The energy shift of the exciton can be written in a linear expansion as:
∆E =−~p·F~1+~p·F~2+p~·F~3+β(∆F)2 (5.7)
~
pis the dipole moment of the exciton which is basically oriented along the external
field F~ext, β is the polarizability of the quantum dot and F~i are the electric fields
of the impurity charge and its mirror charges at the location of the quantum dot. Since the orientation of the exciton dipole is fixed and perpendicular to the electric field of a charge laterally displaced in the InGaAs layer the first term~p·F~1 is0. The
second and third term for the mirror charges are non-zero but their contribution is below 0.4µeV (see red curve in Fig. 5.6(b) ). The polarizability of the quantum
dot arises from the fact that an electric field pulls apart the electron and hole in z-direction as the electric field of the dipole has only a z-component in the quantum dot plane. Therefore the polarizability in x-y-plane is neglected. The polarizability of the quantum dots investigated here is β = 0.25(kVµ/eVcm2)2 which gives the black
curve in Fig. 5.6(b). This implies that the polarization part is dominating and only needs to be considered for lateral charging effects. In Fig. 5.6 (b) the energy shift for lateral distances between 0 nm and 30 nm are computed. Energy shifts down
to5µeV can be detected with the quantum dot investigated and therefore one can
extract that the distance between the charge and the quantum dot needs to be less than11 nm. From this it can be concluded that it is rather unlikely that the jumps
in the exciton dispersion originate from charging events in the quantum dot layer.
5.4
Charge sensing in a modulation doped sample
As a proof of principle another dot in sample 2 (MCV13-2) with a different field effect structure is presented and it is demonstrated that charging events are a general phenomena in self-assembled InGaAs quantum dots. In the previous chapters it is shown that several quantum dots in sample 1 are affected by charging events in their vicinity. The typical charging gate voltages and energy shifts are determined by the composition of the heterostructure itself and the spatial position of quantum dots relative to the impurities. Without loss of generality the electrostatic model can be applied on any other sample with different structure by adapting the sizes of the capacitor to the present sample. In sample 2 the commonly used type of back contact (i.e. a bulk doped quantum well) is substituted with a triangular quantum well grown byδ-doping. A very thin layer is highly doped with silicon. The excess
charges migrate to the triangular well with low energy. It hosts the donator electrons and serves as the back contact 25 nm from the quantum dot layer. The distance
between the δ-doping and the triangular quantum well is 10 nm. The thickness of
the superlattice, which prevents a vertical current through the heterostructure, is changed to246 nm. This leads to new gate voltage regions in which the neutral and
-1400 -1350 -1300 -1250 1.29140 1.29145 1.29150 Ene rg y (e V ) Gate Voltage (mV) 1.29155 1.29160 1.29165 Ene rg y (e V ) (a) (b) Ppump= 100 nW Ppump= 0 nW QD 4 QD 4 2DEG QD 25 nm 30 nm -1400 -1350 -1300 -1250 Gate Voltage (mV)
Figure 5.7: Neutral exciton dispersion of QD4 on MCV13-2 (with modulation doped back contact). (a) A region of the neutral exciton dispersion is displayed which is close to the tunneling regime. The three discon- tinuities attributed to charging events close to the quantum dot have energy jumps between8µeVand12µeV. (b) A non-resonant laser with a power of Pnr = 2 nW is focused onto the sample in addition to the resonant laser. The impurities which are responsible for the jumps in the exciton dispersion are fully saturated by the photo-induced charges. The red dashed line indicates the gate voltage shift due to hole accu- mulation.
sample 1 (inset in Fig. 5.7(b)).
In Fig. 5.7 the left edge of the neutral exciton of a quantum dot in sample 2 is shown. 5.7(a) depicts the neutral exciton measured without non-resonant laser excitation. Three charging events shift the resonance energies by 8µeV, 12µeV and 12µeV
at −1237 mV, −1262 mV and −1316 mV respectively. As it is already known from
QD1 in sample 1 with a non-resonant laser (λnr = 850 nm, Pnr = 2 nW) charging
events are switched off as the impurities are saturated with photo-generated holes. Moreover holes accumulate in the 2D hole gas at the superlattice and evolve into a metallic layer. Therefore the 2D hole gas acts as an opposite electric field diminishing the overall field which results in a shift in gate voltage of the exciton dispersion curve (indicated by the red dashed lines and the arrow). So far the results on this dot are consistent with the previous dots.
The investigated quantum dot has a dipole moment of−e×0.241 nm. The conditions
for carbon in the host material are examined. The results are shown in table 5.2. It turns out that carbon can fully explain the observed jumps in the exciton dispersion. For charging of carbon acceptors the range of z is around 45.5 nm.