sampling of the original data the returned reconstruction is much improved. This example also demonstrates the effects of the tomographic PSF; the reconstruction shows features elongated in Z and distinctive “fan” artifacts

jection of a reconstruction typically shows large variations in intensity when compared to the original projections. This variation is characteristic of the reconstruction technique and the deficiencies of the tilt series as a whole, in effect each projection is blurred by the imperfect contributions from other projections. By constraining the reconstruction to match the original data it should be possible to minimize these inconsistencies and improve the final reconstruction. This approach requires us to apply several iterations of constraint, due to the corrections themselves subject to the same imperfect process of reconstruction as the original images. The simplest way we can implement this constraint corrects the reconstruction to match each tilt in sequence, the algebraic reconstruction technique (ART) (Gordon et al. 1970). With model datasets ART can yield significant improvements in the reconstruction, but it proves unstable in the presence of small amounts of noise. For real, noise containing, data a more robust approach is to compare all projections simultaneously; generating an average difference for each iteration (Gilbert 1972). This simultaneous iterative reconstruction technique (SIRT) is extremely stable, and is particularly suited to tilt series with poor signal-to-noiseratios. A demonstration of the improvement in reconstruction quality between SIRT and weighted backprojection is shown in Fig. 12.7 for a test dataset.

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Part I Fig. 12.7  Tomographic reconstructions from a test object, sampled by 71 projections over 2° increments, from a tilt range of ± 70°. The weighted backprojection demonstrates classical “fan” artifacts, a symptom of the missing wedge, especially outside the reconstruction object. Iterative, constrained, reconstruction techniques (SIRT/ART) can greatly reduce these effects. Unfortunately ART, which offers arguably the best reconstruction, breaks down in the presence of noise, whereas SIRT proves more robust

isolation aids iterative reconstruction, in an isolated object all the intensity being redistributed in the iterative loop can be restored. This is because the tilt series contains all the important Fourier components for the object. By contrast in a continuous object, such as a biological section, there are always unsolvable Fourier components. This also might contribute to the limited success of iterative solution in bio ET. In algorithmic terms this condition is known as ‘compact support’, and is well known to be critical for iterative solution in a variety of fields.

12.3.2 Constraint by Discrete Methods

Chapter 12

One property of materials specimens that we can readily take advantage of by constraint is that we often know, a-priori, which constituent phases are present in the reconstruction volume. As such the number of different gray levels within the reconstruction volume will also be strictly limited. For example, we may be studying tin in aluminum; at room temperature these two elements have little or no solid solubility – as such the volume will consist of only volumetric elements that contain Al, Sn, or open space. The resultant reconstructed volume (assuming some kind of projection related to density or atomic number) should contain only three discrete intensity levels. This vastly simplifies the number of possible solutions

to the reconstruction, which should, in theory, provide a better reconstruction with the same data. This approach is known as discrete reconstruction. In practice, any reconstruction from a finite tilt angle will always contain gray levels as a consequence of the reconstruction PSF. The result of which is that forcing a discrete reconstruction will cause most iterative algorithms to blow up (mathematically speaking). A successful implementation of this technique, known as DART (discrete algebraic reconstruction technique), gets around these problems by restricting not only the gray levels but by only allowing operation on voxels near boundaries (Batenburg et al. 2009). An example of the improvement possible is shown in Fig. 12.8, showing the potential of DART to return a clean, artefact free reconstruction. This has been successfully applied in a number of real materials systems, however it remains difficult to implement in general due to the need for prior selection of gray levels and limitations due to sampling limitations in tilt-angle limited tilt series. For example, in the Al/Sn system above there is also the presence of surface oxides/contaminants that do not resolve into easy discrete steps. Despite this, discrete reconstruction has one extremely attractive aspect: it can combine reconstruction and segmentation in a single step, as demonstrated in Fig. 12.8. Segmentation, and the potential for discrete reconstruction, will be discussed later.

12.3.3 Constraint by Symmetry By definition symmetry implies redundancy in reciprocal space, reducing the sampling required to fully describe an object. As such symmetry is a powerful constraint that can be applied in both the reconstruction and the experimental acquisition of tilt data. The first ET reconstruction used the helical symmetry of the tail of a bacteriophage (De Rosier and Klug 1968) to reconstruct from a single image. There are many examples of symmetry in the realm of biological macromolecules, such as the capsids of viruses or the arrangement of protein chains in molecular machines. Such regular symmetry is unusual in materials science at the nanoscale, but exists in abundance at the atomic scale (but not conversely in the biological sciences where individual proteins have very little useful symmetry). The use of such symmetry constraints for atomistic reconstruction will be discussed in Sect. 12.10.

12.3.4 Metric-Based Constraint What is evolving very rapidly in the field of tomographic reconstruction in electron microscopy is the understanding that all constrained reconstruction algorithms are simply part of the much larger framework of the solution of linear equations with finite data/samples. These issues are relevant across a broad range of digital imaging problems, most notably in image com-

12.3  Constrained Reconstruction

Some of the most recent applications of tomographic reconstruction make explicit use of this more general view, making use of reconstruction algorithms by the approach of ‘compressed sensing’ (Donoho 2006; Candes et al. 2006) (here compressed refers to ‘compression’ of image information). The research of Saghi and co-workers (Saghi et al. 2011) laid down the framework for such a general approach, as well as demonstrating the use of sparsity in the gradient domain. Compressed sensing electron tomography (CSET) has started to see wide application, as it is robust and requires very little user input (in contrast to discrete methods). An example of CSET is shown in Fig. 12.9. This technique has also been applied successfully to achieve a general approach to atomic resolution reconstruction; its application will be discussed in Sect. 12.10.

Sparsity

The term is well understood in the image processing community but almost unknown in the EM world.  9 Sparsity is a parameter that describes the amount of information required for solution of some function in comparison to the amount of information required to solve a maximally complex function in the same sample. In this way it defines how much better we can expect to reconstruct than we would expect based on traditional sampling theory (the Crowther criterion in other words).

Chapter 12

pression. As such, all constraint based techniques can be parameterized in terms of sparsity in some metric – whether that metric be symmetry, gradient (defined by edges), or discrete gray levels.

Part I

Fig.  12.8 A comparison between SIRT and the discrete algebraic reconstruction technique (DART). Sections, in x and z, through the HAADF STEM tomographic reconstruction of a low atomic number carbon nanotube containing a higher atomic number Cu/Cu2O catalyst. a–c  are sections through the reconstruction using SIRT, whereas (d–f) are the same sections from the DART reconstruction. Note both the clarity of the reconstruction and the uniform intensity distributions, essentially pre-segmenting the volume

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Fig.  12.9 A comparison between (a–c) SIRT and (d–f) compressed sensing tomography (CST) reconstruction. The same slice is shown for a range of numbers of projections; (a),  (d)  27  projections, (b),  (e)  13  projections and (c), (f) only 9  projections. This demonstrates both the potential improvement of CST over SIRT, but also its robustness to small number of projections

12.4 Other Reconstruction Approaches There are a number of emerging techniques for tomographic reconstruction that won’t be covered here in detail that also show promise. These include equally sloped tomography (EST), where projection angles are chosen precisely to allow transformation between Radon and real space without the need for interpolation (one of the largest sources for error in tomographic reconstruction) (Miao et al. 2005). This approach has been applied to only a limited number of studies, but shows strong promise for achieving high reconstruction resolutions (Scott et al. 2012).

Chapter 12

One technique which initially showed promise for 3D reconstruction was confocal scanning transmission electron microscopy (CSTEM). While this approach had been used to image buried features in extremely thick specimens (Frigo et al. 2002) the arrival of aberration-corrected instruments with large opening angles and consequent restrictions in depth of field raised the possibility of depth sectioning in the STEM at close to atomic resolutions without the need for tilting (van Benthem et al. 2005). Unfortunately, it has proven to be much more complicated to set up this experiment for general use, and current approaches produce vertical stacks with resolutions comparable to very limited tilt series (on the order of ± 4°!) (Xin and Muller 2010). While in the future this will be a powerful technique for imaging at high 2D resolution inside thick specimens, it is doubtful whether it will be a generally applicable technique for 3D reconstruction.

Another, more speculative, approach to tomographic reconstruction is ‘big bang tomography’, which is an attempt to find an approach to reconstruction of non-crystalline materials at atomic resolution (Van Dyck and Chen 2012). This approach is not based on tilting but on focal series of phase contrast TEM images, and use of algorithms originally coded for determining the relative distance of stars to determine the relative distance of atoms. Clearly, atoms are not independent scatterers in the same way as stars, but the promise of solution to a problem that can’t be practically solved in any other way is enticing.

12.5 Meeting the Projection Requirement At the heart of tomography, electron or otherwise, is an assumption so simple that you could be forgiven for not even considering it; does the imaging technique we are using generate images which are projections of an object’s structure? Essentially, you should ask whether the image generation process is consistent with the Radon transform; either directly or with some analytical relationship. This consideration, known as the ‘projection requirement’, suggests that the recorded signal be at least a monotonic function of some aspect of the structure. For most optical and X-ray tomography there is no doubt this is the case, both absorption and attenuation are clearly consistent. The range of possible interactions between high-energy incident electrons and the periodic/aperiodic atomic potentials in the TEM seems

Classically, electron tomography has been applied to resolve the structure of cellular material and biological macromolecules. This has been done almost exclusively by bright field TEM of stained/unstained biological thin sections. In this situation we can rely on several assumptions about the nature of the specimens and subsequent electron scattering that meet the projection requirement. Biological specimens are typically non crystalline, at least on short (4Gb) spectral images with efficient out-of-core RAM algorithms. Microsc Microanal 9(Suppl. 2):152–153 Kotula PG, Keenan MR (2003b) X-ray Spectral Imaging in the STEM for Microelectronics Failure Analysis. Microsc Microanal 9(Suppl. 2):998–999 Kotula PG, Keenan MR (2006) Application of Multivariate Statistical Analysis to STEM X-ray Spectral Images: Interfacial Analysis in Microelectronics. Microsc Microanal 12(6):538– 544 Kotula PG, Keenan MR, Michael JR (2003a) Automated analysis of EDS spectral images in the SEM: a powerful new microanalysis technique. Microsc Microanal 9(1):1–17 Kotula PG, Klenov DO, von Harrach HS (2012) Challenges to Quantitative Multivariate Statistical Analysis of Atomic-Resolution X-Ray Spectral. Microsc Microanal 18:691–698 Kotula PG, Michael JR (2006) Spectral Imaging and Multivariate Statistical Analysis from Thin Specimens in the SEM with a Four-Channel Silicon Drift Detector. Microsc Microanal 12(Suppl. 2):1390–1391 Loehman RE, Kotula PG (2004) Spectral imaging analysis of interfacial reactions and microstructures in brazing of alumina by a Hf-Ag-Cu alloy. J Am Ceram Soc 87:55–59 Mathematica™ (2015) Commercial generic and multivariate data analysis software. http://wolfram.com Matlab™ (2015) Commercial generic and multivariate data analysis software. http://mathworks.com Mayer TM, Elam JW, George SM, Kotula PG, Goeke RS (2003) Atomic-layer deposition of wear-resistant coatings for microelectromechanical devices. Appl Phys Lett 82(17):2883–2885 Mott RB, Waldman CG, Batcheler R, Friel JJ (1995) Position tagged spectrometry: A new approach for EDS spectrum im-

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Appendix  References

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chored proteins, gangliosides and receptors in native membranes. Mol Biol Cell 15(6):2580–2592 Yang H, Kotula PG, Sato Y, Ikuhara Y, Browning ND (2013) Segregation of Mn2+ Dopants as Interstitials in SrTiO3 Grain Boundaries. Mater Res Lett. http://dx.doi.org/10.1080 /21663831.2013.856815

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17

Part I

 Practical Aspects and Advanced Applications of XEDS Chapter Preview

– Simulation of X-ray spectra for thin-film analysis. – Details of quantitative X-ray analysis of thin-films by the ζ-factor method. – Contemporary topics including recent advances in X-ray analysis. Each section is independent of the others, but closely related to corresponding chapters in W&C. In addition to Chaps. 32-36 of W&C, you can also read Lyman et al (1990), Williams and Goldstein (1991) and Zemyan and Williams (1995) on fundamentals of X-ray analysis in TEM.

Chapter 17

The details and applications of X-ray analysis in TEM were described comprehensively in Chaps. 32–36 of W&C. These chapters cover all essential topics you should know prior to your own applications of X-ray analysis; from the fundamentals of spectrometers, qualitative elemental analysis, and quantitative composition determination through advanced spatial resolution and analytical sensitivity of XEDS. The main objective of this chapter is to complement W&C by introducing more advanced XEDS approaches in the TEM while not increasing the level of difficulty. This chapter consists of four sections – Practical characterization of XEDS detectors in TEM.

© Springer International Publishing Switzerland 2016 C. B. Carter, D. B. Williams (Eds.), Transmission Electron Microscopy, DOI 10.1007/978-3-319-26651-0_17

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17.1 Performance Parameters of XEDS Detectors As we suggested in Chaps. 32 and 33 of W&C, you need to know about your XEDS detector in terms of its fundamental performance parameters before utilizing it for any practical analysis. You should measure some detector parameters at least once when your system is installed or significantly upgraded. Other parameters also need to be measured time to time to monitor your system performance in a consistent manner. Fortunately, you can measure most of the XEDS characteristics using Egerton’s NiOx test specimen (Egerton, Cheng, 1994); this is why W&C strongly recommends that you purchase the NiOx film or similar NiO films – the x is nicely ambiguous! The NiOx Test Specimen

It consists of ~ 50-nm-thick NiO film on ~ 20-nm-thick amorphous carbon support on a 200 mesh Mo grid. Be careful if you make your own! 9 You can use this test specimen for calibrations of the camera length, aperture angles, EELS analysis, etc. Besides those calibrations, the following parameters can be determined for XEDSbased applications from a single XEDS spectrum of the NiOx thin film zz Detector energy resolution: described in Sect. 32.8 of W&C. zz Peak-to-background ratio in general and the Fiori definitions: mentioned in Sect. 33.4A of W&C. zz Inverse hole-count (a.k.a film count): explained in Sect. 33.3A of W&C. zz Mo K/L ratio: described in Sect. 33.3A of W&C. zz Detector collection angle: described in Sect. 32.10A of W&C. zz Detector efficiency: defined in Sect. 33.4B of W&C.

Chapter 17

You can find detailed descriptions about these various determinations in Egerton’s original papers. In addition, you can also monitor some of the detector parameters (such as thicknesses of ice and carbon in front of the active area) if you gather several spectra from the NiOx film over different time periods. The detection of X-rays from light elements (which produce low-energy soft X-rays) is significantly influenced by the thicknesses of these various layers. You can measure quantitatively the growth of ice and carbon layers, which directly degrade detection of these soft X-rays. In this section, we will show you how to measure these parameters in practice and will introduce software that allows you to carry out these measurements easily.

17.1.1 Detector, Fundamental Parameters Energy Calibration:   The X-ray energy range and dispersion must be calibrated before performing any X-ray analysis or even

before applying any measurement of the following fundamental system parameters in AEM. By using the NiOx test specimen, you can easily calibrate the energy dispersive range with the Ni Kα peak at 7.48 keV, in combination with either the O Kα peak (0.52 keV) or the Ni Lα peak (0.85 keV). If you need to calibrate the energy range > 10 keV then you can use the Mo Kα peak at 17.42 keV. Although any characteristic X-ray signal from the grid bar is always undesirable (since it proves there are spurious X-ray signals in your spectrum), the high-energy X-ray peak is actually useful for this calibration. Detector Energy, Resolution:  We define the energy resolution of an XEDS detector as the full-width at half-maximum (FWHM) value at the Mn Kα peak position (5.9 keV). You can derive this value from the FWHM value of the Ni Kα peak in an XEDS spectrum from the NiOx film as described by Bennett and Egerton (1995) RFWHM .MnK ˛/ = 0:926 RFWHM .NiK ˛/

(17.1)

The FWHM value of the Ni Kα peak can be best determined by fitting to a Gaussian, as shown in Fig. 17.1a. You can see that the Gaussian fit curve deviates slightly from the Ni Kα peak on the low-energy side. This deviation from the Gaussian is mainly caused by incomplete charge collection, which can be evaluated if you measure the ratio of the full-width at tenth-maximum (FWTM) to the FWHM values of the peak (see Sect. 32.9A in W&C). Take Time

The longer the process-time setting, the better the detector energy resolution. A higher number on the x-axis of the plot gives a lower energy range. 9 The detector energy resolution depends on how you set the process time (or time constant). If you choose a shorter process time, the energy resolution is degraded despite having higher count rates. Figure 17.1b shows the detector energy resolution measured from three different AEMs with a Si(Li) detector operated at 100, 200 and 300 kV, plotted against the process-time setting. Peak-to-Background Ratio:  We can use the peak-to-background (P/B) ratio as a measure to describe how well the XEDS-AEM system is configured. Typically a higher P/B value indicates a better-configured system. As described in Sect. 33.4A of W&C, there are a number of definitions for P/B. The most common definition is to use the full peak intensity and the background intensity with the same energy window as the peak. The above definition of P/B may depend on the energy resolution of the spectrometer system since the energy window size for the background varies with the energy resolution. To compare the P/B values taken from different instruments (or

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17.1  Performance Parameters of XEDS Detectors

Fig. 17.1  a Example of energy resolution determination using the Ni Kα peak from the NiOx test specimen. For the determination, the NiOx plug-in in Gatan DigitalMicrograph was used. b The determined energy resolution of XEDS systems of three different instruments (100, 200, and 300 kV), plotted against the process time setting

even at different process time setting) fairly, you should use the Fiori definition for P/B (Fiori et al. 1982), in which the average background intensity at a single channel (e.g., 10 eV) is used rather than the full background intensity. The typical energy windows of characteristic X-ray lines for the NiOx are summarized in Table 17.1. The background intensities are ideally determined by averaging two intensities at lower and higher energy regions of the peak. According to Bennett and Egerton, this value for the Ni Kα from the NiOx test specimen can be as high as 3,000 in modern commercial 200-kV-AEMs. If a pure-element film such as a Cr film is used, your measured P/B value should be higher than that from the NiOx film because the Cr Kα intensity corresponds to 100 wt% in the pure Cr film, whereas the Ni Kα intensity represents 78.6 wt% in the NiOx film (50 : 50 in atomic ratio).

Table  17.1  Typical energy windows of characteristic X-ray lines for the NiOx (Lyman et al. 1994)

Inverse Hole Count (Film Count):  The inverse hole count (IHC) is another useful measure we can use to evaluate the presence of stray electrons and X-rays in an AEM column. We define IHC as the intensity ratio of a major X-ray line in the specimen (which should be detected) to an X-ray line from a grid material (which should not be detected in an ideal column). In the NiOx test specimen, IHC is given as the ratio of the intensities of the Ni Kα to the Mo Kα peaks above background. In modern commercial AEMs, this value is usually in range from 3–7.

described in Sect. 33.3.A of W&C. Stray X-rays would produce a high Mo K/L ratio since high-energy bremsstrahlung X-rays preferentially fluoresce the high-energy Mo Kα line. In contrast, stray electrons would excite the Mo Lα rather than the Mo Kα. Generally, the Mo K/L ratio decreases with an increase of the probe-forming aperture size and increases with an increase in the incident electron energy. Thus, using the Mo K/L value, you can diagnose stray irradiations of the illumination system in your instrument.

Using the P/B and IHC values determined from a single spectrum in the NiOx test specimen, you can evaluate the performance of your specific XEDS-AEM. Figure 17.2 shows a plot of P/B (the Fiori definition) against the IHC, measured in three different instruments operated at 100, 200 and 300 kV (these are actually the same instruments in Fig. 17.1b). The error bars indicate a 99 % confidence limit (3σ). As we mentioned above, higher values both of P/B and IHC are preferable. Therefore, instruments at the top right-hand corner should give superior X-ray analyses.

Detector Collection Angle:  As mentioned in Sect. 32.10A of W&C, the collection angle for X-ray detection (Ω) is the most important parameter in all of X-ray analysis. We generally want to detect more X-rays, so a larger Ω value is always preferable. In fact, you may use the latest silicon drift detectors (SDDs) with significantly improved solid angle as described later in Sect. 17.4. You can measure the Ω value nominally from the geometric configuration of your AEM-XEDS interface, using Eq. 32.4 in W&C. However, such a practical measurement of Ω is not very straightforward. The Ω measurement requires that you take a reference spectrum from a known standard in a specific instrument with calibrated Ω in order to compare X-ray intensities.

Mo K/L Ratio:  You can use the ratio of the Mo Kα to the Mo Lα intensities to evaluate stray irradiation in your instrument as was

O Kα

Energy window range (keV) Peak (P)

Back­ground 1 (B1)

0.38–0.64

1.10–1.36

Back­ground 2 (B2)

Ni Lα

0.68–1.00

1.10–1.42

Ni Kα

7.16–7.76

6.50–7.10

8.60–9.20

Mo Lα

2.16–2.50

1.10–1.44

3.00–3.34

Mo Kα

17.04–17.80

16.10–16.86

18.14–18.90

Chapter 17

X-ray line

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17  Practical Aspects and Advanced Applications of XEDS

Part I Fig. 17.2  Determined P/B (Fiori definition) plotted against the IHC, measured from three different instruments operated at 100, 200, and 300 kV

Fig. 17.3  Comparison of X-ray spectra obtained from the same NiOx test specimen in the same instrument at different periods of time

Table  17.2 A prefactor C1 for Ω determination at a given an incident beam energy E0 (Bennett and Egerton, 1995).

