The thermal conductivities of the alloys of wurtzite AlN, GaN and InN are usually analyzed with the virtual crystal model based on the values of the constituent compounds. However, latest experiments and calculations reveal that the thermal conductivity of wurtzite InN is about three times larger than the previously used value. Thus it is necessary to reanalyze the thermal conductivities of these alloys. In this work, the intrinsic thermal conductivities of AlxGa1−xN, InxGa1−xN and InxAl1−xN are calculated with first-principles calculations along with the virtual crystal treatment. It is found that the thermal conductivities of these alloys are strongly suppressed even after a small amount of alloying. For instance, the in-plane and out-of-plane thermal conductivities of In0.99Ga0.01 N are 66 Wm−1K−1 and 76 Wm−1K−1 respectively, while they are 40 Wm−1K−1 and 48 Wm−1 K−1 for In0.99Al0.01 N, compared with the corresponding values of 130 Wm−1 K−1 and 145 Wm−1 K−1 for bulk wurtzite InN. When the fraction x varies from 0.2 to 0.8, the thermal conductivities of the alloys do not change much. Additionally, the distribution of mean free path indicates that the size effect can persist up to 10μm for both pure compounds and their alloys at room temperature.

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