Factors Limiting Spatial Resolution of TEM
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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.



In TEMs we can often estimate the spatial resolution by,

          δ = 0.61 λ/β ------------------------- [4946]

where λ – Wavelength of the electron beam in nm (~ 1.22/E1/2)
          E – Energy of the electron beam in volts (eV)
          β -- Semiangle of collection of the magnifying lens

Equation 4946 implies the wavelength limits the resolution of the TEMs. For an electron beam at an accelerating voltage of 100 keV, we have λ ~ 4 pm (0.004 nm), which is much smaller than the diameter of an atom.

Actually, there are much more factors, than those in Equation 4946, limiting the spatial resolution in electron microscope as discussed on the page of Spatial Resolution in Electron Microscopes. The most important factor in TEMs is that round magnetic lenses suffer from severe aberrations. Because the strongest aberration is the spherical aberration (aberration coefficient Cs), a long standing dream of TEM was the implementation of Cs correctors. The other smaller effects are instabilities of lens currents, high voltage, external vibrations, or AC electric and magnetic fields. That is why for old TEMs, we could not make perfect electron lenses, which limited their resolution. However, after Rusks’s early work on lenses and, since the mid 1970s, many commercial TEMs have been capable of resolving individual columns of atoms in crystals, resulting in developments of HRTEMs.

Round lenses in conventional EMs suffer from spherical aberration as well as off-axial coma. To eliminate the azimuthal or anisotropic coma, the axial magnetic field must change its sign with a dual lens consisting of two spatially separated windings with opposite directions of their currents [1]. The axial chromatic coefficient (Cc) of the coma-free lens is significantly larger (≥ 50%) than that of standard objective lenses. Therefore, in order to obtain sub-Ångstroem resolution it is necessary to greatly minimize the chromatic aberration in coma-free lenses.




[1] H. Rose, Optik 34 (1971) 285.




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