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.

  • Letter
  • Published:

Nanomechanical mass sensing and stiffness spectrometry based on two-dimensional vibrations of resonant nanowires

Nature Nanotechnology volume 5, pages 641–645 (2010)Cite this article

Subjects

Abstract

One-dimensional nanomechanical resonators based on nanowires and nanotubes have emerged as promising candidates for mass sensors1,2,3,4,5,6. When the resonator is clamped at one end and the atoms or molecules being measured land on the other end (which is free to vibrate), the resonance frequency of the device decreases by an amount that is proportional to the mass of the atoms or molecules. However, atoms and molecules can land at any position along the resonator, and many biomolecules have sizes that are comparable to the size of the resonator, so the relationship between the added mass and the frequency shift breaks down7,8,9,10. Moreover, whereas resonators fabricated by top-down methods tend to vibrate in just one dimension because they are usually shaped like diving boards, perfectly axisymmetric one-dimensional nanoresonators can support flexural vibrations with the same amplitude and frequency in two dimensions11. Here, we propose a new approach to mass sensing and stiffness spectroscopy based on the fact that the nanoresonator will enter a superposition state of two orthogonal vibrations with different frequencies when this symmetry is broken. Measuring these frequencies allows the mass, stiffness and azimuthal arrival direction of the adsorbate to be determined.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Thermal displacement fluctuations of silicon nanowires.
Figure 2: Rotation of the fundamental vibration planes of silicon nanowires.
Figure 3: Effect of mass deposition position on frequency splitting.

Similar content being viewed by others

References

  1. Feng, X. L., He, R., Yang, P. & Roukes, M. L. Very high frequency silicon nanowire electromechanical resonators. Nano Lett. 7, 1953–1959 (2007).

    Article  CAS  Google Scholar 

  2. Jensen, K., Kim, K. & Zettl, A. An atomic-resolution nanomechanical mass sensor. Nature Nanotech. 3, 533–537 (2008).

    Article  CAS  Google Scholar 

  3. Li, M. et al. Bottom-up assembly of large-area nanowire resonator arrays. Nature Nanotech. 3, 88–92 (2008).

    Article  CAS  Google Scholar 

  4. Sazonova, V. et al. A tunable carbon nanotube electromechanical oscillator. Nature 431, 284–287 (2004).

    Article  CAS  Google Scholar 

  5. Belov, M. et al. Mechanical resonance of clamped silicon nanowires measured by optical interferometry. J. Appl. Phys. 103, 074304 (2008).

    Article  Google Scholar 

  6. Nichol, J. M., Hemesath, E. R., Lauhon, L. J. & Budakian, R. Displacement detection of silicon nanowires by polarization-enhanced fiber-optic interferometry. Appl. Phys. Lett. 93, 193110 (2008).

    Article  Google Scholar 

  7. Ramos, D., Tamayo, J., Mertens, J. & Calleja, M. Effect of the adsorbate stiffness on the resonance response of microcantilevers. Appl. Phys. Lett. 89, 224104 (2006).

    Article  Google Scholar 

  8. Waggoner, P. S., Varshney, M. & Craighead, H. G. Detection of prostate specific antigen with nanomechanical resonators. Lab on a Chip 9, 3095–3099 (2009).

    Article  CAS  Google Scholar 

  9. Dohn, S., Svendsen, W., Boisen, A. & Hansen, O. Mass and position determination of attached particles on cantilever based mass sensors. Rev. Sci. Instrum. 78, 103303 (2007).

    Article  CAS  Google Scholar 

  10. Spletzer, M., Raman, A. & Reifenberger, R. Elastometric sensing using higher flexural eigenmodes of microcantilevers. Appl. Phys. Lett. 91, 184103 (2007).

    Article  Google Scholar 

  11. Conley, W. G., Raman, A., Krousgrill, C. M. & Mohammadi, S. Nonlinear and nonplanar dynamics of suspended nanotube and nanowire resonators. Nano Lett. 8, 1590–1595 (2008).

    Article  CAS  Google Scholar 

  12. Aebersold, R. & Mann, M. Mass spectrometry-based proteomics. Nature 422, 198–207 (2003).

    Article  CAS  Google Scholar 

  13. 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 

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

    Article  CAS  Google Scholar 

  15. Ilic, B. et al. Attogram detection using nanoelectromechanical oscillators. J. Appl. Phys. 95, 3694–3703 (2004).

    Article  CAS  Google Scholar 

  16. Yang, Y. T., Callegari, C., Feng, X. L., Ekinci, K. L. & Roukes, M. L. Zeptogram-scale nanomechanical mass sensing. Nano Lett. 6, 583–586 (2006).

