Layout Find Redundant Via Candidates Express solution by multiplets Conflict Graph Construction Contraction Graph Construction Solve the MMC Problem Legalization Output Layout MWIS Solver ILP Solver RG DS Fast Assignment for Some Vias

Inserting redundant vias is necessary for improving via yield in circuit designs. Block copolymer directed self-assembly (DSA) is an emerging and promising lithography technology for manufacture of vias and redundant vias, in which guiding templates are used to enhance the resolution. Considering manufacturability of via layer, multiple patterning lithography is also needed in advanced designs. In this paper, we study the redundant via insertion and guiding template assignment for DSA with multiple patterning problem at the post-routing stage. We propose a graph methodology based solution framework: Firstly, by analyzing the structure of guiding templates, we propose a new solution expression by introducing the concept of multiplet to discard redundant solutions. Then, honoring the compact solution expression, we construct a conflict graph on the grid model. Secondly, we formulate the problem with single patterning as a constrained maximum weight independent set problem, for which a fast linear interpolation algorithm is introduced to obtain a local optimal solution. To avoid undesirable local optima, we propose an effective initial solution generation method. Our framework is general and is further extended to solve the problem with double patterning or triple patterning in a two stage manner. Experimental results validate the efficiency and effectiveness of our method. Specifically, compared with the state-of-the-art work for the problem with single, double and triple patterning, our method can save 58%, 82% and 96% runtime, respectively.