This paper presents a novel approach and techniques for physics-based electromigration (EM) assessment in power delivery networks of very large scale integration systems. An increase in the voltage drop above the threshold level, caused by EM-induced increase in resistances of the individual interconnect branches, is considered as a failure criterion. It replaces a currently employed conservative weakest branch 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 branches is described in the approximation of the recently developed physics-based formalism for void nucleation and growth. An 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 multibranch interconnect tree allows to avoid over optimistic prediction of the time-to-failure made with the Blech–Black analysis of individual branches of interconnect tree. Experimental results obtained on a number of International Business Machines Corporation benchmark circuits show that the proposed method will lead to less conservative estimation of the lifetime than the existing Black–Blech-based methods. It also reveals that the EM-induced failure is more likely to happen at the place where the hydrostatic stress predicted by the initial current density is large and is more likely to happen at longer times when the saturated void volume effect is taken into account.
['Xin Huang', 'Armen Kteyan', 'Sheldon X.-D. Tan', 'Valeriy Sukharev']
Physics-Based Electromigration Models and Full-Chip Assessment for Power Grid Networks