Planarized spatially-regular arrays of spectrally uniform single quantum dots as on-chip single photon sources for quantum optical circuits

Realization of on-chip scalable quantum optical circuits (QOCs) that allow controlled photon generation and interference to create reconfigurable unitary operations on a photon state with a fast (ns to ps) time scale has been a long-sought goal in the field of quantum information processing.^1–4 A fundamental obstacle has been the absence of a starting on-chip integrable platform of solid state single photon sources (SPSs) that are in regular arrays and spectrally sufficiently uniform. Consequently, exploration of QOCs has been mostly limited to the use of a laser beam to mimic a non-deterministic SPS for quantum state preparation^5,6 and off-chip sources of heralded photon pairs^7–9 with only a few studies using on-chip probabilistic sources using four-wave mixing.^10,11 Epitaxially grown semiconductor quantum dots (QDs)^2,12 and implanted defect-levels^13,14 have been demonstrated to possess many qualities suitable for solid state SPSs. In principle, both are integrable with optical elements for controlling the SPS emission rate and direction and subsequent manipulation of the emitted photons in an on-chip (i.e., scalable horizontally) architecture that enables controlled interference and entanglement—two phenomena that underpin quantum information processing. However, controlling simultaneously the spatial and spectral uniformity adequately for either the dominantly explored semiconductor QD—the 3D island QD—or defect-based SPSs is still a great challenge.^2,12,15 In this paper, we report on (a) the realization of a new class of semiconductor mesa top single quantum dots (MTSQDs)^16–18 in arrays whose single photon emission purity is ∼99.5% at 18 K and as-grown spectral uniformity is < 2 nm across a 5 × 8 array distributed over 1000 µm² and (b) the demonstration of an approach to embed MTSQD arrays through the overgrowth of a morphology planarizing layer, thus realizing the long-sought platform of planarized ordered uniform arrays of SPSs. Together, this opens the pathway to the fabrication of on-chip integrated QOCs by integrating these MTSQDs with either conventional 2D photonic crystal^2,3,19 or our newly proposed approach of using Mie resonance in dielectric building blocks^12,20,21 that can be used for a large range of applications in quantum information science such as solid-state simulation,²² boson sampling,²³ quantum networking,¹ and quantum sensing.¹² 

Figure 1(a) shows a SEM image of a part of a 5 × 8 array of pyramids containing a single quantum dot (SQD) near their apexes.¹⁶ This unique class of SQD arrays in which the QD location is controllable to within a few nm is synthesized using size-reducing epitaxial growth on nanomesas. The edge orientations of nanomesas were chosen so that the accompanying surface-curvature stress-gradients direct preferentially the migration of adatoms^16,18,24 symmetrically from the sidewalls to the mesa top during growth. This ensures spatially selective growth on mesa tops. The approach dubbed substrate-encoded size-reducing epitaxy (SESRE)^16,18,25 enables accommodation of QDs forming material combinations with significant lattice mismatch owing to the strain relaxation at the “free” surfaces of the laterally nanoscale mesas, unlike growth in arrays of pits that restrict the material combination to nearly lattice matched.²⁶ Following such an approach, we previously reported arrays of GaAs/In_0.5Ga_0.5As/GaAs SQDs on the mesa top (MTSQDs) exhibiting a single photon emission purity of ∼99% [g⁽²⁾(0) < 0.02].¹⁷ These InGaAs MTSQDs were centered around 930 nm and have a spectral uniformity (σ_λ) of 8 nm—a factor of 5 improvement compared to the typically explored lattice-mismatch driven self-assembled quantum dots (SAQDs)—with several pairs of as-grown MTSQDs emitting within 300 µeV²¹ amenable to on-chip tuning technology^12,27,28 to bring them on resonance for realizing photon interference and entanglement. These MTSQDs exhibit a fine structure splitting (FSS) of < 10 µeV,¹⁷ comparable with the SAQDs and droplet QDs,^2,12,29,30 thus making such realization feasible.

Therefore, the logical next steps are to (1) further improve on the characteristics of the MTSQDs in terms of spectral uniformity and (2) find suitable protocols that enable both the size-reducing growth to form MTSQDs [Fig. 1(a)] and subsequently the creation of a morphology planarizing overlayer with continued growth. Here, we report advances on both these fronts as milestones toward assessing the viability of this class of QDs as an on-chip SPS platform needed to realize the long-sought goal of nanophotonic QOCs.

