Numerical and analytical modelling of holed MEMS resonators
Résumé
After consistently progress in Micro-Electro-Mechanical (MEM) resonators, Silicon oscillators are finally being commercialized for time and frequency control applications not requiring huge frequency accuracy. Indeed, they offer size reduction, potentially low cost and CMOS integration. However, frequency shift because of holes, unavoidable for MEMS release or damping effects, is still one of the challenges to address high frequency accuracy applications. In this article, we present the mechanical modelling of holed clamped-clamped (CC) beam resonators. An analytical and a numerical model have been developed to obtain the frequency variations due to holes onto resonant structures. We note a good agreement between both models, presenting less than 1.5% of deviation. We also report the manufacturing of holed clamped-clamped beam resonators in only six major steps using compatible CMOS process. Electrical tests have been performed to check the functionality of our structures. Finally, electrical measurements and analytical model have been compared and a discrepancy less than 0.4% is reported. Analytical models validation enables designers to benefit from a powerful vibrating MEMS design tool, including the influence of holes onto resonant structures for any kinds of applications from sensors to actuators and oscillators.