Effects of temperature and relative humidity on resonant frequency of mems cantilever resonators under atmospheric pressure

In this study, the effects of temperature and relative humidity on the resonant frequency of a micro-electro-mechanical system (MEMS) cantilever resonator under atmospheric pressure (p=101325 Pa) are discussed. The squeeze film damping (SFD) problem of MEMS cantilever resonators is modeled by solving the modified molecular gas lubrication (MMGL) equation, the equation of motion of micro-cantilever, and their appropriate boundary conditions, simultaneously in the eigen-value problem. The effective viscosity (µeff(RH, T)) of moist air is utilized to modify the MMGL equation to consider the effects of temperature and relative humidity under atmospheric pressure. Thus, the effects of temperature (T) and relative humidity (RH) on the resonant frequency of MEMS cantilever resonators over a wide range of gap thicknesses and under atmospheric pressure are discussed. The results showed that the frequency shift increases as the relative humidity and temperature increase. The influence of relative humidity on the resonant frequency becomes more significant under conditions of higher temperature and smaller gap thickness.