Applications
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Hybrid approach to reconstruct nanoscale grating dimensions using scattering and fluorescence with soft X-rays
This work demonstrates a hybrid metrology technique combining soft X-ray scattering and fluorescence to reconstruct the dimensions of a silicon nitride nanoscale grating with high accuracy. To solve the inverse problem, the electric field strength of the standing wave field within the grating was calculated using JCMsuite’s finite element method solver. These near-field calculations were then used to compute diffraction efficiencies and fluorescence intensities, which were fitted to experimental data via an optimization process to determine the grating profile parameters.
L. M. Lohr, et al. Hybrid approach to reconstruct nanoscale grating dimensions using scattering and fluorescence with soft X-rays. Nanoscale, 17, 6017 (2025).
2025 DOI Publication link
Optical Metrology and Sensing, Optical and EUV Lithography, Advanced Finite Element Methods, Light Scattering Computation, Optimization and Parameter Retrieval Methods
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Introduction and application of a new approach for model-based optical bidirectional measurements
A new model-based evaluation method for optical bidirectional measurements, such as linewidth determination on micro- and nanostructures, was developed. JCMsuite's rigorous finite element method (FEM) solver was used to simulate the microscope imaging process, incorporating a modified Hopkins' approximation for computational efficiency. The simulated and measured intensity profiles were compared within a Bayesian Target Vector Optimization (BTVO) framework, also provided by JCMwave, to reconstruct the linewidth and other parameters with high accuracy.
J. Krüger, et al. Introduction and application of a new approach for model-based optical bidirectional measurements. Meas. Sci. Technol., 35, 085014 (2024).
2024 DOI Publication link
Optical Metrology and Sensing, Optical and EUV Lithography, Advanced Finite Element Methods, Optimization and Parameter Retrieval Methods
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Imaging Mueller matrix ellipsometry measurements on measuring fields in the micrometre range
An imaging Mueller matrix ellipsometer is used to measure nanoscale line and grating structures in micron-sized measurement fields. To reconstruct the structural parameters from the ellipsometric data, numerical simulations using the finite element method were performed. The commercial FEM Maxwell solver JCMwsuite was employed to solve the inverse diffraction problem and to fit the measured Mueller matrix images by varying the simulation parameters in an optimization process.
J. Grundmann, et al. Imaging Mueller matrix ellipsometry measurements on measuring fields in the micrometre range. EPJ Web of Conferences 309, 02010 (2024).
2024 DOI Publication link
Optical Metrology and Sensing, Optical and EUV Lithography, Advanced Finite Element Methods, Optimization and Parameter Retrieval Methods
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Impact study of numerical discretization accuracy on parameter reconstructions and model parameter distributions
A Bayesian target vector optimization method is fit to a finite element numerical model (JCMsuite) to a Grazing Incidence X-ray fluorescence data set to obtain the geometrical parameters of line gratin within the nanometer range. Convergence studies are performed to determine the numerical parameters that allow for an efficient and accurate reconstruction of the model parameters.
M. Plock, et al., Impact study of numerical discretization accuracy on parameter reconstructions and model parameter distributions. Metrologia, 60, 054001, 2023.
2023 DOI Publication link
Optical Metrology and Sensing, Optical and EUV Lithography, integrated optics, Optimization and Parameter Retrieval Methods
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Pushing the boundaries of EUV scatterometry: reconstruction of complex nanostructures for next-generation transistor technology
EUV scatterometry measurements and data evaluation on next-generation transistor candidates, the forksheet structures, are presented. The measure of EUV radiation is performed in PTB's compact measurement chamber at the X-ray beamline at BESSY II and the reconstruction of geometry data is performed by Scattering simulations computed with JCMsuite and numerical optimization scheme.
R. Ciesielski, et al. Pushing the boundaries of EUV scatterometry: reconstruction of complex nanostructures for next-generation transistor technology. Proc. SPIE, 447 (2023).
2023 DOI
Optical Metrology and Sensing, Optical and EUV Lithography, Optimization and Parameter Retrieval Methods
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Nanoscale grating characterization using EUV scatterometry and soft x-ray scattering with plasma and synchrotron radiation
A compact source of extreme ultraviolet (EUV) for the characterization of samples in the EUV spectral range is presented and compared to a reference measurement with synchroton radiation. For the parameter reconstruction from the scattering data, numerical simulations with JCMsuite are performed with determined accuracy.
L. M. Lohr, et al. Nanoscale grating characterization using EUV scatterometry and soft x-ray scattering with plasma and synchrotron radiation, Appl. Opt., 62, 117 (2023).
