Electronic structure of transition metal ions in GaN and AlN: Comparing GGA+U with experiment

Abstract

Electronic structure of Cr, Mn, Fe, and Co transition metal (TM) ions in GaN and AlN is studied within the Generalized Gradient Approximation augmented by the +U corrections, which are treated as free parameters. The main impact of U(N) is the opening of the band gap by shifting both valence and conduction band energies. The intracenter transitions between the gap states of TM impurities are weakly affected by U(N), but they are sensitive to U(TM) which directly act on d(TM) orbitals. The impact of U(TM) depends on both the level symmetry and its occupancy (i.e., on the charge state of the TM ions). Degeneracies of partially occupied multiplet levels are lifted, the effect being mainly driven by the +U correction and not by the Jahn-Teller mechanism. The role of the U-induced hybridization between TM and host states is elucidated.A comparison with experimental intracenter optical transition energies demonstrate that the best agreement is obtained for U ≈ 0 for Fe, and even negative U ≈ −1 eV for Mn. The linear response calculations give U(TM)≈3.5–4.0 eV, which leads to severe discrepancies of about 1 eV with experiment. Importantly, the results obtained with U(Fe) = U(Mn) = U(N) = 5 eV are very close to those obtained with hybrid functionals, but the discrepancies with experiment are even larger. Comparison of the results for GaN and AlN shows that relative energies of gap levels of a given TM ion in the two hosts, as well as their dependencies on U(TM), are the same to within ∼0.2 eV. The estimated valence band offset between GaN and AlN is about 0.5 eV, in agreement with experiment.