Abstract
We study the effect of surface roughness on the resonance frequency of micro-cantilever sensors. The analysis demonstrates that surface roughness can enhance, decrease or even annul the effect of surface stress on the resonance frequency, depending on the surface inclination angle and the Poisson ratio of the coating film on the cantilever.
Similar content being viewed by others
References
Chen, G.Y., Thundat, T., Wachter, E.A. and Warmack, R.J., Adsorption-induced surface stress and its effects on resonance frequency of microcantilevers. Journal of Applied Physics, 1995, 77(8): 3618–3622.
Wu, G., Ji, H., Hansen, K., Thundat, T., Datar, R., Cote, R., Hagan, M.F., Chakraborty, A.K. and Majumdar, A., Origin of nanomechanical cantilever motion generated from biomolecular interactions. Proceedings of the National Academy of Sciences of the United States of America, 2001, 98(4): 1560–1564.
Cherian, S. and Thundata, T., Determination of adsorption-induced variation in the spring constant of a microcantilever. Applied Physics Letters, 2002, 80(12): 2219–2221.
Gurtin, M.E., Markenscoff, X. and Thurston, R.N., Effect of surface stress on the natural frequency of thin crystals. Applied Physics Letters, 1976, 29(9): 529–530.
Sharma, P., Ganti, S. and Bhate, N., Effect of surfaces on the size-dependent elastic state of nanoinhomogeneities. Applied Physics Letters, 2003, 82(4): 535–537.
Duan, H.L., Wang, J., Huang, Z.P. and Karihaloo, B.L., Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. Journal of the Mechanics and Physics of Solids, 2005, 53(7): 1574–1596.
Peressadko, A.G., Hosoda, N. and Persson, B.N.J., Influence of surface roughness on adhesion between elastic bodies. Physical Review Letters, 2005, 95(12): 124301–1–4.
Greenwood, J.A. and Williamson, J.B.P., Contact of nominally flat surfaces. Proceedings of the Royal Society of London. Series A-Mathematical and Physical Sciences, 1966, 295(1442): 300–319.
Zhang, H., Lamb, R.N. and Cookson, D.J., Nanowetting of rough superhydrophobic surfaces. Applied Physics Letters, 2007, 91(25): 254106–1–3.
Cheng, Y.-T., Rodak, D.E., Angelopoulos, A. and Gacek, T., Microscopic observations of condensation of water on lotus leaves. Applied Physics Letters, 2005, 87(19): 194112–1–3.
Yang, C., Tartaglino, U. and Persson, B.N., Influence of surface roughness on superhydrophobicity. Physics Review Letters, 2006, 97(11): 116103–1–4.
Fishman, G. and Calecki, D., Influence of surface roughness on the conductivity of metallic and semiconducting quasi-2-dimensional structures. Physics Review B, 1991, 43(14): 11851–11855.
Li, M., Wang, G.-C. and Min, H.-G., Effect of surface roughness on magnetic properties of Co films on plasmaetched Si(100) substrates. Journal of Applied Physics, 1998, 83(10): 5313–5320.
Lavrik, N.V., Tipple, C.A., Sepaniak, M.J. and Datskos, P.G., Enhanced chemi-mechanical transduction at nanostructured interfaces. Chemical Physics Letters, 2001, 336(5–6): 371–376.
Lavrik, N.V., Tipple, C.A., Sepaniak, M.J. and Datskos, P.G., Gold nano-structures for transduction of biomolecular interactions into micrometer scale movements. Biomedical Microdevices, 2001, 3(1): 35–44.
Fabre, A., Finot, E., Demoment, J. and Contreras, S., Monitoring the chemical changes in Pd induced by hydrogen absorption using microcantilevers. Ultramicroscopy, 2003, 97(1–4): 425–432.
Mertens, J., Finot, E., Nadal, M.-H., Eyraud, V., Heintz, O. and Bourillot, E., Detection of gas trace of hydrofluoric acid using microcantilever. Sensors and Actuators: B-Chemical, 2004, 99(1): 58–65.
Godin, M., Williams, P.J., Cossa, V.T., Laroche, O., Beaulieu, L. Y., Lennox, R. B. and Grütter, P., Surface stress, kinetics, and structure of alkanethiol self-assembled monolayers. Langmuir, 2004, 20(17): 7090–7096.
Desikan, R., Lee, I. and Thundat, T., Effect of nanometer surface morphology on surface stress and adsorption kinetics of alkanethiol self-assembled monolayers. Ultramicroscopy, 2006, 106(8–9): 795–799.
Weissmuller, J. and Duan, H.L., Cantilever bending with rough surfaces. Physics Review Letters, 2008, 101(14): 146102–1–4.
Duan, H.L., Surface-enhanced cantilever sensors with nano-porous films. Acta Mechanica Solida Sinica, 2010 (in press).
Brantley, W.A., Calculated elastic constants for stress problems associated with semiconductor devices. Journal of Applied Physics, 1973, 44(1): 534–535.
Shenoy, V.B., Atomistic calculations of elastic properties of metallic fcc crystal surfaces. Physics Review B, 2005, 71(9): 094104–1–11.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Grant Nos.10525209, 10872003 and 10932001), the Foundation for the Author of National Excellent Doctoral Dissertation of PR China (FANEDD, Grant No.2007B2), Research Fund for the New Teacher Program of the State Education Ministry of China (Grant No.200800011011) and Scientific Research Foundation for the Returned Overseas Chinese Scholars State Education Ministry of China.
Rights and permissions
About this article
Cite this article
Duan, H., Xue, Y. & Yi, X. Vibration of cantilevers with rough surfaces. Acta Mech. Solida Sin. 22, 550–554 (2009). https://doi.org/10.1016/S0894-9166(09)60385-2
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1016/S0894-9166(09)60385-2