  Free electron like image potential states are observed in scanning tunneling
spectroscopy on graphene quantum dots on Ir(111) acting as potential wells. The
spectrum strongly depends on the size of the nanostructure as well as on the
spatial position on top, indicating lateral confinement. Analysis of the
substructure of the first state by spatial mapping of constant energy local
density of states reveals characteristic patterns of confined states. The most
pronounced state is not the ground state, but an excited state with a favorable
combination of local density of states and parallel momentum transfer in the
tunneling process. Chemical gating tunes the confining potential by changing
the local workfunction. Our experimental determination of this workfunction
allows to deduce the associated shift of the Dirac point.
