Bright electrically controllable quantum-dot-molecule devices fabricated by in-situ electron-beam lithography
Johannes Schall, Marielle Deconinck, Nikolai Bart, Matthias Florian, Martin von Helversen, Christian Dangel, Ronny Schmidt, Lucas Bremer, Frederik Bopp, Isabell Hüllen, Christopher Gies, Dirk Reuter, Andreas D. Wieck, Sven Rodt, Jonathan J. Finley, Frank Jahnke, Arne Ludwig, Stephan Reitzenstein
BBright electrically controllable quantum-dot-molecule devices fab-ricated by in-situ electron-beam lithography
Johannes Schall Marielle Deconinck Nikolai Bart Matthias Florian Martin von Helversen Christian DangelRonny Schmidt Lucas Bremer Frederik Bopp Dirk Reuter Andreas D. Wieck Sven Rodt Jonathan J. FinleyFrank Jahnke Arne Ludwig Stephan Reitzenstein
J. Schall, M. Deconinck, M. von Helversen, R. Schmidt, L. Bremer, Dr. S. Rodt, Prof. S. ReitzensteinInstitute of Solid State PhysicsTechnische Universität BerlinHardenbergstraße 36, D-10623 Berlin, GermanyEmail Address: [email protected]. Bart, Dr. A. Ludwig, Prof. A. D. WieckLehrstuhl für Angewandte FestkörperphysikRuhr-Universität BochumUniversitätsstraße 150, D-44780 Bochum, GermanyDr. M. Florian, Prof. F. JahnkeInstitute for Theoretical PhysicsUniversity of BremenP.O. Box 330 440, 28334 Bremen, GermanyC. Dangel, F. Bopp, Prof. J. FinleyWalter Schottky Institut and Physik DepartmentTechnische Universität MünchenAm Coulombwall 4, 85748 Garching, GermanyD. ReuterDepartment PhysikUniversität PaderbornWarburger Straße 100, 33098 Paderborn, GermanyKeywords: quantum dot molecule, quantum light source, determinsitic device fabrication, circular Bragg grat-ing, quantum memory
Self-organized semiconductor quantum dots represent almost ideal two-level systems, which have strong potential to applications in photonic quantumtechnologies. For instance, they can act as emitters in close-to-ideal quantum light sources. Coupled quantum dot systems with significantly increasedfunctionality are potentially of even stronger interest since they can be used to host ultra-stable singlet-triplet spin qubits for efficient spin-photoninterfaces and for deterministic photonic 2D cluster-state generation. We realize an advanced quantum dot molecule (QDM) device and demonstrateexcellent optical properties. The device includes electrically controllable QDMs based on stacked quantum dots in a pin-diode structure. The QDMsare deterministically integrated into a photonic structure with a circular Bragg grating using in-situ electron beam lithography. We measure a photonextraction efficiency of up to (23.8 ± g ( ) ( ) = ( . ± . ) · − . These metricsmake the developed QDM devices attractive building blocks for use in future photonic quantum networks using advanced nanophotonic hardware. In the field of photonic quantum technology, individual photons play a prominent role. As flying qubits, theyserve primarily as information carriers for low-loss quantum communication over long distances [1, 2, 3, 4, 5, 6].The information to be transmitted is typically encoded into the polarization of the photons [7, 8]. In the case ofquantum repeater networks, but also for future distributed quantum computers and global quantum networks, itis of central importance to temporarily store and retrieve the quantum information to be transmitted for as longas possible in the form of stationary qubits in quantum memories [9, 10]. In this context it is a great challengeto develop device concepts that simultaneously have a high level of performance in terms of single-photon gener-ation with high rate and high multiphoton suppression and that are also suitable as efficient quantum memories.The NV-center in diamond, for example, has a very long spin coherence time, which makes it ideal as a quantum a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n emory. However, these centers show high Huang-Rhys coupling factors, such that only about 3% of radiativeemission occurs via the preferred zero-phonon line transition. This is highly problematic with respect to on-demand single-photon generation with high photon flux [11].In contrast, self-assembled InGaAs and GaAs quantum dots (QDs) are excellent single-photon emitters withalmost negligible multi-photon emission probability [12], close to ideal indistinguishability [13] and photon ex-traction efficiencies exceeding 80% [14]. However, these nanostructures have relatively short spin coherencetimes, which has a deleterious effect on their possible use as quantum memories when relying on the storage ofsingle carriers [15, 16, 17]. It has recently been shown that the spin coherence times can be increased to about2 µ s by all-optical Hahn echo decoupling [18]. However, such approaches may complicate protocols due to theinfidelity of control pulses. To circumvent this problem, one can go one step further and not work with individualQDs, but rather look at potentially more powerful concepts that are based on singlet-triplet qubits in quantum dotmolecules (QDMs) - This approach promises storage times in excess of 1 ms [19]. In this concept the electricfield dependent charge separation in a QDM is used to initialize and store an exciton-spin