Ultralow thermal conductivity in Si–Ge nanograin mixtures: A cost-effective granular material for thermoelectric applications

Abstract

This paper presents a theoretical study of the thermal conductivity of Si–Ge nanograin mixtures using a multiscale computational methodology based on solving the Boltzmann transport equation for phonons with first-principles techniques. A size-dependent correction factor is developed to account for the spatial dependence of the phonon distribution function on nanograin size, with parameters derived from the phonon properties of infinite Si and Ge crystals. This approach makes it possible to accurately calculate the thermal conductivity within a single nanograin, using force constants obtained from first-principles calculations. Thermal energy transport by phonons across grain boundaries is modeled by accounting for phonon transmission by two-phonon processes, weighting specular, and diffuse transmission for each phonon mode as a function of the root-mean-square roughness of the boundary relative to the phonon wavelength. The boundary thermal conductance model, previously validated against experimental data, is implemented using first-principles techniques. This approach excludes specular transmission for phonon modes with specific symmetries while ensuring conservation of the total number of modes in each symmetry class. The study examines the influence of grain size, nanograin mixture composition, temperature, and boundary asperities on the thermal conductivity of nanograin mixtures.