Inverse image problem of designing phase shifting masks in optical lithography

The continual shrinkage of minimum feature size in integrated circuit (IC) fabrication incurs more and more serious distortion in the optical lithography process, generating circuit patterns deviating from the desired ones. Conventional resolution enhancement techniques (RETs) are facing critical challenges in compensating such increasingly severe distortion. The approach of inverse lithography, which is a branch of mask design methodology to treat the design as an inverse image problem, is adopted in this paper. We apply nonlinear optimization techniques to design masks with minimally distorted output. The output patterns so generated have high contrast and low dose sensitivity. We also propose a dynamic program-based initialization scheme to pre-assign phases to the layout.