Simultaneous high-frequency measurement of direct and inverse transverse piezoelectric coefficients of thin films using longitudinal vibration

A setup and approach for simultaneous measurement of the inverse and direct transverse piezoelectric coefficients of piezoelectric films was constructed. A longitudinal vibration mode resonator with a hydrothermally synthesized (K,Na)NbO₃ film deposited on a SrRuO₃/SrTiO₃ substrate was investigated. The fabricated vibrator consists of two upper electrodes, one for actuation and the other for sensing. A driving voltage was applied to the actuator electrode to generate mechanical vibration at its resonance frequency. The vibration velocity was measured with a laser Doppler vibrometer, and the output current from the shorted sensing electrode was also measured to simultaneously evaluate the inverse and direct piezoelectric responses. The obtained inverse piezoelectric coefficient e₃₁̅ was −3.60 C/m², while the direct piezoelectric coefficient e₃₁̅ was almost same at −3.69 C/m². From these values, the inverse and direct piezoelectric coefficients e_31,f were −4.93 and −5.05 C/m², respectively.