Theoretical Analysis of Cantilever Motion under Electrostatic Force

Abstract

A motion of an electrostatic micromechanism with a cantilever movable electrode and a counter fixed electrode was studied theoretically by using the Rayleigh-Ritz method. As trial functions which express deformation states of the movable electrode approximately, deflection lines under applications of various uniform loads to the movable electrode were selected. In non-contact states of the movable electrode with the counter electrode, a hysteresis was confirmed in displacement (of the movable electrode)-applied voltage (between the both electrodes) curves of a voltage increasing and a voltage decreasing process. In contact states of the both electrodes, a hysteresis didn't appear in contact area-voltage curves and a threshold voltage above which a contact area increases rapidly with an increase of the applied voltage was derived. The threshold voltage, which determines an operation voltage of the mechanism, was almost proportional to L^-2, T^3/2 and d₀ (L, T: the length and the thickness of the movable electrode, respectedly, d₀: the gap width between the movable and the counter electrode).