Analytical study of dual-mode thin film bulk acoustic resonators (FBARs) based on ZnO and AlN films with tilted c-axis orientation

In this paper, we present the analytical study of thin film bulk acoustic wave resonators (FBARs) using ZnO and AlN films with a c-axis tilt angle (off-normal) from 0° to 180°. The tilted c-axis orientation induces normal plane and inplane polarizations, which leads to the coexistence of the longitudinal mode and shear mode in the resonator. The equation for predicting electric impedance of FBARs was derived from the basic piezoelectric constitutive equations. Material properties including elastic, dielectric, and piezoelectric coefficients, bulk wave properties including acoustic velocity and electromechanical coupling coefficient, and impedance of FBARs were calculated and showed strong dependence on the tilt angle. Interestingly, it was found that for ZnO FBARs, pure thickness longitudinal modes occur at 0° and 65.4°, and pure thickness shear modes occur at 43° and 90°. For AlN FBARs, pure longitudinal modes occur at 0° and 67.1°, and pure shear modes occur at 46.1° and 90° for AlN. In other words, pure thickness longitudinal and shear modes exist in ZnO and AlN FBARs at specific tilted polarization angles. In addition, two peaks of shear mode electromechanical coefficient are found at 33.3° and 90° for ZnO, and 34.5° and 90° for AlN. Therefore, ZnO and AlN films with specific tilt angles may provide options in the design and fabrication of FBARs, considering their strong shear resonance with high electromechanical coefficients. The use of dual-mode FBARs for mass sensors is also analyzed; the calculated large resonant frequency shift caused by mass loading shows that they have good prospects for use in sensor applications with high sensitivity. The simulation results agreed well with the reported experiment results, and can be used for design and application of FBARs.