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.

Some key results of a benchmark test, initiated in 1992 by the Working Group 2 of COST Project 240 at a modelling workshop in Teupitz, Germany, are presented. A great number of BPM algorithms, such as the FTBPM, various types of FDBPMs, wide angle approximations and adaptive FE-BPM are compared. The quasi-analytic character of the benchmark tests gains a deeper insight into the absolute accuracy

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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.

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