On the importance of Akhiezer damping to thermal conductivity in silicon at elevated temperatures above 300 K

Abstract

Recently, Chiloyan et al. [Appl. Phys. Lett. 116, 163102 (2020)] have reported that phonon transport could exceed bulk heat conduction if low-frequency phonons with long mean free path (MFP) remain in the nonthermal regime in silicon. To gain a better understanding of their findings, we investigated the effects of temperature-induced anharmonicity on both Landau–Rumer damping and Akhiezer damping, including polarization. To do this, we follow a rigorous procedure for calculating the Akhiezer model and use phonon kinetic theory based on the Boltzmann transport equation. Consequently, we find that in the Akhiezer regime, the longitudinal acoustic phonon modes (LA) are strongly suppressed by phonon anharmonicity compared to the transverse acoustic phonon modes. Therefore, the low-frequency phonons with a long MFP of LA can help to exceed bulk heat conduction if they remain in the regime of nonthermal phonon transport where there are no appreciable scatterings with other phonons. It is also shown that Akhiezer damping eliminates thermal conductivity by 16.8% at 500 K, which is higher than the observed reduction (12.6%) at 300 K in silicon, uncovering a novel regime where the Akhiezer damping, previously deemed insignificant in the thermal conduction of bulk silicon, becomes crucial.