Theoretical studies were made of vibrational excitations on the Si(001) surface. Three different reconstructions, based upon the surface dimer model, were considered. The theoretical model that was used consisted of a tight-binding theory for structural energies that was extended so as to include explicit electron-electron interactions in the form of an on-site repulsion term. Perturbation theory was used to calculate the dynamic matrix of the system. The phonon spectrum of the Si(001)-(2 x 1) surface was presented and analyzed. A number of modes was observed that was characteristic of the dimer reconstruction. Analysis of the vibrational excitations of the surface provided a microscopic explanation for the driving forces that led to higher-order reconstructions, such as p(2 x 2) and c(4 x 2) structures, and provided some insight into the multiplicity of periodicities that were observed on this surface; even at low temperatures. Using linear-response theory, the dipole activity of surface phonons on the 2 x 1, p(2 x 2), and c(4 x 2) surfaces were calculated. The absorption spectra that were obtained could be used to characterize the periodicity of the surface.

Surface Reconstruction and Vibrational Excitations of Si(001). O.L.Alerhand. E.J.Mele: Physical Review B, 1987, 35, 5533-46