  We study the potential and the charge distribution across the interface of a
plasma and a dielectric wall. For this purpose, the charge bound to the wall is
modelled as a quasi-stationary electron surface layer which satisfies Poisson's
equation and minimizes the grand canonical potential of the wall-thermalized
excess electrons constituting the wall charge. 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 potential and the electron distribution for
magnesium oxide, silicon dioxide and sapphire 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 an external surface charge is formed in the image
potential, while for positive electron affinity, electrons penetrate into the
wall and a space charge layer develops in the interior of the dielectric. We
also investigate how the electron surface layer merges with the bulk of the
dielectric.
