Static and Dynamic Pull-in Instabilities Analysis of Partially Affected Clamped Nano Actuators: The Substrate Effect

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, Shahid Chamran University, Ahvaz, Iran

2 Department of Mechanical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran

Abstract

Many researches have been carried out for modeling of micro/nano electromechanical systems instabilities, in which both movable and substrate electrodes are at the same size; however, there is no research considering the static and dynamic pull-in instabilities of micro/nano actuators with a smaller substrate electrode in the presence of small size effects. In the present study, the static and dynamic behaviors of partially affected clamped micro/nano actuators are investigated and the effects of position and length of the substrate electrode are analyzed. The non-linear Euler-Bernoulli governing equation of the beam motion and the corresponding boundary conditions are derived using the Modified couple stress theory. Finite element method is utilized to solve the governing equations. In order to investigate the accuracy of the utilized finite element method, the obtained results are compared with those available in the literature and a good agreement between them was found. The results demonstrate that a decrease of the substrate electrode length leads to an increase of the required pull-in voltage and the pull-in capillary force. Moreover, a small reduction in the pull-in deflection of the nano-beam is observed because of the decrease of the substrate electrode. Finally, a new parameter, named as balanced size effect-capillary force which changes the trend of the behavior of the nano-beam, is introduced.

Keywords

Main Subjects

References

[1] P. Kim, C.M. Lieber, Nanotube nanotweezers, Science, 286(5447) (1999) 2148-2150.
[2] G.-W. Wang, Y. Zhang, Y.-P. Zhao, G.-T. Yang, Pull-in instability study of carbon nanotube tweezers under the influence of van der Waals forces, Journal of Micromechanics Microengineering, 14(8) (2004) 1119.
[3] G.-W. Wang, Y.-P. Zhao, G.-T. Yang, The stability of a vertical single-walled carbon nanotube under its own weight, Materials design, 25(6) (2004) 453-457.
[4] C.K. Adu, G.U. Sumanasekera, B.K. Pradhan, H.E. Romero, P.C. Eklund, Carbon nanotubes: a thermoelectric nano-nose, Chemical Physics Letters, 337(1-3) (2001) 31-35.
[5] P.G. Collins, K. Bradley, M. Ishigami, d.A. Zettl, Extreme oxygen sensitivity of electronic properties of carbon nanotubes, science, 287(5459) (2000) 1801-1804.
[6] J. Arcamone, G. Rius, G. Abadal, J. Teva, N. Barniol, F. Pérez-Murano, Micro/nanomechanical resonators for distributed mass sensing with capacitive detection, Microelectronic Engineering, 83(4-9) (2006) 1216-1220.
[7] M. Dequesnes, Z. Tang, N. Aluru, Static and dynamic analysis of carbon nanotube-based switches, Journal of engineering materials technology, 126(3) (2004) 230-237.
[8] C.-H. Ke, N. Pugno, B. Peng, H. Espinosa, Experiments and modeling of carbon nanotube-based NEMS devices, Journal of the Mechanics Physics of Solids, 53(6) (2005) 1314-1333.
[9] T. Rueckes, K. Kim, E. Joselevich, G.Y. Tseng, C.-L. Cheung, C.M. Lieber, Carbon nanotube-based nonvolatile random access memory for molecular computing, science, 289(5476) (2000) 94-97.
[10] C. Li, E.T. Thostenson, T.-W. Chou, Sensors and actuators based on carbon nanotubes and their composites: a review, Composites science technology, 68(6) (2008) 1227-1249.
