| The relationship between scattered intensity I and cross section σ in scattering processes, such as those observed in EELS, can be given by,
 ------------------------------------------- [4602]
where,
I is the scattered intensity.
N is the number of scattering centers (atoms, for instance) in the material.
σ is the scattering cross section, which represents the probability of scattering occurring.
Φ is the incident electron flux, which is the number of electrons per unit area per unit time hitting the material.
This equation shows that the scattered intensity is directly proportional to the scattering cross section. The larger the cross section, the higher the probability of scattering, leading to greater scattered intensity. In EELS, inner-shell excitations result in relatively low scattered intensity due to their inherently low cross section. This low probability of occurrence means that the mean free path of an electron undergoing inner-shell excitation is long compared to the typical specimen thickness, making it unlikely that a fast electron would produce more than one inner-shell excitation as it passes through the material. That is, inner-shell excitations are relatively rare (due to the low cross section), an electron is less likely to undergo such an excitation as it travels through the material:
- Low Probability of Inner-Shell Excitation: The cross section for inner-shell excitation is small, meaning that the likelihood of an electron causing such an excitation is low. As a result, most electrons will travel through the material without undergoing inner-shell excitation.
- Mean Free Path: The mean free path is the average distance an electron travels before undergoing a scattering event. Since inner-shell excitations are less probable, the mean free path for an electron specifically undergoing inner-shell excitation is longer. This implies that an electron would typically travel a longer distance before causing an inner-shell excitation, compared to other types of excitations or scattering events.
- Comparison to Specimen Thickness: If the mean free path is long, it means that in a thin specimen, it’s even less likely for an electron to undergo inner-shell excitation multiple times. The specimen might not be thick enough to significantly increase the probability of multiple inner-shell excitations within a single electron’s path.
If we consider a scenario where the TEM sample is extremely thick, but we only account for inner-shell excitation and ignore other types of inelastic scattering (such as plasmon losses or outer-shell excitations), the resulting spectrum would primarily consist of repeated inner-shell excitation events. In this case, the spectrum would show a series of steps or peaks corresponding to multiple occurrences of inner-shell excitation, but without any broadening due to other types of inelastic scattering, as shown in Figure 4602a.
| Figure 4602a. Simulated EELS spectrum with inner-shell excitation (extremely thick sample, inner-shell only). The ionization energy edge here is assumed as 500 eV. |
The simulated EELS spectrum for an extremely thick TEM sample, in Figure 4602a, considers only inner-shell excitation and ignors other inelastic scattering events:
- The spectrum shows a series of peaks at regular intervals, corresponding to repeated occurrences of inner-shell excitation as the electron passes through the thick sample. The ionization energy edge here is assumed as 500 eV so that the intervals are 500 eV in this material.
- Each peak represents an energy loss equal to the ionization energy, with subsequent peaks appearing at multiples of this energy, reflecting multiple inner-shell excitations.
This spectrum is simplified compared to a real scenario, where additional inelastic scattering would cause broadening and other features in the spectrum.
However, it is possible for an electron that has already undergone inner-shell scattering to also cause outer-shell excitation. This combination of inner- and outer-shell excitations, referred to as "mixed" inelastic scattering, leads to an energy loss that is the sum of the two separate losses. As shown in Figure 4602b, the result is a broad peak in the EELS spectrum, appearing above the ionization threshold and displaced from it by approximately the plasmon energy, which corresponds to the collective oscillations of the electron cloud in the material. On the other hand, the red curve, from a "thin" TEM sample, only contain two peaks which are generated by inner-shell scatterings only and does not have "mixed" inelastic scattering.
| Figure 4602b. Simulated EELS spectrum with inner-shell excitation (thick vs. thin sample). |
The spectrum for the thick TEM sample in Figure 4602b includes mixed scattering effects:
- Multiple Scattering Contributions: In the thick sample spectrum, the broad peaks added at energy losses above the ionization edge (at 25 eV, 50 eV, 75 eV, and beyond) simulate the effects of multiple scattering events. These events represent situations where an electron has undergone both inner-shell excitation and additional inelastic scattering, such as plasmon excitation or other types of outer-shell excitations.
- Mixed Scattering: The mixed scattering is represented in the spectrum by the broadening and additional peaks displaced from the ionization edge by energies corresponding to plasmon losses or other scattering events. The broadening and additional peaks indicate the contributions from such mixed scattering events.
To achieve more accurate analysis, this mixed-scattering intensity can be removed from the spectrum using deconvolution, a mathematical process that corrects overlapping signals and allows for clearer identification of the inner-shell excitation events.
|
