Importance of volume discretization of single and coupled interconnects

ABSTRACT

This paper presents figures of merit and error formulae to determine which interconnects require volume discretization in the GHZ range. Most of the previous work focused mainly on efficient modeling of volume discretized interconnects using several integration and reduction techniques. However, little work has been done to characterize when using the simple DC model has an impact on critical circuit metrics such as delay, impedance ...etc. Most of the previous work simply assumes that when skin depth becomes smaller than the wire cross section dimensions, volume discretization becomes essential. However, careful analysis in this paper shows that this assumption is invalid and a figure of merit is derived to characterize when volume discretization of single and coupled wires is required. This derived figure of merit is shown to depend solely on the interconnect dimensions and spacing and is independent of the type of the materials used or technology scaling.

REFERENCES

• 1: K. M. Coperich and A. E. Ruehli, "Enhanced skin effect for partial-element equivalent-circuit (PEEC) models," IEEE Transactions on Microwave Theory and Techniques, vol. 48, pages 1435--1442, 2000.
• 2: Min Xu , Lei He, An efficient model for frequency-dependent on-chip inductance, Proceedings of the 11th Great Lakes symposium on VLSI, p.115-120, March 2001, West Lafayette, Indiana, United States [doi>10.1145/368122.368887]
• 3: M. J. Tsuk and A. J. Kong, "A hybrid method for the calculation of the resistance and inductance of transmission lines with arbitrary cross sections, "IEEE Transactions on microwave Theory and Techniques, vol. 39, pages 1338--1347, 1991.
• 4: P. Silvester, "Modal network theory of skin effect in flat conductors," Proceedings of the IEEE, vol. 54, pages 1147--1151,
• 5: H. A. Wheeler "Formulas for the skin effect". Proceeding of the institute of radio engineers, vol. 30, pages 412--424, 1942.
• 6: S. Kim and D. P. Neikirk, "Compact equivalent circuit model for the skin effect," 1996 IEEE-M7T-S International Microwave Symposium, San Francisco, June 1996.
• 7: Shizhong Mei , Yehea I. Ismail, Modeling skin and proximity effects with reduced realizable RL circuits, IEEE Transactions on Very Large Scale Integration (VLSI) Systems, v.12 n.4, p.437-447, April 2004 [doi>10.1109/TVLSI.2004.825863]
• 8: Byron Krauter , Sharad Mehrotra, Layout based frequency dependent inductance and resistance extraction for on-chip interconnect timing analysis, Proceedings of the 35th annual conference on Design automation, p.303-308, June 15-19, 1998, San Francisco, California, United States [doi>10.1145/277044.277133]
• 9: B. E. Keiser, Principles of Electromagnetic Compatibility. Norwood, MA: Artech House, 1979, p. 102.
• 10: E. B. Rosa, "The self and mutual inductance of linear Conductors," Bulletin Nat. Bureau Standards, vol. 4, pp. 301--344, 1908.
• 11: A. R. Djordjevic and T. K. Sarker, "Closed-Formulas For frequency Dependent Resistance and Inductance and Strip Transmission Lines", IEEE transactions on microwave theory and techniques, vol. 42, no. 2, February 1994
• 12: S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and waves in communication electronics, New York: John Wiley & Sons, 1994.
• 13: N. S. Nahman and D. R. Holt, "Transient analysis of coaxial cables using the skin effect approximation A+B s," IEEE Transactions on Circuit Theory, Vol. 19, pp. 443--451, 1972.
• 14: L. C. Calvey and J. L. Bihan, "Coefficient algorithm for timedomain response of skin effect lossy coaxial cables with arbitrary resistive terminations," IEEE Trans. On Circuit and Systems, vol. 9, pp. 915--920, Sept. 1986.

INDEX TERMS

Primary Classification:
  B. Hardware
  B.4 INPUT/OUTPUT AND DATA COMMUNICATIONS
      B.4.3 Interconnections (subsystems)

Additional Classification:
  B. Hardware
  B.6 LOGIC DESIGN
      B.6.3 Design Aids
  B.8 Performance and Reliability
      B.8.2 Performance Analysis and Design Aids
  B.m MISCELLANEOUS
      Subjects: Design management

General Terms:
Design, Performance