Advertisement

Insertion of an Optimal Number of Repeaters in Pipelined Nano-interconnects for Transient Delay Minimization

  • C. Venkataiah
  • K. Satyaprasad
  • T. Jayachandra Prasad
Article

Abstract

A novel and highly accurate finite-difference time-domain model is developed for bundled single-walled carbon nanotube (SWCNT) interconnects by considering a fixed configuration that consists of a CMOS driver, a bundled SWCNT interconnect system, and an optimal number of repeaters. Using superposition theorem, this iterative model is applied to the entire chain of repeaters to calculate the total closed-loop delay. An accurate transfer function is modeled for the chain of equi-spaced repeaters in the interconnect system. The transfer function is further used to develop an analytical model for closed-loop delay, considering the optimum number of repeaters as dependent parameter. Further, in order to determine the minimum delay, an analysis is performed to find out the optimum number of repeaters for a given interconnect length. In addition, a detailed study is carried out to observe the impact of interconnect length on time delay, the time delay reduction on increasing the number of repeaters and the effect of excitation magnitude on time delay with power delay product. It is observed that by using SWCNT interconnects, the total number of repeaters and the time delay are reduced by more than 40 and 50%, respectively, compared with the copper (Cu) interconnects. However, the proposed model achieves extreme accuracy, with 4% relative tolerance at maximum, in predicting interconnect performance based on comparison with the HSPICE simulations.

Keywords

Single-walled carbon nanotube (SWCNT) Finite-difference time domain (FDTD) Repeaters Copper (Cu) Interconnects 

