Exponential Expansion for Rapid and Accurate Extraction of Interconnect Capacitance

  • Hoan H. Pham
  • Arokia Nathan
Conference paper


We report a new approach for efficient computation of capacitance in multi- conductor systems embedded in homogeneous or multiple dielectric media. The technique employs exponential expansion of the Green’s function 1/r for evaluation of the three-dimensional potential and its gradient, enabling rapid and accurate extraction of interconnect capacitance in VLSI and large-area amorphous silicon electronics. Additionally, it can be used for analysis of electrostatic interaction in micro-electro-mechanical systems (MEMS).


Memory Requirement Conductor System Gauss Quadrature Maximum Relative Error Exponential Expansion 
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  1. [1]
    S. Rao, T. Sarkar, and R. Harrington, “The electrostatic field of conducting bodies in multiple dielectric media”, IEEE Trans, on Microwave Theory and Techniques, vol. 32, pp. 1441–1448, 1984.CrossRefGoogle Scholar
  2. [2]
    K. Nabors, S. Kim, and J. White, “Fast capacitance extraction of general three dimensional structures”, IEEE Trans, on Microwave Theory and Techniques, vol. 40, no. 7, pp. 1496–1506, 1992.CrossRefGoogle Scholar
  3. [3]
    L. Greengard, The Rapid Evaluation of Potential Fields in Particle Systems. MIT Press, 1988MATHGoogle Scholar
  4. [4]
    H. Pham and A. Nathan, “Rapid evaluation of the potential fields in three dimensions using exponential expansion”, Canadian Journal of Physics, vol. 75, pp. 689–693, 1997.CrossRefGoogle Scholar
  5. [5]
    H. Pham and A. Nathan, “A new approach for rapid evaluation of the potential field in three dimensions”, Procceedings of Royal Society London SERIES A (to appear)Google Scholar
  6. [6]
    H. Pham and A. Nathan, “Generating Gauss quadratures for Green’s function \(\frac{1}{r}:\) a randomized algorithm”, in IEEE 1998 Canadian Conference on Electrical and Computer Engineering (to appear), (Waterloo, ON, Canada), May 1998Google Scholar

Copyright information

© Springer-Verlag/Wien 1998

Authors and Affiliations

  • Hoan H. Pham
    • 1
  • Arokia Nathan
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of WaterlooWaterlooCanada

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