Our previously reported GaAs/In_0.5Ga_0.5As/GaAs MTSQDs, though exhibiting a 5× better spectral uniformity over typical SAQDs, are limited in spectral uniformity largely due to the alloy composition fluctuation induced confining potential fluctuations for each MTSQD in the 5 × 8 array. One obvious way to improve on the spectral uniformity is to synthesize binary InAs MTSQDs, avoiding the inevitable composition fluctuation of alloys. In the SESRE approach, we have established^26,31 that the free surfaces of the nanomesa sidewalls enable relaxation of high lattice-mismatch strain such as 7% for InAs on GaAs(001) on mesa top openings <50 nm for thickness up to 12 ML without the energetic need for forming strain-relieving surface buckling (i.e., 3D islanding) or defects following capping with GaAs.³¹ Indeed, this provides GaAs/InAs/GaAs MTSQDs with flat morphology.^26,31 Moreover, the use of binary InAs as the QD material naturally extends the emission of the MTSQD to 1120 nm,²⁶ toward telecommunication wavelengths of 1300 nm and potentially up to 1550 nm. We report below on the emission uniformity and single photon characteristics of a 5 × 8 array of 12 ML InAs MTSQDs.

The 5 × 8 array of InAs MTSQDs is grown on starting nanomesas of a lateral size of ∼125 nm and depth of ∼565 nm. A 300 monolayer (ML) GaAs buffer layer with a few monolayer thin AlGaAs interspersed is grown at T = 600 °C (as measured by pyrometer), P_As4 = 2.5 × 10⁻⁶ Torr, and a Ga delivery time of τ_Ga = 4 sec/ML (growth rate of 0.25 ML/s) to (i) recover from any residual contamination remaining after deoxidation and (ii) control the mesa top size reduction to bring it to the desired size of <30 nm for the growth of a single QD on the mesa top. InAs is grown at T = 480 °C, P_As4 = 2.5 × 10⁻⁶ Torr, and an In delivery time of τ_In = 4 s/ML and capped by GaAs to create 3D confinement. Details of the substrate patterning and grown structure can be found in Ref. 18. The InAs QDs formed near the apex of the size-reduced nanomesa are estimated to have a base length of ∼10 to 15 nm and height of ∼5 nm with {101} side walls. Photoluminescence (PL) from each individual MTSQD in the 5 × 8 array was studied using a home-built micro-PL setup with excitation laser at 640 nm and excitation spot focused to 1.25 µm for excitation of individual MTSQDs. The emission from the QD is collected using a 40×, NA0.6 objective lens, spectrally filtered with a spectrometer and detected with a superconducting nanowire detector. The setup is similar to that previously reported^16,17 except that the Si avalanche photodiode detectors are replaced by superconducting nanowire detectors for good quantum efficiency at InAs QD emitting wavelength near 1120 nm. Out of the 37 mesa pixels present in the 5 × 8 array, five InAs MTSQDs are non-emitting and the rest 32 are emitting. The measured emission wavelengths from the InAs MTSQDs in the 5 × 8 array are shown as a color coded image in Fig. 1(b) and as a histogram in Fig. 1(c). A typical PL from an InAs MTSQD in the array is shown in Fig. 1(c) with emission at 1118 nm and an instrument limited linewidth of 0.2 nm (280 µeV). A strikingly narrow spread of 1.8 nm centered at 1120 nm over an area of ∼1000 µm² is found. Equally remarkably, there are 49 different pairs of QDs emitting within 0.2 nm (instrument resolution limit) and two sets of 6–7 QDs emitting within 0.2 nm [like-color circles in Fig. 1(b)]. Given the small difference in range of ∼1 nm, these QDs are within the demonstrated on-chip tuning range to be brought into resonance with each other through the Stark effect^12,27 or local thermal heating.^12,28

The observed highly uniform emission across the entire array is significant improvement on the typically reported 3D island QDs^2,32 and the droplet QDs.³³ It is, to the best of our knowledge, the narrowest spectral emission reported for ordered QD arrays.^34–36 

