Design of van der Waals interfaces for broad-spectrum optoelectronics

Van der Waals (vdW) interfaces based on 2D materials are promising for optoelectronics, as interlayer transitions between different compounds allow tailoring of the spectral response over a broad range. However, issues such as lattice mismatch or a small misalignment of the constituent layers can drastically suppress electron–photon coupling for these interlayer transitions. Here, we engineered type-II interfaces by assembling atomically thin crystals that have the bottom of the conduction band and the top of the valence band at the Γ point, and thus avoid any momentum mismatch. We found that these van der Waals interfaces exhibit radiative optical transitions irrespective of the lattice constant, the rotational and/or translational alignment of the two layers or whether the constituent materials are direct or indirect gap semiconductors. Being robust and of general validity, our results broaden the scope of future optoelectronics device applications based on two-dimensional materials. Type-II van der Waals interfaces formed by different two-dimensional materials enable robust interlayer optical transitions, regardless of common issues such as lattice constant mismatch, layer misalignment or whether the constituent compounds are direct or indirect band semiconductors.

V an der Waals interfaces of interest for optoelectronics consist of two distinct layered semiconductors with a suitable energetic alignment of their conduction and valence bands, such that electron and hole excitations reside in the two separate layers [1][2][3][4] . This allows the interfacial bandgap to be controlled by material selection-as well as by the application of an electrical bias or strain [5][6][7][8][9] -so that electron-hole recombination across the layers generates photons with a frequency determined over a broad range at the design stage. Choosing the interface components among the vast gamut of two-dimensional (2D) materials, which include semiconducting transition metal dichalcogenides (TMDs, such as MoS 2 , MoSe 2 , MoTe 2 , WS 2 , WSe 2 , ReS 2 , ZrS 2 and so on), III-VI compounds (InSe and GaSe), black phosphorous and even magnetic semiconductors (CrI 3 , CrCl 3 , CrBr 3 and so on), enables, at least in principle, us to cover a spectral range from the far infrared to the violet. In practice, however, efficient light emission from interlayer recombination requires the corresponding electron-hole transition to be direct in reciprocal (k) space: the bottom of the conduction band in one layer has to be centred in k space at the same position as the top of the valence band in the other layer 10 . This requirement poses severe constraints as concluded from heterostructures of monolayer semiconducting TMDs, the systems that are most used to realize light-emitting vdW interfaces 7,[11][12][13][14] . Indeed, in this case the minimum of the conduction band and top of valence band are at the K/K′ points in the Brillouin zone and the presence of radiative interlayer transitions requires combining compounds with both matched lattice constants and a virtually perfect rotational alignment 10,15 . If not, the k-space mismatch between the K/K′ points in the two materials prevents interlayer radiative recombination 14,16 . To bypass these limitations, it is important to identify a mechanism that enables the occurrence of robust radiative transitions in vdW interfaces, as well as classes of semiconducting 2D materials to implement it.
