Physics-based electromigration assessment for power grid networks

This paper presents a novel approach and techniques for physics-based electromigration (EM) assessment in power delivery networks of VLSI systems. An increase in the voltage drop above the threshold level, caused by EM-induced increase in resistances of the individual interconnect segments, is considered as a failure criterion. It replaces a currently employed conservative weakest segment criterion, which does not account an essential redundancy for current propagation existing in the power-ground (p/g) networks. EM-induced increase in the resistance of the individual grid segments is described in the approximation of the recently developed physics-based formalism for void nucleation and growth. A statistical approach to calculation of the void nucleation times in the group of branches comprising the interconnect tree is implemented. As a result, p/g networks become time-varying linear networks. A developed technique for calculating the hydrostatic stress evolution inside a multi-branch interconnect tree allows to avoid over optimistic prediction of the time-to-failure (TTF) made with the Blech-Black analysis of individual branches of interconnect tree. Experimental results obtained on a number of IBM benchmark circuits validate the proposed methodology.