Temperature-dependent thermal properties of Mg-doped insulating $β$-$\mathrm{Ga_2O_3}$ bulk along [100] and [001]: thermal diffusivity, thermal conductivity and specific heat capacity

The thermal conductivity $\lambda$, diffusivity $D$, specific heat capacity $C_V$ and the Debye-temperature $\theta_\mathrm{D}$ have been investigated for insulating monoclinic $\beta$-$\mathrm{Ga_2O_3}$. Here, we apply AC current heating techniques and determine the thermal diffusivity and specific heat capacity along the [100] and [001]-direction from the so-called $3\omega$ and $2\omega$ voltage signals, respectively. At low temperatures we find an anisotropy of the thermal conductivity for the [100] and [001] direction ($\lambda_\mathrm{[100]}(109 \mathrm{K})=54\pm 5~\mathrm{Wm^{-1}K^{-1}}$;$\lambda_\mathrm{[001]}(109 \mathrm{K})=67\pm 5~\mathrm{Wm^{-1}K^{-1}}$). The anisotropy diminishes for increasing temperature which is reflected by the diffusivity ratio of $D_\mathrm{[001]}/D_\mathrm{[100]}=1.40\pm 0.08$ at $109~\mathrm{K}$ to $D_\mathrm{[001]}/D_\mathrm{[100]}=1.05\pm 0.07$ at $297~\mathrm{K}$. This may find its explanation in a decreased phonon mean free path for higher temperatures. This is confirmed by the temperature dependence of the thermal conductivity which agrees well with the phonon-phonon Umklapp scattering processes. The temperature dependence of the specific heat is in general accordance with the Debye model.