Internal electric field originated from mismatch effect and its   influence on ferroelectric thin film properties
  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 Pm, leading to appearance of internal thickness dependent field. It has been shown that this field influences drastically all the properties behaviour. In particular the polarization profile becomes asymmetrical, average polarization temperature dependence resembles the one in the external electric field, and there is possibility of external field screening by the internal one. 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 thickness induced ferroelectric-paraelectric phase transition has been shown to exist when the Pm value is smaller than the polarization PS in the bulk. The large enough mismatch effect 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. 
M.D.Glinchuk, A.N.Morozovska