Depth resolution in on-axis TKD 1103


Figure 7. Zoom in the patterns 1, 5, and 9 from Figure 4. Many spots produced by double diffraction are visible in the pattern 5. These spots are the product of the diffraction, in the bottom crystal, of the diffracted waves produced by the top crystal. They are only visible between point 2 and 8 in Figure 4.


Figure 8. Illustration of the bias introduced by the beam broadening at low incident energy in the evaluation of the depth resolution. The electron trajectories were produced by CASINO (Drouin et al., 2007).


depth resolution by up to 50% at 10 keV, while it should be negligible at 30 keV. The model above is convenient because it uses the same


formalism (i.e., cross sections and mean free paths) as the well spread Monte Carlo simulations of electron trajectories in materials. Alternatively, one can use the formalism that Yamamoto (1977) used to account for the depth resolution of electron channeling patterns, which involves the complex lattice potential for electron diffraction. The complex lattice potential represents inelastic scattering (plasmon, phonon, and single electron excitation altogether) and is introduced to the crystal lattice potential in order to account for the damping of the diffracted wave along its travel. From the mean complex lattice potential V0


ficient µ0 can be calculated. For Si, µ0=V0 i /54=0.012nm−1


i , a mean absorption coef-


at 100 keV and room temperature (Reimer, 1997: 309). In the nonrelativistic regime, which is a more valid approximation in SEM than in TEM, this mean absorption coefficient µ0 is


inversely proportional to the energy (Hashimoto, 1964), which means that the depth resolution of Kikuchi diffraction in Figure 5 can be expressed approximately by 2.6/µ0.It might be possible to use this simple relationship to rapidly evaluate the depth resolution for any Z and E, because µ0 is a function of these two parameters (as well as of the tem- perature, because of the phonon scattering). For example, for Ge, µ0=0.026nm−1 at 100 keV and room temperature (Reimer, 1997: 309). Thus the depth resolution for Ge at 30 keV would be 2.6× 30/100/0.026=30nm and 2.6 ×10/ 100/0.026=10nm at 10 keV. It would be very interesting to validate this relationship between the mean absorption coefficient and the depth resolution of on-axis TKD for other atomic numbers. A first study by Sneddon et al. (2017) with conventional TKD confirms that the depth resolution presents a strong dependence with atomic number. Very interestingly, they report a depth resolution of 80, 33, and 13nm for Al, Cu, and Pt, respectively. From this result, it


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