Nanopatterned substrate preparation and characterization

To create large-scale QE arrays in LMs, we place the active material on patterned structures fabricated on the substrate in order to create spatially localized physical disturbances to the otherwise flat LM flakes. To this end, we first pattern arrays of nanopillars of different heights, ranging from 60 to 190 nm, on silica substrates using electron beam lithography. Figure 1a shows a scanning electron microscope image of one such substrate of 130 nm nanopillar height. We place layers of WSe 2 and WS 2 on the nanopillars as follows. Bulk WSe 2 and WS 2 crystals are characterized before exfoliation as described in ref. 22. These are then exfoliated on a polydimethylsiloxane layer by micromechanical cleavage7,25. Single-layer (1L) samples are identified first by optical contrast26, and the selected 1L-WSe 2 and 1L-WS 2 flakes are then placed onto the patterned nanopillar substrate via an all-dry viscoelastic transfer technique due to their higher adhesion to SiO 2 (refs 7, 19, 27), as schematically shown in Fig. 1b. After exfoliation and transfer, the 1L-WSe 2 and 1L-WS 2 flakes are characterized by Raman spectroscopy28,29, photoluminescence (PL)30 and atomic force microscopy (AFM), confirming the transfer and that the process does not damage the samples (see Supplementary Fig. 1 and Supplementary Note 1 for the corresponding spectra and discussion). Figure 1c is an AFM scan of a 1L-WSe 2 flake over a single nanopillar. The bottom panel of Fig. 1c plots the height profile of the 1L-WSe 2 flake taken along the dashed pink line. This reveals how the flake (solid pink line) tents over the nanopillar. The blue-shaded area corresponds to the measured profile of a bare nanopillar. Figure 1d is a dark-field optical microscopy image of part of a 43,000 μm2 1L-WSe 2 flake on a substrate patterned with a 4-μm-spaced nanopillar array with nominal height of 130 nm. The regularly spaced bright spots correspond to nanopillar sites. We see locations providing brighter scattering (two examples are encircled in pink) and others showing fainter intensity (two examples are encircled in blue). By correlating with AFM measurements we find that the former correspond to locations where the 1L-WSe 2 tents over the nanopillars and the latter correspond to locations where the flake is pierced by the nanopillars (see Supplementary Fig. 2). On average, we find that two-third of the sites are not pierced during the deposition step.

Figure 1: Fabrication and characterization of scalable quantum confinement arrays. (a) SEM image of nanopillar substrate, fabricated by electron beam lithography. Black scale bar, 2 μm. (b) Illustration of the fabrication method: (1) mechanical exfoliation of LM on PDMS and all-dry viscoelastic deposition on patterned substrate; and (2) deposited LM on patterned substrate. (c, top) An AFM scan of 1L-WSe 2 on a nanopillar. (bottom) The AFM height profile of a bare nanopillar (blue-shaded region) and of the flake deposited over it (pink line), measured along the dashed pink line cut in the top panel. Colour-scale bar represents height in nm and white scale bar 1 μm. (d) Dark field optical microscopy image (real colour) of 1L-WSe 2 on nanopillar substrate (130 nm high, 4 μm separation). The full image corresponds to a 170 μm by 210 μm area. The green box highlights six adjacent nanopillars within the 1L-WSe 2 region, measured in Fig. 2. The blue circles indicate two pierced nanopillars, and the pink circles indicate two non-pierced nanopillars. PDMS, polydimethylsiloxane; SEM, scanning electron microscope. Full size image

