Effect of structural disorder on the Urbach energy in Cu ternaries - art. no. 195101

From the analysis of the Urbach tail in CuInSe2 and CuInTe2, it is found th at the energy h nu (p) involved in the electron-exciton-phonon interaction is not that of the ordered compound longitudinal or transverse optical mode s. It is established that this energy depends on the structural and cations disorders. An expression of the form E-v(T,P,N) = K Theta/sigma (0){(1 + P )/2+N[exp(Theta /T)-1](-1)}, where P and N are adjustable structural and or der-disorder parameters and Theta the Einstein characteristic temperature, accurately explains the temperature dependence of the Urbach energy. From e xtrapolation of the linear variation of Nand P with h nu (p), the phonon en ergy for a completely ordered and disordered systems can be estimated. We d iscuss the physical meaning of the parameter N as due to the contribution o f localized modes produced by substitutional disorder of low energy of form ation. We find an intriguing relation between the temperature of the chalco pyrite-sphalerite transition and the phonons contributing to the formation of Urbach tails in the strong-disorder limit.