3. Thermoelectric Properties of Graphene-Based Nanostructures

Graphene, a recently discovered form of carbon, has received much attention over the past few years due to its excellent electrical, optical, and thermal properties [22]. The electrical conductance of graphene is as high as that of copper [23]. As a zero band-gap material, pristine graphene has a small Seebeck coefficient [24]. However, one can open up band-gaps by appropriate patterning of the graphene sheets [25,26,27]. Graphene nanoribbons (GNRs) are thin strips of graphene, where the band gap is varied by the chirality of the edge and the width of the ribbon. Zigzag GNRs show metallic behavior, whereas armchair GNRs are semiconductors with a band-gap inversely proportional to the width [25]. Very recently, Zhang and coworkers showed that one can open up a significant band-gap in zigzag GNRs by edge manipulation [63]. In addition, it has been theoretically [64] and experimentally [65] shown that by introducing an array of holes into the graphene sheet a band-gap can be achieved. On the other hand, a large scale method to produce graphene sheets has been reported [30]. Experimental studies have also reported a high Seebeck coefficient in graphene-based devices [66,67].

The high Seebeck coefficient has been achieved by applying voltages (e.g. gate voltage) and magnetic field to the graphene-based devices. The applied voltage is normally used for breaking the symmetry between electron and hole conduction. Without applying a voltage, the symmetry between valence and conduction bands results in a low Seebeck coefficient, and as a result a relatively small thermoelectric power factor for pristine graphene. The thermoelectric figure of merit, however, can be further improved by degrading the lattice thermal conductivity. This was also experimentally demonstrated for traditionally poor thermoelectric materials such as silicon which resulted in $ZT$ values close to $ZT\sim 0.5$ , a large improvement compared to $ZT=0.01$ of bulk silicon [17].

The ability of graphene to conduct heat is an order of magnitude higher than that of copper [28]. The high thermal conductance of graphene is mostly due to the lattice contribution, whereas the electronic contribution to the thermal conduction can be ignored [28,29]. Therefore, for thermoelectric applications it is necessary to reduce its thermal conductance. By proper engineering the phonon transport properties it is possible to reduce the total thermal conductance without significant reduction of the electrical conductance and the power factor.

Recently many theoretical studies have been performed on the thermal conductivity of graphene-based structures. It has been shown that boundaries and edge roughness can strongly influence the thermal conductance [19]. Uniaxial strain can remarkably decrease the thermal conductance of GNRs. In the case of zigzag GNRs, 15% uniaxial strain can decrease the thermal conductance to one fifth of that of an unstrained GNR [68]. Vacancy, defects, and isotope doping have magnificent effects on thermal conductance [58,69]. Furthermore, it has been recently shown that the thermal conductance of GNRs can be reduced by hydrogen-passivation of the edges [70]. In this chapter, therefore, we aim to investigate the thermal and thermoelectric properties of various graphene-based structures. This can help to improve understanding of thermoelectrics in nanostructues and provide some useful guidelines for engineering nanostructures for thermoelectric applications.