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1050 Graphene – Synthesis, Characterization, Properties anWdill-bAe-psept-lbiyc-IaN-tTiEoCnHs Zhang et al. (2009); Zhou et al. (2008)) have highlighted complementary aspects of the energy dispersion of few-layer graphene with different number of layers. Possibly the best device geometry in which to address the electric field tuneability of the FLGs energy dispersion is a double gated design, where the graphene materials are sandwiched between a top- and a back-gate, see Fig. 6a. Double gated geometries have a dual valency, that is they offer a simple way to independently and continuously control in-situ both the band structure and the Fermi level by means of gate voltages (Craciun et al. (2011)). A typical device layout comprises a source and a drain contact to a graphene flake exfoliated onto SiO2/Si substrate -which serves as a back gate- and a nanofabricated top gate. Since the conductance is determined by the features of the energy bands in the thermal shell kB T around the Fermi energy (εF), any modification of the conductivity in response to the perpendicular electric field is purely a consequence of the changes in the energy dispersion. This intimate relation between conductivity and energy dispersion has allowed the discovery that bilayer graphene is the only known semiconductor with a gate tuneable band-gap (Zhang et al. (2009)) and conversely that trilayer graphene is the only known semimetal with a gate tuneable conduction and valence bands overlap (Craciun et al. (2009)). A perpendicular electric field applied onto the few-layer graphene materials breaks the energetic symmetry between the planes of these multilayer systems (see Section 2). This asymmetry is then reflected in the energetic inequivalence between carbon atoms belonging to different sublattices -which in multilayer graphene belong to different layers. Experimentally it was observed that the in-plane electrical transport properties of each specific FLG thickness change in a unique way in response to a finite external perpendicular electric field (Eex). In all cases the resistance exhibits a maximum (Rmax) whose value and position in gate voltage sq depend on the voltage applied to the gate on which a fixed potential is applied during the measurement, see Fig. 6b. When a finite external electric field is applied onto bilayers, the energetic equivalence between the sublattices is broken and a band gap opens up in the energy dispersion. Consequently, Rmax displays a characteristic insulating behaviour as a function of temperature. Once the sq energetic equivalence between the sublattices is restored (i.e. Eex = 0), the energy gap reduces to zero, see Fig. 6c and d. Charge transport experiments have reported large on/off ratios of the current in double gated graphene bilayers when the Fermi level crosses from the conduction (valence) band through the band-gap, see Fig. 6b and c. However, the values estimated for the band-gap from transport experiments are systematically much smaller than the theoretically predicted energy gap. Typically in transport a mobility gap is observed on an energy scale of a few meV for an average perpendicular electric displacement field of D = 2V/nm, whereas a band gap of 200 meV is theoretically expected. Furthermore, the specific temperature dependence of Rmax measured in bilayer graphene is incompatible sq with a simple thermally activated transport over a band gap, but it exhibits the functional dependence typical of variable range hopping due to a finite sub-gap density of states, see Fig. 6d (Oostinga et al. (2008); Russo et al. (2009); Taychatanapat et al. (2010); Yan et al. (2010); Zou et al. (2010)). The dichotomy of a mobility gap in transport experiments and the theoretically expected energy gap is currently fuelling both theoretical and experimental discussions. Though several possible explanations have been put forward, transport studies in different geometries demonstrate that the temperature dependence of the conductance in bilayer graphene in the diffusive regime can be explained by the parallel of a thermally activated current over thePDF Image | GRAPHENE SYNTHESIS CHARACTERIZATION PROPERTIES
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