Analytical Transmission Electron Microscopy

Jürgen Thomas • Thomas Gemming

Analytical Transmission Electron MicroscopyAn Introduction for Operators

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This book is the revised and slightly expanded translation of the German book edition by Jürgen Thomas and Thomas Gemming: “Analytische Transmissionselektronenmikroskopie—Eine Einführung für den Praktiker”, Springer-Verlag, Wien 2013, ISBN 978-3-7091-1439-1.

ISBN 978-94-017-8600-3 ISBN 978-94-017-8601-0 (eBook)DOI 10.1007/978-94-017-8601-0Springer Dordrecht Heidelberg New York London

Library of Congress Control Number: 2014932544

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Jürgen ThomasLeibniz Institute for Solid State and Materials Research (IFW) DresdenGermany

Thomas GemmingLeibniz Institute for Solid State and Materials Research (IFW) DresdenGermany

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Preface

What is the goal of a transmission electron microscope (TEM)? It is expensive and causes large running costs. The understanding of the results is sometimes difficult and they can be wrongly interpreted. It needs specialists and, connected with that, causes additional labour costs.

On the other hand, it is a microscope, i.e. its results are magnified pictures and everybody is able to understand pictures. Apparently, there are no problems under-standing them. Why do we need an additional textbook about this topic?

Goethe: „Mikroskope und Fernrohre verwirren eigentlich den reinen Men-schensinn.“ [1] (Microscopes and telescopes confuse the human mind.)

However, analytical transmission electron microscopy does not only include the microscopic imaging. Electron diffraction and compositional analysis by spectrom-eters for X-rays and energy losses of the electrons complement it. The analytical transmission electron microscope covers four challenging methods: electron micro-scopic imaging, electron diffraction, analysis of characteristic X-rays, and electron energy loss spectroscopy. There are specialists for each of these methods; neverthe-less the operator at the microscope should hold an overview about the possibilities of analytical transmission electron microscopy. He should be able to handle them and should be familiar with the basics of the interpretation of the measured results.

It is the goal of this textbook to give such an overview. The idea to write this book was arising during the work in our electron microscopic laboratory of the Leibniz Institute for Solid State and Materials Research (IFW) Dresden. While teaching the students of materials science in lectures and practical courses about analytical trans-mission electron microscopy as well as while instructing graduate students, Ph.D. students, and technicians at the microscope we have attained experiences regarding frequently asked questions by the beginners and the didactical procedure to explain the function and the practical handling of a transmission electron microscope.

These experiences are integrated in this book. It addresses people who want or have to work at a transmission electron microscope and have not yet a further knowledge about this topic. The book should also be helpful for service engineers to ensure an overview of the basic knowledge about the microscopes maintained by them. Additionally, the book should be also a little bit amusing to receive interest in electron microscopy from non-experts, too.

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The focus lies on explanations with the help of simple models and on hints for the practical electron microscopic work. The headlines of the chapters already indicate this matter. This is the difference to other introductions into electron microscopy. As far as practicable, we tried to avoid explanations based only on mathematical formalisms.

In this context we would like to give a comment on the model assumptions in physics: On the one hand, we speak about electrons as particles, on the other hand as waves. Or the position of the specimen within the electron microscope: Sometimes we draw the specimen outside of the objective lens, sometimes within the magnetic field of the lens. One or two of the readers will see a discrepancy here. However, it is not a discrepancy but a property of models in physics suitable to explain special features in nature. Dependent on the experimental setup we observe sometimes the particle and otherwise the wave character of the electrons. Or: To explain the multi-stage imaging of the electron microscope we draw the specimen outside of the mag-netic field since the beam path within the lens does not play any role in this case. Only the beam path outside of the lens is important. On the other hand, when we discuss the imaging of magnetic samples the direct interaction between the sample and the magnetic lens field is essential and we have to use another model. In other words: The physical models used in this book are chosen to be as simple as possible to explain a specific outcome.

Despite the attempt of plausible explanations some correlations can be better understood with the help of mathematics. Formulas are necessary to obtain quanti-tative values. Especially the last chapter 10 considers this. There are some special basics explained in more detail, where it is applicable we point to such detailed explanations within the text. Here and there equations are also listed in the ear-lier chapters containing elements of the infinitesimal mathematics like differentials and integrals. Describing definitions and physical basics sometimes it is absolutely necessary. This should be no reason to stop reading the book even if the reader has problems with this kind of mathematics.

For specialists the chapter 10 cannot substitute textbooks about special topics of electron microscopy. We suggest some of such books in the hints for further reading at the end of this book.

