Statistical extraction and modeling of inductance considering spatial correlation

Authors:
Zhigang Hao;Sheldon X.-D. Tan;E. Tlelo-Cuautle;Jacob Relles;Chao Hu;Wenjian Yu;Yici Cai;Guoyong Shi
Affiliations:
Shanghai Jiao Tong University, Shanghai, China 200240;University of California, Riverside, USA 92521;INAOE, Puebla, Mexico;University of California, Riverside, USA 92521;Tsinghua University, Beijing, China 10084;Tsinghua University, Beijing, China 10084;Tsinghua University, Beijing, China 10084;Shanghai Jiao Tong University, Shanghai, China 200240
Venue:
Analog Integrated Circuits and Signal Processing
Year:
2012

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Abstract

In this paper, we present a novel method for statistical inductance extraction and modeling for interconnects considering process variations. The new method, called statHenry, 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.