Surface phonon frequencies and eigenvectors onSi(111)3×3: Al

The frequencies and eigenvectors for surface phonons on the $\mathrm{Si}\mathrm{}\left(111\right)\mathrm{}\sqrt{3}\times \sqrt{3}$: Al surface have been determined by evaluation of the force-constant matrix with the local density functional and first-principles pseudopotential methods. A surface phonon exists which has a frequency corresponding to 69 meV, in excellent agreement with that measured in electron-energy-loss experiments. The displacement eigenvector for this mode is localized mainly on the two Si atoms located directly beneath the Al adatom in the $T_4$ site. The Al adatom itself participates very little in the vibration for this mode.