Springer Series in Optical Sciences Volume 36

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1 Springer Series in Optical Sciences Volume 36 Editor: Peter W. Hawkes Springer-Verlag Berlin Heidelberg GmbH

2 Springer Series in Optical Sciences Editorial Board: A. L. Schawlow A. E. Siegman T. Tamir Managing Editor: H. K. V. Latsch 42 Principles of Phase Conjugation By B. Ya. Zel'dovich, N. F. Pilipetsky, and V. V. Shkunov 43 X-Ray Microscopy Editors: G. Schmahl and D. Rudolph 44 Introduction to Laser Physics By K. Shimoda 2nd Edition 45 Scanning Electron Microscopy Physics of Image Formation and Microanalysis By L. Reimer 46 Holography and Deformation Analysis By W. Schumann, J.-P. Ziircher, and D. Cuche 4 7 Tunable Solid State Lasers Editors: P. Hammerling, A. B. Budgor, and A. Pinto 48 Integrated Optics Editors: H. P. Nolting and R. Ulrich 49 Laser Spectroscopy VII Editors: T. W. Hausch and Y. R. Shen 50 Laser-Induced Dynamic Gratings By H. J. Eichler, P. Giinter, and D. W. Pohl 51 Tunable Solid State Lasers for Remote Sensing Editors: R. L. Byer, E. K. Gustafson, and R. Trebino 52 Tunable Solid-State Lasers II Editors: A. B. Budgor, L. Esterowitz, and L. G. DeShazer 53 The CO, Laser By W. J. Witteman 54 Lasers, Spectroscopy and New Ideas A Tribute to Arthur L. Schawlow Editors: W. M. Yen and M.D. Levenson 55 Laser Spectroscopy VIII Editors: W. Persson and S. Svanberg 56 X-Ray Microscopy II Editors: D. Sayre, M. Howells, J. Kirz, and H. Rarback 57 Single-Mode Fibers Fundamentals By E.-G. Neumann 58 Photoacoustic and Photothermal Phenomena Editors: P. Hess and J. Pelzl 59 Photorefractive Crystals in Coherent Optical Systems By M.P. Petrov, S. I. Stepanov, and A. V. Khomenko 60 Holographic Interferometry in Experimental Mechanics By Yu. I. Ostrovsky, V. P. Shchepinov, and V. V. Yakovlev 61 Millimetre and Submillimetre Wavelength Lasers A Handbook of cw Measurements By N. G. Douglas 62 Photoacoustic and Photothermal Phenomena II Editors: J. C. Murphy, J. W. Maclachlan Spicer, L. C. Aamodt, and B. S. H. Royce 63 Electron Energy Loss Spectrometers The Technology of High Performance By H. Ibach 64 Handbook of Nonlinear Optical Crystals By V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan 2nd Edition 65 High-Power Dye Lasers Editor: F. J. Duarte 66 Silver Halide Recording Materials for Holography and Their Processing By H. I. Bjelkhagen 2nd Edition 67 X-Ray Microscopy III Editors: A. G. Michette, G. R. Morrison, and C. J. Buckley 68 Holographic Interferometry Principles and Methods Editor: P. K. Rastogi 69 Photoacoustic and Photothermal Phenomena III Editor: D. Bicanic 70 Electron Holography By A. Tonomura 71 Energy-Filtering Transmission Electron Microscopy Editor: L. Reimer Volumes 1-41 are listed at the end of the book

3 Ludwig Reimer Transmission Electron Microscopy Physics of Image Formation and Microanalysis Fourth Edition With 273 Figures

4 Professor Dr. LuDWIG REIMER Westfalische Wilhelms-Universitat Munster, Physikalisches Institut Wilhelm-Klemm-Strasse 10, D Munster, Germany Guest Editor: Dr. PETER W. HAWKES Laboratoire d'optique Electronique du CNRS, Bolte Postale No F Toulouse Cedex, France Editorial Board ARTHUR L. SCHAWLOW, Ph. D. Department of Physics, Stanford University Stanford, CA , USA ThEODOR TAMIR, Ph. D. Polytechnic University 333 Jay Street, Brooklyn, NY 11201, USA Professor ANTHONY E. SIEGMAN, Ph. D. Electrical Engineering E. L. Ginzton Laboratory, Stanford University Stanford, CA , USA Managing Editor: Dr.-Ing. HELMUT K.V. LOTSCH Springer-Verlag, Tiergartenstrasse 17, D Heidelberg, Germany Cataloging-in-Publication Data applied for Die Deutsche Bibliothek- CIP-Einheitsaufnahme Reimer, Ludwig: Transmission electron microscopy: physics of image formation and microanalysis I Ludwig Reimer ed. (Springer series in optical sciences; Vol.36) ISBN ISBN (ebook) DOI / ISSN ISBN This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 1984, 1989, 1993, 1997 Originally published by Springer-Verlag Berlin Heidelberg New York in 1997 Softcover reprint of the hardcover 4th edition 1997 The use of general descriptive names, registered names, trademarks, 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. Typesetting: Data conversion by Springer-Verlag SPIN / Printed on acid-free paper

