Simultaneous analysis of Grazing Incidence X-Ray reflectivity and X-ray standing waves from periodic multilayer systems

Structural analysis of periodic multilayers with small period thickness (~4 nm) is a challenging task, especially when thicknesses of intermixed interfaces become comparable to individual layer thicknesses. In general, angular dependent X-ray fluorescence measurements, excited by the X-ray standing wave (XSW) that is formed in the Bragg reflection conditions, can provide information about the in-depth distribution of atoms in a multilayer. The atomic depth profiles in periodic multilayer structures can be obtained with high resolution by simultaneously analyzing the fluorescence data from XSW experiments, together with the analysis of grazing incidence X-ray reflectivity (GI-XRR) experiments. As a first step, the electron density distribution in the multilayer period is obtained by fitting of GI-XRR data. Next, the electromagnetic wave distribution in the multilayer is calculated based on the reconstructed electron density profile which is then used to calculate fluorescence yield from specific materials in x-ray standing wave experiments. The traditional data analysis approach is the simultaneous fit of these two sets of data and it depends on two distributions: the atomic distribution and the electron density distribution. In case of unknown atomic intermixture, there may not be a clear connection between these two distributions leading to fit of non physical parameters