Band offset in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As multiple quantum wells calculated with the ${\mathit{sp}}^3$${\mathit{s}}^{\mathrm{*}}$ tight-binding model

By incorporating a block-decimation method to the ${\mathit{sp}}^3$${\mathit{s}}^{\mathrm{*}}$ tight-binding model, we have studied the evolution of ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As electronic band structure as a function of Al composition, including the compositional correlation effect. Using the experimental data of a GaAs/AlAs multiple quantum well, we obtain the band edges of an ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As alloy as functions of x, from which the band offsets Δ${\mathit{E}}_{\mathit{V}}$ and Δ${\mathit{E}}_{\mathit{C}}$ as well as the band-offset coefficient Q=Δ${\mathit{E}}_{\mathit{C}}$/(Δ${\mathit{E}}_{\mathit{C}}$+Δ${\mathit{E}}_{\mathit{V}}$) are derived for arbitrary Al concentration. The result agrees well with experiment.