A pixel-based regularization approach to inverse lithography

Abstract

Inverse lithography attempts to synthesize the input mask which leads to the desired output wafer pattern by inverting the forward model from mask to wafer. In this article, we extend our earlier framework for image prewarping to solve the mask design problem for coherent, incoherent, and partially coherent imaging systems. We also discuss the synthesis of three variants of phase shift masks (PSM); namely, attenuated (or weak) PSM, 100% transmission PSM, and strong PSM with chrome. A new two-step optimization strategy is introduced to promote the generation and placement of assist bar features. The regularization framework is extended to guarantee that the estimated PSM have only two or three (allowable) transmission values, and the aerial-image penalty term is introduced to boost the aerial image contrast and keep the side-lobes under control. Our approach uses the pixel-based mask representation, a continuous function formulation, and gradient-based iterative optimization techniques to solve the inverse problem. The continuous function formulation allows analytic calculation of the gradient in O( MNlog ( MN)) operations for an M × N pattern making it practically feasible. We also present some results for coherent and incoherent imaging systems with very low k 1 values to demonstrate the effectiveness of our approach.