## Introduction

Research on semiconducting transition metal dichalcogenide (TMDs) monolayers1,2,3 and their heterostructures is motivated by collective effects of the electronic system4,5,6 and the potential for emerging optoelectronic and quantum technology devices7,8,9,10,11,12,13,14,15,16,17. The optical and electronic properties of these materials can be tuned by combining different monolayers via van der Waals stacking to create vertical heterostructures18,19,20. But interestingly, tuning of optical properties of TMDs can also be achieved while staying in the ultimate monolayer limit. Recent progress is based on innovative growth techniques such as for Janus monolayers with different top and bottom chalcogen21,22,23,24, as well as in lateral heterostructures (LHs)25,26 within the monolayer plane with an atomically-sharp 1D interface which exhibits p-n junction characteristics27,28. Examples of potential applications for LHs are photodetectors29, p-n junction diodes25,30,31, photovoltaic30, electroluminescent30 and quantum devices32.

LHs can be fabricated following one-step25,26,28,31 or multiple-step33,34 growth processes either by physical vapor deposition (PVD) or by chemical vapor deposition (CVD). Electron beam lithography has also been used for the fabrication of LHs35. One-step CVD approaches with suitable growth conditions are simpler and have the advantage to grow large area TMD LHs at lower temperatures25. Accessing the quality of the monolayer heterojunction is so far mainly based on electron microscopy techniques. A depletion width on the order of few nanometers is reported using scanning tunneling microscopy and spectroscopy techniques36. The electronic structures and band alignments of TMD LHs have been calculated using density functional theory37 and the formation of interface excitons is predicted by tight-binding models, as well as effective mass models38.

To further access carrier dynamics and excitonic properties at the interface optical spectroscopy is needed as a powerful and non-invasive tool. But in as-grown CVD samples details are masked due to the large inhomogeneous broadening reported for the optical transitions, mainly investigated at room temperature26,28,30,31.

Here we perform optical spectroscopy and microscopy experiments in high quality CVD-grown MoSe2-WSe2 monolayer LHs25. We first lift the LHs from the growth substrate. This procedure shows that transfer of the LH to other substrates is possible for device processing. Second, we encapsulate the LHs in high quality exfoliated hBN flakes39 (Fig. 1a). Encapsulation of the TMD monolayer in high quality hexagonal boron nitride (hBN)39 is crucial to access the intrinsic optical properties of exfoliated and CVD grown flakes40,41,42,43,44,45,46,47,48. We report optical transition linewidth of the LH monolayer (≈5 meV at T = 4 K) comparable to high quality exfoliated layers. Our step-by-step scans across the heterojunctions in optical spectroscopy experiments show an abrupt change from WSe2 to MoSe2. In atomic-resolution transmission electron microscopy on our samples we find a transition with a nm-sharp junction from MoSe2 to WSe2. The structural quality is also demonstrated in Raman spectroscopy. Photoluminescence (PL) imaging experiments allow us to investigate excitonic transport governed by the different effective lifetime of the exciton species for MoSe2 and WSe2 at T = 4 K and 300 K. We study exciton transport in sub-wavelength, tip-enhanced PL (TEPL) and Raman scattering (TERS) experiments at T = 300 K. Owing to our spatial resolution of 40 nm we uncover unidirectional exciton transport across the lateral heterojunction from WSe2 to MoSe2, that we model numerically.

## Results and Discussion

### Sample preparation, electron microscopy and optical quality

Our MoSe2-WSe2 lateral monolayer heterojunction is grown by CVD synthesis that we reported recently25. A schematic representation of the encapsulated MoSe2-WSe2 structure is shown in Fig. 1a. Figure 1b shows high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) image recorded at the boundary region of the MoSe2-WSe2 structures. The image was recorded at an operating voltage of 200 kV, see supplement. The atomically resolved HAADF image allows the detection of the roughness of the interface at sub-nm resolution due to exploiting of the Z-contrast, where lighter Mo atoms show darker contrast than heavier W atoms49. Thus, MoSe2 appears darker and WSe2 appears brighter. From these measurements we estimate the transition width of the boundary region between MoSe2 and WSe2 to be as narrow as ≈3 nm. This sharp, high quality junction enables us to gain insights into exciton transport experiments across the heterojuntion with sub-wavelength resolution, see discussion below.

We use water-assisted deterministic transfer to pick up as-grown, CVD LHs using polydimethylsiloxane (PDMS) and deterministically transfer and encapsulate them in hBN47,50. We use these encapsulated samples for all optical spectroscopy measurements.

