Skip to main content Accessibility help
×
Home

Effect of Dielectric-Layer on the Stress Field of Micro Cantilever Beams at the Onset of Pull-In Instability

  • E. Yazdanpanahi (a1), A. Noghrehabadi (a1) and M. Ghalambaz (a1)

Abstract

In this paper, stress distribution of micro cantilever beams in the presence of a dielectric-layer is studied using an analytic method. The Modified Adomian Decomposition Method (MADM) is applied to obtain a semi-analytical solution for a distributed parameter model of the micro cantilever beam. The important parameters for designing and manufacturing micro-actuators such as shear force, bending moment and stress distribution along the cantilevers are computed for different values of the dielectric-layer parameter. The results of MADM are compared with the numerical results, and they found in good agreement. It is found that increase of the dielectric-layer parameter increases the dimensionless pull-in voltage, tip deflection, internal stress and bending moment of the micro cantilever actuators at the onset of pull-in instability.

Copyright

Corresponding author

References

Hide All
1.Toshiyoshi, H. and Chan, C. T., “Linearization of Electrostatically Actuated Surface Micromachined 2-D Optical Scanner,” Journal of Microelectrome-chanical Systems, 10, pp. 205214 (2001).
2.Degani, O. B., Socher, E. and Nemirovsky, Y., “On the Effect of Residual Charges on the Pull-In Parameters of Electrostatic Actuators,” Sensors and Actuators A, 97/98, pp. 563568 (2002).
3.Sattler, R., Plotz, F., Fattinger, G. and Wachutka, G., “Modeling of an Electrostatic Torsional Actuator: Demonstrated with an RF MEMS Switch,” Sensors and Actuators A, 97/98, pp. 337346 (2002).
4.Lin, W. H. and Zhao, Y. P., “Pull-in Instability of Micro-switch Actuators, Model Review,” International Journal of Nonlinear Sciences and Numerical Simulation, 9, pp. 175183 (2008).
5.Osterberg, P. M. and Senturia, S. D., “M-TEST: A Test Chip for MEMS Material Property Measurement Using Electrostatically Actuated Test Structures,” Journal of Microelectromechanical Systems, 6, pp. 257265 (1997).
6.Nathanson, H. C., Newell, W. E., Wickstrom, R. A. and Davis, J. R., “The Resonant Gate Transistor,” IEEE Transactions Electron Devices, 14, pp. 117–33 (1967).
7.Dec, A. and Suyama, K., “Micromachined Electro-Mechanically Tunable Capacitors and Their Applications to RF IC's,” IEEE Transactions on Microwave Theory and Techniques, 46, pp. 2587–96 (1998).
8.Chowdhury, S., Ahmadi, M. and Miller, W. C., “A Closed-Form Model for the Pull-In Voltage of Electrostatically Actuated Cantilever Beams,” Journal of Micromechanics and Microengineering, 15, pp. 756763 (2005).
9.Gorthi, S., Mohanty, A. and Chatterjee, A., “Cantilever Beam Electrostatic MEMS Actuators Beyond Pull-In,” Journal of Micromechanics and Microengineering, 16, pp. 18001810 (2006).
10.Legtenberg, R. and Gilbert, J., “Senturia SD and Elwenspoek M Electrostatic Curved Electrode Actuators.,” Journal of Microelectromechanical Systems, 6, pp. 257265 (1997).
11.Mullen, R. L., Mehregany, M., Omar, M. P. and Ko, W. H., “Theoretical Modeling of Boundary Conditions in Microfabricated Beams,” IEEE Micro Electro Mechanical Systems, 91, pp. 154159 (1991).
12.Chan, E. K., Garikipati, K. and Dutton, R. W., “Characterization of Contact Electromechanics Through Capacitance-Voltage Measurements and Simulations,” Journal of Microelectromechanical Systems, 8, pp. 208217 (1999).
13.Li, G. and Aluru, N. R., “Linear, Nonlinear and Mixed-Regime Analysis of Electrostatic MEMS,” Sensors and Actuators A, 91, pp. 278291 (2001).
14.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, pp. 7384 (2013)
15.Kuang, J. H. and Chen, C. J., “Adomian Decomposition Method Used for Solving Nonlinear Pull-In Behavior in Electrostatic Micro-Actuators,” Mathematical and Computer Modelling, 41, pp. 14791491 (2005).
16.Ghalambaz, M., Noghrehabadi, A., Abadyan, M., TadiBeni, Y., Noghrehabadi, A. R. and Noghre-habadi, M., “A New Power Series Solution on the Electrostatic Pull-In Instability of Nano Cantilever Actuators,” Procedia Engineering, 10, pp. 37163724 (2011).
