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High-frequency nano-optomechanical disk resonators in liquids

Nature Nanotechnology volume 10, pages 810–816 (2015)Cite this article

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Abstract

Nano- and micromechanical resonators are the subject of research that aims to develop ultrasensitive mass sensors for spectrometry, chemical analysis and biomedical diagnosis. Unfortunately, their merits generally diminish in liquids because of an increased dissipation. The development of faster and lighter miniaturized devices would enable improved performances, provided the dissipation was controlled and novel techniques were available to drive and readout their minute displacement. Here we report a nano-optomechanical approach to this problem using miniature semiconductor disks. These devices combine a mechanical motion at high frequencies (gigahertz and above) with an ultralow mass (picograms) and a moderate dissipation in liquids. We show that high-sensitivity optical measurements allow their Brownian vibrations to be resolved directly, even in the most-dissipative liquids. We investigate their interaction with liquids of arbitrary properties, and analyse measurements in light of new models. Nano-optomechanical disks emerge as probes of rheological information of unprecedented sensitivity and speed, which opens up applications in sensing and fundamental science.

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Figure 1: Operation of nano-optomechanical disks in a liquid.
Figure 2: Dissipative and dispersive fluid–structure interactions measured by nano-optomechanical means.
Figure 3: Viscous regime models.
Figure 4: Acoustic regime models.
Figure 5: Interpretation of nano-optomechanical experiments in liquids.

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References

  1. Waggoner, P. S. & Craighead, H. G. Micro- and nanomechanical sensors for environmental, chemical, and biological detection. Lab Chip 7, 1238–1255 (2007).

    Article  CAS  Google Scholar 

  2. Arlett, J. L., Myers, E. B. & Roukes, M. L. Comparative advantages of mechanical biosensors. Nature Nanotech. 6, 203–215 (2011).

    Article  CAS  Google Scholar 

  3. Tamayo, J., Kosaka, P. M., Ruz, J. J., San Paulo, A. & Calleja, M. Biosensors based on nanomechanical systems. Chem. Soc. Rev. 42, 1287–1311 (2013).

    Article  CAS  Google Scholar 

  4. Ramos, D., Tamayo, J., Mertens, J., Zaballos, A. & Calleja, M. Origin of the response of nanomechanical resonators to bacteria adsorption. J. Appl. Phys. 100, 106105 (2006).

    Article  Google Scholar 

  5. Hanay, M. S. et al. Single-protein nanomechanical mass spectrometry in real time. Nature Nanotech. 7, 602–608 (2012).

    Article  CAS  Google Scholar 

  6. Naik, A. K., Hanay, M. S., Hiebert, W. K., Feng, X. L. & Roukes, M. L. Towards single-molecule nanomechanical mass spectrometry. Nature Nanotech. 4, 445–450 (2009).

    Article  CAS  Google Scholar 

  7. Chaste, J. et al. A nanomechanical mass sensor with yoctogram resolution. Nature Nanotech. 7, 300–303 (2012).

    Article  Google Scholar 

  8. Ekinci, K. L. & Roukes, M. L. Nanoelectromechanical systems. Rev. Sci. Instrum. 76, 061101 (2005).

    Article  Google Scholar 

  9. Eom, K., Park, H. S., Yoon, D. S. & Kwon, T. Nanomechanical resonators and their applications in biological/chemical detection: nanomechanics principles. Phys. Rep. 503, 115–163 (2011).

    Article  CAS  Google Scholar 

  10. Sader, J. E. Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. J. Appl. Phys. 84, 64–76 (1998).

    Article  CAS  Google Scholar 

  11. Lee, J., Shen, W., Payer, K., Burg, T. P. & Manalis, S. R. Toward attogram mass measurements in solution with suspended nanochannel resonators. Nano Lett. 10, 2537–2542 (2010).

    Article  CAS  Google Scholar 

  12. Burg, T. P. et al. Weighing of biomolecules, single cells and single nanoparticles in fluid. Nature 446, 1066–1069 (2007).

    Article  CAS  Google Scholar 

  13. Agache, V., Blanco-Gomez, G., Baleras, F. & Caillat, P. An embedded microchannel in a MEMS plate resonator for ultrasensitive mass sensing in liquid. Lab Chip 11, 2598–2603 (2011).

    Article  CAS  Google Scholar 

  14. Bahl, G. et al. Brillouin cavity optomechanics with microfluidic devices. Nature Commun. 4, 1994 (2013).

    Article  Google Scholar 

  15. Kim, K. H. et al. Cavity optomechanics on a microfluidic resonator with water and viscous liquids. Light Sci. Appl. 2, e110 (2013).

    Article  Google Scholar 

  16. Linden, J., Thyssen, A. & Oesterschulze, E. Suspended plate microresonators with high quality factor for the operation in liquids. Appl. Phys. Lett. 104, 191906 (2014).

    Article  Google Scholar 

  17. Ramos, D., Mertens, J., Calleja, M. & Tamayo, J. Photothermal self-excitation of nanomechanical resonators in liquids. Appl. Phys. Lett. 92, 173108 (2008).

    Article  Google Scholar 

  18. Ding, L. et al. High frequency GaAs nano-optomechanical disk resonator. Phys. Rev. Lett. 105, 263903 (2010).

    Article  Google Scholar 

  19. Clark, J. R., Hsu, W. T., Abdelmoneum, M. A. & Nguyen, C. T. C. High-Q UHF micromechanical radial-contour mode disk resonators. J. Microelectromechan. Syst. 14, 1298–1310 (2005).

