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

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 $\epsilon \mathrm{}(+/0\mathrm{})={\epsilon }_v+0.22\mathrm{}$ and ${\epsilon }_v+0.41\mathrm{}$ eV, respectively, and the double donor energies are $\epsilon \mathrm{}(++/+)={\epsilon }_v+0.09\mathrm{}$ and ${\epsilon }_v+0.24\mathrm{}$ eV, respectively. The $p$-like gap wave function is found to be strongly localized on the impurity site. Outward atomic relaxations of $\sim 13\%$ and $\sim 15\%$ 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 $\sim 1\%$ for the positively charged impurities. The impurity-bound exciton binding energy is calculated at $E_b=0.22\mathrm{}$ and $E_b=0.41\mathrm{}$ eV for $\mathrm{GaN}̱:P$ and $\mathrm{GaN}̱:As.\mathrm{}$ The former is in good agreement with the experimental data ${(E}_b=0.232\mathrm{}$ eV) whereas the latter is offered as a prediction. No clear Jahn-Teller symmetry lowering ${(T}_d\to C_{3v})$ distortion, suggested by the one-electron configuration, is found for $\mathrm{GaN}̱:{\mathrm{P}}^{+}$ and $\mathrm{GaN}̱:{\mathrm{As}}^{+}.$