The potential of such highly uniform InAs MTSQDs as near-infrared (NIR) SPSs is confirmed by the second-order correlation function of photon emission statistics. The photoluminescence from the InAs MTSQD after spectral filtering was directed into a Hanbury Brown and Twiss (HBT) setup and subsequently detected with two superconducting nanowire detectors at the transmitted and reflected ports of the beam splitter. The measured coincidence count histogram is shown in Fig. 1(e). The data at 18 K reveal g⁽²⁾(0) < 0.01, indicating the single photon emission purity to be >99.5%. The g⁽²⁾(0) value is extracted by calculating the ratio of peak areas under zero peak vs that of non-zero peaks where the peak areas are obtained from a Gaussian fitting. The extracted g⁽²⁾(0) value of less than 0.01 is independent of the type of peak fitting used and is consistent with the g⁽²⁾(0) value of ∼0.006 extracted from calculation based on theory shown as the red curve in Fig. 1(e).^37,38 These spectrally highly uniform MTSQDs produce highly pure single photon emission. This testifies to the potential of the SESRE approach for generating the critically needed spatially ordered spectrally uniform SPS arrays. To move in the direction of QOC requires, however, planarizing the morphology through appropriate growth of an overlayer for the subsequent processing of light manipulating elements. This is reported next.

For the planarization studies, we employed 3 × 5 arrays of starting square nanomesas fabricated on GaAs(001) substrates using electron beam lithography and wet chemical etching with mesa edges along the $⟨100⟩$ direction and lateral sizes in the range of 50 nm–600 nm. Two different sidewall configurations were employed: (1) vertical sidewalls made of {100} planes^16–18 to a depth of ∼185 nm and (2) sidewalls of vertical {100} planes to a depth of ∼65 nm and contiguous {101} planes to an equivalent depth of ∼65 nm [see Fig. 2(a)]. We dub the latter as mesas with pedestal. The range of the lateral size examined in the same growth enables a study of the evolution of the planarizing overlayer growth as a function of the sidewall configuration and depth without the ambiguity of the growth conditions for all starting nanomesa sizes. The QD layer is 4.25 ML of In_0.5Ga_0.5As for both the vertical mesa and the pedestal mesa shapes and is chosen also as a check on the reproducibility of the MTSQDs grown on vertical wall mesas reported earlier.^16,18 As a proof of concept demonstration of the protocol suitable for planarization overlayer growth on mesas, the In composition—zero to hundred percent—of the few MLs of QD material is not the controlling factor—the mesa shape is. To maintain reproducibility, the growth condition is guided by the RHEED (reflection high energy electron diffraction) determined surface phase diagram of the GaAs(001) surface accessed by aligning the electron beam to the mutually orthogonal L-shaped unpatterned region around the patterned region containing mesas of various sizes. For the findings reported below, a total of 389 ML GaAs with three intervening 80 ML AlAs layers are grown at a pyrometer temperature of T_pryo ∼ 609 °C and As₄ flux of P_As4 = 1.5 × 10⁻⁶ Torr for size-reduction of the mesa top. The substrate temperature is then lowered to 520 °C for the deposition of 4.25 ML In_0.5Ga_0.5As to form MTSQDs. Indium flux relief is introduced before the In_0.5Ga_0.5As MTSQD growth to avoid unintended overshoot of the indium concentration. After the In_0.5Ga_0.5As MTSQD growth, a total of 734 ML GaAs with five intervening 40 ML AlAs layers are grown at a pyrometer temperature of T_pryo ∼ 609 °C and As₄ flux of P_As4 = 1.5 × 10⁻⁶ Torr to cap the QDs and also to planarize the QD bearing mesas.

For the case of growth on starting mesas with pedestal shown in Fig. 2(a), Figs. 2(b)–2(d) show SEM and Figs. 2(e)–2(g) the corresponding AFM images of the final (following the overlayer growth) surface morphology over three mesas of decreasing starting lateral size (L_M) of 280 nm, 160 nm, and 60 nm.

The various stages of planarization for the same amount of overlayer material delivered (∼210 nm) under identical growth conditions are evident. Mesas of ∼280 nm starting size are not completely planarized [Figs. 2(b) and 2(e)] and reveal an expected ridge type remnant structure with a height of ∼20 nm and length of 1 μm along the [1 −1 0] direction. With decreasing starting mesa size, the height of the ridge reduces down to <10 nm, as shown in Figs. 2(d) and 2(g), indicating the reducing angle of the side facet of the ridge structure reaching near zero toward planarization. By contrast, for the straight vertical sidewall mesa shapes, the overlayer profile revealed evolution passing through an initial stage of moat-like pits around the base of the mesas that vanish for decreasing starting lateral sizes less than ∼300 nm. Thus, through choice and control of the starting mesa profile that includes appropriate pedestal, depth, and growth conditions, we have demonstrated achieving the required two growth objectives of (1) initial size-reducing epitaxy for the formation of the MTSQD near the top of the predetermined nanomesa lateral size and sidewall profile [Fig. 1(a)] and (2) subsequent growth of a morphology planarizing overlayer to bury the synthesized MTSQD array in a matrix. Such planarized structures provide the starting platform for subsequent integration of light manipulating structures around each MTSQD, thus enabling fabrication of optical circuits.

