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For the reliable fabrication of the current and next generation ofnanostructures it is essential to be able to determine their materialcomposition and dimensional parameters. Using the grazing incidence X-rayfluoresence technique, which is taking advantage of the X-ray standing wavefield effect, nanostructures can be investigated with a high sensitivity withrespect to the structural and elemental composition. This is demonstrated usinglamellar gratings made of Si$_3$N$_4$. Rigorous field simulations obtained froma Maxwell solver based on the finite element method allow to determine thespatial distribution of elemental species and the geometrical shape with sub-nmresolution. The increasing complexity of nanostructures and demandedsensitivity for small changes quickly turn the curse of dimensionality fornumerical simulation into a problem which can no longer be solved rationallyeven with massive parallelisation. New optimization schemes, e.g. machinelearning, are required to satisfy the metrological requirements. We presentreconstruction results obtained with a Bayesian optimization approach to reducethe computational effort.

Grazing incidence X-ray fluorescence based characterization of nanostructures for element sensitive profile reconstruction