Electromigration Stress Analysis with Rational Krylov-based Approximation of Matrix Exponential

Abstract

With aggressive technology scaling, Electromigration (EM) has become a major concern for the semiconductor industry. Although analytical methods are typically used for accurate EM analysis of interconnects, they cannot be applied to general structures such as multi-segment trees. In this paper, we present a semi-analytical approach for transient EM analysis of interconnect trees, which enables the efficient calculation of EM-induced stress at any time and point independently. The proposed method exploits the rational Krylov subspace to accurately approximate the matrix exponential and accelerate the simulation of large EM models. Experimental evaluation on the OpenROAD benchmarks demonstrates that our method achieves 0.5% average relative error over the COMSOL industrial tool while being up to three orders of magnitude faster.