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

Abstract

One of the major difficulties in measuring the piezoelectric coefficientd33, f for thin films is the elimination of the contribution from substrate bending. We show bytheoretical analysis and experimental measurements that by bonding thin film piezoelectricsamples to a substantial holder, the substrate bending can be minimized to a negligiblelevel. Once the substrate bending can be effectively eliminated, single-beam laser scanningvibrometry can be used to measure the precise strain distribution of a piezoelectric thinfilm under converse actuation. A significant strain increase toward the inside edge of thetop electrode (assuming a fully covered bottom electrode) and a corresponding strain peakin the opposite direction just outside the electrode edge were observed. These peaks werefound to increase with the increasing Poisson’s ratio and transverse piezoelectriccoefficient of the piezoelectric thin film. This is due to the non-continuity of theelectric field at the edge of the top electrode, which leads to the concentration ofshear stress and electric field in the vicinity of the electrode edge. The measuredd33, f was found to depend not only on the material properties such as the electromechanicalcoefficients of the piezoelectric thin films and elastic coefficients of the thin film and thesubstrate, but also on the geometry factors such as the thickness of the piezoelectricfilms, the dimensions of the electrode, and also the thickness of the substrate.