Electroluminescent vertical tunneling junctions based on WSe₂ monolayer quantum emitter arrays: Exploring tunability with electric and magnetic fields

First, we focused on the intentional creation of arrays of quantum emitters in monolayer WSe₂. Our method of choice was nanopillar imprinting, which created SPEs previously attributed to excitonic transitions within strain-induced localization potentials. However, the length scales of the strain profiles induced by the nanopillars appear to be too large to cause quantization of excitonic states. Therefore, we pursued an alternative hypothesis according to which nano-imprinted SPEs originate through the formation of defect centers. To this end, we compared different approaches to create quantum emitters in monolayer (ML) WSe₂ samples: 1) ML-WSe₂ deposited onto bulk hBN, which were irradiated with He ions (20–27) (Fig. 1A), and ML-WSe₂ deposited onto nanopillars (Fig. 1E). The WSe₂/hBN structures were irradiated at low He doses—$10^{15}to{10}^{16}ionsperc{m}^{-2}$. Such small-dose irradiation sites are not detectable in the atomic force microscopy (AFM) topography for depth profile extraction. However, the modifications of the optoelectronic properties are apparent when inspecting the optical response of such irradiated MLs. In the photoluminescence map in Fig. 1B, we saw a significantly quenched intensity of the neutral exciton (X₀) at the emission energy 1.73 eV. The spectra were dominated by narrow emission resonances (labeled as ${\mathrm{X}}_{\mathrm{B}}$) over the irradiated flake area, as seen in the map that represents the integrated emission intensity around 1.64 eV in Fig. 1C, which corresponds to the sharp peaks in the PL spectra in Fig. 1D. Such spectra dominated by lower energy narrow resonances obtained from the entire irradiated area, in combination with the decreased ${\mathrm{X}}_0$ emission, suggest that the defects create radiative recombination channels for bound/localized excitons ${\mathrm{X}}_{\mathrm{B}}$ (and/or intradefect transitions) and nonradiative recombination channels for free excitons ${\mathrm{X}}_0$. The atomic mass difference between the metal and halogen atoms in TMD monolayers provides selectivity in the helium ion irradiation process, leading to a significantly larger probability of creating halogen vacancies (28). However, the positioning of the emitters is still challenging due to the lateral scattering of light helium ions at the interface between the monolayer film and the substrate. Achieving nanoscale lattice modification requires stringent calibration of the ion dosage, which is dependent on many factors such as the crystal structure and masses of the constituent atoms of the implanted material, the underlying substrate material taking into account its roughness resulting in interface imperfections. The systematic data regarding the calibration of the ion dosage for two different materials (WSe₂ and MoS₂) and two different substrates (Si/SiO₂ and Si/SiO₂/hBN) are presented in SI Appendix. Although, ion irradiation has the potential to become a leading method for creating specific SPEs in van der Waals systems with nanoscale positioning, the controllability and reproducibility remain challenging and costly.

In the second approach, ML-WSe₂ was deposited on top of a rectangular array of nanopillars etched in SiO₂ layer. The photoluminescence spectra of WSe₂ imprinted by the nanopillars revealed a modification of the optical response of the WSe₂ monolayer in the form of an emission intensity enhancement (Fig. 1F) from free excitons ${\mathrm{X}}_0$, which we attributed to a strain-induced local reduction of the single particle band gap, leading to excitons being trapped at the potential wells at the pillar sites through funneling of electrons and holes along strain profile (29–34). However, the linewidth and energy of the ${\mathrm{X}}_0$ resonance remain close to the parameters observed in pristine ML-WSe₂ film. The free exciton resonance ${\mathrm{X}}_0$ was accompanied by narrow low energy resonances ${\mathrm{X}}_{\mathrm{B}}$, akin to the He ion irradiated samples. The spatial distribution of the ${\mathrm{X}}_{\mathrm{B}}$ resonances was ordered and correlated with the nano-pillar pattern. Overall, these spectral characteristics, inspected comparatively between WSe₂ monolayers irradiated by focused He ion beams and imprinted by nanopillars arrays, indicate that in both cases the narrow emission lines ${\mathrm{X}}_{\mathrm{B}}$ originate from defect-related optical excitations likely involving selenium vacancies.

