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8122 Graphene – Synthesis, Characterization, Properties anWdill-bAe-psept-lbiyc-IaN-tTiEoCnHs Fig. 5. Resistivity at 4 K vs. sample thickness of different samples obtained from the same HOPG bulk sample. 2.4 Thickness dependence of the resistivity Figure 5 shows the resistivity at 4 K of different samples vs. their thickness. It is clearly seen that the resistivity decreases increasing the sample thickness. The average change in resistivity between ∼ 10 nm to 17 μm thick samples is about two orders of magnitude, far beyond geometrical errors. A possible explanation for the observed behavior is that the larger the thickness the larger the amount of interfaces in the sample, see Fig. 2. As we described in Section 2.3, there is a clear change in the temperature and magnetic field dependence decreasing the sample thickness. It appears unlikely, however, that randomly distributed point-like lattice defects can be the reason for the observed behavior. Also the interpretation provided by Zhang et al. (2005) that the decrease of mobility μ (i.e. an increase in the resistivity at constant carrier density) decreasing sample thickness provides an evidence for boundary scattering is surely not the correct explanation for the observed behavior, taking into account the fact that one graphene layer shows finite and large mobility. Note that thin graphite flakes show ballistic transport with huge mobilities, see Section 3. The overall results suggest the existence of a kind of thickness-threshold around ∼ 50 nm for multigraphene samples of few micrometers size, obtained from HOPG bulk graphite indicating that the interfaces contribute substantially and in parallel to the graphene layers. In the past the influence of the internal interfaces in graphite bulk samples was either completely neglected or the scientific community was not aware of their existence. On the other hand it is well known that grain boundaries in various semiconductors can lead to the formation of quasi-two dimensional carrier systems confined in the boundaries. As early examples in literature we refer to the quasi-two dimensional electron gas system that was found at the inversion layers of n-Ge bicrystals (Uchida et al., 1983; Vul & Zavaritzkaya, 1979) or in p-InSb (Herrmann et al., 1984) as well as in Hg1−xCdxTe grain boundaries (Ludwig et al., 1992). It is important to note that in Ge-bicrystals Uchida et al. (1983) found actually the quantum Hall effect (QHE) at T 4.2 K and at magnetic fields above 6 T. The density of carriers at the interface was estimated to be ∼ 5 × 1012 cm−2. Therefore, we note that the usually reported carrier concentrations for graphite are not intrinsic of ideal graphite,PDF Image | GRAPHENE SYNTHESIS CHARACTERIZATION PROPERTIES
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