Electronic structure of steps on the (001) surface of copper

Abstract

Using the extended-Hückel parameters previously obtained for smooth Cu thin films, we have calculated the energy bands and local densities of states of a (001) Cu film alternately 13 and 11 layers thick with two-dimensional lattice vectors $(\frac{1}{2},\frac{-1\mathrm{}}{2},0)a$ and $\mathrm{}(5,5,0)a$. We find no surface states but several surface resonances, one of which may be designated an edge resonance. The upper atom at a step has a charge deficit of $-0.037\mathrm{}e$ (an order of magnitude smaller than that obtained with ordinary Hückel calculations for atoms on smooth surfaces) but the lower atom at the step has a charge surplus of $0.031e$ and the two surface planes have a net deficit of only $-0.008\mathrm{}e$ per atom without the use of any surface-parameter shifts.