Dynamic analytical modelling and piezoelectric characterization of a Pb(Zr, Ti)O3/SiN cantilever with losses

In this paper a method to determine the piezoelectric constant of thin films is described. The characterization method is based on the dynamic behaviour of a heterogeneous cantilever. The electric behaviour of the bimorph is simplified in order to reach the lumped-element model which is common in the literature. Expressions of the motional elements have quite simple values. The characterization method has the advantage of being based on the resonance and anti-resonance frequencies and is therefore purely electrical. This characterization method includes the dielectric, fluidic and mechanical losses. An experimental protocol was written in order to measure each of these parameters (dielectric losses, quality factor and resonance-anti-resonance frequencies) used to evaluate the piezoelectric constant through an analytical formula which includes the losses. The dynamic characterization developed was compared to a classic static measurement of the piezoelectric constant. The two methods show similar results which validate the technique. The PZT piezoelectric constant has been evaluated on a thin film cantilever and shows a maximum absolute value of 5 C m(-2) for a 120 nm thin film.