Characterization of quantum dot-like emitters in programmable arrays of nanowrinkles of 1L-WSe₂

Solid-state quantum emitters (QEs) are essential for next-generation on-chip quantum photonic devices.^1,2 Yet, significant challenges still need to be overcome for QE systems to be suitable for technological applications. There are stringent requirements on nanoscale positioning, efficient photon outcoupling, photon purity, photon indistinguishability, on-demand generation, and control over the polarization state of the emitted light. Over recent years, 2D semiconductors^3–7 have emerged as a promising platform to realize such emitters.^5,8,9 Their atomic thickness inherently overcomes the issue of inefficient outcoupling, makes them readily addressable both optically and electrically,¹⁰ enables nanoscale positioning when coupled with precisely fabricated nano stressors,¹¹ and facilitates novel functionalities such as highly tunable strong coupling.¹² However, ongoing difficulties with 2D semiconductor QE platforms^9,13—including achieving room-temperature operation, high photon purities, and high photon indistinguishability^1,13—persist and motivate the exploration of new 2D emitter platforms that can address these challenges.

A common feature of QEs in 2D semiconductors is their formation in regions of substantial tensile strain.^4,14–17 Recent theoretical work¹⁸ has unified many experimental reports by proposing a model in which 1L-WSe₂ QEs form when strain lowers the energy of the conduction band enough to hybridize with defects within the bandgap. In these models, exciton funneling efficiently pumps the hybrid defect state from regions of lower strain. Motivated by these recent theoretical and experimental¹⁹ observations, we recently reported the fabrication of samples consisting of high-quality monolayer (1L-) WSe₂ stressed by arrays of sharp gold nanocones.¹⁷ In this previous work, we demonstrated that by programmatically changing the array parameters (i.e., lattice structure and spacing) the geometry of the induced nanoscale wrinkles in the 1L-WSe₂ sheet can be altered and that these wrinkles host localized excitons at room temperature that coincide with QEs that emerge at cryogenic temperatures.¹⁷ 

Here, we build upon these initial reports of exciton localization in the programmable nanowrinkles at room temperature¹⁷ and characterize the strain-induced quantum dot-like states that emerge in these uniquely strained systems at cryogenic temperatures. Narrowband emitters are present over a range of emission energies and exhibit substantial intensity and emission energy fluctuations. Polarization anisotropy measurements confirm that they are linearly polarized with a clear dipole orientation. However, when combined with atomic force microscopy (AFM), an obvious correlation between the microscale (i.e., >50 nm) structure of the wrinkles and the dipole orientation is not observed. The lack of correlation strongly suggests that fine, nanoscale strain distributions within the wrinkle control the orientations of emitter dipoles. Photon antibunching is observed from a localized emitter that is spectrally distinct up to 25 K, confirming that the nanocone arrays can generate QEs in 1L-WSe₂ at temperatures greater than 4 K. However, their emission wavelengths and spatial distributions change when the temperature of the sample is cycled from 4 K to 290 K back to 4 K, highlighting the need to better understand how nanoscopic strain in these wrinkle array QE platforms changes with temperature. Overall, these studies offer insight into how engineered arrays of 1L-WSe₂ wrinkles can be used for solid-state quantum light sources at cryogenic temperatures and how the controllability of the wrinkles can be exploited in future studies to further unravel how strain, exciton localization, and exciton funneling combine to form single-photon emitting QEs in 2D materials.

Figure 1(a) shows a height map of the 1L-WSe₂ flake draped over the array of gold nanocone stressors. The prominence of the nanocones above the substrate causes wrinkles to form between array sites and near the apexes of the nanocones.¹⁷ The widths of the wrinkle range from a few tens of nanometers to hundreds of nanometers. Figure 1(b) shows three height profiles taken from the map in Fig. 1(a) that exemplify the nanoscale structural heterogeneity of the 1L-WSe₂ near the Au cones and across both large and small array wrinkles. The inset in Fig. 1(a) highlights a region that hosts a spectrally isolated QE (cf. Figs. 2 and 4). This region also consists of wrinkles that intersect at angles and wind around one another. Calculations of the strain imparted to 2D sheets by nanocone arrays, the structural factors that control the wrinkle formation and their corresponding room-temperature excitonic properties are comprehensively reported in our past study.¹⁷ 