5 Preface The aim of this monograph is to outline the physics of image formation, electron-specimen interactions and image interpretation in transmission electron microscopy. The preparation of this fourth edition has made it possible to update the text and the bibliography. Meanwhile a book on Energy Filtering Transmission Electron Microscopy has been published as Vol. 71 of the Springer Series in Optical Sciences. This rapidly growing method has therefore been kept brief, and special aspects of energy filtering are discussed together with their conventional counterparts. In the introductory chapter, the various electron-specimen interactions and their applications are summarized, the most important aspects of highresolution, analytical, high-voltage and energy-filtering electron microscopy are reviewed, and the different types of electron microscope are compared. The optics of electron lenses is discussed in Chap. 2 in order to bring out electron-lens properties that are important for an understanding of the modes of operation of an electron microscope. In Chap. 3, the wave optics of electrons and the phase shifts caused by electrostatic and magnetic fields are introduced; Fresnel electron diffraction is treated using Huygens' principle. The recognition that the Fraunhofer diffraction pattern is the Fourier transform of the wave amplitude behind a specimen is important because the influence of the imaging process on the transfer of spatial frequencies can be described by introducing phase shifts and wave aberrations in the Fourier plane. In Chap. 4, the elements of an electron-optical column are described: the electron gun, the condenser and imaging and recording system and equipment for electron energy-loss spectroscopy and energy filtering. A thorough understanding of electron-specimen interactions is essential to explain image contrast. Chapter 5 contains the most important facts about elastic, inelastic and multiple scattering. The origin of scattering and phase contrast of non-crystalline specimens, the introduction of contrast-transfer functions and the background of holographic and tomographic methods are described in Chap 6. Chapter 7 introduces the most important laws about crystals and reciprocal lattices. The kinematical and dynamical theories of electron diffraction are then developed and in Chap. 8 different modes and applications of electron diffraction are presented; convergent-beam electron diffraction ( CBED) is of increasing interest. Electron diffraction is also the

6 VI Preface source of diffraction contrast. This type of contrast is important for the imaging of crystalline specimens and their defects and for the high-resolution study of crystal structure, treated in Chap. 9. Methods of elemental analysis and the formation of images representing the distribution of chemical elements by x-ray microanalysis and electron energy-loss spectroscopy are summarized in Chap. 10. The final chapter contains a brief account of the various specimendamage processes caused by electron irradiation. The author thanks Dr. P.W. Hawkes for thorough correction of the manuscript and many helpful comments. Munster, January 1997 L. Reimer

7 Preface to the Third Edition The aim of this monograph is to outline the physics of image formation, electron-specimen interactions and image interpretation in transmission electron microscopy. The preparation of this third edition has made it possible to remove further blemishes from the first and second editions. A brief discussion of Schottky emission guns is included and a few new references are added. In the introductory chapter, the different types of electron microscope are compared, the various electron-specimen interactions and their applications are summarized and the most important aspects of high-resolution, analytical and high-voltage electron microscopy are discussed. The optics of electron lenses is discussed in Chap. 2 in order to bring out electron-lens properties that are important for an understanding of the functioning of an electron microscope. In Chap. 3, the wave optics of electrons and the phase shifts caused by electrostatic and magnetic fields are introduced; Fresnel electron diffraction is treated using Huygens' principle. The recognition that the Fraunhofer diffraction pattern is the Fourier transform of the wave amplitude behind a specimen is important because the influence of the imaging process on the contrast transfer of spatial frequencies can be described by introducing phase shifts and envelopes in the Fourier plane. In Chap. 4, the elements of an electron-optical column are described: the electron gun, the condenser and the imaging system. A thorough understanding of electron--specimen interactions is essential to explain image contrast. Chapter 5 contains the most important facts about elastic and inelastic scattering and x-ray production. The origin of scattering and phase contrast of non-crystalline specimens is described in Chap. 6. Highresolution image formation using phase contrast may need to be completed by image-reconstruction methods in which the influence of partial spatial and temporal coherence is considered. Chapter 7 introduces the most important laws about crystals and reciprocal lattices. The kinematical and dynamical theories of electron diffraction are then developed. Electron diffraction is the source of diffraction contrast, which is important for the imaging of lattice structure and defects and is treated in Chap. 8. Extensions of the capabilities of the instrument have awakened great interest in analytical electron microscopy: x-ray microanaly-

