Using molecular dynamics simulations, we have predicted the thermal conductivity of Bi${}_2$Te${}_3$ nanowires with diameters ranging from 3 to 30 nm with both smooth and rough surfaces. It is found that when the nanowire diameter decreases to the molecular scale (below 10 nm, or the so-called “quantum wire”), the thermal conductivity shows significant reduction as compared to bulk value. On the other hand, the thermal conductivity for the 30-nm-diam nanowire only shows less than 20% reduction, in agreement with recent experimental data. Also, the thermal conductivity of nanowires shows a weaker temperature dependence than the typical $T$${}^{-1}$ trend, consistent with experimental observations. This is attributed to the strong boundary scattering of phonons. An analytical model is developed to interpret the molecular dynamics data, and the model suggests that phonon softening in thin nanowires and strong phonon scattering on the rough surface are the two major mechanisms leading to the thermal conductivity reduction. Our results indicate that Bi${}_2$Te${}_3$ nanowires need to be in the molecular scale (diameter below 10 nm) in order to achieve better $\mathit{ZT}$ than the bulk phase.

• Received 19 February 2010

DOI:https://doi.org/10.1103/PhysRevB.83.035312