Influences of relative humidity on the quality factors of MEMS cantilever resonators in gas rarefaction

In this paper, the effect of relative humidity of moist air is discussed on the quality factor (Q factor) of micro-electro-mechanical systems (MEMS) cantilever resonators in wide range of gas rarefaction (ambient pressure and accommodation coefficients, ACs). The modified molecular gas lubrication (MMGL) equation is used to model the squeeze film damping problem of MEMS cantilever resonators. Dynamic viscosity and Poiseuille flow rate are used to modify the MMGL equation to consider the coupled effects of relative humidity and gas rarefaction. Thermoelastic damping and anchor loss, which are dominant damping mechanisms of MEMS cantilever resonators, are also included to calculate total Q factor. Thus, the influences of relative humidity are discussed on the Q factors of MEMS cantilever resonators in wide range of gas rarefaction and dimension of cantilever. The results showed that the Q factor decreases as relative humidity increases in wide range of gas rarefaction (pressure, and ACs) and dimension of cantilever (length, width, and thickness). The influences of relative humidity on the Q factor become more significantly in larger length, larger width, smaller thickness of cantilever, and higher gas rarefaction (lower pressure and ACs). Whereas, the influences of relative humidity on the Q factor reduce or are neglected in smaller length, larger thickness of cantilever and lower gas rarefaction (higher pressure and ACs).