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2116 Graphene – Synthesis, Characterization, Properties anWdill-bAe-psept-lbiyc-IaN-tTiEoCnHs assuming a coupling γ0 between nearest in-plane neighbors C-atoms on the graphene plane give a carrier density (per C-atom) n(T) = (0.3...0.4)(kBT/γ0)2 (γ0 ≃ 3 eV and T is the temperature) (Kelly, 1981). Because all experimental values obtained from bulk graphite samples indicated a finite n(T → 0) = n0 > 0 then the straightforward and "easiest" solution to solve this "disagreement" is to start including more free parameters in the tight-binding electronic band structure calculations. For example, introducing a new coupling γ1 between C-atoms of type α in adjacent planes one obtains n(T) = a(γ1/γ02)T + b(T/γ0)2 + c(T3/γ02γ1) + . . . (a, b, c, . . . are numerical constants), where the "accepted" value for γ1 ∼ 0.3 eV. Also in this case n(T → 0) → 0. We stress that neither in single layer graphene nor in graphite such T−dependence was ever reported 3, i.e. a large density background n0 was always measured and assumed as "intrinsic" without taking care of any influence from lattice defects or impurities. To fit experimental data and obtain a finite Fermi energy EF – in the simplest case EF ∼ γ2 (Dillon et al., 1977; Kelly, 1981) – up to seven free parameters were and still are introduced, even for carrier density as small as n ≃ | − 8 × 109| cm−2(EF ≃ −29 meV) as obtained recently from magnetotransport data in bulk pyrolytic graphite (Schneider et al., 2009). Taking into account the exhaustive experience accumulated in gapless or narrow gap semiconductors (Tsidilkovski, 1997) we should actually expect that the measured carrier density n0 1012 cm−2 is not intrinsic of the graphite structure but it is influenced by impurities and/or defects in the graphite/graphene lattice. The reader should keep in mind that a carrier density of the order of 108 cm−2 means one carrier in 1 μm2 graphene area, which could be produced actually by having a single vacancy or impurity in the same graphene area, in case one carrier is generated by one of these defects, as experimental (Arndt et al., 2009) and theoretical (Stauber et al., 2007) work suggests. Experimental evidence published recently and partially reviewed in this chapter speaks against an intrinsic origin of - even a part of - the measured n0 in graphite samples, casting doubts on the relevance of related electronic band structure parameters obtained in the past. On the other hand this new knowledge will help significantly to clarify observed transport phenomena. In Section 3 of this chapter we describe a method that one can use to obtain the carrier density, the mean free path and the mobility of the carriers inside graphite without free parameters. In that Section we review a systematic study of the transport in small multigraphene4 samples that reveals room-temperature mobility values (∼ 6 × 107 cm2V−1s−1) per graphene layer inside graphite, which overwhelm those reported in literature for single graphene layers, indicating the higher quality of the graphene layers inside ideal graphite. This quality is also reflected by the extremely low room-temperature carrier density (∼ 7 × 108 cm−2) obtained for good, but certainly not ideal, quality multigraphene samples. These studies indicate that ballistic transport with mean free path in the micrometer range is possible in graphite at room temperature. In Section 2 we describe the main characteristics of bulk and multigraphene samples, their characterization using transmission electron microscopy (TEM), electron backscattering 3 It is interesting to note that the carrier concentration obtained in bulk graphite by García et al. (2008), using an original and parameter-free method to determine it and the mean free path, can be fitted up to ∼200Kbyn[cm−2]≃n0+105T2+7.5×103T3withTin[K]andn0 ≃2×108 cm−2.Thesamedata, however, can be also well explained by a semiconducting-like exponential function exp(−Eg/2T) with an energy gap Eg ∼ 50 meV. 4 We use this word to refer to graphite samples of not more than a few micrometers in length and width and thickness below ∼ 100 nm. The reason for this kind of geometrical restriction will become clear in Section 2.PDF Image | GRAPHENE SYNTHESIS CHARACTERIZATION PROPERTIES
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