Ferroelectric thin film properties: Peculiarities related to mismatch-induced polarization

The ferroelectric thin film properties were calculated in phenomenological theory framework. Surface energy that defined boundary conditions for Euler-Lagrange differential equation was written as surface tension energy. The latter was expressed via surface polarization and tension tensor related to mismatch of a substrate and a film lattice constants and thermal expansion coefficients. The calculations of the film polarization distribution, temperature, thickness and external electric field dependence and hysteresis loops as well as average dielectric susceptibility dependence on temperature and film thickness have been performed allowing for mismatch-induced polarization P-m. The obtained asymmetry of hysteresis loop makes it possible to suppose that the self-polarization phenomenon recently observed in some films is related to mismatch effect. The large enough mismatch effect (broken vertical bar Pm broken vertical bar/Ps > 1) could be the physical reason of ferroelectric phase conservation in ultrathin film. The possibility to observe the peculiarities of the films properties temperature and thickness dependencies related to mismatch effect is discussed.