Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

A resonant metamaterial clock distribution network for superconducting logic

Abstract

Clock distribution is central to digital technology and influences circuit performance, interconnect overhead and efficiency. However, ensuring reliable clock distribution across large digital systems with low skew and jitter—and in the presence of device variations and thermal noise—is a design challenge. Here we report a superconducting metamaterial resonant clock network that can provide energy-efficient power delivery to large superconducting digital systems. The resonant clock network is based on a metamaterial design with an infinite-wavelength zeroth-order resonance mode and utilizes the ultralow Joule loss of superconductors at microwave frequencies. With this approach, we perform S-parameter measurements for a 10 GHz design and validate a digital reciprocal quantum logic circuit with 48,000 junctions operating at 3.5 GHz. The network supports uniform power distribution with less than 1 dB variation across a 3 × 3 mm2 active chip area and around 30% power efficiency. Static power dissipation is 28 μW, which is similar to that of active devices.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Conceptual design of the resonant clock network.
Fig. 2: Microwave characterization of the resonator at 4.2 K powering RQL circuits at ~10 GHz clock frequency and with 4.5 mm2 active area.
Fig. 3: Functional characterization of resonator uniformity at 4.2 K using a shift-register test circuit covering 3 × 3 mm2 active area of the chip.
Fig. 4: A DynaZOR clock network fills the active area on a 5 mm chip with spines running vertically along the left and right edges and ribs running horizontally between them.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Xiu, L. Clock technology: the next frontier. IEEE Circuits Syst. Mag. 17, 27–46 (2017).

    Article  Google Scholar 

  2. Chueh, J., Sathe, V. & Papaefthymiou, M. C. 900MHz to 1.2GHz two-phase resonant clock network with programmable driver and loading. In IEEE Custom Integrated Circuits Conference 2006 777–780 (IEEE, 2006).

  3. Hansson, M., Mesgarzadeh, B. & Alvandpour, A. 1.56 GHz on-chip resonant clocking in 130nm CMOS. In IEEE Custom Integrated Circuits Conference 2006 241–244 (IEEE, 2006).

  4. Jana, R. K., Snider, G. L. & Jena, D. Energy-efficient clocking based on resonant switching for low-power computation. IEEE Trans. Circuits Syst. I: Regul. Pap. 61, 1400–1408 (2014).

    Article  Google Scholar 

  5. Sathe, V. S. et al. Resonant-clock design for a power-efficient, high-volume x86-64 microprocessor. IEEE J. Solid-State Circuits 48, 140–149 (2013).

    Article  Google Scholar 

  6. Kuttappa, R., Taskin, B., Lerner, S. & Pano, V. Resonant clock synchronization with active silicon interposer for multi-die systems. IEEE Trans. Circuits Syst. I: Regul. Pap. 68, 1636–1645 (2021).

  7. Herr, Q. P., Herr, A. Y., Oberg, O. T. & Ioannidis, A. G. Ultra-low-power superconductor logic. J. Appl. Phys. 109, 103903 (2011).

    Article  Google Scholar 

  8. Takeuchi, N., Ozawa, D., Yamanashi, Y. & Yoshikawa, N. An adiabatic quantum flux parametron as an ultra-low-power logic device. Supercond. Sci. Technol. 26, 035010 (2013).

    Article  Google Scholar 

  9. Likharev, K. K. & Semenov, V. K. RSFQ logic/memory family: a new Josephson-junction technology for sub-terahertz-clock-frequency digital systems. IEEE Trans. Appl. Supercond. 1, 3–28 (1991).

    Article  Google Scholar 

  10. Vernik, I., Kirichenko, A., Mukhanov, O. & Ohki, T. Energy-efficient and compact ERSFQ decoder for cryogenic RAM. IEEE Trans. Appl. Supercond. 27, 1–5 (2016).

    Article  Google Scholar 

  11. Herr, A. Y. et al. An 8-bit carry look-ahead adder with 150 ps latency and sub-microwatt power dissipation at 10 GHz. J. Appl. Phys. 113, 033911 (2013).

    Article  Google Scholar 

  12. Oberg, O. T., Herr, Q. P., Ioannidis, A. G. & Herr, A. Y. Integrated power divider for superconducting digital circuits. IEEE Trans. Appl. Supercond. 21, 571–574 (2010).