    Article  CAS  Google Scholar 

  17. Azak, N. O. et al. Nanomechanical displacement detection using fiber-optic interferometry. Appl. Phys. Lett. 91, 093112 (2007).

    Article  Google Scholar 

  18. Babak, S. & Ashby, P. D. High sensitivity deflection detection of nanowires. Phys. Rev. Lett. 104, 147203 (2010).

    Article  Google Scholar 

  19. Biedermann, L. B., Tung, R. C., Raman, A. & Reifenberger, R. G. Flexural vibration spectra of carbon nanotubes measured using laser Doppler vibrometry. Nanotechnology 20, 035702 (2009).

    Article  Google Scholar 

  20. Fan, H. J., Werner, P. & Zacharias, M. Semiconductor nanowires: from self-organization to patterned growth. Small 2, 700–717 (2006).

    Article  CAS  Google Scholar 

  21. Liew, K. M., Hung, K. C. & Lim, M. K. A continuum three-dimensional vibration analysis of thick rectangular plates. Int. J. Solids Struct. 30, 3357–3379 (1993).

    Article  Google Scholar 

  22. Kang, J.-H. & Leissa, A. W. Three-dimensional analysis of thick, tapered rods and beams with circular cross-section. Int. J. Mech. Sci. 46, 929–944 (2004).

    Article  Google Scholar 

  23. Gil-Santos, E. et al. Mass sensing based on deterministic and stochastic responses of elastically coupled nanocantilevers. Nano Lett. 9, 4122–4127 (2009).

    Article  CAS  Google Scholar 

  24. Spletzer, M., Raman, A., Wu, A. Q., Xu, X. & Reifenberg, R. Ultrasensitive mass sensing using mode localization in coupled microcantilevers. Appl. Phys. Lett. 88, 254102 (2006).

    Article  Google Scholar 

  25. 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 

  26. Braun, T. et al. Quantitative, time-resolved measurement of membrane protein–ligand interactions using microcantilever array sensors. Nature Nanotech. 4, 179–185 (2009).

    Article  CAS  Google Scholar 

  27. Ndieyira, J. F. et al. Nanomechanical detection of antibiotic–mucopeptide binding in a model for superbug drug resistance. Nature Nanotech. 3, 691–696 (2008).

    Article  CAS  Google Scholar 

  28. Cross, S. E., Jin, Y.-S., Rao, J. & Gimzewski J. K. Nanomechanical analysis of cells from cancer patients. Nature Nanotech. 2, 780–783.

  29. Michel, J. P. et al. Nanoindentation studies of full and empty viral capsids and the effects of capsid protein mutations on elasticity and strength. Proc. Natl Acad. Sci. USA 103, 6184–6189 (2006).

    Article  CAS  Google Scholar 

  30. Kol, N. et al. A stiffness switch in human immunodeficiency virus. Biophys. J. 92, 1777–1783 (2007).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors acknowledge financial support from the Spanish Science Ministry through projects TEC2009-14517-C02, CSD2007-00010 and MAT2009-08650 and from CSIC under project PIF06-037.

Author information

Authors and Affiliations

  1. Instituto de Microelectrónica de Madrid, CSIC, Isaac Newton 8 (PTM) Tres Cantos, Madrid, 28760, Spain

    Eduardo Gil-Santos, Daniel Ramos, Javier Martínez, Ricardo García, Montserrat Calleja & Javier Tamayo

  2. Department of Electrical Engineering, Yale University, 15 Prospect Street, New Haven, 06520, Connecticut, USA

    Daniel Ramos

  3. Instituto de Microelectrónica de Barcelona, CSIC, Campus UAB, Bellaterra, 08193, Barcelona, Spain

    Marta Fernández-Regúlez & Álvaro San Paulo

Authors
  1. Eduardo Gil-Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Ramos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Javier Martínez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Marta Fernández-Regúlez
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ricardo García
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Álvaro San Paulo
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Montserrat Calleja
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Javier Tamayo
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.T. and M.C. wrote this manuscript with input from all authors. All authors analysed and interpreted the data. A.S. and M.F.-R. built the CVD reactor and fabricated the devices. E.G. and D.R. performed the detection and mass adsorption experiments and collected the data. J.T., E.G. and D.R. developed the theoretical model. E.G., D.R. and J.T. designed the experiments. J.M. and R.G. designed the set-up for SEM carbon deposition.

Corresponding author

Correspondence to Javier Tamayo.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 517 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gil-Santos, E., Ramos, D., Martínez, J. et al. Nanomechanical mass sensing and stiffness spectrometry based on two-dimensional vibrations of resonant nanowires. Nature Nanotech 5, 641–645 (2010). https://doi.org/10.1038/nnano.2010.151

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nnano.2010.151

This article is cited by

Search

Advanced 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