Air Damping in a Fan-Shaped Rotational Resonator with Comb Electrodes

Abstract

We theoretically and experimentally evaluated the damping effect in a rotational resonator with a comb-drive actuator and sensor. The resonator was fabricated from an SOI wafer and has a fan-shaped mass. The underlying substrate was removed using back side deep reactive ion etching. One set of comb electrodes was attached to each side of the mass: one for electrostatic driving and the other for capacitive detection. In our theoretical analysis, the dynamics of the resonator were simplified so that they could be represented by a lumped system. In this lumped system, the damping coefficient was estimated by assuming the damping to be slide film damping and the air flow to be a Stokes flow. The phase shift due to the slide film damping of thick air layers was included in the lumped system. In the experimental evaluation, one side of the rotational combs was removed step-by-step and a half of the mass using a laser trimming tool so that the individual damping effects caused by the comb electrodes and mass could be determined quantitatively. We compared the experimental results with the results of the theoretical analysis and found that the difference in the damping coefficients between the experimental results and results of the theoretical analysis was less than 40%.