Electron Energy-Loss Spectroscopy in theElectron Microscope

Third Edition

R.F. Egerton

Electron Energy-LossSpectroscopy in theElectron Microscope

Third Edition

123

R.F. EgertonDepartment of PhysicsAvadh Bhatia Physics LaboratoryUniversity of AlbertaEdmonton, AB, Canadaregerton@ualberta.ca

ISBN 978-1-4419-9582-7 e-ISBN 978-1-4419-9583-4DOI 10.1007/978-1-4419-9583-4Springer New York Dordrecht Heidelberg London

Library of Congress Control Number: 2011930092

1st edition: © Plenum Press 19862nd edition: © Plenum Press 1996

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Preface to the Third Edition

The development of electron energy-loss spectroscopy within the last 15 years hasbeen 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 STEMimages and (in combination with Schottky and field-emission sources) much highercurrent in a focused probe. The incorporation of monochromators in commercialTEMs has improved the energy resolution to 0.1 eV, with further improvementspromised. 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 simultaneousrecording of the low-loss and core-loss regions.

Advances in computer software have made routine such processes as spectraland spatial deconvolution, spectrum-imaging, and multivariate statistical analysis.Programs for implementing density functional and multiple-scattering calculationsto predict spectral fine structure have become more widely available.

Taken together, these improvements have helped to ensure that EELS can beapplied to real materials problems as well as model systems; the technique is nolonger mainly a playground for physicists. Another consequence is that radiationdamage is seen to be a limiting factor in electron beam microanalysis. One responsehas 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 alsoconsiderable interest in the use of lasers in combination with TEM-EELS, the aimbeing picosecond or femtosecond time resolution, in order to study excited statesand 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 electrondetectors. 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

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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 recenttheory relating to anisotropic materials and magic-angle measurements. AppendixB contains a brief description of over 20 freeware programs written in MATLAB.They include programs for first-order prism focusing, atomic-displacement crosssections, Richardson–Lucy deconvolution, the Kröger formula for retardation andsurface losses, and translations of the FORTRAN and BASIC codes given in thesecond edition. The table of plasmon energies in Appendix C has been extended toa larger number of materials and now also contains inelastic mean free paths. I haveadded an Appendix F that summarizes some of the choices involved in acquiringenergy-loss data, with references to earlier sections of the book where these choicesare discussed in greater detail.

Throughout the text, I have tried to give appropriate references to topics that Iconsidered outside the scope of the book or beyond my expertise. The reference listnow contains about 1200 entries, each with an article title and page range. Theyare 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 LesAllen, Phil Batson, Gianluigi Botton, Peter Crozier, Adam Hitchcock, FerdinandHofer, Archie Howie, Gerald Kothleitner, Ondrej Krivanek, Richard Leapman,Matt Libera, Charlie Lyman, Marek Malac, Sergio Moreno, David Muller, StevePennycook, Peter Rez, Peter Schattschneider, Guillaume Radtke, Harald Rose, JohnSpence, Mike Walls, Masashi Watanabe, and Yimei Zhu. I thank Michael Bergen forhelp with the MATLAB computer code and the National Science and EngineeringCouncil of Canada for continuing financial support over the past 35 years. Mostof all, I thank my wife Maia and my son Robin for their steadfast support andencouragement.

Edmonton, AB, Canada Ray Egerton

Contents

1 An Introduction to EELS . . . . . . . . . . . . . . . . . . . . . . . 11.1 Interaction of Fast Electrons with a Solid . . . . . . . . . . . . 21.2 The Electron Energy-Loss Spectrum . . . . . . . . . . . . . . 51.3 The Development of Experimental Techniques . . . . . . . . . 8

1.3.1 Energy-Selecting (Energy-Filtering) ElectronMicroscopes . . . . . . . . . . . . . . . . . . . . . . . 12

1.3.2 Spectrometers as Attachments to a TEM . . . . . . . . 131.4 Alternative Analytical Methods . . . . . . . . . . . . . . . . . 15

1.4.1 Ion Beam Methods . . . . . . . . . . . . . . . . . . . . 161.4.2 Incident Photons . . . . . . . . . . . . . . . . . . . . . 171.4.3 Electron Beam Techniques . . . . . . . . . . . . . . . . 19

