Abstract The Surface Green's Function Matching (SGFM) method is useful to distinguish the bulk effects from the surface ones since it calculates the two Green's functions separately in a neat and direct way. We have used this feature of the method to establish the correct interpretation of the Frontier Induced Semi-Infinite Medium (FISIM) states. We discuss the valence band electronic structure of the (001) oriented II–VI wide band gap zinc-blende semiconductor compounds. We have found three characteristic surface resonances besides the known bulk bands. Two of these resonances correspond to the anion-terminated surface and the third one to the cation terminated one. Further, we have shown that three non-dispersive (001)-surface-induced bulk states are also characteristic of these systems. These are neither surface nor Bloch states. These are states localized in planes perpendicular to the surface with non-vanishing spectral weight inside the bulk. They are not Bloch states since they are the consequence of the surface-boundary condition and their characteristics depend on the direction of the surface, they are therefore, surface-induced bulk states. In this talk, I briefly review our description of these systems. I also quote that similar states are present in other systems as calcopirites and at interfaces and superlattices, as well. These states are, actually, a general wave property and appear as the consequence of the boundary condition set by the presence of any frontier. For that reason, we have decided to call them Frontier Induced Semi-infinite Medium (FISIM) states.