BPINN-EM-Post: Bayesian Physics-Informed Neural Network based Stochastic Electromigration Damage Analysis in the Post-void Phase

Electromigration (EM)-induced stress evolution is inherently non-deterministic due to input current fluctuations and manufacturing non-idealities. Existing approaches for estimating stress variations rely on computationally expensive Monte Carlo simulations with industrial solvers. This work presents BPINN-EM-Post, a framework for stochastic analysis of EMinduced post-voiding aging processes. The key contributions are: (1) We integrate closed-form analytical solutions with a Bayesian Physics-Informed Neural Network (BPINN) to accelerate stochastic EM analysis. The closed-form solutions enforce physical laws at individual wire segments, while BPINN satisfies physics constraints at inter-segment junctions and captures stochastic behaviors. (2) By reducing loss function variables through analytical solutions, training efficiency improves substantially without sacrificing accuracy, and variational effects are naturally incorporated. (3) The analytical solutions address the challenge of incorporating initial stress distributions during post-void stress calculations. Experimental results show that BPINN-EMPost achieves over $240 \times$ and $67 \times$ speedup compared to Monte Carlo simulations using FEM-based COMSOL and FDM-based EMSpice, respectively, with marginal accuracy loss.