3.3 Thermoelectrics Engineering in ZGNRs

Graphene is not a useful thermoelectric material. Although its electrical conductance is as high as that of copper [23], its ability to conduct heat is even higher [82], which increases the denominator of $ZT$ . To make things worse, as a zero bandgap material, pristine graphene has a very small Seebeck coefficient [24], which minimizes the power factor $S^2G$ . In order to improve the Seebeck coefficient graphene needs to acquire a bandgap. This can be achieved by appropriate patterning of the graphene sheet into nanoribbons [25,27]. Graphene nanoribbons (GNRs) are thin strips of graphene, where the bandgap depends on the chirality of the edges (armchair or zigzag) and the width of the ribbon. Armchair GNRs (AGNRs) can be semiconductors with a bandgap inversely proportional to their width [25]. Although the acquired bandgap can increase the Seebeck coefficient, when attempting to reduce the thermal conductivity by introducing disorder in the nanoribbon, as described in Sec. 3.1, the electrical conductivity is also strongly affected [58,88], and the thermoelectric performance remains low. Zigzag GNRs (ZGNRs), on the other hand, show metallic behavior with very low Seebeck coefficient, but as described in Ref. [88], the transport in ZGNRs is nearly unaffected in the presence of line edge roughness, at least in the first conduction plateau around their Fermi level.

In this section, by using atomistic electronic and phononic bandstructure calculations, and quantum mechanical transport simulation, it is shown that despite the zero bandgap, the thermoelectric performance of ZGNRs can be largely enhanced. For this a series of design steps are employed: i) Introducing extended line defects (ELDs) as described in Ref. [89] can break the symmetry between electrons and holes by adding additional electronic bands. This provides a sharp band edge around the Fermi level and offers a band asymmetry which constitutes an effective bandgap for thermoelectric purposes. ii) Introducing background impurities enhances the effective bandgap. iii) Introducing edge roughness reduces the lattice part of the thermal conductivity more effectively than it reduces the electrical conductivity. Using these measures, the figure of merit $ZT$ can be greatly enhanced and high thermoelectric performance could be achieved.