Figure 2(a) shows the photoluminescence (PL) spectra over the extent of the 1L-WSe₂ flake on the Au cones. The spectra consist of narrowband emitters with a variety of emission intensities and energies. In the wrinkle array sample here, two main bands of emitters appear in the PL: a high-energy ensemble centered at 1.675 eV and a low-energy ensemble centered at 1.55 eV. Within each of the ensembles are two prominent sets of doublets. To clearly distinguish these emitters in Fig. 2(a), we have labeled the upper and lower branches of each doublet (e.g., 1a and 1b, 2a and 2b) and an additional state that is spectrally between the two main ensembles (emitter 3). Maps of the PL emission from each emitter are shown in Figs. 2(b)–2(j). These images are created by integrating the PL intensity within a small band of energy centered on each emission feature. The PL intensity from emitters 1a, 1b, 2a, 2b, 4a, 4b, 5a, and 5b are distributed over large regions of the sample whereas emitter 3 is more spatially confined. The variations in the PL are likely due to the nanoscale structure of the sample but the near diffraction-limited resolution of the far-field hyperspectral PL measurement limits the ability to search for direct correlations between emitters and the structure of the sample. Nevertheless, these spectra are reminiscent of many prior reports of strained 1L-WSe₂^3–6,20,21 and signify that the sample hosts single-photon emitting states.

All of these emitters blink and spectrally diffuse, which is similar to the behavior observed in semiconductor quantum dots^22,23 and is consistent with previous reports of localized states in 2D materials.^6,24 These fluctuations are shown in Fig. 3(a), which shows the temporal evolution of the PL from the region that is inset in Fig. 1(b) over 4 min. The fluctuations, combined with the high density of emitters within the two main ensembles, make it difficult to track individual emission lines throughout the measurement. Because of this difficulty, we analyzed the fluctuations integrated over each ensemble instead of attempting to track individual emission features. In particular, intensity fluctuations are quantified using the integrated intensity of the respective bands, and emission energy fluctuations are quantified using the spectral median of the band. This ensemble-averaged behavior at 4 K is shown in the histograms in Figs. 3(b), 3(d), 3(e), and 3(g). On the other hand, emitter 3 is distinguishable from the other emitters, which makes it possible to use the same descriptors (i.e., integrated intensity and spectral median) to track its temporal evolution without averaging. The fluctuations of this emitter at 4 K are shown in Figs. 3(c) and 3(f).

The distributions in Fig. 3 indicate that the ensemble of low-energy emitters is more stable than the ensemble of high-energy emitters at 4 K. Figures 3(b) and 3(d) show histograms of the time-dependent intensity fluctuations for each ensemble. The variance of the intensity fluctuations for the low-energy ensemble is approximately 11% of the mean whereas that of the high-energy ensemble is approximately 19% of the mean. The low-energy ensemble also spectrally diffuses less than the high-energy ensemble. The variance of the spectral median of the low-energy ensemble is approximately 2.0 meV and that of the high-energy ensemble is approximately 2.8 meV. The blinking and spectral diffusion of emitter 3 at 4 K is shown by the histograms in Figs. 3(c) and 3(f). The variance of the intensity fluctuations for emitter 3 is 31% of the mean and the variance of the spectral median is 3.55 meV.

