Direct Observation of Thickness Dependence of Ferroelectricity in Freestanding BaTiO₃ Thin Film

In this work, we focus on the thickness dependence of the electric polarization in a freestanding BaTiO₃ thin film. The locations of titanium and oxygen ions as well as their relative displacements were directly observed and measured by using aberration-corrected transmission electron microscopy (AC-TEM). It is found that the freestanding BaTiO₃ thin film keeps the tetragonal distortion when its thickness is thicker than 4.8 nm, while completely loses its ferroelectricity when thinner than 4.4 nm. The method of combining high-resolution AC-TEM imaging with the multiparameter simulation unit cell by unit cell was developed to accurately determine each local thickness of the sample. This method is powerful for quantitative analysis in AC-TEM images.