We first analyze the PL and differential white light reflectivity spectra of the individual monolayer areas (away from the heterojunction), collected at T = 4 K. Figure 1c shows superimposed PL (black) and reflectivity (red) spectra of MoSe2 (top) and WSe2 (bottom) monolayers after transfer and encapsulation in hBN. We measure in PL a neutral exciton (A1s) linewidth of 7 meV in MoSe2 and 5.5 meV in WSe2 (Fig. 1c). These FWHM values are comparable to high-quality exfoliated MoSe2 and WSe2 monolayers15,43,44,45. MoSe2 monolayers exhibit two pronounced PL emission peaks at 1.665 eV and 1.635 eV, assigned to neutral (A1s) and charged (T) excitons, respectively51. In the case of WSe2, the A1s transition is located at 1.734 eV with the singlet trions (T) and dark excitons (XD) lying 35 meV and 40 meV below A1s, consistent with previous reports52. Additional peaks appear at lower energies, attributed to contributions from neutral, charged biexcitons and localized emission from defects53,54. At the heterojunction, additional low energy emission could be expected under certain conditions from the formation of interlayer excitons38.

In Fig. 1c strong excitonic resonances appear in differential reflectivity for both materials with negligible Stokes shift in energy compared to the PL emission, which is a sign of negligible exciton localization effects for these spectra. Clear signatures of B1s exciton states are also observed in both materials. For WSe2 the appearance of the A2s excited exciton state, which has a larger Bohr radius, shows the good quality of the CVD-grown monolayers of the LHs55.

We collect the Raman, PL and reflectivity spectra within our detection spot while moving the sample over a ≈10 μm distance with a step size of ≈150 nm using attocube nanopositioners. Typical Raman PL and reflectivity scans across a heterojunction are shown in the contour plots of Fig. 2a–c. A black dashed line indicates the position of the heterojunction in each contour plot. As a common feature for all three contour plots, we observe abrupt changes in the optical spectra as we scan across the lateral heterojunction, as a result of distinctly different phonon energies and exciton transition energies in the two materials.

Now we discuss Raman spectroscopy results in Fig. 2a for monolayer MoSe2 and WSe2, collected at T = 4 K using an excitation laser wavelength of λ = 633 nm. The main Raman peaks of MoSe2 and WSe2 can be identified in the contour plot (detailed Raman spectra can be found in the Supplementary Material, section B). For monolayer MoSe2 we observe the A$${}_{1}^{\prime}$$(Γ) phonon at 241 cm−1 and the E$$^{\prime}$$(Γ) at 291 cm−156, while a strong peak at 458 cm−1 has been associated to other peaks to form triplets57. Interestingly, we also observe a strong peak at 531 cm−1, recently assigned to multi-phonon processes associated with either both K and M point phonons or a combination of Γ point phonons57. The observation of this Raman peak is a signature of resonant excitation with an excited exciton state in MoSe2. WSe2 phonons are spectrally different compared to MoSe2. The degenerate A$${}_{1}^{\prime}$$(Γ)/E$$^{\prime}$$(Γ) phonons are located at 250 cm−1 and, similar to MoSe2, a strong and recently discovered peak at 495 cm−1 is also observed here and attributed to multi-phonon processes at K and M points or combination of Γ point phonons57.

The PL linescan in Fig. 2b shows emission from the main exciton transitions in WSe2 and MoSe2 (indicated by arrows) and a clear change in transition energy is discernible as we go across the lateral junction, with similar energies as for the individual spectra shown in Fig. 1c. Due to the extreme sensitivity of the PL emission energy spectrum on the defect concentration and dielectric environment19, we see spectral shifts between spectra taken at different positions. This makes the PL contour plot appear less smooth than the Raman and reflectivity linescans.

The reflectivity linescan shown in Fig. 2c shows a clear change in the main exciton energies as we scan from one material to the other. The main neutral exciton A1s feature in MoSe2 in reflectivity is at an energy of 1.665 eV, whereas for WSe2 this transition energy is clearly shifted to 1.734 eV. Reflectivity is less sensitive to the local defect and dielectric environment and therefore the measured transition energies remain comparatively constant from one spectrum to the other19.

A PL imaging experiment is used to probe the effective diffusion length in the two TMD materials that are connected at the junction. First, we concentrate on results away from the lateral junction i.e. neither the excitation nor the PL emission profile have any spatial overlap with the lateral junction. The experiment consists in a local photogeneration of excitons with a He:Ne laser focused on a spot size of about 0.7 μm (see black curve in Fig. 2) and an excitation power of 5 μW. The generated spatial gradient of the exciton concentration (i.e. chemical potential gradient) induces lateral diffusion of excitons which is probed by recording the spatial PL profile with a CMOS camera, see supplement, where we integrate over the full spectral range of the monolayer emission. Figure 2d shows the PL profiles obtained at T = 4 K on WSe2 (red line) and MoSe2 (blue line). We clearly observe that PL emission occurs over a larger spot diameter than the laser excitation58,59,60. At this temperature WSe2 shows a longer effective diffusion length than MoSe2. This difference is also visible in the inset by directly comparing the images of the PL profile from the two materials.

