Confined-phonon effects in the band-gap renormalization of semiconductor quantum wires

We calculate the band-gap renormalization in quasi-one-dimensional semiconductor quantum wires including carrier-carrier and carrier-phonon interactions. We use the quasistatic approximation to obtain the self-energies at the band edge that define the band-gap renormalization. The random-phase approximation at finite temperature is employed to describe the screening effects. We find that confined LO-phonon modes through their interaction with the electrons and holes modify the band gap significantly and produce a larger value than the static ${\epsilon }_0$ approximation.