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

Abstract

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. Copyright © 2015 John Wiley & Sons, Ltd.

Calculations of electron inelastic mean free paths. XI. Data for liquid water for energies from 50 eV to 30 keV

“…These increases were much larger than those predicted by the Mott-like correction of Ashley [3] (a maximum of about 25% at 100 eV) and the Ochkur correction of Fernandez-Varea et al [77] (a maximum of about 14% at 20 eV). The large exchange and correlation corrections found by Emfietzoglou et al [13,76] are surprising because detailed comparisons of calculated IMFPs from the FPA for many elemental solids agree reasonably with IMFPs determined by elastic-peak electron spectroscopy. [28,66] The latter comparisons were made for energies between 100 eV and 5 keV, and the average RMS difference was 12% for one data set with 11 elemental solids, while the average RMS difference was 15% for another data set with 17 elemental solids.…”

“…These large differences must be mainly due to the effects of electron exchange and correlation that were introduced by using the concept of a many-body local-field correction. [13] In a recent review, Emfietzoglou et al [76] described the several theoretical approaches used in calculations of IMFPs for water. They showed comparisons in which water IMFPs from the SSPA, SPA (identified as the Ritchie-Howie model [29] ), FPA, and EM method were plotted as a function of energy from 10 eV to 10 keV.…”

Geant4‐DNA example applications for track structure simulations in liquid water: A report from the Geant4‐DNA Project

“…using the Drude parameterization of by Emfietzoglou . Although more advanced dielectric functions are available, the main advantage of keeping the Drude representation in “option 4” is that due to the mathematical simplicity of the Drude functions both and can be expressed analytically and the f‐sum‐rule is fulfilled for all q regardless of the form of the dispersion relations. The deficiencies related to the truncation of the Drude functions in “option 2” are overcome in “option 4” through the replacement of Eq.…”

A comparison between Monte Carlo method and the numerical solution of the Ambartsumian-Chandrasekhar equations to unravel the dielectric response of metals

“…The ELF, which is only a property of the target material, is thus a fundamental quantity directly related to the energy deposited by charged particles [6,7,8]. Typically, the ELF can be computed by using three different approaches [9,10]: i) from ab initio simulations [11,12]; ii) semi-empirically [13], by using experimental measurements of optical or electron energy loss spectra (EELS); iii) from model calculations within the electron gas theory [14].…”

“…In practice, the accurate computation of the ELF over the whole momentum dispersion, is still challenging for abinitio simulations due to the high computational cost of including local field effects (LFE), and exchange and correlation beyond the Random Phase Approximation (RPA). The dielectric function can be obtained by using either many-body perturbation theory (MBPT) [11,12] or time-dependent density functional theory (TDDFT) [10,13,15].…”