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

Abstract

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 phononmediated 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, multiphonon processes are important. To obtain the desorption time, we use a quantum-kinetic rate equation for the occupancies of the boundelectron 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. For an electron desorbing from a graphite surface at 360 K, we find a desorption time of 2 ϫ 10 −5 s. We also demonstrate that depending on the potential depth and bound-state level spacing, the desorption scenario changes. In particular, we show that desorption via cascades over bound states dominates unless direct one-phonon transitions from the lowest bound state to the continuum are possible.

Wall Charge and Potential from a Microscopic Point of View

“…In order to investigate the dependence of the trapping scenario on material parameters, for instance, the Debye frequency and the dielectric function, and to show trends we applied the model however also to dielectric materials with positive electron affinity [25][26][27]. The basis in which the Hamiltonian is written down, the elementary excitations causing energy relaxation, and the couplingV s depend on the surface.…”

“…We applied the approach just outlined to various uncharged dielectric surfaces assuming electron physisorption to occur in the image potential, which is, as pointed out, rigorously true only for dielectrics with negative electron affinity [25][26][27]. Electron energy relaxation at these surfaces is driven by acoustic phonons whose Debye energy is very often not only too small to connect the lowest bound state to the unbound states but also too small to connect the two lowest bound states.…”

“…The physisorption kinetics of electrons at dielectric surfaces involves therefore multiphonon transitions [25][26][27]. For the plasma context most important is that s e 1 and τ −1 e = 0 [25][26][27], implying that an initially uncharged dielectric surface with a negative electron affinity is not a perfect absorber for electrons. Multiphonon processes contribute very little to it.…”

Surface Electrons at Plasma Walls

“…To remedy this we use a variational procedure to extract the static image potential from [41]. Thereby we keep some recoil effects which make the recoil-corrected image potential ∼ 1/(z + z c ) with a cut-off parameter z c = h/2mω s π 2 [34] divergence free.…”

Quantum mechanics of electrons at plasma boundaries

“…The sticking coefficient turned out to be rather small but the product sticking coefficient times desorption time was of the order expected from our phenomenological study of the charging of grains in low-temperature gas discharges 1 . In the meantime we set up a quantum-kinetic rate equation to investigate physisorption of electrons at dielectric boundaries where phonon-induced up-and downward cascading in the manifold of bound electron surface states may occur 3 . In addition, multi-phonon processes turn out to be important for dielectric boundaries making, in some cases, the desorption time particularly long.…”