8 VIII Preface to the Third Edition sis, electron energy-loss spectroscopy and electron diffraction, summarized in Chap. 9. The final chapter contains a brief account of the various specimendamage processes caused by electron irradiation. Electron microscopy is an interdisciplinary science with a strong physical background. The full use of all its resources and the interpretation of the results requires familiarity with many branches of knowledge. Physicists are in a favourable position because they are trained to reduce complex observations to simpler models and to use mathematics for formulating "theories". There is thus a need for a book that expresses the contents of these theories in language accessible to the "normal" electron microscope user. However, so widespread is the use of electron microscopy that there is no such person as a normal user. Biologists will need only a simplified account of the theory of scattering and phase contrast and of analytical methods, whereas electron diffraction and diffraction contrast used by material scientists lose some of their power if they are not presented on a higher mathematical level. Some articles in recent series on electron microscopy have tried to bridge this gap by over-simplification but this can cause misunderstandings of just the kind that the authors wished to avoid. In the face of this dilemma, the author decided to write a book in his own physical language with the hope that it will be a guide to a deeper understanding of the physical background of electron microscopy. A monograph by a single author has the advantage that technical terms are used consistently and that cross-referencing is straightforward. This is rarely the case in books consisting of review articles written by different specialists. Conversely, the author of a monograph is likely to concentrate, perhaps unconsciously, on some topics at the expense of others but this also occurs in multi-author works and reviews. Not every problem can be treated in a limited number of pages and the art of writing such a book consists of selecting topics to omit. I apologize in advance to any readers whose favourite subjects are not treated in sufficient detail. The number of electron micrographs has been kept to a minimum; the numerous simple line drawings seem better suited to the more theoretical approach adopted here. There is a tendency for transmission electron microscopy and scanning electron microscopy to diverge, despite their common physical background. Electron microscopy is not divided into these categories in the present book but because transmission and scanning electron microscopy together would increase its size unreasonably, only the physics of the transmission electron microscope is considered - the physics of its scanning counterpart has been examined in Vol. 45 of Springer Series in Optical Sciences. A special acknowledgement is due top. W. Hawkes for his cooperation in revising the English text and for many helpful comments. Special thanks go to K. Brinkmann and Mrs. R. Dingerdissen for preparing the figures and to all colleagues who gave me permission to publish their results. Munster, July 1993 L. Reimer

9 Table of Contents 1. Introduction Transmission Electron Microscopy Conventional Transmission Electron Microscopy High-Resolution Electron Microscopy Analytical Electron Microscopy Energy-Filtering Electron Microscopy High Voltage Electron Microscopy Dedicated Scanning Transmission Electron Microscopy Alternative Types of Electron Microscopy Emission Electron Microscopy Reflection Electron Microscopy Mirror Electron Microscopy Scanning Electron Microscopy X-Ray and Auger-Electron Microanalysis Scanning Probe Microscopy Particle Optics of Electrons Acceleration and Deflection of Electrons Relativistic Mechanics of Electron Acceleration Deflection by Magnetic and Electric Fields Electron Lenses Electron Trajectories in a Magnetic Lens Field Optics of an Electron Lens with a Bell-Shaped Field Special Electron Lenses Lens Aberrations Classification of Lens Aberrations Spherical Aberration Astigmatism and Field Curvature Distortion Coma Anisotropic Aberrations Chromatic Aberration Correction of Aberrations and Microscope Alignment Correction of Astigmatism

