Measurements of Piezoelectric Coefficient d₃₃ of Lead Zirconate Titanate Thin Films Using a Mini Force Hammer

Lead zirconate titanate (PbZr_xTi_1-xO₃, or PZT) is a piezoelectric material widely used as sensors and actuators. For microactuators, PZT often appears in the form of thin films to maintain proper aspect ratios. One major challenge encountered is accurate measurement of piezoelectric coefficients of PZT thin films. In this paper, we present a simple, low-cost, and effective method to measure piezoelectric coefficient d₃₃ of PZT thin films through use of basic principles in mechanics of vibration. A small impact hammer with a tiny tip acts perpendicularly to the PZT thin-film surface to generate an impulsive force. In the meantime, a load cell at the hammer tip measures the impulsive force and a charge amplifier measures the responding charge of the PZT thin film. Then the piezoelectric coefficient d₃₃ is obtained from the measured force and charge based on piezoelectricity and a finite element modeling. We also conduct a thorough parametric study to understand the sensitivity of this method on various parameters, such as substrate material, boundary conditions, specimen size, specimen thickness, thickness ratio, and PZT thin-film material. Two rounds of experiments are conducted to demonstrate the feasibility and accuracy of this new method. The first experiment is to measure d₃₃ of a PZT disk resonator whose d₃₃ is known. Experimental results show that d₃₃ measured via this method is as accurate as that from the manufacturer's specifications within its tolerance. The second experiment is to measure d₃₃ of PZT thin films deposited on silicon substrates. With the measured d₃₃, we predict the displacement of PZT thin-film membrane microactuators. In the meantime, the actuator displacement is measured via a laser Doppler vibrometer. The predicted and measured displacements agree very well validating the accuracy of this new method.