Electromigration Check: Where the Design and Reliability Methodologies Meet

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. Results of recent measurements performed on power grid-like structures isolated in the power grid environment have demonstrated that the weak link approach cannot accurately predict lifetime of the power grids. It calls for significant over-design, while, today, there is very little margin left for EM. Numerous observations clearly indicate that there is a need for a new EM checking approach that accurately models EM degradation using physics-based models, combined with a mesh model to account for redundancy, while being fast enough to be practically useful. In this paper, we present a novel approach for power grid EM checking using physics-based models that can account for process, voltage and temperature variations across the die. Existing physical models for EM in metal branches were extended to track EM degradation in multi-branch interconnect trees. 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 2.75x longer than those based on a 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 large VLSI circuits.