Photon superbunching in cathodoluminescence of excitons in WS₂ monolayer

We perform photoluminescence (PL) and CL experiments of a WS₂ monolayer sandwiched between two thin hBN flakes (top and bottom flakes are ca. 35 and 105 nm thick, respectively, see also SI figure S1) on a 50 nm-thin silicon nitride (SiN) membrane. The hBN encapsulation on both sides of the WS₂ monolayer serves three purposes: (i) protecting the WS₂ from electron-beam damage and contamination, (ii) increasing the effective interaction volume of incoming electrons with the monolayer, and (iii) providing layers for the generation of additional charge carriers which can subsequently diffuse into the WS₂ and radiatively recombine, thereby significantly enhancing the CL intensity [13]. We note that even smallest contamination during the assembly of WS₂–hBN heterostructure can cause quick and irreversible degradation of the WS₂ monolayer under the electron beam. Figure 1(a) schematically presents the experimental setup for the electron-beam excitation of the investigated sample and for collection of generated CL. Here, the electron beam of 10 kV and 30 kV is focused onto the WS₂–hBN heterostructure, and generated CL is subsequently collimated by a parabolic mirror and focused onto a spectrometer and an HBT interferometer (see details in SI).

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Photo and electron-beam excitation are essentially different mechanisms of exciton generation in a WS₂ monolayer. An incoming photon typically creates one electron–hole pair in the WS₂ monolayer, while an incoming electron can excite many electron–hole pairs in the sample (figure 1(b)), predominantly in the thicker hBN layers due to a large interaction volume [14]. The latter process can be described by a scattered incoming electron which excites high-energy interband transitions in the sample, also referred to as bulk plasmons in electron spectroscopy literature [5, 15]. Such bulk plasmons (${\sim}30$ eV) are comprised of a coherent sum of interband transitions contrary to the collective intraband oscillations of free charges, e.g. manifesting in surface plasmons (${\lt}5$ eV). Electron induced bulk plasmons subsequently decay into multiple electron–hole pairs which, after a typical excitonic lifetime, exhibit synchronized radiative recombination. The photons appear to arrive as a 'packet' and can be detected with the HBT interferometer as photon bunching ($g_2(0) \gt 1$).

In figure 2(a), we compare spectral emission properties of the WS₂–hBN heterostructure under photo and electron-beam excitation. The PL spectrum is centered around 621 nm and has a red-shifted satellite peak at 635 nm (green line in figure 2(a)). These emission lines are characteristic for the neutral and red-shifted charged exciton (trion) in WS₂ monolayers at room temperature [16]. The CL spectrum in figure 2(a) is dominated by the neutral exciton peak at 626 nm which is red-shifted with respect to the PL spectrum. In general, we observe a sub-10 nm spectral wandering of the excitonic peak in both PL and CL measurements which is possibly due to local strain within the WS₂–hBN heterostructure [17]. Figure 2(b) presents a CL intensity map obtained by scanning the electron beam over the WS₂–hBN heterostructure. The spatial CL distribution reveals areas of lower intensity, which are due to cracks in the WS₂ monolayer. The round dark patches apparent in the CL map can be attributed to bubbles in between the three layers, as the lack of adherence in the stacked sample has been shown to result in quenched luminescence [18]. Figure 2(d) displays a corresponding PL confocal map obtained with laser excitation at 404 nm. We find a similar intensity distribution as in the CL map in figure 2(b), although characterized by a lower spatial resolution than with an electron beam.

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The photon statistics of emission generated from the WS₂–hBN heterostructure drastically depend on the type of excitation. Figure 2(c) presents photon correlation histograms obtained under photo and electron-beam excitation. Electron-beam excitation results in a pronounced photon bunching peak at zero correlation time (blue diamonds in figure 2(c)), while the photon correlation histogram obtained under photoexcitation is flat with $g_2(\tau) = 1$ (green circles in figure 2(c)). Moreover, the bunching amplitude in CL can be tuned by the electron-beam current, unlike the flat photon correlation histogram in PL [5].