state, before the readoutvia fast radiative recombination is triggered by a suitable external voltage pulse. In addition, coupled QDs arealso very interesting nanostructures for the generation of two-dimensional cluster states of polarization encodedphotonic qubits [20].InGaAs QDMs with high optical quality were first implemented in 2001 and optically analyzed with regardto their coupling behavior [21]. The thickness of the tunnel barrier, which separates the lower and upper QDs,was varied during growth and the resulting energy splitting between binding and anti-binding hybrid states wasstatistically investigated. Building on this, QDMs have been studied many times with regard to their coupling andcharge carrier storage properties [22, 23, 24, 25, 26]. Here, the external control of the electronic properties viaan electrical field in doped and contacted structures is decisive for these QDM implementations. For example,the important coherent tunnel-coupling between resonant electronic states of the lower and upper QDs to formhybridized molecular orbits has been be clearly demonstrated, for example via anti-crossings observed in electric-field dependent optical spectra, see e.g. [27].An important aspect in this context, and with regard to possible applications of QDMs in photonic quantumtechnology, is the efficient coupling between stationary and flying qubits. For quantum photonic applications, inaddition to precise control of the electronic states in QDMs, highly efficient spin-photon coupling must also beguaranteed to be able to map spin qubits in a QDM to the polarization of emitted photons and to transmit it to aquantum network [10]. For the purpose of photonic coupling, a QDM was recently integrated into a photonic crys-tal nanocavity [28]. Due to the high quality (Q) factor and the low mode volume of the cavity, a strongly coupledQDM-cavity system in the cavity quantum electrodynamics (cQED) regime could be demonstrated. Although thiscoupling is of interest for the implementation of spin-photon interfaces, the narrow-band high-Q character of thecavity mode prevents simultaneous coupling to the interband transition in both QDs forming the molecule.In recent years, broad-band approaches to increase photon extraction efficiency have been established, whichinclude photonic wires [29], microlenses [30] and circular Bragg gratings (CBGs) [31, 14]. In the case of the veryattractive CBG concept, they almost ideally combine ultra-high photon extraction efficiency with a moderatelyhigh and easily tunable light-matter interaction [14]. So far, approaches of this kind have only been used for indi-vidual QDs, which is partly due to the fact that they are difficult to reconcile with electrical field control, which isinevitably required for QDM quantum photonic devices.In this work we report on the development of electrically tunable single-QDM devices with strongly enhancedphoton extraction efficiency, the potential of selective optical charging [15, 17] and electrical control of spin-spininteraction in the ultra coherent singlet-triplet basis. The devices are based on vertically stacked InGaAs QDMsembedded in pin-diode structures that were grown using molecular beam epitaxy (MBE). Suitable QDMs wereselected using in-situ electron beam lithography (EBL) and deterministically integrated into photonic structures.In the underlying device design, the QDMs are electrically controlled via n- and p-contacts near the surface in a lanar design. An increased photon extraction efficiency is achieved by combining a back-side distributed Braggreflector (DBR) with an upper ring resonator, the design of which has been optimized using the finite elementmethod (FEM). The functionality of the QDM devices is studied spectroscopically in order to demonstrate notonly the increased photon extraction efficiency, but also the coupling character of the QDMs and their single pho-ton emission. Figure 1: Schematic representation of the device design (left) together with the simulated electric field distribution (right). The devicecontains a back-side DBR with 23 λ / ++ and p ++ layers for electrical contacting. A CBG consisting of a central mesa with four rings (see also Fig. 2(c)) is structured on thesurface in order to maximize the photon extraction efficiency η ext for a collecting optics with NA = 0.8 (only one ring is shown here forclarity). The numerical FEM simulation yields η ext = 24.4 % for the specified layer thicknesses and material compositions. More detailson the sample structure are given in the main text. The overarching goal of this work is to develop and manufacture electrically operated QDM devices with highcoupling efficiency for future quantum memory applications in photonic quantum technology. For this purpose,we design, fabricate and study a QDM device with intracavity contacts and a radial Bragg grating on top. Thedevice design is optimized numerically to ensure a good balance between precise electrical field control of theQDM and high photon extraction efficiency. As illustrated in Fig. 1, our design envisages a near-surface GaAspin-diode structure in the center of which the self-organized InGaAs