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

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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 Δs ≈ 0.38 nm, corresponding to the addition of one layer of oxygen atoms. The minimum thickness of s₀ ≈ 0.54 nm is due to a double layer of oxygen. We found a strong and systematic dependence of the barrier height Φ₀ on the thickness s like Φ₀ ≈ 2.5 eV / s²(nm), which nearly coincides with the kinetic electron energy E = h²/2ms² for which the deBroglie wavelength matches the width of the barrier.