Fast physics-based electromigration checking for on-die power grids

Abstract

Due to technology scaling, electromigration (EM) signoff has become increasingly difficult, mainly due to the use of inaccurate methods for EM assessment, such as the empirical Black's model. In this paper, we present a novel approach for EM checking using physics-based models of EM degradation, which effectively removes the inaccuracy, with negligible impact on run-time. Our main contribution is to extend the existing physical models for EM in metal branches to track the degradation in multi-branch interconnect trees. We also propose effective filtering and predictor-based schemes to speed up our implementation, with minimal impact on accuracy. Our results, for a number of IBM power grid benchmarks, confirm that Black's model is overly inaccurate. The lifetimes found using our physics-based approach are on average 3x longer than those based on a (calibrated) Black's model, such as currently used in industry. For the two largest IBM benchmarks (700K branches each), our runtime is comparable to that of the Black's based approach, requiring 3 hours for the largest grid.