Elastic-electron-scattering effects on angular distributions in x-ray-photoelectron spectroscopy

Electron trajectories in x-ray photoemission from solids are partially randomized by elastic collisions, and thus the angular distribution of photoelectrons leaving the surface is different from that for isolated atoms. This problem is approached in the present work by extensive Monte Carlo simulations of electron trajectories resulting from photoionization of the gold 4s, 4${\mathit{p}}_{3/2}$, 4${\mathit{d}}_{5/2}$, and 4${\mathit{f}}_{7/2}$ subshells by Mg characteristic x rays. Calculations were made for the full range of angles of x-ray incidence and for all possible positions of the electron energy analyzer. In comparisons with intensities predicted from the common formalism in which elastic scattering is neglected, it was found that the elastic-scattering effects can be accounted for with two correction factors. These factors are, to a large extent, independent of experimental geometry for certain ranges of angles. The correction factors depend only slightly, for example, on the photoelectron exit angle in the range 0°–30° with respect to the surface normal. The present results indicate that the magic angle (the angle between the direction of x rays and the direction of signal electrons at which the effects of angular anisotropy can be avoided) is not a single constant value of 54.7° (as found for isolated atoms) but a much larger value that depends on the electron exit angle and the photoelectron subshell. Furthermore, it has been found that elastic-scattering effects can be neglected for certain experimental configurations. The current for a given photoelectron line is then equal to the current calculated from the common formalism, but this equality occurs at different angles between the incident x rays and the detected electrons depending on the photoelectron line and the electron exit angle.