Practical Electron Microscopy and Database

Accelerating charged particles e.g. the primary electrons in electron microscopes (EMs), undergo some inelastic scattering processes which do not occur for photons. If the velocity of the electrons is greater than the speed of light in the medium, Cherenkov radiation (also called Cerenkov or Čerenkov radiation) occurs [1-3]. That is, the threshold speed for Cherenkov transitions is determined by the ratio ν > c/n, where ν is the speed of a charged particle in the medium and c the speed of light in vacuum. The charged particles polarize the molecules of that medium, which then turn back rapidly to their ground state, emitting electromagnetic radiation in the process. The characteristic blue glow of nuclear reactors in Figure 4348 is due to Cherenkov radiation. Its existence was predicted by the English polymath Oliver Heaviside in his papers published in 1888–1889, but it is named after Russian scientist Pavel Alekseyevich Cherenkov, the 1958 Nobel Prize winner who was the first to characterize the Cherenkov radiation comprehensively.

Note that the collective components of EEL spectrum mainly include bulk plasmon, surface plasmon, surface guided modes, interband transitions, and Cherenkov radiation losses. The contribution of bulk loss to single scattering distribution (SSD) can be given by,

        I_b(E,t) = t•[I_p(E) + I_int(E)+I_Ch(E)] ------------- [4348a]
where,
          I_p -- The bulk plasmon-loss spectrum unit thickness.
          I_int -- The interband transition spectrum unit thickness (the region of 0 to 10 eV).
          I_Ch -- The Cherenkov radiation in unit thickness (the region of 0 to 10 eV).

Table 4348 shows that electrons interact with 1 electron, many electrons, 1 nucleus, and many nuclei in solids.

The number of Cerenkov photons (per unit charge per unit path length) in respect to the maximal emission rate in a bulk material, is given by,

         --------------------------- [4348b]

where,
          c -- The speed of light.
          v -- The speed of the incident electrons.
          ε₁ -- The real part of the dielectric function.

For instance, assuming ε₁ is 9 [4], P_Cherenkov will be about 0.50 at 80 keV.

[1] P.A. Cherenkov, Visible emission of clean liquids by action of γ radiation, Dokl. Akad. Nauk USSR. 2 (1934).
[2] S.I. Vavilov, On the possible causes of blue γ-glow of liquids, Dokl. Akad. Nauk USSR. 2 (1934).
[3] Egerton R F 1986 Electron Energy-Loss Spectroscopy in the Electron Microscope (New York: Plenum).
[4] I. Hamberg and C.G. Granqvist. Evaporated Sn-doped In₂O₃ films: basic optical properties and applications to energy-efficient windows. J. Appl. Phys., 60(11):R123–R159, 1986.