Abstract
We developed a 3D finite element model taking into account the surface effects which is considered significant in nanostructures and used the model to study the resonant frequencies and Young’s modulus of silicon nanowires on both fixed/fixed and fixed/free boundary conditions with diameters between 50 and 200 nm. We found that Young’s modulus and resonant frequencies significantly decreased with decreasing diameter when the diameter was less than 100 nm for fixed/free boundary condition, while they slightly decreased for fixed/fixed boundary condition. When the diameter is larger than 200 nm, the surface stresses may be neglected.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Craighead H.G.: Nanoelectromechanical systems. Science 290, 1532–1535 (2000)
Feng X.L., He R.R., Yang P.D., Roukes M.L.: Very high frequency silicon nanowire electromechanical resonators. Nano Lett. 7, 1953–1959 (2007)
Cuenot S., Fretigny 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)
Broughton J.Q., Meli C.A., Vashishta P., Kalia R.K.: Direct atomistic simulation of quartz crystal oscillators: Bulk properties and nanoscale devices. Phys. Rev. B 56, 611–618 (1997)
Li X.X., Ono T., Wang Y.L., Esashi M.: Ultrathin single-crystalline-silicon cantilever resonators: Fabrication technology and significant specimen size effect on Young’s modulus. Appl. Phys. Lett. 83, 3081–3083 (2003)
Wang G.F., Li X.D.: Size dependency of the elastic modulus of ZnO nanowires: Surface stress effect. Appl. Phys. Lett. 91, 231912 (2007)
Lee B., Rudd R.E.: First-principles study of the Young’s modulus of Si <001> nanowires. Phys. Rev. B 75, 041305 (2007)
Zhu Y., Xu F., Qin Q.Q., Fung W.Y., Lu W.: Mechanical properties of vapor-liquid-solid synthesized silicon nanowires. Nano Lett. 9, 3934–3939 (2009)
She H., Wang B.: Finite element analysis of conical, dome and truncated InAs quantum dots with consideration of surface effects. Semicond. Sci. Tech. 24, 4 (2009)
She H., Wang B.A.: A geometrically nonlinear finite element model of nanomaterials with consideration of surface effects. Finite. Elem. Anal. Des. 45, 463–467 (2009)
Gao W., Yu S.W., Huang G.Y.: Finite element characterization of the size-dependent mechanical behaviour in nanosystems. Nanotechnology 17, 1118–1122 (2006)
Miller R.E., Shenoy V.B.: Size-dependent elastic properties of nanosized structural elements. Nanotechnology 11, 139 (2000)
Cammarata R.C.: Surface and interface stress effects in thin-films. Prog. Surf. Sci. 46, 1–38 (1994)
Park H.S.: Surface stress effects on the resonant properties of silicon nanowires. J. Appl. Phys. 103, 123504 (2008)
Weaver W., Timoshenko S., Young D.: Vibration Problems in Engineering. Wiley-Interscience, New York (1990)
Jing G.Y., Duan H.L., Sun X.M., Zhang Z.S., Xu J., Li Y.D., Wang J.X., Yu D.P.: Surface effects on elastic properties of silver nanowires: Contact atomic-force microscopy. Phys. Rev. B 73, 235049 (2006)
He J., Lilley C.M.: Surface stress effect on bending resonance of nanowires with different boundary conditions. Appl. Phys. Lett. 93, 263108 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-010-0388-4