17.1.2 Monitoring Detector Contamination

E0 (kV)

80

100

120

200

300

400

C1

2.6

2.9

3.2

4.0

4.8

5.3

Fortunately, we can use an empirical formula for the Ω determination based on a single NiOx spectrum ˝ = C1 cos  INiK =.t  Ip /

(17.2)

where C1 is a factor depending on the incident beam energy (summarized in Table 17.2 or you can calibrate it beforehand), INiK is the Ni Kα intensity above the background, t is the film thickness, τ is the acquisition time and Ip is the probe current, respectively. In addition, θ is the total tilt angle including tilt angles in both x and y directions (θx and θy, respectively) and simply given as: q   = tan−1 tan2 x + tan2 y (17.3)

Chapter 17

Relative Detector Efficiency:  Once you have measured a more accurate Ω value through Eq. 17.2, the relative detector efficiency can be determined. We define this relative detector efficiency in terms of how many X-ray counts per second are collected from a standard specimen (such as the pure Cr film and the NiOx specimen) in the measured collection angle (sr) with the incident probe current (nA). The relative detector efficiency can then be given as: .relative detector efficiency/ = INiK =. Ip ˝/.cps=nA=sr/ (17.4)

You should measure all the parameters described above at least once, ideally when your system is installed. If you don’t know these parameters, it is not too late to determine them now. The determination is straightforward since only a single spectrum needs to be acquired from your NiOx test specimen.

The detection performance of your XEDS detector may change considerably with time, especially in its ability to detect low-energy, soft X-rays. For example, Fig. 17.3 compares two X-ray spectra acquired from the NiOx film in the same instrument with a windowless XEDS detector at different time periods (one was recorded just after detector conditioning and other was a few months later). As you can see, although there is no noticeable difference in the Ni Kα line, the intensity level is significantly reduced in the lower-energy O Kα and Ni Lα peaks. This difference in the X-ray detection efficiency at lower energy regions may lead to serious problems, especially if you are carrying out quantitative analysis using lower-energy soft X-rays. Residual Gases

In a typical microscope column, the major residual gases are water vapor and hydrocarbons. 9 Such degradation of soft X-ray detection can be caused by contamination (mainly in front of the detector window) and the degradation rate is strongly related to the vacuum conditions of your instrument. The active area of your detector (an XEDS detector should be cooled by liquid N2 or by a Peltier device) easily condenses water vapor into an ice layer, and hydrocarbons may also be condensed as a carbonaceous layer. Figure 17.4 shows the absorption ratio of the O Kα, Ni Lα and Ni Kα lines, plotted against thickness of the ice (a) and carbon (b) layers. The ice layer build-up influences the Ni Lα line most severely. When the ice layer reaches ~ 1 μm, 50 % of the Ni Lα intensity is absorbed in the ice layer. For the O Kα, the ice build-up is less sensitive. Over 5 μm of ice layer absorbs ~ 50 % of O Kα intensity. In contrast, the carbon layer significantly influences both the O Kα and Ni Lα lines, as shown in Fig. 17.4b.

17.1  Performance Parameters of XEDS Detectors

471

OK NiK OK O = f.=/O − .=/O gice OK NiK OK C = f.=/C − .=/C gC NiL NiK NiL O = f.=/O − .=/O gice

(17.7)

Part I

with

NiK NiL NiL C = f.=/C − .=/C gC

If you take ratios of the above intensity ratios (IOK/INiK and INiL/ INiK) between two independent measurements (subscripts 1 and 2) you can derive the following equations:   .IOK =INiK /1 OK = exp −OK O tice − C C .IOK =INiK /2   .INiL =INiK /1 NiL = = exp −NiL O tice − C C .INiL =INiK /2

ROK = RNiL

(17.8)

where ∆tice and ∆tC are thickness differences in ice and carbon layers between measurement 1 and 2, respectively, i.e., the relative layer growth of ice and carbon between your two measurements. Then, ∆tice and ∆tC can be derived as: tice =

OK NiL C ln.ROK / − C ln.RNiL / OK NiL OK C O − NiL C O

tC =

NiL OK C ln.RNiL / − C ln.ROK / OK NiL NiL OK C O − C O

(17.9)

With a 1 μm carbon layer, 90 % of the O Kα and 50 % of the Ni Lα X-rays are absorbed. Conversely, absorption of the Ni Kα X-rays is negligible both in the ice and the carbon (up to 10 μm). In addition to the reduction of soft X-ray detection, accumulation of the ice and carbon layers may also cause (1) a decrease in the background intensity even at higher energies (which results in an increase in your P/B ratio) and (2) a decrease in dead time during X-ray acquisition. Therefore, it is essential that you monitor the accumulation of ice and carbon layers on your detector.

In the above equation, the only parameters you need are the densities of ice and carbon, and the MACs, which you can find summarized in Table 17.3. Using these parameters, Eq. 17.9 can be simplified thus:     .INiL =INiK /1 .IOK =INiK /1 − 1689:8 ln tice = 481:4 ln .IOK =INiK /2 .INiL =INiK /2     .INiL =INiK /1 .IOK =INiK /1 tC = 69:0 ln − 397:2 ln .INiLw =INiK /2 .IOK =INiK /2 (nm)

X-ray absorption due to the ice and carbon layers can be modeled as (Hovington et al. 1993)   X A = exp −.=/X (17.5) O ice tice − .=/C C tC



X Where .=/X O and .=/C are the mass absorption coefficients (MACs) of X-ray X in oxygen and carbon, ρice and ρC are the densities of ice (0.917 Mg/m3) and carbon (2.267 Mg/m3), and tice and tC are the thicknesses of ice and carbon layers. You should note that the MAC value for oxygen is used instead of that in ice in the above equation because the MAC value for hydrogen is very low for all X-rays. In particular, for the NiOx test specimen, the following equations are relevant:   OK .IOK =INiK / / exp OK O tice − C tC   (17.6) NiL .INiL =INiK / / exp NiL O tice − C tC

(17.10)

In the derivation of Eq. 17.10, we used the MAC values reported by Heinrich 1987. If you want to determine the contamination layer thicknesses, you have to take two spectra in almost identical conditions, i.e., with the same specimen tilt, time constant, etc. However, by taking the double ratio, you can cancel out any differences in the acquisition time and the probe current.

17.1.3 Software to Determine Detector Parameters You can measure many detector parameters including the decay of detector performance by acquiring a single spectrum

Chapter 17

Fig. 17.4  Calculated absorption ratios of the O Kα, Ni Lα and Ni Kα lines, plotted against the ice thickness (a) and the carbon thickness (b) in front of the detector active area

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17  Practical Aspects and Advanced Applications of XEDS

Part I

Table 17.3   Summary of parameters for determination of contamination layer growth at an XEDS window. The MAC values are calculated from Heinrich’s formula (Heinrich 1987) For ice

For carbon

ρice = 0.917 Mg/m3

ρC = 2.267 Mg/m3

2 .=/OK O  = 119.3 m /kg

2 .=/OK C  = 1,168.6 m /kg

2 .=/NiL O  = 680.3 m /kg

2 .=/NiL C  = 333.3 m /kg

2 .=/NiK O = 1.395 m /kg

2 .=/NiK C  = 0.545 m /kg

or a set of spectra from the NiOx test specimen. To perform these measurements routinely and consistently, use the plug-in for Gatan DigitalMicrograph. To run any functionalities in this plug-in package, you have to have Gatan DigitalMicrograph (see Chap. 6). Next, we’ll introduce two additional plug-ins, in which all the evaluation procedures of detector performance described above are implemented. NiOx: this plug-in determines all the fundamental detector parameters described in Sect. 17.1.1 above. Figure 17.5a shows the dialog of the NiOx plug-in. All you need to do is to i) open a spectrum from the NiOx test specimen, ii) select the detector parameters you want to determine by clicking the check boxes, and (iii) click the ‘Calculate’ button. If you select the ‘Solid angle and Relative detector efficiency’, an additional sub-dialog appears (Fig. 17.5b) so you can input several instrumental and experimental parameters. An example of the output is shown in Fig. 17.5c. NiOxIceC: this plug-in determines the accumulated ice and carbon thicknesses from two spectra measured in different time period from your NiOx test specimen. As we already mentioned above, you must acquire these spectra in the same instrument under almost identical experimental conditions. Figure 17.6 shows the dialog of the plug-in (A) and an example of the output (B) from the two spectra shown in Fig. 17.3. In this particular case, the accumulated ice and carbon layers are 1.67 ± 0.04 μm and 53.1 ± 8.5 nm with 99 % confidence limits (3σ), respectively.

Chapter 17

In addition to these plug-ins, this package also contains a function to import a spectrum in the EMSA/MAS file format (EMSA file import). The EMSA/MAS file format is the one most commonly used in the electron microscopy community and most XEDS manufactures support this format in their systems. You should check the system manual or consult the manufacturer to find out how to save a spectrum in the EMSA format. As long as your spectrum is saved in the EMSA format, you can convert it to DigitalMicrograph and your detector parameters can be determined via the above plug-ins. You can find a standardized description of the EMSA format through the International Organization for Standardization.

17.2 X-ray Spectrum Simulation – a Tutorial and Applications of DTSA Planning your experiments is one of the most important tasks for all microscopists because preparation for TEM experiments, including specimen preparation and actual microscopy sessions, requires significant amounts of time and money – the cost of running and maintaining a TEM – it’s not free! In order to plan (or ideally to optimize) your experiments, it would be very efficient to predict i) the feasibility of each experiment, ii) difficulties of measurements, and iii) the fundamental limits of planned analyses. Theoretical simulation is one of the best approaches to confirm your experimental limits before you conduct actual experiments if, of course, appropriate simulation tools are available. Fortunately, for XEDS, several tools are available to simulate an X-ray spectrum: some are based on a first principles approach such as DTSA (Fiori et al. 1992) while others are combined with Monte Carlo techniques, e.g., the electron flight simulator (Brundle et al. 1996). (See References for Software for both.) In the current version of DTSA-II (Ritchie 2008), however, the function for spectrum simulation is only available for bulk samples. While writing, we are still waiting for a thin-film version of the spectrum generation. Therefore, in this section, we will explain X-ray spectrum simulation using DTSA instead. Perhaps the thin-film version of X-ray spectrum simulation will be implemented in either DTSA-II or other modern software packages by the time you are reading this chapter. DTSA

The most recent version of DTSA is DTSA-II; it includes both a first principles approach and Monte Carlo techniques. Use it to generate X-ray spectra before you go to TEM. 9 In order to simulate an X-ray spectrum properly, you need to understand several fundamental parameters related to X-ray generation and detection. After we introduce DTSA in this section, we’ll illustrate the fundamental parameters for X-ray analysis by a brief tutorial for the X-ray spectrum simulation. Then, we’ll explain further details of X-ray generation and detection by simulating several different stages of X-ray spectra, (which are never actually seen in practice) for example what an X-ray spectrum looks like before it is emitted from your specimen and before it is processed by the XEDS detector electronics, etc. We can only demonstrate this feature by a first principles simulation, which is very useful to help you understand the physics behind X-ray generation and detection. Once you understand the appropriate procedures for X-ray spectrum simulation using DTSA, you will be ready to apply it to

473

Part I

17.2  X-ray Spectrum Simulation – a Tutorial and Applications of DTSA

Fig. 17.6  a Main dialog of the NiOxIceC plug-in package. b An example of the output for determination of the accumulated layer thicknesses of ice and carbon, measured in a 300 kV UHV instrument with a windowless XEDS detector

predict your experimental spectra. Finally, we’ll show you four practical applications of the X-ray spectrum simulation at the end of this section. These four are zz Confirmation of peak overlap (related to Sect. 34.3 of W&C), zz Evaluation of X-ray absorption in a thin specimen (related to Sect. 35.6 of W&C), zz Demonstration of AEM-XEDS interfaces (related to Sect. 33.4A of W&C), zz Estimation of the detectability limits (see Sect. 34.4 and 36.4 of W&C).

17.2.1 What Is DTSA? The function of an electron-excited X-ray spectrum generator is one of the main features of DTSA, which was implemented as a ‘dry lab’ by Fiori to predict experimental limits. This generator is available both for bulk samples and for thin films. Besides this powerful feature, DTSA provides several useful functions for X-ray analysis such as peak deconvolution, background subtraction, quantitative matrix corrections for bulk samples and Cliff–Lorimer quantification for thin speci-

Chapter 17

Fig. 17.5  a Main dialog of the NiOx plug-in package. b Sub-dialog for determination of the collection angle and the relative detector efficiency, and c An example of the output for the determination of the collection angle and the relative detector efficiency in a 200 kV instrument

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17  Practical Aspects and Advanced Applications of XEDS

Part I Fig. 17.7  Screen shot of DTSA running via SheepShaver under a Windows platform

Chapter 17

mens, along with a comprehensive database related to X-ray analysis. Fiori developed the original version of DTSA using the Pascal program language for an Apple Macintosh II and the last versions (2.5 or 3.0.1) run in a Power Macintosh under classic OS 8 and 9. DTSA does run under the so-called classic mode in OS X if the CPU is either G4 or G5. However, the DTSA runs neither in a newer Mac with an Intel CPU nor in any Windows/ Linux PC. So, we keep an iMac (generation 2000) just to run DTSA! While many of you will not have access to such museum pieces, fortunately, DTSA-II (the successor to DTSA) has been developed as a JAVA-based, platform-free, software by Nicho-

las Ritchie at NIST, and hence can run in Windows, Mac OS X and Linux. Therefore, in the near future, all the descriptions in this section may be replaced with those adjusted for DTSA-II, once DTSA-II provides the spectrum generation function for thin films! We should mention that you can run the PowerMac version (2.5) of DTSA either in Windows (as shown in Fig. 17.7) or in Mac OS X, or even in Linux, via a PowerMac emulator called ‘Sheep­ Shaver’ (see References to find this software package). So, while it is a temporary solution for now, it should also work for Mac OS X and Linux systems.

17.2  X-ray Spectrum Simulation – a Tutorial and Applications of DTSA

Typical Detector Configurations

In modern instruments the take-off angle is 20–25o and the specimen-detector distance is ~ 15 mm or less. 9 After setting up the above parameters, click the ‘Detector-Specimen Geometry Dialog’ button (C). Another sub-dialog appears in which you can input the geometry configuration between the XEDS detector and instrument, as shown in Fig. 17.9b. There are two most important parameters you have to input in this dialog, namely the ‘Detector Elevation Angle’ corresponding to the X-ray take-off angle and the ‘Specimen-Detector Distance’ that controls the X-ray collection angle (see Sect. 32.10A of W&C). Again, you should consult the manufacturer if you are not aware of these parameters. Alternatively, you can reverse-calculate the specimen-detector distance from the detector collection angle using Eq. 32.4 in W&C, if your collection angle has been determined using standard specimens such as NiOx or NIST standard specimens, which we describe below. If every parameter looks OK, you can return to the main dialog by clicking the ‘OK’ buttons.

Fig. 17.8  Screen shot of the main dialog for thin-specimen spectrum generation in DTSA

If you prefer to change the energy dispersion (eV/channel), click the ‘Channel Spec’ button to select the eV per channel and the number of channels (Fig. 17.9c). For a typical X-ray spectrum from a thin specimen, 10 eV per channel with 2,048 channels are good values. Then, click ‘OK’ to return to the main dialog. Specimen Information:  Specific information about your specimen should be input in the main dialog. All you need to input is the constituent elements and their compositions, the specimen density and its thickness. For element information, either an atomic number such as ‘8’ or an atomic symbol such as ‘Mg’ can be used. You can also select several different units for compositions. Note that the spectrum simulation does not require the density value for the bulk target (one of the major differences between the bulk and thin targets simulations). As an example, in Fig.  17.8, information about the NIST standard reference material (SRM) glass, thin film, 2063a is shown. This specimen has had its composition, density and thickness already certified by the NIST SRM program – hence by the US government! You can also save the input information to a Database in DTSA. Experimental Information:  Experimental conditions can also be set up in the main dialog (Fig. 17.8). Only three parameters are required for the spectrum simulation: the incident electron energy, probe current, and acquisition time. Physics Choice:  The last parameters you need to set up are related to the physics of X-ray generation. These parameters can be selected by clicking the ‘Physics Choice’ button available in the main dialog. An independent sub-dialog appears, as shown in Fig. 17.10. In this sub-dialog, models of the ionization crosssection for K-, L- and M-shells, and a cross-section model for continuum  X-rays can be selected. In addition, you can also select scaling-factor values for each of the cross-section models. As we will describe in the following subsection, electroninduced X-ray signals are directly proportional to magnitudes of the cross-sections. Therefore, the physics settings chosen in this sub-dialog are very important to match with experimental

Chapter 17

Once you successfully launch DTSA, select ‘Generate > Thin Target Spectrum’ from the pull-down menu to simulate an X-ray spectrum for a thin specimen. Then, the main dialog for thin-specimen spectrum generation appears as shown in Fig. 17.8. In this main dialog and subsequent dialogs, you can fill in or select the parameters required for simulation. Note that you can also simulate an X-ray spectrum for a bulk sample when ‘Bulk Target Spectrum’ is selected. The difference between the bulk and thin targets is minimal with respect to parameter set-up for spectrum simulation. Detector Parameters:  If you click the ‘Detector Parameters’ button in the main dialog, you’ll see that a dialog for detector parameters appears (Fig.  17.9a). In this dialog, you can (A) select/input several detector configuration parameters and (B) define the detector-window parameters. Select your detector type (either Si or Ge) and input the energy resolution that you should have determined using the NiOx specimen and any other parameters associated with your detector and window configurations. If you are not sure about your specific detector configuration, consult the lab manager or the manufacturer, or take values from Table 32.1 in W&C. You can also load typical values by clicking the ‘Load Typical Values’ button (remember however, these typical values could be very different from those for your particular instrument). It should be mentioned that many XEDS detectors attached to modern AEMs are Si(Li) detectors or SDDs with an atmospheric thin-window (ATW), which has a Moxtek polymer layer of ~ 0.3 μm and an Al contact layer of ~ 0.04 μm, as shown in Fig. 17.9a.

Part I

17.2.2 A Brief Tutorial of X-ray Spectrum Simulation for a Thin Specimen Using DTSA

475

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17  Practical Aspects and Advanced Applications of XEDS

Part I

Fig.  17.9 Screen shots of the dialogs for detector parameters (a), for detector geometry configuration (b), and for channel settings (c)

Chapter 17

17.2  X-ray Spectrum Simulation – a Tutorial and Applications of DTSA

477

Part I

Fig. 17.10  Screen shot of the dialog for physics choice

Finally, an X-ray spectrum can be generated by clicking the ‘Generate’ button in the main dialog. Then, the generated X-ray spectrum is displayed as shown in Fig. 17.11a. This spectrum is ideal and clean, i.e., it has none of the spurious effects described in Chaps. 32 and 33 of W&C. At least, noise can be added to this spectrum, which is essential when you need to estimate analytical sensitivity. To add noise, you should select ‘Math > Add Poisson Noise to Work’ from the pull-down menu, and then another spectrum will appear with noise as a ‘Results’ spectrum, as shown in Fig. 17.11b. (Note: DTSA can display ten spectra simultaneously.) Yes, we add noise to the simulation rather than remove noise from the experimental data! As we just described, one of the great advantages of DTSA is that you can go into the software dialog and try setting a whole different set of parameters. This approach allows you to see what effect the different values have on the generated spectrum of your particular specimen on which you are depending for your research. You’ll immediately find which parameters are important and which do not affect your spectrum significantly. This aspect of spectrum simulation will of course help you in your general operation of the AEM. You’ll soon learn which parameters you should select carefully and which you can generally leave to take care of themselves. Let’s now explore further details of the spectrum simulation.

17.2.3 Details of X-ray Simulation in DTSA A thorough understanding of X-ray generation and detection is useful if you need to interpret X-ray spectra acquired from a thin specimen and also for further quantitative analysis. Newbury et al. (1995; see their 2014 article for DTSA-II) reviewed a series of simulation procedures for an X-ray spectrum in DTSA in which the spectrum simulation for bulk targets is mainly featured. Unfortunately, we don’t know of any detailed description available for the spectrum simulation for thin targets. So, here, we explain step-by-step the details of the X-ray spectrum simulation for a thin target. Characteristic X-ray Generation:  In a bulk sample, the generation of characteristic X-rays is a very complicated series of phenomena and many aspects need to be taken into account for spectrum simulation. In contrast, the X-ray generation process in a thin specimen is much more straightforward. In a thin specimen, we can make a few key assumptions: zz The energy loss of the incident electrons is negligible, because the energy loss can be as low as only 3 % (in up to 500-nm-thick specimens) even at 100 kV. zz Electron backscattering loss is also ignored since most of the scattering events in TEM are forwardscattering. zz The depth distribution of X-ray production is unity. With these approximations the characteristic X-ray generation in a thin specimen can be simplified to be proportional to the mass thickness (ρt) and the characteristic X-ray intensity Ic at a given beam current Ip and an acquisition time τ can be expressed as IC =

si Qi !aCN De t A

(17.11)

Chapter 17

spectra. However, unless you have any specific idea in terms of the selection of models and their scaling factor, or are very familiar with these models and concepts, you can leave them with default values or just click the ‘Load Defaults’ button. You can obtain preferential choices of the cross-section models with the corresponding scaling factors in determination of the ζ-factor method, as we explain in the next section. After setting up the physics choices, click the ‘OK’ button to return the main dialog.