Here we propose a general strategy to form vdW interfaces of 2D semiconductors that support interlayer transitions that are direct in k space, irrespective of the crystal symmetry, lattice constant or crystallographic alignment of the constituent materials. If the materials that form the interface are selected so that the conduction-band minimum in one and the valence-band maximum in the other are centred at the Γ point of reciprocal space, interlayer transitions will be direct in k space as long as the energetic alignment of the bands is of type II (because the Γ point resides at k = 0, and hence coincides for all materials). To demonstrate this strategy, we used bilayers and thicker multilayers of different TMDs (WS 2 , MoS 2 and MoSe 2 ) with the maximum of their valence band at the Γ point 17 , and show that they enable a direct interlayer transition in vdW interfaces with InSe multilayers, which have their conduction-band minimum at Γ (refs 18,19 ). Light emission from Γ-point interlayer transitions is well-known in covalently bonded heterostructures of GaAs/AlGaAs and CdTe/ZnSe (refs [20][21][22][23][24], which form the basis for a multitude of technological applications, which include light-emitting diodes, different types of lasers, radiation detectors and so on [25][26][27] . The advantage of vdW interfaces is that the constituent materials neither need to be lattice matched nor satisfy any other stringent conditions, which broadens the choice of materials that can be used and, correspondingly, the range of accessible photon frequencies. We performed photoluminescence (PL) measurements that allow the identification of spectral features in the light emitted by vdW interfaces that originate from interlayer electron-hole recombination. The behaviour representative of the systems we studied is illustrated in Figs. 1 and 2, with data measured on structures formed by bilayer InSe (2L-InSe) and bilayer WS 2 (2L-WS 2 ), assembled to enable separate measurements of the PL that comes from the individual layers and from their interface ( Fig. 1a shows a schematic of the 2L-InSe/2L-WS 2 interface and Fig. 1b shows the relevant aspects of the band structure). Lines of different colour in Fig. 1c represent the PL measured at T = 5 K on 2L-WS 2 (blue line), 2L-InSe (orange line) and on their interface (purple line), and can be readily interpreted in terms of the known band structure of the materials that form the interface (arrows in Fig. 1b). The PL spectrum of 2L-WS 2 shows a (split) peak at approximately 2 eV, which originates from a direct recombination of excitons and trions at the K point, and a lower energy peak at 1.73 eV due to the k-indirect recombination of electrons at the Q point with holes at the Γ point, as expected 28,29 . In the 2L-InSe spectrum a peak at approximately 1.9 eV is present, which corresponds to the so-called A transition in this system 18,30,31 . The vdW interface PL, in contrast, is dominated by a peak close to 1.55 eV, significantly lower than the energy of the peaks identified in the spectra of the constituent materials, without any pronounced feature that corresponds to those of 2L-WS 2 and 2L-InSe. We directly conclude that the interfacial PL cannot be explained in terms of intralayer transitions, and that the 1.55 eV peak originates from an interlayer transition resulting from charge transfer that quenches the PL of the individual layers.
The temperature evolution of the interfacial PL intensity (Fig. 2a) and its dependence on the excitation laser power (Fig. 2c) do, indeed, exhibit the behavioural characteristic of interlayer transitions that are direct in k space. Figure 2a shows that on reducing T from 250 to 5 K, the intensity of the 1.55 eV PL peak steadily increases, as expected for a transition that is direct in k space. For comparison, Fig. 2b shows that in 2L-WS 2 , the amplitude of the 2 eV peak that originates from k-direct recombination at the K point also increases on cooling, whereas the amplitude of the 1.75 eV peak due to the k-indirect transition between the Q and the Γ points decreases, as typical for phonon-mediated processes. On increasing the excitation laser power, the transition energy increases by more than 50 meV before saturating as the power exceeds 100 μW ( Fig. 2c and its inset). The blueshift is a manifestation of the electrostatic potential generated by the 'pumped' interlayer excitons, whose density increases (and eventually saturates) at higher excitation powers. In simple terms, the photogenerated excitons consist of electrons that reside in one layer (InSe) and of holes in the other layer (WS 2 ), so that a higher exciton density results in a net electrostatic potential difference between the two layers and-owing to the interlayer nature of the transition-in a shift of the transition energy (as discussed extensively in the literature 32,33 ; this interpretation in terms of an interlayer electrostatic potential difference is fully equivalent to accounting for the effect of the dipole-dipole interaction between the photoexcited excitons). In the same power range, a virtually identical behaviour is observed in PL studies of interlayer excitons in vdW interfaces formed by MoSe 2 and WSe 2 monolayers 6,34,35 , but it is not observed in individual monolayers. We conclude that the transition responsible for the 1.55 eV line in the PL power spectrum of the 2L-InSe/2L-WS 2 interface originates from an interlayer k-direct transition, as expected for the Γ-Γ transition from the bottom of the conduction band of 2L-InSe to the top of the valence band of 2L-WS 2 .