Quantum light from WSe 2 -based deterministic QEs

Figure 2a is an integrated raster scan map of PL emission at ∼10 K of six adjacent non-pierced nanopillar sites in the region enclosed by the green dashed line in Fig. 1d. The most prominent feature is the ∼ × 10 increase in intensity at the location of every nanopillar. Figure 2b reveals the source of this emission intensity enhancement: spectra taken at each nanopillar location display bright sub-nanometre linewidth emission peaks. Figure 2c demonstrates the single-photon nature of this emission via photon-correlation measurements taken (from left to right) at the first, third and fourth nanopillar locations. Ten nanometre band-pass filters, indicated by the pink, green and blue highlighted areas in the panels of Fig. 2b, select the spectral windows for the photon-correlation measurements. We obtain g(2)(0) values of 0.0868±0.0645, 0.170±0.021 and 0.182±0.028, respectively, uncorrected for background emission or detector response. While these surpass those in early reports11,12,13,14,15, we expect the quality of the single-photon emission from the QEs to improve under resonant excitation31. Out of the 53 unpierced nanopillar sites in this substrate we find sub-nm emission peaks in 51 of them, giving ∼96% yield in QE generation. Their emission wavelength ranges between 730 and 820 nm (see Supplementary Fig. 3 for statistics), equivalent to a redshift distributed between 50 and 280 meV from the unbound exciton emission energy at ∼1.755 eV (ref. 32), as observed for the naturally occurring QEs in WSe 2 (refs 11, 12, 13, 14, 15). The fine-structure splitting (200–730 μeV) and the emission linewidths as narrow as ∼180 μeV (∼0.08 nm) are also consistent with previous reports11,12,13,14,15 (Supplementary Fig. 3) advocating that these deterministically created QEs are of the same nature as the randomly appearing ones.

Figure 2: Creation of quantum emitter arrays in 1L-WSe 2 . (a) Integrated PL intensity raster scan of the region enclosed by the green rectangle in Fig. 1d, taken under 200 nW μm−2, 532 nm laser excitation at 10 K. Green crosses mark the position of the six nanopillars beneath the 1L-WSe 2 . Colour-scale bar maximum, 160 kcounts s−1. (b) PL spectra taken at each of the corresponding green crosses in a, from left to right respectively, showing the presence of narrow lines at each nanopillar location. (c) Photon correlation measurements corresponding to the filtered spectral regions (10 nm wide) enclosed by the blue, green and pink rectangles, in b, with g(2)(0)=0.087±0.065, 0.17±0.02 and 0.18±0.03, and rise times of 8.81±0.80 ns, 6.15±0.36 ns and 3.08±0.41 ns, respectively. (d) Spectrum taken from a 1L-WSe 2 on a 190 nm nanopillar, showing lower background and a single sub-nm emission peak. Higher-resolution spectrum in the inset reveals the fine-structure splitting of this QE peak. An asymmetry can be seen in the spectrum, which has been previously attributed to a phonon sideband in naturally occurring QEs31. (e) Probability distribution (in %) of the number of emission lines per nanopillar for samples using different nanopillar heights (60, 130 and 190 nm in white, blue and purple, respectively). A trend of higher probability of single QE emission peaks per nanopillar location with increasing height is evident, reaching 50% for 190 nm nanopillars. (f) Increasing nanopillar height also leads to a reduction of spectral wandering. Solid black circles represent the mean value of spectral wandering of several QEs for a given nanopillar height, while the error bars represent the standard deviation of each distribution, both extracted from time-resolved high-resolution spectral measurements (Supplementary Fig. 4). A total number of seven samples was used to collect the statistics necessary for Fig. 2e,f. Full size image

