Nano-scale theory of ferroelectric surface predicting skin-deep quantized 2D electron gas

A nm-scale theory of ferroelectric surface is outlined. The distributions of the electron and the spontaneous polarization P in a ferroelectric having a finite bandgap and an ideally clean surface are selfconsistently solved as the minimum Landau free energy point. The quantization of the electron motion and the ∇ P effect are incorporated by extending the formulation for the MOS diode inversion layer. For a plausible range of the ∇ P effect length scale L G , the theory predicts a nm-thin electron surface layer. The quantization enhances the ∇ P effect and locates the electron layer a few lattice below the effective surface where P terminates. Therefore, the fraction of the electron there can be mobile, which is supported by a recent experiment. This donates the freedom and the mobility to the domain configuration of very thin ferroelectric, even when its surface is separated from a conducting electrode.