Fieldstitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry

Schuster, Thomas; Rafler, Stephan; Paz, Valeriano Ferreras; Frenner, Karsten

doi:10.1016/j.mee.2008.11.019

Cited by 18 publications

(8 citation statements)

References 11 publications

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“…E.g. [17] presents the numerical modelling of 2D line edge roughness for optical scatterometry using the field-stitching method in rigorous coupled-wave analysis. In this paper, we will first derive an analytical description of the line edge modulation and will then compare the results to 3D FEM simulations.…”

Section: Analytical Modelingmentioning

confidence: 99%

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

2012

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The influence of edge roughness in angle resolved scatterometry at periodically structured surfaces is investigated. A good description of the radiation interaction with structured surfaces is crucial for the understanding of optical imaging processes like, e.g. in photolithography. We compared an analytical 2D model and a numerical 3D simulation with respect to the characterization of 2D diffraction of a line grating involving structure roughness. The results show a remarkably high agreement. The diffraction intensities of a rough structure can therefore be estimated using the numerical simulation result of an undisturbed structure and an analytically derived correction function. This work allows to improve scatterometric results for the case of practically relevant 2D structures.

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Section: Analytical Modelingmentioning

confidence: 99%

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

2012

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“…(Brill et al ., 2010;Foldyna et al ., 2011;Shyu et al ., 2007). Modeling studies have also been performed, testing new techniques in simulating the effects of LER on scattered light such as the fi eld-stitching method (Schuster et al ., 2009). …”

Section: Scatterometrymentioning

confidence: 99%

Sidewall roughness in nanolithography: origins, metrology and device effects

2014

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“…Germer [26] applied similar design principles for his profile variations of silicon lines investigated in the visible spectral range. Schuster et al [27] have studied the impact of LER for silicon gratings on the basis of sinusoidal perturbations for the line positions with amplitudes in the range of 2-8 nm and for incident light with wavelengths of 400 and 250 nm, respectively.…”

Section: Modeling Line-edge Roughness and Line-width Roughnessmentioning

confidence: 99%

Modeling of line roughness and its impact on the diffraction intensities and the reconstructed critical dimensions in scatterometry

et al. 2012

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We investigate the impact of line-edge and line-width roughness (LER, LWR) on the measured diffraction intensities in angular resolved extreme ultraviolet (EUV) scatterometry for a periodic line-space structure designed for EUV lithography. LER and LWR with typical amplitudes of a few nanometers were previously neglected in the course of the profile reconstruction. The two-dimensional (2D) rigorous numerical simulations of the diffraction process for periodic structures are carried out with the finite element method providing a numerical solution of the 2D Helmholtz equation. To model roughness, multiple calculations are performed for domains with large periods, containing many pairs of line and space with stochastically chosen line and space widths. A systematic decrease of the mean efficiencies for higher diffraction orders along with increasing variances is observed and established for different degrees of roughness. In particular, we obtain simple analytical expressions for the bias in the mean efficiencies and the additional uncertainty contribution stemming from the presence of LER and/or LWR. As a consequence this bias can easily be included into the reconstruction model to provide accurate values for the evaluated profile parameters. We resolve the sensitivity of the reconstruction from this bias by using simulated data with LER/LWR perturbed efficiencies for multiple reconstructions. If the scattering efficiencies are bias-corrected, significant improvements are found in the reconstructed bottom and top widths toward the nominal values.

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Fieldstitching with Kirchhoff-boundaries as a model based description for line edge roughness (LER) in scatterometry

Cited by 18 publications

References 11 publications

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

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

Sidewall roughness in nanolithography: origins, metrology and device effects

Modeling of line roughness and its impact on the diffraction intensities and the reconstructed critical dimensions in scatterometry

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