  General features of finite size effects in the ferroelectric-semiconductor
film under open-circuited electric boundary conditions are analyzed using
Landau-Ginzburg-Devonshire theory and continuum media electrostatics. The
temperature dependence of the film critical thickness, spontaneous polarization
and depolarization field profiles of the open-circuited films are found to be
significantly different compared to the short-circuited ones. In particular, we
predict the re-entrant type transition boundary between the mono-domain and
poly-domain ferroelectric states due to reduced internal screening efficiency
and analyzed possible experimental scenarios created by this mechanism. This
analysis is relevant to the behavior of the free-standing ferroelectric films
and scanning-probe microscopy based experiments on free ferroelectric surfaces.
