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. <p> </p>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. <p> </p>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. <p> </p>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 ILTbased pxOPC tool for DUV metal, contacts, and EUV metal layouts; results are discussed showing benefits of each approach.
Inverse Lithography Technology (ILT) has become a viable computational lithography candidate in recent years as it can produce mask output that results in process latitude and CD control in the fab that is hard to match with conventional OPC/SRAF insertion approaches.<p> </p> An approach to solving the inverse lithography problem as a nonlinear, constrained minimization problem over a domain mask pixels was suggested in the paper by Y. Granik “Fast pixel-based mask optimization for inverse lithography” in 2006. The present paper extends this method to satisfy bridging and pinching constraints imposed on print contours. <p> </p>Namely, there are suggested objective functions expressing penalty for constraints violations, and their minimization with gradient descent methods is considered. This approach has been tested with an ILT-based Local Printability Enhancement (LP<sup>TM</sup>) tool in an automated flow to eliminate hotspots that can be present on the full chip after conventional SRAF placement/OPC and has been applied in 14nm, 10nm node production, single and multiple-patterning flows.