Substitutional and interstitial carbon in wurtzite GaN

Abstract

First-principles theoretical results are presented for substitutional and interstitial carbon in wurtzite GaN. Carbon is found to be a shallow acceptor when substituted for nitrogen $({\mathrm{C}}_{\mathrm{N}})$ and a shallow donor when substituted for gallium $({\mathrm{C}}_{\mathrm{Ga}}\mathrm{).}$ Interstitial carbon $({\mathrm{C}}_I)$ is found to assume different configurations depending on the Fermi level: A site at the center of the c-axis channel is favored when the Fermi level is below 0.9 eV (relative to the valence band maximum) and a split-interstitial configuration is favored otherwise. Both configurations produce partly filled energy levels near the middle of the gap, and ${\mathrm{C}}_I$ should therefore exhibit deep donor behavior in p-type GaN and deep acceptor behavior in n-type GaN. Formation energies for ${\mathrm{C}}_{\mathrm{N}},$ ${\mathrm{C}}_{\mathrm{Ga}},$ and ${\mathrm{C}}_I$ are similar, making it likely that ${\mathrm{C}}_{\mathrm{N}}$ acceptors will be compensated by other carbon species. ${\mathrm{C}}_{\mathrm{Ga}}$ is predicted to be the primary compensating species when growth occurs under N-rich conditions while channel ${\mathrm{C}}_I$ is predicted to be the primary compensating species under Ga-rich growth conditions. Self-compensation is predicted to be more significant under Ga-rich growth conditions than under N-rich conditions. Experimental evidence for self-compensation is discussed. Four carbon complexes are discussed. ${\mathrm{C}}_{\mathrm{N}}{\mathrm{–V}}_{\mathrm{Ga}}$ is found to be unstable when the Fermi level is above the middle of the gap due to the high stability of gallium vacancies $({\mathrm{V}}_{\mathrm{Ga}}\mathrm{).}$ The ${\mathrm{C}}_{\mathrm{N}}{\mathrm{–V}}_{\mathrm{Ga}}$ complex was previously suggested as a source of the broad 2.2 eV luminescence peak often observed in n-type GaN. The present results indicate that this is unlikely. The ${\mathrm{C}}_I–{\mathrm{C}}_{\mathrm{N}}$ complex is capable of forming in carbon doped GaN grown under Ga-rich conditions if the mobility of the constituents is high enough. Experimental evidence for its existence is discussed.