Interestingly, this behavior is reversed at T = 300 K where MoSe2 shows a longer effective diffusion length than WSe2 (Fig. 3b). This is possibly linked to dark excitonic states which have longer lifetimes (PL emission times)61,62. Indeed, the lowest energy state of the conduction band is a dark state in WSe2 while it is a bright state in MoSe2. The PL intensity evolution with the temperature shows opposite trends: WSe2 is darker at low temperature and brighter at room temperature as compared to MoSe263. The contribution of dark exciton states with longer lifetime would increase the effective diffusion length as compared to MoSe2, as dark exciton emission is negligible for MoSe264,65. Therefore, when we compare the two materials WSe2 has a longer diffusion length at 4 K and a shorter one at T = 300 K.

### Near-field studies of the lateral heterojunction

Due to the extremely sharp nature of the junction (2–3 nm, see Fig. 1b) between the two materials, tip-enhanced Raman and PL spectroscopy are necessary to characterize the junction with sub-wavelength resolution. TEPL and TERS were carried out at room temperature and the spatial resolution, determined by the tip diameter, is estimated to be ≈ 40 nm, far below the measured excitonic diffusion lengths we observed in the individual materials66,67,68. For TEPL (TERS) a 633 nm (532 nm) linearly polarized laser was focused onto the silver tip apex using a long working distance x100 objective (0.7 NA). The collection aperture is kept open to ensure that photons emitted a few micrometers away from the tip can be collected. The sample is scanned while recording PL spectra both with the tip in contact mode and 30 nm away from the surface. The near field contribution is then obtained by taking the difference between both recorded signals. Figure 3 shows a color map of the near field PL integrated intensity, excitation power was fixed to 0.4 mW and the sample scanning step size to 60 nm. The transition between WSe2 and MoSe2 can be clearly identified, and those images were used to select an interface region which gives uniform PL.

We then record PL spectra every 30 nm following the dashed line on the color map. Figure 3c displays three typical spectra measured at (1) 500 nm from the interface inside the MoSe2 area, (2) at 100 nm from the interface inside the WSe2 area and (3) at 500 nm from the interface inside the WSe2 area. All measured PL spectra are fitted using a combination of the different excitonic contributions from MoSe2 and WSe2: the WSe2 neutral exciton (A$${}_{1s}^{WS{e}_{2}}$$) at about 1.66 eV (see dashed red line), the dark (out-of-plane) exciton (X$${}_{WS{e}_{2}}^{D}$$) near 1.61 eV (see dashed black line), and the MoSe2 neutral exciton (A$${}_{1s}^{MoS{e}_{2}}$$) at about 1.57 eV (see dashed blue line), in agreement with the different transitions identified in the literature at room temperature69. Figure 3d–f show the results of the global fitting procedure of the PL spectra as a function of tip position. The position of the interface (see vertical dashed line) can be identified precisely thanks to the TERS spectra that show a sharp variation of the A$${}_{1}^{\prime}$$(Γ) phonon energy at the interface. Figure 3e, f display the energy and amplitude of each component of the PL spectra as a function of the tip position. We find the same phonon wavenumbers and exciton transition energies in our near-field and far-field measurements.

We note that the energy of both bright and dark WSe2 exciton are constant away from the interface but show a slight decrease when approaching the interface (≈200 nm), this could be an indication that tensile strain is present in the WSe2 layer to account for the lattice mismatch at the junction with MoSe270,71. Scanning across the junction, the amplitude of both WSe2 bright and dark exciton emission increases, going from zero at the interface to a plateau hundreds of nm away from the interface (see red and black stars in Fig. 3f). Importantly a clear contribution of the MoSe2 bright exciton can be seen when tip-enhanced excitation happens deep inside the WSe2 area (see light blue stars). The amplitude of this A$${}_{1s}^{MoS{e}_{2}}$$ contribution is decreasing as the excitation (tip) moves away from the interface, reaching zero at 400 nm away from the interface in WSe2.

This behavior indicates that excitons excited under the tip inside the WSe2 area are diffusing through the interface and recombine inside the MoSe2 area. Excitons are by consequence able to travel through 400 nm (roughly ten times our spatial resolution) of WSe2 before reaching the interface. Interestingly this is not a symmetric phenomenon: we do not detect any WSe2 related PL emission when the tip (and hence the optical excitation) is positioned inside the MoSe2 area. This behavior shows that the junction acts as an exciton diode, allowing excitons to cross from WSe2 to MoSe2 but not the other way around. This non reciprocal behavior is in agreement with the excitonic energy landscape at the interface and previously observed behavior in far field measurement72. Indeed as illustrated in Fig. 4 a A$${}_{1s}^{WS{e}_{2}}$$ is ≈90 meV above A$${}_{1s}^{MoS{e}_{2}}$$ presenting a potential barrier that exciton cannot cross even at room temperature.

