Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA, USA.
IEEE Trans Ultrason Ferroelectr Freq Control. 2010 Aug;57(8):1840-53. doi: 10.1109/TUFFC.2010.1623.
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 degrees to 180 degrees. 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 degrees and 65.4 degrees, and pure thickness shear modes occur at 43 degrees and 90 degrees. For AlN FBARs, pure longitudinal modes occur at 0 degrees and 67.1 degrees, and pure shear modes occur at 46.1 degrees and 90 degrees 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 degrees and 90 degrees for ZnO, and 34.5 degrees and 90 degrees 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.
本文研究了倾斜 c 轴（偏离法线）角度为 0 度至 180 度的 ZnO 和 AlN 薄膜的体声波谐振器（FBAR）。倾斜 c 轴导致出现法向平面和平面内极化，从而使谐振器中存在纵模和切变模共存。预测 FBAR 电阻抗的方程是从基本压电本构方程中推导出的。计算了包括弹性、介电和压电系数在内的材料特性、包括声波速度和机电耦合系数在内的体波特性以及 FBAR 的阻抗，并发现它们强烈依赖于倾斜角。有趣的是，发现对于 ZnO FBAR，纯厚度纵向模式出现在 0 度和 65.4 度，纯厚度切变模式出现在 43 度和 90 度。对于 AlN FBAR，纯纵向模式出现在 0 度和 67.1 度，纯切变模式出现在 46.1 度和 90 度。换句话说，在特定倾斜极化角下，ZnO 和 AlN FBAR 存在纯厚度纵向和切变模式。此外，在 ZnO 中发现切变机电系数的两个峰值出现在 33.3 度和 90 度，在 AlN 中出现在 34.5 度和 90 度。因此，考虑到具有高机电系数的强剪切共振，具有特定倾斜角的 ZnO 和 AlN 薄膜可能为 FBAR 的设计和制造提供选择。还分析了用于质量传感器的双模 FBAR 的使用；计算得到的由质量负载引起的大谐振频率偏移表明，它们在具有高灵敏度的传感器应用中具有良好的应用前景。模拟结果与报道的实验结果吻合良好，可用于 FBAR 的设计和应用。
