Energy scaling and surface patterning of halogen-terminated Si(0Â 0Â 1) surfaces

We show that steric repulsion energies between halogen dimers on a passivated Si(0 0 1) surface scale with square of the principle quantum number (or period) n of the halogen, and arise principally from bonding with Si substrate. We exemplify the scaling from previously calculated steric interactions of F, Cl, and Br, predict the interactions for I and At, and then verify the prediction by direct density-functional calculations. From the energetics, we explain the patterning of the halogen-terminated Si(0 0 1), for a better understanding of the halogen-roughening process, and predict a crossover to a new vacancy-line defect for large halogens.