Inelastic Diffraction of Low-Energy Electrons from Aluminum: Surface Plasmon Dispersion Relation

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Abstract
A two-step diffraction model is used to calculate the inelastic scattering of low-energy 50≲E≲150 eV electrons from Al (100) and Al (111). Analysis of experimental data for the specular beam of electrons scattered from Al (111) permits the approximate determination of the surface-plasmon dispersion relation; ℏω(P∥)=10.1−0.7P∥+10P∥2eV; and damping Γ(P∥)=1.4+0.7P∥eV for P∥ measured in reciprocal Angstroms. Analysis of data for both faces using several diffracted beams permits the identification of the dynamical origin of most of the prominent structures evident in the inelastic cross sections. The dispersion relation of the bulk plasmons is taken insofar as possible from high-energy-electron-transmission data. However, analysis of the low-energy (reflection) data leads to a lower threshold plasmon energy ℏωb≃14.2 eV, than that extracted from most high-energy (E∼20 keV) experiments (ℏωb≃15 eV). This discrepancy may result from the use in the reflection experiments of single-crystals rather than polycrystalline films.

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