Egerton R.F. Electron Energy-Loss Spectroscopy in the Electron Microscope
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Electron Energy-Loss Spectroscopy in the
Electron Microscope
Third Edition
R.F. Egerton
Electron Energy-Loss
Spectroscopy in the
Electron Microscope
Third Edition
123
R.F. Egerton
Department of Physics
Avadh Bhatia Physics Laboratory
University of Alberta
Edmonton, AB, Canada
regerton@ualberta.ca
ISBN 978-1-4419-9582-7 e-ISBN 978-1-4419-9583-4
DOI 10.1007/978-1-4419-9583-4
Springer New York Dordrecht Heidelberg London
Library of Congress Control Number: 2011930092
1st edition: © Plenum Press 1986
2nd edition: © Plenum Press 1996
© Springer Science+Business Media, LLC 2011
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Preface to the Third Edition
The development of electron energy-loss spectroscopy within the last 15 years has
been remarkable. This progress is partly due to improvements in instrumentation,
such as the successful correction of spherical (and more recently chromatic) aberra-
tion of electron lenses, allowing sub-Angstrom spatial resolution in TEM and STEM
images and (in combination with Schottky and field-emission sources) much higher
current in a focused probe. The incorporation of monochromators in commercial
TEMs has improved the energy resolution to 0.1 eV, with further improvements
promised. These advances have required close attention to the mechanical and elec-
trical stability of the TEM, including thermal, vibrational, and acoustical isolation.
The energy-loss spectrometer has been improved with a fast electrostatic shutter,
allowing millisecond acquisition of an entire spectrum and almost simultaneous
recording of the low-loss and core-loss regions.
Advances in computer software have made routine such processes as spectral
and spatial deconvolution, spectrum-imaging, and multivariate statistical analysis.
Programs for implementing density functional and multiple-scattering calculations
to predict spectral fine structure have become more widely available.
Taken together, these improvements have helped to ensure that EELS can be
applied to real materials problems as well as model systems; the technique is no
longer mainly a playground for physicists. Another consequence is that radiation
damage is seen to be a limiting factor in electron beam microanalysis. One response
has the development of TEMs that can achieve atomic resolution at lower accelerat-
ing voltage, in an attempt to maximize the information/damage ratio. There is also
considerable interest in the use of lasers in combination with TEM-EELS, the aim
being picosecond or femtosecond time resolution, in order to study excited states
and perhaps even to conquer radiation damage.
For the third edition of this textbook, I have kept the previous structure intact.
However, the reading list and historical section of Chapter 1 have been updated.
In Chapter 2, I have retained but shortened the discussion of serial recording,
making room for more information on monochromator designs and new electron
detectors. In Chapter 3, I have added material on energy losses due to elastic scat-
tering, retardation and Cerenkov effects, core excitation in anisotropic materials,
and the delocalization of inelastic scattering. Chapter 4 now includes a discussion
v
vi Preface to the Third Edition
of Bayesian deconvolution, multivariate statistical analysis, and the ELNES simula-
tion. As previously, Chapter 5 deals with practical applications of EELS in a TEM,
together with a discussion of factors that limit the spatial resolution of analysis,
including radiation damage and examples of applications to selected materials sys-
tems. The final section gives examples of TEM-EELS study of electronic, ceramic,
and carbon-based materials (including graphene, carbon nanotubes, and polymers)
and the measurement of radiation damage.
In Appendix A, the discussion to relativistic effects is extended to include recent
theory relating to anisotropic materials and magic-angle measurements. Appendix
B contains a brief description of over 20 freeware programs written in MATLAB.
They include programs for first-order prism focusing, atomic-displacement cross
sections, Richardson–Lucy deconvolution, the Kröger formula for retardation and
surface losses, and translations of the FORTRAN and BASIC codes given in the
second edition. The table of plasmon energies in Appendix C has been extended to
a larger number of materials and now also contains inelastic mean free paths. I have
added an Appendix F that summarizes some of the choices involved in acquiring
energy-loss data, with references to earlier sections of the book where these choices
are discussed in greater detail.