[11] J. Qian, Y.-P. Zhao, Materials selection in mechanical design for microsensors and microactuators, Materials design, 23(7) (2002) 619-625.
[12] S.D. Senturia, Microsystem design, Springer Science & Business Media, 2007.
[13] M. Pedersen, W. Olthuis, P. Bergveld, A silicon condenser microphone with polyimide diaphragm and backplate, Sensors Actuators A: Physical, 63(2) (1997) 97-104.
[14] M. Pederson, W. Olthuis, P. Bergveld, High-performance condenser microphone with fully integrated CMOS amplifier and DC-DC voltage converter, Journal of microelectromechanical systems, 7(4) (1998) 387-394.
[15] J.-J. Ho, Y.-K. Fang, M. Hsieh, S. Ting, G.-S. Chen, M.-S. Ju, T.Y. Chen, C. Huang, C. Chen, Development of a microelectromechanical system pressure sensor for rehabilitation engineering applications, International Journal of electronics, 87(6) (2000) 757-767.
[16] J.-M. Sallese, W. Grabinski, V. Meyer, C. Bassin, P. Fazan, Electrical modeling of a pressure sensor MOSFET, Sensors Actuators A: Physical, 94(1-2) (2001) 53-58.
[17] K. Chik, Precision wavelength light sources for dense WDM system, in: High-Speed Semiconductor Lasers for Communication, International Society for Optics and Photonics, 1997, pp. 56-60.
[18] L. Jiang, Y. Shi, W. Li, Y. Ding, Z. Lai, Z. Zhu, Numerical analysis of pull-in voltage for contact MEMS switches in switched-line phase shifter application, in: Fifth International Conference on Thin Film Physics and Applications, International Society for Optics and Photonics, 2004, pp. 587-591.
[19] R. Batra, M. Porfiri, D. Spinello, Review of modeling electrostatically actuated microelectromechanical systems, Smart Materials Structures, 16(6) (2007) R23.
[20] R. Nadal-Guardia, A.M. Brosa, A. Dehe, AC transfer function of electrostatic capacitive sensors based on the 1-D equivalent model: application to silicon microphones, Journal of microelectromechanical systems, 12(6) (2003) 972-978.
[21] R. Nadal-Guardia, A.M. Brosa, A. Dehé, Constant charge operation of capacitor sensors based on switched-current circuits, IEEE sensors journal, 3(6) (2003) 835-842.
[22] J. Cheng, J. Zhe, X. Wu, Analytical and finite element model pull-in study of rigid and deformable electrostatic microactuators, Journal of Micromechanics Microengineering, 14(1) (2003) 57.
[23] A.G. Arani, A. Jalilvand, M. Ghaffari, M.T. Mazraehshahi, R. Kolahchi, M. Roudbaria, S. Amira, Nonlinear pull-in instability of boron nitride nano-switches considering electrostatic and Casimir forces, Scientia Iranica. Transaction F, Nanotechnology, 21(3) (2014) 1183.
[24] M.I. Younis, E.M. Abdel-Rahman, A. Nayfeh, A reduced-order model for electrically actuated microbeam-based MEMS, Journal of Microelectromechanical systems, 12(5) (2003) 672-680.
[25] G.W. Vogl, A.H. Nayfeh, A reduced-order model for electrically actuated clamped circular plates, in: ASME 2003 international design engineering technical conferences and computers and information in engineering conference, American Society of Mechanical Engineers, 2003, pp. 1867-1874.
[26] R. Batra, M. Porfiri, D. Spinello, Capacitance estimate for electrostatically actuated narrow microbeams, IET Micro Nano Letters, 1(2) (2006) 71-73.
[27] E. Huang, S. Senturia, Generating efficient dynamics models for microelectromechanical systems from a few finite-element simulations runs, J. Microelectromech. Syst, 8 (1999) 280-289.
[28] E. Yazdanpanahi, A. Noghrehabadi, M. Ghalambaz, Pull-in instability of electrostatic doubly clamped nano actuators: Introduction of a balanced liquid layer (BLL), International Journal of Non-Linear Mechanics, 58 (2014) 128-138.
