  The characterization of nanostructured surfaces with sensitivity in the
sub-nm range is of high importance for the development of current and next
generation integrated electronic circuits. Modern transistor architectures for
e.g. FinFETs are realized by lithographic fabrication of complex, well ordered
nanostructures. Recently, a novel characterization technique based on X-ray
fluorescence measurements in grazing incidence geometry has been proposed for
such applications. This technique uses the X-ray standing wave field, arising
from an interference between incident and the reflected radiation, as a
nanoscale sensor for the dimensional and compositional parameters of the
nanostructure. The element sensitivity of the X-ray fluorescence technique
allows for a reconstruction of the spatial element distribution using a
finite-element method. Due to a high computational time, intelligent
optimization methods employing machine learning algorithms are essential for a
timely provision of results. Here, a sampling of the probability distributions
by Bayesian optimization is not only fast, it also provides an initial estimate
of the parameter uncertainties and sensitivities. The high sensitivity of the
method requires a precise knowledge of the material parameters in the modeling
of the dimensional shape provided that some physical properties of the material
are known or determined beforehand. The unknown optical constants were
extracted from an unstructured but otherwise identical layer system by means of
soft X-ray reflectometry. The spatial distribution profiles of the different
elements contained in the grating structure were compared to scanning electron
and atomic force microscopy and the influence of carbon surface contamination
on the modeling results were discussed.
