Simultaneous Buffer Insertion and Wire Sizing Considering Systematic CMP Variation and Random $L_{rm eff}$ Variation

摘要

This paper presents extensions of the dynamic-programming (DP) framework to consider buffer insertion and wire-sizing under effects of process variation. We study the effectiveness of this approach to reduce timing impact caused by chemical-mechanical planarization (CMP)-induced systematic variation and random Leff process variation in devices. We first present a quantitative study on the impact of CMP to interconnect parasitics. We then introduce a simple extension to handle CMP effects in the buffer insertion and wire sizing problem by simultaneously considering fill insertion (SBWF). We also tackle the same problem but with random Leff process variation (vSBWF) by incorporating statistical timing into the DP framework. We develop an efficient yet accurate heuristic pruning rule to approximate the computationally expensive statistical problem. Experiments under conservative assumption on process variation show that SBWF algorithm obtains 1.6% timing improvement over the variation-unaware solution. Moreover, our statistical vSBWF algorithm results in 43.1% yield improvement on average. We also show that our approaches have polynomial time complexity with respect to the net-size. The proposed extensions on the DP framework is orthogonal to other power/area-constrained problems under the same framework, which has been extensively studied in the literature