Temperature dependence of biaxial strain and its influence on phonon and band gap of GaN thin film

Hexagonal GaN epilayer grown on sapphire substrate by metal organic chemical vapour deposition (MOCVD) is studied using Raman scattering and photoluminescence in a temperature range from 100\,K to 873\,K. The model of strain (stress) induced by the different lattice parameters and thermal coefficients of epilayer and substrate as a function of temperature is set up. The frequency and the linewidth of $E_2^{\rm high}$ mode in a GaN layer are modelled by a theory with considering the thermal expansion of the lattice, a symmetric decay of the optical phonons, and the strain (stress) in the layer. The temperature-dependent energy shift of free exciton A is determined by using Varshni empirical relation, and the effect of strain (stress) is also investigated. We find that the strain in the film leads to a decreasing shift of the phonon frequency and an about 10meV-increasing shift of the energy in a temperature range from 100\,K to 823\,K.