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Quantitative Analysis of Energy-Loss Data

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Electron Energy-Loss Spectroscopy in the Electron Microscope

Abstract

This chapter discusses some of the mathematical procedures used to extract quantitative information about the crystallographic structure and chemical composition of a TEM specimen. Although this information is expressed rather directly in the energy-loss spectrum, plural scattering complicates the data recorded from specimens of typical thickness. Therefore it is often necessary to remove the effects of plural scattering from the spectrum or at least make allowance for them in the analysis procedure.

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Notes

  1. 1.

    Here λ characterizes all inelastic scattering in the energy range over which the intensity is integrated, and is given by Eq. (3.96) in the case where several inelastic processes contribute within this range. As discussed in Section 3.4, Poisson statistics still apply to a spectrum recorded with an angle-limiting aperture, provided an aperture-dependent mean free path is used.

  2. 2.

    As an example, the DFT of the unit-area Gaussian is \(\exp ( - {\pi ^2}{n^2}{\sigma ^2}/{N^2})\).

  3. 3.

    Equation (4.28) applies only to isotropic materials; for the anisotropic case, see Daniels et al. (1970).

  4. 4.

    MATLAB freeware for multivariate image analysis is available from http://macc.mcmaster.ca/research/software/maccmia.

References

  • Alexander, D. T. L., Crozier, P. A., and Anderson, J. R. (2008) Brown carbon spheres in east Asian outflow and their optical properties. Science 321, 833–836.

    CAS  Google Scholar 

  • Ankudinov, A. L., Ravel, B., Rehr, J. J., and Conradson, S. D. (1998) Real-space multiple-scattering calculation and interpretation of x-ray-absorption near-edge structure. Phys. Rev. B 58, 7565–7576.

    CAS  Google Scholar 

  • Arenal, R., de la Peña, F., Stéphan, O., Walls, M., Tencé, M., Loiseau, A., and Colliex, C. (2008) Extending the analysis of EELS spectrum-imaging data, from elemental to bond mapping in complex nanostructures. Ultramicroscopy 109, 32–38.

    CAS  Google Scholar 

  • Arslan, I., Ogut, S., Nellist, P. D., and Browning, N. D. (2003) Comparison of simulation methods for electronic structure calculations with experimental electron energy-loss spectra. Micron 34, 255–260.

    CAS  Google Scholar 

  • Bach, F. R., and Jordan, M. I. (2002) Kernel independent component analysis. J. Mach. Learn. Res. 3, 1–48.

    Google Scholar 

  • Batson, P. E., and Silcox, J. (1983) Experimental energy-loss function, Im[−1/É›(q,ω)], for aluminum. Phys. Rev. B 27, 5224–5239.

    CAS  Google Scholar 

  • Batson, P. E., Johnson, D. W., and Spence, J. C. H. (1992) Resolution enhancement by deconvolution using a field emission source in electron energy loss spectroscopy. Ultramicroscopy 41, 137–145.

    Google Scholar 

  • Berger, A., and Kohl, H. (1993) Optimum imaging parameters for elemental mapping in an energy filtering transmission electron microscope. Optik 92, 175–193.

    Google Scholar 

  • Bertoni, G., and Verbeeck, J. (2008) Accuracy and precision in model based EELS quantification. Phys. Rev. B 58, 14031–14035.

    Google Scholar 

  • Bevington, P. R. (1969) Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, New York, NY.

    Google Scholar 

  • Bianconi, A. (1983) XANES spectroscopy for local structures in complex systems. In EXAFS and Near Edge Structure, eds. A. Bianconi, L. Incoccia, and S. Stipcich, Springer, New York, NY, pp. 118–129.

    Google Scholar 

  • Blaha, P., Schwarz, K., and Sorantin, P. (1990) Full-potential, linearized augmented plane wave programs for crystalline systems. Comput. Phys. Commun. 59, 399–415.

    CAS  Google Scholar 

  • Bonnet, R. A., and Nuzillard, D. (2005) Independent component analysis: A new possibility for analysing series of electron energy loss spectra. Ultramicroscopy 102, 327–337.

    CAS  Google Scholar 

  • Borglund, M., Ã…strand, P.-G., and Csillag, S. (2005) Improved background removal method using principal components analysis for spatially resolved electron energy loss spectroscopy. Microsc. Microanal. 11, 88–96.

