Experimental evidence of the size effect in thin ferroelectric films

The phenomenological model based on the Ginsburg–Devonshire equation has been applied to investigate the size effect in thin SrTiO3 and BaxSr1−xTiO3 films. The size effect is caused by two phenomena: spatial correlation of the polarization and boundary conditions for the ferroelectric polarization on electrodes. The experimental data obtained by different groups were used to investigate the boundary conditions. The most remarkable result was found for the SrRuO3/BaxSr1−xTiO3/SrRuO3 structure which is characterized by free boundary conditions for the ferroelectric polarization. Such boundary conditions provide the highest value of the effective dielectric constant of a dielectric layer in the sandwich structure. The strain dependence of the dielectric permittivity of SrTiO3 at finite temperatures was taken into account as well.