k²₃₃Estimation of Thin Films via Piezoelectric Stiffening Using Ultrasonic Reflectometry

A method for estimating intrinsic electromechanical coupling coefficient ${k}_{{33}}^{{2}}$ of piezoelectric thin films using piezoelectrically stiffened acoustic velocity ${V}^{\text {D}}$ and unstiffened acoustic velocity ${V}^{\text {E}}$ was proposed. ${V}^{\text {D}}$ and ${V}^{\text {E}}$ velocities of thin films in the sub-GHz range were estimated by ultrasonic reflectometry. Directly depositing a film specimen on the backside of the ultrasonic delay line eliminates the need for a coupler layer and avoids acoustic attenuation in the layer. The ${V}^{\text {D}}$ velocity can be estimated from the phase differences of the echoes: before and after the film specimen is deposited. In contrast, ${V}^{\text {E}}$ velocity can be estimated from the phase difference when the film specimen is under the open circuit and the short circuit. The intrinsic ${k}_{{33}}^{{2}}{}$ can be obtained from the relationship of ${k}_{{33}}^{{2}}~\text {=}$ 1 – ( ${V}^{\text {E}}$ / ${V}^{\text {D}})^{{2}}$ . For the Sc0.4Al0.6N thin film specimen, ${k}_{{33}}^{{2}}$ was determined to be 11.6% from ${V}^{\text {D}}$ and ${V}^{\text {E}}$ of 8400 m/s and 7900 m/s, respectively. For the ZnO thin film specimen, ${k}_{{33}}^{{2}}$ was estimated to be 4.7% from ${V}^{\text {D}}$ and ${V}^{\text {E}}$ of 6250 m/s and 6100 m/s, respectively. These values are in good agreement with previously reported results.