Inelastic scattering of fast electrons in nanowires: A dielectric formalism approach

The excitations produced by fast electrons impinging perpendicularly on both metallic and semiconductor cylindrical nanowires are investigated within the framework of dielectric theory. The dependence of the electron energy-loss spectra (EELS) on the nanowire radius is studied in detail, and so is the spatial extension of the induced-charge fluctuations associated to the modes that are excited during the loss process. The limits of applicability of dielectric theory to nanowires are discussed. In particular. comparison between the present theory and EELS measurements performed with silicon nanofibers support the use of dielectric theory at the scale of a few nanometers in diameter. and it is shown that this positive result is justified in terms of the longitudinal pattern of the induced surface plasmons. Finally, the effect of nanowire termination on the electron energy-loss probability for electrons passing near the edge is calculated using the boundary charge method, showing that the range of this effect can extend up to tens of nanometers for low-energy m = 0 modes.