Cut Optimization for Redundant Via Insertion in Self-Aligned Double Patterning

Redundant via (RV) insertion helps prevent via defects and hence leads to yield enhancement. However, RV insertion in self-aligned double patterning (SADP) processes is challenging since cut optimization has to be considered together. In SADP, parallel one-dimensional metal lines are divided into signal wires and dummy wires by line-end cuts. If an RV is inserted, signal wires need to be extended to connect to the RV. To this end, an additional cut, which we call RV cut, is introduced to make a space for the extension. Since RV cuts and line-end cuts are manufactured with the same mask set, design rules between those cuts have to be honored, which incurs proper distribution and mask assignment to individual cuts. In this article, we address a problem of integrated RV insertion and cut optimization. We show that the problem can be formulated as an integer linear programming (ILP). We also propose a heuristic algorithm is presented for practical application, in which potential locations of RVs are first identified and used to properly insert as many RVs as possible while minimizing the conflict between RV cuts. Our experimental results demonstrate that 75% of vias receive RVs with 8% increase in total wire length, which is only slightly worse than the optimal result obtained by ILP.