Mitigate self-compensation with high crystal symmetry: A first-principles study of formation and activation of impurities in GaN

Formation and activation energies of common impurities: silicon (Si), germanium (Ge), carbon (C), beryllium (Be), and magnesium (Mg) in wurtzite (wz-) and zincblende (zb-) GaN are investigated by first–principles calculations. Si and Ge are excellent donors with low activation energies (<30 meV). The acceptor activation energies of C and Be in wz-GaN (and zb-GaN) are found to be 590 and 205 meV (and 490 and 134 meV), respectively. Neither C nor Be is a qualified acceptor in general as the former has a large activation energy (>300 meV) and the latter has a strong self-compensation effect (the formation energy of Be_i compensating donor is negative). Be_i is energetically abundant in zb-GaN because it has a 0.66 eV lower formation energy than wz-GaN. This is attributed to the coherence of the symmetricity between the s-orbitals and the interstitial site. The acceptor activation energy of Mg in zb-GaN is found to be 153 meV, which is smaller than its value in wz-GaN, 226 meV. Vibrational analysis suggests that Mg_i compensating donor is less favorable to form in zb- than wz-GaN, since the higher symmetricity of the interstitial site in zb-GaN renders a much smaller vibrational entropy. Contrarily, the differences are insignificant for the impurities residing on Ga sites due to the same tetrahedral symmetricity. The results evidence the importance of self-compensation effects, which can be mitigated by the higher crystal symmetry of zb-GaN.