Thickness-extensional trapped energy vibration of ZnO thin film bulk acoustic wave filters

Thickness-extensional vibration of a rectangular piezoelectric thin film filter symmetrically covered with two driving electrodes was studied in this paper. The Tiersten and Stevens scalar equation was employed. The Ritz method based on the variational formulation constructed in our previous work was used with trigonometric series as basis functions. Free vibration modes and corresponding resonant frequencies were obtained, which shows that the modes can separate into symmetric modes and anti-symmetric modes for this symmetric structure. Trapped modes with vibration mainly under the top electrode regions were illustrated. The six corner-type regions of the filter neglected by Tiersten and Stevens for simplicity were considered in our analysis. Results show that their approximation may lead to an inaccuracy ranging from dozens to hundreds of ppm for the fundamental symmetric modes, which is severe to filter design and operation.