EM-Aware and Lifetime-Constrained Optimization for Multisegment Power Grid Networks

Abstract

This paper proposes a new power-ground (P/G) network sizing technique based on the recently proposed fast electromigration (EM) immortality check method for general multisegment interconnect wires and a new physics-based EM assessment technique for more accurate time to failure analysis. This paper first shows that the new P/G optimization problem, subject to the voltage IR drop and new EM constraints, can still be formulated as an efficient sequence of linear programing problem, where the optimization is carried out in two linear programing phases in each iteration. The new optimization will ensure that none of the wires fail if all the constraints are satisfied. However, requiring all the wires to be EM immortal can be overconstrained. To mitigate this problem, the first improvement is by means of adding reservoir branches to the mortal wires whose lifetime cannot be made immortal by wire sizing. This is a very effective approach as long as there is a sufficient reservoir area. The second improvement is to consider the aging effects of interconnect wires in the P/G networks. The idea is to allow some short-lifetime wires to fail and optimize the rest of the wires while considering the additional resistance caused by the failed wire segments. In this way, the resulting P/G networks can be optimized, such that the target lifetime of the whole P/G networks can be ensured and will become more robust and aging-aware over the expected lifetime of the chip. Numerical results on a number of IBM and self-generated power supply networks demonstrate that the new method can effectively reduce the area of the networks while ensuring immortality or enforcing target lifetime for all the wires, which is not the case for the existing current-density-constrained optimization methods.