10 X Table of Contents Correction of Spherical and Chromatic Aberrations Microscope Alignment Wave Optics of Electrons Electron Waves and Phase Shifts de Broglie Waves Probability Density and Wave Packets Electron-Optical Refractive Index and the Schrodinger Equation Electron Interferometry and Coherence Phase Shift by Magnetic Fields Fresnel and Fraunhofer Diffraction Huygens' Principle and Fresnel Diffraction Fresnel Fringes Fraunhofer Diffraction Mathematics of Fourier Transforms Wave-Optical Formulation of Imaging Wave Aberration of an Electron Lens Wave-Optical Theory of Imaging Elements of a Transmission Electron Microscope Electron Guns Physics of Electron Emission Energy Spread Gun Brightness Thermionic Electron Guns Schottky Emission Guns Field-Emission Guns The Illumination System of a TEM Condenser Lens System Electron-Probe Formation Illumination with an Objective Prefield Lens Specimens Useful Specimen Thickness Specimen Mounting Specimen Manipulation The Imaging System of a TEM Objective Lens Imaging Modes of a TEM Magnification and Calibration Depth of Image and Depth of Focus Scanning Transmission Electron Microscopy (STEM) Scanning Transmission Mode of TEM Dedicated STEM Theorem of Reciprocity

11 Table of Contents XI 4.6 Electron Spectrometers and Filter Lenses Post-column Prism Spectrometer Other Types of Spectrometers Imaging Energy-Filter Operating Modes with Energy Filtering Image Recording and Electron Detection Fluorescent Screens Photographic Emulsions Imaging Plate Detector Noise and Detection Quantum Efficiency Low-Light-Level and Charge-Coupled Device ( CCD) Cameras Semiconductor and Scintillation Detectors Faraday Cages Electron-Specimen Interactions Elastic Scattering Cross-Section and Mean Free Path Energy Thansfer in an Electron-Nucleus Collision Elastic Differential Cross-Section for Small-Angle Scattering Total Elastic Cross-Section Inelastic Scattering Electron Specimen Interactions with Energy Loss Differential Cross-Section for Single Electron Excitation Bethe Surface and Compton Scattering Approximation for the Total Inelastic Cross-Section Dielectric Theory and Plasmon Losses in Solids Surface Plasmon Losses Energy Losses by Inner-Shell Ionization Position and Shape of Ionization Edges Inner-Shell Ionization Cross-Sections Energy-Loss Near-Edge Structure (ELNES) Extended Energy-Loss Fine Structure (EXELFS) Multiple Scattering Effects Angular Distribution of Scattered Electrons Energy Distribution of Thansmitted Electrons Electron-Probe Broadening by Multiple Scattering Electron Diffusion, Backscattering and Secondary-Electron Emission

12 XII Table of Contents 6. Scattering and Phase Contrast for Amorphous Specimens Scattering Contrast Transmission in the Bright-Field Mode Dark-Field Mode Examples of Scattering Contrast Improvement of Scattering Contrast by Energy Filtering Scattering Contrast in the STEM Mode Measurement of Mass-Thickness and Total Mass Phase Contrast The Origin of Phase Contrast Defocusing Phase Contrast of Supporting Films Examples of Phase Contrast Theoretical Methods for Calculating Phase Contrast Imaging of a Scattering Point Object Relation Between Phase and Scattering Contrast Imaging of Single Atoms Imaging of Single Atoms in TEM Imaging of Single Atoms in the STEM Mode Contrast-Transfer Function ( CTF) The CTF for Amplitude and Phase Specimens Influence of Energy Spread and Illumination Aperture The CTF for Tilted-Beam and Hollow-Cone Illumination Contrast Transfer in STEM Phase C<5ntrast by Inelastically Scattered Electrons Improvement of the CTF Inside the Microscope Control of the CTF by Optical or Digital Fourier Transform Electron Holography Fresnel and Fraunhofer In-Line Holography Single-Sideband Holography Off-Axis Holography Reconstruction of Off-Axis Holograms Image Restoration and Specimen Reconstruction General Aspects Methods of Optical Analogue Filtering Digital Image Restoration Alignment by Cross-Correlation Averaging of Periodic and Aperiodic Structures Three-Dimensional Reconstruction Stereometry Electron Tomography

