Ab initio shallow acceptor levels in gallium nitride

Impurity levels and formation energies of acceptors in wurtzite GaN are predicted ab initio. Be_Ga is found to be the shallow (thermal ionization energy $\sim$ 0.06 eV); $Mg_{Ga}$ and $Zn_{Ga}$ are mid-deep acceptors (0.23 eV and 0.33 eV respectively); $Ca_{Ga}$ and $Cd_{Ga}$ are deep acceptors ($\sim$0.65 eV); $Si_N$ is a midgap trap with high formation energy; finally, contrary to recent claims, $C_N$ is a deep acceptor (0.65 eV). Interstitials and heteroantisites are energetically not competitive with substitutional incorporation.