Effects of surface roughness and gas rarefaction on the quality factor of micro-beam resonators

In this paper, the average modified molecular gas lubrication (MMGL) equation is utilized to analyze the squeeze film damping (SFD) of micro-beam resonators. Under thin gas film spacing and low ambient pressure conditions, the effects of surface roughness and gas rarefaction become important due to their larger surface area to volume ratio. The external SFD and the combined structural damping [thermoelastic damping (TED) and anchor loss] are studied on the quality factor (Q-factor) of micro-beam resonators. The coupling effects of surface roughness and gas rarefaction on SFD are discussed. The results show that the effects of surface roughness are diluted by the gas rarefaction. The Q-factor of micro-beam resonators depends significantly on surface roughness (film thickness ratio, Peklenik number) in higher gas rarefaction (low ambient pressure, low accommodation coefficients) and/or higher modes of the resonators.