摘要
随着集成电路工艺进入纳米时代,供电电压波动严重影响电路性能.制造中通孔对位不准,及运行中铜导线电迁移现象,都会在电源线/地线网络(P/G网)中产生大量潜在的开路故障,并使供电电压发生明显波动.为了在测试中对大量的开路故障进行快速测试,迫切需要提高故障分析的算法效率.为此,首次提出了单故障连续过松弛算法(SD-SOR),对发生单开路电阻故障的P/G网节点电压分布进行快速分析.基于无故障P/G网节点电压分布,SD-SOR仅对开路电阻周围受故障影响比较大的少数节点进行松弛计算.与传统的全局SOR方法相比,SD-SOR具有如下3个优点:1)局部松弛.由于电路中只有一个电阻q发生开路故障,SD-SOR不是采用全局电路节点的顺序松弛方法,而是采用从故障q所连的节点不断向周围节点进行松弛的波状松弛方法,当某些节点的IR电压降变化小于一个极小的设定值时,这些节点就不再向外进行松弛计算.2)高效.与传统的全局SOR方法相比,SD-SOR不仅参与松弛的节点非常少,而且松弛次数也有明显减少.3)高精度.与传统的全局SOR方法相比,由于距离故障比较远,电路中绝大多数节点电压变化非常小,所以SD-SOR只需对距离故障比较近的节点进行松弛计算,就能够保持较高的分析精度.大量的实验数据表明:与预条件全局SOR求解方法相比,SD-SOR在保持较高精度(误差小于0.95%)的前提下,速度可以提高57倍.
With IC technology scaling down into nanometer regime, voltage disturbances severely influence the performance of VLSI circuits. Both via mismatches in manufacture and electro- migrations of Cu interconnect wires in working ICs may provide many candidates for open defects in power/ground networks, which in turn significantly impacts voltage disturbances. In order to quickly test these open defects, it is imperative to efficiently analyze the defects＇ influences on P/G networks. Therefore, a single defect successive over-relaxation algorithm （SD-SOR） is firstly proposed in this paper to fast analyze nodal voltage drop distributions of P/G networks resulted from single open defect. Based on the voltage distribution of a defect-free P/G network, SD-SOR only needs to relax on a few nodes that surround the defect and thus suffer visible influences from the defect. Compared with the traditional global SOR method that orderly relaxes all nodes, SD-SOR shows the following advantages. The first advantage is locality. For each open defect, SD-SOR relaxes from the nodes connected with the defect to those surrounding nodes as wave transmission, while the wave stops at the nodes whose IR droop variation is less than a pre-assigned threshold. The second one is efficiency. SD-SOR not only relaxes a small part of the nodes in P/G networks but also needs much less relaxation iterations. The third one is high accuracy. Because most nodes are far away from the defect and suffer invisible influences, SD-SOR can obtain high enough accuracy through relaxing only a few surrounding nodes. Experimental ressults show that the proposed SD-SOR method is 57 times faster than the pre-conditional global SOR method with a maximum error of 0.95 %.
出处
《计算机研究与发展》
EI
CSCD
北大核心
2009年第7期1234-1240,共7页
Journal of Computer Research and Development
基金
国家"八六三"高技术研究发展计划基金项目(2009AA01Z126
2007AA01Z109)
国家自然科学基金项目(60876025
60876029)
NSFC/RGC联合科研基金项目(N_CUHK417/08)~~
