Quantum-size effects in work functions of free-standing and adsorbed thin metal films

Work functions versus film thickness have been calculated self-consistently for free-standing Al(111), Cr(100), Rh(111), and Au(100) films, and for one- and two-layer films of Au(100) adsorbed on Cr(100). The Al, Rh, and Au films show work-function changes of several tenths of an electron volt, between one and four layers, confirming earlier results for free-electron metals and extending them to transition and noble metals. For two- through five-layer films, the work function of Cr(100) is only weakly dependent on film thickness, owing to the existence of a prominent surface state at the Fermi energy, which stabilizes the charge-density profile in the surface region. Adsorbed films of Au on Cr show no work-function quantum-size effects (QSE), because there are no Au-localized states near the Fermi energy. The large Cr density of states at $E_F$ makes it easy for the Au and Cr states to mix. In general, metals with low state densities have low surface energies, and are thus not apt to be thermodynamically stable substrates for high-density-of-states metals. Therefore, there is no obvious candidate for a metal on a metal system in which QSE should be observed.