Energetics of Mg incorporation at GaN(0001) and GaN (000 1̄) surfaces

By using density functional calculations in the generalized gradient approximation, we investigate the energetics of Mg adsorption and incorporation at GaN(0001) and GaN (000 1̄) surfaces under various Ga and Mg coverage conditions as well as in presence of light or electron beam-induced electronic excitation. We find significant differences in Mg incorporation between Ga- and N-polar surfaces. Mg incorporation is easier at the Ga-polar surface, but high Mg coverages are found to cause important distortions which locally change the polarity from Ga to N polar. At the N-rich and moderately Ga-rich GaN(0001) surface, 0.25 ML of Mg substituting Ga in the top bilayer strongly reduce the surface diffusion barriers of Ga and N adatoms, in agreement with the surfactant effect observed in experiments. As the Mg coverage exceeds 0.5 ML, partial incorporation in the subsurface region (second bilayer) becomes favorable. A surface structure with 0.5 ML of incorporated Mg in the top bilayer and 0.25 ML in the second bilayer is found to be stable over a wide range of Ga chemical potential. At the Ga bilayer-terminated GaN(0001) surface, corresponding to Ga-rich conditions, configurations where Mg is incorporated in the interface region between the metallic Ga bilayer and the underlying GaN bilayer appear to be favored. At the N-polar surface, Mg is not incorporated under N-rich or moderately Ga-rich conditions, whereas incorporation in the adlayer may take place under Ga-rich conditions. In the presence of light or electron beam induced excitation, energy differences between Mg incorporated at the surface and in deeper layers are reduced so that the tendency toward surface segregation is also reduced.