arXiv subjects

Victor Soltwisch

Publications and source records attributed to Victor Soltwisch.

17 recordsLinked to original sources

arXiv2024

Hybrid approach to reconstruct nanoscale grating dimensions using scattering and fluorescence with soft X-rays

Scatterometry is a tested method for measuring periodic semiconductor structures. Since the sizes of modern semiconductor structures have reached the nanoscale regime, the challenge is to determine the shape of periodic nanostructures with sub-nanometer accuracy. To increase the resolution of scatterometry, short-wavelength radiation like soft X-rays can be used. But, scatterometry with soft X-rays is an inverse problem whose solutions can be ambiguous and its sensitivity should be further increased to determine the shape of even more complicated periodic nanostructures made up of different materials. To achieve unique solutions with smaller uncertainties, scatterometry can leverage the excitation of low-Z materials with soft X-rays. Additional information from soft X-ray fluorescence analysis in a hybrid measurement approach can mitigate the problem of ambiguous solutions from soft X-ray scattering and could further decrease uncertainty. In this work, the hybrid approach is utilized to perform a comparison of solutions from the inverse problem and determine the actual solution over ambiguous solutions.

physics.optics↗

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

On uncertainties in the reconstruction of nanostructures in EUV scatterometry and grazing incidence small-angle X-ray scattering

Increasing miniaturization and complexity of nanostructures require innovative metrology solutions with high throughput that can assess complex 3D structures in a non-destructive manner. EUV scatterometry is investigated for the characterization of nanostructured surfaces. The reconstruction is based on a rigorous simulation using a Maxwell solver based on finite-elements and is statistically validated with a Markov-Chain Monte Carlo sampling method. Here it is shown that this method is suitable for the dimensional characterization of the nanostructures and the investigation of oxide or contamination layers. In comparison to grazing-incidence small-angle X-rayscattering (GISAXS) EUV allows to probe smaller areas. The influence of the divergence on the diffracted intensities in EUV is much lower than in GISAXS, which also reduces the computational effort of the reconstruction.

physics.app-ph↗

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$\alpha$ and N-K$\alpha$ 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↗

arXiv2020

Extracting Dimensional Parameters of Gratings Produced with Self-Aligned Multiple Patterning Using GISAXS

Background: To ensure consistent and high-quality semiconductor production at future logic nodes, additional metrology tools are needed. For this purpose, grazing-incidence small-angle X-ray scattering (GISAXS) is being considered because measurements are fast with a proven capability to reconstruct average grating line profiles with high accuracy. Aim: GISAXS measurements of grating line shapes should be extended to samples with pitches smaller than 50 nm and their defects. The method's performance should be evaluated. Approach: A series of gratings with 32 nm pitch and deliberately introduced pitchwalk is measured using GISAXS. The grating line profiles with associated uncertainties are reconstructed using a Maxwell solver and Markov-Chain Monte Carlo (MCMC) sampling combined with a simulation library approach. Results: The line shape and the pitchwalk are generally in agreement with previously published transmission small-angle X-ray scattering (SAXS) results; however the line height and line width show deviations of (1.0 +/- 0.2) nm and (2.0 +/- 0.7) nm, respectively. The complex data evaluation leads to relatively high pitchwalk uncertainties between 0.5 nm and 2 nm. Conclusions: GISAXS shows great potential as a metrology tool for small-pitch line gratings with complex line profiles. Faster simulation methods would enable more accurate results.

physics.app-ph↗

arXiv2019

Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction

Numerical optimization is an important tool in the field of computational physics in general and in nano-optics in specific. It has attracted attention with the increase in complexity of structures that can be realized with nowadays nano-fabrication technologies for which a rational design is no longer feasible. Also, numerical resources are available to enable the computational photonic material design and to identify structures that meet predefined optical properties for specific applications. However, the optimization objective function is in general non-convex and its computation remains resource demanding such that the right choice for the optimization method is crucial to obtain excellent results. Here, we benchmark five global optimization methods for three typical nano-optical optimization problems: \removed{downhill simplex optimization, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, particle swarm optimization, differential evolution, and Bayesian optimization} \added{particle swarm optimization, differential evolution, and Bayesian optimization as well as multi-start versions of downhill simplex optimization and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm}. In the shown examples from the field of shape optimization and parameter reconstruction, Bayesian optimization, mainly known from machine learning applications, obtains significantly better results in a fraction of the run times of the other optimization methods.

