An improved analytical model for static pull-in voltage of a flexured MEMS switch

This paper presents the design of low-k meander based MEMS shunt capacitive switch with beam perforations. A closed form model to accurately calculate the pull-in voltage of the designed switch for two cases have been presented viz. a non-uniform meander based MEMS shunt switch and an uniform serpentine meander based MEMS shunt switch with perforated structure. The modified Mejis and Fokkema's capacitance model have been used to propose a generalized closed form expression for the pull-in voltage which takes care of the nonlinear electrostatic force on the switch as well. The proposed model also takes into account the fringing field effect due to beam thickness and etched holes on the beam. The model is validated by calculating the pull-in voltage for both the meander designs under variation of various design parameters. The results obtained under most design specification variation has been found out to be in the range of 1.5-2.3 V for uniform meander based MEMS shunt switch and 3.2-5.2 V for the non-uniform counterpart. The model based results have been further verified by comparison with simulated results of full 3D FEM solver CoventorWare in a wide range of structural parameter variations. It has been observed that the performance of the proposed model is reasonably satisfactory with an average deviation of 4.73% for uniform serpentine flexure and 3.65% for non-uniform flexure based switch.