Model of a tunneling current in an anisotropic Si/Si_1−xGe_x/Si heterostructure with a nanometer-thick barrier including the effect of parallel–perpendicular kinetic energy coupling

Abstract

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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