Transport cross section for electrons at energies of surface-sensitive spectroscopies

Abstract

Analytical description of photoelectron and Auger-electron transport in solids requires values of the transport cross sections ${\ensuremath{\sigma}}_{\mathrm{tr}}$ for electron energies between 50 and 2000 eV. An analytical formula is proposed to provide needed values of ${\ensuremath{\sigma}}_{\mathrm{tr}}$ for energies in this range and for all elements. The derivation of a suitable formula has been made in two stages. In the first stage, an approximate analytical formula for the transport cross section has been derived. In this derivation, the elastic-scattering cross sections were calculated using the first-order Born approximation and a screened Coulomb potential for interaction between the electron and an atom. In the second stage, more accurate values of ${\ensuremath{\sigma}}_{\mathrm{tr}}$ were calculated and used as a reference for determining a correction function for the approximate analytical formula. Calculations were made for atomic numbers between 1 and 96. The resulting analytical function provides values of ${\ensuremath{\sigma}}_{\mathrm{tr}}$ with a relatively high accuracy. For atomic numbers up to 30, the mean deviation between accurate values of ${\ensuremath{\sigma}}_{\mathrm{tr}}$ and values from the analytical formula reaches 0.5%. For several elements with larger atomic numbers, this deviation increases to 5%, although it is much lower for the majority of cases. Examples of applications of transport cross sections in theoretical models of electron transport are briefly discussed.