## Introduction

Monolayer transition metal dichalcogenide (TMD) semiconductors provide a unique platform to study light-matter interaction and many-body effects at the atomic scale. The strong Coulomb interaction in these materials leads to the formation of tightly bound electron-hole pairs (excitons) with binding energies of hundreds of milli-electronvolts1,2,3. Moreover, excitons residing in the two different valleys at the K points of the Brillouin zone can also interact4,5,6,7,8,9,10, giving rise to four- and five-particle states, which have been recently identified in tungsten diselenide (WSe2) as neutral and charged biexcitons11,12,13,14, as well as biexcitons in WS215,16. The radiative emission from such exciton complexes can further be tuned by an external electric field, modifying the doping of the material and thus favoring the formation of either charged or neutral complexes. This rich and complex excitonic scenario could be exploited to develop applications such as valleytronics and (quantum) optoelectronic devices, especially in the case of electrically-driven light emitters. Electroluminescence (EL) from monolayer TMDs has been widely studied in the past, especially at room temperature, where the emission originates from neutral excitons17,18,19,20,21,22,23,24,25,26. At cryogenic temperatures, the emission can also be due to localized exciton states or negatively charged trions27,28,29,30,31,32,33. However, electrically driven emission from more complex exciton species has not yet been observed.

Here, we report on EL from monolayer WSe2 and WS2 by pulsed transient EL34, which triggers the formation of exciton complexes and thus their light emission. The high sample quality, enabled by encapsulating the monolayer semiconductor in hexagonal boron nitride (hBN), allows for the observation of EL from multi-particle exciton complexes, including neutral and negatively charged biexcitons, with narrow emission linewidths down to 2.8 meV (full-width-at-half-maximum (FWHM)). Furthermore, the formation of different exciton species is tunable by tailoring of the electrical pulse parameters. Our results provide crucial insights into electrically-driven light emission in monolayer TMDs and open a new route to applications in novel optoelectronic devices.

## Results

### Sample structure and light emission at room temperature

The sample structure used to study EL in monolayer TMDs is schematically depicted in Fig. 1a. A microscope image of the WS2 sample presented in this article is shown in Fig. 1b (a microscope image of the WSe2 sample is shown in Supplementary Fig. 1): the monolayer TMD (namely WSe2 or WS2) and graphene are encapsulated in between two multilayer hBN flakes. The graphene layer is used as electrical contact to the monolayer semiconductor. Part of the graphene flake is left un-encapsulated in order to make an electrical contact with a Pd/Au electrode. The top hBN serves as encapsulation35 to avoid environment related effects (residues left after sample processing, adsorbents) on the light emission from TMDs, and the bottom hBN also provides an insulating layer to apply a gate voltage to the sample by means of a pre-patterned Ti/Au back-gate electrode, on top of which the entire heterostructure is placed. Graphene was chosen as electrode for two reasons: (i) it is a layered material that can be easily integrated in a van der Waals heterostructure, and (ii) it has been shown that charge carrier injection from graphene for transient EL is more efficient than from standard metals34, resulting in enhanced emission. Details of the sample fabrication can be found in the Methods section.

This sample structure (metal-insulator-semiconductor-graphene) allows for electrically driven light emission by the recently reported method of transient EL in transition metal dichalcogenides34, in which light emission is achieved by alternated injection of electrons and holes into the semiconductor by means of a pulsed gate voltage. In Fig. 1c we show band diagrams that schematically depict the emission process. The shape of the (~9 ns long) electrical pulses used for EL is schematically shown in the inset of Fig. 1c. The gate voltage sweeps from a negative value (V0), where the Fermi level in graphene is below the Dirac point and holes are accumulated in the valence band of the semiconductor (Fig. 1c left), to a positive value (V1), where the Fermi level in graphene shifts upwards in energy and electrons are injected into the conduction band (Fig. 1c right). The steep (lateral) band bending in the TMD due to the large voltage drop at the Schottky contact leads to a transient tunneling current. As a result, injected electrons diffuse in the semiconductor while holes (radiatively) recombine with incoming electrons or partially drift out through the contact34. This process is known as transient EL, as the injected carriers recombine only during the rise and fall periods of the pulse. The light generation can be depicted from Fig. 1d, where we show an optical microscopy picture of the sample presented in Fig. 1b, with a clear red-orangish light emission originating from the WS2 flake.

