Practical Electron Microscopy and Database

In EELS systems, the collection angle, β, of electrons leaving the specimen is determined by the spectrometer entrance aperture and camera length.

In the case that the illumination is highly defocused (over tens of microns), the specimen is homogeneous over tens of microns, and the size of the illuminated area on the viewing screen is much larger than the spectrometer entrance aperture, the electrons that miss the spectrometer entrance aperture due to chromatic aberration will be replaced by a similar number of electrons that enter the aperture in error also due to chromatic aberration. Operating under these conditions is sometimes useful on contamination-prone specimens, or when one needs to spread the illumination over a large are to minimize radiation damage, while maintaining some spatial resolution or a high collection angle.

Table 2400a shows that by using an entrance aperture (or collection angle) that is small enough, the effect of aberrations on energy resolution of the EEL spectrometers will be minimized, although a portion of the signal is lost. Based on Table 2400b, the collection angle for EELS measurements is normally in the range of 0 – 21.5 mrad.

There is a trade-off between the EELS signal strength and energy resolution in the selection of collector aperture (also called entrance aperture) sizes, because of the following reasons:
         i) The aberrations are worse, and thus the energy resolution is degraded as the width of the electron beam entering the prism increases.
         ii) The collector aperture limits the number of electrons entering the prism more significantly, and thus the efficiency of the spectrum detection decreases as the width of the electron beam entering the prism decreases.

Inelastic scattering leads to a Lorentzian angular distribution with a characteristic angle approximately given by the relation for high energy electrons: [1]
         Θ_E = ΔE/2E₀ ------------------------------------------------ [2400]
where,
         ΔE -- The edge energy,
         E₀ -- The primary beam energy (accelerating voltage of the microscope).

To optimize the sensitivity for a given edge, we need:
         i) Let the aperture size (either objective aperture in CTEM image mode, or entrance aperture and camera length in CTEM diffraction mode and in STEM mode) as large as possible in order to collect the majority of inelastically scattered electrons.
         ii) Let the collection angle as small as possible because increasing the collection angle increases both the background and the fraction of electrons that have undergone non-dipolar transitions. [1] Larger angles increase the background contribution quicker than the edge signal, resulting in a drop in the signal-to-background ratio as shown in Figure 2400a.

On the other hand, another consideration is that the magnitude of the entrance aperture is chosen as a compromise between maximizing both the signal-to-noise (SNR) and the signal-to-background ratio (SBR). In practice, a good compromise is to employ a collection angle of ~2-3Θ_E. [1]

Table 2400a. Comparison between effects of large and small collection angles in EELS measurements.

Table 2400b. Examples of optimized collection angles based on Equation 2400 for E₀ = 30 - 400 keV.

Figure 2400b shows the collection efficiency of EELS as a function of the collection angle for a primary electron beam of 200 keV. For instance, with the optimized collection semi-angle of 4.7 mrad for Cu L₃ (931 eV), only ~30 % of the total available signal is collected by the EELS detector. However, as discussed above, in practice, it is not desirable to collect all of the scattered electrons.

[1] C. C.Ahn, Transmission Electron Energy Loss Spectrometry in Materials Science and the EELS Atlas, 2004.