2023 DOI Publication link
Optical and EUV Lithography, Light Scattering Computation, Optimization and Parameter Retrieval Methods
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Opportunities of polarization-resolved EUV scatterometry on photomasks
A polarization-resolved analysis of the scattered EUV radiation to increase the sensitivity and minimize the uncertainties in the reconstruction of EUV Scattering is presented.
Victor Soltwisch, et al., Opportunities of polarization-resolved EUV scatterometry on photomasks. Proc. SPIE 12802, 38th European Mask and Lithography Conference (EMLC 2023), 128020G (2023).
2023 DOI
Optical and EUV Lithography, Optimization and Parameter Retrieval Methods
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Challenges of Grazing Emission X-ray Fluorescence (GEXRF) for the Characterization of Advanced Nanostructured Surfaces
In this paper, the grazing emission X-ray fluorescence (GEXRF) technique is analyzed to determine the spatial distribution of various chemical elements in nanostructures and is compared to the well-established GISAXS method. Simulations of the X-ray standing wave field in the vicinity of and inside the nanostructure are performed with JCMsuite to obtain the angle-resolved fluorescence intensities and the far field scattering intensities.
D. Skroblin et al. Challenges of grazing emission X-ray fluorescence (GEXRF) for the characterization of advanced nanostructured surfaces. Nanoscale, 14, 15475, (2022)
2022 DOI Publication link
Optical Metrology and Sensing, Optical and EUV Lithography, Light Scattering Computation, Optimization and Parameter Retrieval Methods
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Latent Image Characterization by Spectroscopic Reflectometry in the Extreme Ultraviolet
The application of spectroscopic EUV reflectometry for characterizing the latent image of a line grating is investigated. Numerical simulations with JCMsuite are performed to compute the reflectance of latent images of line gratings and simulations to analyze latent image gratings with a surface topography.
S. Schröder, et al. Latent image characterization by spectroscopic reflectometry in the extreme ultraviolet. J Micro Nanolithogr MEMS MOEMS, 21, 021208-021208 (2022).
2022 DOI Publication link
Optical and EUV Lithography, integrated optics, Light Scattering Computation
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Benchmark of Global Optimization Approaches for Nano-optical Shape Optimization and Parameter Reconstruction
Several global optimization methods for three typical nano-optical optimization problems are benchmarked: particle swarm optimization, differential evolution, and Bayesian optimization as well as multistart versions of downhill simplex optimization and the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm. In the shown examples, Bayesian optimization, mainly known from machine learning applications, obtains significantly better results in a fraction of the run times of the other optimization methods.
P.-I. Schneider, et al. Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction. ACS Photonics 6, 2726 (2019).
2019 DOI
Metamaterials, Optical Metrology and Sensing, Optical and EUV Lithography, quantum optics, Optimization and Parameter Retrieval Methods, software benchmarks
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EUV mask feature reconstruction via phase retrieval
JCMsuite has been used in a simulation study to assess the performance of coherent diffractive imaging (CDI) and related phase retrieval methods for the reconstruction of non-trivially shaped and a–periodic nanostructures from far field intensity data.
P. Ansuinelli, et al. EUV mask feature reconstruction via phase retrieval. Proc. SPIE 11089, 110892F (2019).
2019 DOI
Optical Metrology and Sensing, Optical and EUV Lithography, Light Scattering Computation
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Gaussian process regression for efficient parameter reconstruction
Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results through numerical simulations. The performance of Bayesian optimization as implemented in JCMsuite's optimization toolbox is compared to different local minimization algorithms for this numerical optimization problem. Bayesian optimization uses Gaussian-process regression to find promising parameter values. The paper examines how pre-computed simulation results can be used to train the Gaussian process and to accelerate the optimization.
P.-I. Schneider, et al. Using Gaussian process regression for efficient parameter reconstruction. Proc. SPIE 10959, 1095911 (2019).
2019 DOI
Optical Metrology and Sensing, Optical and EUV Lithography, Optimization and Parameter Retrieval Methods, software benchmarks
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Grazing incidence x-ray fluorescence based profile reconstruction
Rigorous field simulations obtained from a Maxwell solver (JCMsuite) in combination with Bayesian optimization allow to determine the spatial distribution of elemental species and the geometrical shape with sub-nm resolution.
A. Andrle, et al. Grazing incidence x-ray fluorescence based characterization of nanostructures for element sensitive profile reconstruction. Proc. SPIE 11057, 110570M (2019).
