MULTILAYER-RELAXATION GEOMETRY AND ELECTRONIC-STRUCTURE OF A W(111) SURFACE

The multilayer-relaxation geometry of a tungsten (111) surface has bee n calculated using both a first-principles approach within the local-d ensity 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 incl uding scalar-relativistic interactions. Within these approximations, t he electronic structure of the W(111) surface is characterized by a su rface resonance near the Fermi level and near the GAMMA point of the s urface 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 seve n-layer films are consistent with the first-principles results; geomet ries calculated for the larger films indicate that the main relaxation effects occur in the first four layers near the surface, although mea surable relaxations occur far from the surface.