BPINN-EM: Fast Stochastic Analysis of Electromigration Damage using Bayesian Physics-Informed Neural Networks

Electromigration (EM) induced aging and degradation in interconnect wires is inherently a stochastic process, with lifetime typically measured in terms of mean time to failure at both wire and circuit levels. However, existing approaches still incur high computing costs, as computing both means and variances is generally expensive. In this work, we propose a novel fast variational analysis framework to tackle the challenges of stochastic estimation of EM stress evolution in multi-segment interconnect wires. We utilize Bayesian networks in conjunction with the recently introduced hierarchical (two-step) physics-informed neural networks (PINN). The resulting method, termed BPINN-EM, enables rapid variational stress analysis of metal wires by leveraging the robust uncertainty quantification capability of Bayesian networks with expedited training over small dataset. Moreover, we devise BPINN-EM to incorporate Bayesian networks only in the first stage of the hierarchical PINN, thereby circumventing the need for sampling across the entire PINN level during training and significantly reducing training costs. Our results on several general multi-segment interconnect structure demonstrate that the proposed BPINN-EM approach is much more efficient than conventional baselines and state-of-the-art algorithms. Compared to a Monte Carlo simulator implemented in COMSOL, BPINN-EM offers a 240× speedup. Moreover, compared to the recently proposed EMSpice simulated by the Monte Carlo method, the new method provides more than an 85× speedup with almost no loss of accuracy.