Lattice thermal conductivity of Bi2Te3 and SnSe using Debye-Callaway and Monte Carlo phonon transport modeling: Application to nanofilms and nanowires

The present work addresses the problem of thermal conductivity simulation in ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ and SnSe thermoelectric nanostructures. It first details phonon lifetime calculation in both thermoelectric compounds assuming polynomial dispersion properties and the Debye-Callaway model for the relaxation-time approximation. For both materials, distinct crystallographic directions are considered, i.e., $\mathrm{\ensuremath{\Gamma}}\ensuremath{-}Z$ (trigonal axis) and $\mathrm{\ensuremath{\Gamma}}\ensuremath{-}X$ (basal plane) for ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ and $\mathrm{\ensuremath{\Gamma}}\ensuremath{-}X$ ($a$ axis), $\mathrm{\ensuremath{\Gamma}}\ensuremath{-}Y$ ($b$ axis), and $\mathrm{\ensuremath{\Gamma}}\ensuremath{-}Z$ ($c$ axis) for SnSe. On this basis, the lifetime model is parametrized and bulk thermal conductivity is computed through the resolution of the phonon Boltzmann transport equation with a Monte Carlo method. Gr\"uneisen parameter and mass-disorder lifetime are adjusted to fit experimental temperature dependence. The second part of the study addresses the calculation of thermal conductivity for these two thermoelectric materials in the case of thin films (cross-plane case) and nanowires. The main goals of this work are to provide a fully parametric description of heat transport in ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ and SnSe nanofilms and nanowires showing reliable behavior on an extended size range, from 20 nm to $2\phantom{\rule{0.0pt}{0ex}}\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$, and large temperature range (100--500 K for ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$; 200--800 K for SnSe). Comparisons to bulk thermal conductivity calculations and measurements as well as to recent investigations on nanowires, demonstrate the effectiveness of the proposed methodology to deal with nanostructured ${\mathrm{Bi}}_{2}{\mathrm{Te}}_{3}$ and SnSe.