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 neighbourhood 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 an infinitely thin mask is assumed. 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, SOLID-CM are made, followed by a juxtaposition of an exact solution, comparisons among existing finite-difference, time-domain (FDTD) Maxwell equation solvers, as well as a comparison to a rigorous coupled wave analysis (RCWA). Finally, benchmarks with focus on CPU consumption will be given in 2D (no material variation in one dimension) compared to two other simulators, both well-known FDTD-based solvers, called VendorA and VendorB. Finally, benchmarks are extended to full 3D geometries using SOLID-CM and VendorA.