    CAS  Google Scholar 

  • Bosman, M., Watanabe, M., Alexander, D.T.L. and Keast, V.J. (2006) Mapping chemical and bonding information using multivariate analysis of electron energy-loss spectrum images. Ultramicroscopy 106, 1024–1032.

    CAS  Google Scholar 

  • Bourdillon, A. J., El Mashri, S. M., and Forty, A. J. (1984) Application of extended electron energy loss fine structure to the study of aluminum oxide films. Philos. Mag. 49, 341–352.

    CAS  Google Scholar 

  • Bracewell, R. N. (1978) The Fourier Transform and Its Applications, McGraw-Hill, New York, NY.

    Google Scholar 

  • Bradley, C. R., and Gibbons, P. C. (1986) How to remove multiple scattering from core-excitation spectra: II. Non-zero-scatteringangles. Ultramicroscopy 19, 317–324.

    CAS  Google Scholar 

  • Brigham, E. O. (1974) The Fast Fourier Transform, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Bringans, R. D., and Liang, W. Y. (1981) Energy bands of the cadmium halides from electron energy loss spectroscopy. J. Phys. C. (Solid State) 14, 1065–1092.

    CAS  Google Scholar 

  • Bruley, J., and Batson, P. E. (1989) Electron-energy-loss studies of dislocations in diamond. Phys. Rev. B 40, 9888–9894.

    CAS  Google Scholar 

  • Citrin, P. H., Eisenberger, P., and Kincaid, B. M. (1976) Transferabilty of phase shifts in extended x-ray absorption fine structure. Phys. Rev. Lett. 36, 1346–1349.

    CAS  Google Scholar 

  • Cochran, W. T. (1967) What is the fast Fourier transform? IEEE Trans. Audio Electroacoust. AU15, 45–55.

    Google Scholar 

  • Colliex, C., Jeanguillaume, C., and Trebbia, P. (1981) Quantitative local microanalysis with EELS. In Microprobe Analysis of Biological Systems, eds. T. E. Hutchinson and A. P. Somlyo, Academic, New York, NY, pp. 251–271.

    Google Scholar 

  • Durham, P. J., Pendry, J. B., and Hodges, C. H. (1981) XANES: Determination of bond angles and multi-atom correlations in ordered and disordered systems. Solid State Commun. 38, 159–162.

    CAS  Google Scholar 

  • Durham, P. J., Pendry, J. B., and Hodges, C. H. (1982) Calculation of x-ray absorption near-edge structure, XANES. Comput. Phys. Commun. 25, 193–205.

    CAS  Google Scholar 

  • Egerton, R. F. (1978a) Formulae for light-element microanalysis by electron energy-loss spectrometry. Ultramicroscopy 3, 243–251.

    CAS  Google Scholar 

  • Egerton, R. F. (1982a) A revised expression for signal/noise ratio in EELS. Ultramicroscopy 9, 387–390.

    CAS  Google Scholar 

  • Egerton, R. F. (1993) Oscillator-strength parameterization of inner-shell cross sections. Ultramicroscopy 50, 13–28.

    CAS  Google Scholar 

  • Egerton, R. F., and Malac, M. (2002) Improved background-fitting algorithms for ionization edges in electron energy-loss spectra. Ultramicroscopy 92, 47–56.

    CAS  Google Scholar 

  • Egerton, R. F., and Wang, Z. L. (1990) Plural-scattering deconvolution of electron energy-loss spectra recorded with an angle-limiting aperture. Ultramicroscopy 32, 137–148.

    CAS  Google Scholar 

  • Egerton, R. F., Williams, B. G., and Sparrow, T. G. (1985) Fourier deconvolution of electron energy-loss spectra. Proc. R. Soc. Lond. A398, 395–404.

    Google Scholar 

  • Egerton, R. F., Qian, H., and Malac, M. (2006a) Improving the energy resolution of X-ray and electron energy-loss spectra. Micron 37, 310–315.

    CAS  Google Scholar 

  • Egerton, R. F., Wang, F., Malac, M., Moreno, M. S., and Hofer, F. (2008) Fourier-ratio deconvolution and its Bayesian equivalent. Micron 39, 642–647.

    CAS  Google Scholar 

  • Eisenberger, P., Shulman, R. G., Kincaid, B. M., and Brown, G. S. (1978) Extended x-ray absorption fine structure determination of iron-nitrogen distances in haemoglobin. Nature 274, 30–34.

