Plane wave propagation in layered piezoelectric film resonators

In this paper, the piezoelectric film, electrodes and the silicon substrate of FBARs are modeled as a layered sandwich structure for studying the wave propagation in it. The harmonic solutions should satisfy the governing equations of each layer. Then, the dispersion relations can be obtained by the continuity conditions and boundary conditions. The dispersion curves are compared with the results when the electrodes are treated as inertia layers for model simplification. As a conclusion, the simplification usually used in dealing with quartz resonator will lead to an unacceptable error due to a big mass ratio of FBARs. Further, the vibration modes of the curves are discussed.