Radiative lifetimes of excitons in quantum wells: Localization and phase-coherence effects

A theory for intrinsic radiative decay of excitons in quantum wells including the effects of excitons bound to width fluctuations and finite phase coherence is presented. The approach is based on Green’s functions at nonzero temperature. In GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum wells of widths 50–150 Å, lifetimes on the order of 100 ps are predicted for localized excitons. We show that the localized excitons play an important role in the photoluminescence (PL) decay times over the entire temperature range T<150 K. The theoretical results explain the large scatter in the published experimental data. The relationship between the homogeneous linewidth ħ${\mathrm{\Gamma }}_{\mathit{h}}$ and the spectrally integrated decay rate at nonzero temperature for the free-exciton population is derived using a Green’s-function approach. The free-exciton contribution to the PL-decay rate reduces to the infinite-lifetime result of L. C. Andreani et al. [Solid State Commun. 77, 641 (1991)] for ${\mathit{k}}_{\mathit{B}}$T≫ħ${\mathrm{\Gamma }}_{\mathit{h}}$. In the limit ${\mathit{k}}_{\mathit{B}}$T≪ħ${\mathrm{\Gamma }}_{\mathit{h}}$, the result of J. Feldmann et P [Phys. Rev. Lett. 59, 2337 (1987)] assuming finite phase coherence is obtained.