    CAS  Google Scholar 

  • Fink, J., Muller-Heinzerling, T., Pflü, J., Bubenzer, A., Koidl, P., and Crecelius, G. (1983) Structure and bonding of hydrocarbon plasma generated carbon films: An electron energy loss study. Solid State Commun. 47, 687–691.

    CAS  Google Scholar 

  • Gibbons, P. C., Bradley, C. R., and Fraundorf, P. B. (1987) How to remove multiple scattering from core-excitation spectra: III. Varying the mean free path. Ultramicroscopy 21, 305–312.

    CAS  Google Scholar 

  • Gloter, A., Douiri, A., Tencé, M., and Colliex, C. (2003) Improving energy resolution of EELS spectra: An alternative to the monochromator solution. Ultramicroscopy 69, 385–400.

    Google Scholar 

  • Hébert, C. (2007) Practical aspects of running the WIEN2k code for electron spectroscopy. Micron 38, 12–28.

    Google Scholar 

  • Heil, T., and Kohl, H. (2010) Optimization of EFTEM image acquisition by using elastically filtered images for drift correction. Ultramicroscopy 110, 745–750.

    CAS  Google Scholar 

  • Higgins, R. J. (1976) Fast Fourier transform: An introduction with some minicomputer experiments. Am. J. Phys. 44, 766–773.

    Google Scholar 

  • Hofer, F. (1987) EELS quantification of M edges by using oxidic standards. Ultramicroscopy 21, 63–68.

    CAS  Google Scholar 

  • Hofer, F., Golub, P., and Brunegger, A. (1988) EELS quantification of the elements Sr to W by means of M45 edges. Ultramicroscopy 25, 81–84.

    CAS  Google Scholar 

  • Hyvärinen, A., Karhunen, J., and Oja, E. (2001) Independent Component Analysis, 1st edition, Wiley-Interscience, New York, NY.

    Google Scholar 

  • Isaacson, M. (1972a) Interaction of 25 keV electrons with the nucleic acid bases, adenine, thymine, and uracil I, outer shell excitation. J. Chem. Phys. 56, 1803–1812.

    CAS  Google Scholar 

  • Johnson, D. W. (1974) Optical properties determined from electron energy-loss distributions. In Electron Microscopy – 1974, 8th Int. Cong., eds. J. V. Sanders and D. J. Goodchild, Australian Academy of Science, Canberra, pp. 388–389.

    Google Scholar 

  • Johnson, D. W. (1975) A Fourier method for numerical Kramers-Kronig analysis. J. Phys. A (Math. Gen. Phys.) 8, 490–495.

    Google Scholar 

  • Johnson, D. W., and Spence, J. C. H. (1974) Determination of the single-scattering probability distribution from plural-scattering data. J. Phys. D (Appl. Phys.) 7, 771–780.

    Google Scholar 

  • Johnson, H. F., and Isaacson, M. S. (1988) An efficient analytical method for calculating the angular distribution of electrons which have undergone plural scattering in amorphous materials. Ultramicroscopy 26, 271–294.

    Google Scholar 

  • Joliffe, I. T. (2002) Principal Component Analysis, 2nd edition, Springer, New York, NY.

    Google Scholar 

  • Joy, D. C., and Maher, D. M. (1981a) The quantitation of electron energy-loss spectra. J. Microsc. 124, 37–48.

    CAS  Google Scholar 

  • Keast, V. (2005) Ab initio calculations of plasmons and interband transitions in the low-loss electron energy-loss spectrum. J. Electron Spectrosc. Relat. Phenom. 143, 97–104.

    CAS  Google Scholar 

  • Kimoto, K., Ishizuka, K., Mizoguchi, T., Tanaka, I., and Matsui, Y. (2003) The study of Al-L 23 ELNES with resolution-enhancement software and first-principles calculation. J. Electron Microsc. 52, 299–303.

    CAS  Google Scholar 

  • Kincaid, B. M., Meixner, A. E., and Platzman, P. M. (1978) Carbon K-edge in graphite measured using electron energy-loss spectroscopy. Phys. Rev. Lett. 40, 1296–1299.

    CAS  Google Scholar 

  • Kohl, H. (1985) A simple procedure for evaluating effective scattering cross sections in STEM. Ultramicroscopy 16, 265–268.

