First-principles calculations of N- and P-type doping in wurtzite and zincblende GaN

The formation energies, activation energies, and self-compensation effects of silicon (Si), germanium (Ge), carbon (C), beryllium (Be), and magnesium (Mg) in wurtzite (wz-) and zincblende (zb-) GaN are explored through a unified hybrid density-functional theory. The common donors (Si and Ge) are promising donors for both wz- and zb-GaN due to small activation energies (< 30 meV). The popular acceptor alternatives (C and Be) have smaller activation energies of 490 and 134 meV in zb-GaN relative to that of 590 and 205 meV wz-GaN, respectively. However, neither C nor Be is expected to outperform Mg as the former suffers from considerable activation energy, and a strong self-compensation effect limits the latter. Mg's activation energy in zb-GaN is 153 meV, which is lower than that of 226 meV in wz-GaN. For the selfcompensation effects, C, Si, and Ge favor the interstitial incorporation in wz-GaN than zb-GaN, while Be and Mg behave oppositely. This is attributed to the coherence between the orbital symmetry and the geometrical symmetry of the interstitial site.