Practical Electron Microscopy and Database

The cross-section of bulk plasmon generation induced by energetic incident electrons can be given by [1, 2],

-[4616]
where,
         E -- The energy loss.
         Ω -- The solid angle.
         n -- The atomic density of specimen.
         a₀ -- The Bohr radius.
         E₀ -- The energy of incident electrons.
         θ -- The scattering angle.
         θ_E -- The characteristic angle with relativistic correction.
         E_P,0 -- The plasmon energy at q = 0 (q is the wave-vector of an electron).
         γ -- A coefficient.
         ΔE_P -- The damping coefficient.         

Figure 4616 shows the cross section of plasmon scattering process in Al as a function of the incident electron energy at the scattering angles of ~ 0°. For comparison, the figure also shows cross sections for the elastic and other inelastic scattering processes.

Figure 4616. Cross sections for the elastic and various inelastic scattering processes in Al as a function of
the incident electron energy at scattering angles of ~ 0°.

In contrast to core electrons, valence electrons have a very large scattering cross section providing higher spatial resolution because smaller spot sizes can be used and induces less sample damage because smaller exposure times can be applied.

[1] H. Raether, in: G. Ho¨ hler (Ed.), Springer Tracts in Modern Physics, vol. 38, Springer, Berlin, 1965, p. 85.
[2] R.H. Ritchie, A. Howie, Philos. Mag. 36 (1977) 463.