Constraint approaches for some Inverse Lithography problems with Pixel-based Mask

An approach of solving the inverse lithography problem as a nonlinear, constrained minimization problem over a domain of mask pixels was suggested in the paper by Yu. Granik "Fast pixel-based mask optimization for inverse lithography" in 2006. This idea was advanced to account for pinching and bridging print contour constraints in the paper "Controlling Bridging and Pinching with Pixel-based Mask for Inverse Lithograph" by S. Kobelkov and others in 2015. The present paper extends this approach further for solving the enclosure print image constraints, getting maximum common depth of focus, and obtaining uniform PV-bands. Namely, we suggest several objective functions that express penalty for constraint violations. Their minimization with gradient descent methods is considered. A number of applications have been tested with ILT-based pxOPC tool for DUV metal, contacts, and EUV metal layouts; results are discussed showing benefits of each approach.