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We report on the structural, electronic and vibrational properties of theGa$_{1-x}$In$_x$N alloy using virtual crystal approximation (VCA) fromfirst-principles. A band gap bowing parameter of 3.85 eV is obtained with theTB09 functional. Phonon density of states shifts to lower frequency as the Incontent is increased. However, VCA ignores disorder effect and is thereforeunable to describe the broadening of the phonon spectra upon alloying. The roleof electron-phonon interaction in the temperature dependence of the band gap isalso studied for GaN, InN and their alloy Ga$_{1-x}$In$_x$N. The calculatedzero-point motion renormalization and the fitted Varshni parameter over theentire composition range are discussed.

Temperature and composition dependence of the band gaps of  Ga$_{1-x}$In$_x$N alloy: a first-principles study based on the virtual  crystal approximation