Specifics of heat transfer in Al$_{x}$Ga$_{1-x}$N/GaN heterostructures on sapphire

The thermal conductivity of Al$_{x}$Ga$_{1-x}$N/GaN heterostructures (0.05 $\le x\le$ 1) fabricated on sapphire by molecular beam epitaxy is measured. The thermal conductivities of thin Al$_{x}$Ga$_{1-x}$N and GaN films at room temperature are found. We analyze the concentration dependence of thermal conductivity using a virtual crystal model for thermal conductivity. A numerical model with a localized heat source is built to model heat transfer in the considered structure, and the layer thicknesses optimal for achieving a high thermal conductivity of the structure of interest are identified.