Multiple Linear Least Squares (MLLS) Fitting in EELS Analysis
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Multiple linear least squares (MLLS) fit technique has many applications:
        i) To evaluate the atomic percentages of each element by computing the relative fit weights and integrating the references over an energy range.
        ii) To interpret the elemental maps and/or EEL spectra due to overlapping edges (e.g. Table 1389). In EELS quantification, if the edges from different elements are too close and thus the peaks overlap, then the conventional edge intensity extraction is not possible. In this case, the MLLS deconvolution can be used to fit suitable standard (reference) spectra to all overlapping edges, and thus the overlapping edges can be effectively separated. However, if the edge onsets are extremely close (e.g., for the case of Ga/Si in Table 1389), the measurement accuracy will be affected by the change of bonding environment.

Table 1389. Deconvolution examples of EELS overlap peaks by using MLLS fit technique. The energy range is used to perform MLLS fit.
Edge separation between edges (eV)
Overlap peaks Energy range (eV) Reference
Element A Element B
Edge (eV)
Window used for signal (eV)
Edge (eV)
Window used for signal (eV)
42 Pb N7,6: 138 145-240 Zr M5,4: 180 180-240 145-240 [2]
4 Si L3,2: 99   Ga M3,2: 103      

        iii) To analyze the fine structure of EELS SI (spectrum image) in order to map out the relative intensities associated with a number of chemical states of core loss edges, e.g. Cu (Cu0+ and Cu2+) and Mn (Mn3+ and Mn4+). The advantage of the MLLS fit technique is that it is able to differentiate the small separation between the primary peaks from different valence states.
        iv) To improve the EELS detection limit and weak signal extraction. 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. [1]

Such standard spectra used in the MLLS fit technique are acquired from reference specimens. Therefore, the selection of proper references is crucial to the success of the MLLS fit method. Furthermore, for accurately quantitative analysis, spectra obtained from different valence states should be used as references.











[1] Riegler, K.; Kothleitner, G.: EELS detection limits revisited: Ruby — a case study, Ultramicroscopy 110 (2010) , S. 1004 – 1013.
[2] Harkins, P. and MacKenzie, M. and Craven, A.J. and McComb, D.W. (2008) Quantitative electron energy-loss spectroscopy (EELS) analyses of lead zirconate titanate. Micron, 39 (6). pp. 709-716. ISSN 0968-4328.