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Because of the dependence of beam size on diffraction and aberrations as shown in Figure 2749, in order to achieve the optimum performance the diffraction and aberrations should be balanced as indicated by the optimum convergence semiangles. For big electron sources, at low convergence semiangles (α), the diffraction mainly determines the beam size, while at high α the spherical aberration is the dominant factor.
The diffraction term is given by,
d_{d}=0.61λ/α  [2749a]
The spherical aberration term is given by,
d_{s}=1/2C_{s}α^{3}  [2749b]
where,
λ  The wavelength of the incident electron beam,
C_{s}  The spherical aberration coefficient,
α  The convergence semiangle.
Figure 2749. Diameter of the electronbeam as a function of beamconvergence semiangle. 1: big electron source. 2: small electron source. 
The FWHM (fullwidth half maximum) of the minimum attainable probe size (d_{0}) and the optimum convergence semiangle (α_{0}) can be given by [1],
 [2749c]
 [2749d]
In STEMrelated measurements, it is possible to reduce the convergence of the electron beam and thus the tail produced by spherical aberration, by reducing the size of the C2 aperture, but this is at the expense of the total probe current.
Note that the use of a large convergence angle, as occurs in the STEM mode with a focused probe minimizes the problems of channeling enhanced Xray emission and electron channeling in EELS measurements.
However, in practice, various convergence semiangles are used by different labs based on the reality of their TEM/STEM systems and the users' preference as shown in page4941. The user can find the semiconvergence angle of the probe in the operation interface in some systems. The default semiconvergence of 1015 mrad is optimum for most systems without Probe Cscorrector.
[1] O. Scherzer, "The Theoretical Resolution Limit
of the Electron Microscope". Journal Of
Applied Physics. 20 2029 (1949).
