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Optimal VLSI Delay Tuning by Wire Shielding

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Abstract

Interconnect shielding is used in VLSI designs to avoid noise interference from the cross-coupling capacitance between adjacent signals. This paper takes advantage of the shields already present in the design and uses them to tune the propagation delay of the clock signals, thus eliminating expensive dedicated delay buffers. The problem of obtaining the desired delay at a minimum shielding cost (silicon area) is formulated as a calculus of variations problem. An analytical solution shows that a square root shield profile is optimal.

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References

  1. Salman, E., Friedman, E.G.: High Performance Integrated Circuit Design. McGraw Hill Professional, New York (2012)

    Google Scholar 

  2. Agarwal, A., Blaauw, D., Zolotov, V.: Statistical timing analysis for intra-die process variations with spatial correlations. In: Proceedings of the 2003 IEEE/ACM International Conference on Computer-Aided Design, pp. 900–907 (2003)

  3. Alioto, M., Palumbo, G., Pennisi, M.: Understanding the effect of process variations on the delay of static and domino logic. IEEE Trans. VLSI Syst. 18(5), 697–710 (2010)

    Article  Google Scholar 

  4. Bakoglu, H.B., Meindl, J.D.: Optimal interconnection circuits for VLSI. IEEE Trans. Electron Devices. 32(5), 903–909 (1985)

    Article  Google Scholar 

  5. Rubinstein, J., Penfield, P.J., Horowitz, M.: Signal delay in RC tree networks. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 2(3), 202–211 (1983)

    Article  Google Scholar 

  6. Fishburn, J.P., Schevron, C.A.: Shaping a distributed-RC line to minimize Elmore delay. IEEE Trans. Circuits Sys. I. 42(12), 1020–1022 (1995)

    Article  Google Scholar 

  7. Fishburn, J.P.: Shaping a VLSI wire to minimize Elmore delay. In: Proceedings of the 1997 European Conference on Design and Test, pp. 244–251 (1997)

  8. Chen, C.-P., Wong, D.F.: Optimal wire-sizing function with fringing capacitance consideration. In: Proceedings of the 34th Annual Design Automation Conference (1997)

  9. Gao, Y., Wong, D.F.: Wire-sizing optimization with inductance consideration using transmission-line model. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 18(12), 1759–1767 (1999)

    Article  Google Scholar 

  10. Zhang, H., Wong, M.D., Chao, K.-Y., Deng, L.: Wire shaping is practical. In: Proceedings of the 2009 International Symposium on Physical Design, pp. 131–138 (2009)

  11. El-Moursy, M.A., Friedman, E.G.: Wire shaping of RLC interconnects. Integr. VLSI J. 40(4), 461–472 (2007)

    Article  Google Scholar 

  12. Fox, C.: An Introduction to the Calculus of Variations. Dover, New York (1987)

    MATH  Google Scholar 

  13. Kahng, A.B., Muddu, S., Sarto, E.: Tuning strategies for global interconnects in high-performance deep-submicron ICs. VLSI Des. 10(1), 21–34 (1999)

    Article  Google Scholar 

  14. Jakushokas, R., Friedman, E.G.: Resource based optimization for simultaneous shield and repeater insertion. IEEE Trans. VLSI Syst. 18(5), 742–749 (2010)

    Article  Google Scholar 

  15. Karami, M.A., Afzali-Kusha, A.: Exponentially tapering ground wires for Elmore delay reduction in on chip interconnects. In: Proceedings of the 2006 International Conference on Microelectronics, pp. 99–102 (2006)

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Acknowledgments

The authors are thankful for the useful comments and corrections made by the editor Prof. D. Hull. This research was supported by the Office of the Israeli Chief Scientist under the HiPer consortium of the MAGNET program.

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Correspondence to Shmuel Wimer.

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Communicated by David G. Hull.

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Frankel, B., Wimer, S. Optimal VLSI Delay Tuning by Wire Shielding. J Optim Theory Appl 170, 1060–1067 (2016). https://doi.org/10.1007/s10957-016-0960-8

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  • DOI: https://doi.org/10.1007/s10957-016-0960-8

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