Practical Electron Microscopy and Database

In many cases, each EEL spectrum should be corrected due to dark current and gain variations between the elements of the CCD detector and due to multiple scattering. Most TEM specimens are so thick that plural scattering is usually significant. The plural scattering is generally unwanted since it distorts the shape of the energy-loss spectrum. Multiple-scattering events remove EELS intensity from the zero- and lower-loss regions of a spectrum into higher-loss region, and thus increases the background for higher-energy losses. Furthermore, the background intensity increases more rapidly than peak intensities.

In general, if the TEM specimen is too thick (t/λ > 0.4), a deconvolution process must be employed to remove the effect of plural scattering. However, if the TEM sample for EELS is very thin, the plural scattering can be negligible impact on the shape of the ionization edges.

Table 4712a. Electron scattering versus TEM sample thickness.

Table 4712b shows that electrons interact with 1 electron, many electrons, 1 nucleus, and many nuclei in solids.

Plural inelastic scattering by plasmon excitation is a special concern when measuring the low energy loss (e.g. Li K-edge) because it is close to the low-energy plasmon region. For instance, double plasmon scattering distorts the pre-edge background and can mask the Li K-edge. On the other hand, plural scattering can originate from the contribution of combined energy losses from core and valence electron excitations.

Artifacts due to plural scattering can be reduced by increasing the inelastic mean-free-path with the increase of the accelerating voltage of the electron beam or by restricting analyses to thin regions of the sample. Furthermore, in general, the EELS and EFTEM backgrounds originate from random, plural inelastic scattering events.

In general, the requirements of TEM specimen thickness for EELS and EFTEM measurements are:
         i) The specimens should be sufficiently thin to prevent any multiple inelastic scattering, but the degree of single inelastic scattering should be relatively high. For most materials, the optimized specimen thickness is in the range of 25-100 nm, depending on the average atomic number and the beam energy.
         ii) To avoid surface effects, the specimen thickness cannot be less than 25 nm if low-loss EELS spectra are measured.

To simplify the analysis of energy-loss spectra, Gaussian functions are often employed to simulate intensity profiles for both thin and thick samples. These functions provide a practical and mathematically straightforward way to model the peaks observed in the spectra, making it easier to interpret the data and understand the underlying physical processes. Gaussian functions are particularly useful due to their flexibility and ability to approximate a wide range of spectral features, facilitating the analysis of complex samples in EELS:

• Thin Sample: Single Scattering

  The intensity of the energy-loss spectrum for a thin sample is modeled as a single Gaussian peak:

  ----------------------------------------------------- [4712a]

  where: 

  • E is the energy loss.
  • E₀​ = 16.7 eV is the peak energy loss of Si, representing the primary inelastic scattering event. Here, we use Si as an example. The plasma energies of other elements can be found at page4623.
  • σ = 5 eV is the standard deviation, determining the width of the peak.

• Thick Sample: Multiple Scattering (Plural Scattering)

  For the thick sample, multiple Gaussian peaks are added to represent plural scattering events. The first peak is the same as for the thin sample, while additional peaks are included at multiples of the primary energy loss:

  ----------------------------------------------------- [4712b]

  where,

  • The first term I_thin(E) represents the primary scattering event.
  • The second term represents the second scattering event (at double the energy loss).
  • The third term represents the third scattering event (at triple the energy loss).

• Both intensities are normalized to have a maximum value of 1 for easier comparison:

  ----------------------------------------------------- [4712c]

  ----------------------------------------------------- [4712d]

Figure 4712 shows the normalized intensities which are then plotted to visually compare the EELS spectrum for thin and thick samples.