Inelastic mean free path from reflectivity of slow electrons

Abstract

The inelastic mean free path (IMFP) of electrons is derived using a new approach based on the low-energy electron reflectivity from ultrathin films. The thickness-dependent quantum size oscillations as a function of electron energy observed in the reflectivity of slow electrons are modeled using an absorbing Fabry-P\'erot interferometer consisting of vacuum, film, and substrate. The absorbing properties of the film are represented by the imaginary part of the complex refractive index associated with the IMFP which determines the amplitude of the electron reflectivity oscillations. Using this formalism for an Fe film on W(110), the IMFP in Fe is found in the energy range from 4 to 18 eV above the vacuum level. In contrast to the common notion, the IMFP in Fe is shown to have a very weak energy dependence at low energy. The results are in good agreement with independent IMFP measurements found in thickness-dependent photoemission experiments.