Anchor Loss Variation in MEMS Wine-Glass Mode Disk Resonators Due to Fluctuating Fabrication Process

With increasing demand for high-frequency, high-quality factor (Q-factor) mechanical resonators, the Q-factor declining issue at high-frequency becomes increasingly prominent. This paper studies the performance variations of disk resonators under the wine-glass vibration mode due to the support beam offset that are caused by process deviations. The formula of the Q-factor in terms of the support loss is derived to further illustrate the change of the Q-factor caused by the beam offset. It is found that the impact of the extensional mode on the performance is more serious than that of the flexural mode, since the extensional mode may destruct the mode shape and decrease the radial size (i.e., amplitude) of the disk. Finally, some design methods on how to improve the Q-factor of the resonator are given. The numerical results show that there are, respectively, 0.07% and 13.7% increase in the resonant frequency and the disk radial size when the support beam offset is 4°, whereas the increase in the resonant frequency and the disk radial size becomes 0.96% and 69.8%, respectively, when the support beam offset reaches 16°. For the Q-factor, although the flexural-mode Q-factor, Q
_f
, increases with increasing support beam offset, the overall Q-factor of the resonator still decreases due to the dominant extensional-mode loss. In the worst case, the largest decline reaches 27.11% from the zero offset position (where there is only flexural-mode loss) to the 16° offset position.