We have investigated the electronic structure of the two-dimensional solid solution Si x Sn 1x /Si(111)-(3 3)R30° at room temperature, with a particular emphasis on the empty states, using both global k //-resolved inverse photoemission spectroscopy KRIPES and local probes scanning tunneling microscopy and spectroscopy, STM and STS, as well as DFT-LDA calculations. This adatom overlayer with a (3 3)R30° symmetry shows drastic evolution with increasing Sn-adatom concentration, including a semiconductor to metal transition. The Si 0.5 Sn 0.5 /Si(111)-3 or mosaic phase has a single empty surface state localized at 0.56 eV above E F at ¯. With an overall bandwidth of 0.15 eV, this sp z-type state localized on Si adatoms does not cross E F : the mosaic phase is semiconducting, with a bandgap between 0.3 and 0.5 eV. This phase is characterized by a large corrugation of 0.75 Å with Sn adatoms higher than Si adatoms. In the Sn-rich limit Si x Sn 1x /Si(111)-3 with x0.05, we follow an empty state U 1 throughout most of the surface Bril-louin zone except near the K ¯ point where it clearly crosses the Fermi level. A second, empty surface state U 2 is detected 1.67 eV above E F. Once correlation effects suggested by the small bandwidth of U 1 are adequately taken into account, we explain our KRIPES results in the framework of a dynamical fluctuations model as originating from an underlying (33) structure. Finally, results pertaining to intermediate Sn-adatom concentrations are interpreted in view of the two limiting cases.