An Efficient Three-Dimensional Capacitance Extraction Based on finite Element Method Adopting Variable Division

가변 분할을 적용한 유한 요소법에 의한 3차원 모형의 효율적인 커패시턴스 추출 방법

  • 김정학 (숭실대 컴퓨터공학과) ;
  • 김준희 (숭실대 컴퓨터공학과) ;
  • 김석윤 (숭실대 컴퓨터공학과)
  • Published : 2003.03.01


This paper proposes an efficient method for computing the 3-dimensional capacitance of complex structures. The proposed method Is based on Finite Element Method(FEM) and expands the conventional FEM by adopting variable division. This method improves the extraction efficiency 50 times when compared to the conventional FEM with equal division. The proposed method can be used efficiently to extract electrical parameters of on/off-chip interconnects in VLSI systems.


Capacitance;Capacitance Extraction;Parasitic Extraction;Element Method


  1. H.B.Bakoglu 'Circuit, Interconnections, and Packaging for VLSI' ADDISON-WESLEY PUBLISHING COMPANY, 1990, pp.137-139
  2. A. Ruehli and P. Brennan, 'Efficient capacitance caluations for three-dimensional multiconductor systems,' IEEE Trans. Microwave Theory Tech., vol. MTT-21, no. 2, Feb. 1973
  3. B. Krauter, Y. Xia, A. Dengi, and L. T. Pileggi, 'A Sparse Image Method for BEM Capacitance Extractions,' Proc 33th Design Automation Conference Proceeding, pp.357-362, 1996
  4. I. Bronshtein and K. Semendyayev, HandBook of Mathematics, 3rd ed. New York, Van Nostrand Reinhold, 1985
  5. C. Wei, R. F. Harrington, J. R. Mautz, and T.K. Sarkar, 'Multiconductor transmission lines in multilayered dielectric media,' IEEE Trans. Microwave Theory Tech., vol. MTT-32, pp. 439-450, 1984
  6. Keith Nabors and Jacob White, 'FastCap: A multipole Accelerated 3-D Capacitance Extraction Program,' IEEE Trans. on Computer-Aided Design, vol. 10, no. 11, Nov. 1991
  7. N. D. Llanda, K. V. Raol, R. Schumann, and L. M. Richardson, 'Modeling and extraction of interconnect capacitances for multilayer VLSI circuits,' IEEE Trans. Computer-Aided Design of integrated circuits and systems, vol. 15, pp. 58-67, 1996
  8. W. H. Dierking and J. D. Bastian, 'VLSI parasitic capacitance determination by flux tubes,' IEEE Circuit System Mag., pp. 11-18, March, 1982
  9. P. Benedeck, 'Capacitances of a planar multiconductor configuration a dielectric substrate by a mixed order finite-element mehtod,' IEEE Trans. Circuits Syst., vol. CAS-23, pp. 279-283, 1976
  10. T. Sakurai and K. Tamaru, 'Simple formulas for two and three dimensional capacitances,' IEEE Trans. Electron Devices, vol. ED-30, pp. 183-185, 1983