Transmission Coefficient of an Electron through a Heterostructure with Nanometer-Thick Trapezoidal Barrier Grown on an Anisotropic Material

Transmission coefficient of an electron incident on a heterostructure potential with nanometer-thick trapezoidal barrier grown on anisotropic materials are derived by solving the effective-mass equation including off-diagonal effective-mass tensor elements. The boundary condition for an electron wave function (under the effective-mass approximation) at a heterostructure anisotropic junction is suggested and included in the calculation. The analytic expressions are applied to the Si(110)/Si0.5Ge0.5/Si(110) heterostructure, in which the SiGe barrier thickness is several nanometers. It is assumed that the direction of propagation of the electrons makes an arbitrary angle with respect to the interfaces of the heterostructure and the effective mass of the electron is position dependent. The transmission coefficient is calculated for energy below the barrier height, varying the applied voltage to the barrier. The transmission coefficient depends on the valley where the electron belongs and it is not symmetric with respect to the incidence angle.