Surface effect on Lamb wave propagation in ZnO-based film bulk acoustic resonators

5G communication technology has spurred piezoelectric film bulk acoustic resonators (FBARs) to higher frequencies and thinner structures, highlighting the surface effect’s significance for their dynamic performance. This study systematically investigates the influence of surface effect on the Lamb wave propagation characteristics in ZnO-based FBARs. The state-space formalism and a Taylor series expansion are employed to formulate the surface piezoelectricity theory, which provides effective boundary conditions to characterize the role of surface effect in FBARs. Based on the displacement method, the dispersion equation is derived by combining the governing equations with the effective boundary conditions. Numerical results show that surface effects play a significant role in the propagation of Lamb waves in FBARs, and that the dispersion characteristics depend strongly on the film thickness and surface material parameters of FBARs. Although the FBAR’s thickness is on the order of micrometers, surface effects introduce a deviation of approximately 50 ppm in the cutoff frequency of the thickness-extensional (TE) mode. Furthermore, as the thickness of the ZnO-based FBAR approaches the nanoscale, the TE mode and the second thickness-shear (TSh2) mode exhibit a mode flip. Therefore, the Lamb wave propagation characteristics in FBARs can be effectively modulated through surface engineering.