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An energy-band calculation has been performed on a 13-layer film of (001) aluminum. Surface states are found at, M, and 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.
Caruthers et al. (Thu,) studied this question.