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

摘要

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. Weshow by theoretical analysis and experimental measurements that by bonding thinfilm piezoelectric samples to a substantial holder, the substrate bending can beminimized to a negligible level. Once the substrate bending can be effectivelyeliminated, single-beam laser scanning vibrometry can be used to measure theprecise strain distribution of a piezoelectric thin film under converseactuation. A significant strain increase toward the inside edge of the topelectrode (assuming a fully covered bottom electrode) and a corresponding strainpeak in the opposite direction just outside the electrode edge were observed.These peaks were found to increase with the increasing Poisson's ratio andtransverse piezoelectric coefficient of the piezoelectric thin film. This is dueto 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 thevicinity of the electrode edge. The measured d(33,f) was found to depend notonly on the material properties such as the electromechanical coefficients ofthe piezoelectric thin films and elastic coefficients of the thin film and thesubstrate, but also on the geometry factors such as the thickness of thepiezoelectric films, the dimensions of the electrode, and also the thickness ofthe substrate.