MEMS Resonators: Numerical Modeling

The thermal stability of the natural frequency of a double-ended tuning-fork MicroElectroMechanical Systems (MEMS) resonator is studied for different orientations of the structure on the silicon wafer and for several doping levels of the single-crystal silicon. An intrinsic minimum for the frequency variation in temperature is found for each doping level and we prove that it is always possible to find the optimal orientation of the structure on the silicon wafer that allows to reach this minimum. The quality factor Q is another fundamental property to take into account during the design process of a MEMS resonator. We prove that the orientation of the mechanical structure on the silicon wafer and the doping level do not influence the Q significatively. An optimization procedure is proposed to maximize the Q by adding slots in the deformable arms of the resonating structure. The best geometry in terms of Q is combined with the best orientation of the structure in terms of thermal stability of the natural frequency and an optimal design for the DETF resonator is obtained. Two prototypes are fabricated and experimental tests are currently in progress.