Resonant spectrum method to characterize piezoelectric films in composite resonators.

In this paper, we present a direct method to characterize a piezoelectric film that is sandwiched with two electrodes and deposited on a substrate to form a four-layer thickness extension mode composite resonator (also known as over-moded resonator). Based on the parallel and series resonant frequency spectra of a composite resonator, the electromechanical coupling factor, the density and the elastic constant of the piezoelectric film can be evaluated directly. Experimental results on samples consisting of ZnO films on fused quartz substrates with different thickness are presented. They show good agreement with theoretical prediction. The mechanical effect of the electrode on the method is investigated, and numerical simulation shows that the effect of the electrodes can be properly corrected by the modified formulae presented in this paper. The effect of mechanical loss in piezoelectric film and in substrate on this method also has been investigated. It is proven that the method is insensitive to the losses.