Skip to main content
Log in

Semiempirical Model for IC Interconnects Considering the Coupling Between the Signal Trace and the Ground Plane

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

A semiempirical, piecewise-defined, and physical model for integrated circuit interconnects is presented. The proposed model accurately represents the corresponding frequency-dependent resistance, and self- and mutual inductances while also accounting for the eddy currents induced in the ground metal layer. For the model implementation, different frequency regions where the resistance, and the self- and mutual inductances exhibit different trends due to the variation in the effective area where the current is flowing are identified, as well as the corresponding transitional frequencies. Experimental results performed to on-chip test structures fabricated on an RF-CMOS technology are used to validate the proposed model up to 40 GHz.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. M.S. Alavi, J. Mehta, R.B. Staszewski, Radio-Frequency Digital-to-Analog Converters: Implementation in Nanoscale CMOS (Academic Press, London, 2017)

    Google Scholar 

  2. B. Bhat, S.K. Koul, Stripline-Like Transmission Lines for Microwave Integrated Circuit (New Age International, New Delhi, 1989)

    Google Scholar 

  3. T. Brozek, Micro- and Nanoelectronics: Emerging Device Challenges and Solutions (CRC Press, Toronto, 2015)

    Google Scholar 

  4. J. Cano, J. Flich, J. Duato, M. Coppola, R. Locatelli, Efficient routing implementation in complex systems-on-chip, in Proceedings of the Fifth ACM/IEEE International Symposium, pp. 1–8 (2011)

  5. M.H. Chowdhury, Y.I. Ismail, C.V. Kashyap, B.L. Krauter, Performance analysis of deep sub micron VLSI circuits in the presence of self and mutual inductance, in IEEE International Symposium on Circuits and Systems, pp. 197–200 (2002)

  6. D.M. Cortés-Hernández, R. Torres-Torres, O. González-Díaz, M. Linares-Aranda, Experimental characterization of frequency-dependent series resistance and inductance for ground shielded on-chip interconnects. IEEE Trans. Electromagn. Compat. 56(6), 1567–1575 (2014)

    Article  Google Scholar 

  7. D.M. Cortés-Hernández, R. Torres-Torres, M. Linares-Aranda, O. González-Díaz, Piecewise physical modeling of series resistance and inductance of on-chip interconnects. Solid State Electron. 120, 1–5 (2016)

    Article  Google Scholar 

  8. A.R. Djordjevic, M. Stojilovic, T.K. Sarkar, Closed-form formulas for frequency-dependent per-unit-length inductance and resistance of microstrip transmission lines that provide causal response. IEEE Trans. Electromagn. Compat. 56(6), 1604–1612 (2014)

    Article  Google Scholar 

  9. S.H. Hall, H.L. Heck, Advanced Signal Integrity for High-Speed Digital Designs (Wiley, Hoboken, 2009)

    Book  Google Scholar 

  10. J.P. Jansson, P. Keränen, J. Kostamovaara, A. Baschirotto, CMOS technology scaling advantages in time domain signal processing. IEEE international instrumentation and measurement technology conference (I2MTC), pp. 1–5 (2017)

  11. V.K. Khanna, Integrated Nanoelectronics: Nanoscale CMOS (Post-CMOS and Allied Nanotechnologies, India, 2016)

    Book  Google Scholar 

  12. D.W. Kim, C. Li, P.L.G. Qiang, Signal integrity and crosstalk analysis of the transmission lines on SOI substrate for high-speed up to 50 GHz, in IEEE 18th Electronics Packaging Technology Conference (EPTC), pp. 633–637 (2016)

  13. H. Kim, D. Kim, Y. Eo, Experimental via characterization for the signal integrity verification of discontinuous interconnect line, in International SoC Design Conference, Seoul, pp. 213–216 (2010)

  14. J.H. Kim, D. Oh, W. Kim, Accurate characterization of broadband multiconductor transmission lines for high-speed digital systems. IEEE Trans. Adv. Packag. 33(4), 857–867 (2010)

