Heat capacity and phonon mean free path of wurtzite GaN

We report on lattice specific heat of bulk hexagonal GaN measured by the heat flow method in the temperature range 20-300 K and by the adiabatic method in the range 5-70 K. We fit the experimental data using two temperatures model. The best fit with the accuracy of 3 % was obtained for the temperature independent Debye's temperature $\theta_{\rm D}=365$ {\rm K} and Einstein's temperature $\theta_{\rm E}=880$ {\rm K}. We relate these temperatures to the function of density of states. Using our results for heat conduction coefficient, we established in temperature range 10-100 K the explicit dependence of the phonon mean free path on temperature $\it{l}_{\rm ph}\propto T^{-2}$. Above 100 K, there is the evidence of contribution of the Umklapp processes which limit phonon free path at high temepratures. For phonons with energy $k_{\rm B}\times 300 $ {\rm K} the mean free path is of the order 100 {\rm nm}