Electrostatic Actuators with Intrinsic Stress Gradient

Electrostatic actuators are used as voltage-controlled oscillators or resonators in high frequency applications. The change in deflection of a cantilever beam due to an applied voltage leads to change in capacitance between the plates of the beam. However, the range of operation of these devices is limited due to the nonlinear nature of the applied electrostatic forces as the cantilever beam moves. The pull-down instability of the beam limits the travel distance of elastically suspended parallel-plate electrostatic actuators to about one-third of the initial gap distance. The movement of curved actuators under application of an electrostatic force is investigated. The initial curvature of the movable electrode was established by using a built-in stress gradient in the metallic cantilever-beam. A two-dimensional, semi-analytical, finite difference model was used to simulate the behavior of the devices. Three-dimensional modeling was also performed to understand the movement of the cantilever beams. The pull-down voltage of the beams was studied as a function of initial tip deflection, shape of the movable electrode, and anchor type. The stable range of operation of these cantilever beams before pull-down was found to be smaller than one third of the tip deflection. After pull-down, the movable electrode was found to uncurl upon further application of voltage. This was attributed to the higher order curvature of the movable electrode with large built-in stress gradient.