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

Abstract

Energy versus momentum (${k}_{\ensuremath{\parallel}}$, ${k}_{\ensuremath{\perp}}$) 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 $\ensuremath{-}15.4l{V}_{0}l\ensuremath{-}13.5$ eV (below the vacuum level). At the zone boundary in the [0001] direction, the occupied $s$,$p$ bands have a $p$-like critical point (${\ensuremath{\Gamma}}_{3}^{+})$ at -3.9 eV below ${E}_{F}$ and an $s$-like critical point (${\ensuremath{\Gamma}}_{4}^{\ensuremath{-}}$) at -2.9 eV, while the NFE final states are found at +46 eV. These NFE final states appear to have slightly different energies (\ensuremath{\sim}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 (${\ensuremath{\Lambda}}_{1}$) $s$,${p}_{z}$-like surface state is found at -3.6 eV in the ${\ensuremath{\Gamma}}_{3}^{+}\ensuremath{-}{\ensuremath{\Gamma}}_{4}^{\ensuremath{-}}$ band gap; the band dispersion $E$ vs ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}_{\ensuremath{\parallel}}$ of this state has been measured over its full range of existence. The final-state lifetime broadening ($2\ensuremath{\Gamma}\ensuremath{\sim}4.5$ eV at +37 eV and $2\ensuremath{\Gamma}\ensuremath{\sim}7$ eV at +54 eV final-state energies, respectively) is reflected in large widths (\ensuremath{\sim}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.