Dynamical theory analysis of X-ray patterns from nanostructured substrates

Characterization of nanopatterned substrates is critical in many applications across various fields, including optics, electronics, and fluidics. Although direct probing techniques; e.g. AFM and SEM, are incredibly informative, they suffer inaccessibility to beneath-surface structures. On the other hand, neutron/x-ray scattering offers a non-destructive approach for in-depth characterization. The caveat is that scattering methods require non-trivial data modeling. Kinematic approximations have facilitated scattering characterization of non-structured materials but are not adequately suited for strong scattering from periodic structures. In contrast, the dynamical theory (DT) offers an advanced model for interpreting off-specular signals from periodic samples. This model has been validated on substrates with various periodic profiles, measured by neutron scattering. Here, we extend this approach to off-specular x-ray scattering. We improve the DT analysis by advancing a fitting package applying covariance matrix adaptation evolution strategy. Our approach yields high efficiency and precision in predicting complex profiles by adopting a Parratt thin-slicing formalism. This opens new possibilities in the characterization of nanostructured substrates for a variety of applications.