Abstract
A new non-retarded hydrodynamic approach to the interaction between a fast electron and a diffuse metal-vacuum interface is presented. The metal is characterized by the parameters of a dispersive bulk dielectric function which slowly fade at the interface. The response of the medium is described by the induced charge density, which is self-consistently calculated. This formalism is applied to the study of the energy loss spectrum (EELS) experienced by a fast electron passing by a metal-vacuum interface. In the case of a sharp interface analytical expressions for the loss probability, fully equivalent to that of the Specular Reflection Model (SRM), are found. In an Al interface the effects of the electron density spill-out (modeled according to Lang-Kohn density) on both the longitudinal (EELS) and transverse components of the momentum transfer are studied. The influence of the interface profile on the surface plasmon dispersion in EELS is also discussed, showing that in agreement with previous theoretical and experimental works the dispersion of surface plasmon turns out to be much weaker than the one calculated in the SRM. A possible extension of the theory to study interfaces between transition metals and insulators is also discussed.
Highlights
Following Ritchie’s seminal paper [1], the local dielectric formalism has been widely used to study the excitation of plasmons in bounded targets by fast electron-probes
The main advantage of the local formalism lies in the possibility of using experimental dielectric functions, a procedure which leads to good qualitative and quantitative agreement in energy loss spectrum (EELS) in Scanning Transmission Electron Microscope (STEM) for a wide range of media [4,5,6,7]
We have presented a new nonretarded approach to the nonlocal interaction between a fast electron-probe and a metallic interface whose unperturbed charge density varies smoothly in the normal direction
Summary
Following Ritchie’s seminal paper [1], the local dielectric formalism has been widely used to study the excitation of plasmons in bounded targets by fast electron-probes. When the probe penetrates the target or travels very close to its surface the local response is not longer appropriate because it fails to describe the decreasing ability of the valence electrons to respond collectively to large wave vector components of the exciting field, a fact which leads to a logarithmic divergence in the induced potential at the probe position. This unphysical divergence is usually avoided by imposing a cutoff to the momentum contribution [22].
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