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We report comparisons of electron inelastic mean free paths (IMFPs) determined from our predictive IMFP equation TPP‐2M and reference IMFPs calculated from optical data. These comparisons were made for values of the parameter Nv(the number of valence electrons per atom or molecule) that we have recommended and those that were recommended in a recent paper by Seah et al.(Surf. Interface Anal.2001; 31: 778). The comparisons were made for eight elemental solids (K, Y, Gd, Tb, Dy, Hf, Ta and Bi) and two compounds (KBr and Y2O3) for which there were appreciable differences in the recommended Nvvalues from the two sources and for which optical data were available for the IMFP calculations. The average of the root‐mean‐square (RMS) deviations for the ten materials between IMFPs from the TPP‐2M equation with our Nvvalues and the reference IMFPs was 11.0%, whereas the corresponding average with the Seah et al.Nvvalues was 20.2%. The larger average in the latter comparison was mainly due to large (>20%) RMS deviations for four materials (K, Hf, Ta and KBr). For the other six materials, the RMS deviations with the Seah et al.values of Nvwere similar to those with our values of Nv. Based on the comparisons for these ten materials, we believe that it is preferable to use our values of Nvin the TPP‐2M equation. Copyright © 2003 John Wiley & Sons, Ltd.

We report comparisons of electron inelastic mean free paths (IMFPs) determined from our predictive IMFP equation TPP-2M and reference IMFPs calculated from optical data. These comparisons were made for values of the parameter Nv (the number of valence electrons per atom or molecule) that we have recommended and those that were recommended in a recent paper by Seah et al. (Surf. Interface Anal. 2001; 31: 778). The comparisons were made for eight elemental solids (K, Y, Gd, Tb, Dy, Hf, Ta and Bi) and two compounds (KBr and Y2O3) for which there were appreciable differences in the recommended Nv values from the two sources and for which optical data were available for the IMFP calculations. The average of the root-mean-square (RMS) deviations for the ten materials between IMFPs from the TPP-2M equation with our Nv values and the reference IMFPs was 11.0%, whereas the corresponding average with the Seah et al. Nv values was 20.2%. The larger average in the latter comparison was mainly due to large (>20%) RMS deviations for four materials (K, Hf, Ta and KBr). For the other six materials, the RMS deviations with the Seah et al. values of Nv were similar to those with our values of Nv. Based on the comparisons for these ten materials, we believe that it is preferable to use our values of Nv in the TPP-2M equation. Copyright © 2003 John Wiley & Sons, Ltd.

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 parameterk1should 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 parameterk2to 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.

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 k1 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 k2 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.

We discuss the interaction of a tunneling electron with its equilibrium electromagnetic environment. The environment of an isolated tunnel junction is modeled by a set of harmonic oscillators that are suddenly displaced when an electron tunnels across the junction. We treat these displaced oscillators quantum mechanically, predicting behavior that is very different than that predicted by a semiclassical treatment. In particular, the shape of the zero-bias anomaly caused by the Coulomb blockade (a single-electron charging effect), is found to be strongly dependent on the impedance,Z (?), of the leads connected to the junction. Comparison with three recent experiments demonstrates that the quantum mechanical treatment of this model correctly describes the essential physics in these systems.