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

2025-03-18

AI Summary

Stress evolution during the void phase of electromigration (EM) exhibits strong stochasticity due to manufacturing variations and current fluctuations, rendering traditional Monte Carlo methods computationally prohibitive and inefficient. Method: This paper proposes an efficient stochastic analysis framework integrating closed-form electromagnetic field analytical solutions with a Bayesian physics-informed neural network (BPINN). For the first time, analytical solutions are embedded into BPINN to enforce physical conservation laws at the segment level and coupling constraints at the node level, naturally encoding parameter variability; uncertainty quantification is achieved via variational inference. Results: Compared to Monte Carlo simulations in COMSOL and EMSpice, the proposed method achieves speedups of over 240× and 65×, respectively, without sacrificing accuracy, and supports modeling of arbitrary initial stress distributions.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Hardware-aware ML
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

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 BPINNEM- Post, for efficient stochastic analysis of EM-induced postvoiding aging processes. This new approach integrates closedform analytical solutions with a Bayesian Physics-Informed Neural Network (BPINN) framework to accelerate the analysis for the first time. 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 the use of 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 speedup compared to Monte Carlo simulations using the FEM-based COMSOL solver and more than 65x speedup compared to Monte Carlo simulations using the FDM-based EMSpice method.

Problem

• Analyzes stochastic electromigration damage post-void phase
• Replaces expensive Monte Carlo simulations with efficient ML
• Integrates physics laws with Bayesian neural networks

Innovation

• Bayesian Physics-Informed Neural Network integration
• Closed-form analytical solutions for efficiency
• Stochastic EM analysis with variational effects