arXiv subjects

Anna Andrle

Publications and source records attributed to Anna Andrle.

5 recordsLinked to original sources

arXiv2021

Grazing incidence X-ray fluorescence based characterization of nanostructures for element sensitive profile reconstruction

For the reliable fabrication of the current and next generation of nanostructures it is essential to be able to determine their material composition and dimensional parameters. Using the grazing incidence X-ray fluoresence technique, which is taking advantage of the X-ray standing wave field effect, nanostructures can be investigated with a high sensitivity with respect to the structural and elemental composition. This is demonstrated using lamellar gratings made of Si$_3$N$_4$. Rigorous field simulations obtained from a Maxwell solver based on the finite element method allow to determine the spatial distribution of elemental species and the geometrical shape with sub-nm resolution. The increasing complexity of nanostructures and demanded sensitivity for small changes quickly turn the curse of dimensionality for numerical simulation into a problem which can no longer be solved rationally even with massive parallelisation. New optimization schemes, e.g. machine learning, are required to satisfy the metrological requirements. We present reconstruction results obtained with a Bayesian optimization approach to reduce the computational effort.

physics.app-ph↗

arXiv2021

Time-frequency analysis assisted reconstruction of ruthenium optical constants in the sub-EUV spectral range 8nm-23.75nm

The optical constants of ruthenium in the spectral range 8 nm to 23.75 nm with their corresponding uncertainties are derived from the reflectance of a sputtered ruthenium thin film in the Extreme Ultraviolet (EUV) spectral range measured using monochromatized synchrotron radiation. This work emphasizes the correlation between structure modelling and the reconstructed optical parameters in a detailed inverse-problem optimization strategy. Complementary X-ray Reflectivity (XRR) measurements are coupled with Markov chain Monte Carlo (MCMC) based Bayesian inferences and quasi-model-independent methods to create a model factoring the sample's oxidation, contamination, and surface roughness. The sensitivity of the modelling scheme is tested and verified against contamination and oxidation. A notable approach mitigating the high dimensionality of the reconstruction problem is elaborated with the results of this work compared to two previously published datasets. The presented dataset is of high interest for the continuing development of Extreme Ultraviolet Lithography (EUVL) and EUV astronomy optical systems.

physics.optics↗

arXiv2021

Shape- and element-sensitive reconstruction of periodic nanostructures with grazing incidence X-ray fluorescence analysis and machine learning

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.

physics.app-ph↗

arXiv2021

Invertible Neural Networks versus MCMC for Posterior Reconstruction in Grazing Incidence X-Ray Fluorescence

Grazing incidence X-ray fluorescence is a non-destructive technique for analyzing the geometry and compositional parameters of nanostructures appearing e.g. in computer chips. In this paper, we propose to reconstruct the posterior parameter distribution given a noisy measurement generated by the forward model by an appropriately learned invertible neural network. This network resembles the transport map from a reference distribution to the posterior. We demonstrate by numerical comparisons that our method can compete with established Markov Chain Monte Carlo approaches, while being more efficient and flexible in applications.

cs.LG↗

arXiv2020

Grazing incidence-X-ray fluorescence for a dimensional and elemental characterization of well-ordered nanostructures

The increasing importance of well-controlled ordered nanostructures on surfaces represents a challenge for existing metrology techniques. To develop such nanostructures and monitor complex processing constraints fabrication, both a dimensional reconstruction of nanostructures and a characterization (ideally a quantitative characterization) of their composition is required. In this work, we present a soft X-ray fluorescence-based methodology that allows both of these requirements to be addressed at the same time. By applying the grazing-incidence X-ray fluorescence technique and thus utilizing the X-ray standing wave field effect, nanostructures can be investigated with a high sensitivity with respect to their dimensional and compositional characteristics. By varying the incident angles of the exciting radiation, element-sensitive fluorescence radiation is emitted from different regions inside the nanoobjects. By applying an adequate modeling scheme, these datasets can be used to determine the nanostructure characteristics. We demonstrate these capabilities by performing an element-sensitive reconstruction of a lamellar grating made of Si$_3$N$_4$, where GIXRF data for the O-K$α$ and N-K$α$ fluorescence emission allows a thin oxide layer to be reconstructed on the surface of the grating structure. In addition, we employ the technique also to three dimensional nanostructures and derive both dimensional and compositional parameters in a quantitative manner.

physics.app-ph↗