Convex-cost flow based redundant-via insertion with density-balance consideration

As VLSI design complexity continues to increase, the yield loss due to via failure becomes more and more significant. Redundant via insertion is highly recommended for improving chip yield and reliability. In this paper, we study the redundant via insertion problem in a postrouting stage, where a single via can have at most one redundant via inserted next to it. The goal is to insert as many redundant vias as possible and, at the same time, try to equilibrate the via density, which is good for the via density rules. We propose a convex-cost flow based approach to solve the problem within up to three routing layers. The experimental results show that, the proposed method can produce optimal solutions on defined density grid structure with maximum redundant via insertion, and achieve an at least 32.61% improvement of via density equalization.