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17  Practical Aspects and Advanced Applications of XEDS

Part I Chapter 17 Fig. 17.11  Example of simulated X-ray spectra from the NIST SRM2063a thin specimen. a Noise-free ideal spectrum. b Spectrum with random noise

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17.2  X-ray Spectrum Simulation – a Tutorial and Applications of DTSA

Fig. 17.12  Simulated result for a generated X-ray spectrum from the SRM2063a thin specimen

where Qi is the ionization cross-section, si is the scaling factor of Qi, ω is the fluorescence yield, a is the line weight (or the relative intensity ratio), C is the weight fraction, A is the atomic weight, Nv is the Avogadro number, and De is the total electron dose defined as (17.12)

where Ne is the number of electrons (electron counts) in a unit electric charge. Continuum X-ray Generation:  The continuum background of an X-ray spectrum can ideally be generated only by bremsstrahlung events. The intensity of the continuum X-ray Ib can be expressed similarly to Eq. 17.11 as a function of the X-ray energy E Ib .E/ =

X sC QC;j .E/Cj N De j

Aj

t



(17.13)

where Qc,j(E) is the continuum X-ray cross-section at an X-ray energy E, sc is the scaling factor of Qc,j, and j is an index for each element included in the thin specimen. So, the continuum X-ray intensity is the sum of contributions from all the elements. In general, Qc,j is based on the classic description by Kramers as described in Eq.(35.7) in W&C. Especially for a thin specimen in an AEM, the angular distribution of continuum X-rays is not homogeneous, as was shown in Fig. 33.6 in W&C. We can handle this angular dependence of the continuum X-ray generation by including the detector elevation angle, and the specimen tilt angles in the proposed cross-section models of continuum X-ray generation in thin specimens. The generated characteristic X-ray peaks are merged with the generated continuum X-ray spectrum in the first step of the spectrum simulation. Figure 17.12 shows an example of a generated spectrum from SRM2063a (thickness of 76 nm), simulated in the same microscope and for the experimental conditions in

Fig. 17.11. Note that this generated spectrum is never seen in practice since the X-rays are not yet emitted from the specimen. In addition, the characteristic X-ray peaks are much sharper than a single channel width (10 eV/channel in this simulation). The actual generated peak width is narrower than 1 eV. You should note that intensities of all simulated spectra are normalized with the detector collection angle to make it easy to compare the spectra. X-ray Emission after Being Absorbed in a Thin Specimen:  Not all the generated  X-rays are emitted from your specimen since some fraction of the generated X-ray is absorbed, even in a thin specimen. We can express the relationship between the generated and emitted X-ray intensities in a differential form: Iemit = Igen exp Œ−.=/z cosec ˛

(17.14)

where ∆Iemit and ∆Igen are the emitted and generated X-ray intensities from a small mass-thickness segment ∆(ρt) at α depth of ρz from the incident surface, respectively, and α is the X-ray takeoff angle. In DTSA, the total emitted X-ray intensity is calculated by integrating all the X-ray intensities, including absorption, in the individual segments. We compare an emitted spectrum from SRM 2063a (red solid line) with a generated one in Fig. 17.13a. Fig. 17.13b, the fraction of X-ray absorption is plotted in percent as a function of the X-ray energy. Despite the very thin SRM 2063a specimen (only 76 nm), you can see that a considerable fraction of the X-rays generated at energies lower than 1 keV (soft X-rays) is absorbed into the specimen and not emitted. For instance, more than 30 % of the generated O Kα is not emitted

Chapter 17

De = Ne Ip 

Fig.  17.13 Comparison between generated (black) and emitted (red) X-ray spectra from the SRM2063a thin specimen (a) and the X-ray signal loss in % due to X-ray absorption within the specimen, plotted against the X-ray energy (b)

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17  Practical Aspects and Advanced Applications of XEDS

Part I Fig. 17.14  Comparison between emitted (red) and detected (blue) X-ray spectra from the SRM2063a thin specimen (a) and the X-ray signal loss in percent due to absorption in the detector, plotted against the X-ray energy (b)

Fig. 17.15  Comparison of X-ray spectra from the SRM2063a thin specimen before (blue) and after (orange) broadening due to the detector electronics (a) and the detector energy-resolution plotted against the X-ray energy (b)

from the film due to absorption. In contrast, X-ray absorption is negligible for X-rays > 2 keV.

In Fig. 17.14a, we compare the detected spectrum (blue solid line) with the emitted spectrum. As we mentioned above, the intensities of both spectra were normalized with the collection angle Ω/(4π). In Fig. 17.14b, detection losses due to window absorption and crystal transmission are plotted (in percent) as a function of the X-ray energy. Again, you can see that the soft X-rays below 2 keV are reduced significantly for a Si(Li) detector (even with an atmospheric ultra-thin window (UTW)). The O Kα intensity drops to only ~ 25 % of the generated intensity due to absorption in the specimen and losses during detection. If your detector window is contaminated with carbon and ice, further intensity loss will occur.

Influence of the Detector Collection Angle:  X-rays are emitted radially into a 4π steradian, spherical space. However, only a small portion of the X-rays can be collected, depending on the XEDS detector geometry, defined by the collection solid angle Ω. As we described earlier, only 0.1 ~ 3 % of all the emitted X-rays are collected in commercial AEMs unless you use the latest SDDs with large solid angles. The X-ray intensity collected by the detector can be expressed as:   ˝ Icol = Iemit (17.15) 4 As we also mentioned above, the background intensity is dependent on the take-off angle of the detector, which is included in the cross-section models of the continuum X-rays.

Chapter 17

X-ray Absorption and Transmission in the XEDS Detector: The collected  X-rays reach the active area of detector crystal through the detector window. In this process, the low-energy soft X-rays may be absorbed by your detector window and by any contamination layers in front of the window. In addition, higherenergy, hard X-rays may transmit through the detector crystal, especially if it is a Si(Li) crystal or an SDD crystal. We describe the loss of X-ray intensity due to the window absorption and crystal transmission in terms of the detector efficiency ε, which is given as Eq. 35.15 in W&C. We can express the detected X-ray intensity as: Idet = Icol "

(17.16)

Influence of Detector Electronics:  The peaks of detected characteristic X-rays are still very sharp in the detected spectrum (Fig. 17.14). However, these sharp peaks are blurred by the X-ray detection process and the detector electronics. This blurring is proportional to the X-ray energy and expressed as RFWHM .E/ =

p 2:5.E − EMnK ˛ / + RFWHM .MnK ˛/2 (17.17)

where EMnKα and RFWHM(MnKα) are the energy and detector resolution at the Mn Kα peak. The spectrum blurred by the detector electronics (orange solid line) is superimposed on the detected spectrum at the top in Fig. 17.15. Fig. 17.15b, the energy resolution RFWHM(E), calculated using Eq. 17.17, is plotted against the X-ray energy. Although the characteristic peak intensities remain the same, you can see that the height of each peak (hence the peak-to-background ratio) is significantly reduced due to the blurring. With such blurring, DTSA finally produces a simulated X-ray spectrum which has the familiar shape we usually see on our computer display.

17.2  X-ray Spectrum Simulation – a Tutorial and Applications of DTSA

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Fig. 17.16  Screen shot of the dialog for output choice

17.2.4 Application 1: Confirmation of Peak Overlap Once you understand the X-ray simulation process in DTSA, you can apply the spectrum simulation feature for your specific research needs. You should perform the spectrum simulation before doing the experiment but after reading this chapter and those in W&C! (Then read the chapters again and repeat the process!) In the rest of this section, we will introduce several useful applications of spectrum simulation. The first application you should always carry out is the confirmation of the energy positions of all the characteristic X-ray peaks from your specimen. As described in Sect. 34.3 of W&C, you can confirm any peak overlaps simply by the spectrum simulation in DTSA. Figure 17.17 shows a simulated X-ray spectrum with a selected energy range of 1–4 keV from MoS2, which is one of the famous ‘pathological overlaps’. To confirm the peak energy positions, KLM markers of the Mo L and S K line families are also shown in Fig. 17.17. You can see that the Mo Lα peak is superimposed on the S Kα peak. In addition, the S Kβ peak lies between the minor Mo Lβ4 and β3 peaks as well. You can easily confirm whether the peak at 2.3 keV is the Mo L or S Kα by checking the presence of the Mo Kα line at 18 keV. However, the

major question is “Is it possible to identify the existence of a S Kα peak in the presence of Mo?”. The answer is “yes” – if a sufficient amount of S is contained in the analyzed region. You can confirm the S presence by comparing (1) the Mo K/L intensity ratio from a pure Mo standard thin specimen and (2) the energy resolution of the peak at 2.3 keV. In contrast, if you try to identify S with a low amount in the presence of Mo, the situation becomes much harder. (Look at the chapter on spectral imaging.) Overlapping Peaks

If there are several characteristic peaks at very similar energy ranges, the peaks might overlap one another and it is important to know this before you carry out your experiments: DTSA can help. 9 If your specimens are not self-supported (such as nanoparticles or FIB lift-out coupons) you must use supporting grids. Selection of the supporting grids is another important task prior to any practical experiments. Again, you can evaluate suitable supporting grids with the aid of a spectrum simulation. For example, a simulated spectrum from HfO2 is shown in Fig. 17.18. HfO2 is used in optical coatings and in DRAM capacitors as a high-k dielectric. It has recently attracted attention as a good candidate for the gate oxide in field-effect transistors to replace current silicon oxides. Therefore, HfO2 is often analyzed in a TEM, either on its own and as one of the components in a semiconductor device. In Fig. 17.18, the KLM markers of Cu and Mo (both are common support-grid materials) are also shown. Both the Cu Kα and Kβ lines overlap with the Hf L peaks. Obviously, you can see that the (more popular) Cu grids

Chapter 17

Using DTSA, you can simulate an X-ray spectrum at each detection step. In the main dialog for thin-specimen spectrum generation (Fig. 17.8), click the ‘Output Choice’ button and then you can select appropriate indices for desired outputs in the output choice dialog (Fig. 17.16).

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17  Practical Aspects and Advanced Applications of XEDS

Part I Fig. 17.17  Simulated X-ray spectrum with a selected energy range of 1–4 keV from MoS2, showing pathological overlaps between the Si Kα (red) and Mo Lα (blue) peaks

should not be your primary choice for XEDS analysis of Hf. Instead, you can use a Mo grid to mount a FIB-cut specimen from a semiconductor device which contains HfO2. In addition to the grid materials, you may check other X-ray peak overlaps with Ga and also with protective deposition materials such as W or Pt.

17.2.5 Application 2: Evaluation of X-ray Absorption into a Thin Specimen We have stressed that  X-ray absorption, even in the thinnest specimens, may not be negligible for lower energy X-rays. As we explained in Eq. 17.14, how X-ray absorption affects your spectrum depends on the thickness, density, and mass absorption coefficient of the specimen and the X-ray take-off angle. You can evaluate the expected X-ray absorption of your specimen using the spectrum simulation in DTSA before you start your actual experiments.

Chapter 17

Figure 17.19a shows three spectra simulated at different thicknesses of 50, 100, and 300 nm of NiAl intermetallic compound in a 200-kV-instrument with an X-ray take-off angle of 25º. To ensure a fair comparison, we have normalized these spectra to the maximum peak intensity of the Ni Kα line. As the specimen thickness increases, you can see that the peak heights of the Ni Lα and Al Kα lines are relatively reduced. The absorption loss of the Ni Kα, Ni Lα, and Al Kα lines are shown as a function of the specimen thickness in Fig. 17.19b. For calculation of the absorption loss, we used an X-ray take-off angle of 25º. We can calculate the MAC of the individual X-ray lines in the specimen by the weighted mean of the individual MAC values of the constituent elements: X .=/X Cj .=/jX sp = (17.18) j

Fig. 17.18  Simulated X-ray spectrum from HfO2 with KLM markers for Cu and Mo. Since the Hf L-line family is superimposed on the Cu L-line family, a Cu grid is not advisable for X-ray analysis of materials containing Hf

In Table 17.4, the MACs of the Ni Kα, Ni Lα and Al Kα lines in Ni, Al and NiAl are summarized. The red dashed line in Fig. 17.19b indicates a 10 % loss of the total intensity due to absorption in the specimen. When more than 10 % of absorption occurs, the absorption correction may be required for good quantitative analysis. We define the specimen thickness which causes 10 % absorption loss as the critical thickness. As shown in Fig. 17.19b, the critical thicknesses for the Al Kα and Ni Lα are 54 and 97 nm, respectively, again confirming the dangers of absorption from lighter elementss, even in thin films. The absorption path length is dependent on the X-ray take-off angle α and given as tcosecα for a specimen thickness t. However, the path length varies with the specimen tilt-angle. You can reduce the absorption path if you tilt your the specimen toward the XEDS detector, or increase it by tilting away. If we define the tilt angle toward the detector as θ, we can express the total take-off angle as α + θ. Fig. 17.20 shows X-ray spectra from a 100 nm thick NiAl film simulated under conditions of no-tilt, +15º tilt (toward the detector, the total take-off angle: 40º) and −15º tilt (away from the detector, the total take-off angle: 10º). Although the peak intensity of Ni Kα is almost unchanged, the peaks of both the Ni Lα and Al Kα vary significantly with the tilt conditions. Therefore, you can control the absorption path length, i.e., the absorption effect, to some degree, by tilting your specimen. In addition, you should know the proper configurations of the specimen-detector geometry in your instrument, if you still insist on tilting your specimen for analysis. Be Aware

You decrease the P/B ratio as you tilt the specimen. 9

Table 17.4  Summary of MAC values of the Ni Kα, Ni Lα and Al Kα lines in Ni, Al and NiAl intermetallic compound. The MAC values in the pure elements are calculated from Heinrich’s formula (Heinrich 1987) and those in NiAl are obtained from Eq. 17.18 using the values in the pure elements Absorber

17.2.6 Application 3: Evaluation of the AEMXEDS Interface Using DTSA, you can also simulate an X-ray spectrum in unusual conditions – sometimes these conditions may be unrealistic. In Sect. 33.3 of W&C, we discuss why an XEDS detector is mounted on the incident-beam side of the specimen, despite the fact that characteristic X-rays are emitted uniformly over a 4π steradian sphere. The major reason for this choice is the angular dependence of the continuum X-ray emission: the background-intensity distribution is maximized in the forward scattering direction and is reduced as the scattering angle increases toward backscattering directions. Using the DTSA spectrum simulation, you can confirm this angular dependence of the background intensity distribution. Figure 17.21a shows a comparison of two spectra from our standard NiOx test specimen, simulated at 200 kV with take-off angles of ± 70º. Although the peak intensity of the Ni Kα line remains almost the same, you can see significant difference in the background intensity. As expected, the background intensity is much higher on the exit-surface side of the specimen, especially at lower energies. Remember, the absorption-path length is the same in both geometries. In Fig. 17.21b, you can see the take-off angle dependence

Ni Kα

Ni Lα

Al Kα

Ni

6.0

181.1

454.3

Al

6.1

179.8

39.7

NiAl

6.0

180.8

323.8

Fig. 17.20  Comparison of three X-ray spectra of NiAl simulated at different tilt angles of −15º, 0º, and +15º

of P/B of Ni Kα peak using the Fiori definition. The P/B value is much lower in the exit-surface side, and hence the higher takeoff angle is desirable since we want to obtain higher P/B values. It’s impractical to change the detector geometry in your microscope instrument (unless you have more money than sense). In contrast, you can easily vary the take-off angle in a DTSA simulation. Thus spectrum simulation is a very handy tool to support all your XEDS experiments.

17.2.7 Application 4: Estimation of the Detectability Limits One of the most useful applications of the spectrum simulation is to evaluate detectability limits. This is why this particular application was the major motivation for the original development of DTSA (Fiori, Swyt 1989; Newbury et al. 1995). A commercialized software package (EELS Advisor for Gatan DigitalMicrograph) expands the concept of detectability evaluations to find experimental configurations for appropriate acquisition of EELS spectra and EFTEM elemental images. You can find the detailed procedures for detectability evaluation in the literature (e.g., Watanabe and Williams 1999). Here, we will show how you can evaluate three different parameters related to the analytical sensitivity, using the spectrum simulation.

Chapter 17

Fig.  17.19  a  Comparison of three  X-ray spectra simulated at different thicknesses of 50, 100, and 300 nm of Ni3Al intermetallic compound in a 200 kV instrument with an X-ray take-off angle of 25º. These spectra were normalized by the maximum peak intensity of the Ni Kα line. b The signal losses (%) of the Ni Kα, Ni Lα and Al Kα lines due to the absorption into the specimen, plotted against the specimen thickness

MAC (m2/kg)

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17  Practical Aspects and Advanced Applications of XEDS

Part I Fig. 17.21  a A comparison of two spectra from a NiOx test specimen, simulated at 200 kV for take-off angles of ± 70º. b The take-off angle dependence of P/B of the Ni Kα peak (using the Fiori definition)

Look Before you Look!

It’s obviously crucial to find out if you can actually detect what you are looking for, before you embark on specimen preparation and all the other time-consuming steps. 9

Chapter 17

Peak Detectability:  After acquisition of an X-ray spectrum from your specimen, you may see that an element of interest only exhibits a small peak. In this situation, you must judge whether the small peak is actually visible or even detectable (is it just a fluctuation in the background noise?). Detailed descriptions of when a peak is visible or not can be found in Sect. 34.5 of W&C. Here we’ll explore the peak visibility and detectability in practice using the spectrum simulation. As an example, let’s consider phosphorus detection in Fe. P is one of the impurities that can cause brittle failure in steels by segregating to grain boundaries. Therefore, the detection of small amounts of P (and other segregants) to GBs has long been one the major problems addressed by XEDS in the AEM. Figure 17.22a shows a typical spectrum simulated for a 100-nm-thick foil of Fe-0.15wt%P in a 200-kV instrument for an acquisition time of 100 s. From the spectrum, the peak (P) and background (B)

Fig.  17.22  a  Comparison of two X-ray spectra from a 100-nm-thick Fe-0.15 wt%P simulated with and without noise in a 200 kV instrument for 100 s. Two highlighted regions indicate the net peak (I) and background (b) intensities. The peak visibility (b) and detectability (c) ratios of the P Kα line in Fe, plotted against the P composition CP for 100-nm-thick films. The error bars represent the 3σ (99 % confidence limit) range determined from 50  simulated spectra with different random noise conditions

intensities are measured in the same channel width, as shown in the shadowed areas in Fig. 17.22a. Then, the net peak intensity (I) is determined by subtracting B from P. As we described in p Sect. 34.5 of W&C, if the net peak intensity exceeds 3 B, the peak is visible with a 99 % confidence limit (3σ). In addition, p when I >3 2B  (slightly stricter than the visibility limit), the peak is detectable as mentioned in Sect. 36.4B of W&C. Let’s denote p p I=3 B and I=.3 B/ aspthe visibility p and detectability ratios, respectively. So, if I=.3 B/ or I=.3 2B/ > 1 in terms of the P Kα peak, then the peak is visible and the phosphorus is detectable in Fe, respectively. Figures 17.22b, c show the visibility and detectability ratios of the P Kα line in Fe, plotted against the P composition (CP) for 100-nm-thick films. As you can see, the

17.2  X-ray Spectrum Simulation – a Tutorial and Applications of DTSA

You should note that the above definitions for the peak visibility and detectability are approximately equivalent to the decision (Lc) and detection (Ld) limits in Currie’s definitions for the analytical sensitivity limits (described with Eqs. (36.16)–(36.20) in Sect. 36.4C of W&C). Furthermore, the above visibility limit also corresponds to the visibility of a 1D image (i.e., the spectrum!) in the Rose criterion. You should be able to work out how these definitions are related to one another in some degree. Minimum Mass Fraction (MMF):  The detectability limit we described above is essentially the same as the MMF, which is the minimum detectable composition. You can calculate the MMF value from the peak and background intensities of a standard specimen with a known composition using the Goldstein–Romig–Michael (GRM) equation (Eq.  35.15) first discussed in Sect. 36.4B of W&C. The MMF values for P in Fe, determined from simulated X-ray spectra of Fe-5wt%P by the GRM equation, are plotted against the specimen thickness in Fig. 17.23. The simulation parameters are same as those in Fig. 17.22 (accelerating voltage: 200 kV and acquisition: 100 s) and the error bars are determined from 50 spectra simulated, with noise, at each thickness condition. As you can see, in comparison with the detectability evaluation shown in Fig. 17.22c, the error bars are much smaller. This is because the CP(MMF) values are calculated using simulated spectra with the high P composition. The calculated CP(MMF) value decreases as the specimen thickness increases simply because the X-ray signal increases. In the 100-nm-thick film, CP(MMF) approaches ~ 0.16 wt% under these conditions. Therefore, the CP(MMF) value calculated using Eq.(36.15) agrees well with the detectability limit determined from simulated spectra with trace amounts of elements. Minimum Detectable Mass (MDM) or Minimum Detectable Atoms (MDA):  Another expression of the analytical sensitivity is the MDM, which is more conveniently defined as the minimum number of atoms detectable in the analysis volume in your thin specimen in the AEM, i.e., MDA. As we already

Fig. 17.23  MMF of P in Fe, determined from simulated X-ray spectra of a thin foil of Fe-5 wt% P using the GRM equation, plotted against the specimen thickness

described in Sect. 36.4D of W&C, the MDA in AEMs is now at or approaching the single atom level as we show below. This value is better than any other analysis technique. (Atom-probe microscopy is the only competition.) To calculate the MDA values by translating from the MMF, you need first to calculate the analyzed volume. To do this, you need to know your probe size and your specimen thickness. Figure 17.24a shows the analyzed volume of Fe determined based on the Gaussian broadening model (see next section) for LaB6AEM (probe size, d = 10 nm), FEG-AEM (d = 2 nm) and aberration-corrected (AC) FEG-AEM (d = 0.2 nm), plotted against the specimen thickness. If you were to analyze a thinner region, the incident probe size becomes the dominant factor rather than the beam broadening. This smaller analyzed volume is more significant if the AC instrument is used. However, the benefit of using an AC instrument is obviously degraded when you are analyzing specimens thicker than ~ 50 nm. So if you’ve paid for an expensive AC AEM, don’t waste time putting thick specimens in it! You can convert the analyzed volume to the total number of atoms using basic crystallographic information. For example, Fe has a bcc structure with 2 atoms in the unit cell (i.e., the unit volume per atom can be given by (a3)/2, where a is the lattice parameter). Then, by multiplying the atomic fraction of the MMF value (you have to convert the MMF value (in wt%) to the atomic fraction), the MDA can be determined. The MDA of P in Fe translated from the MMF in three different instruments is shown in Fig. 17.24b as a function of the specimen thickness. Single-atom AEM!

We can identify single atoms! (See the paper by Lovejoy et al. 2012) 9 Despite having a poorer MMF (higher mass fraction) in thinner regions, the MDA value is improved as the specimen thickness decreases. According to these results, only ~ 20 P atoms are de-

Chapter 17

These simulated results are calculated assuming ideal conditions and could be very different from realistic situations since we have not included any noise associated with signal generation and detection. In DTSA, we can add such random noise to simulated spectra, based on Poisson counting statistics. In Fig. 17.22a, we show another simulated spectrum with random noise as a red line. Obviously, it becomes harder to recognize such a small peak under the noise, which is more similar to practical cases, and hence the peak visibility and detectability are degraded when we add noise to the spectrum simulation. We determined the 3σ range of the peak visibility and detectability from 50 simulated spectra with different random noise conditions for each P composition and these are shown as error bars in Fig. 17.22b, c. The results from the noise-free spectra appear close to the average of those with random noise.

