The combined effects of temperature and relative humidity on resonant frequency and quality factor of MEMS beam resonators in atmospheric pressure and gas rarefaction

In moist air, the combined effects of temperature and relative humidity become important to discuss on the resonant frequency and quality factor of micro-electro-mechanical systems (MEMS) cantilever and bridge beam resonators. The squeeze film damping (SFD), which is the dominant energy loss of MEMS resonators, is modeled by solving the modified molecular gas lubrication (MMGL) equation, transverse vibration of micro-beam, and their appropriate boundary conditions, simultaneously by the Finite Element Modelling (FEM) in the eigen-value problem. The effective viscosity of moist air (µ_eff) is utilized to modify the MMGL equation taking account the combined effects of temperature and relative humidity in a wide range of gas rarefaction conditions as surface accommodation coefficients (ACs (α₁ = α₂)). At atmospheric pressure (p = 101,325 Pa), the SFD, which is function of temperature and relative humidity, is more dominantly than that of the other energy losses such as the thermoelastic damping (TED) and the support loss of MEMS resonators. Thus, the combined effects of temperature (T) and relative humidity (RH) are discussed on the resonant frequencies and quality factors of MEMS beam resonators in atmospheric pressure, gas rarefaction (ACs), and resonator mode. The results showed that resonant frequencies and quality factors increase as temperature and relative humidity increase at atmospheric pressure. The combined effects of temperature and relative humidity on the resonant frequency of cantilever beam are stronger than that of bridge beam. The influence of the combined effects of temperature and relative humidity on resonant frequencies and its frequency shift of MEMS resonators reduces significantly because the dominant SFD decreases as gas rarefaction increases (ACs(α₁ = α₂) decrease), and the resonant mode increases.