Atomic Structure of Multilayered Low-Contrast Fe/Cr Thin Films: Mathematical Formalism and Numerical Experiments

An experimental depth-resolved method for analyzing the local atomic structure of low-contrast multilayered thin films is presented in this work. A combination of X-ray reflectometry and angle-resolved EXAFS spectroscopy is considered. The following methods for solving ill-posed inverse problems are used to determine structural characteristics: the Tikhonov regularization method (for linear integral equations) and the Levenberg–Marquardt algorithm (for nonlinear equations). The proposed algorithms do not require information on the studied system such as the interface width and shape, the thickness of layers of specific elements and the depth at which they are located, and the atomic structure. This allows one to retrieve data on the local atomic structure of individual interface layers and the surface. Model numerical experiments for a Cr/Fe/Cr/Fe/Cr sample were conducted to assess the potential of this method.