Theoretical analysis of electronic structures of short-period superlattices (GaAs${)}_{\mathrm{m}}$/(AlAs${)}_{\mathrm{n}}$ and corresponding alloys ${\mathrm{Al}}_{\mathrm{n}/(\mathrm{m}+\mathrm{n})}$${\mathrm{Ga}}_{\mathrm{m}/(\mathrm{m}+\mathrm{n})}$As

The electronic structures of short-period superlattices (GaAs${)}_{\mathrm{m}}$/(AlAs${)}_{\mathrm{n}}$ and corresponding alloys ${\mathrm{Al}}_{\mathrm{n}/(\mathrm{m}+\mathrm{n})}$ ${\mathrm{Ga}}_{\mathrm{m}/(\mathrm{m}+\mathrm{n})}$As are analyzed and compared with use of the empirical pseudopotential method. The results show that the two kinds of material are similar in many respects: The variation of direct and indirect energy gaps with x=n/(m+n), conservation of the properties of point-Γ and -X states after energy-band folding, and the differences between the optical transition matrix elements to X- and Γ-like states, etc. The variations of direct and indirect gaps of superlattices (GaAs${)}_{\mathrm{n}}$/(AlAs${)}_{\mathrm{n}}$ with n are in agreement with recent experimental results. As n increases to 10, the Γ-like state remains higher than the X-like state. The reason for the divergent conclusions reached by previous theoretical calculations is discussed, and it is found that the valence-band offset and the direct energy gap of AlAs have critical effects on the electronic structures of short-period superlattices.