1.5 Comparison of EELS and EDX Spectroscopy . . . . . . . . . . 221.5.1 Detection Limits and Spatial Resolution . . . . . . . . . 221.5.2 Specimen Requirements . . . . . . . . . . . . . . . . . 241.5.3 Accuracy of Quantification . . . . . . . . . . . . . . . 251.5.4 Ease of Use and Information Content . . . . . . . . . . 25

1.6 Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . 26

2 Energy-Loss Instrumentation . . . . . . . . . . . . . . . . . . . . . 292.1 Energy-Analyzing and Energy-Selecting Systems . . . . . . . . 29

2.1.1 The Magnetic Prism Spectrometer . . . . . . . . . . . . 302.1.2 Energy-Filtering Magnetic Prism Systems . . . . . . . 332.1.3 The Wien Filter . . . . . . . . . . . . . . . . . . . . . 372.1.4 Electron Monochromators . . . . . . . . . . . . . . . . 39

2.2 Optics of a Magnetic Prism Spectrometer . . . . . . . . . . . . 442.2.1 First-Order Properties . . . . . . . . . . . . . . . . . . 452.2.2 Higher Order Focusing . . . . . . . . . . . . . . . . . . 512.2.3 Spectrometer Designs . . . . . . . . . . . . . . . . . . 532.2.4 Practical Considerations . . . . . . . . . . . . . . . . . 562.2.5 Spectrometer Alignment . . . . . . . . . . . . . . . . . 57

2.3 The Use of Prespectrometer Lenses . . . . . . . . . . . . . . . 622.3.1 TEM Imaging and Diffraction Modes . . . . . . . . . . 632.3.2 Effect of Lens Aberrations on Spatial Resolution . . . . 64

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2.3.3 Effect of Lens Aberrations on Collection Efficiency . . 662.3.4 Effect of TEM Lenses on Energy Resolution . . . . . . 682.3.5 STEM Optics . . . . . . . . . . . . . . . . . . . . . . . 70

2.4 Recording the Energy-Loss Spectrum . . . . . . . . . . . . . . 722.4.1 Spectrum Shift and Scanning . . . . . . . . . . . . . . 732.4.2 Spectrometer Background . . . . . . . . . . . . . . . . 752.4.3 Coincidence Counting . . . . . . . . . . . . . . . . . . 762.4.4 Serial Recording of the Energy-Loss Spectrum . . . . . 772.4.5 DQE of a Single-Channel System . . . . . . . . . . . . 822.4.6 Serial-Mode Signal Processing . . . . . . . . . . . . . 83

2.5 Parallel Recording of Energy-Loss Data . . . . . . . . . . . . . 852.5.1 Types of Self-Scanning Diode Array . . . . . . . . . . 852.5.2 Indirect Exposure Systems . . . . . . . . . . . . . . . . 862.5.3 Direct Exposure Systems . . . . . . . . . . . . . . . . 902.5.4 DQE of a Parallel-Recording System . . . . . . . . . . 912.5.5 Dealing with Diode Array Artifacts . . . . . . . . . . . 94

2.6 Energy-Selected Imaging (ESI) . . . . . . . . . . . . . . . . . 982.6.1 Post-column Energy Filter . . . . . . . . . . . . . . . . 982.6.2 In-Column Filters . . . . . . . . . . . . . . . . . . . . 1002.6.3 Energy Filtering in STEM Mode . . . . . . . . . . . . 1002.6.4 Spectrum Imaging . . . . . . . . . . . . . . . . . . . . 1032.6.5 Comparison of Energy-Filtered TEM and STEM . . . . 1062.6.6 Z-Contrast and Z-Ratio Imaging . . . . . . . . . . . . . 108

3 Physics of Electron Scattering . . . . . . . . . . . . . . . . . . . . . 1113.1 Elastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . . 111

3.1.1 General Formulas . . . . . . . . . . . . . . . . . . . . 1123.1.2 Atomic Models . . . . . . . . . . . . . . . . . . . . . . 1123.1.3 Diffraction Effects . . . . . . . . . . . . . . . . . . . . 1163.1.4 Electron Channeling . . . . . . . . . . . . . . . . . . . 1183.1.5 Phonon Scattering . . . . . . . . . . . . . . . . . . . . 1203.1.6 Energy Transfer in Elastic Scattering . . . . . . . . . . 122

