Effects of ordering on the band structure of III–V semiconductors

The band structures of five types of ordered compounds derived from parent zincblende alloys A1−xBxC and AC1−xDx have been determined. Included in this study are two novel x = 14, 34 derived structures, luzonite and famatinite, and three x = 12 structures, chalcopyrite and two 1 × 1 superlattices oriented along the (0,0,1) and (1,1,1) directions. The theory combines an empirical tight-binding model for III-V compounds and a valence force-field model of strain. Strain-induced tetragonal and internal distortion as well as the spin-orbit interaction cause a splitting of the top of the valence band. Trends in this splitting and the band-gap variation are studied for the 18 combinations of III-V elements. The Hopfield quasicubic crystal-field model is found to accurately describe this splitting for all chalcopyrite compounds. But this model fails for several (0,0, 1)- and (1,1, l)-superlattice compounds containing large strain distortions. The extracted Hopfield crystal-field splitting parameter Δcf is found to scale linearly with tetragonal distortion for common-anion compounds ABC2, but follow curvilinearly internal distortion for common-cation compounds. Strain and natural lineup energy modify the band gap significantly from that found in the virtual-crystal approximation for the alloy. For the metastable alloy systems GaAs1−xSbx and GaP1−xSbx, the experimental bowing of the band gap passes quite close to the results for the band gaps of the seven ordered structures.