PHASE-SHIFTING MASKS FOR MICROLITHOGRAPHY - AUTOMATED DESIGN AND MASKREQUIREMENTS

The problem of automated design of phase-shifting masks for enhanced-r esolution optical lithography is examined. We propose a computationall y viable algorithm for the rapid design of phase-shifting masks for ar bitrary two-dimensional patterns. Our approach is based on the use of a class of optimal coherent approximations to partially coherent imagi ng systems described by the Hopkins model. These approximations lead t o substantial computational and analytical benefits, and, in addition, the resultant approximation error can be quite small for imaging syst ems with coherence factor sigma less-than-or-equal-to 0.5. These appro ximate models allow us to reduce the mask-design problem to the classi cal phase-retrieval problem in optics. A fast iterative algorithm, clo sely related to the Gerchberg-Saxton algorithm, is then applied to gen erate (suboptimal) phase-shifting masks. Analytical results related to practical requirements for phase-shifting masks are also presented. T hese results address questions related to the number of discrete phase levels required for arbitrary patterns and provide some insight into alternative strategies for the use of phase-shifting masks. A number o f simulated phase-shifting mask-design examples are provided to illust rate the methods and ideas presented.