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.

采用频谱定量预测 (FSQP) 方法研究了具有在超高频 (UHF) 范围内工作的初始应力的厚度扩展压电薄膜体声波谐振器 (FBAR) 中的模式耦合振动。分别考虑沿面内和厚度方向的单轴均匀初始应力。得到了FBAR中体波与初始应力的色散关系，然后通过在色散曲线中叠加本征模式来构造物理场的解。考虑初始应力的变分公式是通过扰动法。然后，通过将解代入变分公式，获得预测厚度扩展模式与其他本征模式之间耦合强度的频谱。给出了机械位移的模式形状来说明初始应力对 FBAR 中模式耦合行为的影响。结果表明，初始应力会引起频谱曲线的偏移，反映了面内初始应力导致频谱曲线沿横向偏移。纵横比轴，而平面外初始应力同时导致沿频率轴（即频率偏移）和横向纵横比轴的偏移。应根据频谱选择理想的结构参数，以避免初始应力引起的模式耦合强度增加。面外初始应力可用于在不改变模式耦合行为的情况下调整 FBAR 的共振频率。为了方便、快速地判断频谱中所有数据点的模式耦合强度，首先定义了耦合强度因子。所得结果为 FBAR 器件中谐振频率和模式耦合强度的控制提供了重要参考。