The CL intensity and the amplitude of photon bunching can be controlled by the electron-beam current I. As the current is increased, a higher CL intensity is observed due to the larger amount of incoming electrons, generating more electron–hole pairs in the sample, which can subsequently recombine radiatively in the WS₂ monolayer (figure 3(a)). In contrast, the amplitude of the photon bunching peak follows the opposite trend: with increasing I, the contribution of uncorrelated emission is increased, resulting in a lower photon bunching (SI figure S2). Figure 3(b) shows the bunching histograms collected at low and high electron-beam currents, which we fit to extract the values of $g_2(0)$ (see details in SI). At the lowest electron-beam current of 3 pA, we achieve a giant bunching factor $156\,\pm\,16$, indicating the high quality of the investigated sample. In contrast, the bunching factor is greatly reduced to approximately $4.7\,\pm\,0.2$ for the highest electron-beam current of 211 pA, which is summarized in figure 3(c). We fit the examined dynamics with

$$\begin{equation} g_2(0,I)=1-\frac{I_0}{P_\mathrm{e} \times I} \end{equation} \tag{ 1 }$$

as the bunching factor has been observed to be inversely dependent on the applied electron-beam current [5, 19]. Here I₀ relates to the current exciting a bulk plasmon and $P_\mathrm{e}$ is a probability of incoming electrons to interact with emitters.

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The physical reasons behind the photon bunching can be attributed to the synchronization of emission from emitters, where each incoming electron creates a photon packet. With increasing electron-beam current, the electrons arrive closer in time and the photon packets become increasingly indistinguishable, thereby reducing the bunching factor until the Poissonian distribution $g_2(0,{I\rightarrow}\infty) = 1$ is reached. In the WS₂–hBN heterostructure, the inverse I-dependence is confirmed in figure 3(c), although the Poissonian distribution cannot be reached due to sample degradation at high electron-beam currents $I \gt$ 200 pA (SI figure S3).

A further increase of the photon bunching factor by reducing the applied electron-beam current is limited by the instrument. Decreasing the acceleration voltage potentially allows to reduce the current to sub-pA, however in practice, it causes severe sample charging already at 5 kV. To overcome this limit, we suggest to modify the geometry by adding a thin gold nanodisk to induce a local change of electron-beam excitation parameters. We drop-cast monocrystalline gold nanodisks with a diameter ranging from 80 nm to 230 nm on top of the WS₂–hBN heterostructure. Gold nanodisks are well separated from each other across the heterostructure, allowing for a comparison of electron-beam excitation of bare heterostructure and through a gold nanodisk (SI figure S1).

For further CL studies, we chose a gold nanodisk with an approximate thickness of 30 nm and a diameter of 120 nm, as shown in the inset of figure 4(a). The reasoning behind this selection is that the (broad) plasmonic dipole mode spectrally overlaps with the WS₂-exciton, in principle allowing for plasmonic interaction [20]. Figure 4(a) presents the CL spectra of the WS₂–hBN heterostructure excited through the gold nanodisk with increasing electron-beam current. We observe an overall CL brightening with increasing I, similar to the bare WS₂–hBN heterostructure. However, the CL spectra do not reveal significant emission enhancement which would indicate a plasmon-assisted Purcell effect, nor any evidence of strong coupling (figure 4(a)). This observation is in agreement with the PL measurements, where the position of the gold nanodisks distributed over the entire WS₂–hBN heterostructure cannot be made out. We ascribe this lack of luminescence enhancement to the large separation of about 35 nm between the gold nanodisk and the WS₂ monolayer, which does not allow for efficient near-field coupling.

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Remarkably, the addition of gold nanodisks improves the emission synchronization in the WS₂, which manifests in the increase of photon bunching factor. The gold nanodisks themselves—on hBN only—exhibit dim CL emission (see SI figures S3 and S4), which allowed us to quantify the bunching factor $g_2(0) = 43.1\,\pm\, 4.9$ of a similarly sized 120 nm nanodisk (orange in figure 4(b)). Figure 4(b) further compares the photon correlation histograms measured at identical excitation parameters (8 pA, 30 kV) from the bare WS₂–hBN heterostructure (blue), and a system of a gold nanodisk on WS₂–hBN heterostructure (dark red). The fit of the histograms provides information about the lifetime of the generated emission τ and the bunching factor $g_2(0)$. We observe a minor change in radiative lifetime of WS₂ after the addition of the gold nanodisk, extracting values of ${\tau}_{\mathrm{WS}_2} = 365\,\pm\,18$ ps and ${\tau}_{\mathrm{WS}_2}+{\textrm{gold}} = 416\,\pm\,10$ ps. The extracted values of radiative lifetime agree with one obtained via time-correlated single-photon counting (TCSPC) methods using a pulsed laser ($\tau^{\textrm{PL}}_{{\textrm{WS}}_2} = 296\,\pm\,22$ ps, see SI figure S5). We note that the reported lifetimes here do not represent the intrinsic exciton decay rate in WS₂, and are effective radiative lifetimes depending on many factors such as optical environment, available decay channels etc [21]. We conclude that the addition of a gold nanodisk did not facilitate the creation of additional, faster relaxation channels for the WS₂-excitons which is in agreement with the absence of Purcell enhancement. For the bare gold nanodisk, however, we measure a lifetime of $\tau_{{\textrm{gold}}} = 196\,\pm\,34$ ps, which is close to the temporal limit of our setup (180 ps).

