Analysis of frequency stability and thermoelastic effects for slotted tuning fork MEMS resonators

MicroElectroMechanical Systems (MEMS) resonators are attracting increasing interest because of their smaller size and better integrability as opposed to their quartz counterparts. However, thermal drift of the natural frequency of silicon structures is one of the main issues that has hindered the development of MEMS resonators. Extensive investigations have addressed both the fabrication process (e.g., introducing heavy doping of the silicon) and the mechanical design (e.g., exploiting proper orientation of the device, slots, nonlinearities). In this work, starting from experimental data published in the literature, we show that a careful design can help reduce the thermal drift even when slots are inserted in the devices in order to decrease thermoelastic losses. A custom numerical code able to predict the dynamic behavior of MEMS resonators for different materials, orientations and doping levels is coupled with an evolutionary optimization algorithm and the possibility to find an optimal mechanical design is demonstrated on a tuning-fork resonator.