Effective attenuation lengths for photoelectrons emitted by high-energy laboratory X-ray sources

摘要

We report calculations of effective attenuation lengths (EALs) for Si 2s(1/2), Cu 2p(3/2), Ag 3d(5/2), and Au 4f(7/2) photoelectrons excited by Mg K alpha, Al K alpha, Zr L alpha, and Ti K alpha X-rays, where the photoelectron energies ranged from 321 eV to 4.426 keV. These EALs, appropriate for determining overlayer-film thicknesses, were calculated from the transport-approximation formalism and from Monte Carlo simulations using photoionization cross sections from the dipole and non-dipole approximations. Satisfactory consistency was found between EALs determined from the TA formalism and from MC simulations, while differences between EALs for Au 4f(7/2) photoelectrons from the dipole and non-dipole approximations were between 1% (for Mg and Al K alpha X-rays) and 2.5% (for Ti K alpha X-rays) for photoelectron emission angles less than 50 degrees. As in past work for electron energies less than 2 key, we found a simple linear relation between the ratio of the average EAL (for emission angles less than 50 degrees) to the inelastic mean free path (IMFP) and the single-scattering albedo, a function of the IMFP and the transport mean free path. The root-mean-square difference between our average EALs and those from the linear expression was 1.44%. This expression should be useful in determinations of film thicknesses by XPS with unpolarized X-rays for photoelectron energies up to about 5 key. (C) 2015 Elsevier B.V. All rights reserved.