Pull-In Analysis of Torsional Scanners Actuated by Electrostatic Vertical Combdrives

This paper presents pull-in analysis of torsional MEMS scanners actuated by electrostatic vertical combdrives with general comb gap arrangements and cross sections. The analysis is based on a 2-DOF actuator with a single voltage control. Three failure modes of the scanners are identified as in-plane twist, transversal motion, and out-of-plane twist. For each failure mode, analytical expressions of pull-in deflection are obtained by applying 2D analytical capacitance models to the derived pull-in equations. From these, the dominant pull-in mechanism is shown to be in-plane twist for scanners with high-aspect-ratio torsional springs. The analytical calculations for both symmetric and asymmetric capacitances are shown to be in good agreement with simulation results. The optimum scanner design is achieved when the pull-in deflection matches the capacitance maximum angle. The condition can be expressed in terms of the ratio of the comb thickness to the comb gap, which is smaller than the typical aspect ratio of deep reactive ion etching. The optimum tradeoff between the maximum deflection angle and the number of movable combs is achieved by adjusting the overlap of the movable and fixed combs and the distance of the comb sets from the axis of the rotation.