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Finite element analysis of resonant properties of silicon nanowires

  • Dalia ČalnerytėEmail author
  • Vidmantas Rimavičius
  • Rimantas Barauskas
Original Paper

Abstract

This paper presents a 3D nanostructure modal vibration analysis by using finite element models. The modal frequencies and corresponding modal shapes of silicon nanowires of various thickness against length ratios are determined by solving a linear structural eigenvalue problem for the 3D solid finite element model, where surface stress effects are taken into account by using the stress stiffness matrix. The cases of fixed/fixed and fixed/free boundary conditions at the nanowire ends are investigated. The results obtained by 3D solid models and models based on the beam bending theory have been compared with each other, as well as with the results obtained elsewhere in the literature computationally and experimentally. It has been shown that the effects caused by surface stresses are insignificant for wires with length-to-width ratio less than 10.

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Notes

Acknowledgements

This research was supported by the Research, Development and Innovation Fund of Kaunas University of Technology (FEMSHORTWAVE. PP32/1808).

References

  1. 1.
    Shamloo, A., Mehrafrooz, B.: Nanomechanics of actin filament: a molecular dynamics simulation. Cytoskeleton 75, 118–130 (2018).  https://doi.org/10.1002/cm.21429 CrossRefGoogle Scholar
  2. 2.
    Sinnott, S.B., Heo, S.-J., Brenner, D.W., Harrison, J.A., Irving, D.L.: Computer simulations of nanometer-scale indentation and friction. In: Nanotribology and Nanomechanics, pp. 301–370. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-51433-8_7
  3. 3.
    Duan, H.L., Wang, J., Karihaloo, B.L.: Theory of Elasticity at the Nanoscale. Elsevier Masson SAS, Amsterdam (2009).  https://doi.org/10.1016/S0065-2156(08)00001-X CrossRefGoogle Scholar
  4. 4.
    Craighead, H.G.: Nanoelectromechanical systems. Science 290, 1532–1535 (2000).  https://doi.org/10.1126/science.290.5496.1532 CrossRefGoogle Scholar
  5. 5.
    Abazari, A.M., Safavi, S.M., Rezazadeh, G., Villanueva, L.G.: Modelling the size effects on the mechanical properties of micro/nano structures. Sensors (Switzerland) 15, 28543–28562 (2015).  https://doi.org/10.3390/s151128543 CrossRefGoogle Scholar
  6. 6.
    Feng, X.L., He, R., Yang, P., Roukes, M.L.: Very high frequency silicon nanowire electromechanical resonators. Nano Lett. 7, 1953–1959 (2007).  https://doi.org/10.1021/nl0706695 CrossRefGoogle Scholar
  7. 7.
    Pishkenari, H.N., Afsharmanesh, B., Tajaddodianfar, F.: Continuum models calibrated with atomistic simulations for the transverse vibrations of silicon nanowires. Int. J. Eng. Sci. 100, 8–24 (2016).  https://doi.org/10.1016/j.ijengsci.2015.11.005 CrossRefzbMATHGoogle Scholar
  8. 8.
    Yu, H., Sun, C., Zhang, W.W., Lei, S.Y., Huang, Q.A.: Study on size-dependent Young’s modulus of a silicon nanobeam by molecular dynamics simulation. J. Nanomater. (2013).  https://doi.org/10.1155/2013/319302 CrossRefGoogle Scholar
  9. 9.
    Wu, J.X., Li, X.F., Tang, A.Y., Lee, K.Y.: Free and forced transverse vibration of nanowires with surface effects. JVC/J. Vib. Control 23, 2064–2077 (2017).  https://doi.org/10.1177/1077546315610302 MathSciNetCrossRefGoogle Scholar
  10. 10.
    Ansari, R., Sahmani, S.: Bending behavior and buckling of nanobeams including surface stress effects corresponding to different beam theories. Int. J. Eng. Sci. 49, 1244–1255 (2011).  https://doi.org/10.1016/j.ijengsci.2011.01.007 CrossRefzbMATHGoogle Scholar
  11. 11.
    Song, F., Huang, G.L., Park, H.S., Liu, X.N.: A continuum model for the mechanical behavior of nanowires including surface and surface-induced initial stresses. Int. J. Solids Struct. 48, 2154–2163 (2011).  https://doi.org/10.1016/j.ijsolstr.2011.03.021 CrossRefGoogle Scholar
