Polarization Properties Of Ferroelectric Thin Films Under Different Boundary Conditions

By taking into account two types of boundary conditions (BC), free boundary condition (FBC) and zero boundary condition (ZBC), an improved transverse Ising model with the consideration of surface transition layers (STL) is used to describe the polarization properties of ferroelectric thin films in the framework of the mean field approximation. Functions representing the intra-layer and inter-layer couplings are introduced to characterize the BC and STL, which reflect the structure variation of film surface. Comparing the results obtained by employing FBC and ZBC, some effects of BC are derived in the model, which demonstrated that the BC play important roles on the properties of ferroelectric thin films. It is shown that the effect of ZBC can extend to deeper film than that of FBC. When different BC are adopted, competition between the fields (depolarization field and transverse field) and BC induces some different and interesting phenomena. Some theoretical results in this paper are found to be in reasonable accordance with experimental data and have some application importance.