InAs Quantum Dots for Quantum Information Processing

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1 InAs Quantum Dots for Quantum Information Processing Xiulai Xu 1, D. A. Williams 2, J. R. A. Cleaver 1, Debao Zhou 3, and Colin Stanley 3 1 Microelectronics Research Centre, Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom 2 Hitachi Cambridge Laboratory, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom 3 Department of Electronics & Electrical Engineering, University of Glasgow, Glasgow, G12 8QQ, United Kingdom InAs quantum dots attract much interest because of their potential application in quantum information processing. In this paper, two wafers of self-organized InAs quantum dots incorporated in p-i-n junction structures are investigated with both photoluminescence and electroluminescence: one has a single layer of uniform quantum dots at low density; the other has vertically-stacked double layer quantum dots with graded densities across the wafer. For the single layer dot wafer, single-photon emission has been obtained successfully, by pumping optically and electrically at high repetition rates. The coupling between vertically stacked double dots has been observed from the abnormal Stark shifts and from anticrossings in photoluminescence and electroluminescence spectra. 1. Introduction Quantum dots, so-called artificial atoms, attract much interest because potentially they can be used to implement quantum information processing [1,2]. Among several quantum-dot candidates, III-V quantum dots are particularly promising as they have several advantages, providing good stability, high repetition rate, electroluminescence, and compatibility with semiconductor processing techniques. Recently, single-photon emission has been realized using InAs quantum dots in a cavity and applied to quantum cryptography [3] and to quantum teleportation [4]. Based on single qubit (quantum bit) realization with an exciton in a single quantum dot [5], optical quantum gates also have been obtained recently with both an exciton and a biexciton within one dot [6]. It can be seen that a stable single photon emission source is in demand for all these implementations [1]. All the photon sources considered above were excited optically. In practice, it is desirable to excite a specific single quantum dot electrically. Recently, Yuan et al. [7] have obtained electrically-pumped single-photon sources from InAs quantum dots in an intrinsic region of a conventional p-i-n structure; in order to obtain emission from one single dot, the dot density was very low and metal apertures were made on the surface to select the emission site; in this configuration, the low coincidence between quantum dots and metal apertures produces a low yield of functional sites. Coupled quantum dot molecules (QDMs) provide a good candidate for spin-based [8], charge-based [9] and exciton-based [10,11] qubits. Vertically stacked QDMs have been suggested to host a single qubit, or double qubits; these can be controlled by optical pulses, by an electrical field, or by a magnetic field [10,12]. To realize these concepts, a basic requirement is to achieve entangled states between the two dots. Experimentally, coupling from QDMs has been observed with different dot distances between pairs of dots [13,14] X/04/$ IEEE 101

2 Further investigation of QDMs for implementing qubits and entangled-photon sources is desirable. In this paper, we investigated wafers with single layer and double layer InAs quantum dots. Two lateral p-i-n junctions incorporated with quantum dots: one (W2519) has only a single layer of dots with uniform density less than cm -2, from which we successfully obtained electrically pumped single-photon sources without metal masks, a device structure which potentially is well suited to integration into complete systems. Another wafer (A1943) has two layers of InAs quantum dots with dot density graded across the wafer. Coupling from QDMs has been observed from anticrossing of photoluminescence and electroluminescence. For comparison, two single-layer wafers, with graded dot density with different InAs thicknesses, 1.8 monolayers (A1933) and 1.6 monolayers (A1919) respectively, were investigated with photoluminescence spectroscopy. 2. Materials and Structure The structures we used are lateral p-i-n junctions. The layers grown by molecular beam epitaxy (MBE), from top to bottom, are: heavily-doped p-type GaAs, p-type GaAs, i-gaas, single layer InAs quantum dots (or double layer quantum dots with 10 nm GaAs spacer layer from wetting layer to wetting layer), i-gaas, δ-doped n-type GaAs (giving a two-dimensional electron gas, 2DEG) and i-gaas substrate. The structure is designed so that the lower n-type channel is fully depleted if the upper p-type region is in place. When the upper layer is removed, the n-type channel becomes conducting. A p-n junction then forms at the interface adjacent to the edge of the removed upper layer; the quantum dots at the edge will be excited at low forward-bias voltage [15]. Kaestner et al. [16] successfully obtained electroluminescence from the active region at the etched edge and showed by simulation the current flow geometry within this region. For the wafer A1943, the growth of double quantum dots was done by MBE on a GaAs substrate without rotating the wafer. The asymmetry of the In source with respect to the wafer induces a graded In flux, resulting in a variation of the InAs dot density across the wafer [17]; the dot density is negligible on one side of the wafer, and increases to cm -2 on the far side, as shown in Figure 1. Figure 1 AFM images (1µm 1µm) of quantum dots with different densities across the wafer. 102

