Electron surface layer at the interface of a plasma and a dielectric wall

Abstract

We study the plasma-induced modifications of the potential and charge distribution across the interface of a plasma and a dielectric wall. For this purpose, the wall-bound surplus charge arising from the plasma is modeled as a quasistationary electron surface layer in thermal equilibrium with the wall. It satisfies Poisson's equation and minimizes the grand canonical potential of wall-thermalized excess electrons. Based on an effective model for a graded interface taking into account the image potential and the offset of the conduction band to the potential just outside the dielectric, we specifically calculate the modification of the potential and the distribution of the surplus electrons for MgO, SiO${}_{2}$, and Al${}_{2}$O${}_{3}$ surfaces in contact with a helium discharge. Depending on the electron affinity of the surface, we find two vastly different behaviors. For negative electron affinity, electrons do not penetrate into the wall and a quasi-two-dimensional electron gas is formed in the image potential, while, for positive electron affinity, electrons penetrate into the wall and a negative space-charge layer develops in the interior of the dielectric. We also investigate how the non-neutral electron surface layer---which can be understood as the ultimate boundary of a bounded gas discharge---merges with the neutral bulk of the dielectric.