3.2 Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . . 1243.2.1 Atomic Models . . . . . . . . . . . . . . . . . . . . . . 1243.2.2 Bethe Theory . . . . . . . . . . . . . . . . . . . . . . . 1283.2.3 Dielectric Formulation . . . . . . . . . . . . . . . . . . 1303.2.4 Solid-State Effects . . . . . . . . . . . . . . . . . . . . 132

3.3 Excitation of Outer-Shell Electrons . . . . . . . . . . . . . . . 1353.3.1 Volume Plasmons . . . . . . . . . . . . . . . . . . . . 1353.3.2 Single-Electron Excitation . . . . . . . . . . . . . . . . 1463.3.3 Excitons . . . . . . . . . . . . . . . . . . . . . . . . . 1523.3.4 Radiation Losses . . . . . . . . . . . . . . . . . . . . . 1543.3.5 Surface Plasmons . . . . . . . . . . . . . . . . . . . . 1563.3.6 Surface-Reflection Spectra . . . . . . . . . . . . . . . . 1643.3.7 Plasmon Modes in Small Particles . . . . . . . . . . . . 167

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3.4 Single, Plural, and Multiple Scattering . . . . . . . . . . . . . 1693.4.1 Poisson’s Law . . . . . . . . . . . . . . . . . . . . . . 1703.4.2 Angular Distribution of Plural Inelastic Scattering . . . 1723.4.3 Influence of Elastic Scattering . . . . . . . . . . . . . . 1753.4.4 Multiple Scattering . . . . . . . . . . . . . . . . . . . . 1763.4.5 Coherent Double-Plasmon Excitation . . . . . . . . . . 177

3.5 The Spectral Background to Inner-Shell Edges . . . . . . . . . 1783.5.1 Valence-Electron Scattering . . . . . . . . . . . . . . . 1783.5.2 Tails of Core-Loss Edges . . . . . . . . . . . . . . . . 1793.5.3 Bremsstrahlung Energy Losses . . . . . . . . . . . . . 1803.5.4 Plural-Scattering Contributions to the Background . . . 181

3.6 Atomic Theory of Inner-Shell Excitation . . . . . . . . . . . . 1843.6.1 Generalized Oscillator Strength . . . . . . . . . . . . . 1843.6.2 Relativistic Kinematics of Scattering . . . . . . . . . . 1903.6.3 Ionization Cross Sections . . . . . . . . . . . . . . . . 193

3.7 The Form of Inner-Shell Edges . . . . . . . . . . . . . . . . . 1973.7.1 Basic Edge Shapes . . . . . . . . . . . . . . . . . . . . 1973.7.2 Dipole Selection Rule . . . . . . . . . . . . . . . . . . 2033.7.3 Effect of Plural Scattering . . . . . . . . . . . . . . . . 2033.7.4 Chemical Shifts in Threshold Energy . . . . . . . . . . 204

3.8 Near-Edge Fine Structure (ELNES) . . . . . . . . . . . . . . . 2063.8.1 Densities-of-States Interpretation . . . . . . . . . . . . 2063.8.2 Multiple-Scattering Interpretation . . . . . . . . . . . . 2133.8.3 Molecular-Orbital Theory . . . . . . . . . . . . . . . . 2153.8.4 Multiplet and Crystal-Field Effects . . . . . . . . . . . 215

3.9 Extended Energy-Loss Fine Structure (EXELFS) . . . . . . . . 2163.10 Core Excitation in Anisotropic Materials . . . . . . . . . . . . 2203.11 Delocalization of Inelastic Scattering . . . . . . . . . . . . . . 223

4 Quantitative Analysis of Energy-Loss Data . . . . . . . . . . . . . . 2314.1 Deconvolution of Low-Loss Spectra . . . . . . . . . . . . . . . 231

4.1.1 Fourier Log Method . . . . . . . . . . . . . . . . . . . 2314.1.2 Fourier Ratio Method . . . . . . . . . . . . . . . . . . 2404.1.3 Bayesian Deconvolution . . . . . . . . . . . . . . . . . 2414.1.4 Other Methods . . . . . . . . . . . . . . . . . . . . . . 243

