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In general, the TEM samples that are too thin have too few atoms to produce sufficient signals to generate statistical reliability. However, the TEM samples also cannot be too thick for any measurements. The best balance is normally determined experimentally. The list in Table 4487a presents empirical thicknesses for the EELS, EFTEM, EDS, and HAADF STEM measurements.

Table 4487a. Empirical thicknesses for EELS, EFTEM, EDS, and HAADF STEM measurements*.

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. EELS measures the distribution of energies lost by incident electrons (typically 100–1000 keV) as they pass through a thin solid specimen (typically 0.5–50 nm). Table 4487b 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 4487b. Examples of the energy loss of electrons passing through the TEM specimen.

The interpretation of data and images taken from TEM systems can be very complicated if there is a variation of specimen thickness. Especially, for quantitative composition analysis of electron energy loss spectroscopy (EELS) measurements, energy filtered TEM (EFTEM) images, and high angle annular dark field scanning TEM (HAADF STEM) images, a uniform or exactly known sample thickness is preferable because the recorded signal intensity depends strongly on both sample thickness and sample composition.

If the TEM specimen is very thick, both the chromatic and spherical aberrations affect the spatial resolution of EFTEM imaging significantly. For instance, for thick specimen the chromatic broadening (Δd_c) is about 2.5 nm at β = 10 mrad, C_c = 1 mm, ΔE = 50 eV, and E₀ = 200 keV, while for thin specimen, Δd_c will be normally ≤ 0.2 nm for most microscope configurations (see details in page3384). For thick specimen, assuming the spherical aberration constant is 0.7 mm, collection semi-angle 15 mrad, the Δd_S will be ~3.8 nm, while for thin specimen Δd_S is normally negligible for most microscope configurations (see details in page1941).

In the cases that very thick TEM samples are used in EELS or EFTEM measurements, the increase of plural scattering effects induces two main problems:
        i) The background models, e.g. the form of power law, are not convenient to represent the actual background;
        ii) The low energy edge onsets are embedded in the background, meaning some edge becomes invisible.

On the other hand, if the TEM samples are too thin, either inelastic scattering does not occur or is too weak to do EELS and EFTEM measurement.

With a STEM sample thickness less than 50 Å, Voyles et al [1] concluded that ADF-STEM image obtained at 200 kV can show a Si column containing a single Sb atom is more than 25% brighter than a pure Si column. They also suggested that random variations in thickness must be less than the contrast of one Sb atom, and the surfaces must be free from native amorphous SiO₂ layers and amorphized bulk Si layers in ADF-STEM observations.

Investigating individual point defects, e.g. monovacancies, using TEM-related techniques was believed to be difficult because this requires both atomic sensitivity and atomic resolution and the specimens need to be very thin such that one can detect the individual point defects from the image contrast.

Table 4487c. Examples of TEM specimen thicknesses for EELS measurements.

Furthermore, the detection limit is also controlled by the sample thickness because of the background. For instance, the detection limit of oxygen was improved from 2.7 atomic % (130 nm thickness in Figure 4487a (a)) to 1.5 atomic % (40 nm thickness in Figure 4487a (b)), assuming that the minimum detectable counts of oxygen are equal to the 3 sigma of signal/noise ratio under the analytical conditions [3]. Therefore, the oxygen content is not detectable in the 130-nm thick sample because the concentration is lower than the detection limit. Note that the two spectra were taken from the same (Mg, Fe)O-matrix phase.

Figure 4487a. Example of thickness dependence of EELS detection limits. The TEM samples are (Mg, Fe)O-matrix phase in thickness of: (a) 130 nm and (b) 40 nm. Adapted from [2]

Figure 4487b (a) shows a TEM image of a RuO₂/TiO₂ core/shell structure (a RuO₂ nanorod shelled with a TiO₂ layer) in diameter of 160 nm. Figure 4487b (b) shows the EELS spectra taken from the selected positions in Figure 4487b (a) that are marked by A and B for the RuO₂/TiO₂ core/shell structure and a pure RuO₂ nanorod without TiO₂ coating, respectively. For the EEL spectrum from the TiO₂ shell (position B), the ELNESs of Ti L_2,3- and O K-edges are clearly found. In the spectrum obtained from position A, the Ru M-edge is present, while the Ti L_2,3- and O K-edges are not so clear (comparing to noise) because the wire-shaped specimen is too thick (about 220 nm in wire-diameter) for EELS measurements, even though the EELS contribution of TiO₂ thickness (about 60 nm, including top and bottom TiO₂ layers of the nanorod) is almost the same as that at location B and the O atomic percentage is high (about 67 at.%).

