Diagnostics of the atomic structure of multilayer metallic nanoheterostructures from reflectometry data: A new approach to low-contrast systems

A new method for determining the concentration profiles of chemical elements in multilayer metallic nanoheterostructures from X-ray reflectometry data has been developed as applied to low-contrast systems. The method is based on the solution of the Fredholm integral equation of the first kind, which relates the reflection coefficient and the concentration profile of the chemical elements involved in the composition of the sample. The ill-posed inverse problem of the determination of the concentration profile is solved by the regularization method. The efficiency of the proposed method is confirmed by model calculations performed for a four-layer Cr/Gd/Fe/Cr//Si structure with high-contrast Cr/Gd pairs and low-contrast Fe/Cr pairs. The experimental results on the determination of the concentration profile of the surface layer of the epitaxial thin Cr films and three-layer Cr/Fe/Cr structure deposited on the Al$_2$O$_3$ substrate are presented.