Placement optimization for MP-DSAL compliant layout

Sub 10-nm technology node requires contacts whose size and pitch are beyond optical resolution limit. Directed self-assembly lithography with multiple patterning technology (MP-DSAL) has been actively studied to support such fine features. In MP-DSAL, layout decomposition is a key problem, in which close contacts are clustered and assigned to one of masks (or colors). Many practical contact layouts are not MP-DSAL compliant in a sense that layout decomposition is not perfectly performed leaving a few coloring conflicts and unmanufacturable contact clusters. We propose to optimize placement so that layout becomes MP-DSAL compliant. A simple cell flip is employed for this purpose, and placement optimization is formulated as ILP; a practical heuristic is then proposed. Experiments demonstrate that very marginal 0.5% of cells are flipped to achieve our goal.