Electronic structure of rare-earth impurities in GaAs and GaN

The electronic structures of substitutional rare-earth (RE) impurities in GaAs and cubic GaN are calculated. The total energy is evaluated with the self-interaction corrected local spin density approximation, by which several configurations of the open $4f$ shell of the rare-earth ion are investigated. The defects are modeled by supercells of type $\mathit{RE}{\mathrm{Ga}}_{n\ensuremath{-}1}{\mathrm{As}}_{n}$, for $n=4$, 8, and 16. The preferred defect is the rare-earth substituting Ga, for which case the rare-earth valency in intrinsic material is found to be trivalent. The $3+\ensuremath{\rightarrow}2+$ $f$-level is found above the theoretical conduction band edge in all cases and within the experimental gap only for Eu, Tm, and Yb in GaAs and for Eu in GaN. The exchange interaction of the rare-earth impurity with the states at both the valence band maximum and the conduction band minimum is weak, one to two orders of magnitude smaller than that of Mn impurities. Hence the coupling strength is insufficient to allow for ferromagnetic ordering of dilute impurities, except at very low temperatures.