Higher-order thermal transport theory for phonon thermal transport in semiconductors using lattice dynamics calculations and the Boltzmann transport equation

The phonon thermal conductivity of semiconducting periodic solids can be obtained using the lattice dynamics calculations along with the Boltzmann transport equation and with input from density functional theory calculations. These calculations have resulted in an excellent agreement with experiments without requiring any fitting parameters. However, over the last decade, many material systems have been identified where the lowest level lattice dynamics theory, which is based on the relaxation time approximation solution of the Boltzmann transport equation and considers potential energy surface sampling around the static equilibrium positions of atoms with only three-phonon scatterings, is proved insufficient in describing the thermal transport physics. In this article, we review these higher-order developments in the lattice dynamics theory to describe thermal transport in periodic semiconducting solids. We start with a brief discussion of the lowest-order theory and discuss its limitations along with proposed developments to address these limitations. We discuss prominent success cases of these higher-order developments and present our recommendations on their use for various material systems. Considering that many of these higher-order developments are computationally more demanding compared to the lowest-order theory, we also discussed data-driven approaches to accelerate these calculations. This review article is intended to serve as a reference for both novice and experienced researchers in this field.