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 organicchemical vapour deposition (MOCVD) is studied using Raman scatteringand photoluminescence in a temperature range from 100,K to 873,K.The model of strain (stress) induced by the different latticeparameters and thermal coefficients of epilayer and substrate as afunction 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 withconsidering the thermal expansion of the lattice, a symmetric decayof the optical phonons, and the strain (stress) in the layer. Thetemperature-dependent energy shift of free exciton A is determined byusing Varshni empirical relation, and the effect of strain (stress)is also investigated. We find that the strain in the film leads to adecreasing shift of the phonon frequency and an about10meV-increasing shift of the energy in a temperature range from100,K to 823,K.