Abstract: The frequency of the applied electric field and the epitaxial strain can affect the microstructure and the overall properties of ferroelectric thin films. In this study, the ferroelectric characteristics of BaTiO₃ nano single crystal thin films were investigated via phase field simulation under the epitaxial strain of -0.1% and -0.7%, respectively, in the frequency range of 0.1~100 kHz. It is found that, with the increase in frequency, the square-shaped hysteresis loop gradually changes to an elliptic loop and the butterfly loop changes to a kidney-shaped loop. When the applied frequency is below 50 kHz, the coercive field increases rapidly with the increase in frequency, but the change in remnant polarization is not significant. When the frequency is over 50 kHz, the coercive field only increases slightly, and the remnant polarization exhibits a downward trend. It is observed that the frequency dependence of ferroelectric properties is more significantly affected by the epitaxial strain while the frequency is low. The frequency dependence is not very sensitive to the epitaxial strain while the frequency is high. Meanwhile, the compressive epitaxial strain causes significant rise in both the remnant polarization and coercive field, and the tensile epitaxial strain leads to opposite effects. By analysis, it is found that the underlying mechanism of the frequency-dependent hysteresis is due to the competition between the speed of microstructure evolution and the frequency of the applied electric field. The findings of this study serve as theoretical basis for the experiment and design of ferroelectric functional thin films, and they provide knowledge-based support for the application of high-frequency electronic devices.

Key words: ferroelectric thin film, phase field method, BaTiO₃ nano single crystal thin film, Ginzburg-Landau equation, frequency effect, epitaxial strain