Part I

P Kα peak is visible at CP = 0.11wt% and becomes detectable at CP = 0.16wt%.

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Part I

worsened. Furthermore, the X-ray absorption correction for thin specimens in AEM is harder than that for bulk samples in SEM/ EPMA because you need to know some essential prior information about the specimen thickness and the density at every individual analysis point. Several methods are proposed for thickness determination in Chap. 36 of W&C. However, these thickness measurements need to be performed independently of the X-ray analyses and doing this may introduce additional errors, which could also be an additional limiting factor for quantitative X-ray analysis. So, the conclusion we draw is that although applying the Cliff–Lorimer ratio method is straightforward, it cannot achieve the necessary levels of accuracy and precision in quantitative X-ray analysis in many thin specimens. The ζ-factor method is a new and improved quantitative procedure for thin specimens that overcomes some of the limitations in thin-film X-ray analysis listed above by making local thickness determination an integral part of the process. In this section, we go into much greater depth than you saw in Sect. 35.5 of W&C and explore further details of the ζ-factor method.

17.3.1 Why Bother with Quantification? Fig. 17.24  a Analyzed volume of Fe determined based on the Gaussian broadening model for LaB6-AEM (d = 10 nm), FEG-AEM (d = 2 nm) and AC FEG-AEM (d = 0.2 nm), plotted against the specimen thickness. b The MDA of P in Fe calculated from the MMF in Fig. 17.23 with the analyzed volume size

tectable by using the FEG-AEM under these specific conditions. This value may be improved to a single-atom level in the AC instrument. If you use longer acquisition times or the X-ray collection efficiency is improved with better detector geometries (e.g., larger collection angles), it’s possible that the MDA value might be further improved.

Chapter 17

17.3 The ζ-factor Method: a New Approach for Quantitative X-ray Analysis of Thin Specimens In Chap. 35 of W&C, different approaches to quantitative X-ray analysis are described for thin specimens in the AEM. Since the development of the ratio method by Cliff and Lorimer (1995), this particular method has become the standard approach and is widely used due to its simplicity. Unfortunately, even in thin specimens, X-ray absorption may need to be corrected for quantification and the simple Cliff–Lorimer approach is found wanting. As we’ve noted many times, X-ray absorption is more serious in some materials than others, especially if lighter elements are present, and then the accuracy of quantification is

Before explaining what quantitative X-ray analysis via the ζ-factor method is, it’s worth asking whether such an involved quantification process is really required for materials characterization or not. In some cases, you’ll find that elemental distributions can be determined, or a phase can be identified, by qualitatively analyzing a single spectrum. A typical example is shown in Fig. 33.11 in W&C. With prior knowledge of preferential elemental distributions, you can easily distinguish types of carbides in steel. If you can identify the different carbides, you often don’t need further quantification. As another example, a set of X-ray intensity maps of Pb L and O K lines taken from a triple point of a Pb-based oxide Pb(Mg1/3Nb2/3)O3-35 mol%PbTiO3 is shown in Fig. 17.25a along with an ADF-STEM image (Gorzkowski et al. 2004). From these elemental maps, you might infer that both Pb and O are depleted along the boundaries constituting the triple point. Using these elemental maps, quantification was performed by the ζ-factor method and a different set of composition maps of Pb and O obtained, as we show in Fig. 17.25b. In addition, a thickness map was obtained through the ζ-factor quantification process. As we inferred from the elemental map, depletion of O is confirmed at the boundaries and the triple point. However, quantification shows that Pb is actually segregated to the triple point, which is contradictory to the original conclusion from the elemental map. According to the thickness map determined by the ζ-factor method, the thickness decreases along the boundaries and at the triple point, which reduces the X-ray intensity of the Pb L line. Therefore, the discrepancy between the qualitative elemental and

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17.3 The ζ-factor Method: a New Approach for Quantitative X-ray Analysis of Thin Specimens

quantitative compositional maps of Pb has arisen. The thickness reduction along the boundaries constituting the triple point was caused by preferential thinning during specimen preparation by FIB. From this example, you should conclude that qualitative analysis, or simply looking at X-ray intensity changes may result in wrong conclusions. Quantification is an essential process for materials characterization! You will be ready to use quantification procedures via the ζ-factor once you understand and agree with this example!

17.3.2 What Is the ζ-factor? In a thin-film specimen, the measured characteristic X-ray intensity I is proportional to the mass thickness ρt and the composition (weight fraction) C unless the generated X-ray signals are affected by absorption and fluorescence. We can establish the following relationship between the mass thickness and the measured X-ray intensity by normalizing with the total electron dose De (i.e., the number of electrons hitting the analysis region during X-ray acquisition) t = A

IA C A De

(17.19)

Chapter 17

Fig. 17.25  a  Set of X-ray intensity maps of Pb L and O K lines taken from a triple point in a Pb-based oxide Pb(Mg1/3Nb2/3)O3-35 mol%PbTiO3 and an ADF-STEM image. b A set of composition maps of Pb and O with a specimen thickness map quantified by the ζ-factor method (Gorzkowski et al. 2004)

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Part I

where ζA is a proportionality factor to connect IA to ρt and CA. If X-ray absorption and fluorescence are negligible because the specimen is thinner than the critical thickness, the generated characteristic X-ray intensity can theoretically be described as g

IA = N

QA !A aA CA tDe AA

(17.20)

where Nv is Avogadro’s number, QA is the ionization cross-­ section, ωA is the fluorescence yield, aA is the relative transition probability (i.e., the relative line weight) and AA is the atomic weight. You should note that Eq. 17.20 is essentially the same as Eq. 17.11, which we introduced in the previous section – except for the scaling factor to adjust the absolute magnitude for ionization cross-section. By taking into account the X-ray collection efficiency terms such as the collection angle Ω relative to the whole sphere (4π) and the detector efficiency εA, we can express the measured X-ray intensity IA as (see, e.g., Armigliato 1992)   ˝ QA !A aA ˝ g IA = IA "A = N CA tDe "A (17.21) 4 AA 4 By comparing Eq.  17.19 with Eq.  17.21, the ζ factor can be defined as A =

AA N QA !A aA Œ˝=.4/ "A

(17.22)

The ζ factor contains terms for both X-ray generation and detection. In other words, the ζ factor is equivalent to the atomic-number correction term (Z) in the ZAF matrix correction procedure, which is widely employed for quantitative X-ray analyses of bulk samples in SEM/EPMA. Since the same relationship described in Eq. 17.21 is true for any other element (e.g., B), we can derive the following equation by taking a ratio between elements A and B and rearranging: CA AA QB !B aB "B IA A IA IA = = = kAB CB AB QA !A aA "A IB B IB IB

(17.23)

Chapter 17

Obviously, this relationship is exactly same as the definition of the Cliff–Lorimer ratio equation. Therefore, we find the relationship between the k factor and ζ factors is: kAB

A = B

(17.24)

Once you know one of the ζ factors (e.g., from a reference element such as Si and Fe), you can determine other ζ factors from existing k-factor databases (e.g., Tables 35.1 and 35.2 in W&C). You should be clear that the ζ-factor method does not eliminate the widely used Cliff–Lorimer ratio method but expands the way we do quantitative X-ray analysis as described in the following sections.

17.3.3 Quantification Procedure in the ζ-factor Method Fortunately, as we’ll show, the quantification procedure in the ζ-factor method is quite simple. Since a similar relationship to Eq. 17.19 holds for element B independently, we can express CA, CB, and ρt as follows, assuming CA + CB = 1 in a binary system CA =

A IA A IA + B IB

CB =

B IB A IA + B IB

t =

A IA + B IB De (17.25)

Therefore, you can determine CA, CB, and ρt simultaneously by measuring their X-ray intensities. This approach can easily be expanded to any multi-component system as long as the assumption of ΣCi = 1 is reasonable. Once you know the ζ factors, it is straightforward to determine compositions. A Warning

You need to know the electron dose term De for accurate thickness determination: so beam current measurement is essential for quantification via ζ factors. 9 The need for this measurement is the major drawback to the ζ-factor method because measurement of the beam current is not always easy in TEM (unlike the SEM/EPMA). In some TEM instruments, it is straightforward to measure the in-situ beam current because there is an in-built Faraday cap (similar to SEM/ EPMA). If you have an EELS detector on your AEM, you can also monitor the beam current by prior calibration of the detector readout system. Fortunately, if you have a modern instrument with a Schottky FEG source, the beam-current fluctuation over typical time periods for analysis should be less. In this case, the beam current does not need to be monitored frequently and can be calibrated easily through the readout from the viewing screen etc. We should also note that in the ζ-factor method, the mass thickness can be determined as shown in Eq. 17.25. To determine the absolute thickness, you need to know the specimen density at individual measured points. You can find out more about density determination in the Appendix. Information about the mass thickness of your specimen at individual measured points is very useful when you need to correct for X-ray absorption, even in thin specimens. The absorption-correction term for a single X-ray line from a thin specimen is AA =

.=/A sp t cosec ˛ 1 − expŒ−.=/A sp t cosec ˛

(17.26)

where .=/A sp is the mass absorption coefficient of the characteristic X-ray line in the specimen and α is the X-ray take-off

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Fig. 17.27  ζ-factors of K lines determined in a 200-kV JEOL JEM-ARM200CF, plotted against the X-ray energy. The open circles are the measured values from the SRM2063a glass thin-film; the closed circles indicate the estimated values by parameter optimization based on the measured values (Watanabe and Wade 2013)

angle. We incorporate this absorption-correction term into the ζ factor by multiplying it by the corresponding X-ray intensities in Eq. 17.25, via an iteration process. A complete flow chart for the quantification procedure via the ζ-factor method is summarized in Fig. 17.26. The calculation usually converges within five iteration steps. We should also mention that the local mass-thickness value is useful for the fluorescence correction on the very rare occasions when it is necessary. In the Appendix, you’ll find the various steps in the error calculation for the iteration process summarized.

17.3.4 Determination of ζ factors Similar to the Cliff–Lorimer k factors, the accuracy of your quantitative analysis is directly affected by the reliability of your ζ factors. You have to determine reliable ζ factors if you want reliable quantification. For the experimental determination of k factors, you should know that standard thin specimens with known composition (such as alloys and compounds) are required. Such standard thin specimens are also required for ζ-factor determination. However, unlike the k-factor determination, you can use pure element thin-films as standards for ζ-factor determination as might be expected from Eq. 17.19.

The use of pure element thin standards expands the degrees of freedom for the ζ-factor determination. Unfortunately, you’ll still find it very tedious to determine the many ζ factors from standard thin specimens when you need to analyze multi-element materials. This situation can be improved when you use the NIST-issued SRM 2063 or the re-issued 2063a glass thinfilm standard. (Does your lab have such a sample?) Not only the compositions but also the thickness including the density of the SRM2063/2063a are well characterized. By measuring a single spectrum from the SRM2063/2063a, we can determine the ζ factors of the five major components. Then, based on the five ζ-factors determined from the SRM2063/2063a specimen, other ζ factors can be estimated by fitting uncertainty parameters such as absolute values of the ionization cross-section and window thicknesses of the detector. Figure 17.27 shows the ζ-factors measured from a single spectrum of the SRM2063a specimen (open circles) in a JEMARM200CF aberration-corrected STEM at 200 kV with a large collection-angle XEDS detector, plotted against X-ray energy. The closed circles in Fig. 17.27 indicate a series of ζ factors estimated from the measured values by the parameter optimization. Although the NIST SRM2063a specimen is not available currently, similar types of materials can be utilized as standards for ζ-factor determination.

Chapter 17

Fig. 17.26  Flow chart of the quantification procedure for the ζ-factor method with the X-ray absorption correction (Watanabe and Williams 2006)

Being able to use thin films of pure single-element materials is a major advantage and overcomes any limitations associated with thin-film standards since you can relatively easily fabricate pure-element thin films by evaporation, electron deposition or sputtering Such pure-element films are routinely available (in contrast to the tremendous difficulties to prepare multi-element, thin-film, standards with known compositions for k-factor determination). The only disadvantage you’ll find is that the thickness of your standard film needs to be determined, prior to ζ-factor determination. However, if you do a bit of research you’ll find that independent thickness determination is relatively easy in single-element, thin films.

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Table  17.5   Comparison of measured compositions of Pb-based oxide with and without X-ray absorption correction to nominal values (Gorzkowski et al. 2004)

Fig.  17.28  Comparison of the absorption loss of the oxygen Kα intensity in various oxides, plotted against the specimen thickness. Dashed and dot-dashed lines represent 5 % and 10 % losses, respectively

17.3.5 Applications of ζ-factor Method As we noted, there are several advantages to the ζ-factor over the Cliff–Lorimer ratio method. In this section, we’ll highlight some of these advantages, which are mainly due to the availability of simultaneous thickness determination. Light Element Analysis:  Quantitative analysis of the many important materials systems that include light elements (e.g., the commercially important oxide, carbide and nitride systems) is always challenging. You know that X-ray emission from light elements below Si (Z = 14) in the periodic table is generally very low due to their low fluorescence yields. In addition, as we’ve now described several times, these light elements only produce soft X-rays (with energies below 2 keV) which are severely absorbed not only in the detector window but also in the specimen itself. The first effect reduces the detector efficiency and the second reduces the accuracy of our quantifications. Obviously this latter effect is more serious and has to be corrected! Figure 17.28 compares the absorption loss of the oxygen Kα intensity in various oxides, plotted against the specimen thickness. We calculate this absorption loss for an XEDS detector with the take-off angle of 20o using the following equation

Chapter 17

LX A =1−

h i 1 − exp .=/X sp t cosec ˛ .=/X sp t cosec ˛



(17.27)

The dashed and dot-dashed lines in Fig. 17.28 indicate the 5 and 10 % absorption limits respectively. If the X-ray absorption exceeds 10 %, the accuracy of quantification degrades correspondingly. If absorption reduces the accuracy that we reasonably expect from the quantification procedures, we need to correct for it. The oxygen Kα line is more severely absorbed in oxides with heavier elements. For example, 10 % of the X-ray intensity is absorbed at ~ 20 nm in Pb2O3. It is rare that we can expect our specimens to be so thin.

Measured (corrected)

Measured (uncorrected)

Nominal

Mg

1.6

1.2

1.7

Nb

12.7

12.8

12.7

Pb

65.4

75.6

65.3

O

15.1

5.5

15.1

Ti

5.2

4.9

5.2

Total

100.0

100.0

100

Table 17.5 compares experimentally determined compositions with the theoretical values of the Pb-based oxide (this is the same specimen as shown in Fig. 17.26). As shown in Fig. 17.28, the quantified oxygen composition is ~ 1/3 unless we apply the absorption correction to the oxygen Kα. In the ζ-factor method, the X-ray absorption correction is incorporated as we described above and the ζ-factor method has already been shown to work well for several light-element (oxide) quantifications, even for these difficult Pb-based oxides. Extraction of Thickness-Related Information:  Knowing the local composition and thickness via the ζ-factor method allows you to extract further information related to your specimen thickness, such as the beam broadening and the spatial resolution, as described in Sect. 36.1 in W&C. For example, the spatial resolution R can be estimated using the equation proposed by Van Cappellen and Schmitz (1992), derived from the Gaussian beam-broadening model  1=2 R = q  2 + ˇ.t/3 =2

(17.28)

where the scaling parameters q and κ are dependent on the chosen fraction of the incident intensity, e.g., q = 4.29 and κ = 0.68 for the spatial resolution which contains 90 % of the incident intensity, which corresponds to the beam diameter at a thickness of 0.68 t from the top surface. The terms σ and β are associated with the incident-beam size and the beam broadening, respectively, and are given by  2    4ZN  = dTM =4:29; ˇ = 500 (17.29) N E0 M where dTM is the incident beam diameter at full-width-tenth-maxN imum (FWTM), E0 is the incident beam energy (in eV), ZN and M are the averaged atomic number and atomic weight, respectively. Since we can determine all the terms related to the specimen by the ζ-factor method, we can easily extract R at individual measured points if dTM and E0 are known. You should note that the

17.3 The ζ-factor Method: a New Approach for Quantitative X-ray Analysis of Thin Specimens

Part I

Gaussian beam-broadening model is the best description of the interaction volume, as was determined by careful evaluation of experimental and simulated concentration profiles. Figure 17.29 shows a set of maps of impurity segregation in a low-alloy steel. Map (a) is an ADF-STEM image in a vicinity of a grain boundary. Composition maps of (b) Ni and (c) Mo were determined by the ζ-factor method (this particular set of maps is also shown in Fig. 35.11 in W&C), together with (d) thickness and (g) R maps. The R map was determined using Eq. 17.28 and shows that the R value around the GB is ~ 4 nm, which is consistent with the experimentally determined spatial resolution from the concentration profiles across the GB.

491

The knowledge of local compositions and thickness determined by the ζ-factor method allows us to deconvolute any thickness contribution (i.e., the beam broadening) from the compositions we measure. You’ll find that such deconvolution of the thickness contribution can be essential for quantification of fine features embedded in a matrix or on support materials. For example, in quantifying impurity segregation levels at an interface or a grain boundary, the impurity composition you determine may vary depending on the incident probe size, the specimen thickness, the accelerating voltage, etc. The boundary enrichment of impurity element A, which is defined as a number of segregant atoms per unit area Γex, can be determined as (see Alber et al. 1997). Stating the Obvious – Don’t Ignore It

If your results vary with the experimental conditions, then the composition measurements can’t be quantitative.  9

Aex + Abk = Nbk

CA AB V CB AA A

(17.30)

V=

Zt 0

A=

Zt 0

 2 q2  q. 2 + ˇz3 =2/1=2 =2 dz = .8 2 t + ˇt4 / 32 (17.31)  2  q. + ˇz3 =2/1=2 dz



(17.32)

Chapter 17

where Γbk is the number of solute atoms per unit area in the bulk, Nbk is the number of atoms per unit volume in the surrounding bulk region, and AA and AB are the atomic weights for A and B. In addition, V and A are the interaction volume and the area of the boundary inside the interaction volume, respectively. Obviously, the major requirement to determine Γex is knowledge of V and A, which are dependent on the specimen thickness. Since the diameter of the interaction volume in the Gaussian beam-broadening model is given as q(σ2 + βz3 / 2)1/2 at the depth z from the beam-entrance surface (see Van Cappellen and Schmitz 1992), both V and A can be given as

Fig. 17.29  Summary of an application of the ζ-factor method to quantification of boundary segregation in a low-alloy steel. a ADF-STEM image in the vicinity of a grain boundary, b Ni composition, c Mo composition, d thickness, e Ni boundary excess, f Mo boundary excess, and g R maps

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In Fig. 17.29, maps of the boundary enrichment Γex for Ni (e) and Mo (f) determined using Eq. 17.30 are also shown. The average Γex values for Ni and Mo determined from the maps are 3.5 ± 0.4 and 4.8 ± 0.1 atoms/nm2, respectively. Since a single monolayer is ~ 19 atoms/nm2 in the closed packed (110) plane for bcc Fe, the enrichments of Ni and Mo can be estimated as less than ~ 25 %. Since the thickness contribution is deconvoluted in the form of the boundary enrichment, the composition can now be transformed to a truly quantitative measure. This thickness deconvolution approach is also applicable when you need to extract the true composition of a precipitate/particle embedded in matrix/support materials. Evaluation of Analytical Sensitivity:   In Sect. 36.2 in W&C, determination of the MMF for the ratio method is summarized. By spectrum simulation in DTSA, we can predict the analytical sensitivity as we just described. The MMF value can also be determined in the ζ-factor method. The criterion for the minimum detectable peak-intensity in an X-ray spectrum is defined as (Romig, Goldstein 1979) p I > 3 2B (17.33) where I is the X-ray peak intensity above the background and B is the background intensity. We can incorporate this criterion into the ζ-factor method to describe the MMF p A 3 2BA MMFA = (17.34) De t In addition to the MMF, the other descriptions of analytical sensitivity, i.e., MDM or MDA can also be derived by the ζ-factor method. As we described in the previous section, information on the analyzed volume is required if you wish to determine the MDA. Since the analyzed volume is given in Eq. 17.31, you can determine the total number of atoms in the analyzed volume as N V=AN (where AN is the averaged atomic weight). Therefore, you can estimate the MDA for individual elements by multiplying the total number of atoms in the analyzed volume with MMF values in units of atomic fraction.

Chapter 17

Determination of Detector Parameters:  As with the Cliff– Lorimer k factor, the ζ factor also depends on the X-ray detection efficiency. Since we define the ζ-factor for an individual element, the X-ray collection efficiency (controlled by the detector collection angle in different instruments) can be compared with the ζ-factor values. As shown in Fig. 17.27, the ζ-factor values in the JEOL ARM are ~ 1/3 of those in the VG HB603. We can interpret this to show that the analytical sensitivity in the ARM is ~ three times higher than that in the HB603. From the reported value of the X-ray collection angle in the HB603, we can estimate the solid angle of the large-angle SDD in the ARM as ~ 0.53 sr by taking into account the difference in the ionization crosssection at different kV. (note: by further optimization of the SDD position, the solid-angle increases as high as 0.64 sr in the ARM) Furthermore, as mentioned above, we can determine the thickness values of the detector window materials during the ζ-factor esti-

Fig. 17.30  Detector efficiency curve for a JEOL JEM2-ARM200CF with a JEOL Centurio X-ray detector (Watanabe and Wade 2013)

mation. Using the thickness values of the detector window, we can estimate the detector efficiency. Figure 17.30 shows the detector efficiency of the large-angle SDD calculated from the determined thickness values of detector window materials, plotted as a func­ tion of the X-ray energy. Note that the decrease of the detector efficiency after ~ 10 keV is due to the thinner crystal in the SDD. So in summary, there are several clear advantages to the ζ-factor method over the conventional Cliff–Lorimer ratio method; not only for quantification but also for more detailed analysis of specimens. In addition, you can more easily estimate the XEDS detector parameters and compare the performances of individual instruments as well.

