Simulation of electromechanical coupling coefficient by modified modal frequency spectrum method including the electrode effect

An approximate formula has been developed to determine the electromechanical coupling coefficient of the piezoelectric film in a four-layer composite resonator, which includes two electrodes. In this formula, the coupling coefficient can be calculated from the distribution of the effective coupling coefficients, k2eff, which are given by the modal frequency spectrum of the composite resonator. The feasibility of this method has been demonstrated with a ZnO/SiO2 composite resonator for different electrode thickness. The effect of mechanical propagation loss in both piezoelectric layer and substrate has also been studied.