Finally, we would like to thank: our academic teachers, friends and colleagues who introduced us into the topics of electron microscopy or had facilitated the work at modern instruments later on. Some names we would like to mention: Prof. Alfred Recknagel, Dr. Hans-Dietrich Bauer, and Prof. Klaus Wetzig in Dresden as well as Prof. Manfred Rühle, Prof. Frank Ernst, Dr. Günter Möbus, and Prof. Joachim Mayer working at the “Max-Planck-Institut für Metallforschung” in Stuttgart in the relevant time.

Electron microscopic investigations are only possible using suitably prepared thin samples. Many of the electron microscopic images could be only presented in this book because of the careful specimen preparation by Dipl.-Ing. (FH) Birgit Arnold and Dina Lohse.

In an early state of our book project we spoke with Prof. Josef Zweck from Regensburg and Prof. Klaus Wetzig from Dresden about our concept. They had

viiPreface

encouraged us in our project and contributed by their advocacy essentially to the publication of the book by the Springer Verlag.

Stephen Soehnlen B.S., Wil Bruins, and Annelies Kersbergen were our nego-tiants of the Springer Verlag in Dordrecht. Without their benignity this book had not been published.

Nora Thomas M.A. was so kind to help us finding Goethe’s citations with her special knowledge.

We are indebted to the persons mentioned here, as well as to those electron mi-croscopists from Dresden who had been reading the German book manuscript or parts of it, as well as this English version later on, and gave helpful hints for its improvement but also to the colleagues, friends, and students who inspired us by questions and comments to think about facts and circumstances which seemed to be “completely clear”.

Goethe: „Alles Gescheite ist schon mal gedacht worden, man muß nur ver-suchen, es noch einmal zu denken.“ [2] (All the prudent things have been already thought. One just has to try to think about them once more.)

Dresden October 2013 Jürgen ThomasThomas Gemming

References

1. von Goethe, J. W.: Wilhelm Meisters Wanderjahre, ed. Erich Trunz, Goethes Werke—Hamburger Ausgabe Bd. 8, Romane und Novellen III, 12. Aufl. München, II/Betrachtungen im Sinne der Wanderer (1989), p. 293

2. von Goethe, J. W.: ibidem, p. 283

Common remark: Biographic Data: Wikipedia—the free encyclopedia, http://de.wikipedia.org/wiki/Wikipedia

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Contents

1 Why Such an Effort? ............................................................................... 11.1 The Problem with the Magnification ................................................ 11.2 The Limitation of Resolution ............................................................ 21.3 Electron Waves .................................................................................. 61.4 The Role of Magnification ................................................................ 8

2 What Should we Know about Electron Optics and the Construction of an Electron Microscope? ............................................. 112.1 The Principle of Multistage Imaging ................................................ 112.2 Rotational-Symmetric Magnetic Fields as Electron Lenses ............. 122.3 Lens Aberrations ............................................................................... 152.4 Resolution Limit Considering the Spherical Aberration ................... 192.5 Electron Gun ..................................................................................... 202.6 “Richtstrahlwert” (Brightness) .......................................................... 242.7 We Construct an Electron Microscope .............................................. 27

2.7.1 Illumination System .............................................................. 272.7.2 Imaging System .................................................................... 292.7.3 Specimen Stage ..................................................................... 302.7.4 Acquiring the Images ............................................................ 322.7.5 Vacuum System..................................................................... 342.7.6 Miscellaneous ....................................................................... 37

References .................................................................................................. 39

3 We Prepare Electron-Transparent Samples .......................................... 413.1 What is the Challenge? ...................................................................... 413.2 “Classical” Methods .......................................................................... 433.3 Cutting, Grinding, and Ion Milling ................................................... 473.4 Focussed Ion Beam (“FIB”) Techniques ........................................... 51References .................................................................................................. 56

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4 Let us Start with Practical Microscopy.................................................. 574.1 What do We Peripherally Need? ....................................................... 584.2 We Put the Specimen into the Holder and Insert

it into the Microscope ........................................................................ 594.3 We Check the (alignment) State of the Microscope .......................... 614.4 Focussing the Image—Sharpness and Contrast ................................ 694.5 Contamination and Sample Damaging .............................................. 70References .................................................................................................. 73

5 Let us Switch to Electron Diffraction ..................................................... 755.1 Why Diffraction Reflections? ........................................................... 755.2 Crystal Lattices and Lattice Planes ................................................... 785.3 Selected Area and Convergent Beam Electron Diffraction ............... 845.4 What Can We Learn from Selected Area Diffraction Patterns? ........ 90

5.4.1 Radii in Ring Diagrams ........................................................ 905.4.2 Rules for Forbidden Reflections ........................................... 935.4.3 Intensities of the Diffraction Reflections .............................. 985.4.4 Positions of Diffraction Reflections in Point Diagrams ....... 995.4.5 Indexing of Diffraction Reflections ...................................... 103

5.5 Kikuchi- and HOLZ-lines ................................................................. 1065.6 Amorphous Samples.......................................................................... 110References .................................................................................................. 112

