We improve the Mermin-Penn algorithm (MPA) for determining the energy loss function (ELF) within the dielectric formalism. The present algorithm is applicable not only to real metals, but also to materials that have an energy gap in the excitation spectrum. Applying the improved MPA to liquid water, we show that the present algorithm is able to address the ELF overestimation at the energy gap, and the calculated results are in good agreement with experimental data.

We present an approach for introducing damping into the Penn algorithm by using the Mermin dielectric function instead of the Lindhard dielectric function. We find that for a damping of 1.5 eV, the electron inelastic mean free path calculated by the present algorithm for Al is in excellent agreement with experimental values in the energy range 5–9 eV. Meanwhile, for a damping of 2.0 eV, our result for Au is consistent with the GW+T ab initio calculation at several electronvolts. In particular, at an energy of 1 eV, our result for Au is 297 Å and lies within the range 220–330 Å obtained from measurements by ballistic electron emission microscopy.

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Knowledge of electron inelastic mean free paths (IMFPs) is important for electron spectroscopy and microscopy studies. Here, we determine the IMFPs at energies below 100 eV for 10 elemental solids (V, Fe, Ni, Mo, Pd, Ag, Ta, W, Pt, and Au) within the dielectric formalism, using the energy-loss function calculated in the adiabatic local-density approximation of time-dependent density-functional theory. The resulting IMFPs at a few eV above the Fermi energy are comparable to those from ab initio calculations in the GW approximation of many-body theory. The present approach provides an alternative to evaluate hot-electron inelastic lifetimes.

We show that the dielectric approach can determine electron inelastic mean free paths in materials with an accuracy equivalent to those from first-principle calculations in the GW approximation of many-body theory. The present approach is an alternative for calculating the hot-electron lifetime, which is an important quantity in ultrafast electron dynamics. This approach, applied here to solid copper for electron energies below 100 eV, yields results in agreement with experimental data from time-resolved two-photon photoemission, angle-resolved photoelectron spectroscopy, and X-ray absorption fine structure measurements in the energy ranges 2–3.5, 10–15, and 60–100 eV, respectively.

We derive an analytical formula for the electron inelastic mean free path (IMFP) from its definition within the dielectric formalism. The parameters in this formula are determined solely by the optical energy-loss function of the material of interest. This formula is valid for electrons of energy larger than 500 eV, including relativistic electrons.

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