Comparison of the Mermin and Penn models for inelastic mean‐free path calculations for electrons based on a model using optical energy‐loss functions

Abstract

We present detailed comparisons of calculated inelastic mean‐free paths (IMFPs) of electrons with energies up to 10 keV from the full Penn algorithm (FPA) model and the Mermin model using prototypical Drude‐type energy‐loss functions (ELFs). From systematic comparisons of IMFPs obtained from the prototypical ELFs using these two models, we obtain evidence that supports the Mermin model as the more reasonable model for electron IMFP calculations than the FPA model. The deviations between these two models are mainly because of finite plasmon lifetimes and show a strong dependence on the width of the ELFs and electron energy. For instance, the theoretical description of the ELF based on the Mermin model predicts lower values for the IMFPs than those obtained by the FPA approach in most cases. As for those prototypical ELFs with neither very sharp nor very broad structures that describe the ELF of actual materials, the Mermin IMFPs are smaller than the FPA IMFPs by about 5% for energies between 1 and 10 keV. We also found that over the 130 to 10 keV range, the modified Bethe equation fits IMFPs calculated with both algorithms within a 1% relative difference.