Improved depth information from routine analysis of the inelastic background of XPS and HAXPES spectra using optimized two- and three-parameter cross-sections

Determination of the depth distribution of complex nanostructures by X-ray photoelectron spectroscopy (XPS) inelastic background analysis may be complicated if the sample materials have widely different inelastic scattering cross-sections. It was recently demonstrated that this may be solved by using a mixture of cross-sections. This permits retrieval of depth distributions of complex stacks and deeply buried layers with a typical 5% accuracy. This requires however that the cross-sections of the individual sample materials are known which is often not the case and this can complicate practical use for routine analysis. In this paper, we explore to what extent a suitable two- or three-parameter cross-section can be defined independent of prior knowledge of the cross-sections involved but simply defined by fitting the cross-section parameters to the spectrum being analyzed. This paper presents a theoretical study following our recent paper that explored how to make the best choice of inelastic mean free path and inelastic scattering cross-section for the inelastic background analysis with the Quases-Tougaard software. It was previously shown that a rough analysis of the inelastic background could give a good idea of the depth distribution. Here, we demonstrate with model spectra from buried layers created with Quases-Tougaard Generate software that a rather accurate analysis can be performed for very different cases with an average ~5% error. This analysis is easy to apply as it only needs the two- or three-parameter cross-sections generated with the Quases-Tougaard software. This study is aimed to improve routine analysis of the inelastic background of XPS and hard X-ray photoelectron spectroscopy (HAXPES) spectra.