@phdthesis{Heinisch2013,
  author    = {Rafael Leslie Heinisch},
  title     = {Surface electrons at dielectric plasma walls},
  journal    = {Oberfl{\"a}chenelektronen an dielektrischen Plasmaw{\"a}nden},
  url       = {https://nbn-resolving.org/urn:nbn:de:gbv:9-001626-9},
  year      = {2013},
  abstract  = {The concept of the electron surface layer introduced in this thesis provides a framework for the description of the microphysics of the surplus electrons immediately at the wall and thereby complements the modelling of the plasma sheath. In this work we have considered from a surface physics perspective the distribution and build-up of an electron adsorbate on the wall as well as the effect of the negative charge on the scattering of light by a spherical particle immersed in a plasma. In our electron surface layer model we treat the wall-bound electrons as a wall-thermalised electron distribution minimising the grand canonical potential and satisfying Poissons equation. The boundary between the electron surface layer and the plasma sheath is determined by a force balance between the attractive image potential and the repulsive sheath potential and lies in front of the crystallographic interface. Depending on the electron affinity x, that is the offset of the conduction band minimum to the potential in front of the surface, two scenarios for the wall-bound electrons are realised. For x<0 electrons do not penetrate into the solid but are trapped in the image states in front of the surface where they form a quasi two-dimensional electron gas. For x>0 electrons penetrate into the conduction band where they form an extended space charge. These different scenarios are also reflected in the electron kinetics at the wall which control the sticking coefficient and the desorption time. If x<0 electrons from the plasma cannot penetrate into the solid. They are trapped in the image states in front of the surface. The transitions between unbound and bound states are due to surface vibrations. Trapping of electrons is mediated by one-phonon transitions and takes place in the upper bound states. Owing to the large binding energy of the lowest bound state transitions from the upper bound states to the lowest bound state are due to multi-phonon processes. For low surface temperatures relaxation to the lowest bound state takes place while for higher temperature a relaxation bottleneck emerges. Desorption occurs in cascades for systems without relaxation bottleneck and as a one-way process in systems with a relaxation bottleneck. From the perspective of plasma physics the most important result is that the sticking coefficient for electrons is relatively small, typically on the order of 0.001. For x>0 electron physisorption takes place in the conduction band. For this case sticking coefficients and desorption times have not been calculated yet but in view of the more efficient scattering with bulk phonons, responsible for electron energy relaxation in this case, we expect them to be larger than for the case of x<0. Finally, we have studied the effects of surplus electrons on the scattering of light by a spherical particle. For x<0 the electrons form a spherical electron gas around the particle and their electrical conductivity modifies the boundary condition for the magnetic field. For x>0 the electrons in the bulk of the particle modify the refractive index through their bulk electrical conductivity. In both cases the conductivity is limited by scattering with surface or bulk phonons. Surplus electrons lead to an increase of absorption at low frequencies and, most notably, to a blue-shift of an extinction resonance in the infrared. This shift is proportional to the charge and is strongest for submicron-sized particles. The particle charge is also revealed in a blue-shift of the rapid variation of one of the two polarisation angles of the reflected light. From our work we conclude that the electron affinity is an important parameter of the surface which should affect the charge distribution as well as the charge-up. Therefore, we encourage experimentalists to study the charging of surfaces or dust particles as a function of x. Interesting in this respect is also if or under what conditions the electron affinity of a surface exposed to a plasma remains stable. Moreover, we suggest to use the charge signatures in Mie scattering to measure the particle charge optically. This would allow a charge measurement independent of the plasma parameters and could be applied to nano-dust where conventional methods cannot be applied.},
  language  = {en}
}