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Accurate simulations of 2-D phase shift masks with a generalized discontinuous Galerkin (GDG) method
1. | LSEC, Institute of Computational Mathematics, Chinese Academy of Science, Beijing 100190, China |
2. | Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, United States |
References:
[1] |
D. Arnold, F. Brezzi, B. Cockburn and L. D. Marini, United analysis of discontinuous Galerkin methods for elliptic problems,, SIAM J. Numer. Anal., 39 (2002), 1749.
doi: 10.1137/S0036142901384162. |
[2] |
G. A. Baker, Finite element methods for elliptic equations using nonconforming elements,, Math. Comput., 31 (1977), 45.
doi: 10.1090/S0025-5718-1977-0431742-5. |
[3] |
S. Burger and R. Kohle, Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,, Proc. SPIE, 5992 (2005), 368. Google Scholar |
[4] |
W. C. Chew, "Waves and Fields in Inhomogeneous Media,", New York: Van Nostrand Reinhold, (1999). Google Scholar |
[5] |
W. C. Chew and W. H. Weedon, A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates,, IEEE Microwave Guided Wave Lett., 7 (1994), 599. Google Scholar |
[6] |
B. Cockburn, S. Hou and C. W. Shu, Tvb Runge kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case,, Math. Comput., 54 (1990), 545.
|
[7] |
A. Erdmann and P. Evanschitzky, Rigorous electromagnetic field mask modeling and related lithographic effcts in the low k1 and ultrahigh numerical aperture regime,, J. Microlith., 6 (2007). Google Scholar |
[8] |
K. Fan, W. Cai and X. Ji, A generalized discontinuous Galerkin (GDG) method for Schrödinger equations with nonsmooth solutions,, J. Comput. Phys., 227 (2008), 2387.
doi: 10.1016/j.jcp.2007.10.023. |
[9] |
W. Lee and F. L. Degertekin, Rigorous coupled-wave analysis of multilayered grating structures,, J. Lightwave Technol., 22 (2004), 2359.
doi: 10.1109/JLT.2004.833278. |
[10] |
M. D. Levenson, N. S. Viswanathan and R. A. Simpson, Improving resolution in photolithography with a phase-shifting mask,, IEEE Trans. on Electron Devices, 29 (1982), 1828.
doi: 10.1109/T-ED.1982.21037. |
[11] |
K. D. Lucas, H. Tanabe and A. J. Strojwas, Efficient and rigorous three-dimensional model for optical lithography simulation,, J. Opt. Soc. Am., 13 (1996), 2187.
doi: 10.1364/JOSAA.13.002187. |
[12] |
T. Sato and A. Endo, Impact of polarization for an attenuated phase shift mask with ArF hyper-numerical aperture lithography,, J. Microlith., 5 (2006). Google Scholar |
[13] |
A. Taflove and S. C. Hagness, "Computational Electromagnetics: The Finite-Difference Time-Domain Method," 2nd, edition, (). Google Scholar |
[14] |
A. K. Wong and A. R. Neureuther, Rigorous three-dimensional time-domain finite-difference electromagnetic simulation for photolithographic applications,, IEEE Trans. on Semiconductor Manufacturing, 8 (1995), 419.
doi: 10.1109/66.475184. |
show all references
References:
[1] |
D. Arnold, F. Brezzi, B. Cockburn and L. D. Marini, United analysis of discontinuous Galerkin methods for elliptic problems,, SIAM J. Numer. Anal., 39 (2002), 1749.
doi: 10.1137/S0036142901384162. |
[2] |
G. A. Baker, Finite element methods for elliptic equations using nonconforming elements,, Math. Comput., 31 (1977), 45.
doi: 10.1090/S0025-5718-1977-0431742-5. |
[3] |
S. Burger and R. Kohle, Benchmark of FEM, waveguide and FDTD algorithms for rigorous mask simulation,, Proc. SPIE, 5992 (2005), 368. Google Scholar |
[4] |
W. C. Chew, "Waves and Fields in Inhomogeneous Media,", New York: Van Nostrand Reinhold, (1999). Google Scholar |
[5] |
W. C. Chew and W. H. Weedon, A 3D perfectly matched medium from modified Maxwell's equations with stretched coordinates,, IEEE Microwave Guided Wave Lett., 7 (1994), 599. Google Scholar |
[6] |
B. Cockburn, S. Hou and C. W. Shu, Tvb Runge kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case,, Math. Comput., 54 (1990), 545.
|
[7] |
A. Erdmann and P. Evanschitzky, Rigorous electromagnetic field mask modeling and related lithographic effcts in the low k1 and ultrahigh numerical aperture regime,, J. Microlith., 6 (2007). Google Scholar |
[8] |
K. Fan, W. Cai and X. Ji, A generalized discontinuous Galerkin (GDG) method for Schrödinger equations with nonsmooth solutions,, J. Comput. Phys., 227 (2008), 2387.
doi: 10.1016/j.jcp.2007.10.023. |
[9] |
W. Lee and F. L. Degertekin, Rigorous coupled-wave analysis of multilayered grating structures,, J. Lightwave Technol., 22 (2004), 2359.
doi: 10.1109/JLT.2004.833278. |
[10] |
M. D. Levenson, N. S. Viswanathan and R. A. Simpson, Improving resolution in photolithography with a phase-shifting mask,, IEEE Trans. on Electron Devices, 29 (1982), 1828.
doi: 10.1109/T-ED.1982.21037. |
[11] |
K. D. Lucas, H. Tanabe and A. J. Strojwas, Efficient and rigorous three-dimensional model for optical lithography simulation,, J. Opt. Soc. Am., 13 (1996), 2187.
doi: 10.1364/JOSAA.13.002187. |
[12] |
T. Sato and A. Endo, Impact of polarization for an attenuated phase shift mask with ArF hyper-numerical aperture lithography,, J. Microlith., 5 (2006). Google Scholar |
[13] |
A. Taflove and S. C. Hagness, "Computational Electromagnetics: The Finite-Difference Time-Domain Method," 2nd, edition, (). Google Scholar |
[14] |
A. K. Wong and A. R. Neureuther, Rigorous three-dimensional time-domain finite-difference electromagnetic simulation for photolithographic applications,, IEEE Trans. on Semiconductor Manufacturing, 8 (1995), 419.
doi: 10.1109/66.475184. |
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