General Expressions for Ellipsoidal-Valley Quantum Transport in Arbitrary Growth Direction: Non-Equilibrium Green's Function

A theoretical method for the calculation of quantum transport in an ellipsoidal valley is presented. This method is developed using a non-equilibrium Green's function framework. Importantly, it is instructive that kz is separated into two parts so that the wrong figure shape of the transmission coefficients does not exist. The L-electron effect on AlAs–GaAs–AlAs double barrier structures oriented in the [001], [111], and [110] growth directions is explored using the proposed method.