Emission-depth Dependence of the Signal Photoelectron Energy Spectrum

Abstract

An analytical expression for the escape probability of signal photoelectrons as a function of the depth of origin, energy and direction of emission from a solid has been found by solving a kinetic equation. The solution is expressed by a series of partial escape probabilities corresponding to contributions of electrons that have suffered a certain number of inelastic collisions before leaving a target. The universal relationship between the probability for an electron to escape from a certain depth after being scattered inelastically n times (n=0, 1, 2, …) and the pathlength distribution has been derived. The photoelectron spectra from an Si(Au) tracer located at different depths in an Au(Si) matrix has been calculated analytically and by means of the Monte Carlo technique for different XPS configurations. The peak and the background regions have been found to be strongly affected by elastic scattering of electrons in the sample. The neglect of the elastic collisions has been shown to over- or underestimate the photoelectron current (up to 100% in the case of the Au sample and the Si tracer located at a depth of the order of several inelastic mean free paths). The analytical theory predictions are compared with the corresponding Monte Carlo data and good agreement in absolute units is observed. The obtained results indicate that the assumption of a simple exponential attenuation of electrons made in non-destructive depth-profile reconstructions seems to be less valid in the case of materials in which elastic scattering is significant. © 1997 by John Wiley & Sons, Ltd.