It is well known that the physical properties of ferroelectric thin films are considerably different from those of bulk ferroelectrics. The surface effect is one of this important properties observed in ferroelectric thin films. At the surface , the coordination of the atoms is different from that in the volume of the film. The influence of the surface effect on the ferroelectric properties of PbTiO3 films has been investigated based on Ginsburg- Landau-Devonshire (GLD) thermodynamic theory, where the free energy coefficients are calculated for PbTiO3 crystal from microscopic interactions based upon the statistical mean field approximation. In this study, the shift displacement profile, the average the maximal and minimal of central ion shift displacement, the phase transition and Curie temperature (Tc) dependence on the film thickness are numerically modeled and analyzed by an Euler-Lagrange equation with applying a corresponding boundary condition on ion displacement for various values film thicknesses and levels of extrapolation length.

Surface effect, Size effect, Phase transition, Curie temperature, Ginzburg-Landau-Devonshire theory

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