  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.
