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Calculations of Electron Inelastic Mean Free Paths (IMFPs) VI. Analysis of the Gries Inelastic Scattering Model and Predictive IMFP Equation
Author(s) -
Tanuma S.,
Powell C. J.,
Penn D. R.
Publication year - 1997
Publication title -
surface and interface analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 90
eISSN - 1096-9918
pISSN - 0142-2421
DOI - 10.1002/(sici)1096-9918(199701)25:1<25::aid-sia207>3.0.co;2-2
Subject(s) - inelastic mean free path , inelastic scattering , electron , range (aeronautics) , physics , scattering , chemistry , quantum mechanics , materials science , composite material
Gries has recently reported [ Surf . Interface Anal . 24, 38 (1996)] an atomistic model for inelastic electron scattering relevant to Auger electron spectroscopy and x‐ray photoelectron spectroscopy and has derived an equation (designated G1) for the estimation of inelastic mean free paths (IMFPs). We present an analysis of the Gries model and the G1 equation in terms of the similarities and differences of inelastic electron scattering by free atoms and by solids. We also compare the G1 equation with our TPP‐2M equation for estimation of IMFPs. The former equation was developed from fits to our published IMFPs over the 200–2000 eV energy range, and is identical in its energy dependence to the Bethe equation for inelastic scattering cross‐sections and to a simplification of our TPP‐2M equation for the same energy range. Comparison of parameters indicates that the Gries fitting parameter k 1 should be approximately 0.0016 and 0.0022 for non‐transition and transition elements, respectively. We find that the G1 equation could be improved by allowing the Gries fitting parameter k 2 to depend on density (as recommended for the equivalent parameter in TPP‐2M). Although we believe that the Gries model is inconsistent with current theories for the electronic structure of metals, semiconductors and inorganic compounds, we find (from sum‐rule considerations) that the G1 equation can provide an approximate guide to IMFP values. For some compounds, however, there were unexplained deviations (as found by Gries). In contrast to the G1 equation, the TPP‐2M equation provides useful IMFP estimates for all materials over the parameter range that has been explored. Gries claims that the G1 equation can be extrapolated to energies lower than 200 eV on the basis of limited agreement with some experimental IMFPs over the 10–100 eV range for Be and the alkali metals, and has questioned the reliability of our IMFPs for energies below 200 eV. We consider this comparison to be inadequate, and we recommend that the G1 equation not be used in the 50–200 eV range. © 1997 by John Wiley & Sons, Ltd.