4.2 Kramers–Kronig Analysis . . . . . . . . . . . . . . . . . . . . 2434.2.1 Angular Corrections . . . . . . . . . . . . . . . . . . . 2444.2.2 Extrapolation and Normalization . . . . . . . . . . . . 2444.2.3 Derivation of the Dielectric Function . . . . . . . . . . 2454.2.4 Correction for Surface Losses . . . . . . . . . . . . . . 2484.2.5 Checks on the Data . . . . . . . . . . . . . . . . . . . . 248

4.3 Deconvolution of Core-Loss Data . . . . . . . . . . . . . . . . 2494.3.1 Fourier Log Method . . . . . . . . . . . . . . . . . . . 2494.3.2 Fourier Ratio Method . . . . . . . . . . . . . . . . . . 250

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4.3.3 Bayesian Deconvolution . . . . . . . . . . . . . . . . . 2554.3.4 Other Methods . . . . . . . . . . . . . . . . . . . . . . 256

4.4 Separation of Spectral Components . . . . . . . . . . . . . . . 2574.4.1 Least-Squares Fitting . . . . . . . . . . . . . . . . . . . 2584.4.2 Two-Area Fitting . . . . . . . . . . . . . . . . . . . . . 2604.4.3 Background-Fitting Errors . . . . . . . . . . . . . . . . 2614.4.4 Multiple Least-Squares Fitting . . . . . . . . . . . . . . 2654.4.5 Multivariate Statistical Analysis . . . . . . . . . . . . . 2654.4.6 Energy- and Spatial-Difference Techniques . . . . . . . 269

4.5 Elemental Quantification . . . . . . . . . . . . . . . . . . . . . 2704.5.1 Integration Method . . . . . . . . . . . . . . . . . . . . 2704.5.2 Calculation of Partial Cross Sections . . . . . . . . . . 2734.5.3 Correction for Incident Beam Convergence . . . . . . . 2744.5.4 Quantification from MLS Fitting . . . . . . . . . . . . 276

4.6 Analysis of Extended Energy-Loss Fine Structure . . . . . . . 2774.6.1 Fourier Transform Method . . . . . . . . . . . . . . . . 2774.6.2 Curve-Fitting Procedure . . . . . . . . . . . . . . . . . 284

4.7 Simulation of Energy-Loss Near-Edge Structure (ELNES) . . . 2864.7.1 Multiple Scattering Calculations . . . . . . . . . . . . . 2864.7.2 Band Structure Calculations . . . . . . . . . . . . . . . 288

5 TEM Applications of EELS . . . . . . . . . . . . . . . . . . . . . . 2935.1 Measurement of Specimen Thickness . . . . . . . . . . . . . . 293

5.1.1 Log-Ratio Method . . . . . . . . . . . . . . . . . . . . 2945.1.2 Absolute Thickness from the K–K Sum Rule . . . . . . 3025.1.3 Mass Thickness from the Bethe Sum Rule . . . . . . . 304

5.2 Low-Loss Spectroscopy . . . . . . . . . . . . . . . . . . . . . 3065.2.1 Identification from Low-Loss Fine Structure . . . . . . 3065.2.2 Measurement of Plasmon Energy

and Alloy Composition . . . . . . . . . . . . . . . . . 3095.2.3 Characterization of Small Particles . . . . . . . . . . . 310

5.3 Energy-Filtered Images and Diffraction Patterns . . . . . . . . 3145.3.1 Zero-Loss Images . . . . . . . . . . . . . . . . . . . . 3155.3.2 Zero-Loss Diffraction Patterns . . . . . . . . . . . . . . 3175.3.3 Low-Loss Images . . . . . . . . . . . . . . . . . . . . 3185.3.4 Z-Ratio Images . . . . . . . . . . . . . . . . . . . . . . 3195.3.5 Contrast Tuning and MPL Imaging . . . . . . . . . . . 3205.3.6 Core-Loss Images and Elemental Mapping . . . . . . . 321

