Upon room-temperature deposition of minute amounts of Cs on InAs(110) surfaces, one induces probably the highest Fermi-level pinning position (almost-equal-to 0.6 eV) for a semiconductor above the conduction-band minimum. Synchrotron-radiation core-level photoemission spectroscopy was used to follow the Fermi-level movement from the shift of the In 4d and As 3d core levels as a function of Cs coverages at room temperature. Already at very low coverages the Fermi level reaches an extremely high maximum above the conduction-band minimum. The maximum of the Fermi-level position correlates fairly well with the ionization energy of the individual atoms, as expected in the framework of the theory of donor-type surface states induced by metallic adatoms. We thus consider that individual Cs adatoms produce donor-type surface states placed at almost-equal-to 0.6 eV above the conduction-band minimum. This induces a very strong downward band bending which suggests the existence of a two-dimensional electron gas at the open, nearly clean InAs(110) surface.