Transmission and reflection coefficients of carriers at an abrupt GaAs-GaAlAs (100) interface

We present calculations of reflection and transmission coefficients for electrons and holes at an abrupt (100) interface for the GaAs-${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ system. We consider semi-infinite crystals of the two semiconductors joined at a perfect atomically abrupt interface. The calculations are performed using the empirical tight-binding approximation. The transport coefficients were computed as a function of the components of the incident carrier wave vector normal and parallel to the interface. We have investigated the transport coefficients for incident states near various band minima into different final-state channels. The transmission into states with qualitatively similar character to the incident state is found to be much greater than transmission into states of different character. For example, an electron near the $X$ minimum normal to the interface in ${\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ transmits into the $X$ valley of GaAs with much greater probability than it transmits into the $\Gamma$ minimum of GaAs. The dependence of the transport coefficients on the alloy composition has also been investigated.