The samples are characterized at room temperature by their PL spectrum (Fig. 1e) upon optical excitation with a continuous-wave laser (λ = 532 nm, Pd = 2 × 103 Wcm−2), where we observe an emission maximum centered at 1.653 eV for WSe2 and at 2.003 eV in the case of WS2, corresponding to their respective free exciton emission (comparison between spatial resolution of PL and EL is presented in Supplementary Figs. 1a and 2). Similar spectra are observed when an AC voltage is applied between the back-gate and the graphene layer, inducing transient EL near the interface between the TMD monolayer and graphene.

### Electro- and photoluminescence at T = 5 K

At room temperature, only one emission maximum can be identified in the PL and EL spectra of both WSe2 and WS2. However, the scenario becomes more complex when the sample is studied at cryogenic temperatures. At T = 5 K different emission peaks can now be distinguished in the EL spectra of both materials. In WSe2 (Fig. 2a), apart from the well-known bright exciton (X0) centered at 1.7315 eV, the EL spectrum reveals the emission lines associated with other exciton complexes, previously observed upon optical excitation11,12,13,14. On one hand, we are able to distinguish the two negatively charged trions at 1.7007 and 1.6921 eV, attributable to the intravalley ($${\rm{X}}_1^ -$$) and intervalley trions ($${\rm{X}}_2^ -$$), respectively36, and the spin-forbidden dark exciton (XD) at 1.6864 eV, which is the two-particle ground state exciton6,37,38. Furthermore, the neutral biexciton (XX) centered at 1.7121 eV, a four-particle complex, is formed from a long-lived dark (spin-forbidden) and a bright (spin-allowed) exciton, while the charged biexciton centered at 1.6808 eV (XX), a five-particle complex, is formed from a negatively charged trion and a neutral exciton in different K and K′ valleys8,11,12,13,14. It is worth mentioning that the pulsed EL from WSe2 shows a narrow emission linewidth of 2.8 meV FWHM only for both the charged biexciton and the dark exciton. Finally, we also observe a broad peak at 1.675 eV which may be assigned to a positively or negatively charged dark trion (X)39. At energies lower than 1.67 eV, additional emission peaks (labelled L1, L2, and L3) emerge that most probably stem from localized states37,40,41,42,43,44. In Table 1, we summarize the energy of the different exciton complexes with respect to the bright exciton X0.

A similar scenario is uncovered in the EL spectrum of WS2, shown in Fig. 2b (Table 1 provides again a summary of the exciton energies). The bright exciton X0 appears at an energy of 2.075 eV, as well as the charged trions $${\rm{X}}_1^ -$$ and $${\rm{X}}_2^ -$$ at 2.045 and 2.038 eV, respectively. The peak appearing at 2.023 eV has previously been associated to a biexciton15,16, although its charged or neutral nature remains still unclear. Here we anticipate that it is due to a negatively charged biexciton (XX), since its peak height (emission intensity hereafter) increases when a positive gate voltage is applied to the sample, as will be discussed later. Furthermore, we are able to observe additional emission lines corresponding to a dark exciton (XD), centered at 2.028 eV (only observed so far in the PL of non-encapsulated samples45) and to a neutral biexciton (XX), centered at 2.056 eV, which, to our knowledge, has not been previously reported. Importantly, the latter two exciton complexes are hardly visible in the PL spectrum, but can be clearly resolved in the respective EL. To our knowledge, this is the first evidence of EL of such multi-particle complexes in both WSe2 and WS2.

The rich EL scenario in our samples, based on charged and neutral excitonic complexes, motivates the operation of such heterostructures as tunable light emitters by just tailoring the pulse parameters. By shifting the offset of the pulsed voltage, it is possible to create either an electron-rich or a hole-rich environment in the 2D semiconductor, consequently enhancing or diminishing EL from the different exciton complexes in a similar way as it is commonly observed in gated PL measurements. To this end, according to the schematic pulse diagram shown in Fig. 1c, the EL experiment is performed as follows (see also Supplementary Fig. 3): the pulse amplitude Vp = |V1 − V0| is kept constant in all measurements, while the offset voltage V0 is varied over a certain range. In this situation, an offset of V0 = 0 indicates that the voltage applied to the back-gate sweeps in a pulse cycle from 0 to Vp, while with an offset of V0 = −Vp, the voltage applied to the back-gate sweeps from −Vp to 0. Therefore, in the former case an electron-rich (p/n+) environment is induced in the semiconductor, while in the latter the injected charge carrier density will be hole-rich (p+/n). Finally, in the symmetric case, V0 = −Vp/2, the amount of injected electrons and holes is balanced (p/n). Note that this picture applies to the case of undoped devices with contacts that are equally transparent for both electrons and holes. In realistic samples the different regimes may occur at other offset voltages, but the qualitative picture remains the same.

