Disorder effects in angle-resolved photoelectron spectroscopy

Abstract

The effects of compositional, vibrational, long-range positional, and topographical disorders upon the angle-resolved photoemission spectra of tightly bound valence electrons are investigated. In order to take into account the strong potential sensed by the electron in the vicinity of the atomic core, an augmented-planewave final state is employed. With this final state, the interference between atoms in the optical ionization step is identical to that obtained with a plane-wave final state, but the atomic cross sections are those calculated from spherical, not plane waves. The angle-energy dependence of the photoemission spectra of crystalline alloys depends upon the degree of chemical ordering, the concentration, and the atomic photoionization cross sections of each element present. The primary effect of spatial disorder is to weaken $k$ conservation in the optical ionization step, particularly as the momentum of the final state increases. It is found that phonon disorder is not important in the ultraviolet-photoemission (UPS) regime, but it is sufficient to destroy almost totally $k$ conservation in the x-ray-photoemission (XPS) regime in most materials at room temperature. In this limit, the observed angle-resolved spectra ought to reveal the total density of states modulated by atomic-like photoionization cross sections. High-order phonon induced optical transitions might limit the energy resolution obtainable in the XPS regime to a few tenths of an electron volt. Surface roughness is shown to weaken the conservation of the component of the momentum parallel to the surface, possibly even in the XPS regime. Topographical disorder is important as long as refraction of the photoelectron at the surface remains large. It is argued that if the final electron states are very heavily mixed plane waves, then surface roughness and refraction are much more important than when the states are free-electron-like. Photoemission spectra of electrons directed along a crystallographic axis are shown to provide an important test for determining the validity of several recent models for the final electron state.