When the sample is warmed to 50 K, the low- and high-energy emission band as well as the spectrally isolated emitter (i.e., emitter 3) can still be clearly identified, as shown in Fig. 3(h). However, the statistical descriptors of the fluctuations are notably different than at 4 K. First, the intensity [Figs. 3(i)–3(k)] and spectral median [Figs. 3(l)–3(n)] distributions of both bands narrow at the elevated temperature. This effect is anticipated from thermal broadening of the emitters. Notably, although the emission line broadens for emitter 3, its distribution of emission energies does not dramatically increase, suggesting that the spectral diffusion behavior of individual emitters does not dramatically increase with temperature. In addition, some emission features, including emitter 3, develop long periods of inactivity that are truncated by short and intense bursts of emission. These long “off” periods cause the strong positive skew in the histogram of intensity fluctuations of emitter 3 at 50 K [Fig. 3(j)]. These two opposing trends highlight the temperature-dependent interplay between the stability of the ensembles and the darkening of some individual emitters.

At 4 K, emitter 3 is a promising QE candidate because its emission energy does not overlap with other emitters. The lack of background emission promotes high-purity single-photon emission.²⁵ In Fig. 4(a), we reproduce the second-order intensity correlation function, $g ( 2 )(τ)$⁠, of emitter 3 from our original report on the nanowrinkle system¹⁷ along with those recorded at 25 and 50 K to analyze the temperature dependence of its antibunching behavior. The temperature dependence of the anti-bunching of this emitter was recorded only on an upward sweep in temperature because the emitter did not persist through the full thermal cycle from 4 to 300 to 4 K (see below for discussion). At 4 K, $g ( 2 )( τ = 0 ns)$ falls below half of the coincident count rate for the neighboring peaks in the pulse train, which signifies photon antibunching and unambiguously establishes emitter 3 as a QE.^26, Figure 4(b) shows the temperature dependence of the magnitude of the antibunching feature at $g ( 2 )( τ = 0 ns)$⁠. We estimate the strength of the antibunching feature by numerically integrating each peak in the $g ( 2 )$ trace and finding the ratio of the amplitude of the zero time delay peak to the average peak amplitude in the neighboring pulse train.²⁷ The antibunching dip is approximately 0.3 ± 0.1 at 4 K, 0.2 ± 0.1 at 25 K, and 0.5 ± 0.2 at 50 K. The uncertainties in these estimates stem from the noise in the amplitudes of the peaks in the pulse train. We hypothesize that the magnitude of the antibunching dip is obscured at 50 K due to the long “off” cycles that develop at elevated temperatures (cf. Fig. 3) along with the deactivation of emitter due to thermal effects,¹⁶ but note that quantum light statistics might be recovered with much longer integration times than those used here (approximately 15 min). Additionally, Fig. 4(c) shows the time-resolved PL of emitter 3. The lifetime is approximately 5 ns, which is consistent with previous reports of the lifetimes of QEs in 2D semiconductors^5,15,27,28 and exceeds the lifetime of the exciton complexes that are not localized in 1L-WSe₂.^29–32 

Figure 5 probes the relationship between the polarization state of the emitters and the underlying structure of the wrinkled 1L-WSe₂. Figures 5(a) and 5(b) show colormaps of the polarization dependence of the PL emission intensity as a polarization analyzer was swept through two full rotations. Multiple rotations were done to measure the polarization anisotropy over the blinking and spectral diffusion cycles. The same data are plotted in both colormaps, but the saturation value in Fig. 5(b) is lowered significantly to reveal emission features that are much dimmer than the dominant emission lines. Figure 5(a) shows that the high-energy ensemble (blue band), emitter 3 (orange band), and the low-energy ensemble (red band) all exhibit linear polarization anisotropy but their polarization states are slightly offset from one another. In Fig. 5(b), the polarization anisotropy of three substantially dimmer emitters is analyzed. These three emitters exhibit polarization angles that are distinct from the brighter emission lines that are analyzed in Fig. 5(a). Figure 5(c) shows the nanoscale topography of the approximate measurement location with polar plots of the polarization-resolved PL inset. The orientation of the polar plots is aligned to the orientation of the nanoscale topography. While the correspondence of some of the polarization angles with wrinkle orientation suggests a correlation, several additional emitters are observed to have dipole orientations that do not correspond to a wrinkle in the region of interest. These observations suggest that the most important structure–property relationship for the orientation of the transition dipole occurs on a smaller scale. This hypothesis strongly motivates future correlative studies that combine low-temperature PL imaging and spectroscopy, nano-optical imaging of localized states,^12,33,34 and controlled wrinkle formation using different stressor arrays¹⁷ to engineer the polarization state and fine-structure of QEs in wrinkled 1L-WSe₂.

