Benchmark of FEM, waveguide, and FDTD algorithms for rigorous mask simulation

An extremely fast time-harmonic finite element solver developed for the transmission analysis of photonic crystals was applied to mask simulation problems. The applicability was proven by examining a set of typical problems and by a benchmarking against two established methods (FDTD and a differential method) and an analytical example. The new finite element approach was up to 100 times faster than the competing approaches for moderate target accuracies, and it was the only method which allowed to reach high target accuracies.

[1]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[2]  Frank Schmidt,et al.  A new finite element realization of the perfectly matched layer method for Helmholtz scattering problems on polygonal domains in two dimensions , 2006 .

[3]  Frank Schmidt,et al.  Solving Time-Harmonic Scattering Problems Based on the Pole Condition I: Theory , 2003, SIAM J. Math. Anal..

[4]  Martin McCallum,et al.  Benchmarking of available rigorous electromagnetic field (EMF) simulators for phase-shift mask applications , 2001 .

[5]  Frank Schmidt,et al.  Adaptive Multigrid Methods for the Vectorial Maxwell Eigenvalue Problem for Optical Waveguide Design , 2003 .

[6]  Matti Lassas,et al.  On the existence and convergence of the solution of PML equations , 1998, Computing.

[7]  Steven G. Johnson,et al.  Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis. , 2001, Optics express.

[8]  F. Schmidt,et al.  A new Finite Element realization of the Perfectly Matched Layer Method for Helmholtz scattering problems on polygonal domains in 2 D , 2022 .

[9]  Andreas Erdmann,et al.  Rigorous diffraction analysis for future mask technology , 2000, Advanced Lithography.

[10]  Ronald H. W. Hoppe,et al.  Finite element methods for Maxwell's equations , 2005, Math. Comput..

[11]  S. Burger,et al.  FEM modeling of 3D photonic crystals and photonic crystal waveguides , 2005, SPIE OPTO.

[12]  Dirk Michaelis,et al.  Planar High Index‐Contrast Photonic Crystals for Telecom Applications , 2006 .

[13]  S. Burger,et al.  JCMmode: an adaptive finite element solver for the computation of leaky modes , 2005, SPIE OPTO.

[14]  Roland Klose,et al.  Numerical investigation of light scattering off split-ring resonators , 2005, SPIE Optics + Optoelectronics.

[15]  Silvio Teuber,et al.  Determination of mask induced polarization effects occurring in hyper NA immersion lithography , 2004, SPIE Advanced Lithography.

[16]  Kazuaki Sakoda,et al.  Optical Properties of Photonic Crystals , 2001 .

[17]  M. G. Moharam,et al.  Coupled-Wave Analysis Of Two-Dimensional Dielectric Gratings , 1988, Photonics West - Lasers and Applications in Science and Engineering.

[18]  Rolf Rannacher,et al.  A posteriori error control for finite element approximations of elliptic eigenvalue problems , 2001, Adv. Comput. Math..

[19]  Roger Petit,et al.  Electromagnetic theory of gratings , 1980 .

[20]  Andreas Erdmann.  Process optimization using lithography simulation , 2004, International Conference on Micro- and Nano-Electronics.