Rumen K. Krastev This is very interesting, but what information do you expect to receive using the "Shirley-Vegh-Salvi-Castle" background correction? How will you take into account the thickness of the outer oxide layers? And finally: the inelastic background from the outer and inner layers has a completely different shape and intensity, so the removal of the background is applicable only for homogeneous samples.
The article cited in my previous answer refers to a technique for measurement of the mechanical diagram (force-displacement) of a base length that contains at least one pair of surface layers (between two compressed bodies), and a method for analyzing this data. As results, it gives information for the non-linear-elastic properties of these surface layers and their depth.
x-ray photoelectron spectroscopy is a different approach, I am not familiar with.