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

We report calculations of effective attenuation lengths (EALs) for Si 2s1/2, Cu 2p3/2, Ag 3d5/2, and Au 4f7/2 photoelectrons excited by Mg Kα, Al Kα, Zr Lα, and Ti Kα 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 4f7/2 photoelectrons from the dipole and non-dipole approximations were between 1% (for Mg and Al Kα X-rays) and 2.5% (for Ti Kα X-rays) for photoelectron emission angles less than 50°. As in past work for electron energies less than 2 keV, we found a simple linear relation between the ratio of the average EAL (for emission angles less than 50°) 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 keV.