One more direct experimental indication of the origin of the interlayer transition that we observe comes from the analysis of the polarization of the emitted light. At the Γ point, the edge of the InSe conduction band and the WS 2 valence band consist of atomic orbitals whose angular momentum component in a direction perpendicular to the plane is zero 36,37 . Theoretically, this prescribes 38 that the polarization of the photons emitted in the interlayer transition should be perpendicular to the interface. To check if this expectation is satisfied we fabricated dedicated devices-by cutting into a lamella configuration a block of 2 μm × 20 μm × 0.7 μm out of hexagonal boron nitride (h-BN)-encapsulated 2L-WS 2 /6L-InSe using a focused ion beam (FIB) (Fig. 2d)-and measured the light emitted in the plane of the interface from the side of the lamella. The resulting polarization map is shown in Fig. 2e, with a very pronounced out-of-plane photon polarization, as expected.
On the basis of experimental observations similar to those just presented for 2L-InSe/2L-WS 2 interfaces, we also conclude that  all the other interfaces we investigated, based on combinations of thicker WS 2 and InSe multilayers, exhibit a direct interlayer transition at Γ. The same is true for interfaces in which the WS 2 multilayers are substituted by MoSe 2 , or MoS 2 . In all these systems, the PL spectrum of the interfaces exhibits a peak at an energy smaller than that of the spectral features of the individual constituent materials, whose amplitude increases on cooling and whose frequency blueshifts on increasing the power of the exciting laser. The observed behaviour is entirely consistent with the fact that all the semiconducting TMDs employed to assemble the interfaces have their valence-band maximum centred at the Γ point, and the same is true for the conduction-band minimum of all the InSe multilayers 6,32-34 . Interestingly, the PL of the interfaces can be even brighter than that of the individual constituents, which shows that interlayer Γ-Γ transitions can result in an increased efficiency for light emission (Supplementary Section 3). Figure 3 shows representative data reproduced in more than 40 structures that we have investigated experimentally. In Fig. 3a, we show the evolution of the PL spectrum measured at T = 5 K on interfaces that consist of 2L-WS 2 and InSe multilayers of increasing thickness (from 2L to 7L), and in Fig. 3b we compare the thickness dependence of the interlayer transition energy extracted from Fig. 3a (purple dots) to the energy of the intralayer transition in the corresponding InSe multilayers (orange dots). As stated above, for all the thicknesses, the interlayer transition occurs at a lower energy than that of the intralayer one. A similar behaviour is observed on fixing the thickness of the InSe layer and varying that of the WS 2 multilayers, as illustrated in Fig. 3c for interfaces that consist of 4L-InSe and nL-WS 2 , with n varying from 2 to 5. Data measured on interfaces based on InSe and semiconducting TMDs other than WS 2 are presented in Fig. 3e. Figure 3e shows the PL that originates from interlayer electron-hole recombination in 3L-InSe/2L-MoSe 2 and in 4L-InSe/2L-MoS 2 : for these materials we did not systematically study the evolution of the interlayer transition energy on varying thickness, but we did measure several interfaces that combined multilayers of different thickness, and observed in all cases PL (again, with an amplitude that increases on lowering the temperature, at an energy that blueshifts on increasing the excitation laser power). However, for interfaces based on WSe 2 and InSe, we did not observe any PL signal, despite the expected presence of a k-direct interlayer transition at the Γ point. We believe that this is because the transition occurs at an energy of 0.8-0.9 eV, approaching the limit of sensitivity of our detector camera (the presence of a non-radiative recombination path that quenches the PL, for example, due to material-specific impurities that create in-gap states, cannot be entirely ruled out at this stage).
