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42 Electronic Band Structure of Graphene Figure 2.6: ARPES measurement of the dispersion relation of epitaxial graphene (from Ref. [22]). tron, i.e. an electron emitted from the solid to be studied after prior optical excitation by a photon of well-defined energy and momentum, h ̄ν and h ̄k, respectively (see Fig. 2.5). The technique, which measures the spectral func- tion, the imaginary part of the electronic Green’s function 1/(ω−ǫkλ +iη), is based on energy and momentum conservation in a electron-photon scattering process, h ̄ν=Ef −Ei, k=kf −ki, where Ei and ki represent the energy and momentum, respectively, of the initial electronic state and Ef and kf those of the final electronic state, i.e. the state of the photoemitted and detected electron. The direction of the latter, in terms of the angles θ and φ shown in Fig. 2.5, yields precisely the momentum-dependence of the energy and thus the dispersion relation. Fig. 2.6 shows ARPES results obtained by Bostwick et al. on epitaxial graphene [22]. Similar results have been obtained on thin graphitic samples [23]. The studied sample has been obtained by graphitisation of the Si- terminated (0001) surface. Fig. 2.6 (a) shows the energy dispersion of the π band and yields a good agreement with that calculated in Sec. 2.1.3 [see Fig. 2.2 (b)]. In order to obtain an ARPES signal, the initial state must be occupied, and one may see from Fig. 2.6 (a) that the Fermi level is in the π∗ band at roughly EF ≃ 0.45 eV. This is in agreement with the statement in Sec. 1.3.2 that the graphene layer on SiC is naturally electron-doped due to charge transfer from the SiC substrate. Fig. 2.6 (b) shows the form of the first BZ, which is obtained by an energy cut through the dispersion relation at zero energy (at the Dirac points). The energy cut at the Fermi level, EF ≃ 0.45 eV, is shown in Fig. 2.6 (b) and reveals the circular Fermi surface around the K and K′ points. The faint satellites are due to the underlying (hexagonal) structure of the SiC substrate.PDF Image | Physical Properties of Graphene
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