Abstract

GaN is of great importance for optoelectronic and power electronic devices, and carbon is one of its most common impurities, used also actively for preparing semi-insulating buffer layers. Experimental investigations reveal at least five carbon-related centers, however, theory could provide definite assignment so far for only two of those: in terms of simple carbon substitutionals on nitrogen $({\mathrm{C}}{\mathrm{N}})$ and gallium $({\mathrm{C}}{\mathrm{Ga}})$ sites. We apply here an optimized hybrid functional (which reproduces the band gap and is Koopmans' compliant) to investigate small carbon complexes. We find that an increasing carbon concentration, beyond the compensation of the $n$-type doping by the acceptor ${\mathrm{C}}{\mathrm{N}}$, makes its complexes with ${\mathrm{C}}{\mathrm{Ga}}$ and ${(\mathrm{C}\ensuremath{-}\mathrm{N})}_{\mathrm{N}}$ split interstitials competitive in formation energy. Except for $p$-doped samples, these complexes are electrically passive, so the Fermi level is pinned a little below midgap, ensuring the semi-isolating behavior even for high carbon concentrations. The charge transition levels, calculated by the optimized functional, allow the interpretation of all carbon-related deep-level spectra as well as of their relation to the carbon-to-donor ratio.