Surface phonons ofSi(001)−(1×1)dihydride

Abstract

We report the complete surface-phonon dispersions of the hydrogen-terminated $\mathrm{Si}(001)\ensuremath{-}(1\ifmmode\times\else\texttimes\fi{}1)$ dihydride surface as calculated from first principles employing density-functional perturbation theory. Supercells, nonlocal norm conserving pseudopotentials, and plane-wave basis sets are used to describe the surface system. The H adatoms give rise to the canted-row dihydride structure and fully passivate the Si surface. The surface exhibits six salient branches of spatially localized phonon modes. Their physical origin and character is highlighted by atomic displacement patterns and electronic charge-density perturbations. For further reference, we have also carried out ab initio calculations of surface phonons at the center of the surface Brillouin zone employing layer force constants together with a Gaussian orbital basis set. Comparing our mode energies at the Brillouin-zone center with those of previous calculations and contrasting them to experimental data, as obtained from $3\ifmmode\times\else\texttimes\fi{}1$ trihydride or nominal $1\ifmmode\times\else\texttimes\fi{}1$ dihydride surfaces, allows for a number of interesting conclusions concerning the atomic structure and the phonon spectrum of $\mathrm{Si}(001)\ensuremath{-}(1\ifmmode\times\else\texttimes\fi{}1)$ dihydride.