Path-length distribution of photoelectrons emitted from homogeneous noncrystalline solids: Consequences for inelastic-background analysis.

Abstract

The path-length distribution function characterizing the probability for a photoelectron to escape from a homogeneous solid after traveling a certain path length R has been found analytically by solving a Boltzmann-type kinetic equation with appropriate boundary condition. The solution is obtained in the transport approximation and is valid for an arbitrary geometry and under the condition that the typical angular spectrum of photoelectrons is a smooth function of the angular variable. It is shown that, depending on the initial anisotropy of the photoelectron emission, the path-length distribution may either reach a maximum value at a certain path length or be a monotonically decreasing function. The path-length distribution has also been calculated by the Monte Carlo technique employing realistic Mott differential elastic-scattering cross sections. The theoretical results were obtained for a number of photoelectron lines in Al, Cu, and Au with different asymmetry parameters and photoelectron energies. It was shown that within about 10% accuracy the path-length distribution function is a universal function of the path length divided by the transport mean free path. This conclusion is in full accordance with the prediction of the transport approximation. The consequences and implications of elastic-scattering effects for the inelastic background analysis of Auger electron spectroscopy and x-ray photoemission spectroscopy energy spectra are discussed.