2019 DOI
Optical Metrology and Sensing, Optical and EUV Lithography, Advanced Finite Element Methods, Optimization and Parameter Retrieval Methods
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Element sensitive reconstruction of nanostructured surfaces with finite elements and grazing incidence soft X-ray fluorescence
The geometry of lamellar gratings is investigated experimentally with reference-free grazing-incidence X-ray fluorescence analysis. The demonstrated combination of GIXRF and finite-element simulations paves the way for a versatile characterization of nanoscale-structured surfaces.
V. Soltwisch, et al. Element sensitive reconstruction of nanostructured surfaces with finite elements and grazing incidence soft X-ray fluorescence. Nanoscale 10, 6177 (2018).
2018 DOI
Optical Metrology and Sensing, Optical and EUV Lithography, Light Scattering Computation, Optimization and Parameter Retrieval Methods
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Evaluating the effects of modeling errors for isolated finite three-dimensional targets
Optical three-dimensional (3-D) nanostructure metrology utilizes a model-based metrology approach to determine critical dimensions (CDs) that are well below the inspection wavelength. A project at the National Institute of Standards and Technology is evaluating how to attain key CD and shape parameters from engineered in-die capable metrology targets. The performance of simplified models is validated using highly accurate, fully 3D simulations.
M. A. Henn, et al. Evaluating the effects of modeling errors for isolated finite three-dimensional targets. J. of Micro/Nanolithography, MEMS, and MOEMS, 16, 044001 (2017).
2017 DOI
Optical Metrology and Sensing, Optical and EUV Lithography, Advanced Finite Element Methods, Optimization and Parameter Retrieval Methods
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FEM for validation of alternative scattering computation method.
JCMsuite is used for validation of an integral method for computing scattering response of finite dielectric objects.
R. J. Dilz, et al. 2D TM scattering problem for finite dielectric objects in a dielectric stratified medium employing Gabor frames in a domain integral equation. J. Opt. Soc. Am. A 34, 1315 (2017).
2017 DOI
Optical Metrology and Sensing, Optical and EUV Lithography, other fields, Light Scattering Computation, software benchmarks
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Investigating surface structures by EUV scattering
An exploration of soft X-ray and EUV-scatterometry from grazing to near normal incidence is presented. Measurements are performed on e-beam written silicon gratings. The reconstructed geometrical line shape models are statistically validated by applying a Markov-Chain Monte Carlo sampling technique. Experimental data and simulation results provide insight into the potential of EUV scatterometry.
V. Soltwisch, et al. Investigating surface structures by EUV scattering. Proc. SPIE 10143, 101430P (2017).
2017 DOI
Optical Metrology and Sensing, Optical and EUV Lithography, Advanced Finite Element Methods, Optimization and Parameter Retrieval Methods, Uncertainty Quantification Methods
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Quantitative optical imaging for in-die-capable critical dimension targets
FEM simulations are used in a work by U.S. National Institute of Standards and Technology to optimize the design of in-die-capable metrology targets for process control in microlithography.
B. M. Barnes, et al. Enabling quantitative optical imaging for in-die-capable critical dimension targets. Proc. SPIE 9778, 97780Y (2016).
2016 DOI
Optical Metrology and Sensing, Optical and EUV Lithography, Advanced Finite Element Methods, Optimization and Parameter Retrieval Methods
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Modeling of Optical Imaging of Finite Multi-Line Arrays.
The U.S. National Institute of Standards and Technology provides a dataset which contains MATLAB based scripting files and input files for the software package JCMsuite that enable the modeling of optical imaging of fionite multi-line arrays.
M. A. Henn and B. M. Barnes. A Library to Enable the Modeling of Optical Imaging of Finite Multi-Line Arrays. DOI: 10.18434/T42C7D (2016).
2016 DOI
Optical Metrology and Sensing, Optical and EUV Lithography, Light Scattering Computation, other methods
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Efficient Bayesian inversion for shape reconstruction of lithography masks
In order to quantify the uncertainties of reconstructed geometry parameters, a fast-to-evaluate surrogate for the forward model (a polynomial chaos expansion) is introduced. The surrogate allows, e.g., for determining the probability distribution of the geometry parameters given measurement data, and for a global sensitivity analysis of the measurement process. All methods are implemented in JCMsuite's analysis and optimization toolbox.
N. Frachmin, et al. Efficient Bayesian inversion for shape reconstruction of lithography masks. Journal of Micro/Nanolithography, MEMS, and MOEMS, 19(2), 024001 (2020).
2010 DOI Publication link
Optical Metrology and Sensing, Optical and EUV Lithography, Light Scattering Computation, Optimization and Parameter Retrieval Methods, Uncertainty Quantification Methods