[29] G.N. Nielson, G. Barbastathis, Dynamic pull-in of parallel-plate and torsional electrostatic MEMS actuators, Journal of microelectromechanical systems, 15(4) (2006) 811-821.
[30] D. Elata, H. Bamberger, On the dynamic pull-in of electrostatic actuators with multiple degrees of freedom and multiple voltage sources, Journal of Microelectromechanical systems, 15(1) (2006) 131-140.
[31] H.C. Nathanson, W.E. Newell, R.A. Wickstrom, J.R. Davis, The resonant gate transistor, IEEE Transactions on Electron Devices, 14(3) (1967) 117-133.
[32] S. Chaterjee, G. Pohit, A large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams, Journal of sound vibration, 322(4-5) (2009) 969-986.
[33] M.M. Zand, M.T. Ahmadian, Application of homotopy analysis method in studying dynamic pull-in instability of microsystems, Mechanics Research Communications, 36(7) (2009) 851-858.
[34] J. Yang, Y. Hu, S. Kitipornchai, Electro-dynamic behavior of an electrically actuated micro-beam: Effects of initial curvature and nonlinear deformation, Computers Structures, 96 (2012) 25-33.
[35] Y.-G. Wang, W.-H. Lin, Z.-J. Feng, X.-M. Li, Characterization of extensional multi-layer microbeams in pull-in phenomenon and vibrations, International Journal of Mechanical Sciences, 54(1) (2012) 225-233.
[36] Z. Wei, Y.-P. Zhao, Growth of liquid bridge in AFM, Journal of Physics D: Applied Physics, 40(14) (2007) 4368.
[37] P. Van Zwol, G. Palasantzas, J.T.M. De Hosson, Influence of roughness on capillary forces between hydrophilic surfaces, Physical Review E, 78(3) (2008) 031606.
[38] G. Palasantzas, Contact angle influence on the pull-in voltage of microswitches in the presence of capillary and quantum vacuum effects, Journal of Applied Physics, 101(5) (2007) 053512.
[39] C. Mastrangelo, C. Hsu, Mechanical stability and adhesion of microstructures under capillary forces. II. Experiments, Journal of Microelectromechanical systems, 2(1) (1993) 44-55.
[40] H.M. Ouakad, M.I. Younis, Modeling and simulations of collapse instabilities of microbeams due to capillary forces, in: ASME 2008 International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, 2008, pp. 187-195.
[41] E. Yazdanpanahi, A. Noghrehabadi, M. Ghalambaz, Balance dielectric layer for micro electrostatic switches in the presence of capillary effect, International Journal of Mechanical Sciences, 74 (2013) 83-90.
[42] M. Asghari, M. Ahmadian, M. Kahrobaiyan, M. Rahaeifard, On the size-dependent behavior of functionally graded micro-beams, Materials Design, 31(5) (2010) 2324-2329.
[43] S. Park, X. Gao, Bernoulli–Euler beam model based on a modified couple stress theory, Journal of Micromechanics Microengineering, 16(11) (2006) 2355.
[44] Y. Fu, J. Zhang, Size-dependent pull-in phenomena in electrically actuated nanobeams incorporating surface energies, Applied Mathematical Modelling, 35(2) (2011) 941-951.
[45] S. Kong, S. Zhou, Z. Nie, K. Wang, The size-dependent natural frequency of Bernoulli–Euler micro-beams, International Journal of Engineering Science, 46(5) (2008) 427-437.
[46] F. Yang, A. Chong, D.C.C. Lam, P. Tong, Couple stress based strain gradient theory for elasticity, International Journal of Solids Structures, 39(10) (2002) 2731-2743.
[47] J. Reddy, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science, 45(2-8) (2007) 288-307.
[48] A.C. Eringen, Nonlocal continuum field theories, Springer Science & Business Media, 2002.
