Thermal conductivity of AlN, GaN, and Al$_x$Ga$_{1-x}$N alloys as a function of composition, temperature, crystallographic direction, and isotope disorder from first principles

Ultra-wide-band-gap group-III nitrides are of interest for applications in deep-ultraviolet optoelectronics and power electronics. Such devices must be able to efficiently dissipate heat generated from their operation, making the thermal conductivity of the constituent materials an important parameter for high-power applications. We have investigated the phonon-limited thermal conductivity of AlN, GaN, and Al$_x$Ga$_{1-x}$N using first-principles calculations, with a focus on the effects of compositional and isotopic disorder. Our Boltzmann-transport-equation calculations show that the maximum thermal conductivity for AlN (GaN) is 348 W m$^{-1}$ K$^{-1}$ (235 W m$^{-1}$ K$^{-1}$) for with pure $^{14}$N, and 292 W m$^{-1}$ K$^{-1}$ for GaN with pure $^{71}$Ga. Al$_x$Ga$_{1-x}$N alloys reach a minimum thermal conductivity at Al mole fractions of x = 0.60 to 0.71 over the 100-1000K temperature range. Our results provide understanding on the effects of isotope disorder on the thermal conductivity of AlN and GaN. We also present an analytical model for the evaluation of the thermal conductivity of Al$_x$Ga$_{1-x}$N alloys for arbitrary composition and temperature, which can be applied for the thermal design of AlGaN-based electronic and optoelectronic devices.