physics.comp-ph↗

arXiv2019

Applicability of the Debye-Waller damping factor for the determination of the line-edge roughness of lamellar gratings

Periodic nanostructures are fundamental elements in optical instrumentation as well as basis structures in integrated electronic circuits. Decreasing sizes and increasing complexity of nanostructures have made roughness a limiting parameter to the performance. Grazing-incidence small-angle X-ray scattering is a characterization method that is sensitive to three-dimensional structures and their imperfections. To quantify line-edge roughness, a Debye-Waller factor (DWF), which is derived for binary gratings, is usually used. In this work, we systematically analyze the effect of roughness on the diffracted intensities. Two different limits to applying the DWF are found depending on whether or not the roughness is normally distributed.

physics.app-ph↗

arXiv2019

Distortion analysis of crystalline and locally quasicrystalline 2D photonic structures with GISAXS

In this study, grazing incidence small-angle X-ray scattering (GISAXS) is used to collect statistical information on dimensional parameters in an area of 20 mm x 15 mm on photonic structures produced by nanoimprint lithography. The photonic structures are composed of crystalline and locally quasicrystalline two-dimensional patterns with structure sizes between about 100 nm and 10 $μ$m to enable broadband visible light absorption for use in solar energy harvesting. These first GISAXS measurements on locally quasicrystalline samples demonstrate that GISAXS is capable of showing the locally quasicrystalline nature of the samples while at the same time revealing the long-range periodicity introduced due to the lattice design. We describe the scattering qualitatively in the framework of the distorted wave Born approximation using a hierarchical model mirroring the sample design, which consists of a rectangular and locally quasicrystalline supercell which is repeated periodically to fill the whole surface. The nanoimprinted samples are compared to a sample manufactured using electron beam lithography and the distortions of the periodic and locally quasiperiodic samples are quantified statistically. Due to the high sensitivity of GISAXS to deviations from the perfect lattice, the misalignment of the crystallographic axes was measured with a resolution of 0.015°, showing distortions up to +/- 0.15° in the investigated samples.

cond-mat.mes-hall↗

arXiv2018

Characteristic diffuse scattering from distinct line roughnesses

Lamellar gratings are widely used diffractive optical elements; gratings etched into Si can be used as structural elements or prototypes of structural elements in integrated electronic circuits. For the control of the lithographic manufacturing process, a rapid in-line characterization of nanostructures is indispensable. Numerous studies on the determination of regular geometry parameters of lamellar gratings from optical and extreme ultraviolet (EUV) scattering highlight the impact of roughness on the optical performance as well as on the reconstruction of these structures. Thus, a set of nine lamellar Si gratings with a well defined line edge roughness or line width roughness were designed. The investigation of these structures using EUV small-angle scattering reveals a strong correlation between the type of line roughness and the angular scattering distribution. These distinct scattering patterns open new paths for the unequivocal characterization of such structures by EUV scatterometry.

physics.app-ph↗

arXiv2018

Element sensitive reconstruction of nanostructured surfaces with finite elements and grazing incidence soft X-ray fluorescence

The geometry of a Si$_3$N$_4$ lamellar grating was investigated experimentally with reference-free grazing-incidence X-ray fluorescence analysis. While simple layered systems are usually treated with the matrix formalism to determine the X-ray standing wave field, this approach fails for laterally structured surfaces. Maxwell solvers based on finite elements are often used to model electrical field strengths for any 2D or 3D structures in the optical spectral range. We show that this approach can also be applied in the field of X-rays. The electrical field distribution obtained with the Maxwell solver can subsequently be used to calculate the fluorescence intensities in full analogy to the X-ray standing wave field obtained by the matrix formalism. Only the effective 1D integration for the layer system has to be replaced by a 2D integration of the finite elements, taking into account the local excitation conditions. We will show that this approach is capable of reconstructing the geometric line shape of a structured surface with high elemental sensitivity. This combination of GIXRF and finite-element simulations paves the way for a versatile characterization of nanoscale-structured surfaces.

