Excitonic exchange effects on the radiative decay time of monoexcitons and biexcitons in quantum dots

Abstract

Electron-hole exchange interaction splits the exciton ground state into ``dark'' and ``bright'' states. The dynamics of those states depends on the internal relaxation time between bright and dark states (spin-flip time), and on the radiative recombination time of the bright states. On the other hand, the calculated values of these recombination times depend not only on the treatment of correlation effects, but also on the accuracy of the electron and hole wavefunctions. We calculate the radiative decay rates for monoexcitons and biexcitons in $(\mathrm{In},\mathrm{As})\mathrm{Ga}∕\mathrm{GaAs}$ self-assembled and colloidal $\mathrm{CdSe}$ quantum dots from atomistic correlated wave functions. We show how the radiative decay time ${\ensuremath{\tau}}_{R}({X}^{0})$ of the monoexciton depends on the spin-flip relaxation time between bright and dark states. In contrast, a biexciton has no bright-dark splitting, so the decay time of the biexciton ${\ensuremath{\tau}}_{R}(X{X}^{0})$ is insensitive to this spin-flip time. This results in ratios ${\ensuremath{\tau}}_{R}({X}^{0})∕{\ensuremath{\tau}}_{R}(X{X}^{0})$ of 4 in the case of fast spin flip, and a ratio of 2 in the case of slow spin flip. For $(\mathrm{In},\mathrm{Ga})\mathrm{As}∕\mathrm{GaAs}$, we compare our results with the model calculation of Wimmer et al. [Phys. Rev. B 73, 165305 (2006)]. When the same spin-flip rates are assumed, our predicted ${\ensuremath{\tau}}_{R}({X}^{0})∕{\ensuremath{\tau}}_{R}(X{X}^{0})$ agrees with that of Wimmer et al., suggesting that our treatment of correlations is adequate to predict the ratio of monoexciton and biexciton radiative lifetimes. Our results agree well with experiment on self-assembled quantum dots when assuming slow spin flip. Conversely, for colloidal dots the agreement with experiment is best for fast spin flip.