Next, we report the optical behavior of the 3 × 5 array of 4.25 ML In_0.5Ga_0.5As alloy MTSQDs with the 734 ML planarizing overlayer. Photoluminescence (PL) from each individual MTSQD in the 3 × 5 array was studied using the home-built micro-PL setup described above with excitation laser at 640 nm and excitation spot focused to 1.25 µm for excitation of individual MTSQDs. The emission from the QD is collected using a 40×, NA0.6 objective lens, spectrally filtered with a high resolution spectrometer (resolution of 15 µeV) and detected with a superconducting nanowire detector.

Out of the 15 MTSQDs in the 3 × 5 array, three MTSQDs are non-emitting and the rest 12 MTSQDs emit efficiently. Figure 3(a) shows the PL spectrum of a representative MTSQD. The QD shows emission at 892.82 nm with an intrinsic linewidth of 47 µeV measured with an instrument resolution of 15 µeV. The color-coded image of the emission wavelength of all 12 MTSQDs and the histogram of the emission are shown, respectively, in Figs. 3(b) and 3(c). The 12 MTSQDs show emission centered at 880 nm with a standard deviation (σ_λ) of 5 nm. Note that two pairs of QDs in the 12 QDs emit within 0.2 nm (280 µeV). The observed planarized InGaAs MTSQD emission wavelength is blue shifted compared to the emission wavelength for typically studied non-planarized In_0.5Ga_0.5As MTSQDs.^16–18 To check the blue shift that we anticipated as arising from the annealing experienced by the QDs during the continued growth of the planarizing overlayer, we grew a reference non-planarized 4.25 ML In_0.5Ga_0.5As MTSQD 5 × 8 array on mesas of a similar height of ∼180 nm under identical conditions and only the 220 ML (∼62 nm) GaAs to cap the In_0.5Ga_0.5As QD. The optical behavior of this reference sample was examined while mounted side by side in the same cryostat in our micro-PL setup noted above. Out of the 40 MTSQDs, 3 QDs are non-emitting and the rest 37 are emitting. Figure 3(d) shows the PL spectrum of a representative of this non-planarized 4.25 ML In_0.5Ga_0.5As MTSQD exhibiting emission around 917 nm with an intrinsic linewidth of 35 µeV. The color-coded image of the emission wavelength of all 37 MTSQDs and the histogram of the emission are shown, respectively, in Figs. 3(e) and 3(f), revealing the emission centered around ∼912 nm with a standard deviation (σ_λ) of 6 nm and 5 pairs of QDs [marked by like-color circles in Fig. 3(e)] emitting within 0.2 nm (280 µeV). This behavior is essentially the same as our previously grown 5 × 8 array reported in Ref. 16 and is a testimony to controlled reproducibility of the MTSQDs. Compared with this reference sample, the observed blue shift to 880 nm and a slightly improved uniformity of 5 nm in the planarized MTSQDs are thus confirmed to be caused by the intermixing of In and Ga during the growth of the additional 514 ML (∼147 nm) of GaAs for planarization. The resulting effectively reduced concentration of indium is consistent with the observed blue shift of the wavelength and the slightly improved ensemble uniformity while maintaining the intrinsic linewidth of ∼40 µeV.