6 Why Do We See Any Contrast in the Images? ...................................... 1156.1 Elastic Scattering of Electrons Within the Sample ........................... 1156.2 Mass Thickness and Diffraction Contrast ......................................... 1166.3 Brightfield and Darkfield Imaging .................................................... 1206.4 Bending Contours, Dislocations, and Semicoherent Particles .......... 1236.5 Thickness Contours, Stacking Faults, and Twins .............................. 1286.6 Moiré Patterns ................................................................................... 1326.7 Magnetic Domains: Lorentz Microscopy .......................................... 133References .................................................................................................. 136

7 We Increase the Magnification ............................................................... 1377.1 Imaging of Atomic Columns in Crystals: Phase Contrast ................. 1377.2 Contrast Transfer by the Objective Lens ........................................... 1427.3 Wave-optical Interpretation of the Resolution Limit ........................ 1457.4 Periodic Distribution of Brightness in Pictures: Fourier Analysis .... 1477.5 Mass Thickness and Phase Contrast.................................................. 1507.6 Contrast of Amorphous Samples ....................................................... 1527.7 Correction of Astigmatism ................................................................ 1547.8 Measurement of the Resolution Limit ............................................... 1567.9 Correction of Spherical and Chromatic Aberration .......................... 1587.10 Interpretation of High Resolution TEM Images ............................. 161References .................................................................................................. 162

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8 Let Us Switch to Scanning Transmission Electron Microscopy .......... 1638.1 What Happens Electron-Optically? ................................................... 1638.2 Resolution or: What is the Smallest Diameter of the Electron Probe? ......................................................................... 1658.3 Contrast in the Scanning Transmission Electron Microscopic Image ............................................................... 1708.4 Speciality: High Angle Annular Darkfield Detector ........................... 173References .................................................................................................... 174

9 Let us Use the Analytical Possibilities ...................................................... 1779.1 Analytical Signals by Inelastic Interaction ......................................... 177

9.1.1 Emission of X-rays ................................................................. 1789.1.2 Electron Energy Losses .......................................................... 182

9.2 Energy Dispersive Spectroscopy of Characteristic X-rays (“EDXS”) .................................................................................. 185

9.2.1 X-ray Spectrometers and Spectra ........................................... 1869.2.2 Qualitative Interpretation of X-ray Spectra ............................ 1909.2.3 Quantifying X-ray Spectra ...................................................... 1949.2.4 Line Profiles and Elemental Mappings ................................... 202

9.3 Electron Energy Loss Spectroscopy (“EELS”) ..................................... 2049.3.1 Electron Energy Spectrometer ................................................ 2059.3.2 Low-Loss and Core-Loss Regions of the Spectra .................. 2069.3.3 Qualitative Elemental Analysis ............................................... 2099.3.4 Background and Multiple Scattering: Requirements

to the Sample .......................................................................... 2109.3.5 Measurement of the Specimen Thickness .............................. 2139.3.6 Edge Fine Structure: Bonding Analysis .................................. 2169.3.7 Quantifying Energy Loss Spectra ........................................... 219

9.4 Energy Filtered Imaging...................................................................... 2219.5 Comparison Between EDXS and EELS ............................................. 224References .................................................................................................... 225

10 Basics Explained in More Detail (with a Bit More Mathematics) ....... 22710.1 Diffraction at an Edge (Huygens’ Principle) ................................... 22710.2 Wave Function for Electrons ........................................................... 22810.3 Electron Wavelength Relativistically Calculated ............................ 23310.4 Electron Beam Paths in Rotational-Symmetric Magnetic Fields .... 23410.5 Resolution Limit Considering Spherical Aberration ....................... 24310.6 Schottky Effect ................................................................................ 24410.7 Electric Potential in Rotational-Symmetric Arrangements

of Electrodes .................................................................................... 24710.8 Laue Equations and Reciprocal Lattice, Ewald Construction ......... 24910.9 Kinematical Model: Lattice Factor and Structure Factor ................ 26110.10 Debye Scattering ........................................................................... 26810.11 Electrons Within a Field of a Central Force .................................. 272

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10.12 Mean Free Path for Elastic Scattering ........................................... 27710.13 Distances in Moiré Patterns ........................................................... 27910.14 Contrast Transfer Function ............................................................ 28210.15 Scherzer Focus .............................................................................. 29010.16 Delocalisation ................................................................................ 29410.17 Potential in Electrostatic Multipoles ............................................. 29710.18 Electron Probe and Aberrations ..................................................... 29910.19 Classical Inelastic Collision .......................................................... 30610.20 Efficiency of Energy Dispersive X-ray Detectors ......................... 30710.21 Calculation of Cliff-Lorimer k-factors .......................................... 31310.22 Correction of Absorption for EDXS .............................................. 31810.23 Prisms for Electrons ...................................................................... 32010.24 Convolution of Functions .............................................................. 324References .................................................................................................. 327