We conclude that k-direct interlayer transitions at Γ are robust processes, as we have shown them to occur irrespective of the relative orientation of the multilayers that form the interface (in the majority of cases we did not align the crystals when assembling the On lowering T the peak intensity steadily increases as expected for a k-direct optical transition. b, The PL emission spectra of bare 2L-WS 2 (curves offset for clarity) shows that the 2.0 eV peak due to the k-direct transition at the K point also increases on cooling, whereas the intensity of the 1.73 eV peak that originates from the k-indirect transition (from Q to Γ) decreases as T is lowered. c, PL spectra of a 2L-InSe/2L-WS 2 interface measured at T = 5 K with different laser powers (curves offset for clarity). The transition systematically blueshifts on increasing power. Inset: full evolution of the peak position in the range between 80 and 800 μW. d, Scanning electron microscope image of a lamella-shaped sample that consists of the layers shown in the scheme on the right (the interface consists of a 6L-InSe and a 2L-WS 2 ). The lamella structure allows illumination with photons propagating in the plane of the interface, with an electric field polarized normal to the interface plane. Scale bar, 2 μm. e, A polar plot of the PL of the interface in the lamella configuration shows that the emitted light is predominantly polarized in the direction perpendicular to the interface (0° corresponds to a polarization perpendicular to the interface plane; the dashed line represents a fit of the data with a sinusoidal dependence).
structures) with a substantial lattice constant mismatch (approximatively 15%) between the constituents and despite the fact that the band structure of the TMD multilayers changes significantly on varying their thickness. Besides substantiating our initial strategy to engineer systems for broad-spectrum optoelectronics, the ability to detect interlayer transitions in so many different interfaces enables the relative optical band alignment of entire classes of materials to be determined quantitatively in a rather straightforward and reproducible way. This is a significant result, because band offsets of semiconductors are often too complex to measure precisely, and different techniques give different results depending on the details of the experimental procedure.
To understand how the alignment of the different band edges is determined, we discuss in detail the procedure for 2L-InSe/2L-WS 2 interfaces, whose relevant band edges are represented in Fig. 4a. The interlayer transition that occurs at 1.55 eV measures the distance in energy between the bottom of the 2L-InSe conduction band and the top of the 2L-WS 2 valence band at the Γ point. The intralayer transition in 2L-InSe fixes the energy distance between the valence-band maximum and the conduction-band minimum (both near the Γ point) in this 2D semiconductor (approximately 1.93 eV). Similarly, the indirect intralayer transition in 2L-WS 2 (approximately 1.73 eV) fixes the position of the bottom of the conduction band in bilayer WS 2 at the Q point relative to the maximum of the valence band at Γ. As in 2L-WS 2 the conduction band edges at the Q and K points are nearly degenerate 39 (the energy difference is at most a few tens of millielectronvolts, which we neglect here), we can use the k direct 2.0 eV intralayer transition at K in 2L-WS 2 to determine the maximum energy at K of the valence band of 2L-WS 2 . The relative alignments of all the relevant band edges in 2L-InSe and 2L-WS 2 are then entirely determined. The same holds true for all the other layers that we have investigated: for 2L-WS 2 and InSe multilayers up to 7L-InSe with n varying between 2 and 7, measured at 5 K (curves are offset for clarity). In all cases a peak that originates from a k-direct interlayer transition is observed. b, Energy of the interlayer transition at Γ in nL-InSe/2L-WS 2 interfaces (purple dots) as a function of n. The interlayer transition always occurs at an energy lower than the transitions in the two constituent layers (the orange dots represent the intralayer transition energy in nL-InSe). c, Interlayer transition energy in 4L-InSe/nL-WS 2 as a function of the number n of WS 2 layers (purple dots), extracted from the interfacial PL spectrum (the blue dots represent the energy of the intralayer Q-Γ transition in nL-WS 2 ). d, Decomposition of the PL spectrum of a 6L-InSe/2L-WS 2 interface: the measured data (red solid line) are reproduced (blue solid line) by summing multiple Gaussian lines (grey dashed lines) that originate from the interlayer transition, the intralayer transition in 6L-InSe and an additional peak that we attribute to the hybridization of states at the valence band edge of 2L-WS 2 and nL-InSe (see text). e, PL spectra measured at T = 5 K on interfaces realized with TMDs other than WS 2 (light green curve, 3L-InSe/2L-MoSe 2 ; dark green curve, 4L-InSe/2L-MoS 2 ). The observed peaks originate from k-direct interlayer transitions at Γ. (Fig. 4b), for 4L-InSe and WS 2 of thickness that increased from 2L to 5L (Fig. 4c) and for 4L-InSe combined with all the different semiconducting TMDs (Fig. 4d). We estimate the precision of the bandgap values extracted from this procedure to be 100 meV or better. A source of uncertainty comes from neglecting the binding energy of interlayer excitons, which is justified because for all the interfaces investigated in our work this quantity is significantly smaller than 100 meV (Supplementary Section 4). What also limits the precision of our analysis is the assumption that the conduction band edges at the K and Q points of 2L TMDs are energy degenerate (correct to only within a few tens of millielectronvolts) and having neglected the hybridization effects between the valence band edges of InSe and TMD multilayers in which these edges are energetically aligned (based on previous studies of other vdW interfaces reported in the literature 40 , we estimate the phenomenon to cause an indetermination of 50 meV or less).
