Wave propagation in piezoelectric layered structure of film bulk acoustic resonator

In this paper, we consider the sandwich structure composed of silicon substrate, piezoelectric layer and electrode layers in the typical structure of FBAR. We assume a special solution in the form of harmonic wave in the piezoelectric layer, and substitute it into the simplified stress equations of motion and the charge equation of electrostatic. A correction to the solution assumed is obtained in order to satisfy these equations. Similarly, a correctional solution assumed in the form of harmonic wave in the silicon substrate can be obtained. We can substitute these correctional solutions into continuity conditions and boundary conditions. The relations of wave number and frequency are obtained. The dispersion curves are calculated from the relation. The frequencies when wave number is zero, the influence of the mass ratio of piezoelectric layer and electrode plate, and the vibration images are discussed further.