Throughout the text, I have tried to give appropriate references to topics that I
considered outside the scope of the book or beyond my expertise. The reference list
now contains about 1200 entries, each with an article title and page range. They
are listed alphabetically by first author surname, but with multiauthor entries (et al.
references in the text) arranged in chronological order.
I am grateful to many colleagues for comment and discussion, including Les
Allen, Phil Batson, Gianluigi Botton, Peter Crozier, Adam Hitchcock, Ferdinand
Hofer, Archie Howie, Gerald Kothleitner, Ondrej Krivanek, Richard Leapman,
Matt Libera, Charlie Lyman, Marek Malac, Sergio Moreno, David Muller, Steve
Pennycook, Peter Rez, Peter Schattschneider, Guillaume Radtke, Harald Rose, John
Spence, Mike Walls, Masashi Watanabe, and Yi mei Zhu. I thank Michael Bergen for
help with the MATLAB computer code and the National Science and Engineering
Council of Canada for continuing financial support over the past 35 years. Most
of all, I thank my wife Maia and my son Robin for their steadfast support and
encouragement.
Edmonton, AB, Canada Ray Egerton
Contents
1 An Introduction to EELS ....................... 1
1.1 InteractionofFastElectronswithaSolid ............ 2
1.2 The Electron Energy-Loss Spectrum . ............. 5
1.3 The Development of Experimental Techniques . ........ 8
1.3.1 Energy-Selecting (Energy-Filtering) Electron
Microscopes ....................... 12
1.3.2 Spectrometers as Attachments to a TEM ........ 13
1.4 Alternative Analytical Methods ................. 15
1.4.1 Ion Beam Methods . . .................. 16
1.4.2 Incident Photons . . . .................. 17
1.4.3 Electron Beam Techniques . . . ............. 19
1.5 Comparison of EELS and EDX Spectroscopy . . ........ 22
1.5.1 DetectionLimitsandSpatialResolution......... 22
1.5.2 Specimen Requirements ................. 24
1.5.3 Accuracy of Quantification . . ............. 25
1.5.4 EaseofUseandInformationContent .......... 25
1.6 Further Reading . . ....................... 26
2 Energy-Loss Instrumentation ..................... 29
2.1 Energy-AnalyzingandEnergy-SelectingSystems........ 29
2.1.1 The Magnetic Prism Spectrometer ............ 30
2.1.2 Energy-Filtering Magnetic Prism Systems . . . .... 33
2.1.3 The Wien Filter . . . .................. 37
2.1.4 Electron Monochromators . . . ............. 39
2.2 Optics of a Magnetic Prism Spectrometer ............ 44
2.2.1 First-Order Properties .................. 45
2.2.2 Higher Order Focusing .................. 51
2.2.3 Spectrometer Designs .................. 53
2.2.4 PracticalConsiderations................. 56
2.2.5 Spectrometer Alignment ................. 57
2.3 The Use of Prespectrometer Lenses . . ............. 62
2.3.1 TEM Imaging and Diffraction Modes . . ........ 63
2.3.2 EffectofLensAberrationsonSpatialResolution.... 64
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viii Contents
2.3.3 Effect of Lens Aberrations on Collection Efficiency . . 66
2.3.4 EffectofTEMLensesonEnergyResolution ...... 68
2.3.5 STEMOptics....................... 70
2.4 Recording the Energy-Loss Spectrum . ............. 72
2.4.1 Spectrum Shift and Scanning . ............. 73
2.4.2 Spectrometer Background . . . ............. 75
2.4.3 Coincidence Counting .................. 76
2.4.4 Serial Recording of the Energy-Loss Spectrum . .... 77
2.4.5 DQE of a Single-Channel System ............ 82
2.4.6 Serial-Mode Signal Processing ............. 83
2.5 Parallel Recording of Energy-Loss Data ............. 85
2.5.1 Types of Self-Scanning Diode Array . . ........ 85
2.5.2 Indirect Exposure Systems . . . ............. 86
2.5.3 Direct Exposure Systems . . . ............. 90
2.5.4 DQE of a Parallel-Recording System . . ........ 91
2.5.5 DealingwithDiodeArrayArtifacts........... 94
