Theoretical and Numerical Studies of the Air Damping of Micro-Resonators in the Non-Continuum Regime

Abstract

Micromechanical resonators are used in a variety of sensing and filtering applications. In these applications, the accurate performance of micro resonators depends on the sensitivity of these devices to a particular resonance frequency. This sensitivity is measured using the quality factor Q, which is the ratio of the total input energy into the device to the energy dissipated within a vibration cycle. A higher quality factor indicates a smaller resonance bandwidth, which makes the micro-resonator more effective in identifying a desired signal. Higher Q values result from reductions in dissipation losses. Dissipation losses occur through damping by the ambient fluid, anchor losses, thermoelastic damping, and other sources. The squeeze-film effect is of particular interest in micro-resonators as the fluid enclosed between the resonating components can provide significant dissipation.

This work covers investigations into the air damping of oscillating micromachined resonators that operate near a fixed wall, which is parallel to the oscillating surface. The main portion of this work focuses on the theoretical and numerical investigation of the air damping of micromachined resonators when the surrounding gas (air) is in the Free-Molecule regime. Errors and limitations of previous theoretical models have been found and corrected. A molecular dynamics simulation code that is suitable to handle a more general class of resonators has been developed. This code has been used to find the quality factor of a microbeam resonator. The results from the code were compared to existing experimental results, and were found to have very good agreement in the free molecular regime. The simulation was then used to investigate the effects of the oscillation mechanics on the energy dissipation and quality factor.

The second part of this work focuses on the region between the bottom surface of a laterally-oscillating disk resonator and the substrate. The compressibility effects of a 1 micron thick film of air on a laterally-oscillating disk resonator were investigated. The pressure perturbation for this case was found to be minimal, which means that the compressibility effects of the fluid film will negligible.