Multiband tight-binding approach to tunneling in semiconductor heterostructures: Application to ΓXtransfer in GaAs

We study tunneling in semiconductor heterostructures where the constituent materials can have a direct or an indirect band gap. In order to have a good description of the lowest conduction band, we have used the nearest-neighbor sp³{s}*$ tight-binding model put forward by P. Vogl et al. A recursive Green-function method yields transmission coefficients from which an expression for the current density may be written down. The method is applied to GaAs/AlAs heterostructures. Electrons may traverse the AlAs barriers via different tunneling states ψ_Γ and ψX ({Γ}X mixing). With an applied bias V{}0.5 V electrons may enter the GaAs collector contact in both the {Γ} and the X valleys ({Γ}X transfer). We have studied a number of GaAs/AlAs structures. For very narrow barriers there is little {Γ}X transfer, but AlAs barriers wider than about 25 {} act as ``{Γ}X filters,'' i.e., most transmitted electrons have been transferred to the X valley.