Thickness vibration of c-axis inclined ZnO thin film resonators carrying an array of microbeams

We analyze the thickness vibration of c-axis inclined ZnO FBARs carrying an array of microbeams. The microbeams are perfectly bonded to a thin piezoelectric substrate. And for the flexural motion of the beams, we use the Euler-Bernoulli theory of bending. The impedance expression of shear mode 2μm ZnO FBARs has been derived from the basic piezoelectric constitutive equations. The resonant frequencies for ZnO FBARs are in the range of 0.66-0.78GHz. We focus on the effects of the geometric dimensionings including the diameter and the length of the microbeams to the frequency spectrum. The admittance-frequency relations with different numbers, diameters and lengths of the microbeams are given. With the change of the geometric dimensionings, the resonant peak changes, and also the frequency changes in a small scale. Analysis method and calculation results can provide important reference to the c-axis inclined piezoelectric thin film resonators.