Mask Optimization for Directed Self-Assembly Lithography: Inverse DSA and Inverse Lithography

In directed self-assembly lithography (DSAL), a mask contains the images of guide patterns (GPs), which are patterned on a wafer through optical lithography; the wafer then goes through DSA process to pattern contacts. Mask design for DSAL, which is the opposite of the above processes, consists of two key steps, inverse DSA and inverse lithography, which we address in this paper. In inverse DSA, we progressively refine GPs until they produce target contacts as closely as possible. GP is defined as a function of a few geometry parameters, and how sensitive the contacts are to the parameters are calculated which then guides how much the GP should be refined. In inverse lithography, mask is progressively refined so that target GPs are produced. Mask is defined by pixel values and their gradient guides the direction that the mask should be refined. There are too many pixels for gradient calculation; the method to approximate calculation is proposed. Inverse DSA and inverse lithography are extended to handle process variations. We modify basic inverse lithography so that the resulting mask becomes less sensitive to lithography variations; basic inverse DSA is modified so that it provides the way this sensitivity can be checked.