  We consider counterions in the presence of a single planar surface with a
spatially inhomogeneous charge distribution using Monte-Carlo simulations and
strong-coupling theory. For high surface charges, multivalent counterions, or
pronounced substrate charge modulation the counterions are laterally correlated
with the surface charges and their density profile deviates strongly from the
limit of a smeared-out substrate charge distribution, in particular exhibiting
a much increased laterally averaged density at the surface.