This hypothesis of defect creation through nanopillar imprinting was further corroborated by the preservation of narrow resonances ${\mathrm{X}}_{\mathrm{B}}$, when the WSe₂ monolayer was removed from nanopillar arrays and built into the light-emitting diode device, where AFM imaging shows no visible straining or deformation of the ML. The multistep fabrication process of creating vertical tunneling junction based on Gr/hBN/WSe₂/hBN/Gr architecture (Gr—graphene electrodes, hBN—hexagonal boron nitride tunneling barrier, WSe₂—imprinted optically active semiconducting monolayer) is pictorially illustrated in Fig. 2A–E and described in Materials and Methods. Such configuration enables application of electric field and/or injection of charge carriers in the imprinted WSe₂ monolayer by the application of bias between the two graphene electrodes (35–41). The fabrication process preserved the narrow emission resonances ${\mathrm{X}}_{\mathrm{B}}$ in WSe₂ monolayer as demonstrated in Fig. 2F. Those radiative centers demonstrated single photon emission character (3–6) verified via observation of an antibunching in the second-order photon correlation function shown in Fig. 2G.

We inspected the influence of the bias applied between the graphene electrodes on the optical response of our quantum emitters in LED devices (see Fig. 2H for an optical image of a representative device). When applying the bias in the regime that corresponds to subbandgap electrical excitation, we observe predominantly the effects of the electric field on the emission resonances as shown in Fig. 3A. Generally, we identify two types of emitters: those that display emission energy 1) independent and 2) linearly dependent on the applied bias. For the latter type of emitters, we may assign them a dipole moment that corresponds to the spatial separation of the electron and hole in the range of 30 to 50 pm for various emitters under the assumptions discussed in SI Appendix. Tentatively, we attribute the emergence of the two types of emitters to the deformation of the WSe₂ film that is inevitably associated with the process of the creation of the quantum emitters in our method. We may envisage the appearance of wrinkles, folds, and/or other types of distortion of the WSe₂ monolayer that could induce spatial separation of charge carriers that form localized excitonic complexes.

Upon application of the larger bias, we find that our quantum emitters may be electrically excited to raise electroluminescence (EL), as presented in Fig. 3B. We observe a sharp onset at 1.8 V, above which electron and hole tunneling through hBN energy barriers takes place, followed by their radiative recombination in the WSe₂ monolayer. That leads to the emergence of narrow emission resonances in the EL spectra, characterized by the linearly dispersive states. This observation suggests that the nondispersive emitters do not give rise to tunneling pathways that favor efficient radiative recombination. Such conditions may be realized, e.g., when the tunneling times are significantly faster than the radiative lifetimes.

Interestingly, a certain duality of our emitters is also revealed by inspecting their magneto-optical response. In a simple view, we identify one class of emission resonances that display exclusively a Zeeman effect and another one when an anticrossing behavior around zero magnetic field is additionally observed. Representative examples of these two types of emitters are presented in Fig. 4 A and B. We interpret this observation by considering plausible recombination processes that may arise due to the unique character of the band structure of monolayer TMDs.

