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Ultra-wide-band-gap group-III nitrides are of interest for applications indeep-ultraviolet optoelectronics and power electronics. Such devices must beable to efficiently dissipate heat generated from their operation, making thethermal conductivity of the constituent materials an important parameter forhigh-power applications. We have investigated the phonon-limited thermalconductivity of AlN, GaN, and Al$_x$Ga$_{1-x}$N using first-principlescalculations, with a focus on the effects of compositional and isotopicdisorder. Our Boltzmann-transport-equation calculations show that the maximumthermal 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 Almole fractions of x = 0.60 to 0.71 over the 100-1000K temperature range. Ourresults provide understanding on the effects of isotope disorder on the thermalconductivity of AlN and GaN. We also present an analytical model for theevaluation of the thermal conductivity of Al$_x$Ga$_{1-x}$N alloys forarbitrary composition and temperature, which can be applied for the thermaldesign of AlGaN-based electronic and optoelectronic devices.

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