Timing ECO Optimization Via Bézier Curve Smoothing and Fixability Identification

Due to the rapidly increasing design complexity in modern integrated circuit design, more and more timing failures are detected at late stages. Without deferring time-to-market, metal-only engineering change order (ECO) is an economical technique to correct these late-found failures. Typically, a design might need to undergo many ECO runs in design houses; consequently, the usage of spare cells for ECO is of significant importance. In this paper, we aim at timing ECO by using as few spare cells as possible. We observe that a path with good timing is desired to be geometrically smooth. Unlike negative slack and gate delay used in most prior work, we propose a new metric of timing criticality, fixability, by considering the smoothness of timing violating paths. To measure the smoothness of a path, we use the Bézier curve as the golden path. Furthermore, in order to concurrently fix timing violations, we derive a propagation property to divide violating paths into independent segments. Based on Bézier curve smoothing, fixability identification, and the propagation property, we develop an efficient algorithm to fix timing violations. Experimental results show that we can effectively resolve all timing violations with significant speedups over the state-of-the-art works.