Analytical modeling and three-dimensional finite element simulation of line edge roughness in scatterometry

Kato, Akiko; Burger, Sven; Scholze, Frank

doi:10.1364/ao.51.006457

Cited by 28 publications

(35 citation statements)

References 24 publications

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“…Arbitrarily shaped structures must be discretized and require numerical solvers (Chourou et al, 2013). In the optical domain of the electromagnetic spectrum, modelling light scattering by numerically solving the time-harmonic Maxwell equations with a higher-order finite-element method (Pomplun et al, 2007;Kato et al, 2012) is well established. If the periodic structures are invariant in one dimension (e.g.…”

Section: Introductionmentioning

confidence: 99%

Reconstructing detailed line profiles of lamellar gratings from GISAXS patterns with a Maxwell solver

et al. 2017

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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-ofthe-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.

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Section: Introductionmentioning

confidence: 99%

Reconstructing detailed line profiles of lamellar gratings from GISAXS patterns with a Maxwell solver

et al. 2017

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“…For periodic structures, e.g. gratings, it is well established to model the light scattering by numerically solving the time-harmonic Maxwell's equations with a higher-order finite-element method 23,24 . If the periodic structures are invariant in one dimension (along the grating lines), the computational domain can be reduced to a two dimensional problem which decreases the computational effort significantly and allows to calculate also rather large domains as compared to the incident wavelength.…”

Section: Introductionmentioning

confidence: 99%

Correlated diffuse x-ray scattering from periodically nanostructured surfaces

et al. 2016

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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.

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“…Previously the solver has, e.g., been used in scatterometric investigations of EUV line masks (1D-periodic patterns), contact hole masks (2D-periodic patterns) and more complicated 3D patterns. [5][6][7][8][9] Convergence studies in these investigations demonstrate that highly accurate, rigorous results can be attained even for the relatively large 3D computational domains which are typically present in 3D EUV setups.…”

Section: Methodsmentioning

confidence: 87%

Fast simulation method for parameter reconstruction in optical metrology

et al. 2013

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), and is made available as an electronic preprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. ABSTRACTA method for automatic computation of parameter derivatives of numerically computed light scattering signals is demonstrated. The finite-element based method is validated in a numerical convergence study, and it is applied to investigate the sensitivity of a scatterometric setup with respect to geometrical parameters of the scattering target. The method can significantly improve numerical performance of design optimization, parameter reconstruction, sensitivity analysis, and other applications.Keywords: Scatterometry, optical metrology, 3D rigorous electromagnetic field simulations, computational metrology, computational lithography, finite-element methods

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Analytical modeling and three-dimensional finite element simulation of line edge roughness in scatterometry

Cited by 28 publications

References 24 publications

Reconstructing detailed line profiles of lamellar gratings from GISAXS patterns with a Maxwell solver

Reconstructing detailed line profiles of lamellar gratings from GISAXS patterns with a Maxwell solver

Correlated diffuse x-ray scattering from periodically nanostructured surfaces

Fast simulation method for parameter reconstruction in optical metrology

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