Effects of surface tension on the size-dependent ferroelectric characteristics of free-standing BaTiO₃ nano-thin films

Intrinsic surface tension of nanoscale ferroelectric thin film tends to induce tensile stress in its surface layer, whereas the other portion of the film is subjected to compression to maintain mechanical balance. A continuum-based phase-field model accounting for such surface effect has been set up to investigate the evolution of domain structure and thickness-dependent ferroelectric properties of free-standing BaTiO₃ nano-thin films. It was observed that both remnant polarization and coercive field decrease with a decrease of film thickness and increase of surface tension, and that, for film thickness ranging from 10-20 nm, both properties decreased sharply at the surface strain 2-3ε₀ (ε₀ being the spontaneous strain). Further decrease in film thickness or increase in surface tension could result in loss of ferroelectricity. Such a critical state for the ferroelectric-to-paraelectric transition has also been established for the range of film thickness 4-20 nm.