Abstract
The current paper presents a two degree of freedom model for the problem of micromirrors under capillary force. The principal of minimum potential energy is employed for finding the equilibrium equations governing the deflection and the rotation of the micromirror. Then, using the implicit function theorem, a coupled bending–torsion model is presented for pull-in characteristics of micromirrors under capillary force and the concept of instability mode is introduced. It is observed that with increasing ratio of bending and torsion stiffness, the dominant instability mode changes from bending mode to the torsion mode. In order to verify the accuracy of the coupled model, static behavior of a group of micromirrors is investigated both analytically using the presented model and numerically using the commercial finite element software ANSYS. It is observed that results of the coupled model match well with the results of finite element simulations, but they both deviate considerably from the results of the pure torsion model. The presented coupled model can be used for safe and stable design of micromirrors under capillary force.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Maluf N., Williams K.: An Introduction to Microelectromechanical Systems Engineering, 2nd edn. Microelectromechanical Systems (MEMS) Series. Artech House Inc., Boston (1999)
Younis, M.I.: Modeling and simulation of microelectromechanical systems in multi-physics fields. Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Engineering Mechanics
Chao P.C.P, Chiu C.W., Tsai C.Y.: A novel method to predict the pull-in voltage in a closed form for micro-plates actuated by a distributed electrostatic force. J. Micromech. Microeng. 16, 986–998 (2006)
Hornbeck, L.J.: Spatial light modulator and method. US Patent 5,061,049 (1991)
Ford J.E., Aksyuk V.A., Bishop D.J., Walker J.A.: Wavelength add-drop swiching using tilting micromirrors. J. Lightwave technol. 17, 904–911 (1999)
Dickensheets D.L., Kino G.S.: Silicon-micromachined scanning confocal optical microscope. J. Microelectromech. Syst. 7(1), 38–47 (1998)
Zavracky P.M., Majumber S., McGruer E.: Micromechanical switches fabricated using nickel surface micromachining. J. Microelectromech. Syst. 6, 3–9 (1997)
Toshiyoshi H., Fujita H.: Electrostatic micro torsion mirrors for an optical switch matrix. J. Microelectromech. Syst. 5, 231–237 (1996)
Wei Z., Zhao Y.P.: Growth of liquid bridge in AFM. J. Phys. D Appl. Phys. 40(14), 4368–4375 (2007)
Van Zwol P.J., Palasantzas G., De Hosson J.Th.M.: Influence of roughness on capillary forces between hydrophilic surfaces. Phys. Rev. E 78, 03160 (2008)
Mastrangelo C.H., Hsu C.H.: Mechanical stability and adhesion of microstructures under capillary forces-part I: basic theory. J. Microelectromech. Syst. 2(1), 33–43 (1993)
Mastrangelo C.H., Hsu C.H.: Mechanical stability and adhesion of microstructures under capillary forces-part 2: experiments. J. Microelectromech. Syst. 2(1), 44–55 (1993)
Moeenfard, H., Kahrobaiyan, M.H., Ahmadian, M.T.: Aplication of the extended Kantorovich method to the static deflection of microplates under capillary force. In: ASME International Mechanical Engineering Congress and Exposition, IMECE2010-39517 (2010)
Zitzler L., Herminghaus S., Mugele F.: Capillary forces in tapping mode atomic force microscopy. Phys. Rev. B 66, 155436 (2002)
Li X., Peng Y.: Investigation of capillary adhesion between the microcantilever and the substrate with electronic speckle pattern interferometry. Appl. Phys. Lett. 89, 234104 (2006)
Jang J., Schatz G.C., Ratner M.A.: Capillary force in atomic force microscopy. J. Chem. Phys. 120(3), 1157–1160 (2004)
Guo J.G., Zhou L.J., Zhao Y.P.: Instability analysis of torsional MEMS/NEMS actuators under capillary force. J. Colloid Interface Sci. 331(2), 458–462 (2009)
Huang J.-M., Liu A.Q., Deng Z.L., Zhang Q.X., Ahn J., Asundi A.: An approach to the coupling effect between torsion and bending for electrostatic torsional micromirrors. J. Sens. Actuators A 115, 159–167 (2004)
Rao S.S.: Vibration of Continuous Systems. Wiley, New Jersey (2007)
Bochobza-Degani O., Nemirovsky Y.: Modeling the pull-in parameters of electrostatic actuators with a novel lumped two degree of freedom pull-in model. Sens. Actuator A 97–98, 569–578 (2002)
Bochobza-Degani, O., Nemirovsky, Y.: Erratum to “Modeling the pull-in parameters of electrostatic actuators with a novel lumped two degrees of freedom pull-in model [Sensors and Actuators A97–98: 569–578]”, Sens. Actuators A 101, 392 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Darvishian, A., Moeenfard, H., Ahmadian, M.T. et al. A coupled two degree of freedom pull-in model for micromirrors under capillary force. Acta Mech 223, 387–394 (2012). https://doi.org/10.1007/s00707-011-0558-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-011-0558-z