In Fig. 2c, d we show colormaps representing the EL emission from WSe2 and WS2, respectively, for different V0 values and with fixed pulse amplitude of Vp = 7.0 V. We observe in both materials that for higher offset values (p/n+ region), i.e. higher electron injection, the EL is dominated by negatively charged exciton species such as XX, $${\rm{X}}_1^ -$$, and $${\rm{X}}_2^ -$$, where the charged biexciton is the predominant emission and the free exciton is much weaker. For lower offset values (p/n region), the emission from negatively charge exciton complexes vanish and the spectrum is then dominated by neutral species such as the dark and bright excitons and neutral biexciton, as well as localized excitons. This indicates that the charge carrier injection is balanced between electrons and holes, favoring the formation of neutral excitons. Finally, when the offset voltage has a more negative value (p+/n region), the induced charge density in the semiconductor is then hole-rich and the emission from positively charged species such as the positive dark trion in WSe2 becomes stronger. We are not able to resolve positively charged trions in EL neither in WSe2 or WS2, possibly because the induced hole concentration is too low to favor trion formation.

The tunable EL can be compared to the respective PL colormaps (Fig. 2e, f), where the PL emission is measured for different DC gate voltages (Vg). In a similar manner as for EL, negative exciton species become the dominant emission for positive applied gate voltages (Vg > 0), i.e. for n-doping, although in the PL spectra we are able to additionally resolve the negative dark trion in WSe2 and the double-negatively charged trion (X−−), the next charging state of the trion13, in WS2. In the WS2 spectra we also observe XX emission only in the n-doped region, supporting the negatively charged nature of this biexciton as concluded above from the EL measurements. Around Vg = 0, the negatively charged species vanish and only the neutral excitons and biexciton, as well as the localized states, show emission, again in accordance with the EL spectra. Here it is worth noting that we are not aware of any previous reports on the PL emission of neutral biexcitons in WS2, which we are able to resolve both in EL and PL. Finally, for Vg < 0, the positive dark trion appears in the WSe2 PL spectrum, but not in the one of WS2, suggesting that WS2 is unintentionally n-doped and we therefore cannot achieve sufficient p-doping in this material. We refer the reader to the Supplementary Figs. 4 and 5 for a further analysis of the PL spectra as a function of the back-gate voltage.

### Discrimination between different multi-particle excitons

The electrical tunability of the EL and PL spectra permits the discrimination between charged and neutral exciton species. Whether they are formed by two, three, four or five particles cannot be distinguished by this method. We therefore studied the dependence of the emission intensity with the excitation intensity. While the emission intensities of dark and bright excitons, composed by one electron and one hole, follow a linear dependence with the excitation power, biexcitons are expected to show a quadratic behavior11,12,13,14,15,16. In Supplementary Figs. 6, 7, and 8 we show the PL spectra of WSe2 and WS2, at different excitation powers and fits of the respective intensities to the power-law IPLPα, where IPL is the integrated PL emission and P the incident laser power. These fits yield the exponent values α = 1.01 for X0, α = 1.82 for XX, and α = 1.44 for XX in WSe2, and similar values in WS2 (see Supplementary Table 1). The deviation from the quadratic growth for the charged biexciton can be attributed to the lack of equilibrium between exitonic states46,47.

We have also studied the dependence of the emission intensity on the excitation power in EL by keeping a fixed offset voltage and changing the electrical pulse amplitude. For increasing pulse amplitude, the Fermi level shifts deeper in the conduction band and, therefore, more charge carriers are injected, resulting in increased EL emission. The measured spectra are shown in Fig. 3a, c for WSe2 and WS2, respectively, and the corresponding plots of EL intensities against pulse amplitude are presented in Fig. 3b, d. On a semi-logarithmic scale, the dependence of EL intensity versus voltage shows a linear behavior for all exciton species. This observation motivates us to empirically model the EL intensity by the expression $$I_{EL} \propto \exp ( {\alpha \kappa V_{\mathrm{p}}} )$$, where Vp is the applied voltage, κ is a constant related to the injected carrier concentration in the 2D semiconductor, and α is a coefficient that indicates the nature of the exciton, as in the PL measurements. We fix κ to fit the data for the neutral exciton X0 with α ≡ 1, which then serves as reference for determining the α values of all other exciton species.

