††thanks: These two authors contributed equally††thanks: These two authors
contributed equally

# Energy transfer from tunneling electrons to excitons

Sotirios Papadopoulos  Lujun Wang  Photonics Laboratory, ETH Zurich, 8093
Zurich, Switzerland.  Takashi Taniguchi  International Center for Materials
Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki,
Tsukuba 305-0044, Japan  Kenji Watanabe  Research Center for Functional
Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba
305-0044, Japan  Lukas Novotny<EMAIL_ADDRESS>Photonics Laboratory, ETH
Zurich, 8093 Zurich, Switzerland.

###### Abstract

Excitons in optoelectronic devices have been generated through optical
excitation, external carrier injection, or employing pre-existing charges.
Here, we reveal a new way to electrically generate excitons in transition
metal dichalcogenides (TMDs). The TMD is placed on top of a gold-hBN-graphene
tunnel junction, outside of the tunneling pathway. This electrically driven
device features a photoemission spectrum with a distinct peak at the exciton
energy of the TMD. We interpret this observation as exciton generation by
energy transfer from tunneling electrons, which is further supported by a
theoretical model based on inelastic electron tunneling. Our findings
introduce a new paradigm for exciton creation in van der Waals
heterostructures and provide inspiration for a new class of optoelectronic
devices in which the optically active material is separated from the
electrical pathway.

### Exciton generation in TMDs

Transition metal dichalcogenides (TMDs) have attracted attention due to their
interesting electronic and optical properties. In monolayer form, they exhibit
a direct bandgap [1], responsible for radiative electron-hole recombination
[2]. TMDs support excitons with high binding energies due to quantum
confinement [3], making their optical properties to be dominantly defined by
their excitonic states [4, 5, 6]. Exciton generation in TMDs was first studied
through optical excitation [1, 7, 2, 8, 9, 10]. Later, combination with
conductors (i.e. graphene) and insulators (i.e. hexagonal boron nitride) [11,
12] allowed the design and fabrication of light-emitting van der Waals (vdW)
heterostructures with TMDs as the optically active material [13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28]. In these studies, excitons
are electrically generated through direct charge injection [13, 14, 15, 16,
17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27] or through charge impact at high
alternating voltages [28]. Here, we introduce a different way to generate
excitons in TMD based tunneling devices. We use the rich platform of 2D
materials to demonstrate excitonic light emission from tunnel junctions where
the TMD is located outside of the current pathway.

The studied device structure is illustrated in Fig. 1A. The TMD and the tunnel
junction are electrically decoupled, preventing exciton generation through
direct electron-hole injection. The emission spectrum of such a device
features a distinctive peak at the exciton energy, as shown in Fig. 1B. We
attribute the generation of excitons to energy transfer (ET) from tunneling
electrons. ET from a donor to an acceptor is mediated by dipole-dipole
coupling [29, 30]. It is an electromagnetic effect that is dominant at the
near-field region of an emitter and has been extensively studied in biological
systems [31], molecular assemblies [32], solid-state quantum dots [33] and
photosynthetic membranes [34]. It has been also used for color conversion and
broadband source design as an energy exchange channel between different
fluorophores [35, 36]. Recent STM studies discuss the possibility of ET in
tunneling systems [26, 27] without however providing any conclusive
observation. Here we make use of atomically thin 2D materials and the flat
interfaces between them to preserve optical coupling in near-field distances
between a TMD and a tunnel junction. Our results reveal the role of ET between
electrons and excitons in tunneling-based light emitting devices.

Figure 1: Exciton generation in TMD-coupled tunnel junctions. (a) Device
composed of a WSe2-coupled graphene-hexagonal boron nitride (hBN)-gold tunnel
junction. The WSe2 layer is stacked on top of the junction. When a bias
voltage $V\mathrm{{}_{b}}$ is applied between graphene and gold, excitons are
generated in WSe2. (b) Measured spectrum at room temperature of the
electrically generated emission for $V\mathrm{{}_{b}}$ =
$2\text{\,}\mathrm{V}$. The peak position matches the WSe2 exciton energy and
the spectral width matches the thermal energy $k\mathrm{{}_{B}T}$.

### TMD-coupled tunnel junctions

Our devices are fabricated by stacking mechanically exfoliated flakes of 2D
materials with a dry pickup and transfer technique (see supplementary
materials for details). The resulting tunnel junctions consist of a graphene
and a gold electrode separated by a hexagonal boron nitride layer (hBN) of
$2.3\text{\,}\mathrm{n}\mathrm{m}$ thickness acting as a tunneling barrier.
The TMD is stacked on top of the junction and optionally separated from the
graphene electrode by a second hBN layer.

