This paper presents a number of power grid network design and optimization techniques that consider the electromigration (EM) effects for multi-segment interconnect wires. First, we consider a new EM immortality constraint due to EM void saturation volume for multi-segment interconnects. It helps reduce conservativeness in the EM-aware on-chip power grid design. Along with the EM nucleation phase immortality constraint, we show that both EM immortality constraints can be naturally integrated into the existing programming based power grid optimization framework. Second, to mitigate the overly conservativeness of the immortality constrained optimization methods, we further explore three strategies: we first size up failed wires to meet one of the immortality conditions subject to the design rules; second, we consider the EM-induced aging effects on power supply networks for a target lifetime, which allows some short-lived wires to fail and optimizes the remaining wires; third, we propose a large change sensitivity-based optimization scheme to perform localized fixing based on recently proposed coupled EM-IR drop analysis method. Numerical results on a number of IBM-format power grid networks demonstrate that the new method can reduce more power grid area compared to the existing EM immortality constrained optimizations. Moreover, the new method is able to optimize power grids with nucleated wires, which would not be possible with the existing methods. Results also show the sensitivity-based localized power girds fixing can fix EM-induced IR drop violations in a few minutes for synthesized power grid networks from ARM core designs.

本文介绍了许多考虑多段互连线的电迁移（EM）效应的电网网络设计和优化技术。首先，由于多段互连的EM空隙饱和体积，我们考虑了一个新的EM永生性约束。它有助于减少对EM敏感的片上电网设计的保守性。连同EM成核阶段的不朽约束，我们表明这两个EM永恒约束可以自然地集成到现有的基于编程的电网优化框架中。其次，为了减轻永生约束优化方法的过度保守性，我们进一步探索了三种策略：我们首先将失效导线的尺寸增大到满足设计规则规定的永生条件之一；第二，我们考虑了在目标使用寿命内，EM诱发的老化对电源网络的影响，这会使一些短寿命的电线失效并优化其余电线；第三，我们基于最近提出的耦合EM-IR下降分析方法，提出了一种基于大变化敏感性的优化方案来进行局部固定。在许多IBM格式的电网网络上的数值结果表明，与现有的EM不朽约束优化相比，该新方法可以减少更多的电网面积。此外，新方法能够优化带核导线的电网，而现有方法则无法实现。结果还表明，基于灵敏度的局部电源网格修复可以在几分钟内解决EM引起的IR压降违规问题，适用于ARM核心设计的综合电网网络。