Effect of nanopillar height on WSe 2 -based QEs

To study the effect of nanopillar height, we carry out similar optical measurements of 1L-WSe 2 flakes deposited on nanopillars of height ∼60 and ∼190 nm. The spectra taken at the 60-nm nanopillars have multiple peaks of ∼1 nm linewidth on average (see Supplementary Fig. 3 for example spectra). In contrast, Fig. 2d is a representative spectrum taken from the 190 nm nanopillars, displaying a better isolated, single sub-nm emission peak. The inset reveals a 722 μeV fine-structure splitting for this QE. We do not see clear nanopillar height dependence in the emission wavelength and fine-structure splitting (see Supplementary Fig. 3 for statistics). Although we often observe multiple narrow emission lines from nanopillar locations, increasing the nanopillar height reduces the spread in the number of peaks arising at each. We verify this trend in Fig. 2e, a histogram of the probability that a given number of sub-nm emission peaks appear per nanopillar, for the different nanopillar heights (60, 130 and 190 nm in white, blue and purple, respectively). The likelihood of creating a single QE grows as nanopillar height is increased. For the 190 nm nanopillars, 50% of all nanopillar sites host a single QE with one emission peak, as indicated by the purple bars. Spectral wandering of the peaks as a function of time also displays a strong dependence on the nanopillar height. To quantify this dependence, we record the maximum range of emission wavelength wandering per QE over tens of seconds. The solid black circles in Fig. 2f correspond to the mean of these values for each group of QEs pertaining to each nanopillar height, for 17 different QEs in total, with the error bars displaying the standard deviation of these distributions. We observe a reduction from a few meV for 60 nm nanopillars to below 0.25 meV (average) for the tallest 190 nm nanopillars (see Supplementary Fig. 4), reaching as low as 0.1 meV. To the best of our knowledge, this is the lowest spectral wandering seen to date in LM QEs11,12,13,14,15. Hence, these deterministic QEs are comparable, and even superior, in spectral stability to their randomly appearing counterparts. The dependence of certain QE characteristics on nanopillar height, along with shifts in the delocalized neutral exciton peak (X0) at room temperature30 at the nanopillar locations (see Supplementary Fig. 5), suggest that a localized strain gradient induced by the nanopillars might be playing an active role in producing QEs, as well as determining their specific optical properties21,23,24.

Deterministic QE creation in WS 2 monolayers

The method we present for QE creation is not restricted to a specific LM. We predict a similar effect on different LMs and test this by using 1L-WS 2 . Despite previous efforts to measure QEs in 1L-WS 2 , there has only been one previous report of single-photon emission in this material22. Figure 3a shows an integrated PL intensity raster scan map taken at ∼10 K of a 1L-WS 2 on a substrate with 170-nm-high nanopillars square array spaced by 3 μm. The inset shows a true-colour dark-field optical microscopy image of the same flake, where the red areas (due to fluorescence) are 1L-WS 2 . Once again, the brighter spots correspond to the unpierced nanopillar locations, as verified by AFM measurements, and show overlap with the bright fluorescence spots in the PL intensity image where, similar to WSe 2 , intensity is increased (here by a factor ∼4) at every one of the 22 non-pierced nanopillar sites in the flake. Panel 1 of Fig. 3b shows the typical 1L-WS 2 emission spectrum at ∼10 K (ref. 22), measured from a flat region of the same flake away from the nanopillars. The X0 and X− unbound excitons are labelled in the figure, while the broad red-shifted emission band arises from weakly localized or defect-related excitons in the 1L-WS 2 at low temperatures22, and is present in this material regardless of location. Panels 2 and 3 of Fig. 3b show representative PL emission spectra taken at nanopillars of heights ∼170 and∼190 nm, respectively, where once again sub-nm spectral features arise. We note that we observe fine-structure splitting for WS 2 in these QEs, which range from 300 to 810 μeV (Supplementary Fig. 6), as represented in the panel insets corresponding to the spectral regions highlighted in red. We also measure the spectrum of several WS 2 QEs as a function of time (see Supplementary Fig. 6) and find all spectral wandering values below 0.5 meV over 1–2 min. Figure 3c shows statistics on QE emission wavelength collected for over ∼80 QEs for 1L-WS 2 on 170-nm (white bars) and 190-nm (red bars) nanopillars. The wavelength distribution of the sub-nm emission lines, typically in the 610–680 nm region (53–300 meV redshift from X0)22, is as narrow as ∼20 nm for the 190-nm nanopillars. Most nanopillar sites on WS 2 show multiple sub-nm lines, suggesting the creation of several QEs at each site for these nanopillar heights. Figure 3d plots a histogram of the number of sub-nm peaks appearing at each nanopillar for both nanopillar heights. The trend is similar to that seen in WSe 2 , where higher nanopillars lead to a narrower spread in the number of peaks towards a higher likelihood of creating a single QE at each nanopillar site. We note that we obtain a 95% yield of QE creation in 1L-WS 2 on non-pierced nanopillars. Further, ∼75% of these display two or less sub-nm emission peaks. In contrast, the 60- and the 130-nm-high nanopillars do not result in any QE occurrence (see Supplementary Fig. 7 for examples of these measurements).