Carbon is a common impurity in the group-III nitrides, often unintentionally incorporated during growth. Nevertheless, the properties of carbon impurities in the nitrides are still not fully understood. We investigate the impact of carbon impurities on the electrical and optical properties of GaN, AlN, and InN using density functional calculations based on a hybrid functional. We examine the stability of substitutional and interstitial configurations as a function of the Fermi-level position and chemical potentials. In all nitrides studied here, C${}_{\mathrm{N}}$ acts as a deep acceptor and gives rise to deep, broad photoluminescence bands. Carbon on the cation site acts as a shallow donor in InN and GaN, but behaves as a $DX$ center in AlN. A split interstitial is the most stable configuration for the C impurity in InN, where it acts as a double donor and likely contributes to $n$-type conductivity.

Effects of carbon on the electrical and optical properties of InN, GaN, and AlN