Experimental energy band dispersions and lifetimes for valence and conduction bands of copper using angle-resolved photoemission

Abstract

Energy-band dispersions and electron lifetimes have been determined for both valence and conduction-band states of copper using angle-resolved photoemission with polarized synchrotron radiation in the $5\ensuremath{\le}h\ensuremath{\nu}\ensuremath{\le}35$ eV photon energy range. Dispersion relations for the occupied $s\ensuremath{-}p$ and $3d$ bands of Cu along the $\ensuremath{\Gamma}\ensuremath{-}X$ and $\ensuremath{\Gamma}\ensuremath{-}L$ symmetry lines (including critical points at $\ensuremath{\Gamma}$, $X$, and $L$) have been determined with an accuracy of 0.05-0.1 eV and \ensuremath{\lesssim}5% of the zone-boundary momentum. Band symmetries have been deduced using polarization selection rules. The dispersion relation has also been accurately determined for the unoccupied ${\ensuremath{\Delta}}_{1}$ conduction band along $\ensuremath{\Gamma}\ensuremath{-}X$ at \ensuremath{\sim}10-15 eV above the Fermi energy ${E}_{F}$; this band has a reduced effective mass (${m}^{*}\ensuremath{\simeq}0.90\ensuremath{-}0.94$) which is related to self-energy effects. Lifetimes have been directly measured for excited hole states (the lifetime broadening ${\ensuremath{\Gamma}}_{h}$ increases from \ensuremath{\sim}0.2 to 0.5 eV full width at half maximum for $d$-band energies from 2 to 5 eV below ${E}_{F}$) as well as for excited electron states in the ${\ensuremath{\Delta}}_{1}$ conduction band (${\ensuremath{\Gamma}}_{e}\ensuremath{\simeq}1.0\ensuremath{-}2.0$ eV for energies 10-15 eV above ${E}_{F}$). The energy dispersion and $h\ensuremath{\nu}$-dependent photoionization cross section of the $s\ensuremath{-}p$ surface state on Cu(111) are reported. Previous theoretical and experimental studies of copper are compared with our accurate $E$ vs $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ dispersions.