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A primary energetic beam experiences energy loss when it interacts with materials. For instance, during the irradiation of Si by primary electrons, the electrons suffer energy losses due to the excitation of the valenceband electrons towards the conduction band. This inelastic process induces electron–hole (e–h) pair formation. The carriers (holes and electrons) generated inside the interaction volume undergo several processes e.g. escape from the surface, diffuse away from the generation region, undergo recombination, and become partially trapped.
The number of electronhole pairs generated per incident beam electron, called electronhole pair generation factor, is given by,
G_{eh} = E_{0}(1γ)/E_{i}  [4466a]
where E_{0} is the incident beam energy, E_{i} is the ionization energy which is the energy required for the formation of an electronhole pair, and γ represents the fractional electron beam energy loss relating to all of the backscattered and emitted electrons.
The ionization energy (E_{i}) of electronhole pair generation is related to the band gap of the materials, E_{i} = 2.8E_{g} + M (0 < M < 1 eV).
In SEM, if we consider all incident electrons in the primary beam contribute the generation of electronhole pairs, the generation rate G_{eh} inside the interaction volume created by the PE energy beam, E_{0}, and the current I can be given by,
 [4466b]
where E_{0}/E_{eh} is a number of e–h pairs generated by a single primary electron of G_{eh}, and R is the radius of the interaction volume.
For Si (silicon), a 15 keV beam of 10 pA generates ~10^{21} pairs/cm^{3}, assuming E_{eh} ~ 3.4 eV, while for 1 keV and the same beam current, 10 pA, this value reaches ~10^{27} pairs/cm^{3}. That is, the generation rate increases rapidly with decreasing R [1], and thus, a rather enormous number of carriers inside the interaction volume of Si is created in SEM observation.
[1] Joy D.C., (1987) J Microsc 147(1):51
