Influence of crystal structure on the lattice sites and formation energies of hydrogen in wurtzite and zinc-blende GaN

Charge-state calculations based on density-functional theory are used to study the formation energy of hydrogen in wurtzite and zinc-blende GaN as a function of Fermi level. Comparison of these results reveals notable differences including a 0.56 eV lower formation energy for H₂ in wurtzite, and different configurations for H₂ and H^- in the two crystal structures. Furthermore, H⁺ is found to be equally stable at bond-centered and antibonding sites in wurtzite, whereas it is unstable at a bond-centered site in zinc blende. N-H⁺ stretch-mode vibration frequencies, clustering of H⁺ in p-type material, and diffusion barriers for H^- are investigated in wurtzite GaN. A diffusion barrier of 1.6 eV is found for H^- in wurtzite GaN, significantly lower than a previous estimate, and a tendency for H⁺ clustering in p-type material is found.