First principles study of thermal conductivity of In${}_2$O${}_3$ in relation to Al${}_2$O${}_3$, Ga${}_2$O${}_3$, and KTaO${}_3$

Abstract

I use first principles calculations to investigate the thermal conductivity of ${\hat{I}}^2$-In${}_2$O${}_3$ and compare the results with that of $\hat{I}\pm$-Al${}_2$O${}_3$, ${\hat{I}}^2$-Ga${}_2$O${}_3$, and KTaO${}_3$. The calculated thermal conductivity of ${\hat{I}}^2$-In${}_2$O${}_3$ agrees well with the experimental data obtain recently, which found that the low-temperature thermal conductivity in this material can reach values above 1000 W/mK. I find that the calculated thermal conductivity of ${\hat{I}}^2$-Ga${}_2$O${}_3$ is larger than that of ${\hat{I}}^2$-In${}_2$O${}_3$ at all temperatures, which implies that ${\hat{I}}^2$-Ga${}_2$O${}_3$ should also exhibit high values of thermal conductivity at low temperatures. The thermal conductivity of KTaO${}_3$ calculated ignoring the temperature-dependent phonon softening of low-frequency modes give high-temperature values similar that of ${\hat{I}}^2$-Ga${}_2$O${}_3$. However, the calculated thermal conductivity of KTaO${}_3$ does not increase as steeply as that of the binary compounds at low temperatures, which results in KTaO${}_3$ having the lowest low-temperature thermal conductivity despite having acoustic phonon velocities larger than that of ${\hat{I}}^2$-Ga${}_2$O${}_3$ and ${\hat{I}}^2$-In${}_2$O${}_3$. I attribute this to the fact that the acoustic phonon velocities at low frequencies in KTaO${}_3$ is less uniformly distributed because its acoustic phonon branches are more dispersive compared to the binary oxides, which causes enhanced momentum loss even during the normal phonon-phonon scattering processes. I also calculate thermal diffusivity using the theoretically obtained thermal conductivity and heat capacity and find that all four materials exhibit the expected $T^{-1}$ behavior at high temperatures. Additionally, the calculated ratio of the average phonon scattering time to Planckian time is larger than the lower bound of 1 that has been observed empirically in numerous other materials.