Accurate measurement of the piezoelectric coefficient of thin films by eliminating the substrate bending effect using spatial scanning laser vibrometry

One of the major difficulties in measuring the piezoelectric coefficient d(33,f) for thin films is the elimination of the contribution from substrate bending. We show by theoretical analysis and experimental measurements that by bonding thin film piezoelectric samples to a substantial holder, the substrate bending can be minimized to a negligible level. Once the substrate bending can be effectively eliminated, single-beam laser scanning vibrometry can be used to measure the precise strain distribution of a piezoelectric thin film under converse actuation. A significant strain increase toward the inside edge of the top electrode (assuming a fully covered bottom electrode) and a corresponding strain peak in the opposite direction just outside the electrode edge were observed. These peaks were found to increase with the increasing Poisson's ratio and transverse piezoelectric coefficient of the piezoelectric thin film. This is due to the non-continuity of the electric field at the edge of the top electrode, which leads to the concentration of shear stress and electric field in the vicinity of the electrode edge. The measured d(33,f) was found to depend not only on the material properties such as the electromechanical coefficients of the piezoelectric thin films and elastic coefficients of the thin film and the substrate, but also on the geometry factors such as the thickness of the piezoelectric films, the dimensions of the electrode, and also the thickness of the substrate.