Redundancy-Aware Power Grid Electromigration Checking Under Workload Uncertainties

Electromigration (EM) in on-die metal lines is becoming a significant problem in modern integrated circuits technology. Due to the high levels of current density on the die, the large number of metal lines, and the inherent conservatism in classical full-chip EM models, designers are finding it very hard to meet the area and design specs while guaranteeing EM reliability. The EM problem is most significant in power grid lines, because unlike signal and clock lines, they do not benefit from healing due to their mostly unidirectional currents. In this paper, we develop a new model, referred to as the mesh model, for power grid EM checking which takes into account the inherent redundancy of its mesh structure while determining the reliability. To implement the mesh model, we also develop a framework to estimate the change in statistics of an interconnect as its effective-EM current varies. In order to overcome the conservative assumptions that designers usually make about chip workloads, we also propose a novel vectorless mesh model technique to estimate the average minimum time-to-failure of a power grid under workload uncertainties. The results indicate that the series model, which is currently used in the industry, gives a pessimistic estimate of power grid MTF and reliability by a factor of 3-4. Finally, we exploit multithreading and grid locality to speedup our implementation by almost $6{\times }$ .