Element sensitive reconstruction of nanostructured surfaces with finite elements and grazing incidence soft X-ray fluorescence

摘要

The geometry of a Si$_3$N$_4$ lamellar grating was investigatedexperimentally with reference-free grazing-incidence X-ray fluorescenceanalysis. While simple layered systems are usually treated with the matrixformalism to determine the X-ray standing wave field, this approach fails forlaterally structured surfaces. Maxwell solvers based on finite elements areoften used to model electrical field strengths for any 2D or 3D structures inthe optical spectral range. We show that this approach can also be applied inthe field of X-rays. The electrical field distribution obtained with theMaxwell solver can subsequently be used to calculate the fluorescenceintensities in full analogy to the X-ray standing wave field obtained by thematrix formalism. Only the effective 1D integration for the layer system has tobe replaced by a 2D integration of the finite elements, taking into account thelocal excitation conditions. We will show that this approach is capable ofreconstructing the geometric line shape of a structured surface with highelemental sensitivity. This combination of GIXRF and finite-element simulationspaves the way for a versatile characterization of nanoscale-structuredsurfaces.