First-principles calculations by means of the linear-muffin-tin-orbital method were carried out of the electronic band structures, equilibrium lattice constants, energies of formation, and bulk moduli of ${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{-}\mathit{x}}$N alloys in zinc-blende-derived structures with a specific cation ordering. The miscibility and band-gap bowing of disordered alloys were studied using a cluster expansion method. Complete mutual solubility is predicted to occur at typical growth temperatures. The band gap is found to exhibit a weak bowing and to change from being indirect (Γ→X) for x=0 to direct at Γ at a concentration of x≊0.4.

• Received 22 July 1993

DOI:https://doi.org/10.1103/PhysRevB.48.17841