Kinetics of electric double layers at dielectric plasma-facing solids

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A solid surface in contact with an ionized gas collects electrons more efficiently than it looses electrons due to the recombination of ions or the deexcitation of radicals. It thus acquires a negative charge which in turn triggers an electron-depleted region in front of it. The most fundamental manifestation of the interaction of a solid with a plasma is thus the build-up of an electric double layer at the interface. It has been however hardly studied. Only the positve part of the double layer - the plasma sheath - has been investigated in great detail, the negative part in contrast, residing either inside or on top of the surface, depending on the electronic structure, received little attention. Little is also known about the plasma loss at the surface, which for dielectric surfaces has to occur via recombination of electron-hole pairs. To tap the full potential of hybrid electronics - an emerging line of plasma research combining elements of gaseous and semiconductor electronics - it is however crucial to understand the loss process quantitatively, that is, to determine explicitly the fate of the plasma-induced surplus charges inside the solid. Linking plasma production in the gas to plasma loss inside the solid microscopically and describing thereby the kinetics of the electric double layer at the plasma-solid interface is the goal of this project. We develop a kinetic theory specifically for a floating dielectric plasma-solid interface, taking its partial reflectivity, its electronic structure, and collisions on both sides of it into account. Our approach is based on two sets of Boltzmann equations, one for the electrons and ions inside the plasma and one for the electrons and holes inside the dielectric, the Poisson equation for the electric potential energy, and matching/boundary conditions at the interface/far away from it. Utilizing the different time-scales of intraband scattering and interband recombination, we derive a set of equations describing for the first time the charge transfer across the interface selfconsistently with the charge dynamics on both sides of it. Solving the set of equations iteratively, with the Grinberg-Luryi approach for determining distribution functions in halfspaces as the central element, we will be able to identify solid-based ways to control the plasma-induced space charge inside the solid as well as the recombination process itself (radiative vs. non-radiative) and may thus open up new possibilities for hybrid electronics.