Frequency Spectra of Coupling Vibration in High-Frequency Thickness-Shear ZnO Thin Film Resonator Applied in Sensing Field Based on the Hamilton Principle.

Abstract

Mode coupling vibration of a multilayered ZnO thin film bulk acoustic wave resonator (FBAR) with its c-axis along the wave propagation direction operating at the fundamental thickness-shear (TSh) mode is studied in this paper. The accurate dispersion curve from 3-D piezoelectric theory indicates that the operating TSh mode could couple to the flexural mode, which influences the performance of a sensing resonator and needs to be eliminated through the so-called frequency spectrum analysis. Frequency spectra of coupling vibration in this FBAR can be obtained by substituting the displacement solutions consisting of the mode branches in the dispersion curve into several weak boundary conditions, which gives the integral boundary conditions across the plate thickness at the side edge of FBARs. The results show that the content of mode couplings to spurious modes depends on the plate length/thickness ratios. The character of desirable values of plate aspect ratios under which the operating TSh mode dominates among all modes is stated specifically, which provides fundamental guidance to the design of structural parameters of FBARs.