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Resolution limit of mode-localised sensors

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Abstract

In recent years, the mode localisation phenomenon of weakly coupled resonators has been successfully utilised to improve the sensitivity of microelectromechanical system (MEMS) sensors. However, controversy remians about the resolution limits of mode-localised sensors. This paper asks two questions of the community: what are the resolution limits of the mode-localised sensors, and can the resolution improvement be obtained using mode-localised sensing? To answer these questions, we report a series of resolution models of mode-localised sensors. We conclude that mode-localised sensing can realise a higher measuring resolution by orders of magnitude when more than three resonators are weakly coupled, and this will lay the theoretical foundation for a breakthrough for the MEMS sensors industry.

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References

  1. Patsavellas J, Salonitis K. The carbon footprint of manufacturing digitalization: critical literature review and future research agenda. Procedia CIRP, 2019, 81: 1354–1359

    Article  Google Scholar 

  2. Trusov A, Atikyan G, Rozelle D M, et al. Flat is not dead: current and future performance of Si-MEMS Quad Mass Gyro (QMG) system. In: Proceedings of 2014 IEEE/ION Position, Location and Navigation Symposium, Monterey, 2014. 252–258

  3. Ramezani M, Ghatge M, Tabrizian R. High-Q silicon fin bulk acoustic resonators for signal processing beyond the UHF. In: Proceedings of 2017 IEEE International Electron Devices Meeting (IEDM), San Francisco, 2017. 1–4

  4. Abdolvand R, Amini B V, Ayazi F. Sub-micro-gravity in-plane accelerometers with reduced capacitive gaps and extra seismic mass. J Microelectromech Syst, 2007, 16: 1036–1043

    Article  Google Scholar 

  5. Spletzer M, Raman A, Wu A Q, et al. Ultrasensitive mass sensing using mode localization in coupled microcantilevers. Appl Phys Lett, 2006, 88: 254102

    Article  Google Scholar 

  6. Novoselov K S, Mishchenko A, Carvalho A, et al. 2D materials and van der Waals heterostructures. Science, 2016, 353: aac9439

    Article  Google Scholar 

  7. de Lépinay L M, Pigeau B, Besga B, et al. A universal and ultrasensitive vectorial nanomechanical sensor for imaging 2D force fields. Nat Nanotech, 2017, 12: 156–162

    Article  Google Scholar 

  8. Yang J, Zhong J M, Chang H L. A closed-loop mode-localized accelerometer. J Microelectromech Syst, 2018, 27: 210–217

    Article  Google Scholar 

  9. Kang H, Yang J, Chang H L. A closed-loop accelerometer based on three degree-of-freedom weakly coupled resonator with self-elimination of feedthrough signal. IEEE Sens J, 2018, 18: 3960–3967

    Article  Google Scholar 

  10. Zhao C, Wood G S, Xie J B, et al. A force sensor based on three weakly coupled resonators with ultrahigh sensitivity. Sens Actuat A-Phys, 2015, 232: 151–162

    Article  Google Scholar 

  11. Yang J, Kang H, Chang H L. A micro resonant electrometer with 9-electron charge resolution in room temperature. In: Proceedings of 2018 IEEE Micro Electro Mechanical Systems (MEMS), 2018. 67–70

  12. Anderson P W. Absence of diffusion in certain random lattices. Phys Rev, 1958, 109: 1492–1505

    Article  Google Scholar 

  13. Hodges C H, Woodhouse J. Confinement of vibration by one-dimensional disorder. I: theory of ensemble averaging. J Sound Vib, 1989, 130: 237–251

    Article  Google Scholar 

  14. Zhao C, Wood G S, Xie J B, et al. A comparative study of output metrics for an MEMS resonant sensor consisting of three weakly coupled resonators. J Microelectromech Syst, 2016, 25: 626–636

    Article  Google Scholar 

  15. Kraft M. Coupled resonators as a new transduction principle for ultraprecise sensors. In: Proceedings of the 19th ITG/GMA-Symposium on Sensors and Measuring Systems, Nuremberg, 2018. 1–4

  16. Alvarez M, Tamayo J, Plaza J A, et al. Dimension dependence of the thermomechanical noise of microcantilevers. J Appl Phys, 2006, 99: 024910

    Article  Google Scholar 

  17. Gabrielson T B. Mechanical-thermal noise in micromachined acoustic and vibration sensors. IEEE Trans Electron Dev, 1993, 40: 903–909

    Article  Google Scholar 

  18. Sears F W, Salinger G L. Thermodynamics, Kinetic Theory, and Statistical Thermodynamics. Reading: Addison-Wesley Publishing Company Press, 1975

  19. Kittel C. Elementary Statistical Physics. New York: Dover Publications Pressed, 2004

    Google Scholar 

  20. Hodges C H. Confinement of vibration by structural irregularity. J Sound Vib, 1982, 82: 411–424

    Article  Google Scholar 

  21. Thiruvenkatanathan P, Woodhouse J, Yan J, et al. Limits to mode-localized sensing using micro- and nanomechanical resonator arrays. J Appl Phys, 2011, 109: 104903

    Article  Google Scholar 

  22. Zhang H M, Li B Y, Yuan W Z, et al. An acceleration sensing method based on the mode localization of weakly coupled resonators. J Microelectromech Syst, 2016, 25: 286–296

    Article  Google Scholar 

  23. Zhang H M, Huang J, Yuan W Z, et al. A high-sensitivity micromechanical electrometer based on mode localization of two degree-of-freedom weakly coupled resonators. J Microelectromech Syst, 2016, 25: 937–946

    Article  Google Scholar 

  24. Saulson P R. Thermal noise in mechanical experiments. Phys Rev D, 1990, 42: 2437–2445

    Article  Google Scholar 

  25. Juillard J, Prache P, Ferreira P M, et al. Ultimate limits of differential resonant MEMS sensors based on two coupled linear resonators. IEEE Trans Ultrason Ferroelect Freq Contr, 2018, 65: 2440–2448

    Article  Google Scholar 

  26. Zhao C, Wood G S, Xie J B, et al. A three degree-of-freedom weakly coupled resonator sensor with enhanced stiffness sensitivity. J Microelectromech Syst, 2016, 25: 38–51

    Article  Google Scholar 

  27. Kang H, Yang J, Zhong J M, et al. A mode-localised accelerometer based on three degree-of-freedom weakly coupled resonator. In: Proceedings of 2017 IEEE SENSORS, Glasgow, 2017. 1–3

  28. Kang H, Ruan B, Hao Y C, et al. A micromachined electrometer with room temperature resolution of 0.256 e/ Hz. IEEE Sens J, 2020, 20: 95–101

    Article  Google Scholar 

  29. Juillard J, Prache P, Ferreira P M, et al. Impact of output metric on the resolution of mode-localisedlocalised MEMS resonant sensors. In: Proceedings of 2017 Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS), 2017

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Acknowledgements

This work was supported by National Key Research and Development Program of China (Grant No. 2018YFB2002600), National Natural Science Foundation of China (Grant No. 51575454), and Fundamental Research Funds for the Central Universities (Grant No. 3102019JC002). The author would like to show grateful acknowledgment to H. Kang and J. Yang for their helpful discussion.

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Correspondence to Honglong Chang.

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Zhang, Z., Chang, H. Resolution limit of mode-localised sensors. Sci. China Inf. Sci. 64, 142401 (2021). https://doi.org/10.1007/s11432-020-2974-9

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  • DOI: https://doi.org/10.1007/s11432-020-2974-9

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