    CAS  Google Scholar 

  • Kohn, W., and Sham, L. J. (1965) Self-consistent equations including exchange and correlation effects. Phys. Rev. A 140, 1133–1138.

    Google Scholar 

  • Kothleitner, G., and Hofer, F. (1998) Optimization of the signal to noise ratio in EFTEM elemental maps with regard to different ionization edge types. Micron 29, 349–357.

    CAS  Google Scholar 

  • Lakner, H., Rafferty, B., and Brockt, G. (1999) Electronic structure analysis of (In,Ga,Al)N heterostructures on the nanometre scale using EELS. J. Microsc. 194, 79–83.

    CAS  Google Scholar 

  • Leapman, R. D. (1982a) EXELFS spectroscopy of amorphous materials. In Microbeam Analysis – 1982, ed. K. F. J. Heinrich, San Francisco Press, San Francisco, CA, pp. 111–117.

    Google Scholar 

  • Leapman, R. (1992) EELS quantitative analysis. In Transmission Electron Energy Loss Spectrometry in Materials Science, eds. M. M. Disko, and B. Fulz, The Minerals, Metals and Materials Society, Warrendale, PA, pp. 47–83.

    Google Scholar 

  • Leapman, R. D., and Swyt, C. R. (1981a) Electron energy-loss spectroscopy under conditions of plural scattering. In Analytical Electron Microscopy – 1981, ed. R. H. Geiss, San Francisco Press, San Francisco, CA, pp. 164–172.

    Google Scholar 

  • Leapman, R. D., and Swyt, C. R. (1988) Separation of overlapping core edges in electron energy loss spectra by multiple-least-squares fitting. Ultramicroscopy 26, 393–404.

    CAS  Google Scholar 

  • Leapman, R. D., Grunes, L. A., Fejes, P. L., and Silcox, J. (1981) Extended core-edge fine structure in electron energy-loss spectra. In EXAFS Spectroscopy, eds. B. K. Teo and C. D. Joy, Plenum, New York, NY, pp. 217–239.

    Google Scholar 

  • Leapman, R. D., Grunes, L. A., and Fejes, P. L. (1982) Study of the L 23 edges in the 3d transition metals and their oxides by electron-energy-loss spectroscopy with comparisons to theory. Phys. Rev. B 26, 614–635.

    CAS  Google Scholar 

  • Lee, P. A., and Beni, G. (1977) New method for the calculation of atomic phase shifts: Application to extended x-ray absorption fine structure (EXAFS) in molecules and crystals. Phys. Rev. B 15, 2862–2883.

    CAS  Google Scholar 

  • Lee, P. A., and Pendry, J. B. (1975) Theory of the extended x-ray absorption fine structure. Phys. Rev. B 11, 2795–2811.

    CAS  Google Scholar 

  • Lee, P. A., Teo, B.-K., and Simons, A. L. (1977) EXAFS: A new parameterization of phase shifts. J. Am. Chem. Soc. 99, 3856–3859.

    CAS  Google Scholar 

  • Lee, P. A., Citrin, P. H., Eisenberger, P., and Kincaid, B. M. (1981) Extended x-ray absorption fine structure – Its strengths and limitations as a structural tool. Rev. Mod. Phys. 53, 769–806.

    CAS  Google Scholar 

  • Liu, D.-R. (1988) Experimental method of separation of the volume and surface components in an electron energy-loss spectrum. Philos. Mag. B 57, 619–633.

    CAS  Google Scholar 

  • Lo, S. C., Kai, J. J., Chen, F.-R., Chang, L., Chen, L.-C., Chiang, C.-C., Ding, P., Chin, B., Zhang, H., and Chen, F. (2001) Four-dimensional dielectric property image obtained from electron spectroscopic imaging series. J. Electron Microsc. 50, 497–507.

    CAS  Google Scholar 

  • Lucy, L. B. (1974) An iterative technique for the rectification of observed distributions. Astron. J. 79, 745–755

    Google Scholar 

  • Malinowski, E. R. (2002) Factor Analysis in Chemistry, 3rd edition, Wiley, New York, NY.

    Google Scholar 

  • Manoubi, T., Tence, M., Walls, M. G., and Colliex, C. (1990b) Curve fitting methods for quantiative analysis in electron energy loss spectroscopy. Microsc. Microanal. Microstruct. 1, 23–39.

