Modeling and design of variable-geometry electrostatic microactuators

Abstract

We model and analyze the deflections and motions of a shaped microbeam in a capacitive-based MEMS device. The model accounts for the system nonlinearities including mid-plane stretching and electrostatic forcing. The differential quadrature method (DQM) is used to discretize the microbeam partial differential equation. It is shown that the use of 11 grid points in the DQM is sufficient to capture the response of the device. It is also observed that, unlike the shooting methods, DQM does not face the problems of system differential equations stiffness and solution sensitivity to the initial guess. The static response to a dc voltage is first determined to investigate the influence of varying the geometric parameters of the device on the range of travel and pull-in voltage. Analytical expressions approximating the range of travel and pull-in voltage, as functions of the capacitor gap size and microbeam width and thickness, are derived. Symmetric and asymmetric spatial distributions of these parameters are considered. For symmetric distribution, an increase (decrease) in the beam width and/or thickness at the middle with respect to those at the endpoints results in an increase (decrease) in the pull-in voltage and a decrease (increase) in the range of travel. An increase (decrease) in the gap size at the middle with respect to those at the endpoints results in an increase (decrease) in the pull-in voltage and an insignificant effect on the range of travel. The dynamic response of the microbeam to a dc voltage is also determined for various distributions of the microbeam width and thickness and the gap size. It is shown that decreasing the microbeam thickness at the middle is the most effective method to reduce the pull-in time.

A double microbeam MEMS ohmic switch for RF-applications with low actuation voltage

“…Static pull-in, identified by Nathanson et al [11], occurs when the DC voltage exceeds a threshold value. Studies on static pull-in reveal that the maximum static stable deflection varies from 33% to 41% of the original electrode gap distance [12,13].…”

Closed-form empirical relations to predict the static pull-in parameters of electrostatically actuated microcantilevers having linear width variation

“…In this connection, Cheng et al (2004) analyzed the electromechanical response of rigid torsional electrodes having elliptic, parabolic and hyperbolic width variations, and inferred that the onset of pull-in instability can be substantially delayed by suitably varying the actuator width. Later, the investigations reported by Abdalla et al (2005), Najar et al (2005), Raulli and Maute (2005), Lemaire et al (2008), and Joglekar and Pawaskar (2009) substantiated this inference for the cases involving deformable electrodes. In other instance, geometrical alterations to the referential prismatic beam have been exploited to enhance the sensitivity of biosensors (Chen and Yu 2007;Ansari and Cho 2009), and passive tuning of the eigenfrequencies of AFM optical levers (Rinaldi et al 2008).…”

Reducing Pull-In Voltage by Adjusting Gap Shape in Electrostatically Actuated Cantilever and Fixed-Fixed Beams

“…The beam must contact these structures as deflection occurs, which may not be possible or desirable. Other designs with variable geometry have been presented [7,8], but not with the intention of finding specific shapes to reduce the pull-in voltage for a given required displacement.…”