A Deep Learning Framework for Solving Stress-based Partial Differential Equations in Electromigration Analysis

The electromigration-induced reliability issues (EM) in very large scale integration (VLSI) circuits have attracted continuous attention due to technology scaling. Traditional EM methods lead to inaccurate results incompatible with the advanced technology nodes. In this article, we propose a learning-based model by enforcing physical constraints of EM kinetics to solve the EM reliability problem. The method aims at solving stress-based partial differential equations (PDEs) to obtain the hydrostatic stress evolution on interconnect trees during the void nucleation phase, considering varying atom diffusivity on each segment, which is one of the EM random characteristics. The approach proposes a crafted neural network-based framework customized for the EM phenomenon and provides mesh-free solutions benefiting from the employment of automatic differentiation (AD). Experimental results obtained by the proposed model are compared with solutions obtained by competing methods, showing satisfactory accuracy and computational savings.