Electronic collective modes and instabilities on semiconductor surfaces. II. Theory of electron-phonon interaction

The phonon self-energy and the dynamical effective charge are expressed in terms of the non—local density-response function ${\epsilon }^{-1\mathrm{}}(\overrightarrow{q}+\overrightarrow{G},\mathrm{ }\overrightarrow{q}+{\overrightarrow{G}}^{\prime }, z, z^{\prime })$ of a surface. The main purpose is to obtain a consistent description of the energy spectra, lifetimes, and amplitudes of electronic surface excitations, such as surface plasmons, excitons, and magnons, which have been discussed in a previous paper with the dynamical (phonon) excitations. An application to the ideal Si(111) surface reveals two types of instabilities of Rayleigh modes, which can be related to relaxation and (2×1) reconstruction.