Phonon properties and thermal conductivity from first principles, lattice dynamics, and the Boltzmann transport equation

TLDR

The authors present a computational framework to predict phonon frequencies, group velocities, scattering rates, and lattice thermal conductivity. The framework derives harmonic and cubic force constants from density functional theory and density functional perturbation theory, uses harmonic lattice dynamics to obtain phonon properties, computes intrinsic and extrinsic scattering rates via perturbation theory or phenomenological models, and solves the Boltzmann transport equation for mode populations and thermal conductivity, with extensions to higher‑order processes, finite‑temperature effects, and alloys, and is implemented in available software packages. Using first‑principles inputs and modern computational power, the framework yields thermal conductivity predictions that agree with experimental data across diverse crystalline materials and temperatures, as demonstrated by a silicon case study with benchmarking and convergence results.

Abstract

A computational framework for predicting phonon frequencies, group velocities, scattering rates, and the resulting lattice thermal conductivity is described. The underlying theory and implementation suggestions are also provided. By using input from first principles calculations and taking advantage of advances in computational power, this framework has enabled thermal conductivity predictions that agree with experimental measurements for diverse crystalline materials over a wide range of temperatures. Density functional theory and density functional perturbation theory calculations are first used to obtain the harmonic and cubic force constants. The harmonic force constants are the input to harmonic lattice dynamics calculations, which provide the phonon frequencies and eigenvectors. The harmonic properties and the cubic force constants are then used with perturbation theory and/or phenomenological models to determine intrinsic and extrinsic scattering rates. The full set of phonon properties is then used to solve the Boltzmann transport equation for the mode populations and thermal conductivity. The extension of the framework to include higher-order processes, capture finite temperature effects, and model alloys is described. A case study on silicon is presented that provides benchmarking and convergence data. Available packages that implement the framework are compared.