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

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 lₑ were determined by correction of the attenuation lengths for electron-phonon scattering lengths lₚ deduced from the attenuation temperature dependence. Imperfection mean free paths were negligible. The following results were obtained: for aluminum, lₑ~50 {} and lₚ~250 {} near 5 eV above the Fermi level; for gold, 45 >lₑ>15 for energies between 5.5 and 10 eV; and for silver, 42 >lₑ>20 for energies between 5.5 and 8 eV. In the energy range between 5.5 and 7.5 eV, it was found that lₚ~250 {} for gold and lₚ~400 {} for silver. All measured lₚ were only about two-thirds of the value near the Fermi level. Quinn's theory for lₑ in a dense free-electron gas predicts that for aluminum lₑ~60 {} 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 lₑ deduced semiempirically by Krolikowski and Spicer from the density of states obtained from photoemission experiments. Reasonable agreement with presently available data was observed.