physics.app-ph↗

arXiv2017

Reconstructing Detailed Line Profiles of Lamellar Gratings from GISAXS Patterns with a Maxwell Solver

Laterally periodic nanostructures were investigated with grazing incidence small angle X-ray scattering (GISAXS) by using the diffraction patterns to reconstruct the surface shape. To model visible light scattering, rigorous calculations of the near and far field by numerically solving Maxwell's equations with a finite-element method are well established. The application of this technique to X-rays is still challenging, due to the discrepancy between incident wavelength and finite-element size. This drawback vanishes for GISAXS due to the small angles of incidence, the conical scattering geometry and the periodicity of the surface structures, which allows a rigorous computation of the diffraction efficiencies with sufficient numerical precision. To develop dimensional metrology tools based on GISAXS, lamellar gratings with line widths down to 55 nm were produced by state-of-the-art e-beam lithography and then etched into silicon. The high surface sensitivity of GISAXS in conjunction with a Maxwell solver allows a detailed reconstruction of the grating line shape also for thick, non-homogeneous substrates. The reconstructed geometrical line shape models are statistically validated by applying a Markov chain Monte Carlo (MCMC) sampling technique which reveals that GISAXS is able to reconstruct critical parameters like the widths of the lines with sub-nm uncertainty.

physics.comp-ph↗

arXiv2017

Grazing Incidence Small Angle X-Ray Scattering (GISAXS) on Small Targets Using Large Beams

GISAXS is often used as a versatile tool for the contactless and destruction-free investigation of nanostructured surfaces. However, due to the shallow incidence angles, the footprint of the X-ray beam is significantly elongated, limiting GISAXS to samples with typical target lengths of several millimetres. For many potential applications, the production of large target areas is impractical, and the targets are surrounded by structured areas. Because the beam footprint is larger than the targets, the surrounding structures contribute parasitic scattering, burying the target signal. In this paper, GISAXS measurements of isolated as well as surrounded grating targets in Si substrates with line lengths from $50\,{\rmμm}$ down to $4\,{\rmμm}$ are presented. For the isolated grating targets, the changes in the scattering patterns due to the reduced target length are explained. For the surrounded grating targets, the scattering signal of a $15\,{\rmμm}\,\times\,15\,{\rmμm}$ target grating structure is separated from the scattering signal of $100\,{\rmμm}\,\times\,100\,{\rmμm}$ nanostructured surroundings by producing the target with a different orientation with respect to the predominant direction of the surrounding structures. The described technique allows to apply GISAXS, e.g. for characterization of metrology fields in the semiconductor industry, where up to now it has been considered impossible to use this method due to the large beam footprint.

cond-mat.mes-hall↗

arXiv2016

Correlated Diffuse X-ray Scattering from Periodically Nano-Structured Surfaces

Laterally periodic nanostructures were investigated with grazing incidence small angle X-ray scattering. To support an improved reconstruction of nanostructured surface geometries, we investigated the origin of the contributions to the diffuse scattering pattern which is correlated to the surface roughness. Resonant diffuse scattering leads to a palm-like structure of intensity sheets. Dynamic scattering generates the so-called Yoneda band caused by a resonant scatter enhancement at the critical angle of total reflection and higher-order Yoneda bands originating from a subsequent diffraction of the Yoneda enhanced scattering at the grating. Our explanations are supported by modelling using a solver for the time-harmonic Maxwell's equations based on the finite-element method.

cond-mat.mes-hall↗

arXiv2010

Phase diagram of charge order in La1.8-xEu0.2SrxCuO4 from resonant soft x-ray diffraction

Resonant soft x-ray scattering experiments with photon energies near the O K and the Cu L3 edge on the system La1.8-xEu0.2SrxCuO4 for 0.1 <= x <= 0.15 are presented. A phase diagram for stripe-like charge ordering is obtained together with information on the structural transition into the low-temperature tetragonal phase. A clear dome for the charge ordering around x = 1/8 is detected well below the structural transition. This result is quite different from other systems in which static stripes are detected. There the charge order is determined by the structural transition appearing at the same temperature. Furthermore we present results for the coherence length and the incommensurability of the stripe order as a function of Sr concentration.

cond-mat.supr-con↗