Size effect on SrRuO3/BaTiO3/SrRuO3 ferroelectric ultrathin film capacitor

We have carried out a detailed investigation on the size effect on SrRuO3/BaTiO3/SrRuO3 ferroelectric ultrathin film capacitors with film thickness fully strained with a SrTiO3 substrate. We employ the transverse field Ising model, taking into account the incomplete charge compensation of the realistic SrRuO3 electrode and the misfit strain imposed by the SrTiO3 substrate in the Hamiltonian, to quantitatively explain the experimental observation in the literature. It is found that BaTiO3 ultrathin films between two metallic electrodes lose their ferroelectric properties below a critical thickness of about 4.17 nm due to the enhancement of the quantum effect under the influence of the incomplete charge compensation of the electrode.