Characterization of the effective electrostriction coefficients in ferroelectric thin films

Electromechanical properties of a number of ferroelectric films including PbZr_xTi_1-xO₃(PZT), 0.9PbMg_1/3Nb_2/3O₃-0.1PbTiO₃(PMN-PT), and SrBi₂Ta₂O₉(SBT) are investigated using laser interferometry combined with conventional dielectric measurements. Effective electrostriction coefficients of the films, Q_eff, are determined using a linearized electrostriction equation that couples longitudinal piezoelectric coefficient, d₃₃, with the polarization and dielectric constant. It is shown that, in PZT films, electrostriction coefficients slightly increase with applied electric field, reflecting the weak contribution of non-180° domains to piezoelectric properties. In contrast, in PMN-PT and SBT films electrostriction coefficients are field independent, indicating the intrinsic nature of the piezoelectric response. The experimental values of Q_eff are significantly smaller than those of corresponding bulk materials due to substrate clamping and possible size effects. Electrostriction coefficients of PZT layers are shown to depend strongly on the composition and preferred orientation of the grains. In particular, Q_eff of (100) textured rhombohedral films (x = 0.7) is significantly greater than that of (111) layers. Thus large anisotropy of the electrostrictive coefficients is responsible for recently observed large piezoelectric coefficients of (100) textured PZT films. Effective electrostriction coefficients obtained by laser interferometry allow evaluation of the electromechanical properties of ferroelectric films based solely on the dielectric parameters and thus are very useful in the design and fabrication of microsensors and microactuators.