Polarization of thin barium-strontium titanate films by an external electric field

The behavior of polarization of a Ba$_{0.8}$Sr$_{0.2}$TiO$_3$ thin film in an external electric field for a planar geometry of electrodes is described using a simple phenomenological model. The “van der Waals field” $E_z$ formed by the substrate along the normal to the film surface is introduced for fitting to experimental data. This field is estimated as $E_z$ = 1.1 $\times$ 10$^8$ V/m. The phase diagram of the Ba$_{0.8}$Sr$_{0.2}$TiO$_3$ film in the $E_z$ (misfit strain) at room temperature is analyzed.