Investigation on high-frequency and mode-coupling vibrations in thickness-extensional piezoelectric thin-film resonators with initial stress

• Mode-coupling vibrations in PTF resonators with initial stress are first studied. • The robustness of mode-coupling behaviors to initial stress is revealed. • The out-of-plane initial stress can tune resonance frequency of PTF resonators. • The CSF is defined to judge the coupling intensity of all modes in frequency spectra. Mode-coupling vibrations in thickness-extensional piezoelectric thin-film bulk acoustic wave resonators (FBARs) with initial stress operating in the ultra-high frequency (UHF) range are investigated by employing the Frequency Spectrum Quantitative Prediction (FSQP) method. The uniaxial uniform initial stresses along the in-plane and thickness directions are separately considered. The dispersion relation of the bulk wave in the FBAR with initial stress is obtained and then the solutions of physical fields are constructed by superimposing the eigen-modes in the dispersion curve. The variational formulation considering the initial stress is derived through the perturbation method. Then frequency spectra that predict the coupling strength between the thickness-extensional mode and other eigen-modes are obtained by substituting the solutions into the variational formulation. Mode shapes of mechanical displacements are presented to illustrate the influence of initial stress on mode-coupling behaviors in FBARs. The results show that the initial stress could cause the shifts of frequency spectrum curves, reflecting that the in-plane initial stress leads to the shifts of spectrum curves along the lateral aspect ratio axis, while the out-of-plane initial stress leads to the shifts along the frequency axis (i.e., frequency shifts) and lateral aspect ratio axis simultaneously. Desirable structural parameters should be chosen based on frequency spectra to avoid the increases of mode-coupling strength induced by initial stress. The out-of-plane initial stress could be used to tune the resonance frequency of the FBARs without changing the mode-coupling behaviors. The coupling strength factor is first defined for the convenient and fast judgment of mode-coupling intensity of all data points in the frequency spectra. The obtained results provide a crucial reference to the manipulation of resonance frequency and the mode-coupling strength in FBAR devices.