[49] J. Abdi, A. Koochi, A. Kazemi, M. Abadyan, Modeling the effects of size dependence and dispersion forces on the pull-in instability of electrostatic cantilever NEMS using modified couple stress theory, Smart Materials Structures, 20(5) (2011) 055011.
[50] D.C. Lam, A.C. Chong, Indentation model and strain gradient plasticity law for glassy polymers, Journal of materials research, 14(9) (1999) 3784-3788.
[51] M. Rahaeifard, M. Kahrobaiyan, M. Asghari, M. Ahmadian, Static pull-in analysis of microcantilevers based on the modified couple stress theory, Sensors Actuators A: Physical, 171(2) (2011) 370-374.
[52] J. Yang, X. Jia, S. Kitipornchai, Pull-in instability of nano-switches using nonlocal elasticity theory, Journal of Physics D: Applied Physics, 41(3) (2008) 035103.
[53] Y.T. Beni, A. Koochi, M. Abadyan, Theoretical study of the effect of Casimir force, elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS, Physica E: Low-dimensional Systems Nanostructures, 43(4) (2011) 979-988.
[54] M. Rahaeifard, M. Kahrobaiyan, M. Ahmadian, K. Firoozbakhsh, Size-dependent pull-in phenomena in nonlinear microbridges, International Journal of Mechanical Sciences, 54(1) (2012) 306-310.
[55] A.G. Arani, M. Ghaffari, A. Jalilvand, R. Kolahchi, Nonlinear nonlocal pull-in instability of boron nitride nanoswitches, Acta Mechanica, 224(12) (2013) 3005-3019.
[56] S. Pamidighantam, R. Puers, K. Baert, H.A. Tilmans, Pull-in voltage analysis of electrostatically actuated beam structures with fixed–fixed and fixed–free end conditions, Journal of Micromechanics Microengineering, 12(4) (2002) 458.
[57] E.M. Abdel-Rahman, M.I. Younis, A.H. Nayfeh, Characterization of the mechanical behavior of an electrically actuated microbeam, Journal of Micromechanics Microengineering, 12(6) (2002) 759.
[58] H.F. Dadgour, M.M. Hussain, C. Smith, K. Banerjee, Design and analysis of compact ultra energy-efficient logic gates using laterally-actuated double-electrode NEMS, in: Design Automation Conference (DAC), 2010 47th ACM/IEEE, IEEE, 2010, pp. 893-896.
[59] K. Wang, B. Wang, A general model for nano-cantilever switches with consideration of surface effects and nonlinear curvature, Physica E: Low-dimensional Systems Nanostructures, 66 (2015) 197-208.
[60] Y. Hayamizu, T. Yamada, K. Mizuno, R.C. Davis, D.N. Futaba, M. Yumura, K. Hata, Integrated three-dimensional microelectromechanical devices from processable carbon nanotube wafers, Nature nanotechnology, 3(5) (2008) 289.
[61] j. Qian, c. Liu, D. Zhang, Y. Zhao, The problem of the residual stress in microelectronic mechanical systems, Journal Of Mechanical Strength, 23(4) (2001) 393-401.
[62] R. Batra, M. Porfiri, D. Spinello, Vibrations of narrow microbeams predeformed by an electric field, Journal of Sound Vibration, 309(3-5) (2008) 600-612.
[63] J.D. Jackson, Classical electrodynamics, in, AAPT, 1999.
[64] R. Legtenberg, H.A. Tilmans, J. Elders, M. Elwenspoek, Stiction of surface micromachined structures after rinsing and drying: model and investigation of adhesion mechanisms, Sensors actuators A: Physical, 43(1-3) (1994) 230-238.
[65] A. Noghrehabadi, A. Haghparast, Dynamic and static pull-in instability analysis of partially affected nano-cantilevers using modified couple stress theory, Modares Mechanical Engineering, 16(11) (2017) 81-91 (In Persian).
[66] A.H. Nayfeh, D.T. Mook, Nonlinear oscillations, John Wiley & Sons, 2008.
[67] J.N. Reddy, An introduction to the finite element method, McGraw-hill New York, 1993.
Amirkabir Journal of Mechanical Engineering
Volume 50, Issue 5
January and February 2019
Pages 1023-1038

Files

Share

How to cite

Statistics