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A model of leakage current in Al/HfO 2 /SiO 2 /Si MOS (metal-oxide-semiconductor) capacitors is given by adopting the tunnel current model in SiGe-based heterojunction bipolar transistors. The velocity of an electron in the metal gate, which originates from the coupling between longitudinal and transverse (in-plane) kinetic energies, and the anisotropic mass of the substrate were included in the leakage current model. It was found that the leakage current obtained by including the gate electron velocity is lower than that calculated without the coupling effect and the leakage current decreases with an increasing gate electron velocity. However, the leakage current is not significantly influenced by the silicon substrate orientation. If a measured leakage current in the high-K dielectric stack MOS with Si(100) substrate were much higher than that in the MOS with Si(111) as observed in the conventional MOS, then the gate electron phase velocity in the latter would be higher. A small increase of the equivalent oxide thickness (EOT) of HfO 2 will decrease the tunnel current appreciably and tunnel current oscillations become visible as the EOT becomes thicker. Oscillatory behavior of the tunnel current is due to resonance states in the quantum well formed in high-K dielectric stack at high electric fields.

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