Temperature-dependent thermal conductivity in nanoporous materials studied by the Boltzmann Transport Equation

TL;DR

This study uses the Boltzmann Transport Equation to analyze how temperature affects thermal conductivity in nanoporous silicon, revealing the significant role of phonon interactions and ballistic transport in heat conduction reduction.

Contribution

It introduces a MFP-dependent Boltzmann Transport Equation approach to quantify phonon contributions and thermal conductivity in nanoporous materials across temperatures.

Findings

Optical phonons contribute 18% to heat transport at room temperature.

Thermal conductivity remains steady between 200 K and 300 K due to ballistic phonon transport.

Results align with recent experimental data, enhancing understanding of nanostructured heat transfer.

Abstract

Nanostructured materials exhibit low thermal conductivity because of the additional scattering due to phonon-boundary interactions. As these interactions are highly sensitive to the mean free path (MFP) of a given phonon mode, MFP distributions in nanostructures can be dramatically distorted relative to bulk. Here we calculate the MFP distribution in periodic nanoporous Si for different temperatures, using the recently developed MFP-dependent Boltzmann Transport Equation. After analyzing the relative contribution of each phonon branch to thermal transport in nanoporous Si, we find that at room temperature optical phonons contribute 18 % to heat transport, compared to 5% in bulk Si. Interestingly, we observe a steady thermal conductivity in the nanoporous materials over a temperature range 200 K < T < 300 K, which we attribute to the ballistic transport of acoustic phonons with long intrinsic MFP. These results, which are also consistent with a recent experimental study, shed light on the origin of the reduction of thermal conductivity in nanostructured materials, and could contribute to multiscale heat transport engineering, in which the bulk material and geometry are optimized concurrently.