    Article  Google Scholar 

  15. P. Majumdar, A.K. Verma, Comparison of characteristics of transmission lines using different EM simulators, in Fourth International Conference on Advanced Computing & Communication Technologies, pp. 1–7 (2014)

  16. A.M. Mangan, S.P. Voinigescu, Yang Ming-Ta, M. Tazlauanu, De-embedding transmission line measurements for accurate modeling of IC designs. IEEE Trans. Electron Devices 53(2), 235–241 (2006)

    Article  Google Scholar 

  17. L. Moquillon, J.M. Fournier, P. Benech, T. Quemerais, 65-, 45-, and 32-nm Aluminium and copper transmission-line model at millimeter-wave frequencies. IEEE Trans. Microw. Theory Tech. 58(9), 2426–2433 (2010)

    Article  Google Scholar 

  18. B. Nauwelaers, K. Maex, H. Ymeri, New closed-form formula for frequency-dependent resistance and inductance of IC interconnects on silicon substrate. J. Micromech. Microeng. 11(3), 283–286 (2001)

    Article  MATH  Google Scholar 

  19. I. Ndip, S. Guttowski, B. Curran, H. Reichl, A methodology for combined modeling of skin, proximity, edge, and surface roughness effects. IEEE Trans. Microw. Theory Tech. 58(9), 2448–2455 (2010)

    Article  Google Scholar 

  20. D. Pasquet, P. Descamps, D. Lesenechal, L. Nguyen-Tran, E. Bourdel, S. Quintanel, Modelling of an inductor on SiGe: from the measurement to the equivalent scheme, in Microwaves, Radar and Remote Sensing Symposium, pp. 59–64 (2011)

  21. M. Patil et al., Chip-package-board co-design for complex system-on-chip (SoC), in 19th Topical Meeting on Electrical Performance of Electronic Packaging and Systems, pp. 273–276 (2010)

  22. J.C. Rautio, V. Demir, Microstrip conductor loss models for electromagnetic analysis. IEEE Trans. Microw. Theory Tech. 51(3), 915–921 (2003)

    Article  Google Scholar 

  23. F. Schnieder, W. Heinrich, Model of thin-film microstrip line for circuit design. IEEE Trans. Microw. Theory Tech. 49(1), 104–110 (2001)

    Article  Google Scholar 

  24. L.N. Tran, D. Pasquet, E. Bourdel, S. Quintanel, CAD-oriented model of a coplanar line on a silicon substrate including eddy-current effects and skin effect. IEEE Trans. Microw. Theory Tech. 56(3), 663–670 (2008)

    Article  Google Scholar 

  25. M.S. Ullah, M.H. Chowdhury, Analytical models of high-speed RLC interconnect delay for complex and real poles. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 25(6), 1831–1841 (2017)

    Article  Google Scholar 

  26. D.F. Williams, R.B. Marks, Accurate transmission line characterization. IEEE Microw. Guided Wave Lett. 3(8), 247–249 (1993)

    Article  Google Scholar 

  27. L. Zerioul, E. Bourdel, M. Ariaudo, Skin effect modeling in time domain for RF network on chip, in 19th IEEE International Conference on Electronics, Circuits, and Systems (ICECS), pp. 721–724 (2012)

  28. L. Zerioul, M. Ariaudo, E. Bourdel, RF transceiver and transmission line behavioral modeling in VHDL-AMS for wired RFNoC. Analog Integr. Circuits Signal Process. 92(1), 103–114 (2017)

    Article  Google Scholar 

  29. J. Zhang et al., Causal RLGC(\(f)\) models for transmission lines from measured \(S\)-parameters. IEEE Trans. Electromagn. Compat. 52(1), 189–198 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mónico Linares-Aranda.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Linares-Aranda, M., González-Díaz, O., Cortés-Hernández, D.M. et al. Semiempirical Model for IC Interconnects Considering the Coupling Between the Signal Trace and the Ground Plane. Circuits Syst Signal Process 37, 3888–3902 (2018). https://doi.org/10.1007/s00034-017-0742-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-017-0742-z

Keywords

Navigation