Redundant via insertion in directed self-assembly lithography

In directed self-assembly lithography (DSAL), vias that are located close are clustered and patterned together. A large and complex cluster, however, is not allowed in this process due to its potential danger of pattern failure. We address redundant via insertion in DSAL. The goal is to insert maximum number of redundant vias while adjacent vias do not form a large and complex cluster. The problem is formulated as maximum independent set (MIS) of a conflict graph. Experiments demonstrate 13% more redundant vias inserted compared to simple-minded approach, basic insertion with no consideration of DSAL followed by removal of redundant vias in large and complex clusters. We also introduce DSA defect probability in order to quantitatively define which clusters should be allowed during insertion process.