Effects of humidity and temperature on quality factor of micro-beam resonators in atmospheric pressure and gas rarefaction

At atmospheric pressure (p=101325 Pa), the effects of humidity and temperature on moist air become important when discussing the quality factor of micro-cantilever and micro-bridge resonators. The squeeze film damping (SFD) problem, the dominant damping source for micro-beam resonators, is modelled using the modified molecular gas lubrication (MMGL) equation with finite element modelling (FEM) in the eigenvalue problem. The MMGL equation is modified with the effective viscosity of moist air (µeff) to account for the effects of humidity and temperature. Other damping sources, such as thermoelastic damping (TED) and the support loss of micro-beam resonators, are also calculated. The quality factor of micro-beam resonators is then discussed over a wide range of temperatures and relative humidity levels at atmospheric pressure and gas rarefaction. The results show that the quality factor of micro-cantilever and micro-bridge resonators increases as both humidity and temperature rise in atmospheric pressure and gas rarefaction. Furthermore, the quality factor of a micro-bridge resonator with changes in humidity and temperature is significantly higher than that of a micro-cantilever resonator in atmospheric pressure and gas rarefaction.