17.4 Contemporary Aplications of X-ray Analysis In recent years the development of aberration-correction technology in both TEM and STEM has brought a paradigm shift in materials characterization. Just in terms of image resolution, sub-Å resolution is now routinely available (to anyone with enough money) and currently the latest aberration-corrected microscopes offer 0.5 Å resolution both in STEM and TEM modes (Erni et al. 2009; Sawada et al. 2009). Especially in STEM, we now use an incident probe refined by aberration correction to improve the spatial resolution of analysis by both EELS and XEDS. More importantly, we find that the analytical sensitivity can also be improved because more current can be included in the refined probe while maintaining fine probe dimensions. Since these aberration-correction STEM instruments appeared, X-ray analysis is now seeing a resurgence of interest bolstered by the simple nature and robustness of the quantification procedures which we have just described in great detail. Both the hardware and software related to X-ray analysis, especially in aberration-corrected STEM, continue to improve. In this

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Fig. 17.31  Comparison of input/output count rate of a large solid-angle SDD at three different time constants on an aberration-corrected STEM JEM-ARM200CF

section, we’ll introduce you to the latest instrumentation related to X-ray analysis in STEM. Then, we’ll give you two examples of more recent applications of X-ray analysis.

17.4.1 Renaissance of X-ray Analysis

As we show in Fig. 17.31, the high throughput capability of the SDD can handle high count rates (up to ~ 100 kcps) taking advantage of the new geometries. Furthermore, if we integrate the new detector configurations into aberration-corrected instruments, e.g., the FEI Chemi/STEM technology and the JEOL large-angle SDD system, we get detector solid-angles up to ~ 1 sr (3–10 times higher than conventional systems). Figure 17.32 shows two sets of X-ray maps acquired from TiO2-supported Au nano particles in a JEOL JEM-ARM200F aberration-corrected STEM with the large collection-angle SDD system. The Au map and color overlay map (B) were acquired for 1 min in total. While these maps are still noisy, obtaining such X-ray maps with such very short acquisition times is an amazing advance over prior

Fig. 17.32  a HAADF-STEM image of TiO2-supported Au nanoparticles and X-ray maps of Au (left) and RGB color overlay with O, Au and Ti (right), acquired using an JEOL JEM-ARM200F with the large collection angle SDD system: total acquisition times are (b) 1 min and (c) 6 min

technologies. If we acquire these maps for a bit longer (still only 6 min!) we can easily see the distribution of Au nano particles in Fig. 17.32c. In the following sections, we summarize two novel applications of X-ray analysis, which again can only benefit from aberration correction and SDD technology.

Chapter 17

Aberration-corrected STEM instruments have triggered further interest in X-ray analysis as we just above. However, in comparison to EELS, the collectable fraction of the generated X-ray signals remains extremely limited (at most ~ a few percent). This miserable collection efficiency is still the major limitation of X-ray analysis, even in the aberration-corrected instruments. To some extent we can mitigate this drawback by using a silicon drift detector (SDD). The latest SDD technologies are relatively flexible and so we can fabricate more complex detector arrangements. Several new detector geometries have been proposed. For example, an annular detector geometry (similar to a BSE detector in SEM) has been proposed by Kotula et al. (2009). Zaluzec (2009) has proposed a post-specimen geometry for X-ray collection in the forward-scattering direction of electrons, which allows the collection angle of π sr out of the 4π sr sphere (more than 10 times higher than the conventional detector geometry in AEM!).

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Part I Fig. 17.33  Tilt series of Ti Kα maps around a W contact-plug in a pillar-shaped specimen at different tilt angles between 0° and 170° with 10° steps. Signals in these elemental maps were enhanced by applying the MSA reconstruction to the original X-ray SIs

Beginning – A Big Change

We can maximize the X-ray collection efficiency by using arrays of SDDs (FEI, Harrach et al. 2009) by using an SDD with a very large active area (JEOL, Ohnishi et al. 2011) 9

17.4.2 XEDS Tomography for 3D Elemental Distribution Chapter 17

In TEM, we usually view the projected image of a thin specimen, which means that information in the optic-axis direction (the z direction) is not obtainable unless we tilt the specimen. If we want to observe the microstructure through the depth of the specimen, we have to use either stereo microscopy (see Sect.  29.1 in W&C) or electron tomography (introduced for EELS in Sect. 40.9 in W&C). This latter approach requires that multiple images be recorded at various tilt angles to give you the most accurate 3D reconstruction. Much more information can be found in Chap. 12 on electron tomography. Although you can image the 3D microstructure by electron tomography, it would be still be difficult to infer elemental distri-

butions in the z direction through your specimen. Fortunately both EELS and XEDS can give you 3D elemental distributions. However, XEDS-based tomography has seen little usage because of the poor efficiencies of X-ray generation and detection (again!). In addition, if you use a conventional TEM holder for tomographic XEDS analysis, the path length of the X-rays and hence the X-ray absorption change as you change the tilting angle (Möbus et al. 2003). Once again, at larger tilt angles, X-ray absorption in your specimen becomes the limiting factor. We can solve the problem of differences in X-ray absorption at different tilt angles by using a pillar-shape specimen with a specially designed specimen holder. Figure 17.33 shows a tilt series of Ti Kα maps acquired from a pillar-shaped Si device around a W contact plug, using a Hitachi HD-2300 dedicated STEM. The tilt-series of X-ray SIs were acquired over a tilt range from 0 to 175o with five steps. To compensate for the weak X-ray sig­ nals, multivariate statistical analysis (MSA) was applied. (See Chap. 16 for much more on MSA.) The Ti distributions show the metallization layer around the W plug. You can see this layer more clearly in the reconstructed Ti distribution shown in Fig. 17.34. The complex Ti distribution, especially at the bottom part of the pillar, is barely observable in a single X-ray map. So in a conventional XEDS configuration, weak signal enhancement, e.g., by MSA, is essential if you want to see an XEDS tomographic image. Not surprisingly, XEDS tomography is much more suited to an aberration-corrected STEM with an SDD X-ray system.

atomic resolution is still a challenge for X-ray analysis because of its inherently poorer signal collection efficiency (~ 100 times worse than EELS). Therefore, if we want to approach atomic-level resolution X-ray analysis, either we need much greater beam currents (which may induce radiation damage and degrade spatial resolution) or we need to collect our signals for much longer acquisition time (which means more spatial drift). Fortunately, in the best instruments today, the mechanical and electrical stabilities have been significantly improved and large-angle SDDs are routine. In fact, as shown in Fig. 35.11 in W&C, the spatial resolution of X-ray analysis (in 2009) was ~ 0.4 nm. Additionally, as you can now see in Fig. 17.24b, DTSA simulation suggests that the analytical sensitivity in terms of MDA may already have reached the single-atom level in an aberration-corrected STEM.

Figure 17.35 shows another example of XEDS tomography from an In-doped GaN nano pyramid structure for light emitting diode applications. In Fig. 17.35a, HAADF-STEM image and a set of elemental maps of Ga, N and In are shown, which were obtained using an instrument with an SDD X-ray collection system. You can see that the In dopant is mainly located at the top of the pyramid structure. In this field of view, the XEDS tomographic series was acquired by recording two orthogonal-axis tilt-series of X-ray spectrum images with ± 60o in 3o steps (in total, 80 XEDS spectrum images). This took a total acquisition time of ~ 8 h. If you use an instrument with improved X-ray collection efficiency, you can now acquire dual-axis XEDS tomography series in such reasonable times. Selected slices of the In distribution reconstructed from the dual-axes XEDS tomography datasets are shown in Fig. 17.35b. You can see that In is located not only at the top of the nano pyramid structure but also along the sides of the pyramid. Again, this information is not obtainable from a single 2D-projected image or X-ray map.

17.4.3 Atomic Resolution X-ray Mapping If you have access to an aberration-corrected STEM, atomic resolution EELS mapping can be routine. Conversely, such

Figure 17.36 shows a set of X-ray maps with (a) a HAADFSTEM image from interfaces in a [100]-projected LaMnO3/ SrTiO3 multilayer thin-film, acquired by using the JEMARM200CF with a large collection-angle XEDS detector. The X-ray maps were acquired in the SI mode with 256 × 256 pixels for a frame time of 50 ms. The total acquisition time was ~ 40 min and spatial-drift correction was applied during acquisition. The bright and slightly fainter spots appearing in the HAADF-STEM image correspond to heavy atomic columns of La or Sr and to Ti-O or Mn-O columns in the perovskite structure, respectively. From the extracted elemental maps, two RGB color-overlay images were constructed, as you can see in Fig. 17.36 (g, Red: La L, Green: Mn K and Blue: O K) and (h, Red: Sr L, Green: Ti K and Blue: O K), which represent LaMnO3 and SrTiO3 layers, respectively. So we can obtain elemental distributions from much larger fields of view, if we take advantage of the improved stability in the latest instruments, such as the JEM-ARM200CF. An atomic-resolution X-ray SI data set was acquired from a [100]-projected GaAs specimen using the aberration-corrected STEM JEM-ARM200CF. Once we obtain such atomic resolution elemental maps in the latest instruments, can we quantify them? To see how well we can do this, the maps were analyzed by the ζ-factor method. Figure 17.37 shows a set of ζ-factor-processed elemental and compositional X-ray maps along with an HAADFSTEM image. In the [100]-projection of GaAs, Ga and As layers are alternatively separated. As shown in the elemental maps of Ga and As with their color overlay, atomic layers of Ga and As are separated as expected. Conversely in the quantified compositional maps, the compositions do not reach the expected 0 at% or 100 at% in the corresponding atomic layers. The average compositions of whole Ga and As maps were calculated to be 50.8 and 49.2 at%, respectively, which are very close to the nominal value (50:50). Thus, the quantification itself was performed correctly. So why do we not see the correct values for the individual atomic columns? The deviations in compositions from the expected values (0 or 100 at%) are partially due to the beam broadening. According to the thickness map (Fig. 17.37), there appear to be relatively large thickness variations between on-column and

Chapter 17

Fig. 17.34  a 3D-reconstructed Ti distribution around the W contact-plug created using 37 Ti K maps at tilt angles between 0°–180° with a 5° step, partially shown in Fig. 17.33: a at 45° from all primary x, y and z axes and 2D projected Ti distributions along the z axis (b), x axis (c), and y axis (d)

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Part I Chapter 17

Fig. 17.35  a HAADF-STEM image and a set of elemental maps of Ga, N, and In obtained from an In doped GaN nano pyramid structure using an instrument with an improved X-ray collection system. b Selected slices of the In distribution around one of the pyramid structures reconstructed from the dual-axes XEDS tomography datasets (two orthogonal-axis tilt-series of X-ray spectrum images with ± 60o in 3o steps)

497

Fig. 17.36  a An HAADF-STEM image from a LaMnO3/SrTiO3 interface, elemental maps of (b) La, (c) Sr, (d) O, (e) Mn, (f) Ti, (g) RGB color-overlay image of LaMnO3 and RGB color-overlay image of SrTiO3

Chapter 17

Part I

17.4  Contemporary Aplications of X-ray Analysis

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17  Practical Aspects and Advanced Applications of XEDS

Part I Chapter 17 Fig. 17.37  Set of quantitative X-ray maps from a [100]-projected GaAs specimen: a HAADF-STEM image, b Ga K intensity, c As K intensity, d color overlay of Ga K (red) and As K (green), e Ga composition, f As composition, and g thickness

off-column regions: ~ 60 nm and 30 nm at on- and off-column regions, respectively. It is most unlikely that local specimen thickness changes of this magnitude would occur from column to column. Because the specimen thickness was determined directly from the X-ray intensities of Ga K and As K lines, such thickness enhancement at the on-column regions indicates that abnormal X-ray emission occurs due to channeling. Because the map was obtained in a highly symmetric zone axis orientation, we might expect the incident beam propagation to be influenced by the atomic arrangement, i.e., the incident electrons are channeled and de-channeled.

When de-channeling of the incident electrons occurs, they generate X-ray signals from neighboring columns. So, we can conclude that, in addition to regular beam broadening de-channeling is another reason for the apparent deviations in compositions from the expected single column values. When we are quantifying such atomic resolution X-ray maps, we might not need to include the correction for X-ray absorption because the specimens are thin enough for atomic resolution imaging and analysis. Instead, we now have to consider the channeling correction in quantitative X-ray analyses at the atomic level, which is why you’ve already read about channeling in several previous chapters.

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In AEM

Always keep in mind beam broadening and channeling.  9

In this chapter, we reviewed four independent subjects related to the X-ray analysis of thin specimens in TEM to augment the contents of Chaps. 32–36 in W&C.

you use DTSA to first simulate the X-ray spectra from your experimental specimen prior to actual analyzing them, you would save time (and perhaps money).

In the first section, we summarized the systematic procedures to characterize XEDS spectrometers attached to TEMs. You can determine several fundamental parameters such as the energy resolution (as a function of the process time), IHC, P/B, etc., from a single spectrum of a standard NiOx thin specimen. We recommend that these parameters be characterized at least once (preferably prior to first operating the microscope). In addition, you should also monitor the detector performance by periodically measuring spectra from the NiOx.

In W&C, several procedures for quantitative X-ray analysis are summarized, including a brief introduction to the ζ-factor method. So in the third section, we went into much greater detail concerning this quantitative analysis method. In addition, we compared the ζ-factor method with the conventional Cliff–Lorimer k-factor approach and showed that the ζ-factor was much better if the specimen was thick, if absorption was a problem (which it is for light element X-rays) and if k-factor standards were difficult to obtain (which they usually are!).

The second section comprises a comprehensive tutorial of X-ray simulation through the NIST DTSA software package. Then, we described the fundamental physics related to X-ray generation and detection through simulated X-ray spectra, which are never seen in practice. From these simulated spectra, you can learn detailed aspects of X-ray spectrometry. Additionally, we went through four applications of X-ray spectrum simulation including the estimation of X-ray absorption and calculation of analytical sensitivity. If

In the last section of this chapter, we introduced several contemporary applications of X-ray analysis. Because of the recent availabilities of aberration-correction columns in combination with the latest developments of SDD technology, the popularity of X-ray analysis has been revived. With such instrumentation X-ray analysis can now be used to obtain 3D elemental distributions and atomic-resolution elemental distributions. When W&C was first penned, such advanced applications were merely a dream. Now they are a reality!

Chapter 17

Chapter Summary

500

Appendix

Part I

Appendix People Chuck Fiori (1938–September 15, 1992). The DeskTop Spectrum Analyzer (DTSA) software package was originally developed by the late Chuck Fiori with Bob Myklebust and Carol Swyt. They worked at the National Institutes of Standards and Technology (NIST) and the National Institutes of Health (NIH) in late 1980s. Joseph (Joe) I. Goldstein was born in Syracuse, NY, on January 6, 1939 and died on June 27, 2015; he founded the Lehigh short course, inspired a generation using AEM, and recruited a young DBW to join him.

Questions

Chapter 17

Q17.1 Compare and contrast the k-factor and the ζ-factor approaches to quantification. Q17.2 What is the single most important variable that affects your decision to use either of these two approaches? Explain why you chose that variable. Q17.3 Why should you simulate the spectra that you hope will be generated from your specimen before proceeding to gather them experimentally? Q17.4 What can you do to minimize ice and carbon contamination on your XEDS detector Q17.5 Why has it proven so difficult to detect single atoms in thin foils using XEDS while EELS has been able to do this for many years? Q17.6 Distinguish the several different definitions we use for analytical sensitivity. Q17.7 Why does a single column of atoms in a thin foil not give rise to an XEDS spectrum containing the signal from these atoms alone? Q17.8 What does your answer to question 17.5 lead you to conclude about the real spatial resolution of analysis by XEDS? Q17.9 Why are there so many characteristics of your XEDS detector that you have to determine prior to XEDS analysis when, by comparison, an EEL spectrometer is relatively free of such requirements? Q17.10 If you have a single atom of element B in an analyzed volume containing 100 atoms of element A, can you estimate, to a first approximation, how long you need to gather a spectrum in order to say with 99 % confidence that that atom of A is present. Choose a reasonable set of experimental variables (including kV, beam current

Q17.11

Q17.12

Q17.13

Q17.14 Q17.15

probe size, detector collection angle etc.). State any further assumptions. Simulate X-ray spectra to confirm the conditions (the beam current, specimen thickness, acquisition time and accelerating voltage) for 1.0 wt% and 0.3 wt% detection levels of a high Z element in a relatively low Z material, e.g., Cu in Al. Similar to the above question; simulate X-ray spectra to confirm the conditions for 1.0 wt% and 0.3 wt% detection levels of a low Z element in a relatively high Z material, e.g., P in Ga. Questions 17.11 and 17.12 are for estimation of minimum mass fraction (MMF). Based on your estimated conditions in the above question, how many solute atoms are included. The number of solute atoms is equivalent to the minimum detectable mass (MDM). Plot the absorption loss curves of major X-ray lines in your materials systems using Eq. 17.27 and estimate the critical specimen thickness below 10 % absorption. Using Eq.  17.28, estimate spatial resolution values for your specimen in conventional and aberration-corrected AEMs, and plotted as a function of the specimen thickness. This plot is essentially same as Fig. 36.5c in W&C. Using this plot, determine the required specimen thickness especially for the aberration-corrected AEM.

Appendix 1. Error Analysis in the ζ-factor Method As described in Sect. 17.3.3, we need an iterative calculation for determination of compositions and specimen thickness including the absorption correction in the ζ-factor method. It is not very straightforward to estimate errors in such an iterative process but there is an alternative approach for the error calculation. In an n component system, we determine compositions and thickness from n characteristic X-ray intensities via n ζ factors in the ζ-factor method. Obviously, both the n X-ray intensities and n ζ factors are independent variables, and their errors need to be taken into account if you want to determine the error estimation independently. Let’s denote the errors in X-ray intensity and the ζ factor for the jth component as ∆Ij and ∆ζj, respectively. First, we determine the error-free composition(s) Ci and thickness t from n intensities and n ζ factors without their errors. Then, we calculate the compositions and thickness with an error contribution of jth X-ray intensity by substituting Ij + ∆Ij for Ij. The composition and thickness with the error of jth intensity are expressed as Ci(∆Ij) and t(∆Ij), respectively. You have to repeat

Appendix 

j=1

j=1

v uX n u n  2 2 X  t = t t.Ij / − t t.j / − t + j=1

j=1

Part I

this process for all X-ray intensities independently. Similarly, the errors in each individual ζ-factor are incorporated by substituting ζj + ∆ζj for ζj, and composition and thickness with errors of the z-factor are expressed as Ci(∆ζj) and t(∆ζj), respectively. Finally, the errors in the compositions and thickness are given as: v uX n u n  2 X  2 Ci .j / − Ci + Ci .Ij / − Ci Ci = t

501

(17.35)



This approach requires 2n times extra calculations of compositions and thickness after determination of the error-free values (yes, it is a bit complicated and tedious!). However, we can easily adapt this approach to computational codes and it is applicable to any iterative calculation (e.g., the matrix correction procedures for bulk-sample analysis in an EPMA such as ZAF and ϕ(ρz)). The full error analysis procedures for the ζ-factor determination and estimation can be found in the paper by Watanabe and Williams (2006).

Fig. 17.38  Comparison of calculated density values by weighted (dashed line) and harmonic (solid line) means with those determined from reported lattice parameters summarized by Okamoto et al (1987)

References General References

In the ζ-factor method, we first determine the specimen thickness as the mass thickness ρt as we described above. To convert the mass thickness to the absolute specimen thickness, we need values of the specimen density at individual analysis points. The specimen density can be estimated from Eq. 35.27 in W&C, i.e., the mass divided by the unit-cell volume. So we need some crystallographic information to determine the unit-cell volume. Otherwise, the density can be calculated as a first approximation by taking a weighted mean (ρ =  ΣCj ρj) or a harmonic mean (1/ρ =  ΣCi/ρj) from the density values of the individual component elements. For example, Fig. 17.38 shows the composition dependence of the specimen density in the Au-Cu system. All the symbols in this figure represent the densities calculated from reported lattice parameters using Eq. 35.27 in W&C. The dashed and solid lines indicate the estimated values from the simple weighted mean and the harmonic mean, respectively. The ρ values estimated by the harmonic mean describe the density very well. In fact, the harmonic-mean approach may work especially well for closepacked condensed systems, such as metallic alloys and intermetallic compounds. For other materials systems such as ceramics and glasses (even not crystalline), the density value needs to be estimated differently.

