Ferroelectricity in thin films driven by charges accumulated at interfaces†
A simple view of ferroelectricity is proposed for a thin film with uniform polarization oriented perpendicular to its surface, starting from the assumption that this situation is always accompanied by charge accumulation in the outer metal electrodes, in the contamination layers or near the surface, in the ferroelectric film itself. Starting with the formula derived for an “elemental” dipole moment in the film, simple statistical mechanics allows one to derive hysteresis cycles, and their dependence on temperature starting with only two parameters: the dielectric constant of the material and the maximum value of the dipole moment of a unit cell. Values obtained for Curie temperatures and coercive fields agree well with experiments. “Exact” energy dependencies on the asymmetry parameter are derived, and their connection with the Landau–Ginsburg–Devonshire is proven. By considering also the dipolar interaction in a continuous model, in addition to the ordering energy in the presence of surface charge accumulation, one may estimate the distribution of the polarization inside the film and the validity of the hypothesis of uniform polarization.