A Fast Semi-Analytical Approach for Transient Electromigration Analysis of Interconnect Trees using Matrix Exponential

TL;DR

This paper introduces a rapid semi-analytical method using matrix exponential and Krylov subspace techniques to efficiently analyze electromigration stress in interconnect trees, significantly outperforming traditional numerical methods.

Contribution

The paper presents a novel semi-analytical approach leveraging matrix exponential and Krylov subspace methods for fast EM stress analysis in complex interconnect structures.

Findings

Achieves 0.5% average relative error compared to COMSOL.

Up to three orders of magnitude faster than existing methods.

Effectively handles large EM models with high accuracy.

Abstract

As integrated circuit technologies are moving to smaller technology nodes, Electromigration (EM) has become one of the most challenging problems facing the EDA industry. While numerical approaches have been widely deployed since they can handle complicated interconnect structures, they tend to be much slower than analytical approaches. In this paper, we present a fast semi-analytical approach, based on the matrix exponential, for the solution of Korhonen's stress equation at discrete spatial points of interconnect trees, which enables the analytical calculation of EM stress at any time and point independently. The proposed approach is combined with the extended Krylov subspace method to accurately simulate large EM models and accelerate the calculation of the final solution. Experimental evaluation on 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.