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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This refraction effect of secondary electrons (SEs) is given by [1],
                 --------------------------------------------------- [4828a]
 Here,        β -- the inner angle of incident electrons into the sample
                 α -- the corresponding emission angle into the vacuum.
                 E_s -- the SE kinetic energy into the specimen
                 E_k -- the corresponding kinetic energy into the vacuum

Based on Equation 4828a, Figure 4828 shows the schematic of angular SE transmission function, T(α), at the specimen/vacuum (S/V) interface in polar co-ordinates when the specimen is a metal, a semiconductor and an insulator.

Figure 4828. Schematic of angular SE transmission function, T(α), at the specimen/vacuum (S/V) interface in polar co-ordinates when the specimen is a metal, a semiconductor and an insulator. The Lambert-type emission is also schematically shown for comparison. Adapted from [2]

The SE kinetic energy into the specimen, E_s, is given by

                 E_s = E_k+ E_F + Φ (for a metal) -----------------------------------------------[4828b]

                 E_s = E_k+ χ (for a semiconductor or an insulator) ----------------------------[4828c]

 Here,       E_F -- Fermi energy

                Φ - - Work function

                χ -- Electron affinity

                The sum E_F (Fermi energy) and Φ (Work function) for metals is often of ~10 eV.

                Electron affinity, χ, for insulators is generally less than 3 eV.

[1] Henke, B.L., Liesegang, J. & Smith, S.D. (1979) Soft X-ray induced secondary electron emission from semiconductors and insulators. Phys. Rev. B, 19, 3004–3021.
[2] J. Cazaux, (2005) Recent developments and new strategies in scanning electron microscopy, Journal of Microscopy, 217, 16–35.