Figure 2A shows a false-color microscope image of the device with an outline
of the different flakes. The device area is indicated by a white dashed box.
The tunnel junction area is defined by the overlap of the gold electrode and
the graphene flake. The WSe2 flake is only partially covering the tunneling
area. This creates two different tunneling regions, with and without WSe2 on
top. We electrically and optically characterize the device by applying a bias
voltage ($V\mathrm{{}_{b}}$) between the gold and graphene electrodes, as
indicated in Fig. 2A, and we collect the emitted light with a high-numerical
aperture objective (see supplementary materials). The current and conductance
measurements suggest that tunneling occurs between graphene and gold (see Fig.
S1A). The spectra emitted from the whole tunneling area for various
$V\mathrm{{}_{b}}$ values are presented in Fig. 2B. There are two distinct
contributions in the spectra. A broad emission at lower energies and a narrow
emission peak at $1.63\text{\,}\mathrm{e}\mathrm{V}$
($762\text{\,}\mathrm{n}\mathrm{m}$). The broad emission shifts to higher
photon energies as $V\mathrm{{}_{b}}$ is increased. This behavior suggests
that the emission originates from inelastic electron tunneling that couples to
radiative modes of the free-space continuum (photon-coupling) with
e$V\mathrm{{}_{b}}$ being the cut-off energy of emission [37, 38]. The narrow
peak at $1.63\text{\,}\mathrm{e}\mathrm{V}$ corresponds to the neutral 1s
exciton of WSe2 and its narrow width of around
$25\text{\,}\mathrm{m}\mathrm{e}\mathrm{V}$ can be attributed to graphene
filtering [39]. It has been shown that charge transfer between graphene and
TMDs, filters the TMD photoluminescence spectra from any charged exciton
contributions [39]. To further our understanding, we study the emission
distribution for different spectral regions. Real space images of the
photoemission are presented in Fig. 2C, where we observe that the area covered
by WSe2 dominates the emission and in Fig. 2D, where the emission is filtered
by a band-pass filter at $900\text{\,}\mathrm{n}\mathrm{m}$. This is a
spectral region where the excitonic contribution is much reduced and the
emission extends over both device areas. This indicates that the broad low
energy contribution indeed originates from photon-coupling and is not
associated with the presence of WSe2. To understand the angular emission of
the device we record Fourier-space images. Fig. 2E shows the Fourier space
image of the full emission spectrum whereas Fig. 2F depicts the Fourier space
image of the bandpass filtered light around
$900\text{\,}\mathrm{n}\mathrm{m}$. For the spectrally filtered measurement at
900 nm, the emission vanishes at the center of the Fourier space
($k_{x}=k_{y}=0$) (Fig. 2F) indicative for an out-of-plane dipole orientation.
This is characteristic of inelastic electron tunneling where the transition
dipole is oriented along the electron path. On the other hand, when measuring
the full spectrum, the Fourier space image (Fig. 2E) is not zero at
$k_{x}=k_{y}=0$, which indicates an in-plane contribution. This extra
contribution is associated with the excitonic emission of WSe2, which is known
to originate from in-plane transitions [40]. We emphasize that in our devices
any exciton generation due to electron-hole injection is avoided due to the
WSe2 being outside of the tunneling pathway. This is further supported by the
fact that very similar emission spectra are observed for negative
$V\mathrm{{}_{b}}$ (see Fig. S2). For these reasons we conclude that excitons
are generated in the TMD by ET from tunneling electrons.
We continue to investigate this exciton generation process by considering the
band-structure diagram shown in Fig. 3A. Upon application of
$V\mathrm{{}_{b}}$, electrons tunnel from one electrode to the other,
elastically or inelastically. In the latter case, the transition dipole
associated with the energy loss $\Delta E$ couples to available optical modes
of the environment. Some of these modes are radiative (photons) as in the case
of the broad emission observed in Fig. 2A, or non-radiative, as in the case of
ET. This ET mechanism generates excitons in WSe2 and their spontaneous decay
contributes to the narrow emission peak in the spectra of Fig. 2B. Thus, the
excitonic emission observed in our device is a two step process, in which the
transition energy is first transferred to the WSe2 exciton and then
spontaneously emitted (exciton-coupling).
Next, we compare the ET efficiency to the photon-coupling efficiency. To do
that we first break down the processes to the involved interactions (see
pictorial representation in Fig. 3B) and we assign conversion efficiencies.
Both photon- and  exciton-coupling processes describe an electron-to-photon
($e\mathchar 45\relax\gamma$) conversion. Photon-coupling is a first order
process for which we define an $e\mathchar 45\relax\gamma$ conversion
efficiency as $\eta\mathrm{{}_{e\mathchar 45\relax\gamma}}$. Exciton-coupling
is a second order process in which we can assign a combined efficiency
$\eta^{\prime}\mathrm{{}_{e\mathchar
45\relax\gamma}}=\eta\mathrm{{}_{e\mathchar 45\relax
x}}\cdot\eta\mathrm{{}_{x\mathchar 45\relax\gamma}}$, where
$\eta\mathrm{{}_{e\mathchar 45\relax x}}$ is the ET efficiency and
$\eta\mathrm{{}_{x\mathchar 45\relax\gamma}}$ is the exciton to photon
conversion efficiency. From the spectra shown in Fig. 2B, we can infer a value
of 4.3 for the ratio between the photon-coupled emission and the exciton-
coupled emission. By taking into account the values for WSe2 PL efficiency and
the graphene quenching (see supplementary materials) we arrive at an
estimation of the ratio $\frac{\eta_{e\mathchar 45\relax x}}{\eta_{e\mathchar
45\relax\gamma}}\cong 10^{4}$. This result indicates that ET is orders of
magnitude more efficient than direct photon emission. In order to shed light
on this surprising finding we analyze in the next section the density of
optical states near a monolayer TMD.

