An evaluation method for direct piezoelectric coefficients of thin films using both-ends-hinge-supported unimoprh beams

Abstract

We have developed a new method for measuring the direct piezoelectric effect of piezoelectric thin films, consisting of both-ends-hinge-supported unimorph beams (BUBs). This method can determine the precise direct transverse piezoelectric coefficient e31,f of arbitrary piezoelectric films by measuring the displacement and the output voltage between the electrodes of the BUBs. We formulated the e31,f values based on the flexure basic formula, and a constitutive equation of electromagnetic field for the BUBs, including measuring systems such as oscilloscopes, which have an arbitrary input impedance. In this study, we were able to obtain a piezoelectric coefficient of a lead zirconate titanate (PZT) thin film on a Si substrate of e31,f = 4.7 Cm−2, regardless of the input impedance of the measurement instrument. Using this method, we then measured the temperature characteristics of e31,f for the PZT thin film. We clearly observed the increase of e31,f , and the relative dielectric constant, with an increase in temperature. We obtained a temperature gradient for of a = 0.01 Cm−2K−1, a value which is in good agreement with previous research. We also measured the time dependences of the e31,f after polling piezoelecric films. The e31,f value decreased over time, and we were able to obtain a logarithmic time gradient for normalized e31,f of p = −0.01, a value consistent with the results of previous studies.