Highly parallel rigorous simulations of phase-shift masks with a generalized eigen-oscillation spectral element method

We apply a newly developed parallel generalized eigenoscillation spectral element method (GeSEM) for rigorous simulations of 2-D phase-shift masks (PSMs). The GeSEM combines highly parallel Schwarz-domain decomposition iterations and an eigen-oscillationbased spectral method to model high-frequency oscillatory electromagnetic fields in PSMs with dispersive chrome materials in the PSMs. The performance of the GeSEM has been compared to the popular plane wave-based waveguide method for 2-D masks. The numerical results have clearly demonstrated the GeSEM's advantages in modeling the effects of nonperiodic structures such as optical images near mask edges, and its speedup through parallel implementations, which makes the simulation of a large-scale mask possible in whole-chip mask modeling.