Deterministic strain-induced arrays of quantum emitters in a two-dimensional semiconductor — TEI-tagged view

Artur BrannypersName, Santosh KumarpersName, Raphaël ProuxpersName, Brian D GerardotpersName (2017date). “Deterministic strain-induced arrays of quantum emitters in a two-dimensional semiconductor.” Nature Communicationstitle·j.

Object of study — arrays of strain-induced single-photon emitters in mono- and bi-layerterm·dom WSe2 on nanopillarsterm·key

Research question — how to position single quantum emittersterm·key deterministically for scalable quantum photonics

Contribution — near-unity emitter creation at each nanopillarterm·key with about 120 nm positioning accuracyterm·key

Full text — tagged

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Deterministic strain-induced arrays of quantum emittersterm·key in a two-dimensionalterm·dom semiconductor Abstract An outstanding challenge in quantum photonics is scalability, which requires positioning of single quantum emittersterm·key in a deterministic fashion. Site positioning progress has been made in established platforms including defects in diamond and self-assembled quantum dots, albeit often with compromised coherence and optical quality. The emergence of single quantum emittersterm·key in layered transition metal dichalcogenideterm·key semiconductors offers new opportunities to construct a scalable quantum architecture. Here, using nanoscale strain engineeringterm·key, we deterministically achieve a two-dimensionalterm·dom lattice of quantum emittersterm·key in an atomically thin semiconductor. We create point-like strain perturbations in mono- and bi-layerterm·dom WSe 2term·key which locally modify the band-gapterm·key, leading to efficient funnelling of excitons towards isolated strain-tuned quantum emittersterm·key that exhibit high-purity single photon emissionterm·key. We achieve near unity emitter creation probability and a mean positioning accuracyterm·key of 120±32 nm, which may be improved with further optimization of the nanopillarterm·key dimensions.

Nanoscale strain engineeringterm·key of the electronic band structure to create quantum confinement has long been pursued in bulk semiconductors. In particular, the exploitation of local elastic strain to laterally confine carriers has been achieved in epitaxially grown heterostructures such as quantum wells 1 2 3 or wires 4 . Unfortunately, robust strain-induced quantum confinement of carriers suitably isolated from detrimental surface states in bulk systems has not been realized due to the combination of: (i) the limited elastic strain possible before plastic deformation and (ii) small vertical strain propagation distances. Optically active two-dimensionalterm·dom (2Dterm·dom) semiconductors with a high elastic strain limit 5 offer renewed opportunities for nanoscale strain engineeringterm·key of three-dimensional quantum confinement, which we pursue here.

Our approach is to engineer nanoscale strain perturbations in atomically thin WSe 2term·key . Mono-layerterm·dom (1Lterm·dom) WSe 2term·key is a direct band-gapterm·key 2Dterm·dom semiconductor with a dark excitonic ground state 6 7 . In this system, at sufficiently low temperatures, a dense ensemble of localized excitonsterm·key emerges at lower energy than the broad (few meV) delocalized 2Dterm·dom excitons 8 9 10 . While their precise nature is not fully understood, the optically bright localized excitonsterm·key are possibly related to disorder, scattering or crystal imperfections 11 12 . Under certain conditions, such as at flake interfaces or edges 13 14 or at local strain pockets due to flake wrinkling, folding or bubbling 15 16 17 18 19 , individual localized excitonsterm·key with narrow linewidths (sub-100 micro-eV) can be isolated and shown to emit single photons 13 14 15 16 17 18 19 20 21 22 23 .

Here we exploit the correlation of spectrally and spatially isolated single quantum emittersterm·key and point-like strain perturbations 16 to engineer quantum emitterterm·key arrays in a deterministic fashion. Figure 1 shows a sketch of the concept. Owing to Van der Waals' forces a 2Dterm·dom flake conforms to the contours of a lithographically patterned nanopillarterm·key lattice ( Fig. 1a ), inducing significant elastic, point-like strain at the nanopillarterm·key lattice points 24 25 . The bi-axial strain at the nanopillarterm·key locations locally modifies the band-gapterm·key and spatially modulates the potential landscape of the 2Dterm·dom excitons ( Fig. 1b ). As a result, photogenerated excitons funnel from larger band-gapterm·key regions (in between the nanopillarsterm·key) into smaller band-gapterm·key regions (nanopillarterm·key centres) 25 26 27 . Superimposed onto the artificially induced potential energy landscape are a high density of randomly distributed localized excitonsterm·key, shown in Fig. 1b as small perturbations with quantized energy levels. In the unstrained regions (between the nanopillarsterm·key), the localized excitonsterm·key overlap in energy and cannot be distinguished. However, with the appropriate nanopillarterm·key dimensions and localized excitonterm·key density, an individual localized excitonterm·key will be strain tuned at each lattice site. The strain tuned quantum emittersterm·key at the nanopillarterm·key locations will dominate the photoluminescenceterm·mth (PLterm·mth) spectrum at low temperature and excitation power due to efficient exciton funnelling from the surrounding high band-gapterm·key regions to the single lowest energy localized excitonterm·key.

