Sample Thickness Determination using EELS
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As we know that in TEM observation, the transmission of unscattered incident electrons is inversely proportional to the TEM specimen thickness. On the other hand, the increase of the specimen thickness enhances the energy loss of the transmitted electrons. Therefore, the spatial resolution degrades with the increase of specimen thickness because of the chromatic aberration effects. Table 4621 lists examples of the energy loss of incident electrons passing through the specimen. The use of thinner specimen can generally improve spatial resolution because it minimizes the energy loss.

Table 4621. Examples of the energy loss of electrons passing through the TEM specimen.

  Accelerating voltage of incident electrons Penetrated electrons (%) Penetrated electron with energy loss higher than 50 eV (%) Unscattered electrons (%) Elastically scattered electrons (%)
Thin metal foil
50
40
50 nm thick carbon film
50 kV
55
33
10

If diffraction effects are negligible then the normalized scattering intensity I/I0 can be given by, [1]

         I/I0 = 1 − exp(−t/λ) -------------------------- [4621a]
where,
         λ -- The mean free path of the scattering.

The cross-section of the scattering can be extracted by the relation,
         1/λ = Nσ -------------------------- [4621b]
where,
         N = ρ/(Am)
         N -- The atomic density,
         ρ -- The mass density,
         A -- The dimensionless atomic mass,
         m -- The proton mass.

For many solids, especially metals, the bonding electrons can be considered as a free electron gas. Plasmons that are oscillations of the free electrons are generated when an incident electron travels through the gas. Plasmon spectra are routinely used to measure the thickness of a TEM specimen because more plasmons are excited as the electron goes through a thicker specimen. Thickness t of TEM samples can be evaluated as a multiple of the inelastic mean free path using log-ratio method [1]:

         measure the TEM sample thickness using EELS ------------------- [4621c]
where,
         It -- The integral of total spectrum counts (zero-loss peak plus extrapolated loss part).
         I0, -- The integral of zero-loss peak counts (e.g. between -3 and 3 eV).

The mean free inelastic path of electrons ( λ) has to be measured or calculated by an independent method. In practice, It can be replaced by Ip, which is the integral of the low-loss spectrum (e.g. between −3 and 97 eV). This calculation process can be performed with some software, for instance, Gatan digital micrograph (DM). Note that an appropriately modified form of the relationship in Equation 4621c should be applied if the plural scattering has been removed from the spectrum.

For the case of EFTEM, similar to Equation 4621c, two intensity maps are acquired: one is formed by all transmitted electrons (intensity It , unfiltered image), the other one by selecting only those electrons that did not lose any energy (intensity I0, filtered image). The relative drift between the unfiltered and filtered images was corrected by a standard cross-correlation technique when computing the ratio map It /I0.

Furthermore, to accurately evaluate TEM specimen thicknesses, both surface and bulk plasmons need to be considered. However, in calculations, we normally consider that only the bulk effect contributes to the plasmon-loss in specimens thicker than 150 nm. The surface plasmon-loss (Is) has dependence on TEM-specimen thickness only when the specimen is extremely thin (e.g. <10 nm in general). On the other hand, for very thin TEM specimens, e.g. ≤30 nm for Si (or ≤0.25 λP), several surface-induced effects contribute to plasmon signal:
         i) Radiative surface plasmons [2] locate just above bulk plasmon energies (EP).
         ii) Coupling of surface plasmons [3] excited at the two surfaces.
         iii) Coupling of surface and bulk plasmon excitation [4].
         iv) Errors in calculations in the energy region of EP to 2EP due to angular effects. These errors are not considered in the Fourier-log deconvolution process that is the method normally used in the calculations.

The peak-to-background ratio in EELS varies with specimen thickness so that it also can be used to determine the specimen thickness. For instance, Figure 4621 shows that the background increases dramatically with increase of the thickness of TEM specimen, while the signal of Pt M4,5 edge decreases significantly. In this case, the highest signal in the range of these TEM specimen thicknesses for Pt occurs at 20 nm. However, in the method with peak-to-background ratio, a correlation curve between the ratio and thickness should be plotted and used to calibrate the interesting thickness.

EELS of Pt M4,5 edg

Figure 4621. EELS of Pt M4,5 edge.

 

 

 

[1] Egerton, R.F. (1996). Electron Energy Loss Spectroscopy in the Electron Microscope. New York: Plenum Press.
[2] R. Vincent, J. Silcox, Phys. Rev. Lett. 31 (1973) 1487.
[3] R.B. Pettit, J. Silcox, R. Vincent, Phys. Rev. B 11 (1975) 3116.
[4] C.H. Chen, J. Silcox, R. Vincent, Phys. Rev. B 12 (1975) 64.

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