Excitons in Degenerate Semiconductors

The band-to-band optical absorption is calculated for a direct-band-gap semiconductor that has one band degenerate $n$ or $p$ type. The degenerate band is treated as a high-density Fermi gas. It is shown that exciton states, arising from the electron-hole Coulomb attraction, still affect the optical absorption. The calculations show that exciton states cause a logarithmic singularity in the absorption at the Burstein edge. This singularity is present at a moderate density of electrons or holes in the degenerate band, but it gradually disappears in the high-density limit. Lifetime broadening could make the logarithmic singularity difficult to observe at higher densities.