Γ-X mixing effect in GaAs/AlAs superlattices and heterojunctions

The Γ-X mixing effect on the subband structure of superlattice (GaAs${)}_{12}$/(AlAs${)}_{12}$ is investigated with both the pseudopotential method and the effective-mass method. The results derived from the two methods show reasonable agreement, and the best-fitting Γ-X scattering parameter t is determined to be 0.5. The transmission probabilities of the Γ-point electron through the bound X-point states in the AlAs layer are calculated quantitatively. It is found that the resonant peaks correspond completely to the eigenstates of the corresponding superlattice, and the Γ-resonant peak is relatively smaller than the X-resonant peaks. Under the applied electric field, the resonant peaks originating from two barriers separate, resulting in a reduction of the peak-to-valley ratio.