A novel method to predict the pull-in voltage in a closed form for micro-plates actuated by a distributed electrostatic force

Abstract

This study is devoted to finding the precise pull-in voltage/position of a micro-device formed by two parallel charged plates. Pull-in is a phenomenon where the electrostatic force induced by the applied voltage across two plates of the device exceeds the elastic, restoring force exerted by the deformed plates, leading to a contact between the two plates. To offer a precise prediction of the pull-in, a dynamic model in the form of a partial differential equation (PDE) is established based on the equilibrium among plate flexibility, residual stress and distributed electrostatic forces. The Galerkin method is employed to decompose the established PDE into discrete modal equations. By considering lower order modes and solving them, one arrives at a prediction of plate deflection in terms of the applied bias voltage. Approximating the solved deflection by a fifth-order series and full-order numerical integration, the pull-in position and voltage are successfully approximated. The pull-in position in terms of center deflection of the deformed plate is found to be 48% of the air gap between the plates, which presents a better estimation than the commonly used one-third of the gap derived by all past studies based on a less realistic one-dimensional lump model. A closed form of the pull-in voltage is derived to offer design guidelines for the device prior to production. The aforementioned theoretical findings are finally validated by finite element and experimental studies on a MEMS device of parallel charged micro-plates designed and fabricated in the laboratory.

Pull-in instability analysis of electrostatically actuated microplate with rectangular shape

“…1,[5][6][7][8][9] In the category of beam models, Younis et al 2 presented an analytical approach and a reduced-order model (macromodel) to investigate the behavior of electrically actuated microbeam-based MEMS. Then a consistent one-dimensional distributed electromechanical model of an electrically actuated narrow microbeam with width/height ratio between 0.5-2.0 was derived, and the pull-in parameters were extracted using several approaches, including a one-degree-of-freedom model, the Meshless Local Petrov-Galerkin (MLPG) and the finite element method (FEM).…”

“…Among previous efforts based on the plate models, 1,6,8,9 Zhao et al 6 studied the electrically actuated microplate using the hierarchical finite-element method (HFEM), Mukherjee et al 8 developed a fully Lagrangian approach of coupled analysis of MEMS plate, where FEM was employed to analyze mechanical deformation in the plate and the Boundary Element Method (BEM) was used to obtain the electric field outside the plate, Chao et al 1 derived a closed form solution of the pull-in voltage by employing the Galerkin method, Based on the classical von Kármán plate theory, Batra et al 9 considered the von Kármán nonlinearity and the Casimir force for developing reduced-order models of prestressed clamped rectangular and circular electrostatically actuated microplates.…”

Investigation of the nonlinear static and dynamic behaviour of rectangular microplates under electrostatic actuation

“…They have the capability to reveal the effect of different design parameters very conveniently. A common way to model the plate structures in MEMS devices is using the linear plate theory [11][12][13], which is correct when out of plane deflection is small. But in cases when the transverse deflection is comparable to the thickness of the plate, a strong geometric nonlinearity is present due to mid-plane stretching making the predications of linear theories erroneous.…”

Modeling of Pull-In Instability of Nano/Micromirrors Under the Combined Effect of Capillary and Casimir Forces

“…Their low manufacturing cost, batch production, light weight, small size, durability, low energy consumption, and compatibility with integrated circuits, makes them extremely attractive (Maluf and Williams 1999;Younis 2004). Successful MEMS devices rely not only on well developed fabrication technologies, but also on the knowledge of device behavior, based on which a favorable structure of the device can be forged (Chao et al 2006). The important role of MEMS devices in optical systems initiate the development of a new class of MEMS called MicroOptoElectroMechanical Systems (MOEMS).…”