  Following the recent demonstration of grazing-incidence X-ray fluorescence
(GIXRF) based characterization of the 3D atomic distribution of different
elements and dimensional parameters of periodic nanoscale structures, this work
presents a new computational scheme for the simulation of the angular dependent
fluorescence intensities from such periodic 2D and 3D nanoscale structures. The
computational scheme is based on the dynamical diffraction theory in many-beam
approximation, which allows to derive a semi-analytical solution to the Sherman
equation in a linear-algebraic form. The computational scheme has been used to
analyze recently published GIXRF data measured on 2D Si3N4 lamellar gratings,
as well as on periodically structured 3D Cr nano pillars. Both the dimensional
and structural parameters of these nanostructures have been reconstructed by
fitting numeric simulations to the experimental GIXRF data. Obtained results
show good agreement with nominal parameters used in the manufacturing of the
structures, as well as with reconstructed parameters based on the previously
published finite element method simulations, in case of the Si3N4 grating.
