structures on a length scale larger than their bond lengths. As shown in Fig. 1, the wurtzite
structure has three-fold symmetric (trigonal) channels oriented along the [0001] direction
(c-axis) and extending through the length of the crystal. In zinc blende, the analogous
trigonal channels are oriented along <111> directions, but are blocked at intervals of 7.8 A
by a pair of gallium and nitrogen atoms. This structural difference is a direct result of the
different stacking sequences exhibited by wurtzite and zinc blende along the [0001] and
[111] directions, respectively (see Fig. 2).
To provide a starting point for understanding the behavior of hydrogen in wurtzite
GaN and to investigate the structural differences outlined above, we have performed charge-
state calculations for hydrogen in wurtzite and zinc-blende GaN. These calculations
employed the Vienna ab initio simulation package11 (VASP) utilizing ultrasoft
pseudopotentials12 within the framework of the Kohn-Sham formulation of density-
functional theory.13 The gallium and nitrogen atoms were modeled using pseudopotentials
developed by Grossner et al.,14 treating the Ga 3d electrons as valence, and the hydrogen
atoms were modeled using the 200 eV set of pseudopotentials from the VASP database.
Test calculations using gallium and nitrogen pseudopotentials from the VASP database
yielded identical results to those obtained with the Grossner et al. pseudopotentials. We
also performed test calculations using the generalized-gradient approximation (GGA) for
exchange and correlation.15 The results were the same as those obtained using the local-
density approximation (LDA),16 except for a pressure effect to be discussed further below.
We modeled hydrogen in GaN using periodically repeated 72-atom wurtzite and 64-
atom zinc-blende supercells. Test calculations using a 32-atom zinc-blende supercell were
performed to check the convergence of the 64-atom-cell results. No differences were
found. Brillouin-zone sampling was accomplished using Monkhorst-Pack17 parameters
{ 222} which tests indicated was adequate for our purposes. We note that calculations for