A new model for film bulk acoustic wave resonators

Based on cavity resonance and sandwich composite plate theory, this paper presents a universal three-dimensional (3D) theoretical model for frequency dispersion characterization and displacement profile shapes of the film bulk acoustic resonator (FBARs). This model provides results of FBAR excited thickness-extensional and flexure modes, and the result of frequency dispersion is proposed in which the thicknesses and impedance of the electrodes and the piezoelectric material are taken into consideration; its further simplification shows good agreement with the modified Butterworth-Van-Dyke (MBVD) model. The displacement profile reflects the vibration stress distribution of electrode shapes and the lateral resonance effect, which depends on the axis ratio of the electrode shapes a/b. The results are consistent with the 3D finite element method modeling and laser interferometry measurement in general.