Strain and size effects on ferroelectric properties of BaTiO₃ nanofilms

The strain and size effects on the ferroelectric properties of BaTiO ₃ films are studied using the molecular dynamics method based on a shell model. It is found that from microscopic view, these two effects share the same physical nature, i.e., the resulting crystal cell distortions lead to the separation of negative and positive charge centres. The strain and size effects are therefore coupled, and the critical thicknesses of films would depend on the in-plane strains, which provides a possible interpretation on the discrepancies among the experimental measurements of the critical thicknesses. A polarization map is given to clearly reflect the relations among the size, strain and polarization of the nano films.