Counterions at charge-modulated substrates

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 pro le deviates strongly from the limit of a smeared-out substrate charge distribution, in particular exhibiting a much increased laterally averaged density at the surface.