Viscosity sensor using ZnO and AlN thin film bulk acoustic resonators with tilted polar c-axis orientations

Abstract

We present a theoretical analysis of liquid viscosity sensors using ZnO and AlN thin film bulk acoustic wave resonators (FBARs) with tilted polar c-axis orientations. Besides the thickness longitudinal mode, the tilted c-axis orientation induces thickness shear mode in the resonator, which allows resonators operated in liquid medium without significant damping for sensory application. The equation for predicting electric impedance of shear mode film bulk acoustic wave resonators (FBARs) with a viscous liquid loading was derived from the basic piezoelectric constitutive equations. The viscosity sensitivity of shear mode ZnO and AlN resonators was achieved by calculation of resonant frequency shift due to viscous liquid loading. In the simulation, it is assumed that all the resonators have 2 μm thickness and 300 μm×300 μm electrode area; three different liquids (water, acetone, and olive oil) were chosen as the liquid loadings; and different tilt c-axis angles for both ZnO FBARs and AlN FBARs have been examined. It was found that the sensitivities of shear mode resonators to the three liquid loading are very close, and do not change much with the c-axis tilt angle with a value rang from 0.91e-3 to 0.97e-3 (kg m−3 Pa·S)−0.5 for ZnO FBARs and from 1.12e−3 to 1.13 e−3 (kg m−3 Pa·S)−0.5 for AlN FBARs. When the resonator’s mechanical quality factor (Q) is changed from 50 to 10 000, viscosity sensitivities are almost same. However, Q has a great effect on resonator impedance; and if Q is too low or the viscosity of the liquid is high, the maximum phase angle of the resonator will be less than 0, which makes excitation of the oscillation difficult if an oscillator circuit is used for sensor measurement. The results can be used for design and application of ZnO or AlN FBARs to monitor liquid viscosity.