Reference-free grazing incidence x-ray fluorescence and reflectometry as a methodology for independent validation of x-ray reflectometry on ultrathin layer stacks and a depth-dependent characterization

Nanolayer stacks are technologically very relevant for current and future applications in many fields of research. A nondestructive characterization of such systems is often performed using x-ray reflectometry (XRR). For complex stacks of multiple layers, low electron density contrast materials, or very thin layers without any pronounced angular minima, this requires a full modeling of the XRR data. As such a modeling is using the thicknesses, the densities, and the roughnesses of each layer as parameters, this approach quickly results in a large number of free parameters. In consequence, cross correlation effects or interparameter dependencies can falsify the modeling results. Here, the authors present a route for validation of such modeling results which is based on the reference-free grazing incidence x-ray fluorescence (GIXRF) methodology. In conjunction with the radiometrically calibrated instrumentation of the Physikalisch-Technische Bundesanstalt, the method allows for reference-free quantification of the elemental mass depositions. In addition, a modeling approach of reference-free GIXRF-XRR data is presented, which takes advantage of the quantifiable elemental mass depositions by distributing them depth dependently. This approach allows for a reduction of the free model parameters. Both the validation capabilities and the combined reference-free GIXRF-XRR modeling are demonstrated using several nanoscale layer stacks consisting of $HfO2$ and $Al2O3$ layers.