Analytical Post-Voiding Modeling and Efficient Characterization of EM Failure Effects Under Time-Dependent Current Stressing

Electromigration (EM) has become the major concern for integrated circuits (ICs) in advanced technology nodes. Traditional empirical EM models, such as Black's equation, show inaccurate estimation for the time-to-failure of ICs, thus resulting in unnecessary over-design. To address this drawback, we propose a few analytical solutions for calculating the transient stress evolution and void volume in straight multisegment interconnect trees during the post-voiding phase. By employing the Laplace transform, the proposed method aims at solving coupled partial differential equations (PDEs) governed by physics-based EM modeling. The analytical solutions can be tailored to expressions with required accuracy and computational savings, leading to a compact end-to-end system providing results of EM failure effects at arbitrary time instances and locations of interconnect trees with varying geometry under time-dependent current and temperature stressing. The EM lifetime such as the incubation time, related to the void volume evolution, at any desired precision, can be calculated by the analytical solutions. The proposed method shows its accuracy, scalability, and computational savings through results compared with the finite element method (FEM) tool COMSOL and the competing methods and can achieve up to 593x speedup with < 10% error in EM failure time estimation.