Dependence of e _31,f on polar axis texture for tetragonal Pb(Zr_x,Ti_1-x)O₃ thin films

It was shown by Ouyang et al. [Appl. Phys. Lett. 86, 152901 (2005)] that the piezoelectric e_31,f coefficient is largest parallel to the spontaneous polarization in tetragonal PbZr_xTi_1-xO₃ (PZT) films. However, the expected piezoelectric data are typically calculated from phenomenological constants derived from data on ceramic PZT. In this work, the dependence of e_31,f on c-axis texture fraction, f₀₀₁, for {001}PZT thin films was measured by growing films with systematically changed f₀₀₁ using CaF₂, MgO, SrTiO₃, and Si substrates. An approximately linear increase in e_31,f with f₀₀₁ was observed for compositions up to 43 mol. % Zr, and 100% c-domain properties were extrapolated. It was demonstrated that c-axis PZT films can achieve e_31,f exceeding -12 C/m² for many tetragonal compositions. The energy harvesting figure of merit, e_31,f²/ε_r, for c-axis PZT films surpassed 0.8 C²/m⁴. This is larger than the figure of merit of gradient-free PZT films grown on Si substrates by a factor of four.