Light-Matter Coupling in Scalable Van der Waals Superlattices

Two-dimensional (2D) crystals have renewed opportunities in design and assembly of artificial lattices without the constraints of epitaxy. However, the lack of thickness control in exfoliated van der Waals (vdW) layers prevents realization of repeat units with high fidelity. Recent availability of uniform, wafer-scale samples permits engineering of both electronic and optical dispersions in stacks of disparate 2D layers with multiple repeating units. We present optical dispersion engineering in a superlattice structure comprised of alternating layers of 2D excitonic chalcogenides and dielectric insulators. By carefully designing the unit cell parameters, we demonstrate>90 % narrowband absorption in<4 nm active layer excitonic absorber medium at room temperature, concurrently with enhanced photoluminescence in cm2 samples. These superlattices show evidence of strong light-matter coupling and exciton-polariton formation with geometry-tunable coupling constants. Our results demonstrate proof of concept structures with engineered optical properties and pave the way for a broad class of scalable, designer optical metamaterials from atomically-thin layers.


Introduction
Semiconducting Multi-quantum Wells (MQWs) and superlattices form the basis of all modern high performance opto-electronic and photonic components, ranging from modulators to lasers and photodetectors 1-4 . However, most known and scalable MQWs and superlattice structures are epitaxially grown III-V, II-VI or oxide perovskites. While significant progress has been made over the last three decades in the commercialization of II-VI and III-V MQWs and superlattices, the inherent difficulties of their integration onto arbitrary substrates have limited their adoption and applicability 5,6 . The advent of van der Waals (vdW) semiconductors, the ability to grow them uniformly over wafer scales, and to transfer them with high fidelity onto arbitrary substrates opens new avenues towards rational design of both electronic and photonic dispersions in artificially stacked superlattices and MQW structures 7 .
Two-dimensional (2D) vdW materials are a broad and growing family of materials with a diverse range of electronic properties, encompassing metals, semiconductors, ferromagnets, superconductors and insulators [8][9][10][11] . This diversity allows for vdW materials to be combined with one another, or with other thin materials, into heterostructures with new or enhanced properties and improved performance in a variety of applications 7,12 . Most of the previous research has focused on heterostructures that are made using mechanically exfoliated layers that are a few µm 2 in lateral size 13 with uneven thickness. This presents significant challenges in making MQW or superlattice structures with sufficient reproducibility across the number of periods necessary to enable the desired photonic or electronic dispersions. Further, with every increasing layer, stacking mechanically exfoliated flakes reduces the size of the region that has the desired overall stacking sequence, a problem that is exacerbated with each additional layer that is added. This fact prohibits the scalability of this approach. For photonic and optoelectronic applications, there is another major challenge with regards to atomicallythin active layers: the nature of light-matter interaction. Monolayer thickness of 2D materials results in a reduced cross section of light-material interaction implying weak couplings, despite naturally resonant optical responses 14 .
Semiconducting transition-metal dichalcogenides (TMDCs) that consist of Mo, W, Re etc. are a sub-class of vdW materials that have large, complex refractive indices due to the strong in-plane bonding of the transition metals to the chalcogenides, leading to strong light-matter interactions 15,16 . The low dielectric screening and highly-confined exciton wavefunctions present in TMDCs result in excitonic binding energies of 500 meV, creating strong excitonic resonances at room temperature 17 . As the thickness of TMDCs decreases from the bulk to the monolayer limit, they transition from indirect to direct bandgap semiconductors. This reduces the non-radiative energy loss of exciton relaxation and leads to an enhancement in photoluminescent (PL) emission 18,19 . However, reducing the thickness to monolayer dimensions adversely impacts the net interaction with light. Therefore, to engineer strong interaction with light and still maintain the key advantages to monolayer scaling it is necessary to make either a metamaterial or superlattice structure with monolayer repeat units in one dimension 20,21 .
