Thermoelectricity in Nanowires: A Generic Model

By employing a Boltzmann transport equation and using an energy and size dependent relaxation time ($\tau$) approximation (RTA), we evaluate self-consistently the thermoelectric figure-of-merit $ZT$ of a quantum wire with rectangular cross-section. The inferred $ZT$ shows abrupt enhancement in comparison to its counterparts in bulk systems. Still, the estimated $ZT$ for the representative Bi$_2$Te$_3$ nanowires and its dependence on wire parameters deviate considerably from those predicted by the existing RTA models with a constant $\tau$. In addition, we address contribution of the higher energy subbands to the transport phenomena, the effect of chemical potential tuning on $ZT$, and correlation of $ZT$ with quantum size effects (QSEs). The obtained results are of general validity for a wide class of systems and may prove useful in the ongoing development of the modern thermoelectric applications.