Surface-plasmon dispersion on the (100) face of aluminum

Abstract

Measurements of the inelastic low-energy (20 \ensuremath{\lesssim} E \ensuremath{\lesssim} 200 eV) electron-diffraction intensities from A1(100) are reported and analyzed to extract the dispersion relation of surface plasmons on this face of aluminum. Examination of five independent sets of experimental intensities using the two-step model of inelastic diffraction leads to the preferred results $\ensuremath{\hbar}{\ensuremath{\omega}}_{s}({p}_{\ensuremath{\parallel}})=10.4(\ifmmode\pm\else\textpm\fi{}0.1)\ensuremath{-}2(\ifmmode\pm\else\textpm\fi{}1){p}_{\ensuremath{\parallel}}+9(\ifmmode\pm\else\textpm\fi{}3){p}_{\ensuremath{\parallel}}^{2}$, and ${\ensuremath{\Gamma}}_{s}({p}_{\ensuremath{\parallel}})=1.2(\ifmmode\pm\else\textpm\fi{}0.5)+1(\ifmmode\pm\else\textpm\fi{}0.5){p}_{\ensuremath{\parallel}}$ for the surface-plasmon dispersion and damping, respectively. Momenta are measured in ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ and energies in eV. The analytical procedure utilized to extract surface-plasmon dispersion relations is modified, and our prior analyses for Al(111) are corrected by incorporating these modifications. Comparison of the surface-plasmon dispersion on Al(100) with that on Al(111) reveals that Al(100) is associated with a flatter dispersion and smaller damping. Within experimental error $\ensuremath{\hbar}{\ensuremath{\omega}}_{s}({p}_{\ensuremath{\parallel}}=0)$ is the same for both faces. Comparison of the measured dispersion relations with calculated ones reveals the clear failure of all models based on either step-function electron densities or electrons confined by an infinite surface potential barrier. Both bulk-scattering processes and the detailed shape of the electron density profile at the surface must be incorporated into any microscopic model which is proposed for the quantitative description of the surface-plasmon dispersion relations obtained from our analyses.