Coupling between Γ- andX-type envelope functions at GaAs/Al(Ga)As interfaces

Connection rules for envelope functions related to the {Γ}- and X-point conduction-band valleys in GaAs/Al(Ga)As systems are formulated in terms of a transfer matrix. The transfer-matrix elements are calculated using a method in which wave functions, which are obtained using empirical pseudopotentials, are matched at the interface. The nonzero transfer-matrix elements appear to depend weakly on energy which enables us to give a simple prescription for connection rules for envelope functions in which {Γ}-X coupling is incorporated.