Evolution of the band-gap and band-edge energies of the lattice-matched $GaInAsSb∕GaSb$ and $GaInAsSb∕InAs$ alloys as a function of composition

Using atomistic pseudopotential calculations we predict the evolution of the valence-band maximum energy $Eυ(x,y)$ and conduction-band minimum energy $Ec(x,y)$ for a compositionally graded quaternary $Ga1−yInyAsxSb1−x$ alloy lattice matched to GaSb or InAs as a function of $(x,y)$ or, equivalently, as a function of distance from the substrate. We find upward-concave bowing for both $Ec$ and $Eυ$⁠, in contradiction with simple interpolative models. A transition from staggered (type II) to broken-gap (type III) lineup relative to GaSb is predicted to occur at $x=0.81$ and $y=0.92$ on a GaSb substrate, and at $x=0.59$ and $y=0.62$ on an InAs substrate. In the latter case, the quaternary alloy has a minimum gap at $x=0.85$ and $y=0.87$⁠.