Characterization for piezoelectric films using composite resonators

A method is developed to determine the elastic and piezoelectric properties of piezoelectric films by the resonance frequency spectrum of a two-layered composite resonator consisting of a film and a substrate plate. The parallel resonance frequencies are determined from the mechanical properties of the two layers only, allowing the density ρˆ and the elastic constant Cˆ₃₃^D to be determined independently. The electromechanical coupling coefficient, k_t², can be directly calculated from the distribution of the effective coupling coefficients, k_eff², which are given by the parallel and series resonance frequencies of the composite resonator. The accuracy of the method is evaluated by numerical examples