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