Slow-Electron Mean Free Paths in Aluminum, Silver, and Gold

Abstract

Beam-attenuation measurements were made on free-standing polycrystalline films of various thicknesses at energies between the work function and several electron volts above. The electron-electron collision mean free paths ${l}_{e}$ were determined by correction of the attenuation lengths for electron-phonon scattering lengths ${l}_{p}$ deduced from the attenuation temperature dependence. Imperfection mean free paths were negligible. The following results were obtained: for aluminum, ${l}_{e}\ensuremath{\sim}50$ \AA{} and ${l}_{p}\ensuremath{\sim}250$ \AA{} near 5 eV above the Fermi level; for gold, $45 \AA{}>{l}_{e}>15 \AA{}$ for energies between 5.5 and 10 eV; and for silver, $42 \AA{}>{l}_{e}>20 \AA{}$ for energies between 5.5 and 8 eV. In the energy range between 5.5 and 7.5 eV, it was found that ${l}_{p}\ensuremath{\sim}250$ \AA{} for gold and ${l}_{p}\ensuremath{\sim}400$ \AA{} for silver. All measured ${l}_{p}$ were only about two-thirds of the value near the Fermi level. Quinn's theory for ${l}_{e}$ in a dense free-electron gas predicts that for aluminum ${l}_{e}\ensuremath{\sim}60$ \AA{} at 5 eV. Exchange corrections in Kleinman's dielectric screening function tend to bring the value closer to the observed one. In silver and gold, considerable interaction of the beam electrons with the $d$ band occurred for which no theory is available as yet. The resulting data were compared with the energy dependence of ${l}_{e}$ deduced semiempirically by Krolikowski and Spicer from the density of states obtained from photoemission experiments. Reasonable agreement with presently available data was observed.