3.1.1 Ballistic Thermoelectric Properties of AGNRs

Figure 3.1: The geometrical structure of an $N$ -AGNR. The unit cell contains $N$ carbon atoms of sublattices $A$ and $B$ .

GNRs are tailored from the 2D graphene sheet with finite width $W$ . $N$ -AGNR denotes a GNR with armchair edges, the unit cell of which contains $N$ atoms of each sublattice ($A$ and $B$ ), as shown in Fig. 3.1. The band-gap ($E_g$ ) of AGNRs is inversely proportional to the ribbon's width. AGNRs are classified according to their indices into three categories, $N=3m-1$ , $N=3m$ , and $N=3m+1$ , where $m$ in an integer. The lowest band-gap belongs to the category $N=3m-1$ , whereas the category $N=3m+1$ has the highest band-gap. As the band-gap plays an important role in thermoelectrics, only the category $N=3m+1$ is considered. However, similar results are expected for the other categories too.

In this section, ballistic thermoelectric properties of AGNRs with different widths at various temperatures are investigated. In the ballistic regime, the transport properties are independent of channel length $L$ . The features of band structures play an important role in the performance of AGNR-based devices. The channel length, therefore, is chosen to be the length of a unit cell ($3a_{cc}$ ), whereas the ribbon's width varies between $W=1~\mathrm{nm}$ and $6~\mathrm{nm}$ and the temperature between $T=50~\mathrm{K}$ and $750~\mathrm{K}$ .