Effect of structural disorder on the urbach energy in Cu ternaries

From the analysis of the Urbach tail in CuInSe₂ and CuInTe₂, it is found that the energy hν_p involved in the electron-exciton-phonon interaction is not that of the ordered compound longitudinal or transverse optical modes. It is established that this energy depends on the structural and cations disorders. An expression of the form E_U(T,P,N) = KΘ/σ₀((1+P)/2+ N[exp(Θ/T)-1]^-1), where P and N are adjustable structural and order disorder parameters and Θ the Einstein characteristic temperature, accurately explains the temperature dependence of the Urbach energy. From extrapolation of the linear variation of N and P with hν_p, the phonon energy for a completely ordered and disordered systems can be estimated. We discuss the physical meaning of the parameter N as due to the contribution of localized modes produced by substitutional disorder of low energy of formation. We find an intriguing relation between the temperature of the chalcopyrite-sphalerite transition and the phonons contributing to the formation of Urbach tails in the strong-disorder limit.