TEM Sample Thickness Determination through Diffraction
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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 3562a 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 3562a. 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

Table 3562b shows the extinctions (also called forbidden spots) in the diffraction patterns of the crystals with space group Fd-3m such as diamond (C), silicon (Si), germanium (Ge), and tin (Sn) elements as a result of the destructive interference between the two interpenetrating face centred cubic (fcc) lattices displaced by a vector (1/4, 1/4, 1/4). Figure 3562 shows the diffraction pattern of a silicon (Si) crystal in [110] zone axis. The reflections marked in black are extinct in the single scattering approximation when the crystal is very thin, while the ones marked in green exist in the patterns of both thin and thick crystals. When the crystal become thicker, the multiple scattering occurs and thus these reflections can gain intensity and become visible because of more successive scatterings (even though they are probably weak if the sample is still relatively thin), for instance, electrons are indirectly scattered into the (002) reflection because of multiple scattering through the (1 -1 1) and (-1 1 1) scattering vectors. The red arrows represents the multiple scattering paths for forming the visible (002) reflection.

Table 3562b. Conditions of forbidden and allowed reflections (h k l) of common crystal structures
Bravais Lattice Forbidden reflections Allowed reflections Example Compounds
fcc h, k, l are mixed odd and even; or, all even and h + k + l ≠ 4n (Or defined by h + k + l = 4n + 2) As fcc, but if all even and h + k + l ≠ 4n, then absent (n is integer)
Si, Ge, Sn - diamond cubic

Diffraction pattern of a Si crystal in [110] zone axis orientation

Figure 3562. Diffraction pattern of a Si crystal in [110] zone axis
orientation. The spot sizes represent the intensities.

 

 

 

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