Piezoelectric properties of rhombohedral Pb(Zr, Ti)O3 thin films with (100), (111), and “random” crystallographic orientation

The longitudinal $d_{33}$ piezoelectric coefficient was studied in rhombohedral ${\mathrm{Pb(Zr}}_{\mathrm{0.6}}{\mathrm{Ti}}_{\mathrm{0.4}}{\mathrm{)O}}_{\mathrm{3}}$ thin films with (111), (100), and “random” orientation. The largest $d_{33}$ was found in (100)-oriented films and the smallest along the polarization direction in (111)-oriented films. These results are in a good qualitative agreement with recent theoretical predictions [Du, Zheng, Belegundu, and Uchino, Appl. Phys. Lett. 72, 2421 (1998)]. The field dependence of $d_{33}$ was also investigated as a function of crystallographic orientation of the films. It was found that (100)-oriented films with the highest piezoelectric coefficient exhibit the weakest nonlinearity. Observed variation in the piezoelectric nonlinearity with film orientation can be fully explained by taking into account domain-wall contributions, which are dependent on film orientation.