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A theoretical model of an electron tunneling current in an anisotropic Si/Si 1−x Ge x /Si heterostructure was developed. The parallel and perpendicular kinetic energies were coupled and the coupling was included in expressing the electron transmittance through the anisotropic heterostructure. The model was applied to the anisotropic Si(1 1 0)/Si 0.5 Ge 0.5 /Si(1 1 0) heterostructure with a 25 nm thick strained Si 0.5 Ge 0.5 potential barrier, in which each layer of the heterostructure has three valleys (valleys 1, 2 and 3) with different inverse effective mass tensors and a conduction band discontinuity of 216 meV. The Si(1 1 0)/SiGe structure implies that only the four equivalent valleys (valleys 1 and 2) are considered in calculations. It was found that the transmittance for valley 1 is the same as that for valley 2 due to the same barrier height. The transmittance decreases as the electron phase velocity increases because the electron phase velocity enhances the barrier height. Moreover, the total tunneling current density for the phase velocity higher than 3 × 10 5 m s −1 differs significantly from that obtained without including the kinetic energy coupling. As the electron phase velocity gets higher, the total tunneling current density lowers. This implies that the coupling effect cannot be ignored for electrons with high phase velocity. drift-diffusion, energy-transport, hydrodynamic transport and quantum transport, are available in modeling devices based on the heterostructure. However, by now, the most popular model is the drift-diffusion transport model [5][6][7].With shrinking device dimensions, quantum effects become more pronounced and must be taken into account. An analytic expression for a tunnel current at an abrupt semiconductor-semiconductor heterojunction has been derived by assuming that the longitudinal and transverse components of electron motion are decoupled and the

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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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