The internal consistency of the band diagrams extracted from the measured interlayer and intralayer transition energies can be cross-checked directly with the measured data. For instance, all the measurements on interfaces formed by 2L-WS 2 and nL-InSe shown in Fig. 3a were performed with the excitation laser tuned at the K-K transition of 2L-WS 2 . The photoexcited electron at the K point of the 2L-WS 2 conduction band always has enough energy to be transferred to the InSe multilayer (Fig. 4b), which is why the interlayer transition in the PL spectrum is visible. For 5L-InSe and thicker layers, in addition, the top of the 2L-WS 2 K valley becomes nearly degenerate, with the top of the valence band of InSe at the Γ point so the hole in the K valley of 2L-WS 2 can also transfer into InSe. This has measurable consequences, because for 5L-and thicker InSe multilayers it leads to PL that originates from the InSe intralayer transition, as well as to splitting of the transitions that involves the Γ-point valence band edge (due to hybridization of the states in 2L-WS 2 and in InSe). The PL spectra of 5L-, 6L-and 7L-InSe (Fig. 3a) do, indeed, show multiple peaks, one of which is due to the intralayer transition in InSe and another that we attribute to the hybridization-induced splitting (Fig. 3d shows the decomposition of the PL spectrum; a systematic discussion of the hybridization effects will be presented elsewhere). Additional evidence in support of the band diagrams shown in Fig. 4 is obtained from PL energy spectroscopy, that is, from measurements of the PL intensity as a function of the exciting energy of the photon, which we discuss in Supplementary Section 1. Finally, note also the different behaviour of the band edges in the InSe and WS 2 multilayers (compare Figs. 4b,c): whereas in InSe both the conduction and valence band edges shift as thickness is increased (Fig. 4b), in WS 2 the valence band edge remains nearly constant as the thickness is increased past that of the bilayers (Fig. 4c) in agreement with existing angleresolved photoemission spectroscopy experiments 40 .   Besides demonstrating the validity of the proposed strategy for the realization of vdW interfaces that support k-direct transitions, the band diagrams in Fig. 4 show how the interfacial transition energy can be engineered by simply selecting different thicknesses of the most commonly available 2D materials. The heterostructures investigated here densely cover the interval between approximatively 1.0 and 1.6 eV, but a much larger interval can be spanned by employing other known materials. Bilayers or multilayers of MoTe 2 and of GaSe, for instance, will allow the energy interval to be extended further on the lower and higher ends, respectively. It is this versatility and physical robustness that makes the use of interfacial transitions at the Γ point ideally suited for the realization of broad-spectrum optoelectronic applications. There is broad consensus that optoelectronics is one of the most promising domains for the development of devices based on the interfaces of 2D materials, but the large-scale production and commercialization of such devices pose serious challenges as to the required level of material control. This is undoubtedly the case if device operation relies on a very fine control of the different constituents, such as a perfect alignment of 2D crystals, or combining materials with identical crystal lattices and lattice constants. Although some of the challenges may be solved in the long term, these requirements are incompatible with virtually all the large-area manufacturing techniques that are currently available. The results reported here, however, change the situation as, with an appropriate choice of materials, vdW interfaces can be used as radiation sources that cover a very broad frequency spectrum in a mode of operation that is extremely robust against variations of the interfacial structural details. This implies that even the simplest possible techniques to assemble large-area interfaces of atomically thin layers-such as liquid phase exfoliation followed by ink-jet printing-can be employed for the scalable fabrication of structures with useful optoelectronic functionality.

