Ab initio prediction of GaN ($10\overline{1}0$) and (110) anomalous surface relaxation

The results of a study of the surface relaxation of GaN in the framework of the ab initio (all-electron) Hartree-Fock method are presented. We perform total-energy calculations using a two-dimensionally periodic slab model for the most stable nonpolar cleavage faces, namely, the ($10\overline{1}0$) and (110) surfaces of the wurtzite and zinc-blende phases, respectively. For both surfaces, when the energy is minimized the Ga-N surface bonds show a very small rotation angle of about 6° accompanied by a reduction in surface bond length of about 7%. This result differs from the well-accepted model of the GaP (110) and GaAs (110) surfaces, where there is a large rotational angle in the range of 27°-31° and little change in surface bond length. The structure dependence of the calculated density of states suggests that this difference is at least partly due to interaction of the Ga $3d$ states with N $2s$-derived states in GaN. Partial double-bond character in the surface bond may also be important.