References

  1. 1.
    A. Afrooz, Time domain analysis of field effect transistors using unconditionally stable finite difference method. IET Sci. Meas. Technol. 10(7), 686–692 (2016)CrossRefGoogle Scholar
  2. 2.
    K. Afrooz, A. Abdipour, Efficient method for time-domain analysis of lossy nonuniform multiconductor transmission line driven by a modulated signal using FDTD technique. IEEE Trans. Electromagn. Compat. 54(2), 482–494 (2012)CrossRefGoogle Scholar
  3. 3.
    K. Agarwal, D. Sylvester, D. Blaauw, Modeling and analysis of crosstalk noise in coupled RLC interconnects. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 25(5), 892–901 (2006)CrossRefGoogle Scholar
  4. 4.
    N.W. Ashcroft, N.D. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976)MATHGoogle Scholar
  5. 5.
    K. Banerjee, A. Mehrotra, A power-optimal repeater insertion methodology for global interconnects in nanometer designs. IEEE Trans. Electron Dev. 49(11), 2001–2007 (2002)CrossRefGoogle Scholar
  6. 6.
    D. Das, H. Rahaman, Analysis of crosstalk in single- and multiwall carbon nanotube interconnects and its impact on gate oxide reliability. IEEE Trans. Nanotechnol. 10(6), 1362–1370 (2011)CrossRefGoogle Scholar
  7. 7.
    R. Dhiman, R. Chandel, Dynamic crosstalk analysis in coupled interconnects for ultra-low power applications. Circuits Syst. Signal Process. 34, 21–40 (2015).  https://doi.org/10.1007/s00034-014-9853-y MathSciNetCrossRefGoogle Scholar
  8. 8.
    N. Farahat, H. Raouf, R. Mittra, Analysis of interconnect lines using the finite-difference time-domain (FDTD) method. Microw. Opt. Technol. Lett. 34(1), 6–9 (2002)CrossRefGoogle Scholar
  9. 9.
    A. Giustiniani, V. Tucci, W. Zamboni, Modeling issues and performance analysis of high-speed interconnects based on a bundle of SWCNT. IEEE Trans. Electron Dev. 57(8), 1978–1986 (2010)CrossRefGoogle Scholar
  10. 10.
    Y.I. Ismail, E.G. Friedman, Effects of inductance on the propagation delay and repeater insertion in VLSI circuits. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 8(2), 195–206 (2000)CrossRefGoogle Scholar
  11. 11.
    B.K. Kaushik, S. Sarkar, R.P. Agarwal, R.C. Joshi, Crosstalk analysis of simultaneously switching interconnects. Int. J. Electron. 96(10), 1095–1114 (2009)CrossRefGoogle Scholar
  12. 12.
    V.R. Kumar, B.K. Kaushik, A. Patnaik, An unconditionally stable FDTD model for crosstalk analysis of VLSI interconnects. IEEE Trans. Compon. Packag. Manuf. Technol. 5(12), 1810–1817 (2015)CrossRefGoogle Scholar
  13. 13.
    X. Li, J. Mao, M. Swaminathan, Analysis of frequency-dependent lossy transmission lines driven by CMOS gates, in IEEE Electrical Design of Advanced Packaging and Systems Symposium (EDAPS) (Shatin, Hong Kong, 2009), pp. 1–4Google Scholar
  14. 14.
    H. Li, C. Xu, N. Srivastava, K. Banerjee, Carbon nanomaterials for next-generation interconnects and passives: physics, status, and prospects. IEEE Trans. Electron Dev. 56(9), 1799–1821 (2009)CrossRefGoogle Scholar
  15. 15.
    X. Li, J. Mao, M. Swaminathan, Transient analysis of CMOS gate-driven RLGC interconnects based on FDTD. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 30(4), 574–583 (2011)CrossRefGoogle Scholar
  16. 16.
    F. Liang, G. Wang, W. Ding, Estimation of time delay and repeater insertion in multiwall carbon nanotube interconnects. IEEE Trans. Electron Dev. 58(8), 2712–2720 (2011)CrossRefGoogle Scholar
  17. 17.
    F. Liang, G. Wang, H. Lin, Modeling of crosstalk effects in multiwall carbon nanotube interconnects. IEEE Trans. Electromagn. Compat. 54(1), 133–139 (2012)CrossRefGoogle Scholar
  18. 18.
    A. Naeemi, J.D. Meindl, Carbon nanotube interconnects. Annu. Rev. Mater. Res. 39, 255–275 (2009)CrossRefGoogle Scholar
  19. 19.
    A. Pal, A. Chaudhuri, R.K. Pal, A.K. Datta, Hardness of crosstalk minimization in two-layer channel routing. Integr. VLSI J. 56, 139–147 (2017)CrossRefGoogle Scholar
  20. 20.
    J.D. Pursel, P.M. Goggans, A finite-difference time-domain method for solving electromagnetic problems with bandpass-limited sources. IEEE Trans. Antenna Propag. 47(1), 9–15 (1999)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    C. Rutherglen, P.J. Burke, Nanoelectromagnetics: circuit and electromagnetic properties of carbon nanotubes. Small 5(8), 884–906 (2009)CrossRefGoogle Scholar
  22. 22.
    A. Taflove, Computational Electrodynamics (Artech House, Norwood, 1995)MATHGoogle Scholar
  23. 23.
    R. Venkatesan, J.A. Davis, J.D. Meindl, Compact distributed RLC interconnect models—part IV: unified models for time delay, crosstalk, and repeater insertion. IEEE Trans. Electron Dev. 50(4), 1094–1102 (2003)CrossRefGoogle Scholar
  24. 24.
    Q. Xu, Z.F. Li, J. Wang, J.F. Mao, Transient analysis of lossy interconnects by modified method of characteristics. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47(3), 363–375 (2000)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • C. Venkataiah
    • 1
    • 2
  • K. Satyaprasad
    • 1
    • 3
  • T. Jayachandra Prasad
    • 2
  1. 1.Jawaharlal Nehru Technological UniversityKakinadaIndia
  2. 2.Rajeev Gandhi Memorial College of Engineering and TechnologyNandyalIndia
  3. 3.KL UniversityGunturIndia

Personalised recommendations