Stronger role of four-phonon scattering than three-phonon scattering in thermal conductivity of III-V semiconductors at room temperature

Recent studies reveal that four-phonon scattering can be important in determining thermal conductivities of solids. However, these studies have been focused on materials where the thermal conductivity κ is dominated by acoustic phonons, and the role of four-phonon scattering, although significant, is still smaller than that of three-phonon scattering at room temperature. In this work, taking AlSb as an example for which optical phonons contribute significantly to the thermal conductivity under the three-phonon picture, we demonstrate that four-phonon scattering can be more important than three-phonon scattering as it diminishes optical phonon thermal transport and therefore significantly reduces the thermal conductivities of materials. Also, our calculations show that four-phonon scattering can diminish the isotope effect on κ. Specifically, including four-phonon scattering reduces the room-temperature κ of isotopically pure BAs from 3322 W/mK to 1721 W/mK, a $48%$ reduction. Four-phonon scattering reduces the room-temperature κ of the isotopically pure and naturally occurring AlSb by $70%$ and $50%$, respectively, indicating that four-phonon scattering is more important than three-phonon scattering. The reductions for isotopically pure and naturally occurring cubic GaN are about $34%$ and $27%$, respectively. For isotopically pure wurtzite 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 the semiconductor industry.