# Four-phonon scattering diminishes the optical phonon contribution and isotope effect to thermal conductivity of III-V semiconductors

## TL;DR

This study demonstrates that four-phonon scattering significantly reduces optical phonon contributions and isotope effects on thermal conductivity in III-V semiconductors, especially in materials with long-lived optical phonons.

## Contribution

It reveals the critical role of four-phonon scattering in diminishing optical phonon transport and isotope effects, providing new insights for optimizing thermal conductivity in III-V semiconductors.

## Key findings

- Four-phonon scattering reduces AlSb thermal conductivity by 70% in isotopically pure form.
- It decreases isotope effect impact on thermal conductivity by up to 70%.
- The effect varies among materials, with up to 34% reduction in c-GaN.

## Abstract

Recent studies reveal that four-phonon scattering is generally important in determining thermal conductivities of solids. However, these studies have been focused on materials where thermal conductivity $\kappa$ is dominated by acoustic phonons, and the impact of four phonon scattering, although significant, is still generally smaller than three-phonon scattering. In this work, taking AlSb as example, we demonstrated that four-phonon scattering is even more critical to three-phonon scattering as it diminishes optical phonon thermal transport, and therefore significantly reduces the thermal conductivities of materials in which optical branches have long three-phonon lifetimes. Also, our calculations show that four-phonon scattering can play an extremely important role in weakening the isotope effect on $\kappa$. Specifically, four-phonon scattering reduces the room-temperature $\kappa$ of the isotopically pure and natural-occurring AlSb by 70$\%$ and 50$\%$, respectively. The reduction for isotopically pure and natural-occurring c-GaN is about 34$\%$ and 27$\%$, respectively. For isotopically-pure w-GaN, the reduction is about 13$\%$ at room temperature and 25$\%$ at 400 K. These results provided important guidance for experimentalists for achieving high thermal conductivities in III-V compounds for applications in semiconductor industry.