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. hc (a few nanometres), below which the ferroelectricity disappears, and hm (∼10hc), where the polarization exhibits a maximum. The theoretical results describe the available experimental data quite well.