Trotta et al. have reported a linear dependence of the exciton energies on applied voltage [4]
[6]. They have shown when adding approximately ∆0.4% compressive strain, energy shifts of ∼ 15meV are achievable. This section is aimed at confirming this linear behaviour as well as investigating the magnitude of the energy shifts possible in the O717 sample. The voltage is varied in steps of 2V every 0.5s. This is to ensure the piezo is relaxed and to prevent damage to it. Before using the piezo it first has to be poled, as the dipoles in the piezo-electric material tend to disorganize over time. The poling procedure is necessary to realign the dipoles and activate the piezo. This procedure in this case holds nothing more than ramping the voltage from 0V to 200V in the aforementioned small steps and back.
In our experiments the voltage is varied between 0V and 500V . Figure 6.3 shows how the spectra of two different quantum dots evolve as a function of applied voltage. Spectra are taken every 10V with an acquisition time of 10s.
The spectra show many lines which can be assigned to the different exciton-complexes discussed in the previous section. As mentioned, here investigation is limited to the exciton and biexciton peaks which are identified by analyzing the excitation power dependence of the PL intensity. Figure 6.3 shows that with increasing voltage, the wavelength (energy)
Figure 6.4: Fitted peak energies as a function of applied voltage for the exciton (bottom line) and the biexciton (top line). Both show a linear behaviour, changing with about 2µeV /V .
of the lines decreases (increases); they experience a blue-shift. This is caused by a change in the band structure of the quantum dot due to the compressive strain; the conduction bandedge and (heavy hole) valence band edge are pushed away from each other, increasing the bandgap and also increasing the difference between the first hole state in the valence band and the first (and only) electron state in the conduction band. Also, for one particular dot all peaks seem to shift linearly and roughly by the same amount. This is as expected as the only thing that separates the different exciton complexes in energy is their relative binding energy. This relative binding energy is also affected by strain, but since it’s absolute value is relatively small (generally ∼ 1meV ), this effect will also be small compared to the change in exciton energy itself. The magnitude of this effect can be investigated by considering the direct Coulomb integrals (Jij) between the electrons and holes, denoted as respectively e and h. The relative binding energy of the biexciton can then be written as [6]
EB(2X0) = −Jee− Jhh+ 2|Jeh|. (6.1) Since the hole wave function in this type of quantum dots is much more localized than the electron wave function and the centers of mass of the particles are close, the magnitude of Jhh and its change with strain will be small and can be neglected here. It has been calculated that for InGaAs quantum dots that the remaining two terms, Jeeand Jehchange by roughly the same amount under compressive strain [40]. Based on this, one would expect the relative binding energy of the biexciton to increase with increasing compressive strain, which is also what Trotta et al. have shown experimentally.
By making a Gaussian fit to the peaks, the peak positions as a function of voltage can be determined. For the exciton (X0) and biexciton (2X0) peaks of one particular dot this result, including a linear fit, is shown in figure 6.4.
Figure 6.4 shows again that the energies of both the exciton and biexciton peaks depend linearly on applied voltage. We can therefore describe the energy as a function of applied voltage using
E(V ) = E0+ γV (6.2)
Dot E0X0(eV ) E02X0(eV ) γX0(µeV /V ) γ2X0(µeV /V )
Table 6.1: Energies and γ-values for the biexciton and exciton complexes of seven different quantum dots. The values of γ are similar for both exciton and biexciton, but are generally lower for the latter. This is due to an increase in relative binding energy.
where E0 is the energy at zero voltage in eV and γ the energy shift in eV /V . Fitted values for E0and γ for both exciton and biexciton lines for several quantum dots are shown in 6.1, where the values for this particular dot have been highlighted. A few things can be concluded from this table. The γ-values for this sample are generally around 2µeV /V (varying between 1.5 and 2.2), yielding a total shift of around 1meV for the 500V voltage range investigated here. The γ-value will depend on a matter of things. The first important thing is the rate of strain-transfer from the piezo to the actual sample. This is determined by how well the membranes are bonded through the gold layer onto the piezo. On this sample this has proven to be quite bad, as shift values are much lower than reported by Trotta et al, who have reported total energy shifts of 15meV . Secondly, similar to how the exciton energy depends on the exact size, shape and composition of the individual quantum dot, so will the γ-value. This is the cause for the spread in -values as shown in 6.1. By comparing our results to those reported by Trotta, we conclude that we reach a strain of roughly ∆ = 0.02 − 0.03% at 500V . When comparing this with the results of our numerical calculation, we find a good agreement. For the dot investigated there, a shift in emission energy of 1meV is reached at around ∆k = 0.03%. For each individual quantum dot the γ-values for the exciton and the biexciton are similar, with the biexciton value being slightly lower. This can be explained by the fact that the increase in relative binding energy of the biexciton slightly cancels the increase in absolute energy. Trotta et al. have shown for the biexciton a change in relative binding energy of on average 40µeV /meV with a rather large spread. As 500V in our experiment corresponds to a change of 1meV in exciton energy, one would expect the γ-value for the biexciton to be around 0.08µeV /V lower, which is indeed what we observe. Dot 6 has a significantly lower exciton and biexciton energy than the other investigated dots; 1.360 and 1.365 for this dot compared to ∼ 1.39 for the other dots.
This particular dot also shows a higher relative binding energy for the biexciton (5meV ) than the other dots. It is notable that this dot also has the lowest values for γX0 and γ2X0
of all investigated dots, while the dot with the highest exciton energy (dot 2) also has the largest γ-values. This indicates there may be a trend in γ versus E, however seven dots is too small an amount to draw any conclusions from. A larger ensemble of dots will have to be investigated to confirm whether this is a trend or just a coincidence. In 6.1, the uncertainties in the energies are 10µeV , and in the energy shift slopes 0.01µeV /V .
Figure 6.5: Spectra of the quantum dot at different magnetic fields, where the exciton and biexciton lines have been indicated.