Two-Dimensional Plate Theory for the Analysis of Coupling Vibrations in Shear Mode FBARs

The shear mode film bulk acoustic wave resonators (FBARs) have been developed rapidly in recent years due to the increased interest in biosensors. In this article, the mode coupling effects that are unavoidable in real devices are theoretically analyzed and discussed. Mindlin's approximation method of expanding the displacement fields with power series along the plate thickness direction is employed, and a system of 2-D plate equations is obtained. The accuracy of the plate theory is validated through the comparison of dispersion curves with the results calculated by 3-D exact theory. Free coupling vibrations of the cross-sectional plane of finite-sized shear mode FBAR plates are further studied with the derived 2-D theory. The results in this article show that the presented plate theory is accurate and efficient for the structural analyses of shear mode FBARs. Besides, the selection of aspect ratios can be used to avoid strong mode couplings, which is helpful for device designs.