A new analysis of reciprocated beam bending in electrostatic comb drives using a semi-analytical approach

This paper investigates a new modeling and analysis of the voltage induced reciprocated beam bending effects in the unit cell of a planar, variable gap type, capacitive comb drive structures. A semi-analytical approach has been efficiently formulated to solve this coupled electromechanical problem under a steady state condition. The effect of fringe field is also incorporated to improvise on the accuracy of the solution. Additionally, an energy-based method as well as a finite element (FE) based model has been constructed to simulate and validate the semi-analytical approach. The results show that the reciprocated bending of the beams has significant effects on the performance parameters like displacement, capacitance and pull-in characteristics in the comb drive systems. This effect is also seen to vary with applied voltage and stiffness of the combs and springs. Further, a comparison with conventional lumped model shows considerable difference in the estimated values for different parameters indicating a more practical prediction through the proposed approach. Finally, a set of design guidelines is discussed to reduce this bending, so that its effects on the performance of comb drive systems can be minimized.