    CAS  Google Scholar 

  • Mendis, B. G., MacKenzie, M., and Craven, A. J. (2010) A new analytical method for characterising the bonding environment at rough interfaces in high-k gate stacks using electron energy loss spectroscopy. Ultramicroscopy 110, 105–117.

    CAS  Google Scholar 

  • Michel, J., Bonnet, N., Wagner, D., Balossier, G., and Bonhomme, P. (1993) Optimization of digital filters for the detection of trace elements in electron energy loss spectroscopy. II: Experiments. Ultramicroscopy 48, 121–132.

    Google Scholar 

  • Misell, D. L., and Burge, R. E. (1969) Convolution, deconvolution and small-angle plural scattering. J. Phys. C (Solid State Phys.) 2, 61–67.

    Google Scholar 

  • Misell, D. L., and Jones, A. F. (1969) The determination of the single-scattering line profile from the observed spectrum. J. Phys. A (Gen. Phys.) 2, 540–546.

    Google Scholar 

  • Moreno, M. S., Jorissen, K., and Rehr, J. J. (2007) Practical aspects of electron energy-loss spectroscopy (EELS) calculations using FEFF8. Micron 38, 1–11.

    CAS  Google Scholar 

  • Müllejans, H., and Bruley, J. (1994) Improvements in detection sensitivity by spatial difference electron energy-loss spectroscopy at interfaces in ceramics. Ultramicroscopy 53, 351–360.

    Google Scholar 

  • Muller, D. A. (1999) Why changes in bond lengths and cohesion lead to core-level shifts in metals, and consequences for the spatial difference method. Ultramicroscopy 78, 163–174.

    CAS  Google Scholar 

  • Okamoto, J. K., Ahn, C. C., and Fultz, B. (1991) EXELFS analysis of Al, Fe L23 and Pd M45 edges. In Microbeam Analysis – 1991, ed. D. G. Howitt, San Francisco Press, San Francisco, CA, pp. 273–277.

    Google Scholar 

  • Overwijk, M. H. F., and Reefman, D. (2000) Maximum-entropy deconvolution applied to electron energy-loss spectroscopy. Micron 31, 325–331.

    CAS  Google Scholar 

  • Pettifer, R. F., and Cox, A. D. (1983) The reliability of ab initio calculations in extracting structural information from EXAFS. In EXAFS and Near Edge Structure, eds. A. Bianconi, L. Incoccia, and S. Stipcich, Springer, New York, NY, pp. 66–72.

    Google Scholar 

  • Pun. T., Ellis, J. R., and Eden, M. (1984) Optimized acquisition parameters and statistical detection limit in quantitative EELS. J. Microsc. 135, 295–316.

    CAS  Google Scholar 

  • Rabe, P., Tolkiehn, G., and Werner, A. (1980) Anisotropic EXAFS in GeS. J. Phys. C (Solid State Phys.) 13, 1857–1864.

    CAS  Google Scholar 

  • Reimer, L. (1989) Calculations of the angular and energy distribution of multiple scattered electrons using Fourier transforms. Ultramicroscopy 31, 169–176.

    Google Scholar 

  • Richardson, W. H. (1972) Bayesian iterative method of image restoration. J. Opt. Soc. Am. 62, 55–59.

    Google Scholar 

  • Sayers, D. E., Stern, E. A., and Lytle, F. W. (1971) New technique for investigating noncrystalline structures: Fourier analysis of the extended x-ray absorption fine structure. Phys. Rev. Lett. 27, 1204–1207.

    CAS  Google Scholar 

  • Schaffer, B., Kothleitner, G., and Grogger, W. (2006) EFTEM spectrum imaging at high energy resolution. Ultramicroscopy 106, 1129–1138.

    CAS  Google Scholar 

  • Schattschneider, P. (1983a) A performance test of the recovery of single energy loss profiles via matrix analysis. Ultramicroscopy 11, 321–322.

    Google Scholar 

  • Seabourne, C. R., Scott, A. J., Brydson, R., and Nicholls, R. (2009) A systematic approach to choosing parameters for modelling fins structure in electron energy-loss spectroscopy. Ultramicroscopy 109, 1374–1288.

    Google Scholar 

  • Spence, J. C. H. (1979) Uniqueness and the inversion problem of incoherent multiple scattering. Ultramicroscopy 4, 9–12.

