Theoretical study of GaN (0001) surface reconstructions and La and Ga adatoms under N- and Ga-rich conditions

Using density functional theory, we determined that $2\ifmmode\times\else\texttimes\fi{}2$ and $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})\mathrm{R}{30}^{\ensuremath{\circ}}$ surface reconstructions of bulk-terminated GaN (0001) are degenerate in energy but differ in their electronic structure. Consistent with previous reports, our study of the adsorption energy of Ga adatoms shows that a laterally contracted Ga bilayer is the most energetically favorable surface arrangement under Ga-rich conditions, albeit with a different atomic arrangement of the Ga bilayer than previously reported. We also determined the potential energy surfaces for La and Ga adatoms on bulk-terminated GaN (0001) surface and for a La adatom on a bulk-terminated GaN (0001) covered by a contracted Ga bilayer and discuss possible adatom surface migration paths. An exchange reaction of a La adatom with surface Ga was found to be energetically favorable for both the bulk-terminated and the Ga bilayer-covered surfaces, indicating formation of LaN. A careful study of the diffusion of a La adatom through the Ga bilayer toward the bulk-terminated GaN surface suggests that a lower energy arrangement is achieved when the La adatom exchanges positions with a surface Ga atom. This indicates that ${\mathrm{LaGa}}_{2}$ and LaN are potential materials to form a transition layer to facilitate epitaxial integration of oxides on GaN.