Benchmarking of available rigorous electromagnetic field (EMF) simulators for phase-shift mask applications

It is well known that accurate simulation of phase-shifting masks in optical lithography requires representation as full 3D objects, as opposed to binary masks. To simulate these objects, the electromagnetic field in the neighborhood of the mask must be calculated. The additional step of solving Maxwell s equations tends to consume a large amount of CPU time compared to conventional simulation in which Kirchhoffs approximation of an infinitely thin mask is used. Therefore, the question of how much accuracy is gained using EMF solvers for the additional cost in terms of CPU time is relevant for its application in advanced lithography. The paper first addresses accuracy: comparisons from a Kirchhoff-type simulator to the newly developed 3D Maxwell solver, T-MASK (Sigma-C) are made as well as comparisons among existing finite-difference, time-domain (FDTD) Maxwell equation solvers. Next, benchmarks with focus on CPU consumption will be given in 2D (no material variation in one dimension) compared to ProMAX/2D and TEMPEST, both well-known FDTD-based solvers. Finally, benchmarks are extended to full 3D geometries using T-MASK and TEMPEST.