The spin and orbital composition of the fundamental subbands in monolayer WSe₂, which define the recombination path of free neutral excitons, is understood well (42). The optical transitions are active in ${\sigma }^{+}$/${\sigma }^{-}$ polarization and the helicity of light is coupled to ${\mathrm{K}}^{+}$/${\mathrm{K}}^{-}$ valleys, respectively. In the presence of a magnetic field, the energy of excitonic resonances is modified by the Zeeman effect with orbital, spin, and valley contributions (43). The linear dependence of the emission energy on the magnetic field for the emitters characterized by narrow resonances is demonstrated in Fig. 4A. Robust spin–orbit effects (44) lead to a spin splitting ${\mathrm{\Delta }}_{\mathrm{C}}=30$ meV in the conduction band and ${\mathrm{\Delta }}_{\mathrm{V}}=510$ meV in the valence band. The spin-preserving optical transitions related to the ground valence state (commonly referred to as excitons A), involve the electron from the higher energy conduction subband, making the ground state exciton in monolayer WSe₂ in principle dark. However, localization effects leading to the formation of quantum emitters may significantly alter this picture. In our samples, we typically observe narrow emission resonances about 60 meV below the free neutral exciton resonance. The difference in the emission energy between free and bound excitons ($\mathrm{\Delta }{\mathrm{E}}_{\mathit{PL}}$) may arise from the activation of alternative recombination paths, local modulation of the single particle band-gap and/or Coulomb effects as well as the creation of charged states. Under the assumption that the binding of the excitons occurs predominantly due to selenium vacancies, we can consider two types of localized states: 1) a defect-to-band transition related to the recombination of the electron occupying a Se defect level residing below the conduction band (45) with a free hole and 2) an exciton trapped electrostatically by electrons occupying dangling bond states forming a trion-like excitation (46). These two types of bound states constitute a probable origin of the narrow line emitters in our LED devices. Here, we will focus on developing a minimal model that explains the two types of magneto-optical behavior of our quantum emitters in a semiquantitative fashion.

First, let us note that the key parameters that impact the optical process in our quantum emitters fulfill a condition ${\mathrm{\Delta }}_{\mathrm{C}}<\mathrm{\Delta }{\mathrm{E}}_{\mathrm{PL}}<{\mathrm{\Delta }}_{\mathrm{V}}$. Within such an energy landscape, valley-mixing mechanisms between same-spin states in the conduction band constitute a first-order perturbation to the excitonic state and may be expected to naturally influence the quantum state of our single photon sources. For that reason, the intervalley recombination process of the ground state exciton is characterized by a finite oscillator strength via admixture of a bright exciton defined by a common hole state, as illustrated in Fig. 4B. In the case of the optical transitions within the unperturbed band structure as well as the transitions enabled by conduction band intervalley spin mixing, the quantum emitters display a Zeeman effect with an excitonic g-factor acting as a parameter that distinguishes the two recombination paths. The value of the g-factor in the unperturbed system is equal to −4 based on magneto-luminescence spectra of free neutral excitons in WSe₂ monolayers (47). Simple estimations of the g-factors of individual conduction states based on magneto-absorption data for charged excitons (43, 48) demonstrate that the ground state intervalley exciton is characterized by the largest g-factor among all the possible transitions within fundamental subband of WSe₂ monolayer with a tentative value of −10. In our samples, we find that statistically our emitters that display exclusively the Zeeman effect are characterized by the g-factors in the range from −4 to −15. Such observation supports the interpretation that intervalley mixing mechanism occurring in the conduction band of WSe₂ monolayers plays a significant role in the magneto-optical evolution of quantum emitters. The strength of this mixing is directly reflected in the value of the g-factors of individual resonances so that emitters that display a g-factor of −4 follow a recombination path given by the unperturbed band structure and those emitters with larger g-factor values arise due to states characterized by adequately greater intervalley admixtures. The first-order conduction band perturbations are not sufficient to explain the anticrossing behavior between excitons coupled to ${\mathrm{K}}^{+}$ and ${\mathrm{K}}^{-}$ valleys. To that end, we need to allow the intervalley mixing to occur in the valence band as well, which is unlikely to take place in a pristine WSe₂ monolayer lattice. Nevertheless, lattice imperfections that break the inversion symmetry of the WSe₂ monolayer constitute a plausible source of higher-order perturbations to localized excitonic states. Selenium vacancies (49, 50) fulfill such requirement, particularly in the presence of an out-of-plane electric field leading to a difference in electrostatic potential between the two selenium planes (51). In such a case, the typical selection rules imposed by the band structure are abolished, in favor of the creation of excitons formed from mixed ${\mathrm{K}}^{+}$ and ${\mathrm{K}}^{-}$ states, as illustrated in Fig. 5C.

