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Extract Signal

The next step in quantification requires extracting edge intensities from the spectrum while disregarding the underlying background intensity.

Extract signal for EELS quantification

To separate the edge intensity, you must fit, extrapolate, and subtract a background model. It is essential to consider the following items when you perform this critical extraction step:

  • Which background model should I use?

  • Where should I fit the background model to the data?

  • What are the optimal width and position for the signal integration window?

Theory               Step-by-step

Background modeling

To extract the edge intensity, you must determine a model for the background of your spectrum. First, identify a pre-edge fitting region that allows you to determine the parameters of the fit. Then, extrapolate this fit to estimate the background intensity below the edge signal. However, an accurate background subtraction may become difficult below 100 eV due to a large number of scattering processes in this region (e.g., plasmons tails, plural scattering).

Typically, the model is determined using linear least-squares methods using a single pre-edge region. \(\Gamma\).

Background modeling for EELS quantification

where

  • \(\Gamma\) = Background fit window

  • \(\Delta\) = Signal integration window

  • \(I_{b}\) = Background intensity

  • \(I_{k}\) = Signal intensity

Power law

A power law is the most common background model.

\(J\left ( E \right )=AE^{-r}\)

where

  • \(A\) = Scaling constant

  • \(r\) = Slope exponent (usually 2 – 6)

When interpreted as the long energy tails of the preceding energy loss events, this model has a physical basis. 

EELS background modeling using Power law

Background model placement

When you choose the optimal background placement, it is important to consider these parameters:

  • The high-energy side \(E_{be}\) should be as close to but still preceding the edge (e.g., 5 eV) to avoid chemical shifts and broadening detector tails

  • To limit statistical error, the fit region \(\Gamma\) should be as wide as possible

  • To limit systematic error, you need to limit the fit region to 10 – 30% \(E_{k}\)

Background model placement for EELS quantification

Rules of thumb to follow

  • Background window end should be 5 eV from edge onset

  • Background window width should be at most 30% edge energy

  • May need to limit window size to avoid preceding edges where necessary

Troubleshoot background extrapolation errors

Once background placement is made, it is important to review common errors.

  • Unphysical

    • Symptom – Obvious error where the background model crosses the spectrum and may cause the signal to become negative

    • Solution – Increase the window size and/or offset it from the edge onset; you may need to limit the extrapolation distance of your analysis

      Troubleshoot unphysical background modeling errors

  • Systematic errors

    • Symptom – Small changes in the background window width or position have significant effects on the background model

    • Solution – Ensure minor variations in window position do not change background fit significantly; increase the size of window
      Troubleshoot systemic background modeling errors
      In this case, the background changes rapidly as the window position is moved. A larger window and avoiding the edge onset region are recommended.

  • Overlapping edges

    • Symptom – Background extrapolation is ineffective for instances where the pre-edge region is obscured by the preceding edge

    • Solution – Reduce the window size or placement as well as limit the signal window size and offset; a multiple linear least-squares (MLLS) fitting or model-based approach may be necessary

      Troubleshoot overlapping edges background modeling errors

Width and position of the signal integration window

When you choose the optimal signal integration window placement, it is important to consider the following:

  • Statistical error – The region \(\Delta\) should be as wide as possible and start at the steepest intensity increase of the spectrum

    • Hydrogenic edges (e.g., K-, some L-edges) – Place the window at the threshold

    • Delayed edges (e.g., L-, M-, N-, O-edges) – Offset by a few tens of eV

  • Systematic error – Limit fit region to about 10%, but it should cover all of the significant energy loss near edge structure (ELNES) changes

    Signal integration window placement

White lines – Best to avoid inclusion for quantitative evaluation as their intensity can vary with chemical state and are not well modeled in cross-section calculations

Signal integration window placement for white lines

Signal extraction with DigitalMicrograph 3 software

With DigitalMicrograph® 3 software, the signal extraction process is highly automated. However, the guidelines and concepts above still must be considered. DigitalMicrograph 3 quantification utilizes a model-based approach where the spectral background and the edge intensity are treated as a single model. If overlapping edges are present, they are also added to the model to allow separation of the overlap. Follow the below steps for EELS signal extraction in DigitalMicrograph 3 software.

  1. Elemental AnalysisIdentify the edge features within the spectrum.
  2. Show fit regions on the spectrum using the Show signal setup button in the Elemental Analysis window.
  3. The edge model will be shown on the spectrum. Default values are typically adequate, but the user can dynamically change the regions of interest if needed.
  4. The EELS edge setup button allows a specific setup for each edge:
    1. Exclude ELNES – Removes the near-edge structure from the analysis.
    2. Include plural scattering – Enables linking to low-loss spectrum and is required for absolute quantification.
    3. Most settings dynamically update if the fit region is adjusted on the spectrum.
EELS Edge Setup
Exclude ELNES allows the model to begin after a predetermined ELNES region. This leads to more consistent fitting to the calculated cross-section and should be used when fitting strong edges. The ELNES region should be included for semi-quantitative mapping to get the best signal-to-noise (SNR) in the maps.

  1. Edges that are close in energy are automatically tagged for overlap analysis. The Overlaps checkbox in the edge setup dialog allows you to change this default.
  2. The fit to the edge model is less than the models for the background, and any proceeding edges yield the extracted signal intensity for that edge.
Overlaps checkbox
Overlapping edges are fit together as a single model. The total signal for the overlapped edge includes a contribution from the preceding edge background.

References

Joy, D.C.; Maher, D. M. The quantization of electron energy-loss spectra. J. Microsc. 124:37 – 48; 1981.

Egerton, R. F. A revised expression for signal/noise ratio in EELS. Ultramicroscopy. 9:387 – 390; 1982.

Leapman, R. D.; Swyt, C. R. Separation of overlapping core edges in electron energy loss spectra by multiple-least-squares fitting. Ultramicroscopy. 26:393 – 404; 1988.

Kothleitner, G.; Hofer F. Optimisation of the signal to noise ratio in EFTEM elemental maps with regard to different ionisation edge types. Micron. 29349 – 357; 1998.

Verbeeck, J., Van Aert, S. Model based quantification of EELS spectra. Ultramicroscopy. 101(2 – 4):207 – 24; 2004.

Riegler, K.; Kothleitner, G. EELS detection limits revisited: Ruby – a case study. Ultramicroscopy. 110(8); 2010.

Thomas, P.; Twesten, R. A Simple, Model Based Approach for Robust Quantification of EELS Spectra and Spectrum-Images. Microscopy and Microanalysis. 18(S2):968 – 969; 2012.