Novel analytical model for optimizing the pull-in voltage in a flexured MEMS switch incorporating beam perforation effect

Abstract This paper presents a new method for the design, modelling and optimization of a uniform serpentine meander based MEMS shunt capacitive switch with perforation on upper beam. The new approach is proposed to improve the Pull-in Voltage performance in a MEMS switch. First a new analytical model of the Pull-in Voltage is proposed using the modified Mejis-Fokkema capacitance model taking care of the nonlinear electrostatic force, the fringing field effect due to beam thickness and etched holes on the beam simultaneously followed by the validation of same with the simulated results of benchmark full 3D FEM solver CoventorWare in a wide range of structural parameter variations. It shows a good agreement with the simulated results. Secondly, an optimization method is presented to determine the optimum configuration of switch for achieving minimum Pull-in voltage considering the proposed analytical mode as objective function. Some high performance Evolutionary Optimization Algorithms have been utilized to obtain the optimum dimensions with less computational cost and complexity. Upon comparing the applied algorithms between each other, the Dragonfly Algorithm is found to be most suitable in terms of minimum Pull-in voltage and higher convergence speed. Optimized values are validated against the simulated results of CoventorWare which shows a very satisfactory results with a small deviation of 0.223 V. In addition to these, the paper proposes, for the first time, a novel algorithmic approach for uniform arrangement of square holes in a given beam area of RF MEMS switch for perforation. The algorithm dynamically accommodates all the square holes within a given beam area such that the maximum space is utilized. This automated arrangement of perforation holes will further improve the computational complexity and design accuracy of the complex design of perforated MEMS switch.

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