We implement this concept to achieve arrays of robust quantum emittersterm·key in both mono- and bi-layerterm·dom (2L) WSe 2term·key . In addition, by varying the aspect ratio of the lithographically patterned nanopillarterm·key arrays we are able to fully characterize the technique and optimize the positioning accuracyterm·key of the localized excitonsterm·key, ultimately achieving an accuracy of 120±32 nm with near unity yield. This precision can likely be further improved by refining the nanopillarterm·key geometry and dimensions.

Results Fabrication and structural characterization To achieve point-like strain perturbations in atomically thin WSe 2term·key , we use an all-dry transfer technique 28 to place mechanically exfoliated flakes onto a substrate with a square lattice (4 μm pitch) of dielectric nanopillarsterm·key fabricated by electron beam lithography. This technique takes advantage of Van der Waals' forces to ensure the 2Dterm·dom flake conforms to the contours of the patterned substrate and induces significant elastic strain at the locations of the nanopillarsterm·key. A WSe 2term·key flake consisting of 1Lterm·dom and 2L regions is shown in Fig. 2a,b before and after transfer, respectively. In Fig. 2b the nanopillarsterm·key are identified by the change in contrast: the dark points in the micrograph correspond to locations of the nanopillarsterm·key. The transferred flake's topography is characterized by atomic force microscopy (AFM), as shown in Fig. 2c,d . Scanning electron imaging of the same region ( Supplementary Fig. 1 ) confirms the same physical features. Figure 2dterm·dom compares the cross-section of a bare nanopillarterm·key (#0 in Fig. 2c ) with an aspect ratio (height to width) of ∼0.3 to that of a flake over a nanopillarterm·key (#7 in Fig. 2c ). Ideally, the flake conforms to the nanopillarterm·key without significant wrinkling as it does in #7. At other lattice positions, the flake does not conform closely to the substrate topography but rather stretches over the nanopillarterm·key analogously to a canvas over a tent-pole. Randomly oriented pleats emerging from nanopillarsterm·key are observed as well as ripples which in some cases extend towards neighbouring nanopillarsterm·key. These features are typical of 2Dterm·dom flakes suspended over corrugated substrates and can be further engineered 24 25 . Importantly, for the 4 μm pitch array used here, the wrinkles do not mask the point-like strain perturbation created by the nanopillarsterm·key.

A monolayer WSe 2term·dom quantum emitterterm·key array Hyperspectral confocal PLterm·mth imaging is performed to fully characterize the atomically thin WSe 2term·key flake and the effects of strain perturbations. Figure 2f shows a colour-coded spatial map of the peak intensity of the PLterm·mth spectrum (660–830 nm). The PLterm·mth peak (integrated) intensity significantly increases by a factor of 50 (2) at the locations of the nanopillarsterm·key, likely due to efficient diffusion of excitons towards the lower energy states at the strain-tuned sites 25 26 27 . The spectra from several nanopillarterm·key sites as well as typical 1Lterm·dom and 2L regions between the nanopillarsterm·key are exhibited in Fig. 2g . A broad defect band with weak intensity is observed in the homogeneous 1Lterm·dom and 2L regions (at low excitation powers the 2Dterm·dom excitons are not visible). On the other hand, for each spectrum obtained at a location of a nanopillarterm·key (including nanopillarterm·key #1 in the 2L region), a few discrete narrow linewidth (<200 μeV) peaks with high intensity are typically observed. Each of these peaks signify emission from single quantum emittersterm·key 13 14 15 16 17 18 20 21 22 . A second-order correlation measurement is presented in Fig. 2e , where a fit to the data yields g (2) (0)=0.07±0.04 with a decay time of τ =2.8±0.2 ns. This demonstrates photon antibunching and the quantum nature of the 1Lterm·dom discrete lines.

