Deep electronic gap levels induced by isovalent P and As impurities in GaN

Abstract

The electronic and atomic structure of isovalent substitutional P and As impurities in GaN is studied theoretically using a self-consistent plane-wave pseudopotential method. In contrast with the conventional isovalent III-V systems, $\mathrm{GaN}\mathrm{̱}:\mathrm{P}$ and $\mathrm{GaN}\mathrm{̱}:\mathrm{A}\mathrm{s}$ are shown to exhibit deep gap levels. The calculated donor energies are $\ensuremath{\epsilon}(+/0)={\ensuremath{\epsilon}}_{v}+0.22$ and ${\ensuremath{\epsilon}}_{v}+0.41$ eV, respectively, and the double donor energies are $\ensuremath{\epsilon}(++/+)={\ensuremath{\epsilon}}_{v}+0.09$ and ${\ensuremath{\epsilon}}_{v}+0.24$ eV, respectively. The $p$-like gap wave function is found to be strongly localized on the impurity site. Outward atomic relaxations of $\ensuremath{\sim}13%$ and $\ensuremath{\sim}15%$ are calculated for the nearest-neighbor Ga atoms surrounding neutral ${\mathrm{GaN}\mathrm{̱}:\mathrm{P}}^{0}$ and ${\mathrm{GaN}\mathrm{̱}:\mathrm{A}\mathrm{s}}^{0},$ respectively. The relaxation increases by $\ensuremath{\sim}1%$ for the positively charged impurities. The impurity-bound exciton binding energy is calculated at ${E}_{b}=0.22$ and ${E}_{b}=0.41$ eV for $\mathrm{GaN}̱:P$ and $\mathrm{GaN}̱:As.$ The former is in good agreement with the experimental data ${(E}_{b}=0.232$ eV) whereas the latter is offered as a prediction. No clear Jahn-Teller symmetry lowering ${(T}_{d}\ensuremath{\rightarrow}{C}_{3v})$ distortion, suggested by the one-electron configuration, is found for $\mathrm{GaN}̱:{\mathrm{P}}^{+}$ and $\mathrm{GaN}̱:{\mathrm{As}}^{+}.$