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International audience; In this paper, we demonstrate that it is possible to combine two computational approaches, usually used in very different contexts, namely, the Green-Kubo formalism and statistical approaches, to solve the Boltzmann transport equation to calculate the thermal conductivity of semiconductors. In this framework, first the phonon transport is solved by the Monte Carlo method according to the Debye-Callaway or Holland formalisms, then the flux autocorrelation is calculated. This new approach has been implemented to calculate the properties of Si, Ge, GaN, and C (diamond) in an extended temperature range, from 50 to 600 K. The simulation results are compared with those given by experimentation, with very good agreement.

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.