Calculated properties of point defects in Be-doped GaN

The properties of several point defects in hexagonal gallium nitride that can compensate beryllium shallow acceptors $\left({\mathrm{Be}}_{\mathrm{Ga}}\right)$ are calculated using the AIMPRO method based on local density functional theory. ${\mathrm{Be}}_{\mathrm{Ga}}$ itself is predicted to have local vibrational modes (LVM’s) very similar to magnesium acceptors. The highest frequency is about $663{\mathrm{cm}}^{-1}.$ Consistent with other recent studies, we find that interstitial beryllium double donors and single-donor beryllium split interstitial pairs at gallium sites are very likely causes of compensation. The calculations predict that the split interstitial pairs possess three main LVM’s at about 1041, 789, and $738{\mathrm{cm}}^{-1}.$ Of these, the highest is very close to the experimental observation in Be-doped GaN. Although an oxygen donor at the nearest-neighboring site to a beryllium acceptor $({\mathrm{Be}}_{\mathrm{Ga}}-{\mathrm{O}}_{\mathrm{N}})$ is also a prime suspect among defects that are possibly responsible for compensation, its highest frequency is calculated to be about $699{\mathrm{cm}}^{-1}$ and hence is not related in any way to the observed center. Another mode for this defect is estimated to be about $523{\mathrm{cm}}^{-1}$ and is localized on the ${\mathrm{O}}_{\mathrm{N}}$ atom. These two vibrations of ${\mathrm{Be}}_{\mathrm{Ga}}-{\mathrm{O}}_{\mathrm{N}}$ are thus equivalent to those for the isolated substitutional centers perturbed by the presence of their impurity partners.