    Article  Google Scholar 

  13. Bin, M., Gaidis, M., Zmuidzinas, J., Phillips, T. & LeDuc, H. Low-noise 1 THz niobium superconducting tunnel junction mixer with a normal metal tuning circuit. Appl. Phys. Lett. 68, 1714–1716 (1996).

    Article  Google Scholar 

  14. Ricci, M., Orloff, N. & Anlage, S. M. Superconducting metamaterials. Appl. Phys. Lett. 87, 034102 (2005).

    Article  Google Scholar 

  15. High, A. A. et al. Visible-frequency hyperbolic metasurface. Nature 522, 192–196 (2015).

    Article  Google Scholar 

  16. Coulais, C., Sounas, D. & Alù, A. Static non-reciprocity in mechanical metamaterials. Nature 542, 461–464 (2017).

    Article  Google Scholar 

  17. Rabinovich, M. I. & Trubetskov, D. I. Oscillations and Waves: in Linear and Nonlinear Systems, Mathematics and its Applications (Soviet Series) Vol. 50, Ch. 4 (Kluwer Academic Publishers, 1989).

  18. Park, J., Ryu, Y., Lee, J. & Lee, J. Epsilon negative zeroth-order resonator antenna. IEEE Trans. Antennas Propag. 55, 3710–3712 (2007).

    Article  Google Scholar 

  19. Sanada, A., Caloz, C. & Itoh, T. Novel zeroth-order resonance in composite right/left-handed transmission line resonators. In Proc. Asia-Pacific Microwave Conference 3, 1588–1591 (2003).

  20. Khanna, A. & Garault, Y. Determination of loaded, unloaded, and external quality factors of a dielectric resonator coupled to a microstrip line. IEEE Trans. Microw. Theory Techn. 31, 261–264 (1983).

    Article  Google Scholar 

  21. Talanov, V. V., Mercaldo, L. V., Anlage, S. M. & Claassen, J. H. Measurement of the absolute penetration depth and surface resistance of superconductors and normal metals with the variable spacing parallel plate resonator. Rev. Sci. Instrum. 71, 2136–2146 (2000).

    Article  Google Scholar 

  22. Egan, J. et al. Synchronous chip-to-chip communication with a multi-chip resonator clock distribution network. Preprint at https://arxiv.org/abs/2109.00560 (2021).

  23. Berkley, A. et al. A scalable readout system for a superconducting adiabatic quantum optimization system. Supercond. Sci. Technol. 23, 105014 (2010).

    Article  Google Scholar 

  24. Herr, Q. P. A high-efficiency superconductor distributed amplifier. Supercond. Sci. Technol. 23, 022004 (2010).

    Article  Google Scholar 

  25. Egan, J., Brownfield, A. & Herr, Q. True differential superconducting on-chip output amplifier. Supercond. Sci. Technol. 35, 045018 (2021).

    Google Scholar 

  26. Pozar, D. M. Microwave Engineering 2nd edn (John Wiley & Sons, 2012).

Download references

Acknowledgements

We acknowledge the valuable conversation with O. Naaman regarding the clock network design. H. Dai and J. Egan assisted with the physical design of the clock network and functional circuits. J. Goodman and M. Lateef assisted with the microwave measurement. D. Harvey assisted with the circuit design. This research is based on the work supported in part by the ODNI, IARPA, via ARO, contract no. W911NF-14-C-0116. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA, or the US Government.

Author information

Authors and Affiliations

Authors

Contributions

J.A.S. and V.V.T. conceived the idea, performed the analysis and wrote the manuscript. M.E.N. performed the electrical and physical design and modelling, as well as conceived several design improvements. A.C.B. and N.B. performed the measurements and analysed the data. A.Y.H. and Q.P.H. initiated and supervised the work.

Corresponding author

Correspondence to Joshua A. Strong.

Ethics declarations

Competing interests

All authors are or have been employed by Northrop Grumman Corp., which holds several patents relating to work discussed herein. See U.S. Patents 10,591,952; 10,884,450; 10,474,183; 10,461,867; 10,133,299; 9,722,589.

Peer review

Peer review information

Nature Electronics thanks Nobuyuki Yoshikawa and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Strong, J.A., Talanov, V.V., Nielsen, M.E. et al. A resonant metamaterial clock distribution network for superconducting logic. Nat Electron 5, 171–177 (2022). https://doi.org/10.1038/s41928-022-00729-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41928-022-00729-7

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing