Design of experiments based factorial design and response surface methodology for MEMS optimization

This paper presents the application of the design of experiments technique based factorial designs and response surface methodology (RSM) for optimization of MEMS devices. The RSM methodology is used to optimize the geometric parameters of the symmetric toggle RF MEMS switch to minimize the switch pull-in voltage. Fractional factorial based Plackett-Burman screening design is developed and the corresponding pull-in voltage is obtained, through finite element method (FEM) based simulations, for different combinations of the dimensional parameters. Analysis of variance is performed to distinguish the most significant parameters affecting the output response. The significant parameters, obtained using Plackett-Burman screening design, are further investigated using second order Box-Behnken design to obtain the optimal levels of the significant parameters and analyze their interactions. Regression analysis is carried out to check the adequacy of the Box-Behnkan based response surface model for predicting the output response. The effect of the significant parameters and their interactions on the pull-in voltage is analyzed through model based 3D surface and contour plots. The optimal levels of the parameters for a pull-in voltage 15 V, with compact device dimensions, are determined and verified through FEM simulations. A comparison is made for the results obtained through RSM with the analytical results presented in the literature. This showed a close agreement, verifying the practicability of this approach for the optimization of MEMS devices.