Surface effects and diffusive phase transition in ferroelectric thin films: A self-consistent approach

A self-consistent Landau phenomenological approach has been used to study the ferroelectric transition in films in the presence of various surface effects such as depolarization and strain. The polarization distribution of the film is computed and its variation with respect to temperature, thickness and strain is determined. The gradual decrease in polarization across the transition shows the diffusive behavior which is confirmed from the soft mode and the dielectric susceptibility analysis. The critical thickness below which ferroelectricity disappears is also computed. The degree of diffuseness in the transition is obtained from the susceptibility exponent which shows more and more diffusive behavior for smaller and smaller film thickness.