3 3. Fabrication and Measurements The photoluminescence (PL) measurements were carried out using a conventional micro-photoluminescence system excited with a He-Ne laser. An aluminum layer with 0.2µm-1µm apertures was applied to isolate a single dot or a pair of double dots. The devices for EL were mesa structures, typically 1µm 10µm; the n-type material, after the removal of the p layer, was contacted with a AuGeNi annealed contact, whilst the p-type mesa was contacted with Cr/Au which did not have to be annealed because of the heavily-doped surface layer. Figure 2 (a) shows a SEM image of a typical EL device. The injected current was increased until emission occurred from a single quantum dot; because of this self-selecting characteristic, no masking layer was needed. The sample was mounted in a He flow cryostat and cooled to 5K. The emission light was collected by a large numerical aperture objective, dispersed through a 0.46 m spectrometer and then detected with a cooled charge-coupled device camera. Correlation measurements were performed using a Hanbury Brown and Twiss (HBT) system [18] with a 50/50 beam splitter and two single-photon-counting avalanche photodiodes. Figure 2 (a) SEM image of a typical EL device; (b) I-V and (c) di/dv characteristics with different G1 voltages. 4. Results and Discussion 4.1 Typical I-V characteristics Figure 2(b) shows I-V curves for a device with forward bias and gate voltages at -3, -1, 1, and 3 V. The gate voltage is applied to the side gate (G1) on the n-type side (as shown in Fig. 2(a)). No large differences have been observed when controlling the gate voltages of the gate on the p side for the bulk-conducting layer. Two large current jumps are observed at 3.4 V and 3.9 V respectively, and a small jump around 3.7 V. The differential curves are plotted in Fig. 2(c), which clearly show the current changes. The voltage positions around 3.4 and 3.9 V also shifts to high voltage with increasing positive gate voltage. The gate controls the conductance of the n-type electron gas, with the result that tunnelling occurs at higher voltages with an increase of positive gate voltage. The two current jumps can be ascribed to the electron tunnelling to the ground state and to the excited state of the 2DEG. The small peak around 3.7 V varies its position with increasing gate voltage, which might be due to the charging effects of quantum dots during the continuous scanning measurements. The 103

4 tunnelling of current also influences carrier populations of quantum dots, resulting in luminescence intensity variation [15]. 4.2 Positive and negative biexciton energies Interaction between excitons in a single quantum dot has been investigated intensively as it provides fundamental bases for optical controlled-not gate and for entanglement [6, 19]. Normally biexciton energy is several mev less than the biexciton energy because of the Coulomb interaction. For the high-density site of A1919 and A1933, many single-dot emisson peaks can be resolved in photoluminescence spectra, and it is difficult to assign the emission to a specified dot. Figure 3 shows photoluminescence spectra of two wafers at the site where quantum dots are just formed. For wafer W1933, it can be seen that the biexciton energy is 3.3 mev lower than exciton energy (Figure 3(a)), which is similar to other results [7]. However, it is 8.2 mev higher than exciton energy in (b) for A1919. This means that both positive and negative binding energy have been observed in different InAs thickness. Recently, Rodt et al. [20] reported the observation of repulsive exciton-exciton interactions in quantum dots by using cathodoluminescence experiments. They also showed that the binding energy decreases with increasing exciton recombination energy, and that large recombination energies correspond to smaller dot sizes; our results correspond well to their results. For large dot wafer with 1.8 ML InAs, an exciton-exciton interaction is attractive with positive biexciton binding energy. However, for the wafer with 1.6 ML, a repulsive Coulomb interaction is observed, and the resulting biexciton energy is higher than the exciton energy. The overall energies of A1919 are also higher than those of A1933 because the dots are smaller. Figure 3 Photoluminescence of quantum dots with InAs thickness, (a) 1.8 ML; (b) 1.6 ML, at the centre of the wafer. X: exciton, XX: biexciton. 4.3 Single photon source from single quantum dots The second correlation function g (2) (τ) from HBT system has been used to evaluate the emitted photon statistics. For an ideal single-photon source, the value of g (2) (τ) at zero time delay should be equal to 0. Figure 4(a) plots the correlation result of the X line (EL spectrum shown in the inset with width 400 µev) for the low current injection of 90 µa, for a device made from W2519. Clear antibunching at τ=0 can be observed, which shows that the simultaneous emission of two photons is largely suppressed. g (2) (0) is 0.54 ± 0.05 with the presence of background light, and does not reach the theoretical minimum, zero. The correlation function can be corrected with g (2) (τ)=1+( g (2) (τ)-1)/ρ 2, where ρ =S/(S+B) is the 104