13 Table of Contents XIII 6.8 Lorentz Microscopy Lorentz Microscopy and Fresnel Diffraction Imaging Modes of Lorentz Microscopy Imaging of Electrostatic Specimen Fields Theory of Electron Diffraction Fundamentals of Crystallography Bravais Lattice and Lattice Planes The Reciprocal Lattice Construction of Laue Zones Kinematical Theory of Electron Diffraction Bragg Condition and Ewald Sphere Structure Amplitude and Lattice Amplitude Column Approximation Dynamical Theory of Electron Diffraction Limitations of the Kinematical Theory Formulation of the Dynamical Theory as a System of Differential Equations Formulation of the Dynamical Theory as an Eigenvalue Problem Discussion of the Two-Beam Case Dynamical Theory Including Absorption Inelastic-Scattering Processes in Crystals Absorption of the Bloch-Wave Field Dynamical n-beam Theory The Bethe Dynamical Potential and the Critical Voltage Effect Intensity Distribution in Diffraction Patterns Diffraction at Amorphous Specimens Intensity of Debye-Scherrer Rings Influence of Thermal Diffuse Scattering Kikuchi Lines and Bands Electron-Spectroscopic Diffraction Electron Diffraction Modes and Applications Electron Diffraction Modes Selected-Area Electron Diffraction (SAED) Electron Diffraction Using a Rocking Beam Electron Diffraction Using a Stationary Electron Probe Electron Diffraction Using a Rocking Electron Probe Further Diffraction Modes in TEM Some Uses of Diffraction Patterns with Bragg Reflections Lattice-Plane Spacings Texture Diagrams

14 XIV Table of Contents Crystal Structure Crystal Orientation Examples of Extra Spots and Streaks Convergent-Beam Electron Diffraction (CBED) Determination of Point and Space Groups Determination of Foil Thickness Charge Density Distributions High-Order Laue Zone (HOLZ) Patterns HOLZ Lines Large-Angle CBED Imaging of Crystalline Specimens and Their Defects Diffraction Contrast of Crystals Free of Defects Edge and Bend Contours Dark-Field Imaging Moire Fringes The STEM Mode and Multi-Beam Imaging Energy Filtering of Diffraction Contrast Transmission of Crystalline Specimens Calculation of Diffraction Contrast of Lattice Defects Kinematical Theory and the Howie-Whelan Equations Matrix-Multiplication Method Bloch-Wave Method Planar Lattice Faults Kinematical Theory of Stacking-Fault Contrast Dynamical Theory of Stacking-Fault Contrast Antiphase and Other Boundaries Dislocations Kinematical Theory of Dislocation Contrast Dynamical Effects in Dislocation Images Weak-Beam Imaging Determination of the Burgers Vector Lattice Defects of Small Dimensions Coherent and Incoherent Precipitates Defect Clusters High-Resolution Electron Microscopy (HREM) of Crystals Lattice-Plane Fringes General Aspects of Crystal-Structure Imaging Methods for Calculating Lattice-Image Contrast Simulation, Matching and Reconstruction of Crystal Images Measurement of Atomic Displacements in HREM Crystal Structure Imaging with a STEM

15 Table of Contents XV 9. 7 Imaging of Atomic Surface Steps and Structures Imaging of Surface Steps in Transmission Reflection Electron Microscopy Surface-Profile Imaging Elemental Analysis by X-Ray and Electron Energy-Loss Spectroscopy X-Ray and Auger-Electron Emission X-Ray Continuum Characteristic X-Ray and Auger-Electron Emission X-Ray Microanalysis in a TEM Wavelength-Dispersive Spectrometry Energy-Dispersive Spectrometry X-Ray Emission from Bulk Specimens and ZAF Correction X-Ray Microanalysis of Thin Specimens X-Ray Microanalysis of Organic Specimens Electron Energy-Loss Spectroscopy... : Recording of Electron Energy-Loss Spectra Kramers-Kronig Relation Background Fitting and Subtraction Deconvolution Elemental Analysis by Inner-Shell Ionizations Element Distribution Images Elemental Mapping by X-Rays Element Distribution Images Formed by Electron Spectroscopic Imaging Three-Window Method White-Line Method Correction of Scattering Contrast Limitations of Elemental Analysis Specimen Thickness Radiation Damage and Loss of Elements Counting Statistics and Sensitivity Spatial Resolution Specimen Damage by Electron Irradiation Specimen Heating Methods of Measuring Specimen Temperature Generation of Heat by Electron Irradiation Calculation of Specimen Temperature Radiation Damage of Organic Specimens Elementary Damage Processes in Organic Specimens Quantitative Methods of Measuring Damage Effects.. 474

16 XVI Table of Contents Methods of Reducing Radiation Damage Radiation Damage and High Resolution Radiation Damage of Inorganic Specimens Damage by Electron Excitation Radiation Damage by Knock-On Collisions Contamination Origin and Sources of Contamination Methods for Decreasing Contamination Dependence of Contamination on Irradiation Conditions References Index

Transmission Electron Microscopy

L. Reimer H. Kohl Transmission Electron Microscopy Physics of Image Formation Fifth Edition el Springer Contents 1 Introduction... 1 1.1 Transmission Electron Microscopy... 1 1.1.1 Conventional Transmission