Summary and Outlook .................................................................................... 329

Physical Constants ........................................................................................... 331

Hints for Further Reading .............................................................................. 333

Index .................................................................................................................. 335

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Abbreviations

ΔE energy spreadΔf defocusΔfA astigmatic difference of the focal lengthsʌ mean free pathα diffraction angle, aperture, angle between unit cell axesβ illumination aperture, angle between unit cell axes, acceptance angleγ angle between unit cell axesδ resolution limit, distance between slitsδC radius of the chromatic aberration diskδD radius of the diffraction disk, delocalisationδS radius of the spherical aberration diskθ Bragg angleλ wavelength, mean free path(μ/ρ) attenuation (or absorption) coefficient for X-raysν frequencyΦ (crystal) potentialϕ phase, phase shiftρ densityσ visual angle, cross section of scatteringφ angle, azimuth in polar and cylindrical coordinatesΨ magnetic potentialψ wave functionΩ solid angleω radial frequency, fluorescence yieldA areaAM image ratioa exponent, fraction of the Kα X-ray peak, accelerationa1,a2,a3 lattice vectorsb1,b2,b3 reciprocal lattice vectorsB magnetic inductionb Burgers vectorb image distance

xiv Abbreviations

C general constantCBED Convergent Beam Electron DiffractionCC coefficient of chromatic aberrationCS coefficient of spherical aberrationCTF Contrast Transfer Functionc concentrationD dispersion, damping functionDeff detector efficiencyd, dhkl lattice spacing, generally: distanceE energy, electric field strengthE0 primary electron energyEP plasmon energyEDXS Energy Dispersive X-ray SpectroscopyEELS Electron Energy Loss SpectroscopyELNES Energy Loss Near Edge Fine StructureEXELFS Extended Energy Loss Fine Structuref focal lengthF forceFIB Focussed Ion BeamFhkl structure factorG lattice factorg object distanceI electric current, intensityH brightnessHAADF High Angle Annular DarkFieldhkl Miller’s indicesHOLZ High Order Laue ZoneHRTEM High Resolution Transmission Electron Microscopyi imaginary unit, integer numberj, j current density, total momentum quantum number, integer numberk wave number vectorkAB Cliff-Lorimer k-factorL camera lengthl orbital quantum numberM magnification, integer numberMr atomic or molecular weight, respectivelym magnetic quantum numberm, m0 massN integer numbern refractive index, principal quantum number, integer numberNBED Nano Beam Electron Diffractionp momentum, pressurePED Precessing Electron DiffractionQ ionisation cross section (probability), electric chargeq space frequency

xvAbbreviations

R richtstrahlwert (brightness)r radius (also in polar and cylindrical coordinates)S, S definite viewing range, refractive power, parameter of agreements scattering vector, spin quantum numbers, sopt path, way, length, optical pathSAED Selected Area Electron DiffractionSDD Silicon Drift DetectorSTEM Scanning Transmission Electron MicroscopyT period of oscillation, absolute temperatureTEM Transmission Electron MicroscopyTW windows transparency for X-raysU electric potential, voltage, backgroundU0 acceleration voltageUOV overvoltage ratiov velocityVUC volume of a unit cellW work, potential energyWA work functionWAcc acceleration workWDXS Wavelength Dispersive X-ray SpectroscopyWP potential energyx local coordinatey object size, local coordinateyD delocalisationy’ image sizeZ atomic number, general: integer numberz local coordinate (also in cylindrical coordinates), optical axis

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About the Authors

Jürgen Thomas (born in 1948) studied physics at the TU Dresden from 1966 to 1971. In 1970 he had the first contact with electron microscopy and received finally his diploma and doctoral degree on topics of electron microscopy and electron-solid-interactions under supervision of Prof. Alfred Recknagel in Dresden. Between 1978 and 1989 he was responsible for the development of technologies for elec-tron-beam welding and vacuum drying in the industrial research. In 1990 he went back to the electron microscopy and joined the Leibniz Institute for Solid State and Materials Research (IFW) Dresden where he has been working in the laboratory for analytical transmission electron microscopy until today.

Thomas Gemming (born in 1969) studied physics at the University Karlsruhe from 1988 to 1994. He received his doctoral degree on high-resolution transmission electron microscopy in the group of Prof. Manfred Rühle at the Max-Planck-Institut für Metallforschung in Stuttgart in 1998. Afterwards he expanded his field of work to analytical transmission electron microscopy. In 2000 he moved to the Leibniz Institute for Solid State and Materials Research (IFW Dresden) where he is cur-rently working as a department head for Micro- and Nanostructures. Additionally he is currently the executive secretary of the German Society for Electron Micros-copy (DGE).