    CAS  Google Scholar 

  • Steele, J. D., Titchmarsh, J. M., Chapman, J. N., and Paterson, J. H. (1985) A single stage process for quantifying electron energy-loss spectra. Ultramicroscopy 17, 273–276.

    CAS  Google Scholar 

  • Stephens, A. P. (1980) Quantitative microanalysis by electron energy-loss spectroscopy: Two corrections. Ultramicroscopy 5, 343–350.

    CAS  Google Scholar 

  • Stern, E. A. (1974) Theory of the extended x-ray-absorption fine structure. Phys. Rev. B 10, 3027–3037.

    CAS  Google Scholar 

  • Stern, E. A., Bunker, B. A., and Heald, S. M. (1980) Many-body effects on extended x-ray absorption fine structure amplitudes. Phys. Rev. B 21, 5521–5539.

    CAS  Google Scholar 

  • Stöger-Pollach, M. (2008) Optical properties and bandgaps from low loss EELS: Pitfalls and solutions. Micron 39, 1092–1110.

    Google Scholar 

  • Stöger-Pollach, M., Laister, A., and Schattschneider, P. (2008) Treating retardation effects in valence EELS spectra for Kramers-Kronig analysis. Ultramicroscopy 108, 439–444.

    Google Scholar 

  • Su, D. S., and Schattschneider, P. (1992a) Numerical aspects of the deconvolution of angle-integrated electron energy-loss spectra. J. Microsc. 167, 63–75.

    CAS  Google Scholar 

  • Su, D. S., and Schattschneider, P. (1992b) Deconvolution of angle-resolved electron energy-loss spectra. Philos. Mag A 65, 1127–1140.

    CAS  Google Scholar 

  • Su, D. S., Schattschneider, P., and Pongratz, P. (1992) Aperture effects and the multiple-scattering problem of fast electrons in electron-energy-loss spectroscopy. Phys. Rev. B 46, 2775–2780.

    Google Scholar 

  • Su, D. S., Wang, H. F., and Zeitler, E. (1995) The influence of plural scattering on EELS elemental analysis. Ultramicroscopy 59, 181–190.

    CAS  Google Scholar 

  • Swyt, C. R., and Leapman, R. D. (1984) Removal of plural scattering in EELS: Practical considerations. In Microbeam Analysis – 1984, eds. A. D. Romig and J. I. Goldstein, San Francisco Press, San Francisco, CA, pp. 45–48.

    Google Scholar 

  • Tencé, M., Quartuccio, M., and Colliex, C. (1995) PEELS compositional profiling and mapping at nanometer spatial resolution. Ultramicroscopy 58, 42–54.

    Google Scholar 

  • Teo, B.-K., and Lee, P. A. (1979) Ab initio calculations of amplitude and phase functions for extended x-ray absorption fine structure spectroscopy. J. Am. Chem. Soc. 101, 2815–2832.

    CAS  Google Scholar 

  • Teo, B.-K., Lee, P. A., Simons, A. L., Eisenberger, P., and Kincaid, B. M. (1977) EXAFS: Approximation, parameterization and chemical transferability of amplitude functions. J. Am. Chem. Soc. 99, 3854–3856.

    CAS  Google Scholar 

  • Trebbia, P. (1988) Unbiased method for signal estimation in electron energy loss spectroscopy, concentration measurements and detection limits in quantitative microanalysis: Methods and programs. Ultramicroscopy 24, 399–408.

    Google Scholar 

  • Trebbia, P., and Bonnet, N. (1990) EELS elemental mapping with unconventional methods I. Theoretical basis: Image analysis with multivariate statistics and entropy concepts. Ultramicroscopy 34, 165–178.

    CAS  Google Scholar 

  • Turowski, M. A., and Kelly, T. F. (1992) Profiling of the dielectric function across Al/SiO2/ Si heterostructures with electron energy loss spectroscopy. Ultramicroscopy 41, 41–54.

    CAS  Google Scholar 

  • Uhrich, M. L. (1969) Fast Fourier transforms without sorting. IEEE Trans. Audio Electroacoust. AU-17, 170–172.

    Google Scholar 

  • Verbeeck, J., and Bertoni, G. (2008) Model based quantification of EELS spectra: Treating the effect of correlated noise. Ultramicroscopy 108, 74–83.

    CAS  Google Scholar 

  • Verbeeck, J., and Bertoni, G. (2009) Deconvolution of core electron energy loss spectra. Ultramicroscopy 109, 1343–1352.

