New Analytical Capacitance Modeling of the Perforated Switch Considering the Fringing Effect

Movable suspended microstructures are common features of sensors and devices in the field of micro electro mechanical systems (MEMS). This paper addresses the study of approach to model the capacitance for the crab-type meander-based RF MEMS shunt switch with etching holes on the beam. The presented paper evaluates the parallel-plate capacitance and fringing-field capacitance caused by the etching holes on the beam and introduces empirical formulae. From the literature study, an accurate empirical formula is presented. The capacitance involves a parallel plate and a fringing field. The parallel-plate capacitance term is proposed by the authors of this work; the fringing-field capacitance term is adopted from previous work. The proposed accurate empirical capacitance formulae are derived by curve fitting the simulated values through the commercially available FEM solver. The two existing benchmark models of fringing-field capacitance are used to modify the perforated MEMS switch to obtain the proposed formula. With the existing models and presented formula, the capacitances are computed for a wide range of dimensions; the simulated results of the presented formula are validated with the calculated results. The deviation of the presented formula has an error estimation of ±0.1%. The variation of the capacitance with different deictic thicknesses and errors is estimated and analyzed for the presented formula. The Mejis model is found to be satisfactory for a lower air gap and a 1-
$\mu \text{m}$
-thick beam. The Yang’s model is sufficient for a higher air gap and a large number of etching holes. The proposed formulae are good for the ligament efficiency
$\mu \le 0.5$
, with thickness
$> 1~\mu \text{m}$
, and the deviation of error estimation is within ±5%.