An empirical equation including the strain effect for optical transition energy of strained and fully relaxed GaN films

We propose a new equation considering strain effect for the temperature dependence of bandgap transition of GaN films grown on sapphire. By using the chemical lift-off method the GaN films were separated from the sapphire substrate and we evaluated the energy shift of the bandgap transition due to the strain caused by the sapphire substrate quantitatively. The transition energies of the free exciton A (FX_A) in the GaN film at a finite temperature are described by the equation E(T) = E(0) - (αT²/(β + T)) + ΔE(0) + γ(TEC_film - TEC_sub)T, where α and β are the temperature coefficients, γ is the strain coefficient, and TEC_film and TEC_sub are thermal expansion coefficients of the film and the substrate, respectively. This equation is divided into an ordinary temperature component and an additional strain component of the hetero-epitaxial film. The temperature dependence of exciton transition energy of the strained GaN film should be expressed by the above equation with E(0) = 3.4774 eV, α = 0.93 meV K^-1, β = 1280 K, ΔE(0) = 10.87 meV and γ = 2.04 × 10^-3 eV.