Piezoelectric and dielectric tunabilities of ultra-thin ferroelectric heterostructures

The scaling of the piezoelectric and dielectric constants with film thickness in ultra-thin ferroelectric heterostructures is investigated. Epitaxial (001) PbZr_0.2Ti_0.8O₃ films ranging in thickness from 5 nm to 30 nm with top and bottom SrRuO₃ electrodes were grown onto (001) SrTiO₃ substrates via pulsed laser deposition. Piezoelectric and dielectric measurements were performed using an atomic force microscope. The remnant value of the out of plane piezoresponse (d₃₃) decreases from 60 pm/V for the 30 nm film to just 7 pm/V for the 5 nm film. This systematic decline in d₃₃ is accompanied by a corresponding increase in the coercive field. The d₃₃ loops show a systematic increase in tilt towards the applied field axis as function of reducing thickness coupled with a decrease in piezoelectric tunability. The small-signal relative dielectric response in the direction normal to the film-substrate interface decreases from 140 for a 50 nm film to just 60 for a 8 nm film. A similar drop is also observed in the dielectric tunability, from ∼17% to approximately −2% at an electric field of 750 kV/cm with the film thickness decreasing from 50 nm to 8 nm. We show that these observations cannot be explained using a straightforward application of a modified Landau-Devonshire thermodynamic model that incorporates the internal stresses due to the lattice and thermal expansion mismatch between the film and the substrate. We attribute this behavior to degradation in the polarization due to an intrinsic finite size effect.