Fig. 2: Comparison with electron energy-loss spectroscopy (EELS).
Data (black line) are compared to our theoretical modeling (various colored lines) in a bulk silicon from refs. 76,77 with an incident electron beam kinetic energy of T = 100 keV. We model the theoretical EELS rates by calculating the EELS cross section using Eq. (1) with various different approximations for the dielectric function ϵ(ω, k). We normalize the rates to the plasmon peak, ω = ωpl using experimental ϵ(ω, k → 0) from ref. 78, in conjunction with Eqs. (8) and (9), plotted as pink line. The EELS data include multiple scattering, with a secondary scattering peak visible at ω = 2ωpl, which can be included by modeling multiple scatters (see ref. 67 for a discussion). Note that the sharply rising peak in the experimental data towards low energies, ω ≲ 10 eV is due to elastic scatters between incident electrons and the lattice, and is not captured in the models of the dielectric function ϵ(ω, k) considered here. Blue line corresponds to the Lindhard model68, orange and green lines corresponds to DarkELF (Mermin) and DarkELF (GPAW) respectively24,25, and the red line corresponds to QCDark28.
