Abstract
In this study, a new analytical model is developed for an electrostatic Microelectromechanical System (MEMS) cantilever actuator to establish a relation between the displacement of its tip and the applied voltage. The proposed model defines the micro-cantilever as a rigid beam supported by a hinge at the fixed-end with a spring point force balancing the structure. The approach of the model is based on calculation of the electrostatic pressure centroid on the cantilever beam to localize the equivalent electrostatic point load. Principle outcome of the model is just one formula valid for all displacements ranging from the initial to the pull-in limit position. Our model also shows that the pull-in limit position of a cantilever is approximately 44% of the initial gap. This result agrees well with both simulation results and experimental measurements reported previously. The formula has been validated by comparing the results with former empirical studies. For displacements close to the pull-in limit, the percentage errors of the formula are within 1% when compared with real measurements carried out by previous studies. The formula also gives close results (less than 4%) when compared to simulation outcomes obtained by finite element analysis. In addition, the proposed formula measures up to numerical solutions obtained from several distributed models which demand recursive solutions in structural and electrostatic domains.
Highlights
Electrostatic cantilevers have been very popular due to their low-power requirements, small dimensions, and ease of fabrication
The percentage errors of the formula are within 1% when constraint of the fixed-end of the upper beam, our model takes the zero-displacement constraint compared to simulation results of various different cantilever structures for displacements close to into account and neglects the zero-angle constraint
We propose a new model named as the pivot model in order to get a good estimation of the system without requiring substantial computing power
Summary
Electrostatic cantilevers have been very popular due to their low-power requirements, small dimensions, and ease of fabrication. A comparatively ordinary closed-form analytical approach model formula for the capacitance of a VLSI on-chip interconnect They derived a linear and uniform has been studied with errors in [28] as well. Themodel, same which modelconsiders cannot be for the ordinary cantilever structures (OCS) which constraint of the fixed-end of the upper beam, our model takes the zero-displacement constraint into have the matching top and bottom electrode dimensions to get the similar error levels. The percentage errors of the formula are within 1% when constraint of the fixed-end of the upper beam, our model takes the zero-displacement constraint compared to simulation results of various different cantilever structures for displacements close to into account and neglects the zero-angle constraint. Proposed model computing measures up to numerical results obtained from different distributed models while using lower computing efforts
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