We have derived expressions for the linewidth of excitons in a quantum well in the presence of interface roughness scattering, by using the Fermi golden rule and also by introducing the self-consistent Born approximation (SCBA). The fluctuation in the well width is assumed to have a Gaussian autocorrelation and is characterized by a height Δ and a correlation length Λ. The linewidth obtained from the golden rule depends on (ΔΛ${)}^2$ and changes as ${\mathit{L}}^{\mathrm{-}6}$ with well width L. The SCBA expression is proportional to Δ, shows a weak dependence on Λ, and varies as ${\mathit{L}}^{\mathrm{-}3}$. It also agrees with the expression obtained under a statistical-fluctuation model. The calculated results of the linewidth for a GaAs-${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum well under the golden rule are quite high, while the SCBA results are closer to the experimental data.

• Received 9 July 1991

DOI:https://doi.org/10.1103/PhysRevB.44.8798