The significance of the piezoelectric coefficient d31,eff determined from cantilever structures

The method used by SolMateS to determine the effective piezoelectric coefficient d31,eff of Pb(Zr,Ti)O3 (PZT) thin films from cantilever displacement measurements is described. An example from a 48 cantilever dataset using different cantilever widths, lengths and crystal alignments is presented. It is shown that for the layer stack of our cantilevers, the multimorph model is more accurate compared to the bimorph model for the d31,eff determination. Corrections to the input parameters of the model are further applied in order to reduce the geometrical error of the cantilever that is caused by its design and processing, as well as correction to the measured tip displacement caused by resonance amplification. It is shown that after these corrections, the obtained d31,eff values are still up to 10% uncertain as the plate behavior and the non-constant radius of curvature of the cantilevers lead to inconsistent results. We conclude that quantitative determination of d31,eff from the cantilevers is highly subjective to misinterpretation of the models used and the measurement data. The true value of d31,eff was determined as −118.9 pm V−1.