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× faster than the competing approaches for moderate target accuracies, and it was the only method which allowed to reach high target accuracies.

We perform 3D lithography simulations by using a finite-element solver. To proof applicability to real 3D problems we investigate DUV light propagation through a structure of size 9 µm × 4 µm × 65 nm. On this relatively large computational domain we perform rigorous computations (No Hopkins) taking into account a grid of 11 × 21 source points with two polarization directions each. We obtain well converged results with an accuracy of the diffraction orders of about 1%. The results compare well to experimental aerial imaging results. We further investigate the convergence of 3D solutions towards quasi-exact results obtained with different methods.

H. Kawahira, Eds.) and is made available as an electronic preprint with permission of SPIE. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited. ABSTRACTWe present rigorous 3D EMF simulations of isolated features on photomasks using a newly developed finiteelement method. We report on the current status of the finite-element solver JCMsuite, incorporating higherorder edge elements, adaptive refinement methods, and fast solution algorithms. We demonstrate that rigorous and accurate results on light scattering off isolated features can be achived at relatively low computational cost, compared to the standard approach of simulations on large-pitch, periodic computational domains.

Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and optics design of nanostructured components. As has been shown in previous benchmarks some of the presently used methods suffer from low convergence rates and/or low accuracy of the results and exhibit very long computation times 1, 2 which makes application to extended 2D layout patterns impractical. We address 3D simulation tasks by using a finite-element solver which has been shown to be superior to competing methods by several orders of magnitude in accuracy and computational time for typical microlithography simulations.2 We report on the current status of the solver, incorporating higher order edge elements, adaptive refinement methods, and fast solution algorithms. Further, we investigate the performance of the solver in the 3D simulation project of light diffraction off an alternating phase-shift contact-hole mask.

For immersion technology the mask is illuminated under large angles and the features sizes are approaching the illuminating wavelength. At such operating conditions, several publications have shown rigorous diffraction effects having a noticeable effect on the aerial image. For the Kirchhoff assumption, which is commonly employed in lithography simulation, the mask is assumed to be an infinity thin transparency. This assumption implies the diffracted spectrum to be independent of the incident illumination angle and no coupling between polarization states occurs. This work is a fundamental study to deepen the understanding of rigorous off-axis effects for current and future mask technologies. This paper will show simulation studies for standard attenuated-and alternating mask gratings, which look at the diffracted spectrum of a mask grating with respect to polarization orientation and off-axis angle of the illuminating wave.