Electron–Hole (e–h) Pair Generation
due to Energetic Beam Irradiation
- Practical Electron Microscopy and Database -
- An Online Book -

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This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.

 

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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 valence-band 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 electron-hole pairs generated per incident beam electron, called electron-hole pair generation factor, is given by,

             Ge-h = E0(1-γ)/Ei -------------------------------- [4466a]

where E0 is the incident beam energy, Ei is the ionization energy which is the energy required for the formation of an electron-hole pair, and γ represents the fractional electron beam energy loss relating to all of the backscattered and emitted electrons. The ionization energy (Ei) of electron-hole pair generation is related to the band gap of the materials, Ei = 2.8Eg + M (0 < M < 1 eV).

In SEM, if we consider all incident electrons in the primary beam contribute the generation of electron-hole pairs, the generation rate Ge-h inside the interaction volume created by the PE energy beam, E0, and the current I can be given by,

             Electron–Hole (e–h) Pair Generation due to Energetic Beam Irradiation------------ [4466b]

where E0/Ee-h is a number of e–h pairs generated by a single primary electron of Ge-h, and R is the radius of the interaction volume.

For Si (silicon), a 15 keV beam of 10 pA generates ~1021 pairs/cm3, assuming Ee-h ~ 3.4 eV, while for 1 keV and the same beam current, 10 pA, this value reaches ~1027 pairs/cm3. 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

 

 

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