Optical dephasing in semiconductor mixed crystals

The influence of disorder and localization on optical dephasing of excitons in the semiconductor mixed crystals ${\mathrm{CdS}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Se}}_{\mathit{x}}$ and ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As has been investigated by means of time-resolved four-wave mixing and photon echo experiments. A dephasing time of several hundreds of picoseconds is found for resonantly excited localized excitons in ${\mathrm{CdS}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Se}}_{\mathit{x}}$ while the dephasing time in ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As amounts to only a few picoseconds. In ${\mathrm{CdS}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Se}}_{\mathit{x}}$ dephasing results mainly from hopping processes, i.e., exciton-phonon interaction. The contribution of disorder is negligible in terms of phase relaxation in ${\mathrm{CdS}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Se}}_{\mathit{x}}$. In contrast, in ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As elastic disorder scattering yields an essential contribution to the dephasing rate. We present a theoretical model, which treats dephasing of optical excitations in a disordered semiconductor, including the influence of disorder as well as exciton-phonon interaction. On the base of this model, the experimentally observed differences in the dephasing behavior of excitons in ${\mathrm{CdS}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Se}}_{\mathit{x}}$ and ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As are related to the microscopic structure of the disorder potential and the mechanism of exciton localization.