5 ratio of signal S to total counts, including dark counts B [21]. The result for exciton emission is 0.48±0.06 with ρ at The g (2) (0) without dark counts still does not go to the ideal value of zero, which may be due to the finite time resolution and background stray light [15]. Further the exciton lifetime can be obtained around 1.07 ns by fitting the histogram with g (2) (τ)=1-aexp(-τ/b), where 1-a and b are g (2) (0) and the recombination lifetime, respectively. Single-photon sources based on InAs quantum dots can be operated also at high repetition rate, pumped optically [22] or electrically [7]. Figure 4 (b) shows a correlation histogram of exciton emission, driven with 100 MHz pulses with height of 5 V and width 800 ps superimposed on 15 V DC bias. Antibunching can be observed at zero time delay, which implies the possibility of using single-photon sources at high repetition rates. Again, g (2) (0) is 0.45±0.06, and not zero. For this, an additional reason may be that the RF pulse signal was broadened between the pulse generator and the device. The value of g (2) (0) less than 0.5 indicates a single photon emission. Correlation, g 2 (τ) Intensity (a.u.) µev 1200 (b) (a) Energy (ev) Delay Time (ns) Delay time (ns) Figure 4 Second-order correlation function g (2) (τ) of EL with (a) continuous excitation (measured, thin line; fitted, thick line), and (b) pulsed excitation. Inset: EL spectrum. Coincidence Counts n(τ) V+5V(Pulse, period 10ns, width 800ps) (a) 151µW 51.2 (b) 65µA E1 5 E Figure 5 (a) PL spectra with different excitation powers, and (b) EL spectra as a function of injection current. Dashed lines are used to guide the eye. 4.4 Coupling between stacked double quantum dots 105

6 Figure 5(a) shows PL spectra at a site with dot density around 1~ /cm 2, which is in the medium In flux region on wafer A1943. At very low excitation intensity, 490 nw, only one peak can be observed, at mev. With slightly increasing excitation power up to 716 nw, a high-energy peak ( mev) appears. With increasing excitation power, the first peak is blue-shifted and is quenched with excitation power at 1.15 µw. By contrast, the peak at mev is red-shifted. An anticrossing can be observed at µw. We attribute both shifts to the accumulated carrier induced Stark shift under optical excitation [23]. The shifts of the two peaks indicate opposite built-in dipoles in the two dots because of the coupling. The phenomena can be observed also in EL, as shown in Figure 5(b). At low current, only one peak at mev can be observed, and another at mev appears with increasing current. In contrast to the PL, the anticrossing can also observed at 25 µa with 1.6 V. However, the shifts are less than that for PL. The reason for this can be due to that tunneling current in EL induces weak coupling [23]. 5. Summary We investigated single and double layer quantum dots in lateral p-i-n junctions with variations of dot density. Current tunneling has been observed between the 2DEG and the quantum dots. Interaction of two excitons in a single dot shows attraction for large dots, and repulsion for small dots. Electrically-pumped single-photon sources have been obtained successfully at high repetition rates using a self-selecting process that eliminates the need for metal masks. Coupling between two stacked double quantum dots has been observed in both PL and EL. Acknowledgement The project is supported by the Foresight Link Award Nano-electronics at the quantum edge from the UK Department of Trade and Industry and by Hitachi Europe Ltd. Reference: [1] P. Michler, Single Quantum Dot, Springer, Berlin, 2003 [2] D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures, John Wiley & Sons, Chichester, 1999 [3] Edo Waks et al. Nature 420, 762, 2002 [4] D. Fattal, E. Diamanti, K. Inoue, and Y. Yamamoto, Phys. Rev. Lett. 92, 37904, 2004 [5] N. H. Bondeo, J. Erland, D. Gammon, D. Park, D. S. Katzer and D. G. Steel, Science 282, 1473, 1998 [6] Xiaoqin Li et al., Science 301, 809, 2003 [7] Zhiliang Yuan et al., Science 295, 102, 2002 [8] D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120, [9] W. G. van der Wiel, S. D. Franceschi, J. M. Elzerman, T. Fujisawa, S. Tarucha, and L. P. Kouwenhoven, Rev. Mod. Phys. 75, 1, [10] O. Gywat, G. Burkard, and D. Loss, Superlattices and Microstrctures 31, 127, [11] X. Q. Li and Y. Arakawa, Phys. Rev. A 63, , [12] B. W. Lovett, J. H. Reina, A. Nazir, and G. A. Briggs, Phys. Rev. B 68, , [13] T. H. Oosterkamp et al., Nature 395, 873, [14] M. Bayer et al., Science 291, 451, [15] Xiulai Xu, D. A. Williams and J. R. A. Cleaver, Appl. Phys. Lett. in press. [16] B. Kaestner, D. H. Hasko, and D. A. Williams, Jpn. J. Appl. Phys. 41, 2513, 2002 [17] D. Leonard, K. Pond, and P. M. Petroff, Phys. Rev. B 50, 11687, [18] R. Hanbury Brown and R. Q. Twiss, Nature 177, 4497, [19] O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, Phys. Rev. Lett. 84, 2513, [20] S. Rodt, R. Heitz, A. Schliwa, R. L. Sellin, F. Guffarth, and D. Bimberg. Phys. Rev. B 68, 35331, [21] C. Becher et al., Phys. Rev. B 63, , [22] C. Santori, M. Pelton, G. Solomon, Y. Dale, and Y. Yamamoto, Phys. Rev. Lett. 86, 1502, [23] Xiulai Xu, D. A. Williams, and J. R. A. Cleaver, unpublished. 106