The fit of the measurement data to this empirical expression yields for WSe2 a coefficient of α = 1.75 for XX, which is significantly larger than that of the X0 and XD excitons (α ≡ 1 and α = 1.03, respectively) and it is close to a quadratic dependence. For the neutral biexciton XX we obtain a coefficient of α = 1.44. For WS2, the coefficients for X0, $${\rm{X}}_1^ -$$, and $${\rm{X}}_2^ -$$ are α ≡ 1, α = 1.32, and α = 1.33, respectively, and α = 2.33 and α = 2.31 for the neutral biexciton XX and charged biexciton XX. In Supplementary Table 1 we summarize the obtained coefficients for the different exciton complexes. The emission of all exciton species in WS2 saturate at voltage amplitudes larger than ~8 V, in accordance with measurements performed at room temperature by Lien et al.34. We do not observe such saturation in WSe2, most probably because of the lower peak voltage applied in these measurements. Finally, we present EL spectra for both WSe2 and WS2 at different pulse repetition rates in Supplementary Fig. 9.

## Discussion

In summary, we have studied transient EL of monolayer TMD semiconductors (in particular WSe2 and WS2) sandwiched between two layers of hBN and one graphene sheet at low temperatures. The high material quality of our samples, together with the strong Coulomb interaction between electrons and holes in 2D semiconductors, permits the observation of electrically driven light emission of higher-order correlated excitonic states, including bright and dark excitons, negatively charged trions and neutral and negatively charged biexcitons. By tailoring the pulse parameters, it is possible to create either an electron- or a hole-rich environment in the 2D semiconductor, consequently favoring the enhanced or diminished EL from the different exciton species. Our technique extends and complements gate-dependent PL spectroscopy and will enable further investigations of many-body phenomena in 2D materials. From an applied point of view, our devices may find application as wavelength tunable light emitters or furnish new opportunities for quantum light sources, e.g. by quantum-confinement of electrically induced biexcitons.

## Methods

### Sample fabrication

Bulk WSe2 (grown by vapor phase transport; see ref. 48 for details) and WS2 (purchased from HQ Graphene), graphite and hBN were exfoliated by an adhesive tape and transferred onto a SiO2 substrate thermally grown on Si. The substrates were cleaned by an acetone/isopropanol bath and oxygen plasma treatment. They were then annealed at 300 °C for 2 h in a dry-air atmosphere prior to the transfer of the exfoliated materials to remove possible adsorbates. The tape was peeled-off afterward and the atomically-thin flakes were selected with optical microscopy. A pick-up and place technique49 was used to pick up the flakes by means of a polypropylene carbonate/polydimethylsiloxane (PPC/PDMS) stamp, starting with the top hBN flake. The heterostructure (hBN/graphene/WSe2/hBN) was then transferred onto a Ti/Au (5/100 nm) electrode, pre-patterned on a SiO2/Si substrate. The entire exfoliation and transfer process was performed in a nitrogen-purged glovebox. The remaining PPC residues were removed by introducing the sample in an acetone/chloroform bath. Finally, an additional electrode was fabricated by means of electron-beam lithography and metal evaporation to make an electrical contact to the graphene flake (Pd/Au, 60/140 nm).

### PL and EL measurements

For EL measurements a pulse generator (Agilent 8114A) in combination with a source-meter unit (Keithley 2612A) was used. The pulses were applied to the bottom electrode, while the top contact was grounded. Optical and electrical investigations were carried out in a liquid-helium exchange gas cryostat (Oxford Instruments) under high vacuum (10−7 mbar), integrated in a scanning micro-PL setup. The setup includes a dichroic mirror at λ = 550 nm to separate the PL emission from the excitation. PL and EL were collected using a ×50 long working distance objective lens (NA = 0.5). In PL experiments, the sample was optically excited non-resonantly using a continuous-wave 532 nm laser; the diameter of the laser beam on the sample was ~1 μm. The PL/EL emission was spectrally filtered with a monochromator (Horiba iHR320) and detected with a liquid nitrogen cooled charge-coupled device (CCD). EL imaging was performed by using a CCD camera (Thorlabs).