Self-consistently derived sample permittivity in stabilization of ferroelectricity due to charge accumulated at interfaces†
Recently, a simple model was proposed for the microscopic energy associated to the ferroelectric phase, to be used in a statistical approach in order to derive the equations of state for a ferroelectric thin film [C. M. Teodorescu, Phys. Chem. Chem. Phys., 2021, 23, 4085–4093]. The stabilization energy for an elemental dipole in a polar thin film is the result of the interaction of this dipole with the field generated by charges accumulated at surfaces or interfaces of the thin film. An essential parameter of this interaction is the permittivity of the film, assumed to be a material constant, together with the maximum value of an elemental dipole and the density of the elemental dipoles. These can be connected to three experimental parameters which are the saturation polarization Ps, the coercive field at zero temperature E(0)c and the Curie temperature TC. However, for a ferroelectric material both the global and the differential permittivity depend on the temperature and on the polarization. This raises the question whether such a non-constant permittivity should be used in the stabilization energy of the ferroelectric phase, and whether it can be identified self-consistently with the function resulting after applying the statistics based on the microscopic model. In such case, a mutual interdependence should exist between Ps, E(0)c and TC. A model is built up, able to predict coercitivity, however E(0)c and TC yield values several orders of magnitude higher than the experimental ones. Therefore, one has to introduce a background dielectric constant of several hundreds to accommodate the result of the model with the experimental data. The poling history of the film has to be taken into account, together with the presence of a small bias field. The model is able to predict self-consistently the equation of state of a ferroelectric, and in particular the linear decrease of the coercive field with temperature. The microscopic parameters, in particular the background dielectric constant and the density of elemental dipoles may be expressed directly from experimental quantities.