    CAS  Google Scholar 

  • Wachtmeister, S., and Csillag, S. (2011) Implementation of Gold deconvolution for enhanced energy resolution. Ultramicroscopy 111, 79–89.

    CAS  Google Scholar 

  • Wang, F., Egerton, R. F., and Malac, M. (2009a) Fourier-ratio deconvolution techniques for electron energy-loss spectroscopy (EELS) Micron 109, 1245–1249.

    CAS  Google Scholar 

  • Wehenkel, C. (1975) Mise au point d'une nouvelle methode d'analyse quantitative des spectres depertes d'énergie d'électrons diffuses dans la direction du faisceau incident: Application a l'étude des metaux nobles. J. Phys. (Paris) 36, 199–213.

    CAS  Google Scholar 

  • Weng, X., and Rez, P. (1988) Solid state effects on core electron cross-sections used in microanalysis. Ultramicroscopy 25, 345–348.

    CAS  Google Scholar 

  • Wong, K., and Egerton, R. F. (1995) Correction for the effects of elastic scattering in core-loss quantification. J. Microsc. 178, 198–207.

    CAS  Google Scholar 

  • Zaluzec, N. J. (1983) The influence of specimen thickness in quantitative energy-loss spectroscopy: (II). In 41st Ann. Proc. Electron Microsc. Soc. Am., ed. G. W. Bailey, San Francisco Press, San Francisco, CA, pp. 388–389.

    Google Scholar 

  • Zaluzec, N. J. (1985) Digital filters for application to data analysis in electron energy-loss spectroscopy. Ultramicroscopy 18, 185–190.

    CAS  Google Scholar 

  • Zhu, Y., Egerton, R. F., and Malac, M. (2001) Concentration limits for the measurement of boron by electron energy-loss spectroscopy and electron-spectroscopic imaging. Ultramicroscopy 87, 135–145.

    CAS  Google Scholar 

  • Zuo, J. M. (2000) Electron detection characteristics of a slow-scan CCD camera, imaging plates and film, and electron image restoration. Microsc. Res. Tech. 49, 245–268.

    CAS  Google Scholar 

  • Daniels, J., Festenberg, C. V., Raether, H., and Zeppenfeld, K. (1970) Optical constants of solids by electron spectroscopy. In Springer Tracts in Modern Physics, Springer, New York, NY, Vol. 54, pp. 78–135.

    Google Scholar 

  • Egerton, R. F. (1980d) Instrumentation and software for energy-loss microanalysis. In Scanning Electron Microscopy, SEM Inc., A. M. F. O’Hare, Chicago, IL, Vol. 1, pp. 41–52.

    Google Scholar 

  • Egerton, R. F., and Crozier, P. A. (1988) The use of Fourier techniques in electron energy-loss spectroscopy. In Scanning Microscopy, Supplement, Scanning Microscopy International, Chicago, IL, Vol. 2, pp. 245–254.

    Google Scholar 

  • Gold, R. (1964) An iterative unfolding method for response matrices. AED Research and Development Report ANL-6984. Argonne National Laboratories, Chicago, IL.

    Google Scholar 

  • Hagemann, H.-J., Gudat, W., and Kunz, C. (1974) Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3. DESY report SR-74/7, DESY, 2 Hamburg 52, West Germany.

    Google Scholar 

  • Johnson, D. E., Csillag, S., and Stern, E. A. (1981a) Analytical electron microscopy using extended energy-loss fine structure (EXELFS). In Scanning Electron Microscopy, SEM Inc., A. M. F. O'Hare, IL, Part 1, pp. 105–115.

    Google Scholar 

  • Malis, T., and Titchmarsh, J. M. (1986) ‘k-factor’ approach to EELS analysis. In Electron Microscopy and Analysis 1985, Institute of Physics, Bristol, U.K.

    Google Scholar 

  • Riegler, K., and Kothleitner, G. (2010) EELS detection limits revisited: Ruby – a case study. Ultramicroscopy 1004–1013.

    Google Scholar 

  • Scheinfein, M., and Isaacson, M. (1984) Design and performance of second order aberration corrected spectrometers for use with the scannering transmission electron microscope. In Scanning Electron Microscopy, SEM Inc., A. M. F. O’Hare, IL, Part 4, pp. 1681–1696.

