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L. Reimer H. Kohl
Transmission Electron
Microscopy
Physics of Image Formation
Fifth Edition
123
†Prof. Dr.L.Reimer
Prof.Dr.H.Kohl
Univ. Mu¨nster
PhysikalischesInstitut
Wilhelm-Klemm-Str. 10
48149 Mu¨nster
Germany
E-mail: [email protected]
ISBN: 978-0-387-40093-8 e-ISBN: 978-0-387-34758-5
DOI:10.1007/978-0-387-34758-5
Library of Congress Control Number: 2008933458
©2008 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written
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Preface to the Fifth Edition
The aim of this monograph is to outline the physics of image formation,
electron–specimeninteractions,andimageinterpretationintransmissionelec-
tron microscopy. Since the last edition, transmission electron microscopy has
undergone a rapid evolution. The introduction of monochromators and im-
proved energy filters has allowed electron energy-loss spectra with an energy
resolution down to about 0.1 eV to be obtained, and aberration correctors
are now available that push the point-to-point resolution limit down below
0.1 nm.
After the untimely death of Ludwig Reimer, Dr. Koelsch from Springer-
Verlag asked me if I would be willing to prepare a new edition of the book.
As it had served me as a reference for more than 20 years, I agreed without
hesitation. Distinct from more specialized books on specific topics and from
books intended for classroom teaching, the Reimer book starts with the basic
principles and gives a broad survey of the state-of-the-art methods, comple-
mented by a list of references to allow the reader to find further details in the
literature. The main objective of this revised edition was therefore to include
the new developments but leave the character of the book intact.
The presentation of the material follows the format of the previous edi-
tion as outlined in the preface to that volume, which immediately follows.
A few derivations have been modified to correspond more closely to modern
textbooks on quantum mechanics, scattering theory, or solid state physics.
AspecialacknowledgementisduetoM.Silderforpreparingthenewfigures
and helping with TeX and to all colleagues who gave permission to publish
their results.
Mu¨nster, May 2007 H. Kohl
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, the book
Energy-Filtering Transmission Electron Microscopy has been published as
Vol.71 of the Springer Series in Optical Sciences. Discussion of 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 high-
resolution, analytical, high-voltage, and energy-filtering electron microscopy
are reviewed, and the different types of electron microscopes are compared.
The optics of electron lenses are discussed in Chap. 2 in order to bring out
electron-lenspropertiesthatareimportantforanunderstandingofthemodes
ofoperationofanelectronmicroscope.InChap.3,thewaveopticsofelectrons
andthephaseshiftscausedbyelectrostaticandmagneticfieldsareintroduced;
Fresnel electron diffraction is treated using Huygens’ principle. The recogni-
tion 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 in-
troducing 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, the imaging and recording system, and equipment for electron
energy-loss spectroscopy and energy filtering.
Athoroughunderstandingofelectron–specimeninteractionsisessentialto
explain image contrast. Chapter 5 contains the most important facts about
elastic, inelastic, and multiple scattering. The origin of scattering and phase
contrast of noncrystalline 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
VIII Preface
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
sourceofdiffractioncontrast.Thistypeofcontrastisimportantfortheimag-
ingofcrystallinespecimensandtheirdefectsandforthehigh-resolutionstudy
of crystal structure, treated in Chap. 9. Methods of elemental analysis and
the formation of images representingthe 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 specimen-
damage processes caused by electron irradiation.
The author thanks Dr. P.W. Hawkes for thorough correction of the man-
uscript and many helpful comments.
Mu¨nster, January 1997 L. Reimer
Contents
1 Introduction............................................... 1
1.1 Transmission Electron Microscopy ......................... 1
1.1.1 Conventional Transmission Electron Microscopy....... 1
1.1.2 High-Resolution Electron Microscopy ................ 3
1.1.3 Analytical Electron Microscopy ..................... 5
1.1.4 Energy-Filtering Electron Microscopy ................ 7
1.1.5 High-Voltage Electron Microscopy ................... 7
1.1.6 Dedicated Scanning Transmission Electron
Microscopy ....................................... 9
1.2 Alternative Types of Electron Microscopy .................. 10
1.2.1 Emission Electron Microscopy....................... 10
1.2.2 Reflection Electron Microscopy...................... 11
1.2.3 Mirror Electron Microscopy......................... 11
1.2.4 Scanning Electron Microscopy ...................... 12
1.2.5 X-ray and Auger-Electron Microanalysis ............. 14
1.2.6 Scanning-Probe Microscopy......................... 14
2 Particle Optics of Electrons................................ 17
2.1 Acceleration and Deflection of Electrons.................... 17
2.1.1 Relativistic Mechanics of Electron Acceleration........ 17
2.1.2 Deflection by Magnetic and Electric Fields............ 20
2.2 Electron Lenses ......................................... 22
2.2.1 Electron Trajectories in a Magnetic Lens Field ........ 22
2.2.2 Optics of an Electron Lens with a Bell-Shaped Field ... 25
2.2.3 Special Electron Lenses ............................ 29
