NATURE OF ELECTRONIC STATES IN SLABS

Electronic states in metallic slabs ordinarily involve multiple interp lanar 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 cou plings 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 su rface. The effect of multiple interplanar coupling is to cause phase s hifts in the plane-wave states in the bulk of material. These phase sh ifts produce an effective free-electron surface plane, independent of energy to the extent that the bands are parabolic, and affect quantiza tion rules and the energy spectrum in slabs. The corresponding effects must also occur in more accurate representations of the electron stat es.