Finally, Fig. 6 shows evidence that the ensemble of emitters changes by cycling the temperature of the sample from 4 K to 290 K and back down to 4 K. Following the characterization of the quantum emitter in Fig. 4, the sample was heated to 290 K while maintaining the vacuum in the cryostat. The heater was subsequently turned off and the sample was cooled back to 4 K. Before the warm-up, emission from the QE was confirmed and it did not show any signs of photodegradation or bleaching. Figure 6(a) compares the PL spectrum at 4 K before the warm-up, the PL spectrum of the same region at 290 K, and the PL spectrum of the emitter region at 4 K after re-cooling. The original 4 K spectrum (blue curve) shows strong emission from the QE at about 1.62 eV. After returning to 4 K, we were unable to relocate emitter 3. To account for microscope drift and emitter blinking, a hyperspectral map [unpacked and plotted in Fig. 6(b)] and a time series of the PL [Fig. 6(c)] were acquired to confirm that the emitter was no longer present after the temperature cycle. This initial observation reveals that QE formation in 2D material wrinkle arrays may vary on each temperature cycle, which could be due to cooling-induced strain in the system. Such variability necessitates further investigation and may motivate further refinement of temperature-independent strain generation in these systems.

The microscopic origin of the emission lines remains an outstanding question. Although the substantial spectral heterogeneity is likely linked to the distribution of localized strain potentials in the sample, more work remains to establish a quantitative relationship between emitter energy, strain, and crystalline defects.^35,36 The lack of an obvious correlation between the orientation of the transition dipoles and the structure of the wrinkles motivates future studies that more directly probe if uniaxial strain determines the dipole orientation of these emitters, perhaps in connection to pseudomagnetic effects.^37–40 The dim cross-polarized emitters observed in Fig. 5(b) also provide an estimate for a bound of the zero-field splitting of the emitters, providing a foundation for future magneto-optical studies.

In conclusion, we have characterized the spatial distribution, excited state dynamics, temporal stability, polarization anisotropy, and temperature stability of 2D QEs that emerge in 1L-WSe₂ nanowrinkle arrays at cryogenic temperatures. The system hosts single-photon emitting states that may persist up to 50 K. However, the emitters exhibit strong intensity fluctuations (i.e., blinking) and spectral fluctuations (i.e., spectral diffusion), both of which pose technical challenges for characterization and device applications. Polarization-resolved spectroscopy reveals that the ability of the wrinkle geometry to control the transition dipoles may be limited. To unambiguously resolve structure–property relationships between the nanowrinkle array and properties of the emitters, more in-depth and quantitative studies that include greater emitter populations, nanoscale optical spectroscopy, and optimized array geometries are needed. Temperature-dependent spectroscopy reveals the expected thermal broadening of the emitters, which reduces the apparent spectral diffusion in the system. Cycling the temperature from 4 K to 290 K and back to 4 K induces a non-reversible change to the emitter population and highlights a potential issue with quantum light sources that are based on locally strained 2D semiconductors. The characterization in this study provides critical information by which systems such as 1L-WSe₂ on arrays of gold nanocones can be benchmarked and compared to other systems as sources of non-classical states of light, as well as reveal important challenges that need to be solved for their adoption into quantum photonic technologies.

In brief, a layer of gold was evaporated onto a silicon wafer, and electron-beam lithography was used to open circular holes in a layer of PMMA on top. This was followed by the deposition of aluminum oxide and lift-off, leaving a hard mask of Al₂O₃ disks behind. Argon ion milling was then used to produce the gold nanocone structures. The complete nanofabrication details are in a previous report.¹⁷ 

The sample was prepared using mechanically exfoliated flakes of high-quality flux-grown WSe₂. The flake was picked up using PCL on top of a PDMS stamp and transferred onto the gold nanocone array substrate. The sample was then placed in a hot (90 °C) acetone bath for 1 h to remove the remaining polymer, followed by a rinse in IPA and dried with compressed nitrogen.