To get more quantitative understanding of measured exciton transport we perform numerical modeling of the experiment by solving a one-dimensional steady-state diffusion equation in the two materials and through the interface:

$$G(x)+D\frac{{d}^{2}n(x)}{d{x}^{2}}-\frac{n(x)}{\tau (x)}-\mu F(x)\frac{dn(x)}{dx}=0$$
(1)

Where n(x) is the local excitons density, D the diffusion coefficient set to 1 cm2/s and τ is the exciton lifetimes that we set to 200 ps and 150 ps for MoSe2 and WSe2 respectively. We consider a Gaussian generation profile under the tip given by $$G(x)={G}_{0}\exp (-\frac{{x}^{2}}{{w}^{2}})$$, where G0 is the amplitude and w is the width of the Gaussian distribution (set to 40 nm, our effective tip diameter in the experiment).

A change in the exciton energy (i.e. chemical potential variation of the exciton) can act as an effective drift contribution that we simply model by adding an effective field μF in the equation (see Fig. 4a). The mobility is set to μ = 500 cm2/V/s58 and the F is set to 1 mV/nm. The latter value is taken sufficiently high to let the current flow only in one direction. Also the effective field is applied to a small region of 20 nm at the interface. Figure 4b displays the experimental spatially integrated PL value as a function the tip position. To ease the numerical modeling, the contributions of the bright and dark excitons in WSe2 have been added and the PL intensity of each material has been normalized away from the junction. Figure 4c displays the results of the modeling when we spatially integrate the PL profiles. The inset shows the same modeling without considering the effective field F = 0 where a more symmetrical behavior is seen at the interface. The model reproduces the main experimental result: PL signal from MoSe2 is seen when exciting WSe2 up to 400 nm from the junction, whereas exciton transport in the other direction is not possible. This underlines that the junction acts as an excitonic diode (i.e. an excitonic current can only flow from WSe2 to MoSe2). Figure 4d presents the calculated PL intensity taken at the maximum of the PL profile. The main tendency is conserved but we see an increase of the PL intensity of MoSe2 at the interface, indicating an accumulation of excitons as they cannot cross the junction. This PL intensity increase is also seen experimentally. The light density of states linked to the plasmonic resonance at the silver tip can possibly modify the exciton emission rate locally73.

In conclusion, we have performed detailed spectroscopic studies on CVD grown lateral MoSe2-WSe2 heterostructures. As an important step towards device processing and for accessing the intrinsic optical quality of the junction, we have first transferred the sample from its original growth substrate and then encapsulated the lateral heterostructures in top and bottom flakes of high quality hBN. Our experiments give access to the excitonic structures at cryogenic temperatures, with neutral exciton transition linewidth of the order of 5 meV. In exciton diffusion experiments we show that the MoSe2 and WeSe2 exciton transport show opposite trends in temperature dependent experiments, as dark excitons contribute to the PL signal in WSe2 and not in MoSe2. Our near field optical study using tip-enhanced experiments shows the important role of the heterojunction, as we measure that an excitonic current can only flow from WSe2 to MoSe2 and not the other way. This behavior is reproduced by a simple diffusion model where the exciton energy difference between the two materials acts as a barrier over a distance of a few nm. Our findings highlight the high structural quality of the heterojunction at the interface that can be regarded as an efficient excitonic diode, in the context of the broader research field of excitonic devices11,74,75,76.

## Methods

We use water-assisted deterministic transfer to pick up as-grown, chemical vapor deposition (CVD) LHs using polydimethylsiloxane (PDMS) and deterministically transfer and encapsulate them in hBN47,50. Raman, PL and differential white light reflectivity spectra are collected at T = 5 K in a closed-loop liquid helium (LHe) system. For the Raman and PL experiments we use a 633 nm HeNe laser as an excitation source with a spot size diameter of ≈1μm and 6 μW power. In reflectivity we use a tungsten-halogen white light source with a power of a few nW to collect the intensity reflection coefficient of the sample with the monolayer (RML) and the reflection coefficient of the substrate (RS) so that ΔR = (RML − RS)/RS. The PL images are recorded by a Hamamatsu Fusion-BT CMOS camera. For STEM investigation, the samples were transferred to Quantifoiltm grids using PMMA assisted transfer protocol. The high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image was acquired with a Thermofisher Talos 200X microscope operated at 200 kV. TERS and TEPL are carried out with state-of-the-art commercial system (Trios OmegaScope-R coupled with LabRAM spectrometer, Horiba Scientific). Silver coated tips with an apex radius of 20 nm were use for tip enhanced measurements. More details on experimental set-ups and procedures are given in the supplement.