Fast Physics-Based Electromigration Analysis for Full-Chip Networks by Efficient Eigenfunction-Based Solution

Abstract

Electromigration (EM) becomes one of the most challenging reliability issues for current and future ICs in 10-nm technology and below. In this article, a novel method is proposed for the EM hydrostatic stress analysis on 2-D multibranch interconnect trees, which is the foundation of the EM reliability assessment for large-scale on-chip interconnect networks, such as on-chip power grid networks. The proposed method, which is based on an eigenfunction technique, could efficiently calculate the hydrostatic stress evolution for multibranch interconnect trees stressed with different current densities and nonuniformly distributed thermal effects. The proposed method solves the partial differential equations of transient EM stress more efficiently since it does not require any discretization either spatially or temporally, which is in contrast to numerical methods, such as the finite difference method and finite element method. The accuracy of the proposed transient analysis approach is validated against the analytical solution and commercial tools. The convergence of the proposed method is demonstrated by numerical experiments on practical power/ground networks, showing that only a small number of eigenfunction terms are necessary for the accurate solution. Thanks to its analytical nature, the proposed method is also utilized in efficient EM analysis techniques, such as searching for the void nucleation time by a modified bisection algorithm. The numerical results show that the proposed method is 10X–100X faster than the finite difference method and scales better for larger interconnect trees.