Analysis of thickness-extensional waves propagating in the lateral direction of solidly mounted piezoelectric thin film resonators.

In a solidly mounted piezoelectric thin film resonator (SMR), acoustic waves propagate not only in the thickness direction but also in the lateral direction. In this study, we analyzed the acoustic wave in the SMR-type piezoelectric thin film resonator and derived the dispersion relation between the lateral wave number and frequency, considering wave propagation in the lateral direction. The lateral wave number was shown to be a complex number due to the leak of the acoustic energy to a substrate. It also was shown that the Q factor could be calculated from the complex cutoff frequency, and it becomes higher when the number of quarter-wave (lambda/4) layers increases. Using the dispersion relation, the trapped-energy resonant modes of an SMR were analyzed, considering the boundary conditions at the edge of the electrode.