Materials property dependence of the effective electromechanical coupling coefficient of thin film bulk acoustic resonators

The input electric impedance, Z_ω, for a three-layer (electrode/piezoelectric film/electrode) and a four layer (electrode/piezoelectric film/electrode/substrate) thin film bulk acoustic wave resonator, is derived by a one-dimensional transfer matrix method to describe the thin film resonator behavior, especially the effect of electrode and substrate layers on resonator properties. Based on the impedance spectra, the effective coupling coefficient, k_eff², of a thin film resonator can be evaluated with respect to the resonator structure and thin film properties. The calculation results for both AlN and PZT thin film resonators reveal that the mechanical Q factor of the thin film piezoelectric material has a significant effect on the k_eff² of the device. k_eff² decreases with the increase of the mechanical quality factor, Q, and reaches a stable value when the Q value is sufficiently high. k_eff² is also dependent on the thickness and material properties of the electrode and substrates. For a specific electrode material, a maximum value can be obtained at an appropriate electrode/piezoelectric layer thickness ratio. The frequency temperature stability of thin film resonators is also evaluated with respect to the resonator structure and material properties.