PATH-LENGTH DISTRIBUTION OF PHOTOELECTRONS EMITTED FROM HOMOGENEOUS NONCRYSTALLINE SOLIDS - CONSEQUENCES FOR INELASTIC-BACKGROUND ANALYSIS

The path-length distribution function characterizing the probability f or a photoelectron to escape from a homogeneous solid after traveling a certain path length R has been found analytically by solving a Boltz mann-type kinetic equation with appropriate boundary condition. The so lution is obtained in the transport approximation and is valid for an arbitrary geometry and under the condition that the typical angular sp ectrum of photoelectrons is a smooth function of the angular variable. It is shown that, depending on the initial anisotropy of the photoele ctron emission, the path-length distribution may either reach a maximu m value at a certain path length or be a monotonically decreasing func tion. The pathlength distribution has also been calculated by the Mont e Carlo technique employing realistic Mott differential elastic-scatte ring cross sections. The theoretical results were obtained for a numbe r of photoelectron lines in Al, Cu, and Au with different asymmetry pa rameters and photoelectron energies. It was shown that within about 10 % accuracy the path-length distribution function is a universal functi on of the path length divided by the transport mean free path. This co nclusion is in full accordance with the prediction of the transport ap proximation. The consequences and implications of elastic-scattering e ffects for the inelastic background analysis of Auger electron spectro scopy and x-ray photoemission spectroscopy energy spectra are discusse d.