Band gap bowing in quaternary nitride semiconducting alloys

Structural properties of In(x)Ga(y)Al(1-x-y)N alloys are derived from total-energy minimization within the local-density approximation (LDA). The electronic properties are studied by band structure calculations including a semiempirical correction for the LDA gap error. The effects of varying the composition and atomic arrangements are examined using a supercell geometry. An analytical expression for the band gap is derived for the entire range of compositions. The range of (x, y) values for which In(x)Ga(y)Al(1-x-y)N is lattice matched to GaN, and the ensuing energy gaps, are given. This range of available gaps becomes smaller when In atoms form clusters. Comparison to experimental data is made. (C) 2011 American Institute of Physics. [doi:10.1063/1.3597795]