An ab initio-based approach to phase diagram calculations for GaN(0 0 0 1) surfaces

Surface phase diagrams of GaN(0 0 0 1)-(2 × 2) and pseudo-(1 × 1) surfaces are systematically investigated by using our ab initio-based approach. The phase diagrams are obtained as functions of temperature T and Ga beam equivalent pressure p_Ga by comparing chemical potentials of Ga atom in the vapor phase with that on the surface. The calculated results imply that the (2 × 2) surface is stable in the temperature range of 700-1000 K at 10⁻⁸ Torr and 900-1400 K at 10⁻² Torr. This is consistent with experimental stable temperature range for the (2 × 2). On the other hand, the pseudo-(1 × 1) phase is stable in the temperature range less than 700 K at 10⁻⁸ Torr and less than 1000 K at 10⁻² Torr. Furthermore, the stable region of the pseudo-(1 × 1) phase almost coincides with that of the (2 × 2) with excess Ga adatom. This suggests that Ga adsorption or desorption during GaN MBE growth can easily change the pseudo-(1 × 1) to the (2 × 2) with Ga adatom and vice versa.