Stability, diffusivity, and vibrational properties of monatomic and molecular hydrogen in wurtzite GaN

The stability and diffusivity of monatomic (H⁺ and H^-) and molecular (H₂) hydrogen in wurtzite GaN are studied via first-principles calculations. Stable configurations are identified and the formation energies are studied as a function of the Fermi level. Diffusion barriers in the direction parallel to [0001] $(||c)$ and perpendicular to [0001] (⊥c) are calculated. For H⁺ the diffusion barriers are slightly higher than in the zinc-blende phase and modestly anisotropic (0.85 eV ⊥c, 0.94eV||c). For H^- the diffusion barriers are lower than in zinc-blende GaN, with values of 1.99 eV and 2.17 eV for $||c$ and ⊥c, respectively. The diffusion barriers for H₂ are relatively high (2.0 eV for $||c$ and 2.2 eV for ⊥c), and we propose that diffusion of H₂ is more likely to proceed by dissociation followed by diffusion of monatomic H⁺. The vibrational frequency of the molecule in wurtzite GaN is redshifted from the free molecule; for wurtzite GaN the frequency is 129 cm^-1 lower than in free H₂. Finally, we find that the H₂* complex is only slightly higher in energy than interstitial H₂, and we calculate its vibrational frequencies.