Physics-Informed Learning Based Multiphysics Simulation for Fast Transient TSV Electromigration Analysis

Through Silicon Vias (TSVs) are vulnerable to electromigration (EM) degradation due to their high local current densities, thereby reducing the reliability of 3D ICs with stack dies and TSVs. Due to the broad application of 3D ICs, it is necessary to analyze the electromigration reliability of TSVs. To overcome the weakness of traditional method for EM modeling of TSVs, we propose a physics-informed learning approach for transient analysis of electromigration modeling in TSV by solving the conventional mass balance equation. The proposed method allows simultaneous consideration of atomic depletion and accumulation, effective resistance degradation, electric current evolution, and stress distribution. In particular, we propose a customized neural network to simulate the EM process in TSV without the need for fine grid meshing and temporal iteration in traditional methods. Considering that the loss function of the proposed model is a combination of different loss terms, we propose a modified self-adaptive loss balanced method to automatically adjust the weights of multiple loss terms to enhance network performance. Given the prediction uncertainty due to data randomness or model architecture constraints, Gaussian probabilistic model is constructed to define the self-adaptive weights and update the dynamic weights per epoch built on maximum likelihood estimation. Compared with the finite element method, the proposed physics informed neural network method can lead to a speedup with less than 0.1% mean square error. Experimental results also show that the proposed model achieves excellent performance over other competing methods and high robustness under values of initial weights, different numbers of hidden layers and neurons per layer.