Here, we report the experimental realization of superlattices that are specifically designed to achieve near-unity absorption while concurrently maintaining the enhanced PL emission and optoelectronic properties of monolayer TMDCs. Our superlattices are cm 2 in scale and comprise of repeating unit cells of metal organic chemical vapor deposition (MOCVD) grown TMDCs (MoS2 and WS2) + insulating spacers (h-BN and Al2O3) stacked on an Au back reflector ( Figure 1A). We observe the emergence of strongly coupled exciton-polaritons in the superlattices when light is coupled into the superlattices at incident angles > 45⁰. Further, both the exciton-polariton dispersion and coupling strength are observed to be tunable by altering geometric parameters of the superlattice and its unit cells. This assembly process is both general and simple and allows extreme flexibility regarding materials choice due to the lack of microfabrication constraints. Thus, it can be expanded to allow the integration of several different 2D chalcogenides and spacer layers, as demonstrated here. The resulting approach opens up a broad field of artificially engineered, scalable vdW superlattices for electronic, opto-electronic, and photonic applications.

Results and Discussion
We adopt a highly scalable approach to the fabrication of vdW MQWs and superlattice structures. Wafer-scale samples of WS2, MoS2 and h-BN grown using the MOCVD technique were used for sample fabrication. Details of sample growth and synthesis are available in the methods section and supporting information. We have adopted and demonstrated two different structures in this work, as shown in Figure 1a: 1) An all-vdW superlattice comprised of alternating layers of TMDC and h-BN, and 2) a mixed dimensional superlattice with alternating layers of TMDC and 3D oxides grown via atomic layer deposition (ALD). The all-vdW superlattice predominantly studied in this work is comprised of a unit cell of monolayer WS2 as the excitonic layer with insulating h-BN (3 nm) as a spacer layer which was repeated on top of an Al2O3/Au substrate. In the TMDC-oxide superlattice, the h-BN layers are replaced by Al2O3 layers. Our proposed concept and fabrication scheme is quite general and has been extended to monolayers of WS2, MoS2, and few-layer MoSe2 as the excitonic media in this study. We prepare our superlattice structures via wet transfer of the 2D chalcogenide and h-BN layers. In addition, we use atomic layer deposition growth of aluminum oxide for the base spacer layer as well as a component of unit cells, in some cases. These large area superlattice samples require wafer-scale grown TMDCs and h-BN with uniform thicknesses. The MoS2, WS2 and h-BN samples were grown via MOCVD while the MoSe2 samples were grown via selenization of Mo thin films in H2Se gas at elevated temperatures (see methods and supporting info, Figure S1 and S2). The increased absorption of the superlattices as the number of unit cells increases can be seen by the naked eye, as shown in Figure 1b. WS2based superlattices transition from a near transparent film at N=1 to a deep green color at N=5. The large area (cm 2 ) realization of these superlattices ( Figure 1b) is a particularly important demonstration of this study, given that any practical application of 2D TMDCs in photonics/optoelectronics will require large area, uniform material. Experimentally measured absorptance spectra for two-different superlattices have been shown in Figure 1c. A detailed discussion on the absorption properties is in following section.
To examine the spatial uniformity of this multilayer superlattice structure, we perform cross-sectional transmission electron microscopy of our representative sample (WS2/h-BN: N=5) (Figure 1d). An annular bright field (ABF)-STEM image of the cross section of our superlattice sample (Figure 1e) clearly shows the multilayer structure and five dark lines running horizontally in the image contrast, indicating the heavy element layer (WS2).
Corresponding energy dispersive X-ray spectroscopic (EDS) elemental maps shows the layers clearly. Layers of W, S and N signals are apparent, as are weak signals for B and Au corresponding to the substrate location ( Figure 1f). The white contrast (gap) between the TMDC layers and the bottom alumina ( Figure 1d) is a result of delamination of the superlattice during the ion milling process (Xe + ions) for cross-sectional TEM sample preparation (see supporting info, Figure S3).
