The dimensional effect in thin ferroelectric layers

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Abstract
The dimensional effect in layers of BaTiO3-type ferroelectrics consists of the reduction of the dielectric constant of the material and in the diffusion of the phase transition as the thickness of the layers is decreased. This effect is usually explained on the basis of the surface layer model dealing with the non-stoichiometric thin surface regions of BaTiO3.In this paper the equation of motion for the ferroelectric polarization was analyzed taking into account the spatial dispersion of polarization and the semiconductor properties of the surface layer. In order to gain consistent relations we had to assume specific boundary conditions and drop the specifications of the dielectric constant and thickness of the surface layer. The quantitative results obtained are in a good agreement with available experimental data.