Multi-physics-based FEM analysis for post-voiding analysis of electromigration failure effects

Abstract

In this paper, we propose a new multi-physics finite element method (FEM) based analysis method for void growth simulation of confined copper interconnects. This new method for the first time considers three important physics simultaneously in the EM failure process and their time-varying interactions: the hydrostatic stress in the confined interconnect wire, the current density and Joule heating induced temperature. As a result, we end up with solving a set of coupled partial differential equations which consist of the stress diffusion equation (Korhonen's equation), the phase field equation (for modeling void boundary move), the Laplace equation for current density and the heat diffusion equation for Joule heating and wire temperature. In the new method, we show that each of the physics will have different physical domains and differential boundary conditions, and how such coupled multi-physics transient analysis was carried out based on FEM and different time scales are properly handled. Experiment results show that by considering all three coupled physics - the stress, current density, and temperature - and their transient behaviors, the proposed FEM EM solver can predict the unique transient wire resistance change pattern for copper interconnect wires, which were well observed by the published experiment data. We also show that the simulated void growth speed is less conservative than recently proposed compact EM model.