Determination of the concentration profile of interfaces in multilayered nanostructures according to the angular dependence of X-ray photoelectron spectra: A new approach

The possibility of determining the concentration profile of interfaces in multilayered nanoheterostructures according to the data of the angular dependence of X-ray photoelectron spectra was shown. To solve this ill-posed inverse problem, we used Tikhonov’s regularization method with iterative refinement. To determine the optimum parameter of regularization, we used the L curve technique. The programs used for this study allowed high accuracy of calculations. All this made it possible to obtain information about the distribution of atoms of a definite sort with a resolution of 0.1–0.15 nm in depth. The results of numerical simulation of XPS spectra are given for a three-layered Cr/Fe structure. Solving the inverse problem for the initial data distorted by the statistical noise afforded a concentration distribution over depth for Cr and Fe atoms. The stability of the solution against experimental errors was determined.