Lyman CE, Newbury DE, Goldstein JI, Williams DB, Romig AD Jr., Armstrong JT, Echlin PE, Fiori CE, Joy D, Lifshin E, Peters KR (1990) Scanning Electron Microscopy, X-Ray Microanalysis and Analytical Electron Microscopy; A Laboratory Workbook. Plenum Press, New York Williams DB, Goldstein JI (1991) Quantitative X-ray Microanalysis in the Analytical Electron Microscope. In: Heinrich KFJ, Newbury DE (eds) Electron Probe Quantification. Plenum Press, New York., pp 371–398 Zemyan SM, Williams DB (1995) Characterizing an Energy-Dispersive Spectrometer on an Analytical Electron Microscope. In: Williams DB, Goldstein JI, Newbury DE (eds) X-Ray Spectrometry in Electron Beam Instruments. Plenum Press, New York., pp 203–219

Specific References Alber U, Müllejans H, Rühle M (1997) Improved Quantification of Grain Boundary Segregation by EDS. Ultramicroscopy 69:105–116 Bennett JC, Egerton RF (1995) NiO test specimen for analytical electron microscopy: round-robin results. J Microsc Soc Am 1:143–149 (Following up on using NiOx in the journal now known as Microscopy & Microanalysis) Van Cappellan E, Schmitz A (1992) A Simple Spot-size Versus Pixel-size Criterion for X-ray Microanalysis of Thin Foils. Ultramicroscopy 41:193–199 Cliff G, Lorimer GW (1975) The Quantitative Analysis of Thin Specimens. J Microsc 103:203–207 (Historical classic)

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Appendix 2. Calculation of the Specimen Density

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17  Practical Aspects and Advanced Applications of XEDS

Part I

Egerton RF, Cheng SC (1994) The use of NiO test specimens in analytical electron microscopy. Ultramicroscopy 55:43–54 (All about using NiOx) Lovejoy TC, Ramasse QM, Falke M, Kaeppel A, Terborg R, Zan R, Dellby N, Krivanek O (2012) Single atom identification by energy dispersive X -ray spectroscopy. Appl Phys Lett 100:154101-1-4 Newbury DE, Ritchie NWM (2015) Performing elemental microanalysis with high accuracy and high precision by scanning electron microscopy/silicon drift detector energy-dispersive X-ray spectrometry (SEM/SDD-EDS. J Mater Sci 50(2):493–518 (A very useful review) Rose A (1970) Quantum limitations to vision at low light levels. Image Technol 12:13–15 (See also pp. 30–31) Watanabe M, Williams DB (1999) Atomic-Level Detection by X-ray Microanalysis in the Analytical Electron Microscope. Ultramicroscopy 78:89–101 Watanabe M, Williams DB (2003) Quantification of Elemental Segregation to Lath and Grain Boundaries in Low-alloy Steel by STEM X -ray Mapping Combined with the ζ-factor Method. Z Metallk 94:307–316 (We think that this and the 2006 paper are worth reading!) Watanabe M, Williams DB (2006) The Quantitative Analysis of Thin Specimens: a Review of Progress from the Cliff-Lorimer to the New ζ-Factor Methods. J Microsc 221:89–109 (As in the 2003 paper, you’ll find more details and references to the original work.) We include more references than usual because this is such a new field. We’ll add other references to the website.

References for Software

Chapter 17

(http://www.cstl.nist.gov/div837/837.02/epq/dtsa2/index.html). Brundle D, Uritsky Y, Chernoff D (1996) Real-time simulation for X-ray microanalysis. Solid State Technology 39(3):105– 111 (Electron Flight Simulator is commercialized at http:// www.small-world.net/efs.htm) Find a standardized description of the EMSA format through the International Organization for Standardization (ISO 22029:2003). ISO  22029-2003 2003 is the Standard file format for spectral data exchange. Also available at ANSI (American National Standard Institute) web site (www.ansi. org). Find SheepShaver at http://sheepshaver.cebix.net/ Fiori CE, Swyt CR, Myklebust RL (1992) NIST/NIH Desk Top Spectrum Analyzer. Public domain software available from the National Institute of Standards and Technology, Gaithersburg, MD. http://www.cstl.nist.gov/div837/Division/outputs/ DTSA/DTSA.htm Ritchie NWM (2008) DTSA-II. Public domain software available from the National Institute of Standards and Technology, Gaithersburg, MD Watanabe has developed a simple software package as a set of plug-ins for Gatan DigitalMicrograph. This plug-in package is freely available through his home page (http://www.lehigh. edu/~maw3/msh/xutilmain.html ). You can find the installa-

tion procedure and usage details in the help file, which comes with the plugin package. Watanabe has summarized how to install DTSA in Windows on his web site (http://www.lehigh.edu/~maw3/msh/dtsaonwintop.html ).

17.1 – XEDS Detector Characterization Fiori CE, Swyt CR, Ellis JR (1982) The Theoretical Characteristic to Continuum Ratio in Energy Dispersive Analysis in the Analytical Electron Microscope. In: Microbeam Analysis-1982. Ed. Heinrich KFJ, San Francisco Press, San Francisco, CA., pp 57–71 Heinrich KFJ (1987) Mass absorption coefficients for electron probe microanalysis. In: Brown JD, Packwod RH (eds) Proc 11th Int Cong on X-Ray Optics Microanalysis. University of Western Ontario, London., pp 67–377 Hovington P, L’Espérance G, Baril E, Rigaud M (1993) A standard procedure for the modeling of the decrease in detection efficiency with time for low-energy EDS spectra. Microsc Microanal 2:277–288

17.2 – X-ray Spectrum Simulation (see also References for Software above) Fiori CE, Swyt CR (1989) The use of theoretically generated spectra to estimate detectability limits and concentration variance in energy-dispersive X-ray microanalysis. In: Russell PE (ed) Microbeam Analysis-1989. San Francisco Press, San Francisco, CA. Newbury DE, Myklebust RL, Swyt CR (1995) The use of simulated standards in quantitative electron probe microanalysis with energy-dispersive X-ray spectrometry. Microbeam Analysis 4:221–238

17.3 – ζ-factor Method Armigliato A (1992) X-ray Microanalysis in the Analytical Electron Microscope. In: Merli PG, Antisari MV (eds) Electron Microscopy in Materials Science. World Scientific, Singapore, pp 431–456 Gorzkowski EP, Watanabe M, Scotch AM, Chan HM, Harmer MP (2004) Direct Measurement of Oxygen in Lead-Based Ceramics Using the ζ-factor Method in an Analytical Electron Microscope. J Mater Sci 39:6735–6741 Lyman CE, Goldstein JI, Williams DB, Ackland DW, von Harrach HS, Nicholls AW, Statham PJ (1994) High Performance X-ray Detection in a New Analytical Electron Microscopy. J Microsc 176:85–98 Romig AD Jr., Goldstein JI (1979) Detectability Limit and Spatial Resolution in STEM  X -ray Analysis: Application to Fe-Ni. In: Newbury DE (ed) Microbeam Analysis – 1979. San Francisco Press, San Francisco, CA., pp 124–128 (The

17.4 – New Detector Configurations Erni R, Rossel MD, Kisielowski C, Dahmen U (2009) Atomic-Resolution Imaging with a Sub-50-pm Electron Probe. Phys Rev Lett 102:096101 ((4 pages).) von Harrach HS, Dona P, Freitag B, Soltau H, Niculae A, Rohde M (2009) An Integrated Silicon Drift Detector System for FEI Schottky Field Emission Transmission Electron Microscopes. Microsc Microanal 15(Suppl. 2):208–209 (The FEI approach) Kotula PG, Michael JR, Rohde M (2009) Results from Two Four-Channel Si-drift Detectors on an SEM: Conventional and Annular Geometries. Microsc Microanal 15(Suppl. 2):116–117 Ohnishi I, Okunishi E, Yamazaki K, Aota N, Miyatake K, Nakanishi M, Ohkura Y, Kondo Y, Yasunaga K, Toh S, Matsumura S (2011) Development of a Large Solid Angle SDD for TEM and its Applications. Microsc Microanal 17(Suppl. 2):Late Breaking 22 (The JEOL approach) Sawada H, Tanishiro Y, Ohashi N, Tomita T, Hosokawa F, Kaneyama T, Kondo Y, Takayanagi K (2009) STEM Imaging of 47-pm-Separated Atomic Columns by a Spherical Aberration-Corrected Electron Microscope with a 300-kV Cold Field Emission Gun. J Electron Microsc 58:357–361 Watanabe M (2011) Chapter 7: X-ray Energy Dispersive Spectrometry in Scanning Transmission Electron Microscopes. In: Pennycook SJ, Nellist PD (eds) Scanning Transmission Electron Microscopy: Imaging and Analysis. Springer, New York., pp 291–351

Zaluzec NJ (2009) Innovative Instrumentation for Analysis of Nanoparticles: The π Steradian Detector. Microscopy Today 17(4):56–59

17.4 – XEDS Tomography Möbus G, Doole RC, Inkson BJ (2003) Spectroscopic electron tomography. Ultramicroscopy 96:433–451 Yaguchi T, Konno M, Kamino T, Watanabe M (2008) Observation of Three-dimensional Elemental Distributions of a Si-device Using a 360-degree-tilt FIB and the Cold Field-emission STEM System. Ultramicroscopy 108:1603–1615 (The Hitachi approach) Zaluzec NJ (2012) The Confluence of Aberration Correction, Spectroscopy and Multi-Dimensional Data Acquisition. Proc. European Microscopy Congress

17.4 – Atomic Resolution X-ray Analysis Watanabe M (2013) Microscopy Hacks: Development of Various Techniques to Assist Quantitative Nanoanalysis and Advanced Electron Microscopy. Microscopy 62(2):217–241

17. Appendix 2 – Calculation of Specimen Density Okamoto H, Chakrabarti DJ, Laughlin DE, Massalski T (1987) The Au-Cu (Gold-Copper) System. Bull Alloy Phase Diagrams 8:454–473

Chapter 17

criterion for the minimum detectable peak-intensity in an X-ray spectrum) Watanabe M, Wade CA (2013) Practical Measurement of X-ray Detection Performance of a Large Solid-Angle Silicon Drift Detector in an Aberration-Corrected STEM. Microsc Microanal 19(Suppl. 2):1264–1265

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Appendix  References

Figure and Table Credits

Chapter 1 Figure  1.6 Courtesy Bronsgeest MS and Delft University of Technology. Figure  1.7 Courtesy Bronsgeest MS and Delft University of Technology.

Chapter 2 Figure 2.1 Reprinted from Svensson K, Olin H, Olsson E (2004) Nanopipettes for Metal Transport Phys Rev Lett 93(14) 1459011-4, Fig. 4. With permission of the American Physical Society. Figure 2.3 Robertson IM, Ferreira PJ, Dehm G, Hull R, Stach EA (2008) Visualizing the behavior of dislocations – seeing is believing. MRS Bulletin 33, 122–131. Figure 5. Reproduced by permission of Cambridge University Press. Figure 2.4 Rudolph AR, Jungjohann KL, Wheeler DR, Brozik SM (2014) Drying Effect Creates False Assemblies in DNAcoated Gold Nanoparticles as Determined Through In Situ Liquid Cell STEM. Microsc Microanal 20, 437–444. Figures 4 & 7. Reproduced by permission of Cambridge University Press. Figure 2.5 Panciera F, Chou Y-C, Reuter MC, Zakharov D, Stach EA, Hofmann S, Ross FM (2015) Synthesis of nanostructures in nanowires using sequential catalyst reactions. Nature Materials 14, 820–826. Reproduced by permission of Nature Publishing Group. Figure  2.6 Reprinted from Creemer JF, Helveg S, Hoveling GH, Ullmann S, Molenbroek AM, Sarro PM, Zandbergen HW (2008) Atomic-scale electron microscopy at ambient pressure, Ultramicroscopy 108, 993–998. Figure 3b. With permission from Elsevier. Figure 2.7 Reprinted from LaGrange T, Campbell GH, Reed BW, Taheri M, Peravento JB, Kim JS, Browning ND (2008) Nanosecond time-resolved investigations using the in situ of dynamic transmission electron microscope (DTEM. Ultramicroscopy 108, 1441–1449. Fig. 1. With permission from Elsevier.

Figure 2.8 Reprinted from Shorokhov D, Zewail A (2008) 4D Electron imaging: principles and perspectives. Phys Chem Chem Phys 10(20), 2869–3016. Figure 2. Reproduced by permission of Royal Society of Chemistry. Figure 2.9 Reprinted from Kulovits A, Wiezorek JMK, LaGrange T, Reed BW, Campbell GH (2011) Revealing the transient states of rapid solidification in aluminum thin films using ultrafast in situ transmission electron microscopy. Philos Mag Lett 91, 287– 296. Figure 2. Reproduced by permission of Taylor and Francis. Figure  2.10 Reprinted from LaGrange T, Reed BW, McKeown JT, Santala MJ, Dehope WJ, Huete G, Shuttlesworth RM, Campbell GH, Microsc. Microanal. 19, 1154 (2013) Reprinted as Figure 2 in: Movie-mode Dynamic Electron Microscopy, MRS Bulletin 40(1), 22–28. Reproduced by permission of Cambridge University Press. Figure 2.11 Lobastov VA, Weissenrieder J, Tang J, Zewail AH (2007) Ultrafast Electron Microscopy (UEM: Four-Dimensional Imaging and Diffraction of Nanostructures during Phase Transformations. Nano Lett 7(9), 2552–2558. Fig. 1. Reproduced by permission of American Chemical Society. Figure 2.12 Adapted after Boyes ED, Gai PL (2014) Aberration corrected environmental STEM (AC ESTEM) for dynamic in situ gas reaction studies of nanoparticle catalysts. J Physics: Conf Ser 522, 012004. Reproduced by permission of IOP Publishing. Figure 2.13 Reprinted from Boyes ED, Gai PL (2014) Visualising reacting single atoms under controlled conditions: Advances in atomic resolution in situ Environmental (Scanning) Transmission Electron Microscopy (E(S)TEM. CR Phys 15, 200–213. Fig. 1 Reproduced by permission of Elsevier France. Figure 2.14 Courtesy of (a) Protochips, (b) Poseidon electrochemical cell, (c) Hummingbird Scientific, (d) Hitachi. DensSolutions: The Ocean series Figure 2.15 Reprinted from Creemer JF, Helveg S, Hoveling GH, Ullmann S, Molenbroek AM, Sarro PM, Zandbergen HW (2008) Atomic-scale electron microscopy at ambient pressure. Ultramicroscopy 108, 993–998. Figure 3b. Reproduced by permission of Elsevier.

© Springer International Publishing Switzerland 2016 C. B. Carter, D. B. Williams (Eds.), Transmission Electron Microscopy, DOI 10.1007/978-3-319-26651-0

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Figure  2.16 Reprinted from Yoshida H, Omote H, Takeda S (2014) Oxidation and reduction processes of platinum nanoparticles observed at the atomic scale by environmental transmission electron microscopy. Nanoscale 6, 13113–13118. Reproduced by permission of Royal Society of Chemistry. Figure 2.17 Reprint from Alan T, Yokosawa T, Gaspar J, Pandraud G, Paul O, Creemer F, Sarro PM, Zandbergen HW (2012) Micro-fabricated channel with ultra-thin yet ultra-strong windows enables electron microscopy under  4-bar pressure. APL, 100, 081903-1-4, Fig. 5. With permission from AIP Publishing LLC. Figure 2.18 After Jungjohann KL (2012) Ph.D. Thesis, UC Davis. Nanoscale imaging and analysis of fully hydrated materials. Figure 3.10. Figure 2.19 Photo by Carter CB courtesy Furuya K. Figure  2.20 Reprint from Mehraeen S, McKeown JT, Desh­ mukh PV, Evans JE, Abellan P, Xu P, Reed BW, Taheri ML, Fischione PE, Browning ND (2013) A (S)TEM Gas Cell Holder with Localized Laser Heating for In Situ Experiments. Microsc Microanal 19(2), 470–478, Fig. 1. Reproduced by permission of Cambridge University Press. Figure 2.21 Reprinted from Niu K-Y, Park J, Zheng H, Alivisatos AP (2013) Revealing Bismuth Oxide Hollow Nanoparticle Formation by the Kirkendall Effect. Nano Letters 13, 5715–5719. Reproduced by permission of American Chemical Society. Figure 2.22 Reprinted from Wang C, Qiao Q, Shokuhfar T, Klie RF (2014) High-Resolution Electron Microscopy and Spectroscopy of Ferritin in Biocompatible Graphene Liquid Cells and Graphene Sandwiches. Advanced Materials 26, 3410–3414. Fig. 1. Reproduced by permission of John Wiley and Sons. Figure 2.23 Reprinted from White ER, Singer SB, Augustyn V, Hubbard WA, Mecklenburg M, Dunn B, Regan BC (2012) In Situ Transmission Electron Microscopy of Lead Dendrites and Lead Ions in Aqueous Solution. ACS Nano, 6(7), 6308–17, Fig. 1. Reproduced by permission of American Chemical Society. Figure 2.24 Reprinted from Mortensen PM, Hansen TW, Wagner JB, Jensen AD (2015) Modeling of temperature profiles in an environmental transmission electron microscope using computational fluid dynamics. Ultramicroscopy 152, 1–9, Fig 7 and 10. Reproduced by permission of Elsevier. Figure 2.25 Reprinted by permission from Macmillan Publish­ers Ltd: Gao Y, Bando Y (2002) Carbon Nanothermometer Containing Gallium. Nature 415, 599. Copyright 2002. Fig. 1. Reproduced by permission of Nature Publishing Group. Figure 2.26 Courtesy Basu J, Ravishankar N, Carter CB. Unpublished research.

Figure 2.27a–e Reprinted from Saka H, Kamino T, Ara S, Sasaki K (2008) In Situ Heating Transmission Electron Microscopy. MRS Bull, 33, 93–100, Fig. 1. Reproduced by permission of Cambridge University Press. Figure 2.27f Reprinted from Gandman M, Kauffmann Y, Koch CT, Kaplan WD (2013) Direct Quantification of Ordering at a Solid-Liquid Interface Using Aberration Corrected Transmission Electron Microscopy. Phys Rev Lett 110, 086106. Fig. 1. Reproduced by permission of American Physical Society. Figure  2.28 Reprinted from Kasama T, Dunin-Borkowski RE, Matsuya L, Broom RF, Twitchett AC, Midgley PA, New­ comb SB, Robins AC, Smith DW, Gronsky JJ, Thomas CA, Fischione PE (2005) A versatile three-contact electrical biasing transmission electron microscope specimen holder for electron holography and electron tomography of working devices. Mater. Res. Soc. Symp. Proc., 907E, MM13.02. “In situ Electron Microscopy of Materials”, Eds Ferreira PJ, Robertson IM, Dehm G, Saka H. Fig. 8. Reproduced by permission of Cambridge University Press. Figure 2.29 Reprinted from Asoro MA, Kovar D, Ferreira PJ (2013) In Situ Transmission Electron Microscopy Observations of Sublimation in Silver Nanoparticles. ACS Nano, 7(9), 7844–7852, Figs 1&2. Reproduced by permission of American Chemical Society. Figure 2.30 Reprinted from Delalande M, Guinel MJ-F, Allard LF, Delattre A, Le Bris R†, Yves Samson Y, Bayle-Guillemaud P, Peter Reiss P (2012) L10 Ordering of ultrasmall FePt Nanoparticles Revealed by TEM in situ annealing. J Phys Chem C 116, 6866–6872. Fig.  7. Reproduced by permission of American Chemical Society. Figure 2.31 Reprinted from Vendelbo1 SB, Elkjær CF, Falsig H, Puspitasari I, Dona P, Mele L, Morana B, Nelissen BJ, van Rijn R, Creemer JF, Kooyman PJ, Helveg S (2014) Visualization of oscillatory behaviour of Pt nanoparticles catalysing CO oxidation. Nature Mater 13(9), 884–890. Reproduced by permission of Nature Publishing Group. Figure 2.32 Reprinted from Evans JE, Jungjohann KL, Wong PCK, Chiu P-L, Dutrow GH, Arslan I, Browning ND (2012) Visualizing macromolecular complexes with in situ liquid scanning transmission electron microscopy. Micron 43 1085–1090. Fig. 3. Reproduced by permission of Elsevier. Figure 2.33 Wirix MJM, Bomans PHH, Friedrich H, Sommerdijk NAJM, de With G (2014) Three-Dimensional Structure of P3HT Assemblies in Organic Solvents Revealed by Cryo-TEM. Nano Lett 14, 2033–2038. Fig. 2. Reproduced by permission of American Chemical Society. Figure 2.34 Tai K, Liu Y, Dillon SJ (2014) In Situ Cryogenic Transmission Electron Microscopy for Characterizing the Evolution of Solidifying Water Ice in Colloidal Systems. Microsc

