Domain decomposition methods for the rapid electromagnetic simulation of photomask scattering

An integrated methodology has been developed for computer simulation of electromagnetic scattering from large, nonperiodic, two- dimensional layouts of advanced photomasks (masks with optical prox- imity correction and phase-shifting masks). The domain decomposition method consists of three steps: First, by virtue of the linearity of the Kirchhoff-Fresnel diffraction integral, the mask layout is decomposed into a set of constituent single-opening masks. Second, the rigorous electromagnetic simulation of each three-dimensional structure from the set of these single-opening masks is circumvented and, instead, the re- sult for the scattered field is synthesized based on two two-dimensional rigorous electromagnetic simulations that model the mask geometry in two cross-sectional planes. Subsequently, compact equivalent source models are used to describe the scattered fields on a reference plane. These models are constructed in such a way as to minimize the error in the part of the diffraction spectrum that passes through the projection system, allowing accurate and efficient image simulation. The normal- ized mean square error of the near scattered field is typically a fraction of 1% and speed-up factors for the total simulation time in excess of 400 (compared with the rigorous mask model) are achieved. The use of a look-up table approach facilitates orders of magnitude of further speed improvement. © 2002 Society of Photo-Optical Instrumentation Engineers.