  12. 12.
    Jiang, L.Y., Yan, Z.: Timoshenko beam model for static bending of nanowires with surface effects. Phys. E Low-Dimens. Syst. Nanostruct. 42, 2274–2279 (2010).  https://doi.org/10.1016/j.physe.2010.05.007 CrossRefGoogle Scholar
  13. 13.
    Park, H.S., Klein, P.A.: A surface Cauchy–Born model for silicon nanostructures. Comput. Methods Appl. Mech. Eng. 197, 3249–3260 (2008).  https://doi.org/10.1016/j.cma.2007.12.004 MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Nasr Esfahani, M., Yilmaz, M., Sonne, M.R., Hattel, J.H., Alaca, B.E.: Selecting the optimum engineering model for the frequency response of FCC nanowire resonators. Appl. Math. Model 44, 236–245 (2017).  https://doi.org/10.1016/j.apm.2016.10.022 CrossRefGoogle Scholar
  15. 15.
    Nasr Esfahani, M., Alaca, B.E.: Surface stress effect on silicon nanowire mechanical behavior? Size Orient. Depend. 127, 112–123 (2018)Google Scholar
  16. 16.
    Eltaher, M.A., Khater, M.E., Emam, S.A.: A review on nonlocal elastic models for bending, buckling, vibrations, and wave propagation of nanoscale beams. Appl. Math. Model. 40, 4109–4128 (2016).  https://doi.org/10.1016/j.apm.2015.11.026 MathSciNetCrossRefGoogle Scholar
  17. 17.
    Park, H.S.: Surface stress effects on the resonant properties of silicon nanowires. J. Appl. Phys. 103, 123504 (2008).  https://doi.org/10.1063/1.2939576 CrossRefGoogle Scholar
  18. 18.
    Wang, Z.Q., Zhao, Y.P., Huang, Z.P.: The effects of surface tension on the elastic properties of nano structures. Int. J. Eng. Sci. 48, 140–150 (2010).  https://doi.org/10.1016/j.ijengsci.2009.07.007 CrossRefGoogle Scholar
  19. 19.
    Wang, G.F., Feng, X.Q.: Effects of surface elasticity and residual surface tension on the natural frequency of microbeams. Appl. Phys. Lett. 90, 1–4 (2007).  https://doi.org/10.1063/1.2746950 CrossRefGoogle Scholar
  20. 20.
    Feng, Y., Liu, Y., Wang, B.: Finite element analysis of resonant properties of silicon nanowires with consideration of surface effects. Acta Mech. 217, 149–155 (2011).  https://doi.org/10.1007/s00707-010-0388-4 CrossRefzbMATHGoogle Scholar
  21. 21.
    Cuenot, S., Frétigny, C., Demoustier-Champagne, S., Nysten, B.: Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Phys. Rev. B. 69, 165410 (2004).  https://doi.org/10.1103/PhysRevB.69.165410 CrossRefGoogle Scholar
  22. 22.
    Wang, G., Li, X.: Size dependency of the elastic modulus of ZnO nanowires: surface stress effect. Appl. Phys. Lett. 91, 231912 (2007).  https://doi.org/10.1063/1.2821118 CrossRefGoogle Scholar
  23. 23.
    Lee, B., Rudd, R.E.: First-principles study of the Young’s modulus of Si \(<\)001\(>\) nanowires. Phys. Rev. B. 75, 041305 (2007).  https://doi.org/10.1103/PhysRevB.75.041305 CrossRefGoogle Scholar
  24. 24.
    Fan, T., Yang, L.: Effective Young’s modulus of nanoporous materials with cuboid unit cells. Acta Mech. 228, 21–29 (2017).  https://doi.org/10.1007/s00707-016-1682-6 MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Zhu, Y., Xu, F., Qin, Q., Fung, W.Y., Lu, W.: Mechanical properties of vapor–liquid–solid synthesized silicon nanowires. Nano Lett. 9, 3934–3939 (2009).  https://doi.org/10.1021/nl902132w CrossRefGoogle Scholar
  26. 26.
    Stokey, W.F.: Vibration of systems having distributed mass and elasticity. In: Harris, C.M., Piersoll, A. (eds.) Shock and Vibration Handbook, Chap. 7. McGraw-Hill, New York (2002)Google Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Dalia Čalnerytė
    • 1
    Email author
  • Vidmantas Rimavičius
    • 1
  • Rimantas Barauskas
    • 1
  1. 1.Department of Applied Informatics, Faculty of InformaticsKaunas University of TechnologyKaunasLithuania

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