Electron Phonon Interaction at the $\mbox{Si(111)-7}\times \mbox{7}$ Surface

In recent years, it has become possible to study the electron-phonon interaction of metals by high resolution photoelectron spectroscopy. However, virtually no such experimental information is available for the case of semiconductors. It is shown that electron-phonon interaction at the $\mbox{Si(111)-7}\times \mbox{7}$ surface provides a natural explanation for the unusual band dispersion of the metallic surface states. While local density theory predicts a hole-like dispersion for the adatom bands that cross the Fermi level $E_F $, photoemission finds an electron-like band with a break in the slope at 0.1~eV below $E_F $. Such behavior follows naturally from electron phonon interaction with the surface phonon mode at $\hbar \omega =70\mbox{ meV}$ that dominates electron energy loss spectra. It has been assigned to adatom vibrations by molecular dynamics calculations. Two independent determinations of the electron-phonon coupling parameter from the band dispersion and the temperature dependent phonon broadening yield very similar coupling parameters around $\lambda =1.1$.