BPINN-EM-Post: Bayesian Physics-Informed Neural Network based Stochastic Electromigration Damage Analysis in the Post-void Phase
This work addresses the need for faster stochastic analysis in semiconductor reliability for engineers, though it is incremental as it builds on existing physics-informed neural network methods by integrating closed-form solutions.
The paper tackled the problem of efficiently analyzing stochastic electromigration-induced stress in post-void phases, which is computationally expensive with traditional Monte Carlo simulations, and introduced BPINN-EM-Post, achieving over 240x speedup compared to FEM-based solvers and over 67x speedup compared to FDM-based solvers with marginal accuracy loss.
In contrast to the assumptions of most existing Electromigration (EM) analysis tools, the evolution of EM-induced stress is inherently non-deterministic, influenced by factors such as input current fluctuations and manufacturing non-idealities. Traditional approaches for estimating stress variations typically involve computationally expensive and inefficient Monte Carlo simulations with industrial solvers, which quantify variations using mean and variance metrics. In this work, we introduce a novel machine learning-based framework, termed BPINN-EM- Post, for efficient stochastic analysis of EM-induced post-voiding aging processes. For the first time, our new approach integrates closed-form analytical solutions with a Bayesian Physics- Informed Neural Network (BPINN) framework to accelerate the analysis. The closed-form solutions enforce physical laws at the individual wire segment level, while the BPINN ensures that physics constraints at inter-segment junctions are satisfied and stochastic behaviors are accurately modeled. By reducing the number of variables in the loss functions through utilizing analytical solutions, our method significantly improves training efficiency without accuracy loss and naturally incorporates variational effects. Additionally, the analytical solutions effectively address the challenge of incorporating initial stress distributions in interconnect structures during post-void stress calculations. Numerical results demonstrate that BPINN-EM-Post achieves over 240x and more than 67x speedup compared to Monte Carlo simulations using the FEM-based COMSOL solver and FDM-based EMSpice, respectively, with marginal accuracy loss.