Discrete saturation thickness and anomalous potential height of native ultrathin aluminum oxide tunnel barriers

We have investigated planar metal - insulator - metal tunnel junctions with aluminum oxide as dielectricum. These oxide barriers were grown on an aluminum electrode in pure oxygen at room temperature till saturation. We observed discrete barrier widths separated by \Delta s \approx 0.38 nm, corresponding to the addition of one layer of oxygen atoms. The minimum thickness of s_0 \approx 0.54 nm is due to a double layer of oxygen. We found a strong and systematic dependence of the barrier height \Phi_0 on the thickness s like \Phi_0 \approx 2.5 eV / s^2(nm), which nearly coincides with the kinetic electron energy E = h^2/2ms^2 for which the deBroglie wavelength matches the width of the barrier.