Phonon-mediated desorption of image-bound electrons from dielectric surfaces

A complete kinetic modeling of an ionized gas in contact with a surface requires the knowledge of the electron desorption time and the electron sticking coefficient. We calculate the desorption time for phonon-mediated desorption of an image-bound electron, as it occurs, for instance, on dielectric surfaces where desorption channels involving internal electronic degrees of freedom are closed. Because of the large depth of the polarization-induced surface potential with respect to the Debye energy multi-phonon processes are important. To obtain the desorption time, we use a quantum-kinetic rate equation for the occupancies of the bound surface states, taking two-phonon processes into account in cases where one-phonon processes yield a vanishing transition probability, as it is sufficient, for instance, for graphite. Besides producing an estimate for the desorption time of an electron image-bound to a graphite surface, we investigate the desorption scenario and show that desorption via cascades over bound states dominates unless direct one-phonon transitions from the lowest bound state to the continuum are possible.