Highly parallel rigorous simulations of phase-shift masks with a generalized eigen-oscillation spectral element method

Ke Zong; Xuan Zeng; Xia Ji; Wei Cai

doi:10.1117/1.3158611

Highly parallel rigorous simulations of phase-shift masks with a generalized eigen-oscillation spectral element method

Ke Zong^*, Xuan Zeng, Xia Ji, Wei Cai

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We apply a newly developed parallel generalized eigenoscillation spectral element method (GeSEM) for rigorous simulations of 2-D phase-shift masks (PSMs). The GeSEM combines highly parallel Schwarz-domain decomposition iterations and an eigen-oscillationbased spectral method to model high-frequency oscillatory electromagnetic fields in PSMs with dispersive chrome materials in the PSMs. The performance of the GeSEM has been compared to the popular plane wave-based waveguide method for 2-D masks. The numerical results have clearly demonstrated the GeSEM's advantages in modeling the effects of nonperiodic structures such as optical images near mask edges, and its speedup through parallel implementations, which makes the simulation of a large-scale mask possible in whole-chip mask modeling.

Original language	English
Article number	031403
Journal	Journal of Micro/ Nanolithography, MEMS, and MOEMS
Volume	8
Issue number	3
DOIs	https://doi.org/10.1117/1.3158611
Publication status	Published - 2009
Externally published	Yes

Keywords

Discontinuous Galerkin method
Eigen oscillations
Lithography simulation
Phase-shifting mask
Schwarz domain decomposition iteration
Spectral method

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10.1117/1.3158611

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title = "Highly parallel rigorous simulations of phase-shift masks with a generalized eigen-oscillation spectral element method",

abstract = "We apply a newly developed parallel generalized eigenoscillation spectral element method (GeSEM) for rigorous simulations of 2-D phase-shift masks (PSMs). The GeSEM combines highly parallel Schwarz-domain decomposition iterations and an eigen-oscillationbased spectral method to model high-frequency oscillatory electromagnetic fields in PSMs with dispersive chrome materials in the PSMs. The performance of the GeSEM has been compared to the popular plane wave-based waveguide method for 2-D masks. The numerical results have clearly demonstrated the GeSEM's advantages in modeling the effects of nonperiodic structures such as optical images near mask edges, and its speedup through parallel implementations, which makes the simulation of a large-scale mask possible in whole-chip mask modeling.",

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T1 - Highly parallel rigorous simulations of phase-shift masks with a generalized eigen-oscillation spectral element method

AU - Zong, Ke

AU - Zeng, Xuan

AU - Ji, Xia

AU - Cai, Wei

PY - 2009

Y1 - 2009

N2 - We apply a newly developed parallel generalized eigenoscillation spectral element method (GeSEM) for rigorous simulations of 2-D phase-shift masks (PSMs). The GeSEM combines highly parallel Schwarz-domain decomposition iterations and an eigen-oscillationbased spectral method to model high-frequency oscillatory electromagnetic fields in PSMs with dispersive chrome materials in the PSMs. The performance of the GeSEM has been compared to the popular plane wave-based waveguide method for 2-D masks. The numerical results have clearly demonstrated the GeSEM's advantages in modeling the effects of nonperiodic structures such as optical images near mask edges, and its speedup through parallel implementations, which makes the simulation of a large-scale mask possible in whole-chip mask modeling.

AB - We apply a newly developed parallel generalized eigenoscillation spectral element method (GeSEM) for rigorous simulations of 2-D phase-shift masks (PSMs). The GeSEM combines highly parallel Schwarz-domain decomposition iterations and an eigen-oscillationbased spectral method to model high-frequency oscillatory electromagnetic fields in PSMs with dispersive chrome materials in the PSMs. The performance of the GeSEM has been compared to the popular plane wave-based waveguide method for 2-D masks. The numerical results have clearly demonstrated the GeSEM's advantages in modeling the effects of nonperiodic structures such as optical images near mask edges, and its speedup through parallel implementations, which makes the simulation of a large-scale mask possible in whole-chip mask modeling.

KW - Discontinuous Galerkin method

KW - Eigen oscillations

KW - Lithography simulation

KW - Phase-shifting mask

KW - Schwarz domain decomposition iteration

KW - Spectral method

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DO - 10.1117/1.3158611

M3 - Article

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SN - 1932-5150

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JO - Journal of Micro/ Nanolithography, MEMS, and MOEMS

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ER -

Highly parallel rigorous simulations of phase-shift masks with a generalized eigen-oscillation spectral element method

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