A two-variable optimization scheme using Transfer Matrix Method (TMM)-based modelling combined with a genetic algorithm-based optimization approach was used to determine the desired thickness of the superlattice samples. The objective of the optimization was to maximize (minimize) narrow band absorptance (reflectance) at the excitonic resonance. The unit cell spacer and bottom spacer thicknesses were optimized to maximize the excitonic absorptance (see methods and supporting info, Figure S4-S7 for details). We performed this TMM modelling and optimization for four different superlattices (WS2/h-BN, WS2/Al2O3, MoS2/Al2O3 and MoSe2/Al2O3) where the number of unit cells varied from N= 1 to 8. We found a distinct absorptance enhancement up to N=4 and N=5 for Al2O3 and h-BN based superlattices, respectively, as experimentally demonstrated in Figure 2. The modelling and optimization identifies three key features in terms of designing superlattice geometric parameters for maximizing (minimizing) absorption (reflection) at the excitonic resonance. They are: 1) the thickness of the spacer layer in the unit cells must be as low as possible (Figure 2a and b); 2) the bottom alumina thickness should be reduced as the number of unit cells (N) increases (see supporting Figure S5-S8); and 3) the peak absorptance (at exciton resonance) approaches near unity with increasing N and then dips again, suggesting that there is an optimal unit cell number (N) for perfect absorption (Figure 2 d-i).
We note that this optimal N can vary with spacer index and thickness. Given that electronic interactions between two TMDC layers are non-negligible at spacer thicknesses of 1-1. It also suggests that there is no electronic interaction between neighbouring the WS2 layers when they are separated by h-BN or Al2O3. Therefore, they maintain their monolayer electronic character when integrated into this superlattice stack. The insulating layers serve two primary purposes: 1) they act as spacer layers between TMDCs to reduce the electronic coupling between individual TMDCs layers, allowing them to maintain monolayer properties and 2) they act as light trapping agents, because the refractive index difference between the TMDCs and insulating layers also results in enhanced reflection. Given the low reflectance (high absorption) at the excitonic resonance, an important parameter to consider is the extent of useful absorption in the semiconductor vs parasitic absorption in the underlying Au. This absorption into individual components of the superlattice was extracted through the TMM simulations ( Figure 2 f, i), where a negligible contribution from the bottom Au layer is observed around the primary exciton wavelength (613 nm for WS2) (see supporting info, Figure S8 for additional details). It is further worth noting that there is a pronounced dip in reflectance in the bottom Au at the excitonic resonance. This is a peculiar observation and is attributed to lack of sufficient incident light intensity reaching the Au surface because of multiple reflections and trapping in the layers above. This observation can be generalized to other bottom metals such as Ag, where the parasitic absorptance is further diminished, yet the reflectance dip remains (see supporting info, Figure S9). Likewise, MoS2/Al2O3 superlattices also show similar behavior (see supporting Figure S10). We have also analyzed and compared the reflectance behaviour of a multilayer, mechanically exfoliated WS2 control sample with similar thickness to that of the WS2 present in the superlattices (WS2/Al2O3: N=4 and WS2/h-BN: N=5) (see supporting info, Figure S11, S12). The comparative analysis confirms that while a similar degree of absorbance can be achieved with equivalent thickness of WS2 on an alumina spacer, there is loss of the direct band gap nature of the TMDC. Additionally, the superlattice exciton peaks remain unshifted, as opposed to the red-shift seen in few-layer WS2 of equivalent absorber thickness. This lack of energy shift further confirms that the WS2 is electronically isolated in the multilayer. Finally, it is worth nothing that the oscillator strength of the exciton is higher in monolayers. This is because of the reduced dielectric screening and quantum confinement, which also results in larger absorption per unit thickness (see supporting info, Figure S12).