The single photon emission behavior of the planarized 4.25 ML In_0.5Ga_0.5As MTSQDs is examined by studying the second-order intensity correlation function using our Hanbury Brown and Twiss (HBT) setup. Figure 4(a) shows the measured coincidence count histogram of one representative planarized MTSQD. The data collected at 18 K reveal g⁽²⁾(0) ∼ 0.04, indicating a single photon emission purity around 98%. In comparison, the reference non-planarized 4.25 ML In_0.5Ga_0.5As MTSQD shows single photon emission purity around 99.5% [g⁽²⁾(0) ∼ 0.01]. Overall, the GaAs planarizing layer growth does not compromise the MTSQD spectral uniformity as well as single photon emission purity. It only blue shifts the emission wavelength of the MTSQD due to intermixing of In and Ga. One can further control and reduce the In and Ga intermixing by growing the GaAs planarizing layer at a low temperature (<400 °C) using migration enhanced epitaxy.^39,40 The planarization growth protocol demonstrated here is driven by the mesa-shape, i.e., the pedestal region surface curvature and attendant stress gradients following mesa-top pinch off. The protocol is thus robust against a few MLs of InGaAs (with In content varying from 50% down to zero or up to hundred) interjected in an overall growth of over 1000 MLs of GaAs on GaAs for the typical depths of these starting mesas.

The planarized ordered spectrally uniform single photon source arrays provide the long-sought platform for deterministic on-chip integration with light manipulating structures to create quantum optical circuits. Further work on integrating planarized InAs MTSQD single photon source arrays with light manipulating structures is underway. In particular, to examine the photon indistinguishability characteristics of these MTSQDs, a local enhancement of the spontaneous emission rate by a factor of about six is needed to make the well-established typical spontaneous emission lifetime of 0.8 ns to 1 ns shorter than the typical dephasing time of 200 ps in the InGaAs class of quantum dots.^2,3,12 Efforts to create arrays of appropriate MTSQDs for such studies are underway.

Employing a unique class of semiconductor quantum dots, the mesa-top single quantum dots (MTSQDs), in this paper, we have demonstrated reaching the two needed milestones toward realizing the basic platform of planarized spatially ordered and spectrally uniform single photon sources: First, we demonstrated the realization of a 5 × 8 array of binary InAs MTSQDs with a remarkable emission spectral uniformity of 1.8 nm over an area of ∼1000 µm² with emission centered at 1120 nm. Such highly uniform as-grown MTSQDs with a large number (up to 6–7) emitting within 0.2 nm (280 µeV) are also found to be highly pure single photon emitters with >99.5% purity at 18 K revealed by the measured g⁽²⁾(0) < 0.01. Second, we have examined the role of the starting mesa profile in controlling the growth front profile evolution at various stages of epitaxial growth and identified mesas with a pedestal profile as well-suited for morphology planarizing growth following the formation of the mesa top SQD. Such planarized In_0.5Ga_0.5As MTSQD arrays emit at around 880 nm, blue shifted due to the intermixing of In and Ga induced by the thermal annealing the QD experiences during the GaAs planarizing layer growth. Under the employed growth conditions, the planarized array maintains highly pure single photon emission with purity around 98% at 18 K [g⁽²⁾(0) ∼ 0.04] and high uniformity (∼5 nm). Importantly, there are pairs of QDs emitting within 0.2 nm (280 µeV). Such MTSQDs can be on-chip tuned, using the Stark effect^12,27 or local thermal heating,^12,28 to be resonant with each other (i.e., energy difference smaller than the intrinsic linewidth) for realizing indistinguishable single photons from different QDs.

With the two advances demonstrated here showing the path to the long-sought starting platform of planarized high-quality ordered arrays of single photon emitting SQDs, one can finally embark upon deterministic on-chip integration of the single photon source SQDs with light manipulating structures in a horizontal architecture. To this end, one can follow two approaches to on-chip incorporation of co-designed light manipulation structures—the 2D photonic crystal^41,42 or the newly proposed approach of exploiting the collective Mie-like resonance of all-dielectric metastructures.^20,21 Further work on such integration is underway.

In closing, we note that although the specific results presented here are for material combinations within the AlGaInAs system, the approach to MTSQD array fabrication and its subsequent planarization demonstrated here are general and applicable to a wide range of material combinations. Engineering the MTSQD material combination (III–V arsenides, nitrides, antimonides, etc.), size, and shape, the emission wavelength can be tailored not only for fiber-based optical communication at 1300 nm and 1550 nm but also over the wide range from long- to mid- to near-infrared to visible and ultraviolet regimes for applications ranging from quantum communication, sensing, and metrology, to environmental monitoring and health.

This work was supported by the U.S. Army Research Office (ARO) (Grant No. W911NF-19-1-0025) and the Air Force Office of Scientific Research (AFOSR) (Grant No. FA9550-17-01-0353).

The data that support the findings of this study are available within the article.