Electron-energy losses in silicon: Bulk and surface plasmons and Čerenkov radiation

Abstract

Characteristic electron-energy-loss processes in crystalline silicon foils are examined for scattering angles less than 2.5 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ rad. The relatively high energy of the electron beam (75 keV), combined with a low angular divergence (8 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}6}$ rad), allows identification of retardation effects in both volume and surface excitations. The results are consistent with complete probability distribution maps, calculated as a function of energy loss $\ensuremath{\hbar}\ensuremath{\omega}$ and scattering angle $\ensuremath{\theta}$, using recent optical data for the dielectric constants of Si. The half-width of the angular intensity distribution in the volume plasmon ($\ensuremath{\hbar}{\ensuremath{\omega}}_{p}=16.6$ eV) agrees with the theoretical value to within 3%. Below 4 eV (${\ensuremath{\epsilon}}_{1}g10$), a dispersive peak in the loss spectrum is observed which is interpreted as a volume loss due to \ifmmode \check{C}\else \v{C}\fi{}erenkov radiation for $\ensuremath{\theta}\ensuremath{\ge}5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ rad, and which, at small angles, transforms into multiple surface modes propagating parallel to the specimen surface in a waveguide fashion. Between 4.3 eV and $\ensuremath{\hbar}{\ensuremath{\omega}}_{p}=16.6$ eV (${\ensuremath{\epsilon}}_{1}$ negative), the prominent excitation is the surface plasmon in which the wave fields decay exponentially on both sides of the surface. The dispersion follows the light line and then approaches an asymptotic energy (8.2 eV) which is less than the energy calculated for a clean Si surface ($\ensuremath{\hbar}{\ensuremath{\omega}}_{s}=11.0$ eV), but dispersion curves calculated for 20- and 50-\AA{} $\mathrm{Si}{\mathrm{O}}_{x}$ ($x\ensuremath{\approx}1.5$) approximately fit the data.