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

Abstract

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 was 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 timely provision of results. Here, a sampling of the probability distributions by Bayesian optimization is not only fast, but 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. This novel approach enables the element sensitive and destruction-free characterization of nanostructures made of silicon nitride and silicon oxide with sub-nm resolution.

Traceable Characterization of Nanomaterials by X-ray Spectrometry Using Calibrated Instrumentation

“…This local tunability of the XSW field with respect to the spatial elemental distribution of the nanostructure to be probed ensures the high discrimination capability of this hybrid method. A recent work [73] demonstrates the corresponding reconstruction capabilities of GIXRF analysis used at periodic nanostructures to reveal both detailed dimensional and analytical information. For the calibration of laboratory GIXRF instruments, i.e., for a combined determination of unknown experimental and instrumental parameters, specific nanolayered structures could be qualified by means of SR-based reference-free GIXRF analysis [74].…”

“…The GEXRF approaches have been successfully explored for more than two decades at various large-scale facilities and in academic laboratories [75][76][77][78][79][80][81], in particular regarding the characterization of nanolayered systems. To complement angular GIXRF studies [22,72] and related reconstruction works on nanostructures [73], GEXRF also allows for the scanning-free detection of the angular distribution of fluorescence radiation emitted by a nanostructure using position-sensitive detectors such as CCDs or CMOS devices [82].…”

Bayesian Target-Vector Optimization for Efficient Parameter Reconstruction

“…Grazing Incidence X-Ray Fluorescence (GIXRF) [53,54] is an indirect optical measurement method that can be used to quantify samples both in terms of their geometry as well as in their material composition. To investigate a sample, it is illuminated using X-ray light.…”

“…In this model, a simulation of the electromagnetic fields of the XSW is performed. The modified 2D Sherman equation is then used to determine the numerical fluorescence intensity for each angle of incidence found in the experimental dataset [54].…”

“…A listing of the employed parameter optimization intervals is given in Table 1. The densities of Si3N4 and SiO2, Si3N4 = 2.836 g cm −3 and SiO2 = 2.093 g cm −3 , were obtained by means of a separate X-ray reflectometry experiment [54]. The parameterized forward model was created using the finiteelement Maxwell solver JCMsuite.…”