| Electromigration (EM) is a key reliability concern in chip power/ ground (p/g) grids, which has been exacerbated by the high current levels and narrow metal lines in modern grids. EM checking is expensive due to the large sizes of modern p/g grids and is also inherently difficult due to the complex nature of the EM phenomenon. Traditional EM checking is based on empirical models, but better models are needed for accurate prediction due to the very small margins between the allowed failure rates (spec) and the failure rates at which the chips actually operate in the field. Thus, recent more accurate physics-based EM models have been proposed, which remain computationally expensive because they require solution of a system of partial differential equations (PDEs). In this work, we extend the existing physics-based models for EM in metal branches to track EM degradation in multi-branch interconnect trees and propose a fast and scalable methodology for power grid EM verification. We speed up our implementation by using filtering schemes (that focus the computation only on the most EM susceptible trees) and by developing optimized numerical methods to solve the PDE system arising out of the physics-based EM models. The lifetimes found using our physics-based approach are on average 2.35x longer than those based on a (calibrated) Black's model, as extended to handle mesh power grids. With a runtime of only 10 minutes for a 4.1M node grid, our approach is extremely fast and should scale well for large integrated circuits. |
