Theory of EELS in atomically thin metallic films

Abstract

We study strongly confined plasmons in ultrathin gold and silver films by simulating electron energy-loss spectroscopy (EELS). Plasmon dispersion relations are directly retrieved from the energy- and momentum-resolved loss probability under normal incidence conditions, whereas they can also be inferred for aloof parallel beam trajectories from the evolution of the plasmon features in the resulting loss spectra as we vary the impinging electron energy. We find good agreement between nonlocal quantum-mechanical simulations based on the random-phase approximation and a local classical dielectric description for silver films of different thicknesses down to a few atomic layers. We further observe only a minor dependence of quantum simulations for these films on the confining out-of-plane electron potential when comparing density-functional theory within the jellium model with a phenomenological experimentally-fitted potential incorporating atomic layer periodicity and in-plane parabolic bands of energy-dependent effective mass. The latter shows also a small dependence on the crystallographic orientation of silver films, while the unphysical assumption of energy-independent electron mass leads to spurious features in the predicted spectra. Interestingly, we find electron band effects to be more relevant in gold films, giving rise to blue shifts when compared to classical or jellium model simulations. In contrast to the strong nonlocal effects found in few-nanometer metal nanoparticles, our study reveals that a local classical description provides excellent quantitative results in both plasmon strength and dispersion when compared to quantum-mechanical simulations down to silver films consisting of only a few atomic layers, thus emphasizing the in-plane nearly-free conduction-electron motion associated with plasmons in these structures.