QDMs are integrated. The device contains ap-side Al . Ga . As barrier, that serves to suppress hole tunneling. This design was chosen in order to ensure acomparatively simple electrical contact layout that does not require any nanostructured top contacts that are com-plex to fabricate and potentially enhance the optical losses. This approach allows a flexible choice of the photonicdesign for enhanced photon extraction without having to pay attention to impeding contact structures. However,certain compromises have to be made with regard to the maximum achievable photon extraction efficiency, forexample in comparison to CBG based single photon sources that are optimized solely for their optical properties.In the numerical FEM simulations performed using JCMSuite [32, 33], we considered a backside AlAs/GaAsDBR and a surface CBG with the pin-doped central region and a QDM in between. Varying the layer design andthe geometry of the CBG, we maximized the photon extraction efficiency for the experimental collection optics µ PL spectrumof the manufactured QDM-CBG device. with an NA of 0.8. The corresponding electric field distribution is presented on the right hand side of Fig. 1. Oursimulations showed that η ext increases marginally when adding more than 3 rings. Therefore, the number of ringsin the technological implementation was limited to four. Following the design specifications, the planar semiconductor heterostructure was grown using MBE on an un-doped (100) oriented GaAs wafer as described in Sec. 4.1. A sample piece of 3 mm ×
10 mm with a QD density of ( . − ) · cm − was selected. Its n- and p-doped layers were accessed near two corners of the sample by UVlithography and reactive ion etching for electrical contacting. For the n-contact, 20 nm Ni, 100 nm Au . Ge . and 250 nm Au were deposited. The p-contact consists of layers of 20 nm Ti, 50 nm Pt and 250 nm Au. Aftercontacting, a trench around the desired pin-diode area was processed by vertical etching and stopping right belowthe p-layer to isolate the diode from possible electrical short circuits at the edge of the sample. Finally, the diodestructure was mounted onto a chip carrier and electrical connections were realized by wire bonding.For the identification of promising QDMs and their on-spot integration below CBG structures we used thein-situ EBL nanotechnology concept. We used this nanophotonic technology platform previously for the fab-rication of bright microlenses [30], mesas [34] and waveguide structures [35] using proximity-corrected grayscale patterns [36] with deterministically integrated QDs. It should be noted here that functional QDMs cannot beidentified definitely without performing bias-voltage dependent optical spectroscopy to probe for tunnel-coupling-related luminescence features. Such a time-consuming investigation and the related high electron dose per site isnot compatible with the in-situ EBL process since the electron-beam sensitive resist would become overexposed µ PL intensity map showing the spectral tuning and coupling of excitonic states of QDM1. Tunnelcoupling and the existence of hybridized binding and anti-binding states of the QDM are identified by the anti-crossing behavior (indi-cated by the green and red rectangles). The associated coherent mode-splitting of ∆ h = t h = µ eV , is consistent with the 7 . J eh = µ eV , Γ = µ eV , ∆ X + = (cid:113) t h + ( J eh ) = µ eV ). Thefield strength is plotted relative to the point at which the hole ground state resonance occurs. Trion states are labeled e B e T h B h T X + , wherethe left superscripts (subscripts) denote the number of electrons (holes) in the bottom and top QD. Optical transitions are labeled by un-derlining the recombining carriers. Following the notation of Ref. [37] the QDM states are labeled e B , e T h B , h T X Q , where the left superscripts(subscripts) give the number of electrons (holes) in the bottom e B (h B ) and top e T (h T ) dots and Q is the total charge of the system. Thetransitions are indicated by underlining the recombining carriers. during the spectral and bias-dependent cathodoluminescence (CL) mapping. Consequently, in the in-situ EBLprocess we concentrated on the selection of spatially isolated emission sites with high CL intensities (cf. Fig. 2(a)with three QDM related emission spots). This together with the high QDM formation probability of ≈
80 % (seediscussion of Fig. 3) leads to a high yield of functional QDM devices. The envisaged CBG structures were numer-ically optimized for an emission wavelength of 930 nm. However, the broadband enhancement of our structuresenables also the boost of extraction efficiency in the wavelength range around 925 nm at the center of the inho-mogeneously broadened emission band of our QDMs. This way, stacked QDs (with high probability for actingas QDMs) were deterministically integrated into CBG structures as exemplarily shown in Fig. 2(b). This figureshows a CL map of the same sample area as presented in Fig. 2(a) after device processing. The deterministicintegrated QDM1 shows significantly higher CL intensity than the other two QDMs due to the CBG-enhancedphoton extraction.
