Lattice parameter and energy band gap of cubic AlxGayIn1−x−yN quaternary alloys

First-principles total energy calculations, combined with a generalized quasichemical approach to disorder and compositional effects, are used to obtain the lattice parameter and the energy band gap of cubic AlxGayIn1−x−yN quaternary alloys. It is found that the lattice parameter a(x,y) fulfills a Vegard’s-like law; that is, it shows a linear dependence on the alloy contents x and y. The range of compositions for which the alloy is lattice-matched to GaN is obtained. The energy band gap Eg(x,y) of the quaternary alloy deviates from a planar behavior displaying a two-dimensional gap bowing in the x–y plane. Analytical expressions that fit the calculated a(x,y) and Eg(x,y) surfaces are derived in order to provide ready access to the lattice parameter and energy band gap of the alloy for the entire range of compositions. The results are compared with data for the wurtzite phase alloys.