Binary mask optimization for forward lithography based on the boundary layer model in coherent systems

Recently, a set of generalized gradient-based optical proximity correction (OPC) optimization methods have been developed to solve for the forward and inverse lithography problems under the thin-mask assumption, where the mask is considered a thin 2D object. However, as the critical dimension printed on the wafer shrinks into the subwavelength regime, thick-mask effects become prevalent, and thus these effects must be taken into account in OPC optimization methods. OPC methods derived under the thin-mask assumption have inherent limitations and perform poorly in the subwavelength regime. This paper focuses on developing model-based forward binary mask optimization methods that account for the thick-mask effects of coherent imaging systems. The boundary layer (BL) model is exploited to simplify and characterize the thick-mask effects, leading to a model-based OPC method. The BL model is simpler than other thick-mask models, treating the near field of the mask as the superposition of the interior transmission areas and the boundary layers. The advantages and limitations of the proposed algorithm are discussed, and several illustrative simulations are presented.