Mode selection for electrostatic beam resonators based on motional resistance and quality factor.

An analytical comparison between the fundamental mode and higher modes of vibration for an electrostatic beam resonator is presented. Multiple mode numbers can be matched to a desired resonance frequency through appropriate scaling. Therefore, it is important to determine which mode yields the best performance. A dynamic model of the resonator is derived and then used to determine the motional resistance for each mode. The resulting equation provides the basis for comparing performance between modes using motional resistance and quality factor. As a demonstration of the approach, a quality factor model that has been previously validated experimentally is introduced. Numerical results for silicon resonators indicate that the fundamental mode can provide a lower motional resistance and higher quality factor when the resonators under comparison have the same aspect ratio or the same stiffness.