Efficient Simulation of Electromigration Damage in Large Chip Power Grids Using Accurate Physical Models (Invited Paper)

Abstract

Due to continued 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 review the state of the art for EM verification in on-die power/ground grids, with emphasis on a recent finite-difference based approach for power grid EM checking using physics-based models. The resulting model allows the EM damage across the power grid to be simulated based on a Linear Time Invariant (LTI) system formulation. The model also handles early failures and accounts for their impact on the grid lifetime. Our results, for a number of IBM power grid benchmarks, confirm that existing approaches for EM checking can be highly inaccurate. The lifetimes found using our physics-based approach are on average about 2X, or more, those based on the existing approaches, showing that existing EM design guidelines are overly pessimistic. The method is also quite fast, with a runtime of about 8 minutes for a 4M node grid, and so it is suitable for large circuits.