Figure and Table Credits

Microanal 20, 330–337. Fig. 1a. Reproduced by permission of Cambridge University Press. Figure 2.35 Haque MA, Saif MTA (2002) In situ tensile testing of nano-scale specimens in SEM and TEM. Experimental Mech  42(1), 123–128, Fig.  1. Reproduced by permission of Springer Publishing Company. Figure  2.36 Reprinted from Ye J, Mishra RK, Pelton AR, Minor AM (2010) Direct observation of the NiTi martensitic phase transformation in nanoscale volumes. Acta Mater 58, 490–498. Fig 1b & 2b. Reproduced by permission of Elsevier. Figure 2.37 Reprinted from Espinosa HD, Bernal RA, Filleter T (2012) In Situ TEM Electromechanical Testing of Nanowires and Nanotubes. Small 8(21), 3233–3252, Fig. 4. Reproduced by permission of John Wiley and Sons. Figure 2.38 Reprinted from Nowak JD, Mook WM, Minor AM, Gerberich WW, Carter CB (2007) Fracturing a Nanoparticle. Philos Mag 87(1), 29–37, Fig. 1. Reproduced by permission of Taylor and Francis. Figure  2.39 Reprinted from Bernal RA, Filleter T, Connell JG, Sohn K, Huang J, Lauhon LJ, Espinosa HD (2014) In situ electron microscopy four-point electromechanical characteri­ zation of freestanding metallic and semiconducting nanowires. Small 10 (4), 725–733. Reproduced by permission of John Wiley and Sons. Figure 2.40 Reprinted from Lau JW, Schofield MA, Zhu Y, Neumarl GF (2003) In situ Magnetodynamic Experiments Achieved with the design of an In-plane Magnetic Field Specimen Holder. Microsc. Microanal. 9, (Suppl 2), 130–131. Reproduced by permission of Cambridge University Press. Figure 2.41 Reprinted from Budruk A, Phatak C, Petford-Long AK, De Graef M (2011) In situ Lorentz TEM magnetization studies on a Fe–Pd–Co martensitic alloy. Acta Mater 59, 6646– 6657, Fig. 1. Copyright 2011, with permission from Elsevier. Figure 2.42 Reprinted from Wang J, Zeng Z, Weinberger CR, Zhang Z, Zhu T, Scott  X. Mao (2015) In situ atomic-scale observation of twinning dominated deformation in nanoscale body-centred cubic tungsten Nature Mater 14, 594–560. Figure 13 of Supplementary data. Reproduced by permission of Nature Publishing Group. Figure 2.43 Reprinted from Spence JCH (1988) A Scanning Tunneling Microscope in a Side-Entry Holder for Reflection Electron-Microscopy in the Philips EM400, Ultramicroscopy 25, 165–170, Fig. 4. Copyright 1988 with permission from Elsevier. Figure 2.44 Reprinted from Costa PMFJ, Golberg D, Shen G, Mitome M, Bando Y (2008) ZnO low-dimensional structures:

electrical properties measured inside a transmission electron microscope. J Mater Sci 43, 1460–1470. Fig 6. Reproduced by permission of Springer Publishing Company. Figure  2.45 Liu XH, Huang JY (2011) In situ TEM electrochemistry of anode materials in lithium ion batteries. Energy & Environmental Sci, 4(10), 3844–3860, Fig. 1. Reproduced by permission of Royal Society of Chemistry. Figure 2.46 Wang CM, Li X, Wang Z, Wu W, Liu J, Gao F, Kovarik  L, Zhang J-G, Howe J, Burton DJ, Liu Z, Xiao  X, Thevuthasan S, Baer DR (2012) In Situ TEM Investigation of Congruent Phase Transition and Structural Evolution of Nanostructured Silicon/Carbon Anode for Lithium Ion Batteries. Nano Lett 12, 1624–1632. Fig. 4. Reproduced by permission of American Chemical Society. Figure 2.47 Liu Y, Liu XH, Nguyen BM, Yoo J, Sullivan JP, Picraux ST, Huang JH, Dayeh SA (2013) Tailoring Lithiation Behavior by Interface and Bandgap Engineering at the Nanoscale. Nano Letters, 13(10), 4876–4833, Fig. 1, 3. Reproduced by permission of American Chemical Society. Figure 2.48 Leenheer AJ, Jungjohann KL, Zavadil KR, Sullivan JP, Harris CT, Lithium electrodeposition dynamics in aprotic electrolyte observed in Situ via Transmission Electron Microscopy, Fig. 2. Reproduced by permission of American Chemical Society. Figure 2.49a Zhang C, Tian W, Xu Z, Wang X, Liu J, Li S-N, Tang D-M, Liu D, Liao M, Bando Y, Goldberg D (2014) Photosensing performance of branched CdS/ZnO heterostructures as revealed by in situ TEM and photodetector tests. Nanoscale 6, 8084–8090, Fig. 4, 5. Reproduced by permission of Royal Society of Chemistry. Figure 2.50 Zhang L, Miller BK, Crozier PA (2013) Atomic Level In Situ Observation of Surface Amorphization in Anatase Nanocrystals During Light Irradiation in Water Vapor. Nano Lett 13, 679–684, Fig. 1, 2, 4. Reproduced by permission of American Chemical Society. Figure 2.51 Reprinted from Picher M, Mazzucco S, Blankenship S, Sharma R (2015) Vibrational and optical spectroscopies integrated with environmental transmission electron microscopy. Ultramicroscopy 150, 10–15, Fig. 1, 2, 4c. Copyright 2015 with permission from Elsevier. Figure 2.52 Reprinted from Hillerich K, Dick KA, Wen C-Y, Reuter MC, Kodambak S, Ross FM (2013) Strategies To Control Morphology in Hybrid Group  III–V/Group IV Heterostructure Nanowires. Nano Lett 13, 903–908. Reproduced by permission of American Chemical Society. Figure  2.53 Reprinted from Simonsen SB, Chorkendorff  I, Dahl S, Skoglundh M, Sehested J, Helveg S (2010) Direct Observation of Oxygen-induced Platinum Nanoparticle Ripening

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Studied by In Situ TEM. JACS 132, 7968–7975, Fig. 3. Reproduced by permission of American Chemical Society. Figure 2.54 Reprinted Woehl TJ, Evans JE, Arslan I, Ristenpart WD, Browning ND (2012) Direct in Situ Determination of the Mechanisms Controlling Nanoparticle Nucleation and Growth. ACS Nano 6(10), 8599–8610, Fig. 1. Reproduced by permission of American Chemical Society. Figure 2.55 Reprinted from Schneider NM, Norton MM, Mendel BJ, Grogan JM, Ross FM, Bau HH (2014) Electron-water interactions and implications for liquid cell electron microscopy. J Phys Chem C 118, 22373–22382, Fig. 1, 2, 5 Reproduced by permission of American Chemical Society. Figure 2.56 Reprinted from Hattar K, Bufford DC, Buller DL (2014) Concurrent in situ ion irradiation transmission electron microscope. Nucl Instrum Meth B 338, 56–65, Fig. 2. Reproduced by permission of Elsevier. Figure 2.57 Reprinted from Hattar K, Bufford DC, Buller DL (2014) Concurrent in situ ion irradiation transmission electron microscope. Nucl Instrum Meth B 338, 56–65. Fig. 8. Reproduced by permission of Elsevier.

Chapter 3 All Chapter 3 figures are unpublished works, with the exception of Figure  3.11 Sundararaman M, Mukhopadhyay P, Banerjee S (1988) Precipitation of the δ-Ni3Nb phase in Two Nickel Base Superalloys. Met. Trans., 19A, 453. Reproduced by permission of Springer Publishing Company.

Chapter 4 Figure 4.2 Unpublished work courtesy Hseih KC. Figure  4.3 Kaufman MJ, Eades JA, Loretto MH, Fraser HL (1983) A Study of a Cellular Phase Transformation in the Ternary Ni-Al-Mo Alloy System. Met. Trans., 14A, 1561–1571. Reproduced by permission of Springer. Figure 4.4 as Figure 4.3 Figure 4.5 as Figure 4.3 Figure 4.6 as Figure 4.3 Figure 4.7 as Figure 4.3

Figure 4.8 as Figure 4.3 Figure 4.13 as Figure 4.3 Figure 4.11 From: Tanaka M, Saito R, Sekii H (1983a). PointGroup Determination by Convergent-Beam Electron Diffraction. Acta Cryst., A39, 357–368. Reproduced by permission of John Wiley and Sons. Figure 4.16 From: Morniroli JP (2002) Large-Angle Convergent-Beam Electron Diffraction. Paris, Société Française des Microscopies, Figure VI.21. Reproduced by permission of John Wiley and Sons. Figure 4.17 From: Eades JA, Kiely CJ (1987) Convergent-beam diffraction. EMAG 87, Inst. Phys Conf Series, 90, 109–114. Reproduced by permission of Taylor and Francis. Figure  4.19 From Cherns D, Preston AR (1989) Convergent Beam Diffraction Studies of Interfaces, Defects and Multilayers. J. Electron Microsc. Tech., 13, 111–122. Reproduced by permission of John Wiley and Sons Figure 4.20 From Tanaka M, Terauchi M, Kaneyama T (1988) Convergent-Beam Electron Diffraction  II. JEOL, Tokyo, page 165. Reproduced by permission of the authors and JEOL. Figure  4.21 From Morniroli JP (2002) Large-Angle Convergent-Beam Electron Diffraction. Paris, Société Française des Microscopies, Figure XI.31. Reproduced by permission of John Wiley and Sons. Figure  4.23 From Tanaka M, Terauchi M (1985) Convergent-Beam Electron Diffraction. JEOL, Tokyo, Page 83. Reproduced by permission of the authors and JEOL. Figure 4.24 From Humphreys CJ, Eagelsham DJ, Maher DM, Fraser HL (1988) CBED and CBIM from semiconductors and superconductors. Ultramicroscopy 26(1–2), 13–23. Reproduced by permission of Elsevier. Figure 4.25 Courtesy Christenson KK, Eades JA. Figure 4.26 With permission from Christoph T. Koch Table 4.3 After: Eades JA (1988) Symmetry Determination by Convergent-beam Diffraction. EUREM 88; IOP Conf. Series 93, 1, 3–12. Table 4.5 After: Buxton BF, Eades JA, Steeds JW, Rackham GM (1976) The Symmetry of Electron Diffraction Zone Axis Patterns Phil. Trans. A281, 171–194. Table 4.6 Adapted from: Eades JA, Shannon MD, Buxton BF. SEM (1983) Crystal Symmetry from Electron Diffraction III, 1051–1060.

Figure and Table Credits

Chapter 5

Chapter 11

Figure 5.6: Zuo J, Kim M, O’Keeffe M, Spence JCH (1999) Direct observation of d-orbital holes and Cu-Cu bonding in Cu2O. Nature, 401, 49–52. Reproduced by permission of Nature Publishing Group.

Figure 11.1 Adapted from Pennycook SJ, Browning ND, McGibbon MM, McGibbon AJ, Jesson DE, Chisholm MF (1996a) Philos. Trans. R. Soc. A. 354, 2619.

Figure 5.7: Courtesy Mayer J, unpublished. For more details see Krämer S, Mayer J (1999) Using the Hough transform for HOLZ line identification in Convergent Beam Electron Diffraction. J Microsc 194, 2–11 (1999) Figure 5.9a: Tanaka M et al (2003) CBED. JEOL, Vol. 3. Reproduced by permission of the authors and JEOL.

Chapter 6

Figure 11.2 From Pennycook SJ, Jesson DE (1992) Acta Metall. Mater. 40, S149. Reproduced under US Govt agreement. Figure 11.3 Adapted from Pennycook SJ, Jesson DE, Chisholm MF, Browning ND (1993) Atomic-Resolution Imaging and Analysis with the STEM, Vol. 130, X-Ray Optics and Microanalysis 1992, edited by Kenway PB, Duke PJ, Lorimer GW, Mulvey T, Drummond IW, Love G, Michette AG and Stedman M, pp. 217. Bristol: Institute of Physics. Figure 11.4 From Pennycook SJ, Jesson DE (1991) Incoherent characteristics; the probe propagating Ultramic. 37, 14. Reproduced under US Govt agreement.

All Figures are the product of the author.

Figure 11.5 Reproduced from Peng Y, Oxley MP, Lupini AR, Chisholm MF, Pennycook SJ (2008) Microsc. Microanal. 14, 36.

Chapter 7

Figure 11.6 Adapted from Pennycook SJ, Jesson DE, Chisholm MF, Ferridge AG, Seddon MJ (1992) Sub-Ångstrom Microscopy through Incoherent Imaging and Image Restoration, Vol. Scanning Microscopy Supplement 6, Signal and Image Processing in Microscopy and Microanalysis, edited by PW. Hawkes, Cambridge, UK: Scanning Microscopy International.

All Figures are the product of the author.

Chapter 8 All Figures are the product of the author.

Chapter 9 All Figures are the product of the author.

Chapter 10 Most Figures are the product of the author. Figure 10.1: Courtesy EMAT center for Electron Microscopy, University of Antwerp. Figure 10.8: Courtesy Jia CL, Thust A (1999) Phys Rev Lett 82, 5052. Reproduced by permission.

Figure 11.7 (a) Adapted from Abe E, Pennycook SJ (2005) J. Crystallog. Soc. Japan 47, 26. (b) is from Steinhardt PJ, Jeong HC, Saitoh K, Tanaka M, Abe E, Tsai AP (1998) Nature 396, 55. For Figure 7a,b Reproduced under US Govt agreement. Figure 11.8 (a) From Merli PG, Missiroli GF, Pozzi G (1976) Am. J. Phys. 44, 306, Reproduced by permission of … (b) from Tonomura A, Endo J, Matsuda T, Kawasaki T, Ezawa H (1989) Am. J. Phys. 57, 117. Reproduced with permission. Figure 11.14 From Nellist PD, Pennycook SJ (1999a) Inst Phys Conf Ser 315. Reproduced under US Govt agreement. Figure 11.16 Images a,b and c courtesy of McGibbon MM, Varela M, Lupini AR, respectively. Figure 11.17 Images from (A) Nellist PD, Pennycook SJ (1996) Science 274, 413 Reproduced under US Govt agreement (B) Sohlberg K, Rashkeev S, Borisevich AY, Pennycook SJ, Pantelides ST (2004) Pt atoms on γ-alumina Chemphyschem 5, 1893 Reproduced under US Govt agreement (C) Wang SW, Borisevich AY, Rashkeev SN, Glazoff MV, Sohlberg K, Pennycook SJ, Pantelides ST (2004) On a γ-alumina flake Nature Mat. 3, 143 Reproduced under US Govt agreement.

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Figure 11.18 Adapted from Zhou W, Kapetanakis M, Prange M, Pantelides S, Pennycook S, Idrobo JC (2012a) Phys. Rev. Lett. 109, 206803.

Figure 11.39 Simulated Ronchigrams courtesy Lupini AR.

Figure 11.19 Adapted from Zhou W, Kapetanakis M, Prange M, Pantelides S, Pennycook S, Idrobo JC (2012a) Phys. Rev. Lett. 109, 206803.

Figure 11.41 Adapted from Jesson and Pennycook (1995).

Figure 11.20 Adapted from Lee J, Zhou W, Pennycook SJ, Idrobo JC, Pantelides ST (2013) Graphene nanopore Nature Communications 4, 1650.

Figure 11.43 Adapted from Pennycook et al. (1996b).

Figure 11.21 Adapted from Borisevich AY, Lupini AR, Pennycook SJ (2006a) Proc. Nat. Acad. Sci. USA 103, 3044.

Figure 11.45 Adapted from Borisevich et al. (2006a)

Figure 11.22 From Borisevich AY, Lupini AR, Pennycook SJ (2006a) Proc. Nat. Acad. Sci. USA 103, 3044. Reproduced under US Govt agreement. Figure 11.23 Adapted from van Benthem K, Lupini AR, Kim M, Baik HS, Doh S, Lee JH, Oxley MP, Findlay SD, Allen LJ, Luck JT, Pennycook SJ (2005) Appl. Phys. Lett. 87, 034104. A movie version of Figure 11.23. Figure 11.24 From van Benthem K, Lupini AR, Kim M, Baik HS, Doh S, Lee JH, Oxley MP, Findlay SD, Allen LJ, Luck JT, Pennycook SJ (2005) Appl. Phys. Lett. 87, 034104. A movie version of Figure 11.23. Reproduced under US Govt agreement. Figure 11.29 From James EM, Browning ND (1999) Practical aspects of atomic resolution imaging and analysis in STEM. Ultramicroscopy 78, 125–139 Reproduced by permission of Elevier. Figure 11.30 Adapted from Pennycook et al. (2003). Figure 11.31 From Nellist PD, Chisholm MF, Dellby N, Krivanek OL, Murfitt MF, Szilagyi ZS, Lupini AR, Borisevich A, Sides WH, Pennycook SJ (2004) Science 305, 1741. Supplementary Online Material. Reproduced under US Govt agreement. Figure 11.31 Courtesy Duscher G. Figure 11.32 Ronchigrams courtesy of Gerd Duscher. Figure 11.33b (Pennycook et al. (2009) The original data points from Browning et al. (1993a). Adapted from Browning et al. 1993a; Browning et al. (1993b) Figure 11.34 Adapted from Peng et al. (2008). Figure 11.35 Adapted from Pennycook and Nellist (1999). Figure 11.36 Adapted from Jesson and Pennycook (1993). Figure 11.38 Simulated Ronchigrams courtesy Lupini AR.

Figure 11.40 Adapted from Nellist and Pennycook (1998b).

Figure 11.42 Adapted from Jesson and Pennycook (1995).

Figure 11.44 Adapted from Nellist and Pennycook (2000).

Figure 11.46 Adapted from Varela et al. (2005). Figure 11.48 Courtesy Miyoung Kim. Figure 11.49 From Perovic DD, Rossouw CJ, Howie A (1993) Ultramicroscopy 52, 353. Reproduced with permission. Figure 11.50 From Xin Y, Pennycook SJ, Browning ND, Nellist PD, Sivananthan S, Omnes F, Beaumont B, Faurie JP, Gibart P (1998) Appl. Phys. Lett. 72, 2680. Dislocations emerging at the surface of GaN. Reproduced under US Govt agreement. Figure 11.51 Adapted from Kadavanich et al. (2001) McBride et al. (2006) Pennycook et al. (2003). Figure 11.52 Adapted from Roberts et al. (2008). Figure  11.53 From Shibata N, Pennycook SJ, Gosnell TR, Painter GS, Shelton WA, Becher PF (2004) Nature 428, 730. Reproduced under US Govt agreement. Figure 11.54 Adapted from Pennycook (2002); Yan et al. (1999). Figure  11.55 From LeBeau JM, D’Alfonso AJ, Findlay SD, Stemmer S, Allen LJ (2009) Phys Rev B 80, 214110. No Stobbs factor. Reproduced with permission. Figure 11.56 From Molina SI, Varela M, Ben T, Sales DL, Pizarro J, Galindo PL, Fuster D, Gonzalez Y, Gonzalez L, Pennycook SJ (2008) J. Nanosci. Nanotech. 8, 3422. Calibrated by high resolution X-ray diffraction. Reproduced under US Govt agreement.

Chapter 12 Figure 12.8 Reprinted from Ultramicroscopy, Vol 109, Batenburg KJ, Bals S, Sijbers J, Kübel C, Midgley PA, Hernandez JC, Kaiser U, Encina ER, Coronado EA, Van Tendeloo G (2009) 3D imaging of nanomaterials by discrete tomography, 730–740. Copyright 2009, with permission from Elsevier.

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Figure 12.9 Saghi Z, Holland DJ, Leary R, Falqui A, Bertoni G, Sederman AJ, Gladden LF, Midgley PA (2011) Three-Dimensional Morphology of Iron Oxide Nanoparticles with Reactive Concave Surfaces. Nano Letters, 11, 4666–4673. Reproduced by permission of American Chemical Society. Figure 12.10 Jinnai H, Nishikawa Y, Spontak RJ, Smith SD, Agard DA, Hashimoto T (2000) Direct measurement of interfacial curvature distributions in a bicontinuous block copolymer morphology. Physical Review Letters, 84(3), 518–521. Reproduced by permission of American Physical Society. Figure 12.11 Midgley PA, Thomas JM, Laffont L, Weyland M, Raja R, Johnson BFG, Khimyak T (2004) Reprinted with permission of American Chemical Society. Figure  12.12 Ercius P, Weyland M, Muller DA, Gignac LM (2006) Three-dimensional imaging of nanovoids in copper interconnects using incoherent bright field tomography. Applied Physics Letters, 88(24). Reproduced by permission of AIP Publishing LLC. Figure 12.13. Reprinted from Micron, Vol. 47, Lepinay K, Lorut F, Pantel R, Epicier T (2013) Chemical 3D tomography of 28 nm high K metal gate transistor: STEM XEDS experimental method and results, 43–49. Copyright 2013, with permission from Elsevier. Figure 12.14 Reprinted from Scripta Materialia, Vol. 55, Weyland M, Yates TJV, Dunin-Borkowski RE, Laffont L, Midgley PA (2006) Nanoscale analysis of three-dimensional structures by electron tomography, 29–33. Copyright 2006, with permission from Elsevier. Figure 12.15 Gass MH, Koziol KKK, Windle AH, Midgley PA (2006) 4-dimensional spectral-tomography of carbonaceous nano-composites. Nano Letters, 6(3), 376–379. Reproduced by permission of American Chemical Society. Figure  12.16 Reprinted from Ultramicroscopy, Vol.  109, Jarausch K, Thomas P, Leonard DN, Twesten R, Booth CR (2009) Four-dimensional STEM-EELS: Enabling nano-scale chemical tomography, 326–337. Copyright 2009, with permission from Elsevier. Figure 12.17 Image courtesy of Barnard J. Figure 12.18 Reprinted from Scripta Materialia, Vol. 59, Tanaka M, Higashida K, Kaneko K, Hata S, Mitsuhara M (2008) Crack tip dislocations revealed by electron tomography in silicon single crystal, 901–902. Copyright 2008, with permission from Elsevier. Figure  12.19 Reprinted from Ultramicroscopy, Vol.  108, Twitchett-Harrison AC, Yates TJV, Dunin-Borkowski RE, Midgley PA (2008) Quantitative electron holographic tomography for the 3D characterization of semiconductor device

structures, 1401–1407. Copyright 2008, with permission from Elsevier. Figure 12.20 Phatak C, Petford-Long AK, De Graef M (2010) Three-Dimensional Study of the Vector Potential of Magnetic Structures. Physical Review Letters, 104, 253901. Reproduced by permission of the American Physical Society. Figure 12.21 Van Aert S, Batenburg KJ, Rossell MD, Erni R, Van Tendeloo G (2011) Three-dimensional atomic imaging of crystalline nanoparticles. Nature, 470, 374–377. Reproduced by permission of Nature. Figure 12.24 Sample courtesy of Xiong X.

Chapter 13 Figure 13.5 Midgley PA, Saunders M (1996) Quantitative electron-diffraction – from atoms to bonds. Contemp. Phys., 37, 441 . Reproduced by permission of Taylor & Francis. Figure 13.14 Sigle W, Krämer S, Varshney V, Zern A, Eigenthaler U, Rühle M (2003) Plasmon energy mapping in energy-filtering transmission electron microscopy. Ultramicroscopy, 96, 565–571. Reproduced with permission of Elsevier. Figure 13.15 Sample provided courtesy of Lin W of the Mayo Clinic, Jacksonville. Figure 13.17 After: Hofer F, Grogger W, Kothleitner G, Warbichler P (1997) Quantitative analysis of EFTEM elemental distribution images. Ultramicroscopy, 67, 83–103. Figure 13.18 After: Thomas PJ, Midgley PA (2001) Image-Spectroscopy  2: the Removal of Plural Scattering from Extended Energy-Filtered Series by Fourier Deconvolution Techniques. Ultramicroscopy, 88, 187–194. Figure 13.20 After: Walther T (2003) Electron energy-loss spectroscopic profiling of thin film structures: 0.39 nm line resolution and 0.04 eV precision measurement of near-edge structure shifts at interfaces. Ultramicroscopy, 96, 401–411. Figure 13.21 After Midgley PA (2009).

Chapter 14 Figure  14.1 Spectra replotted from the following sources. i) 1974: Egerton RF, Whelan MJ, J Electron Spectroscopy and Related Phenomena, 3 (1974) 232; ii) 1989: Weng X, Rez P, Ma H, Phys. Rev. B 40 (1989) 4175; iii) 2001: Soininen JA,

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Shirley EL, Phys. Rev. B 64 (2001) 165112. iv) 1998 and Exp: Merchant AR, McCulloch DG, Brydson R, Diamond and Related Materials 7 (1998) 1303. Figure 14.3 Singh DJ, Planewaves, Psuedopotentials and the LAPW Method, Kluwer, Boston (1994) Reproduced by permission of Springer (formerly Kluwer). Figure  14.4 After: Keast VJ, Bosman M. Microsc Res Techn 70:211–219 (2007)

Figure 16.19 reproduced by permission of The Meteoritical Society from Goldstein et al. 2007. Figure 16.22 B&C reproduced by permission of Taylor &Francis from Yang et al 2013. Figure 16.23 reproduced by permission of The American Chemical Society from Guiton et al. 2011.

