Finite difference method for electromigration analysis of multi-branch interconnects

Electromigration (EM) in VLSI chips has become a major reliability issues in nanometer VLSI design. Traditional compact EM models cannot give accurate predictions about the stress evolution over all stress conditions for complicated multi-branch interconnect structures. In this paper, we try to mitigate this problem by performing finite difference method (FDM) for the EM effects in multi-branch interconnects based on the kinetics of the first principle of EM physics. We start with the partial differential equations that describe the fundamental hydrostatic stress evolution for both the void nucleation and void growth phases with proper boundary and initial conditions for typical multi-branch metal wires: the single 2-terminal wire, and the straight-line 3-terminal wires. The new FDM for EM analysis approach can easily accommodate existing non-uniformly distributed residual stress, while existing compact EM models cannot. Time varying temperature and current, which are also difficult to model with existing methods, can also be considered with this method. Numerical results show that the proposed FDM EM analysis method agrees with the COMSOL based finite element method in terms of accuracy.