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Recent theoretical work has provided evidence that hybrid functionals, whichinclude a fraction of exact (Hartree Fock) exchange in the density functionaltheory (DFT) exchange and correlation terms, significantly improve thedescription of band gaps of semiconductors compared with local and semilocalapproximations. Based on a recently developed order-$N$ method for calculatingthe exact exchange in extended insulating systems, we have implemented anefficient scheme to determine the hybrid functional band gap. We use thisscheme to study the band gap and other electronic properties of the ternarycompound In$_{1-x}$Ga$_{x}$N using a 64-atom supercell model.

Hybrid density functional calculations of the band gap of Ga$_x$In$_{1-x}$N