2.6 Energy-SelectedImaging(ESI) ................. 98
2.6.1 Post-column Energy Filter . . . ............. 98
2.6.2 In-Column Filters . . .................. 100
2.6.3 Energy Filtering in STEM Mode ............ 100
2.6.4 Spectrum Imaging . . .................. 103
2.6.5 Comparison of Energy-Filtered TEM and STEM .... 106
2.6.6 Z-ContrastandZ-RatioImaging............. 108
3 Physics of Electron Scattering ..................... 111
3.1 ElasticScattering......................... 111
3.1.1 General Formulas . . .................. 112
3.1.2 Atomic Models ...................... 112
3.1.3 DiffractionEffects.................... 116
3.1.4 Electron Channeling . .................. 118
3.1.5 Phonon Scattering . . .................. 120
3.1.6 EnergyTransferinElasticScattering .......... 122
3.2 InelasticScattering........................ 124
3.2.1 Atomic Models ...................... 124
3.2.2 Bethe Theory ....................... 128
3.2.3 DielectricFormulation.................. 130
3.2.4 Solid-StateEffects.................... 132
3.3 Excitation of Outer-Shell Electrons . . ............. 135
3.3.1 VolumePlasmons .................... 135
3.3.2 Single-ElectronExcitation................ 146
3.3.3 Excitons ......................... 152
3.3.4 RadiationLosses..................... 154
3.3.5 SurfacePlasmons .................... 156
3.3.6 Surface-Reflection Spectra . . . ............. 164
3.3.7 Plasmon Modes in Small Particles ............ 167
Contents ix
3.4 Single, Plural, and Multiple Scattering ............. 169
3.4.1 Poisson’sLaw ...................... 170
3.4.2 Angular Distribution of Plural Inelastic Scattering . . . 172
3.4.3 Influence of Elastic Scattering . ............. 175
3.4.4 Multiple Scattering . . .................. 176
3.4.5 Coherent Double-Plasmon Excitation . . ........ 177
3.5 The Spectral Background to Inner-Shell Edges . ........ 178
3.5.1 Valence-Electron Scattering . . ............. 178
3.5.2 Tails of Core-Loss Edges . . . ............. 179
3.5.3 BremsstrahlungEnergyLosses ............. 180
3.5.4 Plural-Scattering Contributions to the Background . . . 181
3.6 Atomic Theory of Inner-Shell Excitation ............ 184
3.6.1 Generalized Oscillator Strength ............. 184
3.6.2 RelativisticKinematicsofScattering .......... 190
3.6.3 IonizationCrossSections ................ 193
3.7 The Form of Inner-Shell Edges ................. 197
3.7.1 Basic Edge Shapes . . .................. 197
3.7.2 DipoleSelectionRule .................. 203
3.7.3 EffectofPluralScattering................ 203
3.7.4 ChemicalShiftsinThresholdEnergy .......... 204
3.8 Near-EdgeFineStructure(ELNES)............... 206
3.8.1 Densities-of-States Interpretation ............ 206
3.8.2 Multiple-Scattering Interpretation ............ 213
3.8.3 Molecular-Orbital Theory . . . ............. 215
3.8.4 Multiplet and Crystal-Field Effects . . . ........ 215
3.9 Extended Energy-Loss Fine Structure (EXELFS) ........ 216
3.10 CoreExcitationinAnisotropicMaterials ............ 220
3.11 DelocalizationofInelasticScattering .............. 223
4 Quantitative Analysis of Energy-Loss Data .............. 231
4.1 Deconvolution of Low-Loss Spectra . . ............. 231
4.1.1 FourierLogMethod ................... 231
4.1.2 FourierRatioMethod .................. 240
4.1.3 Bayesian Deconvolution ................. 241
4.1.4 Other Methods ...................... 243
4.2 Kramers–KronigAnalysis.................... 243
4.2.1 Angular Corrections . .................. 244
4.2.2 Extrapolation and Normalization ............ 244
4.2.3 Derivation of the Dielectric Function . . ........ 245
4.2.4 CorrectionforSurfaceLosses .............. 248
4.2.5 Checks on the Data . . .................. 248
4.3 Deconvolution of Core-Loss Data . . . ............. 249
4.3.1 FourierLogMethod ................... 249
4.3.2 FourierRatioMethod .................. 250