After deterministic device fabrication and post-characterization performed using CL mapping, the QDM deviceswere further examined via optical spectroscopy. First, µ PL measurements were carried out under non-resonantexcitation with a 80 MHz pulsed 860 nm laser at a temperature of 4.2 K. A corresponding µ PL spectrum of thedevice (CBG with integrated QDM1) previously examined using CL is shown in Fig. 2 for zero bias voltage.The spectrum shows clear single QD features with narrow, resolution-limited linewidths of ≈
12 pm (20 µ eV). he observed emission lines can be assigned to direct and indirect excitons of the QDM as detailed below whendiscussing Fig. 3.For the intended applications in photonic quantum technology, it is crucial to verify the coherent coupling ofthe electronic states in stacked QDs and to control it externally. For this purpose, a voltage applied to the externalcontacts of the pin-diode generates an electrical field in the device along the growth direction. In this configuration,a bias-voltage dependent µ PL map shows optical transitions with large electric field dependencies (Stark shifts) aswell as a crossing and anticrossing pattern that can be clearly seen in Fig. 3 for QMD1. Emission of a direct exciton( , , X ), which arises from an electron and hole confined primarily in the same QD, shows a significantly weakershift compared to the indirect exciton ( , , X ) (please see Fig. 3 and Sec. 4.2 for the nomenclature and details ofthe underlying model). Here, electron and hole states are located in different QDs [37] and the recombinationobeys a strong linear Stark shift ∆ E = e [ d + ( h B + h T ) / ] F that depends on the barrier thickness ( d = . F is the strength of the electric field and h B ( h T ) the heights of the bottom (top) QD. Anticrossings are observedwhen direct and indirect transition energies approach each other and a hole (electron) becomes delocalized acrossboth QDs, forming bonding and antibonding molecular states. Here the width of the anticrossing splitting dependson the strength of QDM tunnel coupling. In addition to these basic signatures, Fig. 3 shows a significantly morecomplex fingerprint of the coupled QDs with an intricate X-shape pattern with several anticrossing splittings. Thisproperty is due to the existence of charged excitonic states where a strong indirect transition ( , , X + ) anticrossestwo direct transitions ( , , X + , , , X + ) [37]. In our layer design with a p-side tunnel barrier, positively chargedexcitonic states are preferably expected. Characteristic for singly charged exciton transitions is the singlet-tripletmixing with an apparent triplet transition that wiggles through the X + resonance (green box in Fig. 3) as well asthe single hole anticrossing at the hole ground state resonance (red box in Fig. 3) [38].Overall, these spectral properties of the vertically coupled QDs clearly show the existence of QDM states,which, like the charge state of the coupled system, can be controlled by the externally applied bias voltage. Itis worth noting that a statistical analysis of the emission properties shows that ≈
80 % of the devices containstacked QDs with a suitable electronic structure to form QDMs via tunnel coupling at electric fields that are smallenough to perform optical experiments. This makes the developed quantum devices very attractive candidates forspin-photon interfaces and 2D cluster-state generators.
