Generalized continuum theory for ferroelectric thin films

A generalized Ginzburg-Landau-Devonshire free energy has been used to describe the influence of imperfect surface layers or interface layers in ferroelectric thin films. The natural boundary condition has been employed in solving the polarization profile, which can reflect a more realistic situation compared to the previous treatments of the same problem using the so-called extrapolation length. We show that the unscreened portion of the depolarization field makes the polarization distribution more uniform while reducing the amplitude of the effective polarization. The less perfect layer can lower the effective phase-transition temperature. We also used the model to study the effect of asymmetric boundary conditions, which will cause a shift of the hysteresis loop from the center point, similar to the effect of a bias field.