Ideal interband absorption spectra in an indirect-gap-semiconductor quantum well

We have derived the expression for an absorption coefficient in a quantum well made of an indirect-gap semiconductor, considering phonon-assisted and no-phonon (alloy-disorder) processes. The absorption coefficient varies as (ħ${\mathrm{\omega }}_{\lambda }$-${\mathit{E}}_{\mathit{g}}$±ħ${\mathrm{\omega }}_{\mathit{p}}$${)}^{\mathit{s}}$, where ħ${\mathrm{\omega }}_{\lambda }$ (ħ${\mathrm{\omega }}_{\mathit{p}}$) is the photon (phonon) energy and ${\mathit{E}}_{\mathit{g}}$ is the band gap; s=0 for bound excitonic absorption and s=1 for band-to-band or continuum-state transitions. For transitions to the excitonic continuum states, the absorption coefficient increases linearly for high values of photon energy.