J. Comp. & Math. Sci. Vol.3 (3), 288-293 (2012)
Pull-in Voltage Study of Microcantilever using ANSYS/Multiphysics and COMSOL/Multiphysics RAJESHWARI SHEEPARAMATTI1, S. V. HALSE2, K. M. VINAYAKA SWAMY1, SHIVASHANKAR A. HUDDAR1, and B. G. SHEEPARAMATTI1 1
Department of Electronics, Basaveshwar Engineering College, Bagalkot, INDIA 2 Department of Electronics, Karnataka State Women’s University, Bijapur, INDIA. (Received on: April 28, 2012) ABSTRACT The present work involves the study of the pull-in voltage of a MEMS electrostatic cantilever. This model analysis is done using ANSYS & COMSOL. This software allows the user to apply voltage stimuli, material properties and geometrical dimensions. The ANSYS & COMSOL model developed is able to measure the pull in voltage for various length, width & thickness. Impact of any combination of these geometrical parameters on the electro-mechanical system behavior that is, the voltage-electrode position dependence can be easily measured and are helpful for design decision making on the early design stages of this type of structures. This cantilever with appropriate modification can be made as switch, wherein electrodes and contact pads can be added. Keywords: Pull-in voltage, electrostatic cantilever, ANSYS, COMSOL.
1. INTRODUCTION MEMS actuators require low-input power, which can be provided by thermal, magnetic, piezoelectric, and electric actuations. However, the vast majority of devices have relied on electric actuation because of its high-energy density, high mechanical flexibility, and low-current requirement1. Topredict performance and
enable design optimization of such devices, a coupled electromechanical simulation is necessary. In general, this requires solving Laplace’s equation for the electrostatic field with certain boundary conditions. As the deformation of mechanical structures is unknown a prior, this problem usually prohibits an exact solution2,3. The commercial software such as COMSOL and ANSYS, where the mechanical structure is
Journal of Computer and Mathematical Sciences Vol. 3, Issue 3, 30 June, 2012 Pages (248-421)
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Rajeshwari Sheeparamatti, et al., J. Comp. & Math. Sci. Vol.3 (3), 288-293 (2012)
discretized using the finite-element method and the electric field is discretized using the boundary element method. 2. GEOMETRICAL MODELING
The cantilever of length (l), width (w) and of thickness (t) is modeled as shown in Figure 1.The electric potential is applied to the bottom surface of top electrode and bottom electrode is grounded with a gap (g).
Figure1. Geometric model of cantilever
When the cantilever is subjected to electrical potential, the capacitance is formed and the electric potential between the two plates leads to electrostatic force1. Therefore, one can change the displacement of the movable plate by controlling the applied voltage. When the gap between the two plates is decreased by one third the original gap, a pull-in (or snapdown) phenomenon occurs and drag the cantilever to the fixed electrode4-7, leading the gap to zero. In this paper an attempt has been made to calculate and simulate pull in for different geometry. Silicon is selected as material for the top electrode. The material properties of
the silicon accounted are young’s modulus (E=163GPa), Poisson’s ratio (v=0.23), density (Ď =2330 Kgm3). The analytical equation used to calculate pull-in voltage is given by equation (1)
ŕ°Ź
.
(1)
ŕ°Ź
Where g0 is the gap between two electrodes at zero voltage, K is spring constant of the beam and C0 is capacitance.
Figure 2. Microcantilever in COMSOL Journal of Computer and Mathematical Sciences Vol. 3, Issue 3, 30 June, 2012 Pages (248-421)
Rajeshwari Sheeparamatti, et al., J. Comp. & Math. Sci. Vol.3 (3), 288-293 (2012)
3. MODELING IN COMSOL The Figure 2 shows the developed Microcantilever in COMSOL. The top electrode where voltage is applied is separated by ground electrode by a gap of 2Âľm.
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The micro cantilever of length (l), width (w) and of thickness (t) is surrounded by air as dielectric medium is modeled in COMSOL multiphysics and in ANSYS and are respectively shown in Fig 2 and 4. Fig 3 and Fig.5 show the deflected cantilever due to applied voltage.
Figure 3. Microcantilever showing deflection due to applied voltage.
4. MODELING IN ANSYS The Figure 4 shows the developed micro cantilever in ANSYS. The top
electrode where voltage is applied is separated by grounded electrode by a gap of 2Âľm.
Figure 4. Microcantilever in ANSYS showing auto meshing. Journal of Computer and Mathematical Sciences Vol. 3, Issue 3, 30 June, 2012 Pages (248-421)
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Rajeshwari Sheeparamatti, et al., J. Comp. & Math. Sci. Vol.3 (3), 288-293 (2012)
Figure 5. Microcantilever showing deflection due to applied voltage.
5. RESULTS The graphs of pull-in versus length, width and thickness are plotted.
Fig. 6 The plot of pull in voltage versus length of the cantilever
Journal of Computer and Mathematical Sciences Vol. 3, Issue 3, 30 June, 2012 Pages (248-421)
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Fig. 7 The plot of pull in voltage versus width of the cantilever.
Fig. 6 shows that, with the increase in length of the beam the pull-in voltage decreases. Fig. 7 shows that the width of cantilever has no effect on pull in voltage. Fig. 8 shows that, with the increase in thickness of the
beam the pull in voltage increases. All the three results are in close agreement with each other. However, the results of ANSYS more closely match with analytical results.
Fig. 8 The plot of pull in voltage versus thickness of the cantilever Journal of Computer and Mathematical Sciences Vol. 3, Issue 3, 30 June, 2012 Pages (248-421)
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Fig. 9 shows that, with the increase in the gap between the beam and base of the beam, the pull in voltage increases. Thus, we can
conclude that increase in gap increases pullin voltage.
Fig 9 Variation of Pull-in Voltage as function of cantilever gap
6. CONCLUSION The voltage-deflection behavior of the micro cantilever is studied. The pulldown voltage of the actuator with long and movable electrode was found to be smaller than the actuator with short and fully anchored movable electrode. The pull-down voltage of the beam increases with the initial deflection of the cantilever. The behavior of model is predicted using both analytical model and finite element model. The simulation results are shown in Figures 6, 7, 8 and 9. Thus a cantilever with appropriate modification can be made as switch, wherein electrodes and contact pads can be added and this can be called as switch driven by electrostatic means.
2. 3. 4.
ACKNOWLEDGMENT Authors acknowledge the support of NPMASS (National program on micro and smart systems) of Govt. of India.
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REFERENCES 1. Stephen D. Senturia a text book of
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“Microsystem Design”, Kluwer Academic Publishers, (2002). www.comsol.com www.ansys.com Emmanuel Saucedo-Flores “Study of the Pull-In Voltage for MEMS Parallel Plate Capacitor Actuators”, MRS Materials Research Society Fall Meeting, Boston, Dec. 1-5 (2003). Anil K. Chinthakindi and Paul A. Kohl “Electrostatic Actuators with Intrinsic Stress Gradient”, Journal of the Electrochemical Society, 149(8) H146H152 (2002). J.I. Siddique “An experimental investigation of the theory of electrostatic deflections”, Journal of Electrostatics 69, 1e6 (2011). Rajeshwari Sheeparamatti, S V Halse, K.M Vinayaka Swamy, Shivashankar A Huddar, B G Sheeparamatti, “Study of Pull-in Voltage using ANSYS & COMSOL”, 9th International Workshop on Nanomechanical Sensing (NMC2012), IIT Bombay, Mumbai, India, June 6-8, (2012).
Journal of Computer and Mathematical Sciences Vol. 3, Issue 3, 30 June, 2012 Pages (248-421)