Surface reconstruction and vibrational excitations of Si(001)

We present theoretical studies of vibrational excitations on the Si (001) surface. Three different reconstructions based on the surface dimer model are considered. The theoretical model that we use consists of a tight-binding theory for structural energies that we have extended to include explicit electron-electron interactions in the form of an on-site repulsion term. Perturbation theory is applied to calculate the dynamical matrix of the system under study. The phonon spectrum of the Si (001) 21 surface is presented and analyzed: we observe a number of modes that are characteristic of the dimer reconstruction. The analysis of the vibrational excitations of the surface provides a microscopic explanation for the driving forces that lead to higher-order reconstructions, namely, p (22) and c (42) structures, and provides an insight into the question of the multiplicity of periodicities that are observed on this surface, even at low temperatures. Using linear-response theory, we calculate the dipole activity of surface phonons on the 21, p (22), and c (42) surfaces. The absorption spectra that we obtain can be used to characterize the periodicity of the surface; effects of surface symmetry and surface polarizability on the spectra are also discussed.