Lattice model for strained nanoscale ferroelectric capacitors: Investigation on fundamental size limits in ferroelectricity

To study the size effect for ferroelectricity of epitaxial SrRuO3/BaTiO3/SrRuO3 capacitors, we modify the mean-field Landau-type theory by incorporating the dipole-dipole interaction energy density, realistic lattice structure, epitaxial stress, and metal electrodes. The calculated depolarization field is consistent well with the experimental data. The critical thickness tc is predicted to be six unit cells, according to the result calculated by first-principle calculations. We demonstrate that tc can be reduced to four unit cells by selecting the Pt electrode. The compressive strain can reduce the tc. We discover the decrease of the lateral dimensions of the film can enhances the spontaneous polarization.