Influence of confinement on biexciton binding in semiconductor quantum dot ensembles measured with two-dimensional spectroscopy

The emission energy dependence of the biexciton binding energy is investigated in three semiconductor quantum dot (QD) systems that exhibit different quantum well $\to$ QD confinement. Using two-dimensional Fourier-transform spectroscopy, we demonstrate that in strongly confining InAs QDs, the binding energy is independent of exciton emission energy and fluctuations in the ground state $\to$ exciton transition energy are strongly correlated with those of the exciton $\to$ biexciton. In contrast, the biexciton binding energy increases with emission energy in weakly confining interfacial GaAs QDs, and the level of correlation of exciton-biexciton broadening is reduced. A comparison with simulations reveals the significance of the strength and nature of confinement on Coulomb interactions responsible for biexciton renormalization.

Figure 1

(a) 2DFTS experimental setup. Three pulses are focused onto the sample to generate a FWM signal that is heterodyned and spectrally resolved with a reference pulse. The excitation pulse sequence is shown in (b). Interferograms are taken while stepping $\tau$, and a Fourier transform of the signal is taken with respect to $\tau$ to generate a 2D spectrum. (c) An energy level scheme indicating the exciton states separated by the fine-structure splitting ${\delta }_1$, the two-exciton state, and the bound biexciton state with binding energy ${\Delta }_{\mathrm{XX}}$.

Figure 2

Normalized cross-linearly polarized (HVVH) rephasing amplitude spectra for the InAs QDs annealed at (a) 900 ${}^{\circ }$C and (b) 980 ${}^{\circ }$C and (c) for the GaAs QDs. The diagonal (D) and biexciton (XX) peaks are indicated. The solid line in (c) follows the biexciton maximum amplitude while the dashed lines are on at 45${}^{\circ }$. Insets: horizontal slices taken at the maximum diagonal peak amplitude.

Figure 3

The biexciton binding energy dependence on the emission energy relative to the maximum diagonal peak amplitude is shown for (a) the InAs QDs annealed at 900 ${}^{\circ }$C (circles) and at 980 ${}^{\circ }$C (squares) and for (b) the GaAs QDs.

Figure 4

Simulated spectra for the InAs QDs annealed at 900 ${}^{\circ }$C are shown for (a) perfect correlation ($R=1$), equal inhomogeneous linewidths, ${\Gamma }_{\mathrm{XX}}={\Gamma }_{\mathrm{X}}$, and a homogeneous linewidth relation of ${\gamma }_{\mathrm{XX}}=3{\gamma }_{\mathrm{X}}$; (b) $R=1$, ${\Gamma }_{\mathrm{XX}}=1.5{\Gamma }_{\mathrm{X}}$, and ${\gamma }_{\mathrm{XX}}=3{\gamma }_{\mathrm{X}}$; and (c) $R=0.9999$, ${\Gamma }_{\mathrm{XX}}={\Gamma }_{\mathrm{X}}$, and ${\gamma }_{\mathrm{XX}}=0$.