Figure 4487b. (a). The TEM image of a RuO₂/TiO₂ core/shell structure in diameter of 160 nm. (b) EELS spectrum for the Ti L-edge and O K-edge ELNEFS of the RuO₂/TiO₂ core/shell structure taken from two points, labeled A and B for the RuO₂/TiO₂ wire and the TiO₂ shell, respectively. The bottom EELS spectrum was obtained from a pure RuO₂ nanorod as reference. Adapted from [5]

Furthermore, the spatial resolution of STEM measurements is also determined by the specimen thickness, due to cone shape of the probe. For instance, if we have the experimental conditions below:
        i) A specimen is in thickness of 600 nm.
        ii) The incident electron spot size is ~1 nm.
        iii) The convergence angle of the incident electron is 10 mrad.
Then, the diameter of the electron at the bottom surface of the specimen is about 10 nm. Therefore, the spatial resolution will be about 10 nm in diameter.

For very thin TEM specimens, e.g. ≤30 nm for Si (or ≤0.25 λ_P), several surface-induced effects contribute to plasmon signal:
         i) Radiative surface plasmons [6] locate just above bulk plasmon energies (E_P).
         ii) Coupling of surface plasmons [7] excited at the two surfaces.
         iii) Coupling of surface and bulk plasmon excitation [8].
         iv) Errors in calculations in the energy region of E_P to 2E_P due to angular effects. These errors are not considered in the Fourier-log deconvolution process that is the method normally used in the calculations.

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.

A common measurement for selecting appropriate sample thickness is to test the ratio of the count of the zero-loss peak, I₀, to that of the first plamon peak, I_p. A number of values have been suggested for the maximum acceptable I_p/I₀ ratio, range form 1 to 0.1 depending on the chemistry of the analyzing materials. It is not possible to give a reliable general value for an acceptable I_p/I₀ ratio. However, it is evident that a strong zero-loss peak is an important feature for a usable specimen thickness.

The maximum usable specimen thickness can be increased by
         i) using a higher accelerating voltage,
         ii) by removing multiple-scattering effects from the spectrum by deconvolution. However, deconvolution can also introduce artifacts.

Note that for high resolution STEM analysis, very thin high-quality TEM specimens are needed as discussed in page2939.

[1] P. M. Voyles, D. A. Muller, J. L. Grazul, P. H. Citrin, and H.-J. L. Gossmann, Atomic-scale imaging of individual dopant atoms and clusters in highly n-type bulk Si, Nature, 416 (2002) 826.
[2] N. Miyajima, C. Holzapfel, Y. Asahara, L. Dubrovinsky, D.J. Frost, D.C. Rubie, M. Drechsler, K. Niwa, M. Ichihara, and T. Yagi, Combining Fib milling and conventional Argon ion milling techniques to prepare high-quality site-specific TEM samples for quantitative EELS analysis of oxygen in molten iron, Journal ofMicroscopy , Vol. 238, Pt 3 2010, pp. 200–209.
[3] Egerton, R.E. (1996) Electron Energy-Loss Spectroscopy in the Electron Microscope. Plenum Press, New York, 485 p.
[4] L.A.J. Garvie and P.R. Buseck, Determination of Ce4+/Ce3+ in electron-beam-damaged CeO2 by electron energy-loss spectroscopy, Journal of Physics and Chemistry of Solids 60 (1999) 1943–1947.
[5] Yu-Lun Chueh, Chin-Hua Hsieh, Mu-Tung Chang, Li-Jen Chou, Chang S. Lao, Jin H. Song, Jon-Yiew Gan, and Zhong L. Wang, RuO₂ Nanowires and RuO₂/TiO₂ Core/Shell Nanowires: From Synthesis to Mechanical, Optical, Electrical, and Photoconductive Properties, Advanced Materials, 2007, 19 (1), 143–149.
[6] R. Vincent, J. Silcox, Phys. Rev. Lett. 31 (1973) 1487.
[7] R.B. Pettit, J. Silcox, R. Vincent, Phys. Rev. B 11 (1975) 3116.
[8] C.H. Chen, J. Silcox, R. Vincent, Phys. Rev. B 12 (1975) 64.