Quantification of Elements using EELS
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Quantitative analysis is normally based on physical models of inelastic electron scattering with empirical corrections for instrumental effects.

Although the fine structures of core loss spectra give information of the unoccupied density of states, the main application of EELS had still been the elemental quantification until the end of the 1980s mainly because the lack of modeling methods of the ELNES spectra. ELNES analysis has now been commonly applied since theoretical ELNES calculations become easier.

The intensity of EELS signal mostly depends on the TEM specimen but does not depend on the properties of the detector (spectrometer) and the structure of the microscope; therefore, the elemental quantification based on EELS does not require specimen standards. The core-loss intensities can be obtained from EEL spectrum and converted to elemental ratios by inputting the numbers of cross sections, the collection semi-angle (β), energy loss window, incident electron voltage, etc.

The collection semi-angle (β) of the spectrometer is the most important variable in several aspects of EELS. Significant uncertainty of data is often induced if different β angle is used in elemental comparisons unless a very high β is used. The main reason is that the intensity variation in the EELS spectrum depends on the range of electron-scattering angle collected by the spectrometer.

Quantitative analysis is almost impossible in the TEM imaging mode because the electrons with different energies are spread over areas of different size in the image. If the illumination is focused to a small area, or the specimen is not homogeneous, the intensity ratio between low-energy edges and high energy edges can be changed by as much as a factor of ~ 10 in the imaging mode simply by changing the focus of the objective lens. As a consequence, attempting to quantify the specimen composition without taking account of this effect is likely to be highly spurious. It is therefore almost always better to collect EELS spectra for quantitative analysis in the diffraction mode.

The conventional procedure to perform quantification with core-loss EELS spectra consists of the steps below:
        i) Remove the background by extrapolating a power-law function.
        ii) Remove the effect of multiple scattering by a deconvolution with the low-loss spectrum.
        iii) Integrate the number of counts in a certain energy region under the thus obtained excitation edge.
        iv) Convert this number into an absolute chemical concentration making use of a calculated cross section for the same energy region.

In practice, some serious challenges for quantitative EELS analyses are:
        i) Difficulties in background fitting, e.g. power-law fit.
        ii) Effects of variation of specimen thickness (see page2401).
        iii) Insufficient signal to noise ratio (e.g., poor signal-to-noise-ratio for EELS of nanostructures).
        iv) Edge overlaps (see page3378).
        v) Poor quality of experimental standards.
        vi) Inaccurate normalization of signal including elastic scattering effects.