Abstract
The use of the full Penn algorithm (FPA) for calculating the inelastic mean free path (IMFP) in materials with a band gap Eg was explained. Additionally, the details of applying relativistic corrections to both the FPA and the single pole approximation (SPA) by Penn for calculating the IMFP in high-energy regions exceeding such as 100 keVwere discussed. There are two factors regarding the effect of Eg on IMFP calculations. The first is that the minimum and maximum values of the electron energy loss change, and the second is how to express the momentum transfer that is altered due to the presence of Eg. For these aspects, the FPA-BABC method, developed based on the work by Boutboul et al. [ J. Appl. Phys. 79, 6714(1996)], and refined by Shinotsuka et al.[Surf. Interface Anal. 54, 534 (2022)] was explained. Regarding the application of relativistic corrections to FPA and SPA, it is shown that for energy regions below 500 keV, the corrections can be relatively easily incorporated by applying relativistic kinematic adjustments to electron motion. Furthermore, a comparative study was conducted on the IMFPs obtained from relativistic SPA and relativistic FPA-BABC across 45 inorganic compounds and 14 organic compounds in the energy range from 200 eV to 500 keV. The results indicated that, at around 200 keV, the relative differences between the SPA-IMFPs and FPA-BABC-IMFPs were on average below approximately 2% for inorganic compounds and below 1% for organic compounds. The maximum deviation between the two methods in the energy range of 200 eV to 500 keV was about 3%. From the above, it becomes clear that the relativistic SPA can be used to calculate the IMFP in the energy range of 200 eV- 500 keV even for materials with Eg.
https://ror.org/026v1ze26 
