  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.
