EM Lifetime Constrained Optimization for Multi-Segment Power Grid Networks

This chapter provides techniques for power grid network sizing while considering electromigration reliability. Starting with power grid network and electromigration (EM) fundamentals. Specifically the concerns here are EM immortality and aging effects used as EM constraints when formulating the optimization problems. The chapter first shows that the new power/ground (P/G) optimization problem, subject to the voltage IR drop and new EM constraints, can still be formulated as an efficient sequence of linear programming (SLP) problem, where the optimization is carried out in two linear programming phases in each iteration. The new optimization will ensure that none of the wires fails if all the constraints are satisfied. However, requiring all the wires to be EM immortal can be over-constrained. To mitigate this problem, the improvement is to consider the aging effects of interconnect wires in 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.

Symmetry in Complex Systems

Complex systems with symmetry arise in many fields, at various length scales, including financial markets, social, transportation, telecommunication and power grid networks, world and country economies, ecosystems, molecular dynamics, immunology, living organisms, computational systems, and celestial and continuum mechanics [...]