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Nature Materials
Methods Sample fabrication. The fabrication of the heterostructures was performed according to a previous work 16 and is reproduced here for completeness. The fabrication of the heterostructures used to perform the measurements discussed in the main text relies on conventional techniques that are commonly employed to manipulate atomically thin crystals, that is, 2D materials. Atomically thin layers of TMDs and InSe were obtained by the mechanical exfoliation of bulk crystals with a parts per million concentration of oxygen and water in a glove box filled with nitrogen gas. The TMD crystals were purchased from HQ graphene and the InSe originate from a Bridgman-grown crystal of γ-rhombohedral InSe. The exfoliated crystals were transferred onto a Si/SiO 2 substrate and suitable flakes were identified by looking at their optical contrast under an optical microscope. The heterostructures were then assembled in the same glove box with a conventional pick-up and release technique based on either poly(propylene carbonate)/ polydimethylsiloxane or polycarbonate/polydimethylsiloxane polymer stacks placed on glass slides. The samples, encapsulated in between exfoliated h-BN crystals of a few tens of nanometres, were removed from the glove box and placed into the cryostat for optical investigations.
Optical measurements. PL measurements in a backscattering geometry (illumination direction out-of-plane) were performed by using an optical microscope to illuminate the device with the incoming laser beam and to collect the resulting emitted light. The light source was a supercontinuum white-light laser combined with a contrast filter, which allowed us to tune the laser wavelength between 400 and 1,100 nm. The illumination wavelength for every spectrum was as specified in the main text and the laser power was kept at 50 μW, unless stated otherwise. All the measurements were done with the sample placed in the vacuum chamber with a cryostat mounted on a piezoelectric driven x-y stage that allowed a positioning precision down to 50 nm (Cryovac KONTI). The laser beam was coupled onto the sample using an optical microscope with long working-distance objectives to produce a spot of approximately 1 μm in diameter that could be focused anywhere on the sample surface. The light collected from the sample was sent to a Czerny-Turner monochromator with 150 gratings mm -1 (Andor Shamrock 500i) and detected with a silicon charge coupled device array (Andor Newton 970 EMCCD).
PL on lamella samples. The fabrication of the lamella samples was performed according to a previous work 37 and is reproduced here for completeness. Heterointerfaces for the investigation of the in-plane PL were obtained in a similar manner as described for the sample fabrication. However, an additional layer of thick (>100 nm) h-BN was transferred on top of the encapsulated heterointerface, followed by 3 nm of AuPd + 5 nm of amorphous carbon to protect the sample from ion damage. An area for extraction was then identified using atomic force microscopy and covered with an additional protective platinum mask (~1 μm thick) using a FEI Helios FIB dual-beam system. FIB milling was performed using a 30 kV Ga + beam to extract the selected area. An OmniProbe micromanipulator was used to lift the lamella, rotate it by 90° and secure it onto an Omicron transmission electron microscopy grid. Finally, damaged edges of the lamella were polished by further FIB milling with a decreasing series of acceleration voltages (for example, 5 kV, 47 pA and 2kV, 24 pA). The final thickness of the specimen is <1 μm, to suppress multiple internal reflections of the emitted light. The polarization measurements were taken at 4 K in an AttoDry 100 cryostat (AttoCFM inset) using a Princeton Instruments Acton Spectrapro SP-2500i CCD with 300 gratings mm -1 .

Data availability
The data supporting the findings of this study will be made available free of charges as soon as possible on the Yareta repository of the University of Geneva (https:// yareta.unige.ch/). In the meantime, data are available from the corresponding authors without any restriction.