Unoccupied bulk and surface states on Ag(111) studied by inverse photoemission

We present k-resolved inverse photoemission spectroscopy (KRIPES) results for Ag(111) in the Γ¯ K¯ direction of the surface Brillouin zone. The spectra were taken as a function of electron energy and angle of incidence at a fixed photon energy (9.7 eV) of the emitted radiation. The crystal-induced surface state and the image-potential-induced surface state are observed with final-state electron energies at Γ¯ in good agreement with a recently proposed multiple reflection model and with dispersion characterized by effective masses $m^{\mathrm{*}}$=0.7m and $m^{\mathrm{*}}$≊m, respectively. The measured intensity of the surface state roughly follows a ${\cos }^2$α dependence, where α is the angle between the sample normal and the polarization vector of the detected photons. Transitions into bulk-derived final states are observed, with final-state electron energies ranging from $E_F$ to $E_F$+20 eV. The dispersions of these bulk-derived final states agree with very simple ‘‘empty-lattice isochromats’’ derived from free-electron bands of proper symmetry, as well as with results of a band-structure calculation based upon a combined interpolation scheme.