Mechanism of ferroelectric thin films self-polarization phenomenon

In present work we calculated the three components of polarization in phenomenological theory framework by consideration of three Euler-Lagrange equations, which include mismatch effect and influence of misfit dislocations, surface tension and depolarization field. These equations were solved with the help of variational method proposed by us earlier. This approach lead to the free energy in the form of algebraic equation of different powers of polarization components with the coefficients dependent on film thickness, mismatch effect, temperature and other parameters. Several new terms proportional to misfit strain appeared in the free energy expression: built-in electric field normal to the surface originated from piezoelectricity in vicinity of surface even in the cubic symmetry of bulk ferroelectrics, renormalization of bulk transition temperature via electrostriction, odd powers of normal to the surface component of polarization. The obtained free energy made it possible to calculate all properties of the film by conventional procedure of minimization. As an example we calculated phase diagrams of PZT 50/50 films on different substrates, that lead to compressive or tensile strain u in coordinates T , u , l , where l is a film thickness, for two cases – without and with external electric field, that compensate built-in field. It was shown that in both cases self-polarized phase does exist in definite regions of aforementioned coordinates, its nature being mismatch effect. The calculations of pyroelectric coefficient and dielectric permittivity dependencies on T , u and l had shown the unusual behaviour of these quantities, e.g. existence of pyroelectricity at l < l cr , where l cr is critical thickness of ferroelectric-paraelectric phase transitions.