5.4 Elemental Analysis from Core-Loss Spectroscopy . . . . . . . 3245.4.1 Measurement of Hydrogen and Helium . . . . . . . . . 3275.4.2 Measurement of Lithium, Beryllium, and Boron . . . . 3295.4.3 Measurement of Carbon, Nitrogen, and Oxygen . . . . 3305.4.4 Measurement of Fluorine and Heavier Elements . . . . 333

5.5 Spatial Resolution and Detection Limits . . . . . . . . . . . . . 3355.5.1 Electron-Optical Considerations . . . . . . . . . . . . . 335

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5.5.2 Loss of Resolution Due to Elastic Scattering . . . . . . 3365.5.3 Delocalization of Inelastic Scattering . . . . . . . . . . 3375.5.4 Statistical Limitations and Radiation Damage . . . . . . 340

5.6 Structural Information from EELS . . . . . . . . . . . . . . . . 3465.6.1 Orientation Dependence of Ionization Edges . . . . . . 3465.6.2 Core-Loss Diffraction Patterns . . . . . . . . . . . . . . 3505.6.3 ELNES Fingerprinting . . . . . . . . . . . . . . . . . . 3525.6.4 Valency and Magnetic Measurements

from White-Line Ratios . . . . . . . . . . . . . . . . . 3575.6.5 Use of Chemical Shifts . . . . . . . . . . . . . . . . . . 3615.6.6 Use of Extended Fine Structure . . . . . . . . . . . . . 3625.6.7 Electron–Compton (ECOSS) Measurements . . . . . . 366

5.7 Application to Specific Materials . . . . . . . . . . . . . . . . 3685.7.1 Semiconductors and Electronic Devices . . . . . . . . . 3685.7.2 Ceramics and High-Temperature Superconductors . . . 3745.7.3 Carbon-Based Materials . . . . . . . . . . . . . . . . . 3785.7.4 Polymers and Biological Specimens . . . . . . . . . . . 3865.7.5 Radiation Damage and Hole Drilling . . . . . . . . . . 389

Appendix A Bethe Theory for High Incident Energiesand Anisotropic Materials . . . . . . . . . . . . . . . . . 399A.1 Anisotropic Specimens . . . . . . . . . . . . . . . . 402

Appendix B Computer Programs . . . . . . . . . . . . . . . . . . . . . 405B.1 First-Order Spectrometer Focusing . . . . . . . . . . 405B.2 Cross Sections for Atomic Displacement

and High-Angle Elastic Scattering . . . . . . . . . . 406B.3 Lenz-Model Elastic and Inelastic Cross Sections . . . 406B.4 Simulation of a Plural-Scattering Distribution . . . . 407B.5 Fourier-Log Deconvolution . . . . . . . . . . . . . . 408B.6 Maximum-Likelihood Deconvolution . . . . . . . . 409B.7 Drude Simulation of a Low-Loss Spectrum . . . . . 409B.8 Kramers–Kronig Analysis . . . . . . . . . . . . . . 410B.9 Kröger Simulation of a Low-Loss Spectrum . . . . . 412B.10 Core-Loss Simulation . . . . . . . . . . . . . . . . . 412B.11 Fourier Ratio Deconvolution . . . . . . . . . . . . . 413B.12 Incident-Convergence Correction . . . . . . . . . . . 414B.13 Hydrogenic K-Shell Cross Sections . . . . . . . . . 414B.14 Modified-Hydrogenic L-Shell Cross Sections . . . . 415B.15 Parameterized K-, L-, M-, N-, and O-Shell

Cross Sections . . . . . . . . . . . . . . . . . . . . . 416B.16 Measurement of Absolute Specimen Thickness . . . 416B.17 Total Inelastic and Plasmon Mean Free Paths . . . . 417B.18 Constrained Power-Law Background Fitting . . . . . 417

Appendix C Plasmon Energies and Inelastic Mean Free Paths . . . . . 419

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Appendix D Inner-Shell Energies and Edge Shapes . . . . . . . . . . . 423

Appendix E Electron Wavelengths, Relativistic Factors,and Physical Constants . . . . . . . . . . . . . . . . . . . 427

Appendix F Options for Energy-Loss Data Acquisition . . . . . . . . 429

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485