Multilayer-relaxation geometry and electronic structure of a W(111) surface

The multilayer-relaxation geometry of a tungsten (111) surface has been calculated using both a first-principles approach within the local-density approximation and an empirical approach using an embedded-atom-type potential with angular forces. Both calculations predict the same relaxation pattern of a triplet of W layers moving toward each other and an expansion of the layer spacing between each triplet. The first-principles calculations were carried out for three-, five-, and seven-layer thin films using mixed-basis pseudopotential techniques and including scalar-relativistic interactions. Within these approximations, the electronic structure of the W(111) surface is characterized by a surface resonance near the Fermi level and near the point of the surface Brillouin zone, which is insensitive to surface relaxation. The empirical calculations were carried out for 3- to 15-layer thin films. The relaxation geometries calculated for the three-, five-, and seven-layer films are consistent with the first-principles results; geometries calculated for the larger films indicate that the main relaxation effects occur in the first four layers near the surface, although measurable relaxations occur far from the surface.