Practical correction procedures for elastic electron scattering effects in ARXPS

Angle-resolved XPS and AES (ARXPS and ARAES) are widely used for determination of the in-depth distribution of elements in the surface region of solids. It is well known that elastic electron scattering has a significant effect on the intensity as a function of emission angle and that this has a great influence on the determined overlayer thicknesses by this method. However the applied procedures for ARXPS and ARAES generally neglect this because no simple and practical procedure for correction has been available. However recently, new algorithms have been suggested. In this paper, we have studied the efficiency of these algorithms to correct for elastic scattering effects in the interpretation of ARXPS and ARAES. This is done by first calculating electron distributions by Monte Carlo simulations for well-defined overlayer/substrate systems and then to apply the different algorithms. We have found that an analytical formula based on a solution of the Boltzmann transport equation provides a good account for elastic scattering effects. However this procedure is computationally very slow and the underlying algorithm is complicated. Another much simpler algorithm, proposed by Nefedov and coworkers, was also tested. Three different ways of handling the scattering parameters within this model were tested and it was found that this algorithm also gives a good description for elastic scattering effects provided that it is slightly modified so that it takes into account the differences in the transport properties of the substrate and the overlayer. This procedure is fairly simple and is described in detail. The model gives a much more accurate description compared to the traditional straight-line approximation (SLA). However it is also found that when attenuation lengths instead of inelastic mean free paths are used in the simple SLA formalism, the effects of elastic scattering are also reasonably well accounted for. Specifically, from a systematic study of several overlayer/substrate systems it was found that by ARXPS analysis of the overlayer signal, the mean percentage deviation from the nominal heights is ∼5% when using the procedure proposed by Nefedov, and ∼10% with the SLA using attenuation lengths while the deviation is 13–68% with the SLA using IMFPs. For ARXPS analysis of the substrate signal, the mean percentage deviation from the nominal heights is ∼10% both when using the modified Nefedov algorithm and when using the SLA with attenuation lengths as compared to 16–31% with the SLA using IMFPs.