Effect of interface roughness on excitonic linewidth in a quantum well: Golden-rule and self-consistent-Born-approximation calculations

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 ({Δ}{Λ})² and changes as L^-6 with well width L. The SCBA expression is proportional to {Δ}, shows a weak dependence on {Λ}, and varies as L^-3. It also agrees with the expression obtained under a statistical-fluctuation model. The calculated results of the linewidth for a GaAs-Alₓ{Ga}_{1{{-}}x}$As quantum well under the golden rule are quite high, while the SCBA results are closer to the experimental data.