A bilayerterm·dom WSe 2term·key quantum emitterterm·key array To demonstrate the universality of nanoscale strain engineeringterm·key to generate strain-induced quantum emittersterm·key in atomically thin semiconductors, we create an array of pure single photon emitters in 2L WSe 2term·key . Bi-layerterm·dom WSe 2term·key is an intriguing host for quantum emittersterm·key as it offers an additional pseudo-spin based on the layer degree of freedom 29 . While 2L WSe 2term·key is an intrinsically indirect band-gapterm·key semiconductor, the indirect and direct transitions are nearly degenerate and under tensile strain the band structure can be modified such that the direct transition becomes preferred 30 . We exfoliate a flake with a large 2L region (see Fig. 3a ) and transfer it to an array of nanopillarsterm·key (with h:w ∼0.3) on an Si substrate ( Fig. 3b ). Once again, we observe a significant increase of 150 × (3 × ) in the peak (integrated) PL intensityterm·mth at the nanopillarterm·key sites ( Fig. 3c ), evidencing the transition to a direct electronic gap and the exciton funnel effect due to local strain. We note there is also a small 1Lterm·dom and a large 3L region of the flake in Fig. 3b that cover nanopillarterm·key sites. While the 1Lterm·dom region shows similar properties to the flake in Fig. 2 , the 3L remains dark in PLterm·mth. Crucially, bright narrow-linewidth spectral lines ( Fig. 3h ) are again observed at the strain-induced sites. Figure 3d shows a high-resolution spatial map of six nanopillarsterm·key in the centre of the array superimposed with the locations of the quantum emittersterm·key in Fig. 3h . A wavelength histogram (2 nm binning) of all strain-induced emitters (53 in total) created in the 2L WSe 2term·key array is shown in Fig. 3e . The histogram shows that emitters span a wavelength region from 775 to 835 nm. A Gaussian fit to the data is used to quantify the inhomogeneous distribution of the emitters, yielding 33 meV full width at half maximum (FWHM). Notably, several emitters at very similar wavelengths are observed (for example, in Fig. 3h peaks at 793 nm in spectra 2 and 5; peaks at 785 nm in spectra 4 and 6). The second-order correlations from each individual peak measured exhibit highly pure single photon emissionterm·key, for example, the single peak at λ =801.08 nm from nanopillarterm·key #1 in Fig. 2g shows g (2) (0)=0.03±0.02 with a decay time of τ =4.8±0.1 ns ( Fig. 3f ). For spectra recorded over a 20-h period, this emitter does not blink. Figure 3g shows a histogram of the spectral jitter recorded over 20 h (using 3 s time-bin, as shown in Supplementary Fig. 2 ) from the 2L emitter at nanopillarterm·key #1. The histogram is fit by a Gaussian distribution with 131 μeV FWHM. Further, these quantum emitterterm·key arrays are optically stable and robust, surviving multiple sample cooling and heating cycles.

Optimization of strain-induced arrays of quantum emittersterm·key Having established a technique to successfully create robust strain-induced quantum emittersterm·key, we seek to optimize the process. We tailor the local elastic strain by varying the height to change the aspect ratio of five rows of nanopillarsterm·key, from h:w 0.15 to 0.59, as shown in the scanning electron micrograph in Fig. 4a . Further information on these nanopillarsterm·key is provided in Supplementary Fig. 3 . Precise measurements of the pillar size are made by AFM which confirms uniform pillar dimensions within each row. Their cross-sections are displayed in Fig. 4c . Figure 4b shows an optical micrograph of a large (∼100 × 25 μm) 1Lterm·dom WSe 2term·key flake covering 101 nanopillarsterm·key in the array. Here the pillar locations are identified by the bright points in the micrograph. Also visible in Fig. 4b in some cases for the high aspect ratio nanopillarsterm·key (for example, Row 5, Columns 3–5) is a small ring surrounding the pillar. This feature is not observed for any of the low aspect ratio nanopillarsterm·key in Rows 1 and 2 or with the nanopillarsterm·key used in Figs 2 and 3 . Figure 4d,e shows a spatial map of the integrated and peak intensities (logarithmic scale) of the entire PLterm·mth spectrum (690–850 nm) from Columns 2 to 5 (as labelled in Fig. 4b ). Mapping the peak intensity reveals the locations of the intense, narrow linewidth peaks that signify quantum light emission. PLterm·mth maps of the entire flake with several spectra are shown in Supplementary Fig. 4 . A mixture of peaks with large (700–900 μeV) fine-structure splittings (for example, Supplementary Fig. 5 ) and single linearly polarized peaks are observed, as reported previously 18 . The PL intensityterm·mth at the nanopillarsterm·key increases with increasing nanopillar aspect ratioterm·mth, as expected for the diffusion of excitons towards the local regions with strain-tuned band-gapsterm·key. In the cases for the high aspect ratio nanopillarsterm·key where the ring surrounding the pillar is visible in Fig. 4b (for example, Row 5, Columns 3–5), low intensity emission at the nanopillarterm·key centre is surrounded by a ring of intense PLterm·mth. We believe this effect is caused by the flake being pierced during the transfer process for some high aspect ratio nanopillarsterm·key. Alternatively, the flake could conform quite closely to the nanopillarterm·key topography and sit flat at the top and then bend at the top edge of the nanopillarterm·key, leading to high strain at the circumference.