    Article  Google Scholar 

  20. Favero, I. & Karrai, K. Optomechanics of deformable optical cavities. Nature Photon. 3, 201–205 (2009).

    Article  CAS  Google Scholar 

  21. Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).

    Article  Google Scholar 

  22. Baker, C. et al. Photoelastic coupling in gallium arsenide optomechanical disk resonators. Opt. Express 22, 14072–14086 (2014).

    Article  Google Scholar 

  23. Ding, L. et al. Wavelength-sized GaAs optomechanical resonators with gigahertz frequency. Appl. Phys. Lett. 98, 113108 (2011).

    Article  Google Scholar 

  24. Nguyen, D. T. et al. Ultrahigh Q-frequency product for optomechanical disk resonators with a mechanical shield. Appl. Phys. Lett. 103, 241112 (2013).

    Article  Google Scholar 

  25. Nguyen, D. T. et al. Improved optomechanical disk resonator sitting on a pedestal mechanical shield. New J. Phys. 17, 023016 (2015).

    Article  Google Scholar 

  26. Baker, C. et al. Critical optical coupling between a GaAs disk and a nanowaveguide suspended on the chip. Appl. Phys. Lett. 99, 151117 (2011).

    Article  Google Scholar 

  27. Parrain, D. et al. Damping of optomechanical disks resonators vibrating in air. Appl. Phys. Lett. 100, 242105 (2012).

    Article  Google Scholar 

  28. Love, A. E. H. A Treatise on the Mathematical Theory of Elasticity (Cambridge Univ. Press, 1906).

    Google Scholar 

  29. Onoe, M. Contour vibrations of isotropic circular plates. J. Acoust. Soc. Am. 28, 1158–1162 (1956).

    Article  Google Scholar 

  30. Hosaka, H., Itao, K. & Kuroda, S. Damping characteristics of beam-shaped micro-oscillators. Sens. Actuators A 49, 87–95 (1995).

    Article  CAS  Google Scholar 

  31. Oestreicher, H. L. Field and impedance of an oscillating sphere in a viscoelastic medium with an application to biophysics. J. Acoust. Soc. Am. 23, 707–714 (1951).

    Article  Google Scholar 

  32. Ekinci, K. L., Yang, Y. T. & Roukes, M. L. Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems. J. Appl. Phys. 95, 2682–2689 (2004).

    Article  CAS  Google Scholar 

  33. Cleland, A. N. & Roukes, M. L. Noise processes in nanomechanical resonators. J. Appl. Phys. 92, 2758–2769 (2002).

    Article  CAS  Google Scholar 

  34. Zhu, H. & Lee, J. E. Y. Reversed nonlinear oscillations in lame-mode single-crystal-silicon microresonators. IEEE Electron Device Lett. 33, 1492–1494 (2012).

    Article  CAS  Google Scholar 

  35. Kaajakari, V., Mattila, T., Oja, A. & Seppa, H. Nonlinear limits for single-crystal silicon microresonators. J. Microelectromech. Syst. 13, 715–724 (2004).

    Article  Google Scholar 

  36. Philip, J. & Breazeale, M. A. Third-order elastic-constants and Grüneisen parameters of silicon and germanium between 3 and 300 °K. J. Appl. Phys. 54, 752–757 (1983).

    Article  CAS  Google Scholar 

  37. Olcum, S. et al. Weighing nanoparticles in solution at the attogram scale. Proc. Natl Acad. Sci. USA 111, 1310–1315 (2014).

    Article  CAS  Google Scholar 

  38. Millero, F. J. High precision magnetic float densimeter. Rev. Sci. Instrum. 38, 1441–1444 (1967).

    Article  CAS  Google Scholar 

  39. Taylor, M. A. et al. Subdiffraction-limited quantum imaging within a living cell. Phys. Rev. X 4, 0011017 (2014).

    Google Scholar 

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Acknowledgements

E.G. and D.T.N. acknowledge support from the Research in Paris programme of the Ville de Paris and by the French National Research Agency through the NOMADE Project. E.G., C.B., W.H. and I.F. acknowledge support from the European Research Council through the GANOMS Project.

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Authors and Affiliations

  1. Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS, Sorbonne Paris Cité, UMR 7162, 10 rue Alice Domon et Léonie Duquet, Paris, 75013, France

    E. Gil-Santos, C. Baker, D. T. Nguyen, W. Hease, S. Ducci, G. Leo & I. Favero

  2. Laboratoire de Photonique et Nanostructures, CNRS, Route de Nozay, Marcoussis, 91460, France

    C. Gomez & A. Lemaître

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  1. E. Gil-Santos
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Contributions

E.G. and I.F. conceived and designed the experiments, and developed the models. C.B., D.T.N. and W.H. contributed to the fabrication and experimental techniques. C.G. and A.L. grew the epitaxial material. E.G. performed the systematic experiments. All the authors discussed the results and wrote the paper.

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Correspondence to I. Favero.

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The authors declare no competing financial interests.

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Gil-Santos, E., Baker, C., Nguyen, D. et al. High-frequency nano-optomechanical disk resonators in liquids. Nature Nanotech 10, 810–816 (2015). https://doi.org/10.1038/nnano.2015.160

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