The description of quantum dielectric function for insulators over Bethe surface

Abstract

A new expression for the dielectric function is suggested here, which is the Mermin–Belkacem-Sigmund (MBS) model derived from the Belkacem–Sigmund (BS) model based on the conservation of a local particle number in the Mermin model. The energy loss function expressions are reviewed analytically for both models, and these dielectric functions were used to calculate the Bethe sum rule, the energy loss function (ELF), as well as the differential inelastic inverse mean free path (DIIMP) for \(\mathrm{H}_2\mathrm{O}\). The indication from the results is that, compared to the BS dielectric function, the MBS dielectric function is more compatible in its consistency with the exact Bethe sum rule. The ELF for the MBS type is compatible relatively in high and low momentum transfers, while the ELF for the BS type is suitable for high-k. The two models of ELF were also applied to evaluate DIIMP for electron kinetic energy 1 keV, and these were compared with the results predicted in several ways via the SESINIPAC program, using the Mermin dielectric function and the extended Drude and Monte–Carlo method. These predicted results are in reasonable agreement with those estimated from other methods at the range of energy transfer (0–50) eV.