Figure 2:  WSe2-coupled tunnel junction. (a) Optical microscope image in
false-color of a fabricated WSe2-Graphene-hBN-gold device. The different
flakes are outlined. The encapsulating hBN flake is not shown for clarity. The
dashed frame indicates the device area depicted in (c) and (d). (b) Recorded
emission spectra from the whole device area. Contributions from radiative mode
coupling (photon-coupling) and non-radiative mode coupling (exciton-coupling)
are observed. Real space (c,d) and Fourier space (e,f) images of the emission
from the dashed box in (a) for $V\mathrm{{}_{b}}$ = $2\text{\,}\mathrm{V}$.
The full emission spectrum is used in (c) and (e) whereas a bandpass filter
with center wavelength 900 nm and 40 nm FWHM is used in (d) and (f). Only half
of every Fourier space is imaged for ease of comparison. The white solid lines
are the rotational averages of the two Fourier spaces in (e) and (f).

### Optical density of states near monolayer TMDs

Figure 3:  Photon and exciton coupling of inelastic tunneling electrons. (a)
Band diagram of the TMD-coupled tunnel junction. A voltage $V\mathrm{{}_{b}}$
is applied across the hBN barrier between graphene and gold electrodes. Part
of the electrons tunnel inelastically. They either couple to radiative modes
(1) or couple non-radiatively to the TMD via ET (2). The generated excitons
decay radiatively making the ET process detectable in the farfield. (b)
Pictorial representation of the physical processes involved in the light
emission. In (1) electron-hole recombination is followed by photon emission.
In (2) ET is depicted as a virtual photon $\gamma_{v}$ that couples to the TMD
and creates an electron-hole pair (x). (c) Angular spectral density of
$\mathrm{\rho_{opt}}$ for the case of an out-of-plane dipole placed
$2\text{\,}\mathrm{nm}$ away from a monolayer WSe2. Optical properties are
taken from [4]. The contribution of non-radiative modes ($\mathrm{\rho_{nr}}$)
is substantially higher than the contribution of radiative modes
($\mathrm{\rho_{r}}$). The calculation assumes a photon energy of
$1.68\text{\,}\mathrm{e}\mathrm{V}$, matching the exciton energy of [4]. The
x-axis is normalized by the vacuum wavenumber $k_{0}$ and the y-axis is
normalized by $\rho_{0}/k_{0}$, where $\rho_{0}$ is the vacuum LDOS. Inset in
(c) illustrates the calculated system.

When a dipole interacts with an absorbing material at a distance much smaller
than the wavelength, the largest fraction of the dissipated power is
associated with non-radiative energy transfer (ET) from the dipole to the
material [41, 42]. The rate of this process is related to the local density of
optical states (LDOS) $\mathrm{\rho_{opt}}$. In Fig. 3C we show the calculated
angular spectral density of the LDOS,
$\frac{\mathrm{d\rho\mathrm{{}_{opt}}}}{\mathrm{d}k\mathrm{{}_{\parallel}}}$,
as a function of $k_{\parallel}$ for the simple case of a dipole at
$2\text{\,}\mathrm{n}\mathrm{m}$ distance from a TMD monolayer. Here,
$k_{\parallel}$ is the wavevector component along the plane of the TMD
monolayer (see inset in Fig. 3C) and $k\mathrm{{}_{0}}$ is the wavenumber for
a photon energy equal to the exciton energy of WSe2. The calculated
$\mathrm{\rho_{opt}}$ for $k_{\parallel}<k_{0}$ includes radiative modes
associated with photon emission ($\mathrm{\rho_{r}}$) whereas the region
$k\mathrm{{}_{\parallel}}>k\mathrm{{}_{0}}$ accounts for non-radiative modes
($\mathrm{\rho_{nr}}$) associated with ET. $\mathrm{\rho_{nr}}$ is orders of
magnitude higher than $\mathrm{\rho_{r}}$. Moreover, the influence of the TMD
on $\mathrm{\rho_{r}}$ enhancement is negligible. Hence, the TMD introduces
mainly additional non-radiative decay channels that are associated with near-
field ET ($\rho\mathrm{{}_{opt}}\cong\rho\mathrm{{}_{nr}}$), and is the reason
for the high $\frac{\eta\mathrm{{}_{e\mathchar 45\relax
x}}}{\eta\mathrm{{}_{e\mathchar 45\relax\gamma}}}$ ratio. The ET process in
our measurements is highly efficient and shows that near-field interactions at
nanoscale distances are dominating the LDOS. Here, we probe this non-radiative
interaction by using a direct-gap semiconductor whose luminescence is a direct
measure for the ET efficiency. In essence, the TMD acts as a receiving optical
antenna that enhances the LDOS and converts non-radiative modes to a
measurable signal. We refer to this process as electron-photo-luminescence
(ePL) since it is triggered by an electron that transfers energy through
optical modes to WSe2.

### Dependence on TMD-Graphene separation

To further test our interpretation, we study the dependence of the excitonic
emission on the distance between the TMD and the tunnel junction. A device
schematic is shown in Fig. 4A where we vary the coupling to the TMD by
changing the thickness $d_{\mathrm{s}}$ of a hBN spacer layer (s-hBN) in
different device regions. Figure 4B shows the emitted light from a device
where the s-hBN presents steps in thickness in the tunnel junction area. Four
regions of emission are created. Three with different s-hBN thicknesses (6, 5
and 4 layers) and one without WSe2 on top. We observe that the emission gets
stronger the thinner the s-hBN is. As evidenced by the spectra shown in Fig.
4C the enhanced emission can be entirely attributed to the strength of the
excitonic peak. We thus find that the excitonic contribution increases for
thinner s-hBN in contrast to the broadband background that doesn’t show any
major change. A comparison of the excitonic emission intensity
$I\mathrm{{}_{x}}$ for different $d\mathrm{{}_{s}}$ at $V\mathrm{{}_{b}}$ =
$2\text{\,}\mathrm{V}$ is given in Fig. 4D. To compare different devices we
normalize $I\mathrm{{}_{x}}$ by the area of emission, the PL efficiency and
the background level (see supplementary materials). The data points in Fig. 4D
clearly show that the rate of exciton generation, and hence the ET rate, decay
superlinearly with the separation $d_{\mathrm{s}}$.

$I\mathrm{{}_{x}}$ can be modeled by calculating the exciton generation rate
$\Gamma\mathrm{{}_{x}}$. By using inelastic tunneling theory [43]
$\Gamma\mathrm{{}_{x}}$ assumes the following expression:

$\displaystyle\Gamma\mathrm{{}_{x}}(V\mathrm{{}_{b}},d\mathrm{{}_{s}})\propto$
(1) $\displaystyle\int_{0}^{\infty}\eta\mathrm{{}_{abs}}(\omega)$
$\displaystyle\frac{\gamma\mathrm{{}^{0}_{inel}}(\omega,V\mathrm{{}_{b}})}{\rho\mathrm{{}_{0}}(\omega)}[\rho\mathrm{{}_{opt}}(\omega,d\mathrm{{}_{s}})-\rho\mathrm{{}_{opt}}(\omega,\infty)]d\omega$

where $\omega$ is the angular frequency, $\eta\mathrm{{}_{abs}}$ is the
absorption spectrum of monolayer WSe2 [7], $\gamma\mathrm{{}^{0}_{inel}}$ is
the inelastic tunneling spectral rate in vacuum and $\rho\mathrm{{}_{0}}$ is
the vacuum LDOS. We approximate the LDOS responsible for exciton generation by
$\rho\mathrm{{}_{opt}}(\omega,d\mathrm{{}_{s}})-\rho\mathrm{{}_{opt}}(\omega,\infty)$
which assumes that the states provided by the TMD, leading to exciton
generation, vanish for $d\mathrm{{}_{s}}\shortrightarrow\infty$. See
supplementary materials for more information on the calculation. The
calculated $\Gamma\mathrm{{}_{x}}$ as a function of distance
$d\mathrm{{}_{s}}$ and for $V\mathrm{{}_{b}}$ = $2\text{\,}\mathrm{V}$ is
plotted in Fig. 4D. It agrees well with the distance dependent measurement.
Interestingly, both $\Gamma\mathrm{{}_{x}}$ and the measured data can be
described by a simple inverse square law, as shown in Fig. 4D. Similar
observations were reported for ET between optically excited TMDs [44]. The
good agreement between our theoretical model and our experimental measurements
supports our interpretation.

Figure 4: Distance dependent energy transfer. (a) Schematic of a TMD separated
from the tunnel junction by a spacer-hBN (s-hBN). The coupling strength
between TMD and the tunnel junction is varied using different s-hBN
thicknesses $d_{\mathrm{s}}$. (b) Real-space image of emission from the
WSe2/s-hBN/Gr/b-hBN/gold device. Strongest emission is observed from the
thinnest s-hBN region. The emission is filtered with a bandpass filter
($\lambda_{center}$ = $750\text{\,}\mathrm{nm}$ and fwhm =
$40\text{\,}\mathrm{nm}$). The scale bar is
$4\text{\,}\mathrm{\SIUnitSymbolMicro m}$. (c) Spectra measured on areas with
different s-hBN thickness and for $V\mathrm{{}_{b}}$ = $2\text{\,}\mathrm{V}$.
The broad spectral background corresponds to direct photon coupling and is
also observed in areas with no WSe2. (d) Excitonic emission Ix as a function
of $d\mathrm{{}_{s}}$. The values are normalized with the PL efficiency, the
emission area and the intensity of background emission. The measurement point
at $d\mathrm{{}_{s}}$ = $0\text{\,}\mathrm{n}\mathrm{m}$ refers to the device
presented in Fig. 2. The three points between $d\mathrm{{}_{s}}$ =
$1\text{\,}\mathrm{n}\mathrm{m}$ and $2.5\text{\,}\mathrm{n}\mathrm{m}$ refer
to the device presented in Fig.4B and the point at $d\mathrm{{}_{s}}$ =
$5\text{\,}\mathrm{n}\mathrm{m}$ refers to a third device, for which spectra
are presented in Fig. S2. The dashed curve is the result of Eq. 1 and the
solid curve is a fit with an inverse square distance function.
$\mathrm{D+d_{s}}$ is the distance between the TMD and the center of the b-hBN
layer as illustrated in (a).

### Monolayer vs bilayer TMD

We continue our study by using a different TMD (MoSe2) and by comparing ET for
monolayers (1L) and bilayers (2L). Figure 5A shows a schematic of the device
and the measured ePL spectra. The emission for 2L MoSe2
($I\mathrm{{}_{2L}^{ePL}}$) is less intense than for 1L MoSe2
($I\mathrm{{}_{1L}^{ePL}}$) owing to the indirect bandgap of 2L MoSe2. To
compare this ET-mediated photoluminescence (ePL) with optically excited
photoluminescence (PL) we optically excite the two regions with a laser and
measure the corresponding emission spectra $I\mathrm{{}_{1L}^{PL}}$ and
$I\mathrm{{}_{2L}^{PL}}$, respectively. The measurements are presented in Fig.
5B. The center wavelengths and the shapes of PL and ePL spectra match very
well, which supports the interpretation that ePL corresponds to spontaneous
exciton emission. We note however, that the ratios
$I\mathrm{{}_{1L}^{PL}}$/$I\mathrm{{}_{2L}^{PL}}$ and
$I\mathrm{{}_{1L}^{ePL}}$/$I\mathrm{{}_{2L}^{ePL}}$ are different.
Interestingly, the $I\mathrm{{}_{1L}^{ePL}}$/$\mathrm{I_{2L}^{ePL}}$ ratio
depends on $V\mathrm{{}_{b}}$. In fact, $I\mathrm{{}_{2L}^{ePL}}$ is stronger
than $I\mathrm{{}_{1L}^{ePL}}$ for low voltages and a crossing occurs near
$V\mathrm{{}_{b}}$ = $1.75\text{\,}\mathrm{V}$, as shown in Fig. 5C, which
depicts the integrated spectra for different voltages. By employing the model
in Eq. 1 we are able to reproduce this effect. The result of this calculation
is given in the inset of Fig. 5C. The reason for this voltage dependence are
the different optical properties of 1L and 2L MoSe2, i.e. the absorption
spectrum $\eta\mathrm{{}_{abs}}$ of 2L MoSe2, which features a cut-off energy
at lower energies and stronger absorption than the 1L MoSe2. This explains the
earlier onset-voltage for $I\mathrm{{}_{2L}^{ePL}}$ in Fig. 5C. Moreover, the
two curves are also affected by the dependence of the LDOS on flake thickness.
In fact, our model predicts that the rate of ET to a 2L TMD is lower compared
to a 1L despite the fact that the 2L TMD is thicker. This surprising behavior
has been studied in the past in optically excited systems [45].

Figure 5: Tunnel junctions coupled to monolayer and bilayer MoSe2. (a) ePL
emission spectra from a device with monolayer (1L) and bilayer (2L) MoSe2.
Spectra taken at $V\mathrm{{}_{b}}$ = $1.9\text{\,}\mathrm{V}$. The inset
shows the device schematic. (b) PL emission from 1L and 2L regions of the same
device. (c) Integrated intensities of the ePL spectra in (a) as a function of
$V\mathrm{{}_{b}}$. The inset shows corresponding theoretical curves based on
Eq.1.

### Discussion

The exciton generation mechanism, discussed in this work, is an
electromagnetic phenomenon that is usually neglected in the analysis of
tunneling driven systems. The tunneling probability of an electron relies on
the available electronic states but also optical states. In semiconducting
materials, exciton resonances provide non-radiative optical states that couple
strongly with inelastic electrons increasing the tunneling probability. This
leads to near-field generation of excitons even for applied voltages below the
electronic bandgap of the material, thus contributing to sub-bandgap emission.
Such low voltage emission has been previously studied with interpretations
varying from direct exciton formation [16] to Auger scattering [24]. Here we
show that ET from tunneling electrons can contribute to this sub-bandgap
emission.

### Conclusions

We investigated ET from a tunnel junction to TMD excitons. Our studies are
based on vdW tunnel devices in which the TMD is placed outside the electronic
pathway, ensuring that there is no direct charge injection into the TMD. We
studied photoemission spectra as well as real space and Fourier space emission
patterns and we concluded that excitons are generated when the tunnel junction
is under bias. This surprising observation is understood by ET from tunneling
electrons to excitons. Emission from excitons is observed even when the TMD is
separated from the junction by a hBN spacer layer. Our calculations reveal
that non-radiative modes of the LDOS are strongly increased at the exciton
energy. These non-radiative modes are responsible for the efficient energy
transfer from the tunnel junction to the TMD. Our theoretical model based on
inelastic tunneling theory and near-field coupling is in agreement with our
experimental measurements.
The electrical generation of excitons via ET provides new perspectives for the
development of optical sources, detectors and sensors. For example, it can be
employed for truly chip-scale light sources with applications in electrical
pumping scheme for vdW heterostructure lasers [46, 47] or optical sensing
schemes [48] that do not rely on external laser sources.

## Acknowledgments

The authors would like to thank Mathieu Luisier, Achint Jain, Martin Frimmer,
Ronja Khelifa, Anna Kuzmina, Shengyu Shan and Massimiliano Rossi for fruitful
discussions. This study was supported by funding from ETH Zurich under ETH
Grant No. ETH-15 19-1 SYNEMA, the ETH Zurich Foundation project number 2013-08
(11) with a donation from the Stavros Niarchos Foundation, and the Swiss
National Science Fund under grant number $200020\\_192362$. K.W. and T.T.
acknowledge support from the JSPS KAKENHI (Grant Numbers 19H05790, 20H00354
and 21H05233).

## Author contributions

S.P., L.W. and L.N. conceived the experiment. S.P. fabricated the devices,
performed the measurements, analysed the data, developed the theoretical model
and performed the calculations. L.W. supported in the device fabrication. L.W.
and L.N. helped with the data interpretation. K.W. and T.T. provided the high-
quality hBN crystals, L.N. initiated and supervised the project. S.P. wrote
the paper and all authors discussed the results and worked on the manuscript.

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