Ab initio prediction of GaN (10(1)over-bar0) 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(1)over bar 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 degrees 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 degrees-31 degrees 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.