Line Search-Based Inverse Lithography Technique for Mask Design

Abstract

As feature size is much smaller than the wavelength of illumination source of lithography equipments, resolution enhancement technology (RET) has been increasingly relied upon to minimize image distortions. In advanced process nodes, pixelated mask becomes essential for RET to achieve an acceptable resolution. In this paper, we investigate the problem of pixelated binary mask design in a partially coherent imaging system. Similar to previous approaches, the mask design problem is formulated as a nonlinear program and is solved by gradient-based search. Our contributions are four novel techniques to achieve significantly better image quality. First, to transform the original bound-constrained formulation to an unconstrained optimization problem, we propose a new noncyclic transformation of mask variables to replace the wellknown cyclic one. As our transformation is monotonic, it enables a better control in flipping pixels. Second, based on this new transformation, we propose a highly efficient line search-based heuristic technique to solve the resulting unconstrained optimization. Third, to simplify the optimization, instead of using discretization regularization penalty technique, we directly round the optimized gray mask into binary mask for pattern error evaluation. Forth, we introduce a jump technique in order to jump out of local minimum and continue the search.