Mask assignment and synthesis of DSA-MP hybrid lithography for sub-7nm contacts/vias

Integrating Directed Self Assembly (DSA) and Multiple Patterning (MP) is an attractive option for printing contact and via layers for sub-7nm process nodes. In the DSA-MP hybrid process, an optimized decomposition algorithm is required to perform the MP mask assignment while considering the DSA advantages and limitations. In this paper, we present an optimal Integer Linear Programming (ILP) formulation for the simultaneous DSA grouping and MP decomposition problem for contacts and vias. Then we propose a heuristic and develop an efficient algorithm for solving the same problem. In comparison to the optimal ILP results, the proposed algorithm is 197x faster and results in 16.3% more violations. The proposed algorithm produces 56% fewer violations than the sequential approaches which perform DSA grouping followed by MP decomposition and vice versa.