Surface roughness effects on vibration characteristics of AT-cut quartz crystal plate

With the miniaturization and high-frequency requirements of quartz crystal resonators (QCRs), microscopic issues affecting operating performance, e.g., the surface roughness, are receiving more and more attention. In this study, the surface roughness is considered as a Gaussian distribution, and mode coupling properties of AT-cut QCRs is systematically investigated under different temperature environments with the aid of two-dimensional thermal field equations. The resonant frequency, frequency-temperature curves, and mode shapes of QCRs are obtained through the partial differential equation (PDE) module of COMSOL Multiphysics software for free vibration analysis. For forced vibration analysis, the admittance response and phase response curves of QCRs are calculated via the piezoelectric module. The results from both free and forced vibration analyses demonstrate that surface roughness reduces the resonant frequency of QCRs. Additionally, mode coupling is more likely to occur in a crystal plate with a surface roughness, leading to activity dip and reduced working performance of QCRs, which should be avoided in device fabrication.