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

than in zinc-blende GaN, with values of 1.99 eV and 2.17 eV for uuc and ’c, respectively. The diffusion barriers for H2 are relatively high ~2.0 eV for uuc 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 1 . The vibrational frequency of the molecule in wurtzite GaN is redshifted from the free molecule; for wurtzite GaN the frequency is 129 cm 21 lower than in free H2. Finally, we find that the H 2 complex is only slightly higher in energy than interstitial H2, and we calculate its vibrational frequencies. I. INTRODUCTION Hydrogen plays a very important role in GaN. It is abundantly present in many of the techniques used for growth of GaN, including metal-organic chemical vapor deposition ~MOCVD!, hydride-vapor-phase epitaxy ~HVPE!, and molecular-beam epitaxy ~MBE! when NH3 is used as the nitrogen source. Hydrogen is known to be responsible for the passivation of Mg acceptors, resulting in the lack of p-type conductivity in Mg-doped layers grown in the presence of hydrogen. A post-growth anneal that removes H from the vicinity of the acceptors is necessary to activate the Mg. Detailed knowledge about the behavior of hydrogen is essential to optimize this process. Previous studies 1‐3 have addressed some aspects of the diffusion of monatomic hydrogen, but not of molecular hydrogen. In this paper, we report the first comprehensive study of the diffusion of hydrogen in wurtzite GaN. This includes explicit investigations of the migration paths of monatomic hydrogen, with particular attention to potential anisotropies. Indeed, the symmetry of the wurtzite structure is such that differences may exist between motion along @0001# (uuc) versus motion in planes perpendicular to @0001# (’c) ~which we will also refer to as ‘‘inplane’’ diffusion !. Our recent study of beryllium in GaN indicated that Be interstitials exhibit very anisotropic diffusion. 4 Given the importance of removing hydrogen from acceptor-doped layers, knowledge about any anisotropy in the hydrogen diffusion characteristics is very important. Although we find that molecular hydrogen is only stable over a limited range of Fermi levels, information about its migration is essential to complete our picture of hydrogen motion in GaN. In other semiconductors, H2 can be formed when H is released from acceptor-hydrogen complexes. Although the formation energy of H2 is relatively higher ~when compared with the monatomic species! in GaN than in other semiconductors such as Si or GaAs, the possibility exists that H2 is formed. If it is, then means of detecting it also need to be explored. Vibrational spectroscopy has been a powerful tool for detecting hydrogen-related configurations, including H2, and in order to facilitate interpretation of experiment we will present calculated vibrational frequencies for interstitial H2 molecules. Due to the light mass of the hydrogen atoms the anharmonicity is very large, and it is fully included in our calculations. We also address other diatomic hydrogen complexes, in particular H 2 , which we find to be only slightly higher in energy than H2. Vibrational frequencies for other hydrogen-related configurations relevant for p-type GaN have been reported elsewhere. 5