Statistical extraction and modeling of inductance considering spatial correlation
Statistical extraction and modeling of inductance considering spatial correlation
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DOI：
10.1007/s10470-011-9720-8
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发表时间：
2012-10
影响因子：
1.4
通讯作者：
Zhigang Hao;S. Tan;E. Tlelo-Cuautle;Jacob Relles;Chao Hu;Wenjian Yu;Yici Cai;G. Shi
中科院分区：
文献类型：
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作者：
Zhigang Hao;S. Tan;E. Tlelo-Cuautle;Jacob Relles;Chao Hu;Wenjian Yu;Yici Cai;G. Shi
在本文中，我们提出了一种考虑过程变化的统计电感提取和互连建模的新方法。新方法，称为stathenry，是基于配位的谱随机方法，其中正交多项式被用来表示统计过程。采用稀疏网格下的快速多维高斯正交法，通过配点法计算了部分电感正交多项式的系数。为了进一步提高该方法的效率，采用了随机变量约简方案。在给定互连线变化参数的情况下，该方法可以推导出电感值的参数化封闭形式。我们表明，在给定宽度和高度变化的情况下，局部和环路电感的变化都是显著的。这种新方法可以与任何现有的电感提取工具一起提取变分部分和环路电感或阻抗。实验结果表明，对于几种实际的互连结构，我们的方法比蒙特卡罗方法快几个数量级。
In this paper, we present a novel method for statistical inductance extraction and modeling for interconnects considering process variations. The new method, calledstatHenry, is based on the collocation-based spectral stochastic method where orthogonal polynomials are used to represent the statistical processes. The coefficients of the partial inductance orthogonal polynomial are computed via the collocation method where a fast multi-dimensional Gaussian quadrature method is applied with sparse grids. To further improve the efficiency of the proposed method, a random variable reduction scheme is used. Given the interconnect wire variation parameters, the resulting method can derive the parameterized closed form of the inductance value. We show that both partial and loop inductance variations can be significant given the width and height variations. This new approach can work with any existing inductance extraction tool to extract the variational partial and loop inductance or impedance. Experimental results show that our method is orders of magnitude faster than the Monte Carlo method for several practical interconnect structures.