We study three carbon defects in GaN, isolated CN and its two complexes with donors CN–ON, and CN–SiGa, as a cause of the yellow luminescence using accurate hybrid density functional calculation, which includes the semi-core Ga 3d electrons as valence electrons and uses a larger 300-atom supercell. We show that the isolated CN defect yields good agreement with experiment on the photoluminescence (PL) peak position, zero-phonon line, and thermodynamic defect transition level. We find that the defect state of the complexes that is involved in the PL process is the same as that of the CN defect. The role of the positively charged donors (ON or SiGa) next to CN is to blue-shift the PL peak. Therefore, the complexes cannot be responsible for the same PL peak as isolated CN. Our detailed balance analysis further suggests that under thermal equilibrium at typical growth temperature, the concentration of isolated CN defect is orders of magnitude higher than the defect complexes, which is a result of the small binding energy in these complexes.

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