Photoemission studies of the K/Si(111)7 X 7 and K/Si(111) (square-root 3 X square-root 3)R30-degrees-B interfaces show that both interfaces are semiconducting at room temperature saturation coverage. At both types of interfaces, a dispersionless K-induced surface state is observed below the Fermi level. We argue that these interfaces are correlated systems. We provide conclusive evidence that the onset of metallization and long-range conductivity occurs during the development of the second and third layers at cryogenic temperatures.