Heat transport in silicon from first principles calculations

TL;DR

This paper introduces a first-principles method combining density-functional calculations, force constants, and molecular dynamics to accurately compute the thermal properties and heat transport in crystalline silicon, addressing limitations of semi-empirical models.

Contribution

The paper presents a general, first-principles approach to model heat transport in crystals, integrating harmonic and anharmonic force constants with MD and perturbation theory, improving accuracy over semi-empirical potentials.

Findings

Accurate thermal conductivity of silicon computed using first-principles force constants.

Method captures high-temperature phonon interactions with minimal empirical assumptions.

Comparison shows differences between MD-based and perturbation theory results.

Abstract

Using harmonic and anharmonic force constants extracted from density-functional calculations within a supercell, we have developed a relatively simple but general method to compute thermodynamic and thermal properties of any crystal. First, from the harmonic, cubic, and quartic force constants we construct a force field for molecular dynamics (MD). It is exact in the limit of small atomic displacements and thus does not suffer from inaccuracies inherent in semi-empirical potentials such as Stillinger-Weber's. By using the Green-Kubo (GK) formula and molecular dynamics simulations, we extract the bulk thermal conductivity. This method is accurate at high temperatures where three-phonon processes need to be included to higher orders, but may suffer from size scaling issues. Next, we use perturbation theory (Fermi Golden rule) to extract the phonon lifetimes and compute the thermal conductivity $\kappa$ from the relaxation time approximation. This method is valid at most temperatures, but will overestimate $\kappa$ at very high temperatures, where higher order processes neglected in our calculations, also contribute. As a test, these methods are applied to bulk crystalline silicon, and the results are compared and differences discussed in more detail. The presented methodology paves the way for a systematic approach to model heat transport in solids using multiscale modeling, in which the relaxation time due to anharmonic 3-phonon processes is calculated quantitatively, in addition to the usual harmonic properties such as phonon frequencies and group velocities. It also allows the construction of accurate bulk interatomic potentials database.