Measurement of Transverse Piezoelectric Coefficients of Pb(Zr_0.52Ti_0.48)O₃ Thin Films by a Mechano-electrical Multiphysics Coupling, Bulge Test Method

On the measuring of transverse piezoelectric coefficients of Pb(Zr_0.52Ti_0.48)O₃ (PZT) thin films, we derived the mechano-electrical coupling bulge constitutive equations of PZT thin films on the basis of bulge test model and ferroelectric constitutive equations. The bulge samples were prepared by sol-gel and chemical etching methods. Mechano-electrical coupling bulge tests were performed by using modified force-electric experimental platform under the applied voltage between 0-14 V. The results showed that the elastic modulus and residual stress of PZT thin films were 91.9 GPa and 36.2 MPa under pure force field, respectively. The transverse piezoelectric coefficients d₃₁ of PZT thin films increased from -28.9 pm/V to -45.8 pm/V when the voltage increased from 2 V to 14 V. Our work provides an effective analysis method for the transverse piezoelectric properties of other ferroelectric thin film materials by using the modified mechano-electrical coupling bulge test and the corresponding constitutive equations.