Thickness dependence of polarization in ferroelectric perovskite thin films

The dependence of the polarization of ferroelectric perovskite thin films on the film thickness is explicitly calculated by using a generalized Landau-Ginzburg-Devonshire thermodynamic theory. Both residual stress and stress relaxation in the films have a significant effect on the thickness-dependent polarization. Our calculations demonstrate that the coexistence or competition between the surface effect and the constraint effect results in significant size effects at a finite nanoscale. This is especially so for the compressively strained perovskite films, in which there are two characteristic thicknesses, i.e. h_c (a few nanometres), below which the ferroelectricity disappears, and h_m (∼10h_c), where the polarization exhibits a maximum. The theoretical results describe the available experimental data quite well.