Statistics of all emitters identified (285 in total) in the entire 1Lterm·dom WSe 2term·key flake over the 101 nanopillarsterm·key is shown in Fig. 4f,g . Here we do not account for the possibility that multiple emission lines arise from a single emitter (for example, due to different charge states or bi-excitons 23 ) and assume that each narrow linewidth peak in a spectrum is an individual quantum emitterterm·key. Second-order correlation measurements on numerous narrow linewidth peaks yield g (2) (0)<0.5, unambiguously demonstrating the quantum nature of the emission. Figure 4f shows the statistics for the number of emitters per pillar. While distinct emitters are sometimes found at the nanopillarterm·key sites in Row 1 (for example, the spectra in Supplementary Fig. 4c ), they tend to be difficult to distinguish from the broad background. With the increased aspect ratio of the nanopillarsterm·key in Row 2, one or two distinct bright emitters are found with a yield of 85% (17 of 20 nanopillarsterm·key contain pure single emitters). Rows 3 and 4 have near unity yields: 96% (45 of 47 nanopillarsterm·key yield at least 1 quantum emitterterm·key).

Figure 4g shows the emitter wavelength histogram. While the overall energy distribution of the single emitters is broad (spanning ∼200 meV), all emitters emit at lower energy than the bright 2Dterm·dom exciton peak in WSe 2term·key (∼1.74 eV). The emitter wavelength histogram is also post-selected for emitter brightness (the peak intensity at ∼0.8 saturation power) for this flake. Fitting a Gaussian distribution to the histogram gives 73 meV FWHM, more than twice as large as the 2L emitters.

Positioning accuracyterm·key To determine the positioning accuracyterm·key of the strain-induced quantum emittersterm·key we map the emitter locations relative to the centre of the nanopillarterm·key. While the individual emitters are resolved by the hyperspectral spatial maps (see Figs 4e and 5c ) the precise position of the nanopillarsterm·key is not known a priori but can be extracted using spectral weighted averaging (WA λ ), as illustrated in Fig. 5 . WA λ accounts for the global shift in the PLterm·mth spectrum due to the strain, as can be observed in two representative spectra from the centre of the nanopillarterm·key and the nominally unstrained region between the nanopillarsterm·key shown in Fig. 5a . At each spatial location, we quantify this spectral shift using the formula: The outcome yields smooth, clean contour maps, as shown in Fig. 5b for nanopillarsterm·key from Column 5 and Rows 2–5. Assuming the strain is at its highest in the middle of the nanopillarterm·key, we fit Gaussian curves to the WA λ cross-sections to determine the centre of each nanopillarterm·key with high accuracy. Further, a rough estimate of the strain can be based on the spectral shift 30 . For example, a maximum change in WA λ =30.8 meV (13.3 nm) for nanopillarterm·key 4 corresponds to 0.60% strain. This value is three times larger than that previously reported for local strain pockets 16 . Finally, in order to obtain the emitter displacement, we distill the locations of the single quantum emittersterm·key from the peak intensity maps (for example, as in Fig. 5c ) and overlap them with the centres of the nanopillarsterm·key determined by the Gaussian fits to WA λ , as shown in Fig. 5d for Column 5. To assess the accuracy of emitter positioning we combine emitter displacements from Columns 2 to 5 and arrive with distributions as displayed in Fig. 5e . Here the red rings represent the mean distance and the ring thickness corresponds to one standard deviation.

