Inverse lithography source optimization via compressive sensing.

Abstract

Source optimization (SO) has emerged as a key technique for improving lithographic imaging over a range of process variations. Current SO approaches are pixel-based, where the source pattern is designed by solving a quadratic optimization problem using gradient-based algorithms or solving a linear programming problem. Most of these methods, however, are either computational intensive or result in a process window (PW) that may be further extended. This paper applies the rich theory of compressive sensing (CS) to develop an efficient and robust SO method. In order to accelerate the SO design, the source optimization is formulated as an underdetermined linear problem, where the number of equations can be much less than the source variables. Assuming the source pattern is a sparse pattern on a certain basis, the SO problem is transformed into a l1-norm image reconstruction problem based on CS theory. The linearized Bregman algorithm is applied to synthesize the sparse optimal source pattern on a representation basis, which effectively improves the source manufacturability. It is shown that the proposed linear SO formulation is more effective for improving the contrast of the aerial image than the traditional quadratic formulation. The proposed SO method shows that sparse-regularization in inverse lithography can indeed extend the PW of lithography systems. A set of simulations and analysis demonstrate the superiority of the proposed SO method over the traditional approaches.