CALCULATIONS OF ELECTRON INELASTIC MEAN FREE PATHS (IMFPS) .6. ANALYSIS OF THE GRIES INELASTIC-SCATTERING MODEL AND PREDICTIVE IMFP EQUATION

Gries has recently reported [Surf. Interface Anal. 24, 38 (1996)] an a tomistic model for inelastic electron scattering relevant to Auger ele ctron spectroscopy and x-ray photoelectron spectroscopy and has derive d an equation (designated G1) for the estimation of inelastic mean fre e paths (IMFPs). We present an analysis of the Cries model and the G1 equation in terms of the similarities and differences of inelastic ele ctron scattering by free atoms and by solids. We also compare the G1 e quation with our TPP-2M equation for estimation of IMEPs. The former e quation was developed from fits to our published IMFPs over the 200-20 00 eV energy range, and is identical in its energy dependence to the B ethe equation for inelastic scattering cross-sections and to a simplif ication of our TPP-2M equation for the same energy range. Comparison o f parameters indicates that the Cries fitting parameter k(1) should be approximately 0.0016 and 0.0022 for non-transition and transition ele ments, respectively. We find that the G1 equation could be improved by allowing the Gries fitting parameter k(2) to depend on density (as re commended for the equivalent parameter in TPP-2M). Although we believe that the Cries model is inconsistent with current theories for the el ectronic structure of metals, semiconductors and inorganic. compounds, we find (from sum-rule considerations) that the G1 equation can provi de an approximate guide to IMFP values. For some compounds, however, t here were unexplained deviations (as found by Cries). In contrast to t he G1 equation, the TPP-2M equation provides useful IMFP estimates for all materials over the parameter range that has been explored. Cries 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 questi oned the reliability of our IMFPs for energies below 200 eV. We consid er this comparison to be inadequate, and we recommend that the G1 equa tion not be used in the 50-200 eV range.