Structural characterization of Cr/Gd/Cr and Cr/Gd/Fe/Cr multilayer nanostructures by X-ray reflectometry

It is shown that the new approach to low-contrast systems upon the interpretation of X-ray reflectivity data can be applied to multilayer samples such as Cr/Gd/Fe/Cr/Si. The method is based on solving the Fredholm integral equation of the first kind, which connects the reflectivity with the concentration profiles of elements that enter into the sample composition. The inverse ill-posed problem of the determination of the concentration profile is solved using the regularization method. The efficiency of the method proposed is verified by model calculations fulfilled for a Cr/Gd/Fe/Cr/Si four-layer structure, where there are both high-contrast pairs of layers (Cr/Gd) and pairs with a low contrast (Fe/Cr). Experimental data for Cr/Gd/Cr and Cr/Gd/Fe/Cr multilayer nanoheterostructures have been obtained under laboratory conditions. The thicknesses of all layers of all the elements and of the Cr/Gd, Gd/Fe, and Fe/Cr interfaces have been determined.