Frequency shift prediction of a shear mode multi-layered FBAR sensor in viscous media using transfer matrix method

In this paper, new frequency equations of a shear mode c-axis tilted FBAR (Film Bulk Acoustic Wave Resonator) sensor operating in viscous liquid media are derived by using the transfer matrix method to predict the frequency shift (FS) induced by fluid viscosity. Top and bottom electrodes of FBAR are considered as a superposition of a pure elastic model and a perfectly conducting model. Employing the perturbation method and developed frequency equations, an approximate FS expression is obtained to study the effects of viscous liquid properties on frequency shifts for the sensor operating in water-glycerol solutions. Numerical results by the developed frequency equations are compared with the published experimental results and those predicted by the traditional Stockbridge-Kanazawa equation, which was originally derived for quartz crystal microbalances (QCMs). Meanwhile, the influence of the electrode material and thickness on FS is also discussed to demonstrate the outperformance of the developed equations over the Stockbridge-Kanazawa equation. Results show that the analytical equations for frequency shift analysis have more potential than the well-known Stockbridge-Kanazawa equation to predict frequency shift characteristics of FBAR sensors in terms of accuracy and efficiency.