Effects of epitaxial strain, film thickness and electric-field frequency on the ferroelectric behavior of BaTiO₃ nano films

Ferroelectric nano films exhibit distinctive properties that are influenced by aspects such as the epitaxial strain, film thickness, and electric-field frequency. In this work, we studied the effects of the above factors on the ferroelectric behavior of BaTiO₃ nano films with a phase-field model based on the time-dependent Ginzburg–Landau kinetic equation. For the study of the epitaxial strain, we considered the cases with either compressive or tensile strain, ranging from −3.2% to 1%. Our results showed that the compressive epitaxial strain can generally enhance the remnant polarization and the coercive field, as opposed to the effect of the tensile one. As the film thickness reduces from 100 to 5 nm, the remnant polarization and the coercive field tend to increase, whereas the dielectric constant and the piezoelectric constant tend to decrease. We further investigated the effect of the high-strength electric-field frequency that varies from 0.1 to 100 kHz under two epitaxial-strain values, i.e., −0.1% and −1.74%, respectively. It was found that, at low frequencies, the coercive field increases sharply and the remnant polarization increases slightly with the rise of the applied frequency. Once the frequency gets higher than 20 kHz, the remnant polarization drastically reduces with the increasing frequency. In the meanwhile, the hysteresis loop exhibits an elliptic shape and the sharp tails of the butterfly loop are diminishing. We noticed that the frequency dependency is more sensitive to the epitaxial strain within the low-frequency range. Based on the obtained microstructural evolution process, we found that the 180° polarization reversal is more likely to occur under low-frequency field, while the polarization cannot be fully reversed in high-frequency hysteresis.