Thermal amplitudes of surface atoms on Si(111) 2×1 and Si(001) 2×1

Atomic displacement-displacement correlation functions for the surface atoms of the Si(111) 2×{}1 and Si(001) 2×{}1 surfaces are calculated using phonon energies and eigenvectors obtained from a tight-binding theory of the lattice dynamics of Si. The temperature dependence and the possible anisotropies of the amplitudes of vibration of the surface atoms are investigated. For the {π}-bonded chain model of Si(111) 2×{}1 it is found that the surface atoms have larger vibrational amplitudes perpendicular to the surface than parallel to it, and this anisotropy (1.8 in the mean-squared amplitudes at 270 K) increases rapidly with increasing temperature. This is attributed to the existence of a small-wavelength acoustic phonon with an unusually low energy. For the surface atoms on Si(001) 2×{}1 the anisotropy between perpendicular and parallel vibrations is not as marked. The interatomic vibrational correlations between surface atoms reveal the strength of the new bonds that are formed in the reconstruction of these surfaces.