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 $5\le h\nu \le 35$ eV photon energy range. Dispersion relations for the occupied $s-p$ and $3d$ bands of Cu along the $\Gamma -X$ and $\Gamma -L$ symmetry lines (including critical points at $\Gamma$, $X$, and $L$) have been determined with an accuracy of 0.05-0.1 eV and ≲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 ${\Delta }_1$ conduction band along $\Gamma -X$ at ∼10-15 eV above the Fermi energy $E_F$; this band has a reduced effective mass ($m^{*}\simeq 0.90-0.94$) which is related to self-energy effects. Lifetimes have been directly measured for excited hole states (the lifetime broadening ${\Gamma }_h$ increases from ∼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 ${\Delta }_1$ conduction band (${\Gamma }_e\simeq 1.0-2.0$ eV for energies 10-15 eV above $E_F$). The energy dispersion and $h\nu$-dependent photoionization cross section of the $s-p$ surface state on Cu(111) are reported. Previous theoretical and experimental studies of copper are compared with our accurate $E$ vs $\overrightarrow{\mathrm{k}}$ dispersions.