Excited-state bands of Cu determined by VLEED band fitting and their implications for photoemission

Abstract

We derive the excited-state bands of Cu above the vacuum level along the $\ensuremath{\Gamma}X$ and $\ensuremath{\Gamma}L$ lines, utilizing very-low-energy electron diffraction (VLEED) experimental data from the (100) and (111) surfaces, respectively. This is done by a band-fitting technique, based on empirical pseudopotential calculations of the excited-state bands and the corresponding reflectivity $R(E).$ The calculations are iterated until a good fit is obtained between calculated and experimental energies of $dR/dE$ extrema, each of which corresponds to a band irregularity point. We analyze how the excited-state bands are connected with VLEED and photoemission, and introduce a partial transmission (PT) to characterize the coupling properties of each band: If the absorption ${V}_{i}$ is small, the current adsorbed in the crystal from an incident-beam-excited Bloch wave in VLEED, or the photocurrent from a photoexcited final-state Bloch wave, are both proportional to the PT of the Bloch wave. The excited-state bands, obtained from VLEED band fitting, are found to deviate from free-electron bands notably enough to influence photoemission spectra. In particular, along $\ensuremath{\Gamma}X$ we identify two different bands, which constitute final states in the photoemission from the (100) surface. As similar effects are far more prominent for nonmetals, we conclude that determination of the upper bands by VLEED is essential for accurate photoemission band mapping.