Evaluation of dielectric function models for calculation of electron inelastic mean free path

Abstract

This work investigates the detailed difference between dielectric function models, the Mermin model and the full Penn algorithm (FPA) model, for the determination of an electron inelastic mean free path (IMFP) with optical energy loss function (ELF), as an extension of our previous study [Da et al., Surf. Interface Anal. 51, 627 (2019)] by using the simple Drude-type ELF. In the conventional normal Mermin (NM) model, the approximations of ELF by the Drude equation will introduce inevitable fitting error. In order to enhance the accuracy of the NM model, our previous proposed extended Mermin model [Da et al., Phys. Rev. Lett. 113, 063201 (2014)], which is renamed as a super-extended Mermin algorithm (SE-MA) now, is employed to eliminate the error by expanding the definition of Drude oscillators used in the NM. In the SE-MA, the Drude-like oscillators allow the existence of negative strengths to express the fine structures of phonon–electron scattering and the plasmon lifetime broadening effect. Because in our previous study, the simple Drude-type ELF cannot include these complex structures, in this work, the electron IMFPs are calculated for five realistic materials, Al, Si, Cu, Au, and MgO. The difference between IMFPs calculated by the SE-MA model and the FPA model is material dependent and is significant in the low energy region, which is analyzed by using the Fano plot. This is due to the more important role played by the plasmon lifetime broadening effect.