Numerical analysis of thickness shear thin film piezoelectric resonators using a laminated plate theory

Finite element matrix equations are derived from a two-dimensional, piezoelectric high frequency laminated plate theory. Two-layer ZnO/Si and three-layer ZnO/SiO/sub 2//Si thin film resonators vibrating at the fundamental thickness shear mode are investigated using the finite element models. Straight crested waves propagating in a resonator are studied. Resonant frequency, mode shapes and electromechanical coupling coefficient of the fundamental thickness shear mode are calculated and presented with respect to the C-axis orientation of the ZnO layer, and thickness ratios of the layers in a resonator. The results from the laminated plate model are checked against the three dimensional finite element solution and found to be accurate for the fundamental thickness shear and its anharmonic overtones. The plate model does not yield as accurate a frequency spectrum for flexure, face shear and extensional modes.<>