Absolute surface energies of polar and nonpolar planes of GaN

Accurate values for absolute surface energies are required to understand bulk and thin-film growth. Using first-principles calculations based on hybrid density functional theory we determine energies for bare and hydrogenated surfaces of wurtzite GaN in polar and nonpolar orientations. We find that the energies of the nonpolar $m$ and $a$ planes are similar and constant over the range of Ga, N, and H chemical potentials studied. In contrast, the energies of the polar planes are strongly condition dependent. We find that the $+c$ polar plane is systematically lower in energy than the $-c$ plane.

Figure 1

(a) Cross section of a zb-GaN triangular wedge used to determine the energy of the (111) surface. The bottom surface is a N-terminated (001)N surface, the other surfaces are symmetrically equivalent $\left(111\right)$ and $\left(\overline{1}\overline{1}1\right)$ surfaces. All surfaces are passivated with fractional H atoms. (b) Cross section of the zb-GaN slab used to determine the energy of the passivated $\left\{001\right\}$ surface.

Figure 2

Absolute surface energies of GaN nonpolar and polar planes as a function of Ga chemical potential.

Figure 3

Absolute surface free energies of hydrogenated GaN polar planes for different temperature and pressure conditions, as a function of Ga chemical potential. Hydrogenation of nonpolar surfaces does not lower the surface energy at these $T$ and $p$ conditions.