Complex band structure and superlattice electronic states

The complex band structures of the bulk materials which constitute the alternating layer (001) semiconductor-semiconductor superlattice are investigated. The complex bands near the center of the Brillouin zone in the [001] direction are studied in detail. The decay lengths of superlattice states whose energies lie in the bulk band gaps of one of the semiconductors are determined from the dispersion curves of these bands for imaginary $\overrightarrow{\mathrm{k}}$. This method is applied using a tight-binding band-structure calculation to two superlattices: the AlAs-GaAs superlattice and the CdTe-HgTe superlattice. The decay lengths of AlAs-GaAs superlattice conduction-band minimum states are found to be substantially shorter than those for the CdTe-HgTe superlattice. These differences in the decay of the states in the two superlattices result in differences in the variation of the conduction-band effective masses with the thickness of the AlAs and CdTe layers. The conduction-band effective masses increase more rapidly with AlAs thickness in the AlAs-GaAs superlattice than with CdTe thickness in the CdTe-HgTe superlattice.