Impact of geometry on chemical analysis exemplified for photoelectron spectroscopy of black silicon

For a smooth surface, the chemical composition can be readily evaluated by a variety of spectroscopy techniques; a prominent example is X-ray photoelectron spectroscopy (XPS), where the relative proportions of the elements are mainly determined by the intensity ratio of the element-specific photoelectrons. This deduction, however, is more intricate for a nanorough surface, such as black silicon, since the steep slopes of the geometry mimic local variations of the local emission angle. Here, we explicitly quantify this effect via an integral geometric analysis, by using so-called Minkowski tensors. Thus, we match the chemical information from XPS with topographical information from atomic force microscopy (AFM). Our method provides reliable estimates of layer thicknesses for nanorough surfaces. For our black silicon samples, we found that the oxide layer thickness is on average comparable to that of a native oxide layer. Our study highlights the impact of complex geometries at the nanoscale on the analysis of chemical properties with implications for a broad class of spectroscopy techniques