Mask Assignment and DSA Grouping for DSA-MP Hybrid Lithography for Sub-7 nm Contact/Via Holes

Directed self assembly (DSA) is a very promising candidate for the sub-7 nm technology nodes. To print such small dimensions, multiple patterning (MP) is likely to be used to print the guiding templates for DSA. Therefore, algorithms are required to perform the DSA grouping at the same time as the mask assignment. In this paper, we present an optimal integer linear program (ILP) to solve this problem for two schemes of hybrid DSA-MP process. Scalable heuristic algorithms are also proposed to solve the same problem. In comparison to the ILP, the proposed heuristics are $4\boldsymbol \times$ – $213\boldsymbol \times$ faster, and result in an increase of total number of violations by 4%–29%.