Optical measurements were conducted using a home-built laser-scanning confocal microscope. Luminescence was collected in a backscattering geometry and directed to a Czerny-Turner optical spectrometer, dispersed with a mechanically ruled grating (groove density = 600 g/mm), and measured with a scientific CCD camera (Andor iDus 416, cooled to −55 °C) after laser light was rejected by a series of interference filters. PL mapping was conducted by scanning the beam over the sample using a 4f-imaging system in conjunction with a two-axis galvanometric scan mirror.

Cryogenic measurements (T = 4 K) were conducted by cooling the sample in a closed-cycle liquid helium cryostat with optical access (Montana Instrument S50 Cryostation). The samples were illuminated with pulsed laser light generated from a supercontinuum fiber laser (NKT photonics SuperK EXTREME, pulse width = 55 ps, rep. rate = 78 MHz) that was filtered with an acoustic-optic tunable filter (Gooch and Housego) to 540 nm (filter bandwidth ≈ 4 nm). Time-resolved measurements were conducted with the supercontinuum laser described above. PL was collected and filtered using a monochromator exit port on a Czerny-Turner optical spectrometer (Horiba iHR320, monochromator bandwidth ≈ 4 meV). The spectrally filtered PL was then optically relayed onto a single-photon avalanche photodiode (MPD photonics, timing jitter ≈ 25 ps). Time-correlated single-photon counting was achieved by using ultra-fast time-tagging electronics (PicoQuant HydraHarp 400), which generated histograms of the detection events from the avalanche photodiode with respect to a synchronizing pulse from the laser. Hanbury-Brown and Twiss interferometry was conducted by directing spectrally filtered light onto a balanced beam splitter aligned to two separate avalanche photodiodes. The counts on each arm of the interferometer were time-tagged by the HydraHarp 400 using identical hardware settings (e.g., triggering and onboard binning) for each antibunching dataset. The coincident count rate was calculated in post-processing by cross-correlating the intensities on each arm of the interferometer.

This work was supported by the National Science Foundation through Award NSF DMR No. 2004437. Nanostressor fabrication was partially supported through a U.S. Department of Energy, Office of Science Graduate Student Research (SCGSR) award (E.Y.) and Honda Research Institute USA, Inc. The SCGSR-supported effort utilized the Nanofabrication facility of the Center for Functional Nanomaterials (CFN), which is a U.S. Department of Energy Office of Science User Facility, at Brookhaven National Laboratory under Contract No. DE-SC0012704. T.P.D., M.C.S., J.C.H., and P.J.S. acknowledge support for nano-characterization of wrinkles from Programmable Quantum Materials, an Energy Frontier Research Center funded by the U.S. DOE, Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0019443. This work was performed in part at the Nanofabrication Facility at the Advanced Science Research Center at The Graduate Center of the City University of New York. M.C.S and N.J.B. also acknowledge the MonArk NSF Quantum Foundry supported by the National Science Foundation Q-AMASE-i program under NSF Award No. DMR-1906383. Synthesis of WSe₂ was supported by the NSF MRSEC program at Columbia through the Center for Precision-Assembled Quantum Materials (No. DMR-2011738).

The authors have no conflicts to disclose.

Matthew C. Strasbourg: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Emanuil S. Yanev: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Methodology (equal); Writing – review & editing (equal). Thomas P. Darlington: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Writing – review & editing (equal). Kavika Faagau: Methodology (supporting). Luke N. Holtzman: Formal analysis (supporting); Investigation (supporting); Methodology (equal); Writing – review & editing (equal). Katayun Barmak: Methodology (supporting); Writing – review & editing (equal). James C. Hone: Investigation (equal); Methodology (equal); Writing – review & editing (equal). P. James Schuck: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). Nicholas J. Borys: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Supervision (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.