Effect of Environmental Conditions on Quality Factors of MEMS Cantilever Beam Resonator in Gas Rarefaction

This paper discussed the effect of environmental conditions (moisture and temperature) on the quality factors (Q-factor) of micro-electro-mechanical systems (MEMS) cantilever beam resonators in wide range of gas rarefaction (pressure (p), and accommodation coefficients (ACs)), and flexural mode of resonator. The modified molecular gas lubrication (MMGL) equation is applied for modeling the dominant squeeze film damping (SFD) problem on the quality factor of MEMS cantilever beam resonators to discuss the effect of environmental conditions. The external SFD and the internal structure damping (thermoelastic damping) and support loss) are accurately taken into account. Effective viscosity, which is ratio of dynamic viscosity and Poiseuille flow rate of moist air, is utilized to modify the MMGL equation to consider the environmental effects of moisture and temperature in gas rarefaction. In low pressures, mean free path changes more significantly with relative humidity and temperature than that of dynamic viscosity of moisture in gas rarefaction. Thus, effect of environmental conditions such as moisture and temperature must be discussed to improve Q-factors of MEMS cantilever beam resonators in wide range of gas rarefaction (p and ACs) and flexural modes of resonator. The results showed that Q-factor of SFD decreases significantly as moisture and temperature increase at higher gas rarefaction (lower p, and ACs), while Q-factor of SFD decreases and then increases slightly as moisture and temperature increase at lower gas rarefaction (higher p, and ACs). The total Q-factor is highly sensitive to the relative humidity and temperature in higher gas rarefaction (lower p and ACs) and lower flexural modes of resonator.