Application of the generalized differential quadrature method to the study of pull-in phenomena of MEMS switches

Journal of Microelectromechanical Systems

Volumn 16, Issue 6, 2007, Pages 1334-1340

  Sadeghian, Hamed ^a   Rezazadeh, Ghader ^b   Osterberg, Peter M ^c  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b URMIA UNIVERSITY   (Iran)

^c UNIVERSITY OF PORTLAND   (United States)

Author keywords

Approximation methods; Electromechanical coupled system; Electrostatic actuators; Generalized differential quadrature method (GDQM); Microelectromechanical systems (MEMS) switch; Microswitches; Pull in voltage; Voltage

Indexed keywords

APPROXIMATION THEORY; CANTILEVER BEAMS; ELECTROSTATIC ACTUATORS; INTEGRODIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; RESIDUAL STRESSES; SWITCHES;

DIFFERENTIAL QUADRATURE METHOD; MICROSWITCHES; NONLINEAR MICROELECTROMECHANICAL COUPLED SYSTEMS; PULL-IN VOLTAGE;

MEMS;

EID: 36949015590     PISSN: 10577157     EISSN: None     Source Type: Journal    
DOI: 10.1109/JMEMS.2007.909237     Document Type: Article

References (28)

1. S. Senturia, Microsystem Design. Norwell, MA: Kluwer, 2001.
2. J. I. Seeger and S. B. Crary, "Stabilization of electrostatically actuated mechanical devices," in Proc. Transducers, 1997, pp. 1133-1136.
3. P. M. Osterberg, H. Yie, X. Cai, J. White, and S. Senturia, "Self-consistent simulation and modelling of electrostatically deformed diaphragms," in Proc. IEEE Conf. Micro Electro Mech. Syst., Osio, Japan, Feb. 25-28, 1994, pp. 28-32.
4. J. R. Gilbert, R. Legtenberg, and S. D. Senturia, "3D coupled electro-mechanics for MEMS: Applications of CoSolve-EM," in Proc. MIMS, Amsterdam, The Netherlands, Feb. 1995, pp. 122-127.
5. R. Legtenberg, J. Gilbert, S. Senturia, and M. Elwenspoek, "Electrostatic curved electrode actuators," J. Microelectromech. Syst., vol. 6, no. 3, pp. 257-265, Sep. 1997.
6. E. S. Hung and S. D. Senturia, "Leveraged bending for full-gap positioning with electrostatic actuation," in Proc. Solid-State Sens., Actuator Workshop, Hilton Head, SC, 1998, pp. 83-86.
7. E. S. Hung and S. D. Senturia, "Extending the travel range of analog-tuned electrostatic actuators," J. Microelectromech. Syst. vol. 8, no. 4, pp. 497-505, Dec. 1999.
8. H. Sadeghian and G. Rezazadeh, "Some design considerations on the electrostatically actuated fixed-fixed end type MEMS switches," J. Phys.: Conf. Ser., vol. 34, pp. 174-179, 2006.
9. H. Sadeghian and G. Rezazadeh, "The influence of stress gradient on the pull-in phenomena of microelectromechanical switches," J. Phys.: Conf. Ser., vol. 34, pp. 1117-1122, 2006.
10. H. Sadeghian G. Rezazadeh, E. Malekpour, and A. Shafipour, "Pull-in voltage of fixed-fixed end type MEMS switches with variative electrostatic area," Sens. Transducers, vol. 66, no. 4, pp. 526-533, Apr. 2006.
11. G. Rezazadeh, H. Sadeghian, and E. Abbaspour, "A comprehensive model to study nonlinear behaviour of multilayered micro beam switches," Microsyst. Technol., vol. 14, no. 1, p. 143, 2008. DOI: 10.1007/s00542-007-0404-3.
12. G. Rezazadeh, "A comprehensive model to study nonlinear behaviour of multilayered micro beam switches," Microsyst. Technol., vol. 14, no. 1, pp. 135-141, 2008. DOI: 10.1007/s00542-007-0398-x.
13. S. Pamidighantam, R. Puers, K. Baert, and H. A. C. Tilmans, "Pull-in voltage analysis of electrostatically actuated beam structures with fixed-fixed and fixed-free end conditions," J. Micromech. Microeng. vol. 12, no. 4, pp. 458-464, Jul. 2002.
14. Y. Nemirovsky and O. Bochobza-Degani, "A methodology and model for the pull-in parameters of electrostatic actuators," J. Microelectromech. Syst., vol. 10, no. 4, pp. 601-615, Dec. 2001.
15. L. X. Zhang and Y.-P. Zhao, "Electromechanical model of RF MEMS switches," Microsyst. Technol., vol. 9, no. 6/7, pp. 420-426, Sep. 2003.
16. R. E. Bellman, B. G. Kashef, and J. Casti, "Differential quadrature: A technique for the rapid solution of nonlinear partial differential equations," J. Comput. Phys., vol. 10, no. 1, pp. 40-52, Aug. 1972.
17. F. Civan and C. M. Sliepcevich, "Differential quadrature for multidimensional problems," J. Math. Anal. Appl., vol. 101, no. 2, pp. 423-443, Jul. 1984.
18. C. Shu and B. E. Richards, "Parallel simulation of incompressible viscous flows by generalized differential quadrature," Comput. Syst. Eng., vol. 3, no.1-4, pp. 271-281, 1992.
19. J. Y. Park, G. H. Kim, K. W. Chung, and B. Ju, "Monolithically integrated micromachined RF MEMS capacitive switches," Sens. Actuators A, Phys., vol. 89, no. 1/2, pp. 88-94, Mar. 2001.
20. E. S. Hung and S. D. Senturia, "Generating efficient dynamical models for microelectromechanical systems from a few finite-element simulation runs," J. Microelectromech. Syst., vol. 8, no. 3, pp. 280-289, Sep. 1999.
21. S. D. Senturia, "Microfabricated structures for the measurement of mechanical properties and adhesion of thin films," in Proc. Transducers, Tokyo, Japan, 1987, pp. 11-16.
22. J. Qian, C. Liu, D. C. Zhang, and Y. P. Zhao, "Residual stresses in microelectro-mechanical systems," J. Mech. Strength - Special Issue MEMS, vol. 23, no. 4, pp. 393-401, 2001. (in Chinese).
23. R. K. Gupta, "Electrostatic pull-in test structure design for in-situ mechanical property measurements of microelectromechanical systems (MEMS)," Ph.D. dissertation, MIT, Cambridge, MA, 1997.
24. T. Mukherjee, G. K. Fedder, and R. D. Blanton, "Hierarchical design and test of integrated microsystems," IEEE Des. Test Comput., vol. 16, no. 4, pp. 18-27, Oct.-Dec. 1999.
25. W. Chen, C. Shu, W. He, and T. Zhong, "The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates," Comput. Struct., vol. 74, no. 1, pp. 65-76, Jan. 2000.
26. X. Wang and C. W. Bert, "A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates," J. Sound Vib., vol. 162, no. 3, pp. 566-572, Apr. 1993.
27. Y. C. Hu, C. M. Chang, and S. C. Huang, "Some design considerations on the electrostatically actuated microstructures," Sens. Actuators A, Phys., vol. 112, no. 1, pp. 155-161, Apr. 2004.
28. P. M. Osterberg and S. Senturia, "M-TEST: A test chip for MEMS material property measurement using electrostatically actuated test structures," J. Microelectromech. Syst., vol. 6, no. 2, pp. 107-118, Jun. 1997.