NATURE OF ELECTRONIC STATES IN SLABS

Electronic states in metallic slabs ordinarily involve multiple interplanar couplings even in a nearest-neighbor-atom-coupling approximation, except for special cases such as (100) and (111) face-centered-cubic surfaces. A tight-binding study with nonzero multiple interplanar couplings shows that there can be many, depending upon the orientation of the slab, exponentially decaying states within the energy band. Their existence is needed to satisfy the boundary conditions at the slab surface. The effect of multiple interplanar coupling is to cause phase shifts in the plane-wave states in the bulk of material. These phase shifts produce an effective free-electron surface plane, independent of energy to the extent that the bands are parabolic, and affect quantization rules and the energy spectrum in slabs. The corresponding effects must also occur in more accurate representations of the electron states.