In this chapter calculations performed on an In40Ga60As quantum dot with a height of 2.5nm and a radius of 10nm were discussed. Strain calculations of this dot in a GaAs host showed the in-plane strain to be −2.5%, roughly the value that was to be expected. The strain component in the growth direction was 1.7%. The deviations from predictions made in chapter 3 were explained by considering the effect of the host material surrounding the dot also in the growth direction, which was not taken into account in our theoretical descrip-tion. We were able the show that the strain could reliably be altered by introducing a GaAs stressor under the quantum dot structure and changing its lattice constant. A decrease of 0.1% in this lattice constant lead to a decrease of 0.1% of in-plane strain. Subsequently, an increase of roughly 0.1% in the z-direction was found, analogous to what was previously shown for the unstrained case. When calculating the hole and energy ground states as a function of magnetic field, a linear dependence of the Zeeman splitting was found. Mean-while, the diamagnetic shift showed small deviations from the expected quadratic behaviour, of which the exact origin is unknown, but can possibly be explained by higher order terms in the diamagnetic shift. When calculating the hole and energy ground states as a function of added strain, both showed an increase in energy. This increase originated from the extra confinement induced by the strain. The hole experienced an increase of 2meV , while for the electron an increase of 6meV was found. The difference between the two came from the difference in localization of the electron and hole states. Over the entire range, the quantum dot emission energy shifted 4meV . The electron g-factor turned out to be two orders of
magnitude smaller than the hole g-factor. They both changed linearly with about 10% over the investigated range. The change in electron g-factor could easily be explained in terms of orbital momentum quenching; an increase in confinement leads to a decrease of orbital momentum and therefore the effective electron g-factor moves closer to the free electron value. The diamagnetic shift showed a decrease as function of strain. This could intuitively be explained by considering the change in confinement induced by the strain; a larger con-finement leads to a more localized wavefunction and therefore a smaller diamagnetic shift.
For the electron some strange behaviour was observed which could not conclusively be ex-plained. Fluctuations in the electron confinement energy were suggested to be the cause of this. Including the Coulomb interactions in future calculations was suggested as a way to solve this. In this report only one size of quantum dot has been investigated. It would be interesting to see how the size, and possibly even the shape, of the quantum dot affects the results found in this research. Also, the investigated dot was chosen to have a homogeneous In-concentration. In reality this will not exactly be the case. Therefore, checking how this affects the outcome of the calculations will be something that has to be done. The effect of a change in g-factor induced by strain becomes useful when one is able to use it to tune the g-factor around zero. Therefore it is necessary to find quantum dots with smaller g-factors closer to zero. Another interesting aspect is to see how the system responds when increasing the compressive strain even further. One would expect the linear behaviour to hold, but future research will have to test this hypothesis. Tensile strain is also a regime that remains untouched. It might be very interesting to also look into this area, as tensile strain will bring the light hole and heavy hole bands close to each other. At one point a regime will be entered where the mixing between these two becomes important and nonlinearities kick in.
Chapter 6
Tuning electronic properties using strain: an experimental approach
In this chapter the experiments performed on sample O717 will be presented. These exper-iments will test the predictions made by our numerical model in chapter 5. In total seven quantum dots have been investigated. First the dependence of the quantum dot spectra on the applied voltage will be discussed. Experiments show a linear behaviour, which agrees with literature. Secondly the magnetic field dependence is discussed. This explains how the g-factor and diamagnetic shift can be extracted from the experimental data. In the final section both voltage and magnetic field are combined to research the strain-dependence of both the g-factor and diamagnetic shift. A linear relation between exciton g-factor and ad-ditional strain is discovered. For the diamagnetic shift a dependence is also found, however the exact relation between the two is unclear. For one particular dot an additional splitting is observed. This is assigned to the fine structure splitting, which allows for determination of the electron and hole g-factors separately.
The quantum dot density in the used sample has proven to be extremely low, < 1/100µm2, meaning each membrane contains only a few quantum dots. This unfortunately makes statis-tical analysis of any kind impossible on this sample; in total seven dots have been analyzed.
The wetting layer signal is clearly visible around 860nm, showing large fluctuations in both structure and intensity when scanning the membranes. This indicates that the wetting layer is unusually inhomogeneous. The dots are generally found between 890nm and 910nm. For the excitation a 780nm laser diode is used. To analyze the light the triple monochromator is used in single stage mode. The 750grooves/mm grating is used for locating the quantum dots. This is switched to the 1800grooves/mm grating for the actual measuring of the quantum dots to achieve the highest possible resolution of ∼ 15µeV .
6.1 Identifying peaks
Figure 6.1 shows a typical quantum dot spectrum. The spectrum shows several lines which generally can be assigned to several exciton complexes. The line width is typically ∼ 100µeV , meaning the resolution is not limited by the spectrometer, but mainly by the quantum dot
Figure 6.1: A typical photoluminescence spectrum of a quantum dot. Many lines are present which can be assigned to multiple exciton complexes. Here the exciton and biexciton have been indicated, which are identified by measuring the PL-intensity as a function of excitation power.
emission. Emission visible from other dots is very unlikely here due to the low quantum dot density. The exciton (X0) and biexciton (2X0) lines are indicated in the figure. The other lines originate from either charged exciton complexes (X−, X+, etc.) or higher order neutral excitons (3X0, etc.). We can rule out the possibility of the lines originating from another quantum dot due to the exceptionally low quantum dot density in this sample.
By decreasing the excitation power, higher order lines will start to vanish and one is left with only the neutral exciton (X0) line. Other lines require a more thorough manner of identification. When increasing the excitation power, the quantum dot is more and more likely to be occupied by more than one exciton. The single exciton line therefore has to initially increase (linearly) with excitation power before saturating and eventually even decreasing. The biexciton line on the other hand will have a superlinear (ideally bilinear) dependence and saturate at higher excitation powers than the single exciton line. The exciton and biexciton lines can therefore be identified by making a log-log plot of excitation power versus photoluminescence intensity and determining the slopes of these lines. For the single exciton line this slope should be 1, while for the biexciton line this should ideally be 2. Deviations from this latter value are often found and depend on mainly the sample properties and the excitation wavelength. This analysis for two different quantum dots is shown in figure 6.2.
In both cases the single exciton lines show a linear behaviour, as expected, with slopes of respectively 0.95 and 1.02. The biexciton lines show superlinear behaviour, with slopes of 1.87 and 1.68. Identifying charged excitons would require polarization dependent mea-surements. As this research is in the first place focussed on the single exciton complex (and to lesser extent the biexciton) this is omitted.
Figure 6.2: Log-log plots of excitation power versus PL-intensity for two different quantum dots. The exciton and biexciton lines can be identified by determining the slopes of the data, which should ideally be 1 for the exciton and 2 for the biexciton. Here deviations from the ideal value of 2 are found, which is generally the case.
Figure 6.3: Colourplots of the photoluminescence spectra as function of voltage taken for two different quantum dots. The peak positions are seen to shift linearly with applied voltage.