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Fingerprint of the emission from a single QD is the quantization of the energy levels, thus the presence of excited states emission lines in the spectra and their grouping into shells. Increasing the excitation power causes the statistical occupancy with more than one exciton and the subsequent filling of the “atomic like” shell energy structure of the QD. Fig. 5.10 shows a power dependent experiment on a single QD, which is typical for the series of spectra acquired in the present work.

As expected, an isolated single line (labelled Ex in the following) appears at low excitation power due to recombination of a single exciton in the QD. For this experiment the resolution of the spectrometer was set to 2 wave numbers (~250 µeV) to speed up the collection of the spectra. The integration time was set to 50 min and 14 spectra have been acquired at different excitation powers.

Figure 5.10 Power dependence of the emission from a single QD, with the successive appearance in

the spectra of the ground state Ex and the biexciton Exx lines and at higher pump powers the

emission from excited states (p- and d-shells).

At the lowest pump power only the ground state emission line (Ex) is present in the spectrum. As excitation power increases a second line (Exx) appears on the low energy side of the Ex line, which originates from recombination of a second exciton in the QD. The two excitons in the dot form a biexciton complex, the Exx line arises from a sequential biexciton decay, i.e. the radiative recombination of a bound biexciton configuration into a single exciton state in the s-shell. The lower emission

energy indicates a positive biexciton binding energy (ΔExx) whose magnitude is the distance between the Ex and the Exx lines (in this case 2,4 meV).

The power dependence of the intensity of the two lines confirms the interpretation as single exciton and biexciton emissions. In the double-logarithmic plot (fig. 5.11a) the integrated intensity of the Ex line exhibits a linear increase with the excitation intensity, whereas the biexciton line intensity shows a superlinear increase with an exponent of 2,1. In the case of resonant excitation, a quadratic dependence of the integrated intensity of the biexciton line at low excitation powers is the fingerprint of the two photon absorption process needed for the creation of the two excitons. For non-resonant excitation conditions this behaviour has been modelled with a rate equation system based on a four level exciton-biexciton model [30][123][124]. The basic idea is to relate both exciton and biexciton states by steady-state transition rates. The model predicts a linear and bilinear increase of the Ex and Exx integrated intensities at low excitation powers and a saturation with increasing pump power. Another approach consists in the random capture model [25][125], based on the assumption that the generation of biexcitons is a result of random capture of two excitons at the same time by the dot. Both models show an overall good agreement with the experimental data.

Figure 5.11 (a) Power dependence on a double-logarithmic scale of the intensity of the exciton and

biexciton emission lines at low excitation powers and (b) power dependence of Ex, Exx and the two

main emission in the p- and d-shells. Note the saturation of the Ex and Exx lines and the linear

increase of the excited states emission intensities.

Another tool for the identification of the biexciton emission peak has been recently proposed by means of photon-correlation measurements, by demonstrating its strong correlation with the single exciton emission [126][127]. In ref. [49] both laser power dependent and time resolved PL measurements have been used to identify the exciton, biexciton and their charged complexes emission lines from an individual QD.

The occupancy with two excitons fills the ground state s-shell of the dot, but at higher excitation powers the QD becomes populated with statistically more that two excitons at a time. Because of the Pauli exclusion principle these excitons have to occupy higher energy shells (p, d) and other lines appear on the high energy side of the Ex one. The peaks observed at 1,633 eV and 1,676 eV are associated to

recombination of the three-exciton up to six-exciton complexes, when the first excited energy level (p-shell) becomes saturated. For this QD the centre of the p- shell group lies ~23 meV above the s-shell, while the d-shell emission lines are spread in an interval from about 20 to 30 meV above the p-shell. The integrated intensity of the excited states emission lines shows with good approximation a linear increase, while the Ex and the Exx lines saturate (fig. 5.11b). Additional lines appearing in the s-shell region on the low-energy side of Ex arise from recombination of an s-shell exciton, perturbed by the presence of excitons occupying higher lying shells [68][128]. At the highest pump power a broadening of the s-shell emission is observed which may be caused by Coulomb interaction between carriers in the dot and in the wetting layer [129] and in the surrounding barrier.