A semi-analytical approach for the characterization of ordered 3D nanostructures using grazing-incidence X-ray fluorescence

Abstract

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 a semi‐analytical solution to the Sherman equation to be derived 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 nanopillars. Both the dimensional and structural parameters of these nanostructures have been reconstructed by fitting numerical 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 the case of the Si3N4 grating.

Simultaneous Dimensional and Analytical Characterization of Ordered Nanostructures

“…We use an array (1 mm × 15 mm large) of Cr nanostructures, which are nominally 300 nm × 300 nm × 20 nm (width × length × height) sized squares with a period of 1 μm in both directions. The GIXRF based characterization [ 30,31 ] of the sample allowed for a reconstruction of the dimensional properties of the Cr structure. As the identical structural model must also well‐describe the GEXRF experimental data taken on the same sample, one can now directly plot the GEXRF data against a calculation using the very same parameters exchanging only the incident photon energy to the Cr‐Kα fluorescence line energy.…”

“…We are showing how the recently established reconstruction capabilities for 2D and 3D nanostructures employing grazing incidence XRF (GIXRF) [ 29–31 ] can be readily transferred to GEXRF measurements such that the dimensions and composition of a nanostructure can be reconstructed from the experimental data. The reconstruction relies on a finite‐element based solver of the Maxwell equations [ 32 ] or many‐beam dynamical diffraction theory (MB‐DDT) [ 30 ] as well as an machine learning based highly efficient Bayesian optimizer (BO). [ 33,51 ] We also compare the results to TEM and AFM data for validation.…”

Grazing Emission X‐Ray Fluorescence: Novel Concepts and Applications for Nano‐Analytics

“…This 2D information on the dependence of the XRF intensity on both angles is useful for investigations of structured surfaces in two or three dimensions, such as line gratings or periodic patterns of identical nanostructures, as already been shown by means of GIXRF. [ 94,95 ]…”

“…This class of samples has until recently not been considered for GIXRF and GEXRF investigations such that novel modeling, computationally demanding approaches are required which take into consideration the surface distribution pattern in terms of height, width, and periodicity in particular. Indeed, calculation approaches of the X‐ray standing wavefield based on ray‐tracing, [ 149 ] the finite element method [ 94,150 ] or on many‐beam dynamical diffraction theory [ 95 ] were presented. Due to the 2D detection inherent to scanning‐free GEXRF, recording the 2D angular‐dependent XRF signals of such samples is straightforward and we expect future developments in this field of application.…”

Shape- and Element-Sensitive Reconstruction of Periodic Nanostructures with Grazing Incidence X-ray Fluorescence Analysis and Machine Learning

“…The intensity modulation inside the XSW field significantly influences the X-ray fluorescence intensity of an element depending on its spatial position within the electromagnetic field distribution. Recent studies have shown the potential of the GIXRF technique for the dimensional and compositional nanometrology of periodic 2D [ 20 ] and 3D [ 21 , 22 ] nanostructures.…”