Inelastic mean free path of low-energy electrons in condensed media: beyond the standard models

摘要

The most established approach for ‘practical’ calculations of the inelastic mean free path (IMFP) of low-energy electrons (~10 eV to ~10 keV) is based on optical-data models of the dielectric function. Despite nearly four decades of efforts, the IMFP of low-energy electrons is often not known with the desired accuracy. A universal conclusion is that the predictions of the most popular models are in rather fair agreement above a few hundred electron volts but exhibit considerable differences at lower energies. However, this is the energy range where their two main approximations, namely, the random-phase approximation (RPA) and the Born approximation, may be invalid. After a short overview of the most popular optical-data models, we present an approach to include exchange and correlation (XC) effects in IMFP calculations, thus going beyond the RPA and Born approximation. The key element is the so-called many-body local-field correction (LFC). XC effects among the screening electrons are included using a time-dependent local-density approximation for the LFC. Additional XC effects related to the incident and struck electrons are included through the vertex correction calculated using a screened-Hubbard formula for the LFC. The results presented for liquid water reveal that XC may increase the IMFP by 15–45% from its Born–RPA value, yielding much better agreement with available experimental data. The present work provides a manageable, yet rigorous, approach to improve upon the standard models for IMFP calculations, through the inclusion of XC effects at both the level of screening and the level of interaction.