Finite size effects in ferroelectric-semiconductor thin films under open-circuited electric boundary conditions

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.