Accurate simulations of 2-D phase shift masks with a generalized discontinuous Galerkin (GDG) method

Xia Ji; Wei Cai

doi:10.3934/dcdsb.2011.15.401

Article Contents

2011, Volume 15, Issue 2: 401-415. Doi: 10.3934/dcdsb.2011.15.401

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Accurate simulations of 2-D phase shift masks with a generalized discontinuous Galerkin (GDG) method

Xia Ji^1, and
Wei Cai^2,

1.
LSEC, Institute of Computational Mathematics, Chinese Academy of Science, Beijing 100190
2.
Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223

Received: October 31, 2009

Revised: February 28, 2010

Published: August 2011

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Abstract

In this paper, we apply a newly developed generalized discontinuous Galerkin (GDG) method for rigorous simulations of 2-D phase shift masks (PSM). The main advantage of the GDG method is its accurate treatment of jumps in solutions using the Dirac $\delta$ generalized functions as source terms of partial differential equations. The scattering problem of the PSM is cast with a total field/scattering field formulation while the GDG method is used to handle the inhomogeneous jump conditions between the total and scattering fields along the physical and perfectly matched layer (PML) interfaces. Numerical results demonstrate the high order accuracy of the GDG method and its capability of handling the non-periodic structures such as optical images near mask edges.

Keywords:

Generalized discontinuous Galerkin method (GDG),
discontinuous Galerkin method (DG),
phase shift masks (PSM),
perfectly matched layer (PML).

Mathematics Subject Classification: Primary: 35Q60; Secondary: 35J05.

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