Sensitivity/Detection Limit of EELS
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Generally speaking, EELS (Electron Energy Loss Spectroscopy) has better sensitivity than EDS (Energy-dispersive X-ray spectroscopy), due to utilizing signals generated from larger ionization cross sections (L rather than K) and the much greater collection efficiency. [1 - 2]
Similar to EDS spectra, the peak-to-background ratio (P/B ratio) in EELS spectra increase with the accelerating voltages from 100 kV to 400 kV, resulting in an increase in the detection sensitivity of any trace elements. For other elements, low accelerating voltage electron beams can enhance the sensitivities for EELS and EDS because the reduced acceleration voltage increases the ionization cross-section, which is determined by the overvoltage ratio.
Using a field emission STEM and PEELS, the sensitivity of EELS was down to concentration ~10 ppm for transition metals and lanthanides , and ~20 ppm for calcium (Ca) in organic test specimens .
In general, the detection limit of EELS in TEM is similar to that of EDS, namely about 0.1 %. However, multiple linear least squares (MLLS) fit technique can be used to improve the EELS detection limit. For instance, by using the MLLS fit technique instead of conventional background subtraction, Cr concentrations as low as 0.03% in Al2O3 was possibly detected at a particular microscope setting. 
Furthermore, the energy resolution of the EELS system can also affect the chemical sensitivity of spectroscopy especially when the signals are very weak for some elements and some edges. Figure 4793a shows how the energy resolution affects EELS sensitivity by comparing the C(carbon) 1s spectrum of poly(ethylene terephthalate) (PET) recorded by two different microscopes. The higher energy resolution with a cold field emission gun (VG-HB501) increases the chemical sensitivity of a spectroscopy comparing to a LaB6 thermionic emission electron source.
Figure 4793b shows experimental EEL spectra of the N (nitrogen) K edge obtained from a GaN film with the three different energy resolutions versus the DFT simulations with the indicated energy broadening. The spectrum with an energy resolution of 1.0 eV was obtained with the JEOL2010F, the spectrum with the resolution of 0.4 eV was obtained with the Cs-corrected Nion VG HB501, and the 0.2 eV spectrum by using the monochromated FEI Tecnai G2. Those profiles indicate the EELS sensitivity to the detection of extended energy loss fine structure (EXELFS) depending on the energy resolution.
Figure 4793b. Experimental EEL spectra of the N (nitrogen) K edge from a GaN film obtained with the three different energy resolutions versus the DFT simulations with the indicated energy broadening. 
An energy resolution of close to 100 meV is required to reveal the spectroscopic details, while an energy resolution of less than 50 meV will most likely not provide additional information.
Furthermore, the detection limit is also controlled by the sample thickness because of the background. For instance, the detection limit of oxygen was improved from 2.7 atomic % (130 nm thickness in Figure 4793c (a)) to 1.5 atomic % (40 nm thickness in Figure 4793c (b)), assuming that the minimum detectable counts of oxygen are equal to the 3 sigma of signal/noise ratio under the analytical conditions . Therefore, the oxygen content is not detectable in the 130-nm thick sample because the concentration is lower than the detection limit. Note that the two spectra were taken from the same (Mg, Fe)O-matrix phase.
Another term to describe the detection limitation is minimum detectable mass (MDM), which is given by, 
Figure 4793d shows the comparison of the relative MDMs, obtained from 50 nm SrTiO3 TEM specimen, versus analysis time t by EDS with a Si(Li) detector and a large SDD detector, and by EELS. This SDD detector had a total active area of 120 mm2,  resulting in even better MDM than that of EELS. Furthermore, in general, the techniques are more sensitive to the elements if the detection time is longer.
 M. Isaacson, D. Johnson, Ultramicroscopy 1 (1975) 33.