Influences of temperature on the quality factors of micro-beam resonators in gas rarefaction

Abstract

In this study, the effect of temperature on the quality factor (Q-factor) of a micro-beam resonator is analyzed in a wide range of gas rarefaction conditions (ambient pressure and accommodation coefficients (ACs)). Squeeze film damping (SFD), thermoelastic damping (TED), and anchor loss, which are dominant damping mechanisms of micro-beam resonators, are included in the total Q-factor. The increase in the mean free path of gas with temperature is more significant than that of the gas viscosity in high gas rarefaction. Thus, the effect of temperature in gas rarefaction is discussed to improve the Q-factors of the resonators. The modified molecular gas lubrication (MMGL) equation is utilized to model SFD. Dynamic viscosity and Poiseuille flow rate are used to modify the MMGL equation considering the coupled effects of temperature and gas rarefaction. Finally, the effect of temperature on the Q-factors is discussed under various gas rarefaction conditions (pressure and ACs), types of gases and resonator modes. The results show that the Q-factor increases with temperature in higher gas rarefaction (lower pressure and ACs), whereas the Q-factor decreases as temperature increases in lower gas rarefaction (higher pressure and ACs). The decrease in the Q-factor with temperature is improved by the gas rarefaction effect. Furthermore, the Q-factor of a micro-beam resonator increases considerably with temperature by using hydrogen in higher gas rarefaction and the 1st mode of the resonator.