Figure  14.5 Experimental data from Phys. Rev. B  66 (2002) 125319 and Mizoguchi T et al, 34 Micron (2003) 249.

Chapter 17

Figure 14.6 Experimental data and multiplet calculations from FM. de Groot et al Phys. Rev. B 41 (1990) 928.

Figure 17.25 Gorzkowski EP, Watanabe M, Scotch AM, Chan HM, Harmer MP (2004) Direct Measurement of Oxygen in LeadBased Ceramics Using the ζ-factor Method in an Analytical Electron Microscope J. Mater. Sci. 39 6735–6741.Reproduced by permission of Springer.

Figure 14.7 From Wu ZY, Ouvard G, Gressier P, Natoli CR. Phys. Rev. B 55 (1997) 10382. Reproduced by permission of American Physical Society. Figure 14.8 Related calculations given in J Electron Spectroscopy and Related Phenomena 143 (2005) 97–104 Figure 14.9 From Vast N et al. Phys. Rev. Lett 88 (2002) 037601. Reproduced by permission of American Physical Society.

Chapter 15 All Figures are the product of the author.

Chapter 16 Figure 16.2 reproduced by permission of Cambridge University Press from Kotula & Keenan 2006. Figure 16.10a,b reproduced by permission of Cambridge University Press from Kotula & Keenan 2006. Figure 16.11 reproduced by permission of Cambridge University Press from Kotula & Keenan 2006. Figure 16.12 reproduced by permission of Cambridge University Press from Kotula & Keenan 2006. Figure 16.13 (parts) reproduced by permission of Cambridge University Press from Kotula, Keenan & Michael 2003a. Figure 16.18 reproduced by permission of Cambridge University Press from Kotula & Keenan 2006.

Figure 17.26 Watanabe M, Williams DB (2006) The Quantitative Analysis of Thin Specimens: a Review of Progress from the CliffLorimer to the New ζ-Factor Methods J. Microsc. 221 89–109. As in the 2003 paper, you’ll find more details and references to the original work. Reproduced by permission of John Wiley and Sons. Figure 17.27 From Watanabe M (2013) Microscopy Hacks: Development of Various Techniques to Assist Quantitative Nanoanalysis and Advanced Electron Microscopy, Microscopy, 62, 217–241. Reproduced by permission of Oxford University Press. Figure 17.30 From Watanabe M (2013) Microscopy Hacks: Development of Various Techniques to Assist Quantitative Nanoanalysis and Advanced Electron Microscopy, Microscopy, 62, 217–241. Reproduced by permission of Oxford University Press. Figure 17.32 Courtesy of Okunishi E, JEOL Reproduced by permission of JEOL. Figure  17.33 Yaguchi T, Konno M, Kamino T, Watanabe M (2008) Observation of Three-dimensional Elemental Distributions of a Si-device Using a 360-degree-tilt FIB and the Cold Field-emission STEM System Ultramicrosc., 108, 1603–1615. Reproduced by permission of Elsevier. Figure  17.34 Yaguchi T, Konno M, Kamino T, Watanabe M (2008) Observation of Three-dimensional Elemental Distributions of a Si-device Using a 360-degree-tilt FIB and the Cold Field-emission STEM System Ultramicrosc., 108, 1603–1615. Reproduced by permission of Elsevier . Figure 17.35 Zaluzec N (2012) The Confluence of Aberration Correction, Spectroscopy and Multi-Dimensional Data Acquisition. Proc. European Microscopy Congress 2012. Reproduced by permission of the author.

Figure and Table Credits

Figure 17.36 Specimen courtesy of Varela M, Lee HN at Oak Ridge National Lab. Figure 17.37 From Watanabe M (2013) Microscopy Hacks: Development of Various Techniques to Assist Quantitative Nanoanalysis and Advanced Electron Microscopy, Microscopy, 62, 217–241. Reproduced by permission of Oxford University Press.

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Index

A A2 phase  85 Aberration coefficients  257 correction  222, 256, 295, 300, 434 Absorption  11, 67, 150, 155, 157, 161, 163, 201, 216 Accelerating voltage  11, 19, 147, 149, 150, 151, 154, 155, 162, 210, 211 Achromatic circles  160 Acicular morphology  87, 101 Actuator  50, 52, 55, 56, 58, 76 AEM  469, 473 AFM-TEM holders  51, 58 Airy  3, 292, 293, 294, 295, 298, 302, 316, 317, 325, 337 disc  292, 293, 294, 295, 298, 302, 316, 317, 325 function  3, 316, 317 ALCHEMI  425, 426, 427, 428, 429, 430, 431, 432, 434, 435, 436 systematic  426 Alloy  54, 55, 81, 83, 85, 87, 93, 94, 96, 97, 101, 146, 159, 351, 356, 429, 435, 489, 501 Aluminum  142, 211, 348, 384, 391, 392, 393, 450 Amplitude contrast transfer function (ACTF)  204, 216 Amplitude normalization  221, 223 Angular current density  2, 5, 8, 10, 14 Applied field  20, 56 Arbitrary waveform generator (AWG)  26 Argand  273, 274, 275 ASAC software package  154 Atmospheric  475 Automated  448 Automated acquisition  157 Axial  429, 430, 431, 432, 436 Azimuthally  298 B B2-ordered structure  85 B32-ordered phase  83, 85 Back-etching  35 Background  302, 310, 393, 468, 469, 471, 480, 483, 485, 492 Background intensity  132 Bagaryatski  97, 101

Basis  410, 411, 420, 421 Basis set  152 Bend  287, 426 Bend contour  54, 123 Berkovich-type indenter  53 Bessel  317 Bethe  421 Bethe potentials  154 B-field  217 Bloch  323, 324, 325, 326, 327, 329, 332, 333, 334, 409, 425, 431 Bloch wave  152 Boersch effect  3, 6, 7 Bohr  412 Boltzmann constant  4 Bootstrap method  145, 153 Bosons  3, 207 Bragg angle  121, 146, 148, 149, 150, 154, 156, 157, 158, 159, 160, 317, 322, 352, 356, 432 beam intensities  146 law  109, 154, 159 reflections  109, 111, 112, 114, 117, 119, 121, 122, 125, 128, 129, 132, 146, 149, 150, 156, 158, 160, 162, 317, 356, 426 scattering  109, 122, 132, 146, 147, 148, 150, 154, 156, 157, 158, 159, 160, 162, 322, 352 Bravais lattice  148 Bright tomography  351, 354 Bright field (BF)  70, 83, 84, 93, 105, 107, 112, 114, 115, 117, 118, 119, 123, 126, 128, 129, 130, 132, 133, 134, 136, 137, 138, 142, 160, 174, 189 Brillouin  322 Brownian motion  34, 35 C Carbon  4, 10, 17, 18, 21, 27, 33, 35, 36, 38, 42, 43, 45, 46, 54, 58, 60, 61, 63, 70, 96, 97, 98, 162 nanotubes (CNTs)  18 thin films  43 Cerenkov  398 Chemical  396

Chemical doping  29 Child-Langmuir effect  26 Chromatic aberration  3, 11, 12, 13, 20, 36, 211, 216, 219 Cliff  458 Close-packed directions  97 Confocal  350 Continuum  479 Converging  292, 293 Convolution  185, 186, 202, 204, 213, 216, 219, 244, 246, 268, 284, 305, 307, 312, 313, 315, 329, 332, 333, 334, 345, 346 Corrosion resistance  87, 93 Cosinusoidal interference pattern  200, 205, 206, 230 Coulomb  2, 6, 7, 9, 13, 46, 225, 237, 314, 408, 409 interaction  2, 6, 7, 9, 13, 46, 237, 314, 409 repulsion  409 Crack dependence  21 Critical  482, 488 Crystallographic R-factor  158 CuL  391 Cuprite  147, 152, 153 D D0a-ordered orthorhombic structure  87 D03-ordered phase  85 Dark  239, 268, 284, 314, 318, 320, 328, 356, 357, 358, 377, 440, 444, 446, 449, 458 Dark field (DF) holography  229 de Broglie wavelength  205 Deconvolution  162 filter  162 Defect-free region  53, 132, 147 Delocalization  32, 36, 206 Demagnification  10 DeskTop  500 Detective quantum efficiency (DQE)  162 Detector  381, 394, 468, 471, 472, 475, 476, 480, 492 Dielectric constant  7 Diffraction mode  136 pattern  27, 33, 103, 129, 188, 218

515

516

Index Diffractogram  188, 189, 218, 230, 311 Diffuse  284, 334, 337, 432 Diffuse scattering  145, 146, 158, 159, 162 Digital  384, 391, 462, 469, 472, 483 Digital Micrograph  22, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 183, 185, 187, 188, 189, 191, 192, 193, 194, 195 Dimensionless X-ray structure factors  151 Direct  267, 268, 271, 274, 276, 279, 280, 329 Discrete  348, 349 Disk of least confusion  12 Disordered A2 (bcc) structure  83, 85 Dopant distribution  227 Drift correction  24, 446 Dwell times  69 E Eigenvalues  331, 453 Eikonal equation  217 Einstein  322, 323, 326, 333 scattering  322, 323, 326, 333 Einstein model  159 scattering  159 Electrochemical impedance spectroscopy  41 Electrode materials  40, 59, 60 Electron  261, 378, 387, 427, 446, 472, 479, 487, 488 Electron dose  22, 26, 30, 46, 47, 60, 69, 70, 188, 224 Electronic phase transitions  29 Electron irradiation  33, 59, 69, 70, 71 Electropolishing  100 EMiSPEC  442 Emittance  2 Energy calibration  468 distribution  6, 152 Ensemble coherence  212 Environmental gas cell holder  37 Euler’s formula  187 Ewald  321, 322 Ewald sphere  88, 122, 146, 149, 150, 156 Exchange  408, 409, 421 Excitation error  149, 150, 156, 157, 158 Ex-situ analysis  20 Extinction  111, 112, 113, 119, 123, 127, 129, 140, 141, 142, 146, 147, 148, 151, 156, 158, 226 Extractor potential  5 F Fcc Cr-rich M23C6 carbide  93 Fcc NbC carbides  94 FEFF  417 Fermi  3, 9, 207, 227, 337, 407, 412, 414, 418

golden  412, 418 level  9, 227, 407 Fermions  3, 207 Ferritic Steels  96, 97 Field-enhancement factor  5, 9 Field ion microscopy (FIM)  83 Fienup (1982) algorithm  145, 161 First-order lattice spacing  160 First-order reflection  159 Fraunhofer diffraction  161, 203 Fresnel  56, 202, 203, 205, 218, 236, 351 contrast  351 fringes  202, 205 integral  56, 202 propagator  202 Full width at half maximum (FWHM)  3, 11, 211 G Galvanostatic hold  41, 59, 63 Gaussian broadening  485, 486, 490, 491 fit  468 focus  11, 302, 309, 380 image  248 image plane  11, 12 noise  153 orbitals  411 source  3, 11, 12, 14, 210, 305, 306, 307, 334 Global minima  148 Gold-plated titanium mirror  38 Goodness-of-fit index  148 Gottfried Möllenstedt  213, 230 G-phase  98, 99 Grain boundary, orientations  21 Grain growth  27, 93 Green  412, 416, 417 G-spacings  33 H Hairpin metals  26 Hamiltonian  273, 280, 407, 408, 409, 410, 416 Heating holders  41, 42, 43, 44, 45, 65 Heisenberg Uncertainty Principle  198, 206 Helmholtz equation  198, 199, 205 Hf  302, 304 Higher-order Laue zone (HOLZ)  105, 121, 124 High-speed electrostatic deflector  26 High temporal-resolution imaging  30 Holtsmark regime  7 Huygens’ principle  202, 213 Hysitron picoindenter  51 I Illumination  3, 19, 26, 27, 65, 127, 130, 131, 135, 147, 148, 149, 159, 160,

162, 211, 213, 216, 224, 225, 229, 230

Image calibration  178, 179, 180 display  171, 173, 174, 175, 177, 178, 179, 180 filter  162, 185, 187, 189, 191 noise  72, 162, 189, 191 plane  177, 189, 219 In  495 InAs  334 Incoherent  3, 82, 93, 94, 97, 101, 148, 163, 207, 208, 211, 212, 213, 216, 217, 219 Inelastic  36, 38, 64, 67, 132, 138, 149, 150, 159, 163, 211, 212, 217, 223, 224, 225, 226 interaction  211, 212 Infinite  312, 316 Information loss  178 Infrared imaging  35, 38 InGaN  226 Interference fringe  160 pattern  160, 207 Intermetallic  426, 428, 434, 482, 483, 501 International Technology Roadmap for Semiconductors (ITRS)  153 Inverse  468 Ion-beam deposition (IBD)  37 Iron jump-ratio image  174 Isoplanatic  210 J Jump-ratio image  174, 195 K Kinematic interaction  217 Kirchhoff diffraction integral  197, 199, 201, 202, 203 KLM  481, 482 Klug’s approach  46, 75 L LaAlO  327, 328 LaB  379 LaB6 electron source  27 Landau  394 Laser  4, 10, 19, 24, 25, 26, 27, 38, 51, 64, 65, 67, 207 Laws of wave optics  198 liquid-N2,  152, 162 Log of Modulus  177, 188 Longitudinal coherence  4 Lorentz  7, 55, 56, 226, 227, 314, 462 angular  314 force  55 lens  55, 226, 227 mode  55, 227 low  449

Index Low-loss  35 M Magnetic flux  55, 218, 230 Mass-thickness contrast  63 Mathematica™  3, 24, 170, 175, 176, 183, 185, 187, 188, 198, 200, 202, 210, 212, 213, 230 Matlab™  24 Maxwell  418 Mean-free path  36 Microdiffraction  81, 82, 85, 100, 146, 148, 159, 160, 163 Microelectromechanical systems (MEMS)  20, 29 Micromanipulators  50, 65 Minimum  485 Möllenstedt biprism  205, 220, 222, 230 Monochromators  3 Most  393 Mott formula  145, 152 Multipole expansion  148, 152 Multiva  456 N Nanoelectromechanical systems  56 Nanofactory STM holder  51 Nanoindentation  20, 49, 50, 51, 52, 53, 54, 55 Nanorods  67, 127, 329, 462 AG  462 growth of  67 Nanoscale loops  158 Neutron diffraction  148, 158, 163 Ni3Nb-type  87 NiAl  429 NiOx  468, 469, 470, 471, 472, 483, 484, 494 NiOxIceC  472, 473 NIST Standard Reference Data Base  156 Non  383, 384, 385, 391 Nylon gas tubes  39 O Object transmission function  201, 203 Ohmori  96, 98 Omega  379, 380 Omega (Ω) filter  147, 149, 152, 154, 158, 162 Optical imaging  160, 210 Optical pyrometry  41 Orthogonal  55, 119, 207, 217 Ostwald ripening  30, 39, 69 Oxygen plasma cleaning  35 ‘Oxygen-sponge’ crystals  157 P Pairwise  238, 239 Paraxial rays  161

Pauli  408 Pb  486, 487, 490 Peak  468, 480 Peak (X-ray characteristic)  67, 149, 158, 171 Peltier  470 Pencil-beam regime  7 Phase Contrast Transfer Function (PCTF)  204, 216, 218 Phase display  178 Phonon  149, 156, 158, 162, 163, 211 Photoelectric effect  198 Photo-emission effect  10 Piezo  24, 49, 50, 51, 53, 56, 58, 59, 64, 65, 104, 137, 226 Piezoelectric polarization  226 Pixon  331 Plane wave  148, 152, 162, 198, 199, 200, 201, 202, 203, 205, 213, 217 Plasma cleaning  35 Plasmon  41, 150, 158, 211 Point P  109, 147, 202, 208 Point Q  203 Point spread function (PSF)  7, 11, 204, 213, 216 Point-symmetric masks  185 Poisson  145, 148, 151, 157, 255, 381, 386, 452, 453, 454, 455, 456, 458, 477, 485 equation  148, 157, 255, 453 noise  381, 452, 453, 454, 456, 458, 477, 485 scaled  452, 456 statistics  145, 151, 381, 386, 452, 453, 455, 456, 485 weighted  452, 453 Pole-piece  18, 19, 29, 30, 31, 32, 33, 36, 37, 38, 43, 52, 53, 56, 65, 66, 67, 71, 73, 74, 227 Post mortem analysis  20, 49 Potential distribution  219, 227, 228, 230 Potentiostatic hold  41 Powder electron diffraction  156 Poynting vector  198 Practical coherence width  3 Pre  393 Precession method  123, 145, 157, 158 Princip  331, 454 Principal Components Analysis (PCA)  194 Probe current  12 size  11, 148 Probe-forming lens  12, 147, 148 Profile extraction tool  181, 182, 183, 193 Projection  344, 346, 347, 373 Protein monolayers  146 Protochips version  45 Pseudo-Contours  171 Pseudopotential  410, 413 Ptychography  145, 159, 160, 162, 163 Pythagoras  202

Q Quantitative convergent-beam method (QCBED)  146 Quantitative density map  151 Quasicrystals  288, 289, 327, 337 R Radial function  152 Radon  344, 345, 346, 347, 350, 373 Rate of evaporation  8 Rayleigh  293, 300 Reference wave  219, 220, 221, 222, 226, 229 Region-of-interest (ROI)  180, 181 Relative  394, 470, 472, 473 Relativistic electron velocity  217 Relativity-corrected acceleration voltage  3 Relrod  88, 123 Residual coherent aberrations  216 Residual gas analyzer (RGA)  32, 39 Reversible processes  25, 27 RGB values  175 Richardson equation  4 Riemann  346 Rietveld method  148, 163 Ring collapse  8 Rocking curve  146, 147, 148, 156, 157, 163 Ronchigrams  145, 154, 159, 160, 161, 163 Rose  485 Rutherford  284, 314, 315, 332, 337 S Sampling Theorem  170 Saxton  362 Scaling factor  174 Scanning  350 Scattered intensity  151 Scherzer  294, 297, 319 Schottky effect  4, 5, 13 emitter  13 Schrödinger  407, 408, 410, 411 Scintillator  22, 32, 162, 222 Secondary Ion Mass Spectroscopy (SIMS)  227 Segmentation  347, 348, 362, 369, 370, 371, 372 Selected area diffraction (SAD)  81, 111, 123, 128, 141, 147, 223 Shadow image  130, 131, 136, 154, 157, 159, 160, 161 Si  286, 288, 303, 308, 310, 312, 321, 326, 443, 468, 475, 480 Signal-to-noise (SNR) ratio  224, 225 Silicon (111) 7x7 surface reconstruction  22, 31, 33, 35, 36, 45, 60, 61, 75, 109, 134, 136, 137, 141, 146, 149, 155, 157 Simplex algorithm  145, 151 Simultaneous  347 SiN membranes  33, 34, 35, 38, 39, 40, 70

517

518

Index Slater  415 Sobel  383 Solid angle  2, 13, 210 Space-charge effects  26, 27 Sparrow  293 Spatial  238, 241, 242, 243, 244, 248, 249, 250, 252, 253, 254, 268, 270, 295, 305, 318, 319, 320, 325, 344, 346 Spatial coherence  4, 160, 205, 208, 210, 211, 212, 213, 224 Spatial frequency  162, 187, 188, 189, 195, 200, 201, 203, 205, 213, 216, 218, 219, 220 Spherical aberration  11, 12, 13, 132, 137, 159, 160, 161, 216, 218, 219, 227 Spherical charge density  152 Spherical harmonic function  152 Spinodal alloy  83, 101 Spinodal decomposition  83, 85, 98, 154 Static cells  40 Stereographic projection  100, 101, 113, 120 Stobbs  334 Strain mapping  145, 153 Superlattice  83, 84, 85, 87, 88, 101, 134 reflection  88 Surface oxide films  100 T Ta  432 Ta disk cathode  26 Temporal coherence  4, 211, 212, 219 Thermal-diffuse scattering  158, 159 Thermal energy  2 Thermal expansion  38, 42, 43, 54 Thermionic emitter  6, 7, 13, 25, 26 Thin-film elastic relaxation  154 Three  387, 388, 389 Total  378, 387, 446, 479, 487 Total electron dose  47 Transmission  350, 354, 377, 378, 379, 400 Transmission electron diffraction (TED)  146 Transmission electron microscopy (TEM)  120, 122 Transverse  316, 317, 320 Tungsten filament  43 Type 329 duplex stainless steel  98 U Ultrafast electron microscopes (UEM)  10 Ultra high vacuum (UHV)  18, 36 Uncertainty principle  4, 153, 198, 206 V Vacanc  429, 430, 432, 434 Vacancy  54, 69, 72, 158, 335 Vanadium-bearing steel  100 Varimax  455

Verwey transition  163 Virtual source  2, 6, 7, 8, 9, 10, 11, 12, 13, 14, 55, 148, 159, 160 Voxel  171 W Warren  322, 337 Wave amplitude  200, 201, 229 modulation  201, 216 properties  223 spherical  199 Wave transfer function  204, 216 Weight coefficient  150 Wet-etch methods  35 WIEN  411, 418, 421 X X-ray Bragg intensities  146, 157 X-ray crystallography  41, 113, 145, 146, 147 X-ray energy dispersive spectroscopy (XEDS)  35 spectroscopy  35 Y YAG scintillator  162 Young  292 Young’s fringes  160 Z ZAF  354 Z-contrast  160 high-angle scattering  160 Ze  321 Zeolite structures  157 Zernike phase  203, 218 Zero-field image-force potential  5 Zero-frequency  188 Zero-loss  149, 223 Zero-order Laue zone  105, 107, 112, 113, 114, 121, 123, 124, 126, 141, 150 Zero scattering angle  151 Zincblende structure  222, 223 ZOLZ intensity distribution  153