Tight-binding theory for the thermal evolution of optical band gaps in semiconductors and superlattices

A method to handle the variation of the band gap with temperature in direct band-gap III-V semiconductors and superlattices using an empirical tight-binding method has been developed. The approach follows closely established procedures and allows parameter variations which give rise to perfect fits to the experimental data. We also apply the tight-binding method to the far more complex problem of band structures in type-II infrared superlattices for which we have access to original experimental data recently acquired by our group. Given the close packing of bands in small band-gap type-II designs, k-•p- methods become difficult to handle, and it turns out that the sp3s^* tight-binding scheme is a practical and powerful asset. Other approaches to band-gap shrinkage explored in the past are discussed, scrutinized, and compared. This includes the lattice expansion term, the phonon softening mechanism, and the electron-phonon polaronic shifts calculated in perturbation theory.