Fast physics-based electromigration analysis for multi-branch interconnect trees

Electromigration (EM) becomes one of the most challenging reliability issues for current and future ICs in 10nm technology and below. In this paper, we propose a new analsys method for the EM hydrostatic stress evolution for multi-branch interconnect trees, which is the foundation of the EM reliability assessment for large scale on-chip interconnect networks, such as power grid networks. The proposed method, which is based on eigenfunctions technique, could efficiently calculate the hydrostatic stress evolution for multi-branch interconnect trees stressed with different current densities and non-uniformly distributed thermal effects. The new method can also accommodate the pre-existing residual stresses coming from thermal or other stress sources. The proposed method solves the partial differential equations of EM stress more efficiently since it does not require any discretization either spatially or temporall, which is in contrast to numerical methods such as 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 efficiency of the proposed method is demonstrated and compared to finite difference method. The proposed method is 10X∼100X times faster than finite difference method and scales better for larger interconnect trees.