High-resolution photoemission from a tunable quantum well: Cu(111)/Na

High-resolution photoemission $(\Delta E=5\mathrm{}\mathrm{meV})$ at a low photon energy (3.82 eV) is used to probe discrete quantum-well-type subband states near, below, and above $E_F$ for Cu(111) covered with 2 ML or less of Na. A subband characteristic of the monolayer range shifts gradually to lower energy as the coverage is increased, extending below the Fermi level for coverages above 0.85 ML. Combined with previous observations of shifts for filled and empty states the present results show that the Na monolayer has continuously tunable quantum-well state energies. Beyond the monolayer range quantum-well states characteristic of both one and two atomic layers are observed, indicating growth of the second layer via monolayer high islands. A small downshift, by 25 meV, with increasing coverage in the second layer is ascribed to an increase of the island size. Lorentzian photoemission line shapes are observed for well-ordered samples. The linewidth varies linearly with temperature in the probed range (130–295 K) and this is ascribed to the phonon contribution to the width. Structural disorder leads to an asymmetric line, which is Lorentzian on the steeper, low-kinetic-energy side.