Free-electron-like bulk and surface states for Zn(0001)

Abstract

Energy versus momentum ($k_{\parallel }$, $k_{\perp }$) energy-band dispersions for $s$,$p$-like bulk and surface states of a Zn(0001) surface have been determined using angle-resolved photoemission with synchrotron radiation. We find nearly-free-electron (NFE) bulk $s$,$p$ bands with an inner potential of $-15.4<V_0<-13.5\mathrm{}$ eV (below the vacuum level). At the zone boundary in the [0001] direction, the occupied $s$,$p$ bands have a $p$-like critical point (${\Gamma }_3^{+})$ at -3.9 eV below $E_F$ and an $s$-like critical point (${\Gamma }_4^{-}$) at -2.9 eV, while the NFE final states are found at +46 eV. These NFE final states appear to have slightly different energies (∼2 eV) for transitions from occupied $s$ and $p$ states which can be described by an effective $s$- and $p$-dependent inner potential or by multiple band effects. A fully symmetric (${\Lambda }_1$) $s$,$p_z$-like surface state is found at -3.6 eV in the ${\Gamma }_3^{+}-{\Gamma }_4^{-}$ band gap; the band dispersion $E$ vs ${\overrightarrow{\mathrm{k}}}_{\parallel }$ of this state has been measured over its full range of existence. The final-state lifetime broadening ($2\Gamma \sim 4.5$ eV at +37 eV and $2\Gamma \sim 7$ eV at +54 eV final-state energies, respectively) is reflected in large widths (∼2-3 eV) of bulk $s$,$p$-band emission peaks. Surface-state peaks are much narrower (0.7 eV) and are limited only by initial-state lifetime broadening.