17.Ghalambaz, M., Noghrehabadi, A., Abadyan, M., TadiBeni, Y., Noghrehabadi, A. R. and Noghre-habadi, M., “A Deflection of Nano-Cantilevers Using Monotone Solution,” Procedia Engineering, 10, pp. 37253732 (2011)
18.Soroush, A., Koochi, A., Kazemi, A. S., Noghre-habadi, A., Haddadpour, H. and Abadyan, M., “Investigating the Effect of Casimir and Van Der Waals Attractions on the Electrostatic Pull-In Instability of Nano-Actuators,” Journal of Physica Scripta, 82, p. 045801 (2010)
19.Koochi, A., Kazemi, A. S., Noghrehabadi, A., Yekrangi, A. and Abayan, M., “New Approach to Model the Buckling and Stable Length of Multi Walled Carbon Nanotube Probes Near Graphite Sheets,” International Journal of Materials and Design, 32, pp. 29492955 (2011).
20.Wazwaz, A. M., “A Reliable Modification of Adomian Decomposition Method,” Applied Mathematical Computer, 102, pp. 7786 (1999).
21.Adomian, G. and Rach, R., “Generalization of Adomian Polynomials to Functions of Several Variables,” Communications Mathematical Applied, 24, pp. 1124 (1992).
22.Makinde, O. D., “Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting Using Adomian Decomposition Method,” Applied Mathematical Computer, 186, pp. 1722 (2007).
23.Makinde, O. D., “Adomian Decomposition Approach to a SIR Epidemic Model with Constant Vaccination Strategy,” Applied Mathematical Computer, 184, pp. 842848 (2007).
24.TadiBeni, Y., Koochi, A. and Abadyan, M., “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, 43, pp. 979988 (2011).
25.Rollier, A. S., Legrand, B., Collard, D. and Buchaillot, L., “The Stability and Pull-In Voltage of Electrostatic Parallel-Plate Actuators in Liquid Solutions,” Journal of Micromechanics and Microengineering, 16, pp. 794801 (2006).
26.Yazdanpanahi, E., Noghrehabadi, A. and Ghalambaz, M., “Balance Dielectric Layer for Micro Electrostatic Switches in the Presence of Capillary Effect,” International Journal of Mechanical Sciences, 74, 8390 (2013)
27.Jonnalagadda, K., Chob, S. W., Chasiotisa, I., Friedmannc, T. and Sullivanc, J., “Effect of Intrinsic Stress Gradient on the Effective Mode-I Fracture Toughness of Amorphous Diamond-Like Carbon Films for MEMS,” Journal of Mechanics and Physics of Solids, 56, pp. 388401 (2008).
28.Witvrouw, A., Tilmans, H. A. C. and Wolf, I. D., “Materials Issues in the Processing, the Operation and the Reliability of MEMS,” Microelectronic Engineering, 76, pp. 245257 (2004).
29.Pugno, N., Peng, B. and Espinosa, H. D., “Predictions of Strength in MEMS Components with Defects — A Novel Experimental-Theoretical Approach,” International Journal of Solids and Structures, 42, pp. 647661 (2005).
30.Ke, C. H. and Espiona, H. D., “Nanoelectromechanical Systems (NEMS) and Modeling,” Handbook of Theoretical and Computional Nanotechnology, American Scientific Publishers, 121 (2006).
31.Ramezani, A., Alasty, A. and Akbari, J., “Closed-Form Approximation and Numerical Validation of the Influence of Van Der Waals Force on Electrostatic Cantilevers at Nano-Scale Separations,” Nanotechnology, 19, pp. 1550115511 (2008).
32.Sadeghian, H. and Rezazadeh, Gh., “Some Design Considerations on the Electrostatically Actuated Fixed-Fixed End Type MEMS Switches,” Journal of Physics: Conference Series, 34, pp. 174179 (2006).
33.Timoshenko, S., Theory of Plates and Shells, McGraw Hill, New York (1987).
34.Wazwaz, A. M., “A Comparison Between Adomian Decomposition Method and Taylor Series Method in the Series Solutions,” Applied Mathematical Computer, 97, pp. 37–14 (1998).
35.Fehlberg, E., “Low-Order Classical Runge-Kutta Formulas with Step Size Control and Their Application to Some Heat Transfer Problems,” NASA Technical Report, 315 (1969).
36.Fehlberg, E., “Klassische Runge-Kutta-Formeln vierter Und Niedrigerer Ordnung Mit Schrittweiten-Kontrolle Und Ihre Anwendung Auf Wärmeleitungsprobleme,” Computing, 6, pp. 6171 (1970).

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed