Overbias Photon Emission from Light-Emitting Devices Based on Monolayer Transition Metal Dichalcogenides

Tunneling light-emitting devices (LEDs) based on transition metal dichalcogenides (TMDs) and other two-dimensional (2D) materials are a new platform for on-chip optoelectronic integration. Some of the physical processes underlying this LED architecture are not fully understood, especially the emission at photon energies higher than the applied electrostatic potential, so-called overbias emission. Here we report overbias emission for potentials that are near half of the optical bandgap energy in TMD-based tunneling LEDs. We show that this emission is not thermal in nature but consistent with exciton generation via a two-electron coherent tunneling process.

A typical device architecture is shown in Fig. 1a.It consists of a Gr-hBN-WSe 2 -hBN-Gr heterostructure, with two monolayer Gr flakes acting as transparent electrodes and two hBN multilayers defining the tunnel barriers.A monolayer WSe 2 is sandwiched in the middle and serves as the active material.Such double-tunnel barrier LEDs provide large-area exciton light emission with an external quantum efficiency (EQE) on the order of 10 −2 at room temperature [1,2].Here, excitons are formed by charge injection of both electrons and holes into the active layer.This requires the applied bias potential (eV b , where e is the elementary charge, V b is the bias voltage) to be larger than the optical bandgap energy so that electrons and holes can tunnel from the Gr electrodes to WSe 2 , thereby forming excitons [8].
However, there are also alternative ways to generate excitons for light emission, such as by energy transfer.This process involves inelastic electron tunneling (IET), in which the electron couples its energy to TMD excitons during the tunneling process [9][10][11].Such energy transfer can occur efficiently in van der Waals (vdW) heterostructures and is due to strong near-field coupling between the tunneling electrons and the active material.Thus, excitons in TMDs can be generated either by charge injection or by energy transfer.In both processes energy conservation requires that the bias potential eV b is larger than the optical bandgap energy hω BG (hω BG 1.64 eV for monolayer WSe 2 at room temperature [12], where h is the reduced Planck constant, and ω BG is the angular transition frequency); no excitonic photon emission is expected for eV b < hω BG [8,9].
In this paper, we report on exciton light emission from a monolayer TMD tunneling LED driven by bias potentials (eV b 1.00 eV) much smaller than the optical bandgap energy (hω BG 1.64 eV).To identify the physical origins of this overbias emission we perform electroluminescence (EL) measurements on various LED designs and at different temperatures.
In addition to double-barrier LEDs we also investigate single-barrier Gr-TMD-hBN-gold heterostructures, with TMD = {WSe 2 , MoSe 2 }.Compared with double-barrier LEDs, single-barrier LEDs can reach higher currents under the same bias voltage, thus allowing us to observe exciton emission at very low bias voltages.With this architecture, we start to detect light emission from the A-exciton in WSe 2 at 0.81 V and at 0.74 V in MoSe 2 .The measured threshold voltages correspond to approximately half the optical bandgap energies.This observation hints at a second-order energy transfer process based on multielectron tunneling [21][22][23].We first describe our results for the double-barrier LED shown in Fig. 1a.The core structure is a vertical assembly of Gr-hBN-WSe 2 -hBN-Gr, in which two Gr flakes serve as electrodes.The hBN thickness corresponds to 4±1 atomic layers.This tunnel junction is encapsulated between two thick hBN flakes.We fabricate our devices by using the dry pick-up and transfer method [26], where we transfer the entire device onto a glass coverslip.After transfer we fabricate edge contacts to the two graphene electrodes [27,28].EL is collected with an oil-immersion objective from the glass side and detected by a spectrometer.(See the Supplemental Material [29], Sec.I, II).
Monolayer WSe 2 has an electronic bandgap of ∼1.82 eV [30] and an optical bandgap of ∼1.64 eV at room temperature [12].To electrically generate excitons, the bias potential eV b has to be larger than the optical bandgap energy [8]. Figure 1b shows a representative EL spectrum for V b = 1.65 V.The peak of the spectrum centers at ∼1.64 eV, which corresponds to the A-exciton of WSe 2 [8].The asymmetric broadening at lower energy can be associated with the trion [8].However, we also observe exciton light emission for eV b significantly smaller than the optical bandgap.As an example, Fig. 1c shows the EL spectrum for V b = 1.04 V. Compared to Fig. 1b, this spectrum has the same main peak position and sim-ilar linewidth, indicating that the spectrum is also dominated by the contribution from A-exciton.The spectral shape remains similar, but the intensity and hence the EQE decreases.We define EQE as η EQE = Γ X I/e , where Γ X is the photon count rate in the spectral range from 1.4 to 1.8 eV and I is the electrical current (for more details, see the Supplemental Material [29], Sec.III).As shown in Fig. 1d, the EQE drops exponentially with decreasing V b and disappears in the noise floor at ∼0.93 V. To extend the measurement range to even lower bias voltages we require a higher emission intensity and hence a higher tunnel current.Therefore, in a next step, we eliminate one of the tunnel barriers and repeat the measurements for a single-barrier device.The architecture of a single-barrier LED is shown in Fig. 2a.The device is composed of a Gr-WSe 2 -hBN-gold heterostructure, where the monolayer Gr is contacted to a gold electrode.As shown in Fig. 2c, by using a singlebarrier device (hBN with 3±1 atomic layers) we are able to increase the current density by ∼4 orders of magnitude over the previous double-barrier device.The EL spectra of the single-barrier device are shown in Fig. 2b for different bias voltages.The spectra have a peak at ∼1.62 eV (horizontal dotted line), which is slightly redshifted compared to the double-barrier LED.Consequentially, we assign this peak to the neutral A exciton, which is shifted to lower energies due to the stronger dielectric screening of the directly contacting Gr [31].The overall EL is moderately quenched and becomes trion-free due to both charge and energy transfer [31,32].As we gradually lower V b , the exciton peak remains visible in the spectrum, even for eV b = 0.81 eV (vertical dotted line), corresponding to half of the WSe 2 optical bandgap energy (hω BG = 1.62 eV).The EL spectrum for V b = 0.81 V is shown in Fig. 2d (light orange area).Its shape is almost identical to the spectrum recorded for 1.62 V (solid orange curve).This observation hints at a second-order process involving two electrons.

OVERBIAS LIGHT EMISSION FROM A MOSE2-BASED SINGLE-BARRIER LED
In order to further strengthen our interpretation, we replace WSe 2 by MoSe 2 , which has a lower bandgap and should therefore lead to EL at even lower bias voltages.Furthermore, it is known that the exciton emission from MoSe 2 is less affected by Gr quenching [31], thus yielding stronger EL emission and providing a better signal-tonoise ratio.Figure 3a shows voltage-dependent EL spectra, in which the peak near 1.56 eV (horizontal dotted line) is assigned to the red-shifted A-exciton (1s state) of monolayer MoSe 2 [31].This feature appears at the lowest voltage of 0.74 V (vertical dotted line), which again is much lower than the photon energy of 1.56 V.At higher biases, two side peaks appear near 1.66 eV and 1.71 eV.According to their energy offsets relative to the A-exciton we assign the first to the 2s and 3s state of A-exciton and the second to the B-exciton [33].
To analyze the voltage dependence of these three features, we fit the spectra with three pseudo-Voigt functions.The corresponding fitting amplitudes are plotted in Fig. 3b as a function of the bias voltage (see the Supplemental Material [29], Sec.IV).We observe that the three peaks emerge at different bias voltages: the lowest state of A-exciton with a peak position near 1.56 eV appears for V b > 0.74 V, the 2s and 3s excited states near 1.66 eV have an onset voltage of 0.82 V, and the Bexciton with the highest energy (∼1.71 eV) emerges at V b = 0.84 V. Altogether, each of the three features in MoSe 2 emerges at bias potentials of half the photon energy (eV b hω/2), similar to the WSe 2 device.

ANALYSIS OF UNDERLYING MECHANISMS
Besides a second-order process involving two electrons, other processes can also give rise to overbias emission.These include: 1. Blackbody radiation of hot carriers, in which the effective temperature is related to the bias voltage or the input power [17-19, 34, 35].
2. Recombination of out-of-equilibrium carriers [20], in which electrons and holes in the high energy tail of the Fermi-Dirac distribution tunnel into the TMD to form excitons.
3. Second-order nonlinear optical processes, in which photons generated by IET [36,37] excite excitons in the TMD.
4. Second-order energy transfer, in which the energy from pairs of coherently tunneling electrons [21][22][23] is forming excitons in the TMD.
To exclude the first two effects, we fabricated yet another single-barrier MoSe 2 LED and measured its EL at cryogenic temperature (∼10 K). (See the Supplemental Material [29], Sec.V).To rule out a thermal origin for the observed overbias emission we use the following black-body radiation model for the radiated power [17][18][19]: where c is the speed of light, ω the photon angular frequency, k B the Boltzmann constant, T the effective hot carrier temperature and the emissivity of the TMD exciton, which can be derived from the refractive index [38].For resistive heating we obtain the linear dependence [18,19]: where T 0 is the lattice temperature and κ is a temperature-independent dimensionless constant that can be derived from experimental data at room temperature.With this κ, Eq. ( 1) predicts that the radiated power in the spectral region of the exciton should decrease by roughly 9 orders of magnitude when T 0 is reduced from 300 K to 10 K.However, our measurements show only a decrease of less than 2 orders of magnitude.This huge discrepancy between model and measurement indicates that blackbody radiation is not the source of the observed overbias emission.The same is true for the second scenario, the recombination of out-of-equilibrium carriers, since our measurements reveal that the dependence of the radiated power on bias voltage is unaffected by the lattice temperature.(See the Supplemental Material [29], Sec.V for analysis details).The third scenario involves two steps, namely photon emission by IET [36,37] and a subsequent nonlinear optical process.Comparing the photon emission efficiencies of IET and the observed overbias emission, we require a nonlinear optical process with unit efficiency to explain our measurements.Therefore, it is safe to discard the third scenario as an explanation for our observation.
We are left with the fourth scenario, illustrated in Fig. 4a.In this scenario, excitons are generated by the action of two electrons.This process is supported by two recent observations.First, it has been demonstrated that excitons can be efficiently excited by tunneling electrons via nonradiative energy transfer [9].Second, it has been reported that multielectron coherent tunneling can generate overbias emission in plasmonic tunnel junctions [21][22][23][24][25]. Therefore, we identify multielectron IET as the most likely mechanism responsible for the observed overbias emission.

THEORY OF TWO-ELECTRON ENERGY TRANSFER
In plasmonic tunnel junctions, overbias light emission based on two-electron IET depends on the interplay between higher-order quantum noise and the local density of optical states (LDOS) [21,22].Here we adopt this theory to a TMD-coupled tunnel junction.The nonsymmetrized power spectral density of the fluctuating tunnel current reads as [39,40] S where I(V b ) is the bias-dependent tunnel current and n B (x) = (exp(x/k B T ) − 1) −1 is the Bose-Einstein distribution at temperature T. We are concerned with the absorption of electromagnetic energy generated by the fluctuating tunneling current, which is described by the positive frequency part of S ii [41].
The absorption depends on the local environment of the tunnel junction, and is mathematically described by the LDOS (ρ) and the system's Green's function [42].For frequencies near the TMD exciton the absorption is dominated by the LDOS of the TMD (ρ TMD ).In a twoelectron process, the locally absorbed energy is no longer linearly dependent on S ii .In analogy to previous studies [23][24][25] the two-electron absorption rate γ 2e can be represented as where ρ TMD is calculated by following Ref.[37].Equation (4) describes a two-electron tunneling process, in which the energy of two electrons is absorbed by the TMD to generate an exciton (Fig. 4a).Since excitons can only be generated by energies larger than the exciton energy (hω > E X ) we can represent the exciton emission intensity Γ X as Γ X (V b ) ∝ ∞ EX/h γ 2e (ω, V b )dω. (5) As can be seen in Fig. 4b, the exciton EL intensity increases exponentially with increasing V b , and the calculated Γ X (V b ) according to Eq. ( 5) agrees well with the experimental results.(See the Supplemental Material [29], Sec.VI).This agreement supports our interpretation that the overbias emission in our TMD-based LEDs results from two-electron tunneling followed by energy transfer.
In summary, we investigated exciton light emission for potentials lower than the optical bandgap energy in TMD-based tunneling LEDs.We are able to measure exciton emission for bias potentials of only half the optical bandgap energy.We explain this overbias emission by a second-order energy transfer process.

12 FIG. 1 .
FIG. 1. a, Illustration of a double-barrier tunneling LED.The junction is encapsulated in hBN on both sides (not shown).b, c, EL spectra of the double-barrier LED for V b = 1.65 V and V b = 1.04 V, respectively.The measured spectra (green areas) are fitted with the sum of two pseudo-Voigt functions (black lines) representing A-exciton and trion.d, EQE (in the spectral range from 1.4 to 1.8 eV) as a function of applied bias.The green dots represent data points and the black curve is a guide-to-the-eye.

FIG. 2 .
FIG. 2. a, Illustration of a single-barrier LED.The stack is encapsulated by a top hBN flake (not shown).b, EL spectra for V b ranging from 0.7 V to 0.95 V.The horizontal dotted line indicates the neutral exciton energy (1.62 eV) and the vertical dotted line denotes the threshold for exciton emission.There is a factor of 10 difference between the two dashed contour lines.c, Current density-voltage (J-V) curve of a single-and a double-barrier LED.d, Normalized EL spectra for V b = 0.81 V and 1.62 V.
FIG. 3. a, EL spectra of a single-barrier LED based on MoSe2.The horizontal dotted line indicates the neutral exciton energy (1.56 eV) and the vertical dotted line denotes the threshold for exciton emission.There is a factor of 10 between adjacent dashed contour lines.b, Dependence of the integrated EL intensity of A1s, A2s + A3s, and B1s excitons on bias voltage.

FIG. 4 .
FIG. 4. a, Energy transfer based on two-electron coherent tunneling.A pair of electrons tunnel inelastically and their combined energy generates excitons in the TMD.b, Exciton EL intensity (Γ X ) of a single-barrier WSe2 LED as a function of bias voltage V b .The inset shows the data on a semilogarithmic scale.The data points correspond to the integrated EL photon count rate in the spectral range from 1.4 to 1.8 eV.The dashed curve is the fitting result of Eq. (5).