2.3 Lens Aberrations ........................................ 31
2.3.1 Classification of Lens Aberrations ................... 31
2.3.2 Spherical Aberration............................... 32
2.3.3 Astigmatism and Field Curvature ................... 34
2.3.4 Distortion ........................................ 36
2.3.5 Coma............................................ 37
X Contents
2.3.6 Anisotropic Aberrations............................ 38
2.3.7 Chromatic Aberration ............................. 38
2.4 Correction of Aberrations and Microscope Alignment ........ 40
2.4.1 Correction of Astigmatism.......................... 40
2.4.2 Correction of Spherical and Chromatic Aberrations .... 42
2.4.3 Microscope Alignment ............................. 43
3 Wave Optics of Electrons .................................. 45
3.1 Electron Waves and Phase Shifts .......................... 45
3.1.1 De Broglie Waves ................................. 45
3.1.2 Probability Density and Wave Packets ............... 49
3.1.3 Electron-Optical Refractive Index
and the Schro¨dinger Equation....................... 51
3.1.4 Electron Interferometry and Coherence............... 53
3.2 Fresnel and Fraunhofer Diffraction......................... 55
3.2.1 Huygens’ Principle and Fresnel Diffraction............ 55
3.2.2 Fresnel Fringes.................................... 59
3.2.3 Fraunhofer Diffraction ............................. 61
3.2.4 Mathematics of Fourier Transforms .................. 63
3.3 Wave-Optical Formulation of Imaging...................... 70
3.3.1 Wave Aberration of an Electron Lens ................ 70
3.3.2 Wave-Optical Theory of Imaging .................... 73
4 Elements of a Transmission Electron Microscope .......... 77
4.1 Electron Guns .......................................... 78
4.1.1 Physics of Electron Emission........................ 78
4.1.2 Energy Spread .................................... 81
4.1.3 Gun Brightness ................................... 82
4.1.4 Thermionic Electron Guns.......................... 84
4.1.5 Schottky Emission Guns ........................... 88
4.1.6 Field-Emission Guns............................... 89
4.2 The Illumination System of a TEM ........................ 90
4.2.1 Condenser-Lens System ............................ 90
4.2.2 Electron-Probe Formation .......................... 93
4.2.3 Illumination with an Objective Prefield Lens.......... 96
4.3 Specimens .............................................. 98
4.3.1 Useful Specimen Thickness ......................... 98
4.3.2 Specimen Mounting................................ 99
4.3.3 Specimen Manipulation ............................100
4.4 The Imaging System of a TEM............................103
4.4.1 Objective Lens....................................103
4.4.2 Imaging Modes of a TEM ..........................104
4.4.3 Magnification and Calibration.......................107
4.4.4 Depth of Image and Depth of Focus .................108
4.5 Scanning Transmission Electron Microscopy (STEM) ........109
Contents XI
4.5.1 Scanning Transmission Mode of TEM................109
4.5.2 Dedicated STEM..................................112
4.5.3 Theorem of Reciprocity ............................113
4.6 Electron Spectrometers and Imaging Energy Filters..........115
4.6.1 Postcolumn Prism Spectrometer.....................116
4.6.2 Wien Filter.......................................119
4.6.3 Imaging Energy Filter .............................119
4.6.4 Operating Modes with Energy Filtering ..............124
4.7 Image Recording and Electron Detection ...................126
4.7.1 Fluorescent Screens................................126
4.7.2 Photographic Emulsions............................127
4.7.3 Imaging Plate.....................................131
4.7.4 Detector Noise and Detection Quantum Efficiency .....132
4.7.5 Low-Light-Level and Charge-Coupled-Device
(CCD) Cameras...................................134
4.7.6 Semiconductor and Scintillation Detectors ............138
4.7.7 Faraday Cages ....................................139
5 Electron–Specimen Interactions............................141
5.1 Elastic Scattering........................................141
5.1.1 Cross Section and Mean Free Path ..................141
5.1.2 Energy Transfer in an Electron–Nucleus Collision......143
5.1.3 Elastic Differential Cross Section for Small-Angle
Scattering ........................................146
5.1.4 Total Elastic Cross Section .........................152
5.2 Inelastic Scattering ......................................153
5.2.1 Electron–Specimen Interactions with Energy Loss .....153
5.2.2 Differential Cross Section for Single-Electron
Excitation........................................156
5.2.3 Bethe Surface and Compton Scattering...............158
5.2.4 Approximation for the Total Inelastic Cross Section....162
5.2.5 Dielectric Theory and Plasmon Losses in Solids .......163
5.2.6 Surface-Plasmon Losses ............................171
5.3 Energy Losses by Inner-Shell Ionization ....................174
5.3.1 Position and Shape of Ionization Edges ..............174
5.3.2 Inner-Shell Ionization Cross Sections.................177
5.3.3 Energy-Loss Near-Edge Structure (ELNES)...........179
5.3.4 Extended Energy-Loss Fine Structure (EXELFS)......182
5.3.5 Linear and Circular Dichroism ......................183
5.4 Multiple-Scattering Effects................................184
5.4.1 Angular Distribution of Scattered Electrons...........184
5.4.2 Energy Distribution of Transmitted Electrons.........186
5.4.3 Electron-Probe Broadening by Multiple Scattering.....188
5.4.4 Electron Diffusion, Backscattering,
and Secondary-Electron Emission....................192
