  We studied the phase diagram of thin ferroelectric films with incommensurate
phases and semiconductor properties within the framework of
Landau-Ginzburg-Devonshire theory. We performed both analytical calculations
and phase-field modelling of the temperature and thickness dependencies of the
period of incommensurate 180 degree domain structures appeared in thin films
covered with perfect electrodes. It is found that the transition temperature
from the paraelectric into the incommensurate phase as well as the period of
incommensurate domain structure strongly depend on film thickness, and surface
and gradient energy contributions. The results may provide insight on the
temperature dependence of domain structures in nanosized ferroics with inherent
incommensurate phases.