The ability of these multilayer superlattices to both trap light and retain their monolayer electronic and optical character is a defining feature of our approach. In contrast to their bulk counterparts, the presence of strong quantum confinement in monolayer WS2 and MoS2 leads to a direct band gap, which in turn leads to high intensity PL due to low, non-radiative energy loss during electron-hole recombination 24 . This extraordinary feature of monolayer TMDCs makes them strong candidates for light emitting devices. The superlattice structures demonstrated herein -which combine insulating spacer layers -between monolayer TMDCs allows the monolayers to maintain their direct-gap electronic structure. We verify this using a series of vibrational and luminescence spectroscopy measurements shown in Figure 3. We observe that our multilayer superlattices remain highly luminescent with an increasing number of unit cells (Figure 3a). Not only are the luminescent properties maintained, but the luminescence intensity is even enhanced with increasing N due to the increased due to enhanced light-material interactions (Figure 3b). When normalized to total useful light absorption with increasing N, using layer resolved absorption calculations we observe that the luminescence intensity increases with N which is expected due to stronger light-material interaction (see supporting info, Figure S13 for additional details). We also observe a small In addition to PL, Raman spectra provide a strong signature of interlayer interaction and hybridization. Specifically, the out-of-plane vibration mode (A1g: 418 cm -1 ) stiffens with increasing number of layers and therefore the separation between 2LA(M) and A1g modes reduces with increasing layer thickness 28 . We observe no noticeable peak shifts in the Raman spectra of WS2 in our superlattices with increasing N. Once again this suggests no interaction between layers and no detectable strain within the layers. The only noticeable difference with increasing N is the rising peak intensity and narrowing FWHM of the peaks (Figure 3e). This is likely due to increased Raman scattering signal due to strong interaction of the medium with pump laser, again caused by the light trapping geometry in addition to the increased total volume of WS2. In addition, we also observe a defect-bound Raman mode (LA(M): 176 cm -1 ) appearing for the N=5 structure of the WS2/h-BN superlattice (Figure 3e). This is likely due to  Thus far, our discussion concerning the light trapping and optical properties of these multilayer superlattices has been focused on normal incidence illumination. We now explore angle dependent coupling of light into this multilayer superlattice structure. Standard TMM simulations show that the excitons in the superlattice hybridize with cavity modes to form exciton-polaritons, with their splitting energy depending on the incident angle and number of unit cells (Figure 4a). With a fixed number of unit cells and angle of incidence, a characteristic anti-crossing behavior, signifying exciton coupling with polaritons, can also be seen when the cavity resonance is tuned by varying bottom alumina layer thickness. We use a coupled oscillator model to fit to the simulation data and calculate the Rabi splitting of the system.

Figure 3: Maintenance of monolayer properties. (a) Room temperature photoluminescence (PL) spectra of the multilayer superlattice as a function of increasing number of unit cells for the WS2/h-BN superlattice. (b) Corresponding PL peak intensity and absorption normalized PL vs. number of unit cells, showing increasing PL intensity with increasing number of unit cells The net PL intensity saturates when the total absorption saturates, while the increase in normalized absorption
Our analytical model is in good agreement with the simulated UEP and LEP energies (see supporting info and detailed discussion, Figure S20-24). The Rabi splitting can be increased to 170 meV for a stack of N=8 at >80⁰ incident angles. The Rabi splitting can also be achieved at lower incident angles as the number of unit cells is increased, due to a sharpening in the cavity mode peak, which indicates a lower mode volume, Vm (based on the pathlength of the light inside the superlattice for N layers). The lower mode volume for increased unit cells also results in higher Rabi splitting since the Rabi splitting is inversely proportional to the √ .