A central objective of this work is to realize QDM devices with high photon extraction efficiency. In order to eval-uate the photon extraction efficiency of our approach 6 QDM devices with integrated CBGs (named QDM1-6)and 19 QDMs in an unstructured sample area as reference, were investigated by µ PL measurements under non-resonant (860 nm) pulsed excitation with a laser repetition rate of 80 MHz. For each QDM the measurement wascarried out at saturation pump power of the brightest excitonic line in a calibrated µ PL setup with a detectionefficiency of (4.6 ± ( . ± . ) % for a count rate of 730 kHz.The determined photon-extraction efficiencies of all 6 devices (QDM1-6) are presented in Fig. 4. All de-vices show photon-extraction efficiencies larger than 10% and a maximum value of (23.8 ± ± the reliability of the numerical simulations, whereby deviations from the expected photon-extraction efficiency tolower values in case of the CBG-QDMs are attributed to a slight lateral offset of the QDMs relative to the CBGand to structural imperfections of the CBGs. In addition to the QDM coupling behavior and the high photon extraction efficiency, non-classical light emissionis an important property envisioned for application of the developed devices in photonic quantum technology. Inparticular, it is important to demonstrate the single-photon emission character through photon auto-correlationstudies. Corresponding measurements were carried out with a Hanbury Brown and Twiss setup equipped withsuperconducting nanowire single-photon detectors (SNSDPs) under pulsed p-shell excitation at 909.8 nm with arepetition rate of 80 MHz (T = 4.5 K). To study the photon statistics of the QDM-device emission we investigateda direct exciton transition of QDM1. We applied about 80% of the saturation intensity and set a bias voltage of-0.1 V to study the emission line outside the intersection area. The corresponding normalized auto-correlationfunction is shown in Fig. 5. It clearly shows single-photon emission with a very high multi-photon suppressionassociated g ( ) ( ) = ( . ± . ) · − . It is worth noting that this value was obtained directly by integrating the g ( ) ( τ ) function in the range -6.25 ns < τ < 6.25 ns of the central peak without any background subtraction. Thevery high multi-photon suppression reflects again the high optical quality of the developed QDM devices, whichmakes them very attractive for applications in photonic quantum technology. In summary, we have developed QDM devices with excellent optical and quantum optical emission properties.The devices are based on vertically stacked self-assembled InGaAs quantum dots in a pin-diode heterostructure.Strong enhancement of the photon extraction efficiency with a maximum value of (23.8 ± g ( ) ( ) = ( . ± . ) · − makes the QDM g ( ) ( ) = ( . ± . ) · − . devices very attractive building blocks for applications in photonic quantum technology such as quantum repeaterbased quantum networks and photonic cluster state generators. The sample growth using molecular beam epitaxy starts with initial smoothing layers grown at 620°C consistingof 20 thin (2.5 nm) and annealed GaAs layers and a short period superlattice (19 × · / cm wasgrown, followed by 5 nm GaAs grown at 575°C to prevent Si segregation to subsequent layers. After a 163.6 nmGaAs buffer layer, InAs was deposited at 525°C in 11 cycles of 4 s deposition and 4 s break, of which 4 cycleswere done without rotation of the wafer. The QDs formed this way were capped with 2.7 nm GaAs at ≈ . Ga . As) and 166.5 nm ofGaAs. Next, the C-doped epitaxial gates were grown, consisting of 10 nm GaAs:C with a doping concentrationof 3 · / cm and 45 nm with 8 · / cm . Finally, the sample was capped with 313 nm GaAs for the laterstructuring of CBGs. Theoretical spectra of positively charged trions in QDM that are shown in Fig. 3 are obtained following theapproach of Ref. [38]. The X + can be effectively described by a 6 × H X + = E X + + − γ − pF t h t h t h t h t h t h − Γ − pF + J eh t h t h − Γ − pF − J eh − Γ − pF + J eh
00 0 0 0 0 − Γ − pF − J eh (1)which is represented in the basis | (cid:105) = ↑ , , ⇑⇓ X + , | (cid:105) = ↑ , ⇑⇓ , X + , | (cid:105) = ↑ , ⇓ , ⇑ X + , | (cid:105) = ↑ , ⇑ , ⇓ X + , | (cid:105) = ↑ , ⇓ , ⇓ X + , | (cid:105) = ↑ , ⇑ , ⇑ X + and spin projections are explicitly written for clarity. Here, E X + is the energy of the trion state with both holes ocated in the lower QD. t h denotes the tunnel coupling, J eh the electron-hole exchange interaction strength, p thedipole moment, F the electric field strength and Γ ( γ ) the energy that is necessary to bring a single (both) holefrom the bottom to the upper QD.Recombination of an electron-hole pair leaves behind a single hole state, which can be represented by two(spin-degenerate) basis states | (cid:105) = , , h + and | (cid:105) = , , h + : H h + = (cid:18) t h t h − pF (cid:19) (2)Transitions between the six initial trion states and the final hole states that are obtained by diagonalizing H X + and H h + , respectively, give the PL energies shown in Fig. 3 as dashed lines. Data availability
The data that support the findings of this study are available from the corresponding author upon reasonablerequest.
Acknowledgements
This work was supported by the German Federal Ministry of Education and Research (BMBF) through the ProjectQ.Link.X. J.J.F. gratefully acknowledges the German Research Foundation (DFG) for financial support via projectFI947/6-1. We further acknowledge Technichal Support by the group of Tobias Heindel funded via the BMBF-project ‘QuSecure’ (Grant No. 13N14876) within the funding program Photonic Research Germany.
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