Unoccupied electronic band structure of Na on Cu(111) as studied by inverse photoemission

We have determined the unoccupied part of the electronic structure of sodium on Cu(111), employing k-resolved inverse photoemission in the isochromat mode. For Na coverages above 0.15 monolayer, an image-potential surface state is observed 2.3 eV above ${\mathit{E}}_{\mathit{F}}$. For the completed p(2×2) Na phase at 0.25-monolayer coverage, a pronounced Na ${3\mathrm{p}}_{\mathrm{z}}$–derived feature occurs 0.4 eV above ${\mathit{E}}_{\mathit{F}}$, which exhibits a nearly-free-electron-like energy dispersion. For wave vectors ${\mathit{k}}_{\mathrm{?}}$≥0.6 A${\mathrm{̊}}^{\mathrm{-}1}$, the unoccupied part of the Na 3s band appears close to the Fermi level. We compare our results with recent band-structure calculations for free and adsorbed Na monolayers.