Dispersion of surface bands and chain coupling at Si and Ge(1 1 1) surfaces

The dispersion of quasi-one-dimensional dangling-bond electrons in π-bonded chains at the Si(1 1 1)-2 × 1 and Ge(1 1 1)-2 × 1 surfaces has been experimentally investigated by angle-resolved photoemission spectroscopy, in the direction perpendicular to the chains, with a high energy and angle precision. The results show a very small dispersion in the case of Si(1 1 1)-2 × 1 and instead a much larger (downward) dispersion (156 meV) in the case of Ge(1 1 1)-2 × 1. Accurate density-functional calculations with GW corrections are in very good agreement with the experimental results. Then the surface chains are somewhat interacting in Ge(1 1 1)-2 × 1 - the coupling occurring mainly through the subsurface region - while in Si(1 1 1)-2 × 1 they are essentially decoupled. Therefore the one-dimensional character of electrons in surface chains is enhanced in Si(1 1 1)-2 × 1 with respect to Ge(1 1 1)-2 × 1.