Excitonic complexes in natural InAs/GaAs quantum dots

The quantum confinement in a typical quantum dot (QD) is determined primarily by the nanosystem's dimensions and average composition. We demonstrate, however, that excitonic properties of natural QDs formed in the InAs/GaAs wetting layer are governed predominantly by effects of random fluctuations of the lattice composition. It is shown that the biexciton binding energy is a very sensitive function of the lattice randomness with a nearly flat dependence on the exciton energy. The large variation in different random realizations of a QD structure is shown to lead in some cases to the reversal of the order of excitonic lines. Results of theoretical calculations correspond to statistical properties of neutral excitons and biexcitons as well as trions confined to single natural QDs studied in our microspectroscopic measurements. We observe substantial variation of the biexciton and trion binding energies as well as a correlation of the trion and the biexciton energies. The transition from the negative to the positive binding energy of the trion is also observed, which strongly supports the attribution of the observed trion to the positively charged exciton.

Figure 1

View of local atomic arrangement inside wetting-layer quantum dots demonstrating the effect of alloy fluctuations. Gallium atoms are shown as red (light gray) spheres, whereas indium atoms are shown as blue (dark gray) spheres. Common ions (arsenic atoms) as well as background atoms are not shown to improve clarity.(a)–(d) Different distribution samples correspond to different random realizations (local atomic arrangements), whereas the average composition (indium fraction) remains constant in all samples and equals $\sim 50$%.

Figure 2

The low-temperature photoluminescence related to the recombination of carriers in the InAs/GaAs wetting layer. The results of polarization-sensitive measurements in the low-energy range of the spectrum are shown in inset (a). Photoluminescence spectra detected with vertical (V) and horizontal (H) linear polarization the difference spectrum (V-H) are presented. The power dependence of the observed features is shown in inset (b).

Figure 3

Ground-state energies of neutral excitons confined in WLQDs calculated as a function of the average indium composition. Note the eight different random realizations for each average indium content. For comparison, dashed lines and arrows mark the spectral range of WLQD excitonic emission energies typically observed in the experiment.

Figure 4

(a) The emission spectra calculated for several samples (see the text) with similar $E_X\approx 1405$ meV energy, which comprise emission lines due to the exciton ($X$), the biexciton ($XX$), and the positively charged exciton ($X^{+}$). (b) Photoluminescence spectra of several WLQDs with the neutral exciton ($X$), biexciton ($XX$), and the trion ($X^{*}$) emission lines. Measurements are taken at $T=1.6\text{K}$. Note the energy scale relative to the exciton emission energy, which is also shown for each spectrum.

Figure 5

(a) The trion binding energy and (b) the exciton emission energy, measured as a function of the biexciton binding energy. The line in (a) is a guide to the eye.

Figure 6

(a) The binding energy of a positively charged exciton ($X^{+}$) and (b) the exciton emission energy calculated for all distribution samples considered in the calculation.

Figure 7

The biexciton ($XX$), the positively ($X^{+}$) and negatively ($X^{-}$) charged binding energies calculated using (a) the configuration interaction (CI) approach and (b) the perturbative approach (Hartree-Fock approximation, HF). (c) Electron-electron ($J^{ee}$), electron-hole ($J^{eh}$), and hole-hole ($J^{hh}$) Coulomb integrals for electrons and holes occupying their ground states. (d) The biexciton ($XX$) and the positively charged ($X^{+}$) exciton line spacings calculated using the CI and HF approaches. The results shown here were obtained for four different random realizations (samples) identical to those in Fig. 4 (with up-down ordering replaced with 1, 2, 3, and 4). Lines are guides to the eye.