Electron Transmittance through a Heterostructure on Anisotropic Materials using the Airy Function and the Transfer Matrix Method

Abstract

Derivation of the transmittance of an electron incident on a heterostructure potential with nanometer-thick trapezoidal barrier grown on anisotropic materials is done by solving the effective-mass equation including off-diagonal effective-mass tensor elements. The analytic expressions are applied to the Si(110)/Si0.5Ge0.5/Si(110) heterostructure. 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 calculation of transmittances is done for incident energy at z direction below and above the barrier height by varying the applied voltage to the barrier. The maximum transmittance depends on the incident energy and the bias voltage given to the potential barrier. The transmittance value obtained from the Airy function has the same value obtained from the transfer matrix method. It was also found that the transmittance depends on the valley and it is not symmetric with the incident angle.