Energy Bands for the (001) Surface of Aluminum

Abstract

An energy-band calculation has been performed on a 13-layer film of (001) aluminum. Surface states are found at $\overline{\ensuremath{\Gamma}}$, $\overline{M}$, and $\overline{\mathrm{X}}$ in the two-dimensional Brillouin zone, and along the lines connecting these points. Wave functions are plotted and decay constants tabulated for some of these surface states. The charge density in the [001] direction has also been plotted for various positions in the planar unit cell, and for an average over the unit cell. Finally, the 13-layer energy bands are compared to a (001) projection of the three-dimensional energy bands, and effects of film thickness as well as the surface perturbation are shown.