Temperature Dependence Modeling and Thermal Sensitivity Reduction of Bulk Micromachined Silicon MEMS Lame Resonators

The elastic properties of structural materials con-siderably influence the resonant frequency of silicon MEMS resonators and their sensitivity to temperature variations. This work studies the effect of several methods on the temperature coefficient of frequency (TCF) of bulk micromachined silicon Lame resonators. These include depositing a thin silicon oxide layer onto the resonating structure, including holes within the structure, and modifying the crystalline orientation of the structural layer. Devices variants are fabricated in a standard fabrication process (PiezoMUMPs by MEMSCAP) and are characterized with respect to their temperature dependence. An analytical model is proposed to predict the effects of each of the studied design variations on the resonant frequency and the temperature stability of the devices, and the results stemming from the model agree with the experimental measurements. It is found that a 45-degree rotated Lame resonator with holes and a top oxide layer exhibits a 31.7% improvement in total TCF in comparison to a simple Lame resonator structure without rotation. This results in a 51.9% frequency drift reduction over a temperature range of 30 degrees C to 100 degrees C in comparison to a conventional structure.