A first-principles study of carbon-related energy levels in GaN. Part I - complexes formed by substitutional/interstitial carbons and gallium/nitrogen vacancies

摘要

Various forms of carbon based complexes in GaN are studied withfirst-principles calculations employing Heyd-Scuseria-Ernzerhof hybridfunctional within the framework of density functional theory. We considercarbon complexes made of the combinations of single impurities, i.e.$\mathrm{C_N-C_{Ga}}$, $\mathrm{C_I-C_N}$ and $\mathrm{C_I-C_{Ga}}$, where$\mathrm{C_N}$, $\mathrm{C_{Ga}}$ and $\mathrm{C_I}$ denote C substitutingnitrogen, C substituting gallium and interstitial C, respectively, and ofneighboring gallium/nitrogen vacancies ($\mathrm{V_{Ga}}$/$\mathrm{V_N}$), i.e.$\mathrm{C_N-V_{Ga}}$ and $\mathrm{C_{Ga}-V_N}$. Formation energies arecomputed for all these configurations with different charge states after fullgeometry optimizations. From our calculated formation energies, thermodynamictransition levels are evaluated, which are related to the thermal activationenergies observed in experimental techniques such as deep level transientspectroscopy. Furthermore, the lattice relaxation energies (Franck-Condonshift) are computed to obtain optical activation energies, which are observedin experimental techniques such as deep level optical spectroscopy. We compareour calculated values of activation energies with the energies ofexperimentally observed C-related trap levels and identify the physical originsof these traps, which are unknown before.