Simulation and measurements of the piezoelectric properties response (d33) of piezoelectric layered thin film structures influenced by the top-electrode size

The properties of piezoelectric thin film layered structures are in the focus of many investigations. Significant decreasing piezoelectric properties have been observed with decreasing top-electrode size. These results are obtained by measurements of the effective piezoelectric small-signal coefficient d_33,eff and the piezoelectric large signal-strain S using a double-beam laser interferometer. Samples are investigated with squared top-electrodes with dimensions of 0.1 mm to 1 mm edge length. The loss of d_33,eff is as high as 50 %, whereas the influence on the relative permittivity is only small. This work investigates this behaviour by calculating the influence of varying elastic and geometrical properties of substrate, electrodes, and piezoelectric thin film on the effective piezoelectric small-signal coefficient d_33,eff by means of finite element simulations. Beside the clamping effect of the substrate under electrical operating conditions also the influence of thermally induced mechanical stresses after cooling from 4000°C to room temperature is calculated. From measurements and simulations it can be concluded that the source of the pad size effect on the measured piezoelectric properties can he attributed to the mechanics of the layered structure.