Abstract
An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency (RF) micro electro-mechanical system (MEMS) switch is developed based on the Euler-Bernoulli beam and a modified couple stress theory, and is validated by comparison with the finite element results. The sensitivity functions of the pull-in voltage to the designed parameters are derived based on the proposed model. The sensitivity investigation shows that the pull-in voltage sensitivities increase/decrease nonlinearly with the increases in the designed parameters. For the stepped cantilever beam, there exists a nonzero optimal dimensionless length ratio, where the pull-in voltage is insensitive. The optimal value of the dimensionless length ratio only depends on the dimensionless width ratio, and can be obtained by solving a nonlinear equation. The determination of the designed parameters is discussed, and some recommendations are made for the RF MEMS switch optimization.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Zhang, W. M., Yan, H., Peng, Z. K., and Meng, G. Electrostatic pull-in instability in MEMS/NEMS: a review. Sensors and Actuators, A: Physical, 214, 187–218 (2014)
Nathanson, H. C., Newell, W. E., Wickstrom, R. A., and Davis, J. R., Jr. The resonant gate transistor. IEEE Transactions on Electron Devices, 14, 117–133 (1967)
Osterberg, P. M. Electrostatically Actuated Microelectromechanical Test Structures for Material Property Measurement, Ph.D. dissertation, Massachusetts Institute of Technology, Massachusetts (1995)
Rokni, H., Seethaler, R. J., Milani, A. S., Hosseini-Hashemi, S., and Li, X. F. Analytical closedform solutions for size-dependent static pull-in behavior in electrostatic micro-actuators via Fredholm integral equation. Sensors and Actuators, A: Physical, 190, 32–43 (2013)
Noghrehabadi, A., Eslami, M., and Ghalambaz, M. Influence of size effect and elastic boundary condition on the pull-in instability of nano-scale cantilever beams immersed in liquid electrolytes. International Journal of Non-Linear Mechanics, 52, 73–84 (2013)
Baghani, M. Analytical study on size-dependent static pull-in voltage of microcantilevers using the modified couple stress theory. International Journal of Engineering Science, 54, 99–105 (2012)
Raeisifard, H., Bahrami, M. N., Yousefi-Koma, A., and Fard, R. H. Static characterization and pull-in voltage of a micro-switch under both electrostatic and piezoelectric excitations. European Journal of Mechanics, A: Solids, 44, 116–124 (2014)
Huang, Y. T., Chen, H. L., and Hsu, W. An analytical model for calculating the pull-in voltage of micro cantilever beams subjected to tilted and curled effects. Microelectronic Engineering, 125, 73–77 (2014)
Zhang, J. and Fu, Y. Pull-in analysis of electrically actuated viscoelastic microbeams based on a modified couple stress theory. Meccanica, 47, 1649–1658 (2012)
Wang, B., Zhou, S., Zhao, J., and Chen, X. Size-dependent pull-in instability of electrostatically actuated microbeam-based MEMS. Journal of Micromechanics and Microengineering, 21, 027001 (2011)
Yang, J., Jia, X., and Kitipornchai, S. Pull-in instability of nano-switches using nonlocal elasticity theory. Journal of Physics, D: Applied Physics, 41, 035103 (2008)
Schrag, G., Kunzig, T., and Wachutka, G. Modeling reliablity issues in RFMEMS switches. International Conference on Simulation of Semiconductor Processes and Devices (SISPAD), Glasgow, 432–435 (2013)
Rebeiz, G. M. RF MEMS Theory, Design, and Technology, John Wiley and Sons, New York (2003)
Kong, S. Size effect on pull-in behavior of electrostatically actuated microbeams based on a modified couple stress theory. Applied Mathematical Modelling, 37, 7481–7488 (2013)
Zhang, Y. and Zhao, Y. P. Numerical and analytical study on the pull-in instability of microstructure under electrostatic loading. Sensors and Actuators, A: Physical, 127, 366–380 (2006)
Hu, Y. C. Closed form solutions for the pull-in voltage of micro curled beams subjected to electrostatic loads. Journal of Micromechanics and Microengineering, 16, 648–655 (2006)
Spiegel, M. R., Lipschutz, S., and Liu, J. Mathematical Handbook of Formulas and Tables, McGraw-Hill, New York (2009)
Hu, Y. C., Chang, C. M., and Huang, S. C. Some design considerations on the electrostatically actuated microstructures. Sensors and Actuators, A: Physical, 112, 155–161 (2004)
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 51505089 and 61204116), the Opening Project of the Science and Technology on Reliability Physics and Application Technology of Electronic Component Laboratory (Nos. ZHD201207 and 9140C030605140C03015), and the Pearl River S&T Nova Program of Guangzhou (No. 2014J2200086)
Rights and permissions
About this article
Cite this article
Zhu, J., Liu, R. Sensitivity analysis of pull-in voltage for RF MEMS switch based on modified couple stress theory. Appl. Math. Mech.-Engl. Ed. 36, 1555–1568 (2015). https://doi.org/10.1007/s10483-015-2005-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10483-015-2005-6
Keywords
- stepped cantilever beam
- pull-in voltage
- modified couple stress theory
- radio frequency (RF) micro electro-mechanical system (MEMS) switch
- analytical solution
- sensitivity analysis