We observe that when the flake is pierced or bends over the circular edge of a flat-topped nanopillarterm·key, the emitters are found at the circumference of the nanopillarterm·key. On the other hand, the quantum emittersterm·key are created in the centre of the nanopillarsterm·key for flakes that conform to the substrate topography to create a point-like strain perturbation. In particular, the statistics of the positioning accuracyterm·key of the emitters in Row 2 reveals high precision: =120±32 nm, where σ D is the average displacement of the emitter from the nanopillarterm·key centre. Displacement statistics of the emitters in Rows 3–5 are: =262±46 nm, =476±85 nm and =521±64 nm. Row 1 did not yield sufficient emitter numbers for useful statistics. In the best case (Column 5, Row 2), the displacement is 30 nm.

Discussion Layered transition metal dichalcogenideterm·key semiconductors are attractive hosts for quantum emittersterm·key due to the unique valley degree of freedom and strong spin-orbit coupling. Using nanoscale elastic strain engineeringterm·key, we have achieved local modification of the electronic and optical properties to deterministically generate robust quantum emittersterm·key in this emerging quantum photonic platform. The straightforward fabrication procedure presented here is scalable and likely to be applicable to other 2Dterm·dom materials. We obtain the best results, including near unity success in generating an emitter at each nanopillarterm·key and a positioning accuracyterm·key of 120 nm, using nanopillarsterm·key with 0.3 aspect ratio. Further improvement in the positioning accuracyterm·key of single emitters is likely possible with smaller diameter nanopillarsterm·key that maintain an aspect ratio similar to 0.3. Notably, we observe negligible background signal at the base of the discrete spectral lines, enabling high purity single photon emissionterm·key in both 1Lterm·dom and 2L WSe 2term·key . Compared to mono-layer WSe 2term·dom , the bi-layerterm·dom appears additionally attractive as a host for single excitons due to a narrower inhomogeneous distribution and the potential for spin-layer locking. These results open a path to deterministically embed 2Dterm·dom quantum emittersterm·key in electronic devices for further investigation of their spin, electronic and optical properties or to couple to cavity or waveguide modes for cavity quantum electrodynamics experimentsterm·mth and integrated quantum photonics applications 31 32 .

Methods Sample fabrication We fabricate the nanopillarsterm·key out of negative resist (AZ 2070 from MicroChemicals) using electron beam lithography. First the resist was spin-coated (∼200 nm thickness) onto the Si substrate (for the samples in Figs 1 and 2 ) or an Si substrate with 285 nm SiO 2 (for the sample in Fig. 3 ) and then exposed using electron beam lithography (Raith Pioneer). For Samples 1 and 2 a constant dose was used for all nanopillarsterm·key. For Sample 3 the dose was varied but the pillar size was kept constant. The nanopillarsterm·key were then developed (AZ 726 MIF Developer from Electronic Materials) and structurally characterized by SEM and AFM. Mechanical exfoliation was used to obtain mono- or bi-layerterm·dom WSe 2term·key flakes which are identified by optical microscopy. The chosen flakes were then transferred to the nanopillarsterm·key using the all-dry viscoelastic stamping procedure outlined in ref. 28 . Each flake's thickness is then confirmed by low-temperature PLterm·mth.

Low-temperature confocal photoluminescenceterm·mth A home-made confocal microscope with an objective lens (NA of 0.82 yielding a diffraction limited focus of ∼560 nm at λ =750 nm) is used to spatially map the PLterm·mth from the sample which is placed on automated nanopositioners in a T =3.5 K closed-cycle cryostat. All spectra were acquired with a 0.5 m focal length spectrometer and a nitrogen-cooled charge-coupled device with a measured spectral resolution of ∼75 μeV at λ =750 nm for an 1,800 l mm −1 grating. A fibre-based Hanbury-Brown and Twiss interferometer was used for second-order correlation measurements, and photon counting was performed using Si APDs.

Data availability The data that support the findings of this study are available from the corresponding author on request.

Additional information How to cite this article: BrannypersName, A. et al . Deterministic strain-induced arrays of quantum emittersterm·key in a two-dimensionalterm·dom semiconductor. Nat. Commun. 8, 15053 doi: 10.1038/ncomms15053 (2017).

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Supplementary Material Supplementary Figures and Supplementary Notes