Study on the Pull-In Instability of Gold Micro-Switches Using Variable Length Scale Parameter

Document Type: Research Paper

Authors

1 Department of Mechanical Engineering, Khoy Branch, Islamic Azad University

2 Department of Mechanical Engineering, University of Tabriz

Abstract

In this paper, the size dependent behavior of the gold micro-switches has been studied. This behavior becomes noticeable for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter. The size dependent effect is insignificant for the high ratio of the characteristic size to the length-scale parameter, which is the case of the silicon base micro-beams. On the other hand, in some types of micro-beams like gold base, the size dependent effect cannot be overlooked. In such cases, ignoring this behavior in modeling will lead to incorrect results. Some previous researchers have applied classic beam theory on their models and imposed a considerable hypothetical value of residual stress to match their theoretical results with the experimental ones. In this study, by obtaining the equilibrium positions or fixed points of the gold micro-beam, a considerable difference between the obtained fixed points using classic beam theory and modified couple stress theory has been shown. In addition, it has been shown that the calculated pull-in voltages using modified couple stress theory are much closer to the experimental results than those obtained by classic beam theory. Finally, it has been shown that considering a unique value of length scale parameter, especially for the smallest values of the beam thicknesses, may leads to inaccurate results and variable length scale parameter should be considered.

Keywords


[1] Madou M., 2002, Fundamentals of Microfabrication, CRC Press, NewYork, USA, p. 497.

[2] Holliday R., Goodman P., 2002, Going for the gold, IEE Review, 48: 15-19.

[3] Knarr R.F., Quon R.A., 1998, Direct force measurements at the smooth gold/mica interface, Langmuir 14(22): 6414-6418.

[4] Caol Y., Nankivil D.D., Allameh S., Soboyejo W.O., 2007, Mechanical properties of au films on silicon substrates, Materials and Manufacturing Processes 22: 187-194.

[5] Younis M.I., Abdel-Rahman E.M., Nayfeh A., 2003, A reduced-order model for electrically actuated microbeam-based MEMS, Journal of Microelectromechanical Systems 12(5): 672-680.

[6] Sadeghian H., Rezazadeh G., Osterberg P.M., 2007, Application of the generalized differential quadrature method to the study of pull-in phenomena of MEMS switches, Journal of Microelectromechanical Systems 16 (6): 1334-1340.

[7] Osterberg P.M., Senturia S.D., 1997, M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures, Journal of Microelectromechanical Systems 6: 107-118.

[8] Rezazadeh G., Fathalilou M., Shabani R., 2009, Static and dynamic stabilities of a microbeam actuated by a piezoelectric voltage, Journal of Microsystem Technologies 15:1785-1791.

[9] Papargyri-Beskou S., Tsepoura K.G., Polyzos D., Beskos D.E., 2003, Bending and stability analysis of gradient elastic beams, International Journal of solids and structures 40: 385-400.

[10] Lazopoulos K.A., Lazopoulos A.K., 2010, Bending and buckling of thin strain gradient elastic beams, European Journal of mechanics A/solids 29: 837-843.

[11] Asghari M., Ahmadian M.T., Kahrobaiyan M.H., Rahaeifard M., 2010, On the size-dependent behavior of functionally graded micro-beams, Materials and Design 31: 2324-2329.

[12] Park S.K., Gao X.L., 2006, Bernoulli-Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16: 2355-2359.

[13] Fu Y., Zhang J., 2011, Size-dependent pull-in phenomena in electrically actuated nanobeams incorporating surface energies, Applied Mathematical Modelling 35: 941-951.

[14] Shengli K., Shenjie Z., Zhifeng N., Kai W., 2009, Static and dynamic analysis of micro beams based on strain gradient elasticity theory, Journal of Engineering Society 47: 487-498.

[15] Lam D.C.C., Chong A.C.M., 1999, Indentation model and strain gradient plasticity law for glassy polymers, Journal of Material Research 14: 3784-3788.

[16] Park S.K., Gao X.L., 2006, Bernoulli-Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16(11): 2355-2359.

[17] Shengli K., Shenjie Z., Nie Z., Wang K., 2008, The size-dependent natural frequency of Bernoulli–Euler micro-beams, Journal of Engineering Society 46: 427-437.

[18] Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structure 39: 2731-2743.

[19] Park S.K., Gao X.L., 2006, Bernoulli-Euler beam model based on a modified couple stress theory, Journal of Micromechanics and Microengineering 16(11): 2355-23559.

[20] Zong Z., Soboyejo W.O., 2005, Indentation size effects in face centered cubic single crystal thin films, Materials Science and Engineering A 404(1–2): 281-290.

[21] Zhang Y., Zhao Y., 2010, Numerical and analytical study on the pull-in instability of micro- structure under electrostatic loading, Journal of Sensors Actuators A: Physics 127: 366-367.

[22] Samaali H., Najar F., Choura S., Nayfeh A., Masmoudi M., 2011, A double microbeam MEMS ohmic switch for RF-applications with low actuation voltage, Nonlinear Dynamics 63: 719-734.

[23] Nayfeh A., Younis M.I., 2005, Dynamics of MEMS resonators under superharmonic and subharmonic excitations, Journal of Micromechanics and Microengineering 15: 1840-1847.

[24] Younis M.I., Miles R., Jordy D.L., 2006, Investigation of the response of microstructures under the combined effect of mechanical shock and electrostatic forces, Journal of Micromechanics and Microengineering 16: 2463-2474.

[25] Ballestra A., Brusa E., Pasquale G., Munteanu G., Soma A., 2010, FEM modelling and experimental characterization of microbeams in presence of residual stress, Analog Integrated Circuites Signals Process 63: 477-488.

[26] Vummidia K., Khater M., Abdel-Rahman E., Nayfeh A., Raman S., 2009, Dynamic pull-in of shunt capacitive MEMS switches, Procedia Chemistry 1: 622-625.

[27] Pacheco S.P., Katehi L.P.B., Nguyen C.T.C, 2000, Design of low actuation voltage RF MEMS switch, IEEE MTT-S Digest 1: 165-168.

[28] Son S., Kim J., Kwon D., 2005, Tensile properties and fatigue crack growth in LIGA nickel MEMS structures, Materials Science and Engineering A 406: 274-278.

[29] Nix W.D., Gao H., 1998, Indentation size effects in crystalline materials: a low for strain gradient plasticity, Journal of Mechanical and Physical Solids 46: 411-425.

[30] Zong Z., Soboyejo W., 2005, Indentation size effects in face centered cubic single crystal thin films, Materials Science and Engineering A 404: 281-290.

[31] Rezazadeh G., Fathalilou M., Shabani R., Tarverdilou S., Talebian S., 2009, Dynamic characteristics and forced response of an electrostatically actuated microbeam subjected to fluid loading, Journal of Microsystem Technologies 15: 1355-1363.

[32] Hung E.S, Senturia S.D., 1999, Generating efficient dynamical models for Microelectromechanical systems from a few finite-element simulation runs, Journal of Microelectromechanical Systems 8: 280-289.