Low cross-plane thermal conductivity of $κ$-Ga$_2$O$_3$ thin films
The thermal conductivities of (001) $κ$-Ga$_2$O$_3$ thin films deposited on $c$-plane sapphire substrates were measured with frequency-domain thermoreflectance (FDTR). The thermal conductivity increases from 1.83 $^{+0.19}_{-0.18}$ W/m$\cdot$K to 2.26 $^{+0.35}_{-0.40}$ W/m$\cdot$K as the thicknesses increase from 159 nm to 689 nm. This weak thickness dependence indicates that the majority of the intrinsic phonon mean free paths are smaller than the range of investigated film thicknesses. First-principles-based calculations that include phonon-phonon and phonon-boundary scattering capture this size-dependent behavior and support our experimental observation. Temperature-dependent measurements of a 689 nm film from 293 to 400 K show a decrease in thermal conductivity with increasing temperature due to enhanced phonon-phonon scattering. A weaker temperature dependence is observed in a 159 nm film where phonon-boundary scattering becomes more prominent. At comparable film thicknesses, our measured $κ$-Ga$_2$O$_3$ films exhibit lower values of cross-plane thermal conductivity than the other experimentally measured Ga$_2$O$_3$ polymorphs. Our experimental observations are supported by prior predictions, which suggest that the low thermal conductivity of $κ$-Ga$_2$O$_3$ results from its complex crystal structure, which leads to increased anharmonicity and lower phonon group velocities relative to other polymorphs. Thermal management strategies, such as integration with high-thermal-conductivity substrates, may thus be required to mitigate self-heating for $κ$-Ga$_2$O$_3$-based electronic devices.