Effect of gas rarefaction on the quality factors of micro-beam resonators

The external squeeze film damping (SFD) of microelectromechanical systems (MEMS) resonators is a dominant factor to lower the quality factor (Q-factor) due to their large surface area to volume ratio and small spacing. To improve the Q-factor of MEMS resonators, the effect of gas rarefaction (low gas ambient pressure in thin gas film thickness) or operating in higher mode should be considered in SFD analysis. The modified molecular gas lubrication (MMGL) equation is applied for modeling the SFD with gas rarefaction effects taken into consideration. The effects of inverse Knudsen number, surface accommodation coefficients (ACs) and operating frequency on SFD are discussed. The combined effects of SFD, thermoelastic damping (TED) and anchor loss on the total Q-factors of MEMS resonators are considered. The contribution of SFD on the total Q-factor (weighting of SFD) is also discussed. The results show that weighting of SFD could be decrease at low inverse Knudsen number or low ACs or operating at high resonant frequencies.