    Google Scholar 

  • Stephens, A. P. (1981) Energy-Loss Spectroscopy in Scanning Transmission Electron Microscopy. Ph.D. Thesis, University of Cambridge, Cambridge.

    Google Scholar 

  • Stephens, A. P., and Brown, L. M. (1981) EXELFS in graphitic boron nitride. In Quantitative Microanalysis with High Spatial Resolution, The Metals Society, London, pp. 152–158.

    Google Scholar 

  • Schattschneider, P. (1983b) Retrieval of single-loss profiles from energy-loss spectra. A new approach. Philos. Mag. B 47, 555–560.

    CAS  Google Scholar 

  • Egerton, R. F. (1982b) Organic mass loss at 100 K and 300 K. J. Microsc. 126, 95–100.

    CAS  Google Scholar 

  • Egerton, R. F. (1982c) Electron energy-loss spectroscopy for chemical analysis. Philos. Trans. R. Soc. Lond. A305, 521–533.

    Google Scholar 

  • Verbeeck, J., Van Aert, S., and Bertoni, G. (2006) Model based quantification of EELS spectra: Including the fine structure. Ultramicroscopy 106, 976–980.

    CAS  Google Scholar 

  • Verbeeck, J., and Van Aert, S. (2004) Model based quantification of EELS spectra. Ultramicroscopy 101, 207–214.

    CAS  Google Scholar 

  • Egerton, R. F. (1976b) Coupling between plasmon and K-shell excitation in electron energy-loss spectra of amorphous carbon, graphite and beryllium. Solid State Commun. 19, 737–740.

    CAS  Google Scholar 

  • Muto, S., Puetter, R. C., and Tatsumi, K. (2006a) Spectral resoration and energy resolution improvement of electron energy-loss spectra by pixon reconstruction: I. Principle and test examples. J. Electron Microsc. 55, 215–223.

    CAS  Google Scholar 

  • Bradley, C. R., Wroge, M. L., and Gibbons, P. C. (1985) How to remove multiple scattering from core-excitation spectra. I. Forward scattering. Ultramicroscopy 16, 95–100.

    CAS  Google Scholar 

  • Lozano-Perez, S., de Castro Bernal, V., and Nicholls, R. J. (2009) Achieving sub-nanometre particle mapping with energy-filtered TEM. Ultramicroscopy 109, 1217–1228.

    CAS  Google Scholar 

  • de la Peña, F., Berger, M.-H., Hochepied, J.-F., Dynys, F., Stephan, O., and Walls, M. (2011) Mapping titanium and tin oxide phases using EELS: An application of independent component analysis. Ultramicroscopy 111, 169–176.

    Google Scholar 

  • Moreno, M. S., Lazar, S., Zandbergen, H. W., and Egerton, R. F. (2006) Accuracy of the calculated unoccupied states in GaN phases as tested by high-resolution electron energy-loss spectroscopy. Phys. Rev. B 73, 073308 (4 Pages).

    Google Scholar 

  • Lazar, S., Botton, G. A., and Zandbergen, H. W. (2006) Enhancement of resolution in core-loss and low-loss spectroscopy in a monochromated microscope. Ultramicroscopy 106, 1091–1103.

    CAS  Google Scholar 

  • Keenan, M. R., and Kotula, P. G. (2004) Accounting for Poisson noise in the multivariate analysis of ToF-SIMS spectrum images. Surf. Interf. Anal. 36, 203–212.

    CAS  Google Scholar 

  • Stavitski, E., and de Groot, M. F. (2010) The CTM4XAS program for EELS and XAS spectral shape analysis of transition metal L edges. Micron 41, 687–694.

    CAS  Google Scholar 

  • Craven, A. J., Buggy, T. W., and Ferrier, R. P. (1981) Post-specimen lenses in electron spectroscopy. In Quantitative Microanalysis with High Spatial Resolution, The Metals Society, London, pp. 3–6.

    Google Scholar 

  • Cheng, S. C., and Egerton, R. F. (1993) Elemental analysis of thick amorphous specimens by EELS. Micron 24, 251–256.

    CAS  Google Scholar 

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  1. Department of Physics, Avadh Bhatia Physics Laboratory, University of Alberta, Edmonton, AB, Canada

    R.F. Egerton

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Egerton, R. (2011). Quantitative Analysis of Energy-Loss Data. In: Electron Energy-Loss Spectroscopy in the Electron Microscope. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9583-4_4

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