We extract a photon bunching factor of $105\,\pm\,11$ for the bare WS₂–hBN heterostructure, which greatly increases to $829\,\pm\,114$ for the system of a gold nanodisk on the WS₂–hBN heterostructure at 30 kV. A simple addition of the bunching factors of the bare gold nanodisk and that of the hBN-encapsulated WS₂ cannot explain the huge increase of bunching to $829\,\pm\,114$ (which we will focus on in the next section). The highest bunching factor of $2152\,\pm\,236$, we observe at the lowest electron-beam current of 3 pA (at 10 kV) for the gold nanodisk on the WS₂–hBN heterostructure (pink circles in figure 3(c)). Finally, we confirm the inverse electron-beam current dependence of the photon bunching using a different geometry and a reduced acceleration voltage (from 30 kV to 10 kV allowing for a further reduction in I). We plot the summary of the results in figure 4(c), including fits of the $g_2(0,I)$-data with an inverse current function (red curves). We extract from the fit a large change in I₀ from $I_0^{\textrm{WS}_2}/P_\mathrm{e} = 477\,\pm\,14$ pA to $I_0^{\textrm{WS}_2+{\textrm{gold}}} /P_\mathrm{e} = 5257\,\pm\,154$ pA, which indicates a drastic change in the probability of electrons to interact with the sample due to the presence of a gold nanodisk.

We perform Monte Carlo simulations [22] to shed light on the change in electron interaction probability and photon superbunching caused by the addition of a gold nanodisk. Figures 5(a) and (c) present results for electron trajectory simulations of the investigated geometries using a 10 kV-electron beam with a spot size of 5 nm. In case of the bare WS₂–hBN heterostructure, the hBN interface barely affects the direction of incoming electrons, which is visualized using ten simulated electron trajectories in figure 5(a) (blue lines). We further accumulate 1000 trajectories to calculate the electron angular divergence histogram (figure 5(b)). Evidently, it reveals the principal direction of electron propagation normal to the sample plane with a small divergence of $\Theta_{1/2}^{\textrm{WS}_2} = 45^{\circ}$ (the full width at half power). The addition of a 30 nm thick gold nanodisk in figure 5(c) drastically changes the direction of electron propagation within the WS₂–hBN heterostructure as it is shown in the corresponding angular divergence histogram in figure 5(d). The incoming electrons are widely scattered by the gold nanodisk so the principal direction of electron propagation cannot be identified, while electrons propagate omnidirectionally with divergence $\Theta_{1/2}^{\textrm{WS}_2+{\textrm{gold}}} = 155^{\circ}e$. We summarize the simulation results in figure 5(e), which presents the electron divergence for a range of gold thickness and acceleration voltage.

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The divergence of the electron beam serves to (on average) provide impinging electrons with a significant in-plane momentum which further enhances coupling to the in-plane dipole moment of the excitons. Moreover, the redirection of electrons by a gold nanodisk from the normal-to-sample plane extends the geometrical path of the electrons in the WS₂–hBN heterostructure. This increases the probability of electrons $P_\mathrm{e}$ to interact with the thin sub-100 nm sample and to excite bulk plasmons in it. As the interaction length and the probability of bulk plasmon excitation are both increased, one would expect to observe an increase in CL emission intensity while preserving the degree of bunching in the experiment. Figure 5(f) presents the results of such an experiment, where we collect both the $g_2(0)$ and the corresponding CL intensity from the bare heterostructure and that with an additional gold nanodisk. We average the $g_2(0)$-intensity data sets in figure 5(f) and fit the result with an intensity inverse function since the CL intensity is proportional to the electron-beam current. The fit results clearly demonstrate the brightening of CL intensity after adding a gold nanodisk, which is due to the increase in probability of electrons to interact with the sample. Such a change in excitation efficiency improves the synchronization of an ensemble, which results in increase of the degree of photon bunching according to equation (1) [5, 8], which we observe in figure 4(c).