# Reference-free GIXRF-XRR as a methodology for independent validation of XRR on ultrathin layer stacks and a depth-dependent characterization

## TL;DR

This paper introduces a reference-free GIXRF-XRR methodology for validating and improving the modeling of complex ultrathin layer stacks, reducing free parameters and enabling depth-dependent characterization.

## Contribution

It presents a novel validation approach combining reference-free GIXRF with XRR, reducing model complexity and improving accuracy for nanolayer stack analysis.

## Key findings

- Validated layer stack models with reduced free parameters.
- Demonstrated depth-dependent elemental distribution in multilayers.
- Enhanced accuracy in ultrathin layer characterization.

## Abstract

Nanolayer stacks are technologically very relevant for current and future applications in many fields of research. A non-destructive 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 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 consquence, cross-correlation effects or interparameter dependencies can falsify the modeling results. Here, we 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 HfO$_2$ and Al$_2$O$_3$ layers.