Aberrations & Beam Spread/Convergence
- Practical Electron Microscopy and Database -
- An Online Book -


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


In most modern, practical TEMs/STEMs, the gun lens is used to position the first crossover in relation to the beam-defining aperture (normally the C2 aperture). The crossover locates high above the aperture with a strong gun lens, while the crossover is close to the aperture with a weak gun lens. Both the beam current and aberrations on the beam are higher for the latter case. Therefore, when small, intense and low-aberration electron beams are needed, e.g. for diffraction in TEM and analytical STEM, a strong gun lens is selected; while a weak gun lens is selected when high probe currents are needed (e.g. TEM imaging). In the TEM mode, the beam is spreaded, therefore, the aberrations do not significantly affect the small imaging area.

The beam broadening in inelastic imaging in TEMs (e.g. EFTEM imaging) can be expressed by the following equation,

         spatial resolution of the inelastic images ---------- [3586a]

         R -- An inelastic scattering delocalization factor;
         ΔEslit -- The energy slit width;
         E0 -- Eenergy of incident electron beam.

The first term in Equation 3586a is related to a beam broadening factor due to chromatic aberration (Cc) of the objective lens because of the finite width of the energy-selecting slit. The second term is related to spherical aberration (Cs) of the objective lens.

In STEM mode, beam spreading caused by chromatic aberration dc can be given by,

          Beam Spreading in STEM Caused by Chromatic Aberration ---------------------------------- [3586b]

         ΔE -- The energy spread of the electron beam;
         E0 -- Eenergy of incident electron beam;
         α -- The convergence semi-angle;
         Cc -- The non-relativistic chromatic aberration and its coefficient.

From Equation 3586b we know that both Cc and ΔE should be low enough in order to suppress beam spreading at low acceleration voltages, especially since Cc depends strongly on the accelerating voltage.

Note that in electron microscopes (EMs), the magnetic lenses are only convergent because they are in rotational symmetry. However, the absence of divergent lenses prevents spherical aberration correction.





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