Diameter dependence of thermoelectric power of semiconducting carbon nanotubes

Abstract

We calculate the thermoelectric power (or thermopower) of many semiconducting single wall carbon nanotubes (s-SWNTs) within a diameter range $0.5--1.5\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$ by using the Boltzmann transport formalism combined with an extended tight-binding model. We find that the thermopower of s-SWNTs increases as the tube diameter decreases. For some s-SWNTs with diameters less than $0.6\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$, the thermopower can reach a value larger than $2000\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{V}/\mathrm{K}$ at room temperature, which is about 6 to 10 times larger than that found in commonly used thermoelectric materials. The large thermopower values may be attributed to the one dimensionality of the nanotubes and to the presence of large band gaps of the small-diameter s-SWNTs. We derive an analytical formula to reproduce the numerical calculation of the thermopower and we find that the thermopower of a given s-SWNT is directly related with its band gap. The formula also explains the shape of the thermopower as a function of tube diameter, which looks similar to the shape of the so-called Kataura plot of the band gap dependence on tube diameter.