Model independent x-ray standing wave analysis of periodic multilayer structures

Abstract

We present a model independent approach for the analysis of X-ray fluorescence yield modulated by an X-ray standing wave (XSW), that allow a fast reconstruction of the atomic distribution function inside a sample without fitting procedure. The approach is based on the direct regularized solution of the system of linear equations that characterizes the fluorescence yield. The suggested technique was optimized for, but not limited to, the analysis of periodic layered structures where the XSW is formed under Bragg conditions. The developed approach was applied to the reconstruction of the atomic distribution function for LaN/BN multilayers with 50 periods of 43 Å thick layers. The object is especially difficult to analyze with traditional methods, as the estimated thickness of the interface region between the constituent materials is comparable to the individual layer thicknesses. However, using the suggested technique, it was possible to reconstruct width of the La atomic distribution showing that the La atoms stay localized within the LaN layers and interfaces and do not diffuse into the BN layer. The analysis of the reconstructed profiles showed that the positions of the center of the atomic distribution function can be estimated with an accuracy of 1 Å.