Boundary conditions on ferroelectricity in ultrathin SrTiO$_3$ films on silicon

The properties of SrTiO$_3$ films expitaxially grown on Si(001) are strongly influenced by the electronic structure of the interface. Using density functional theory, we demonstrate the presence of an intrinsic interface dipole, the direction of which is independent of the particular combination of Sr, Ti, O, and Si atoms at the interface, and therefore independent of growth conditions. As a result of this intrinsic dipole, a local, positive polarization is induced in the SrTiO$_3$ interfacial region, fixing the electrostatic boundary conditions at the interface and preventing the formation of a negatively polarized state with a single domain. We suggest ways in which this constraint on the ferroelectric behavior can be overcome by interfacial cation doping, allowing for the integration of ferroelectricity with traditional silicon-based devices.