Temperature dependence of the E2 and A1(LO) phonons in GaN and AlN

The frequencies and dampings of the zone-center optical phonons $E_2$ and $A_1(\mathrm{LO})$ in wurtzite-type GaN and AlN layers have been measured by Raman spectroscopy in the temperature range from 85 to 760 K. The GaN layer was grown by metalorganic vapor phase epitaxy and the AlN layer by molecular beam epitaxy both on sapphire substrate. The experimentally obtained frequencies and dampings are modeled by a theory taking into account the thermal expansion of the lattice, a symmetric decay of the optical phonons into two and three phonons of lower energy, and the strain in the layers induced by the different thermal expansion coefficients of layer and substrate. The results were used to determine the local temperature of a GaN $\mathrm{pn}$ diode in dependence on the applied voltage.