Power Grid Electromigration Checking Using Physics-Based Models

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 finite-difference-based approach for power grid EM checking using physics-based models, that can account for process, voltage, and temperature variations across the die. Our main contribution is to extend existing physical models for EM in metal branches to track EM degradation in multibranch interconnect trees. The extended model is represented as a homogeneous linear time invariant system. We also detect early failures and account for their impact on grid lifetime. We speed up our implementation by proposing a macromodeling-based filtering scheme and a predictor-based approach. 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 $ {2.75\times }$ longer than those based on a (calibrated) Black’s model, as extended to handle mesh power grids. With a maximum runtime of 2.3 h among all the IBM benchmarks, our method appears to be suitable for very large scale integration circuits.