Auger recombination in self-assembled quantum. dots: Quenching and broadening of the charged

Transcription

1 Supporting material: Auger recombination in self-assembled quantum dots: Quenching and broadening of the charged exciton transition Annika Kurzmann 1*, Arne Ludwig 2, Andreas D.Wieck 2, Axel Lorke 1, and Martin Geller 1 1. Fakultät für Physik and CENIDE, Universität Duisburg-Essen, Lotharstraße 1, Duisburg 47048, Germany 2. Chair of Applied Solid State Physics, Ruhr-Universität Bochum, Universitätsstr. 150, Bochum, Germany S1

2 1. Sample structure Figure S1. (a) Schematic sample structure of the active region, containing the QD layer (red area), the tunneling barrier and the Ohmic back contact. (b) Conduction band and Fermi energy for zero bias, calculated with the Poisson solver. 1 S2

3 2. Photoluminescence signal from the QD A photoluminescence scan of the measured QD is shown in Fig. S2. We changed the gate voltage form V to 0.6 V and observed a photoluminescence signal at four different wave lengths. The signals at about nm and nm were identified as exciton and trion, respectively. Note that in our sample structure the different excitonic complexes overlap strongly in the gate voltage, an effect that can be attributed to a thick tunneling barrier between the QD and the charge reservoir. 2 Furthermore, we observe a hot-trion that was already observed before in Ref. (3). Figure S2. Photoluminescence scan of the investigated QD. Beside the exciton (X) and trion (X-) transition, that overlap strongly in gate voltage, the signature of the hot-trion can be seen at wavelength around 952 nm. S3

4 3. Resonant measurement of exciton and trion In Fig. 1(c) of the main text we measured the RF signal of the exciton and the trion while we excite both transitions simultaneously using two different lasers. The RF signal of both transitions is collected by a CCD camera behind a spectrometer having a grating with a 1200 lines per mm. This wavelength resolved RF signal was measured for different gate voltages shown here in Fig. S3 (a). The white line in Fig. S3 (a) at λ=953.6 nm for gate voltage between 0.31 and 0.33 V originates from the laser background. On top of this background, the exciton resonance appears at V g = V. Taking now two line cuts from the measurements in Fig. S3 (a) at a wavelength λ=953.6 nm and λ=958 nm, we observe the typical trion and exciton RF in Fig. S3 (b), respectively. The same RF signal is shown in Fig. 1(c) in the main text. The CCD detector used for this measurement is less sensitive than an APD, hence, we integrated the signal for 5 seconds to measure the exciton and the trion transition. Figure S3. (a) The RF signal is measured for different wavelengths to separate the exciton and the trion emission. We use a spectrometer with a Si-CCD detector. (b) RF signal of the exciton and trion as function of the gate voltage, obtain by line cuts from Fig. S3 (a). S4

5 4. Background correction of the laser signal We always measure a laser background in the resonance fluorescence measurement, i.e. the laser is never completely suppressed by the cross polarized polarizers. However, the laser background can be subtracted from the measurements after determination by a gate pulse that shifts the QD resonance out of resonance. In Fig. S4 at t=0 µs the laser is switched on and we observe, for a gate voltage where the QD is in resonance with the trion transition, the quenching of the RF signal together with the laser background. At t= 18 µs, the gate voltage is switched to a situation where the QD is out of resonance with the laser and only the laser background is observed. This laser background is subtracted from the RF measurements in the entire manuscript. Figure S4. (a) Laser intensity during one shot of the measurement. (b) Pulsed gate used for subtraction of the laser background. (c) Time-resolved RF with laser background. S5

6 5. Tunneling rate of the electrons into the QD We measured previously in Ref. (4) the tunneling rate of electron tunneling into the QD in a time-resolved measurement with a pulsed gate voltage. At t= 17 µs the gate voltage is switched to a gate voltage where the QD exciton transition is in resonance with the laser and electron tunneling into the dot is possible. The additional electron switches the exciton transition off, as the charged QD is out of resonance with the laser and we directly measure the tunneling rate in the exponential decay in Fig. S5 (a). We performed these measurements for different laser excitation power and observe a dependence between tunneling rate and the laser power. The tunneling rate into the QD decreases for increasing laser power, as the tunneling probability decreases for increasing average occupation of the dot with an optically excited electron hole pair. We measured this tunneling rate for different laser powers before in Ref. (4) and shown in Fig. S5 (b). We used one value for the low laser power from theses previous measurements ( in the main text. Figure S5. (a) Transient that directly shows the tunneling of electrons into a single selfassemble QD. The measurements were performed with a pulsed gate voltage. (b) The tunneling rate depends on the laser excitation power. When the QD is occupied by a electron hole pair the degeneracy for the tunneling is changed. S6

7 6. Non-resonant measurements on the trion transition We also performed pulsed measurements on the trion with an additional non-resonant laser excitation. This experiment verifies the resonant effect of the Auger-recombination. The first laser is in resonance with the trion transition and drives the QD constant with a low intensity. The second laser is out of resonance with the QD and the intensity is pulsed. As a result, we observe in Figure S6 an increased RF signal when the second laser is switched on. This increase in RF intensity has its origin in an increased laser background. More important, we do not observe an exponential decay when the non-resonant laser is switched on, i.e. the trion transition is quenched by an Auger recombination in the main text, which is a resonant effect. Figure S6. Time-resolved measurement of the trion transition, with an additional pulsed nonresonant laser excitation. The non-resonant laser has no influence on the trion transition, as the Auger recombination is a resonant effect. S7

8 7. Exciton We performed time-resolved pulsed laser measurement on the trion transition in the main text, shown in Fig. 2(a). Figure S7 shows in addition RF measurements that were performed on the exciton transition. As expected, we do not observe an exponential decay. This constant RF signal of the exciton shows that there is no influence of the laser excitation on the exciton transition, as no Auger recombination is possible. Note further that at t= 20 µs the second resonance of the exciton transition (fine structure splitting) is for a short time shifted into resonance with the laser. Figure S7. Time-resolved measurement of the exciton transition with a pulsed laser intensity. We do not observe an intensity reduction in the RF signal as no Auger recombination is possible for the exciton transition. S8

9 REFERENCES (1) G. Snider, 1D Poisson (2) Gerardot, B. D.; Brunner, D.; Dalgarno P. A.; Öhberg, P.; Seild, S.; Kroner, M.; Karrai, K.; Stoltz, N. G.; Petroff, P. M.; Warburton, R. J. Nature 2008, 451, (3) Jovanov, V.; Kapfinger, S.; Bichler, M.; Abstreiter, G.; Finley, J. J.; Phys. Rev. B 2011, 84, No (4) Kurzmann, A.; Merkel, B.; Labud, P. A.; Ludwig, A.; Wieck, A. D.; Lorke, A.; Geller, M.; arxiv: [cond-mat.mes-hall]. S9