We may write a valley exciton Hamiltonian in the presence of a magnetic field that captures the magneto-optical behavior of our quantum emitters. In the basis of an electron–hole pair residing in ${\sigma }^{+}$ and ${\sigma }^{-}$ valley, corresponding to vectors (1,0) and (0,1), respectively, the excitonic Hamiltonian ${\mathrm{H}}_{\mathrm{X}}$ takes the form:

where ${\mathrm{E}}_0$ is the transition energy, g is the excitonic g-factor, ${\mu }_B$ is the Bohr magneton and δ is the intervalley mixing parameter. The exciton energy, as seen in the magneto-photoluminescence spectra, is given by the eigenvalues ${\mathrm{E}}_0\pm \frac{1}{2}\sqrt{{\left(g{\mu }_{B}B\right)}^2+{\delta }^2}$. The eigenvectors are indicative of the mixing strength between ${\sigma }^{+}$ and ${\sigma }^{-}$ valley and define the oscillator strength of the transitions detected in ${\sigma }^{+}$ and ${\sigma }^{-}$ polarizations:

The energy and oscillator strength of the optical transitions active in ${\sigma }^{+}$ polarization with the parameters adjusted to reproduce the experimental spectra are presented in Fig. 4 C and D as color maps. The introduced parameters allow us to distinguish between the three recombination processes presented in Fig. 5A–C via the following conditions:

These three scenarios can be understood as different levels of preservation of the orbital Bloch functions of the free exciton in the localized state. Electrostatically bound excitons may exhibit wave function close to one originating from the unperturbed band structure, while transitions involving defect states and band carriers lead to valley mixing effects.

Our magneto-photoluminescence spectra detected in ${\sigma }^{+}$ polarization allows a straightforward identification of the type of quantum emitter by recognizing the dominant recombination paths as given by the proposed parameterization. The particulars of the excitonic states displayed by quantum emitters characterized by the excitonic Hamiltonian can be illustrated on the valley Bloch sphere as schematically presented in Fig. 4E. For $\delta =0$, the quantum emitters exist naturally in pure ${\mathrm{K}}^{+}$ and ${\mathrm{K}}^{-}$ states, which reside on the north and south poles of the Bloch sphere. For $\delta >0$, the excitonic states are magnetic field dependent. Without a magnetic field, the excitonic states take the form: $\frac{\text{1}}{\sqrt{\text{2}}}\left({\text{|K}}^{\text{+}}\rangle \pm {\text{|K}}^{\mp }\rangle \right)$, so that they reside on the opposite sides on the equator of the Bloch sphere. Upon application of a magnetic field, the eigenstates are gradually shifted along the meridian, eventually reaching the north and south poles in the limit of $\mathrm{g}{\mu }_{B}B\gg \delta$.

In conclusion, we have fabricated electrically driven light-emitting diodes that host intentionally created quantum emitters in a monolayer WSe₂. By inspecting the evolution of the photoluminescence and electroluminescence spectra in electric and magnetic fields, we identified various types of quantum emitters. We have proposed a minimal model, that allows the classification of our emitters by their dominant recombination processes within the fundamental subbands of monolayer WSe₂, which are determined by valley mixing mechanisms. Our findings identify quantum emitters as valley qubits, whose energy and composition of wave function are tunable, to a certain degree, by external fields.

This project was supported by the Ministry of Education (Singapore) through the Research Centre of Excellence program (Grant EDUN C-33-18-279-V12, I-FIM), and AcRF Tier 3 (MOE2018T3-1-005). This research is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (T2EP50122-0012). This material was based upon work supported by the Air Force European Office of Aerospace Research and Development Office of Scientific Research and the Office of Naval Research Global under Award No. FA8655-21-1-7026. The work was supported by the National Science Centre, Poland (Grant No. 2022/46/E/ST3/00166). K.S.N. acknowledges support from the Royal Society (UK, Grant No. RSRP/R/190000).