The increased Rabi splitting with increased incident angles is due to sharpening in the cavity mode peak, which can be observed in the increased Q-factor (see supporting Info, Figure S23). This Rabi-splitting is also observed in our superlattice samples and matches well with the simulations (Figure 4c (Figure 4 c-d). This is because monolayer TMDCs can only support TE waveguide modes, unlike their bulk counterparts which can support both TE and TM waveguide modes 18 . As the reflection spectra are acquired away from normal incidence the exciton mode stays unperturbed up until an incident angle of 50° in the simulation. Thereafter, the cavity-induced splitting of the exciton mode emerges with increased incident angles. The emergence of the cavity mode at slightly higher incident angles in experiments when compared to the simulated values can be attributed to presence of polymer and other contamination between the layers, which reduces the quality of the cavity. The Q-factor was obtained by fitting the absorptance peaks to a Lorentzian line shape and was found to follow similar trends to incident angle and number of unit cells as the Rabi splitting ( Figure S19). TMM simulations show that the Q-factor of 100 nm thick N=5 WS2/Al2O3 superlattices can reach 300 at a moderate incident angle of 70⁰ at room temperature (see supporting Figure S23). The observation of high Q factors in un-patterned multilayer films over square centimetre length scales is potentially valuable for colorimetric sensing applications. In this regime, the exciton-polariton splits into an upper exciton-polariton (UEP) and lower exciton-polariton (LEP) branch for WS2. Both branches were observed simultaneously at room temperature. A third branch was observed in MoS2 since the energy of the A and B excitons are closer than for WS2, and both excitons interacted with the microcavity (see supporting info, Figure S26). The Q-factor of the cavity mode was found to be 300 at an incident angle of 70⁰ in a subwavelength thick device (100 nm). Since excitonpolaritons maintain light-like and matter-light characteristics, they can be used for non-linear effects in devices such as lasing.

Conclusions:
In summary, we have demonstrated a centimetre square scale, multilayer superlattice structure based on atomically-thin 2D chalcogenide monolayers acting as quantum wells. The structure of the superlattice was deterministically designed to maximize light trapping at the exciton (90 %) in < 4 nm thickness of active layer absorber. These superlattices not only maintain a monolayer structure but also support exciton-polaritons at room temperature, with Rabi splitting of up to 170 meV, and cavity modes with quality factors as large as 300 in deep-subwavelength thick devices. Our results show a proof of concept for optical dispersion engineering using atomically thin layers over scalable and arbitrary substrates with broad applications ranging from lasing, sensing as well as optical-modulator devices and lays the foundation towards a materials platform for substrate agnostic integrated nanophotonics. Microscopes (F200-JEOL). Images were captured by a Gatan annular detector using Gatan's GMS Software. Cross-sectional samples were prepared with Xe + plasma based focused ion beam / scanning electron microscope (S8000X-TESCAN).

Theoretical Modelling:
A 2x2 transfer matrix method 31 was used to simulate the reflectance of the superlattice structure/heterostructures. We adopted the open-source TMM code 32  based TMDCs samples and kept in air to dry overnight to prepare for wet chemical delamination process of atomic thin layers. PMMA thin film was deposited with a controlled thickness of 200 nm. PMMA coated samples were dipped in de-ionized (DI) water heated to 85° C on a hot plate, for 20-30 minutes until air-bubbles began to form at the outer edges of the sapphire substrate. Following the formation of air bubbles, samples were taken out of the hot water and placed on the top of 3M KOH solution which was maintained at 85° C. Crucial delamination of PMMA-supported TMDC layers from sapphire substrate occurred at this step where sapphire substrate was held manually with 45° inclination and slowly dipped inside the KOH solution with extremely slow movement. This allowed the delamination of the PMMAsupported TMDCs layers which finally floated to the top of the KOH solution. Using a cleaned glass slide, the floating PMMA-supported TMDCs layers were transferred to the fresh DI water, and this step was repeated multiple times to remove any residual contamination from the delamination steps. Finally, floating PMMA supported TMDCs were scooped on desired Si substrate covered with Au (Si/SiO2/Au/Al2O3) and left to air-dry overnight. The final lift-off process (to remove the PMMA film) was done with the help of acetone for 6 hours at moderate temperature (45° C). To allow for better adhesion of the wet-chemical transferred TMDCs layers to their new substrate, they were heated for 1-2 hours at 70° C on a hot plate.
The processes described above for producing the multilayer stacks including precise manual alignment at each scooping step were followed for the synthesisation of each heterostructure. Alumina-based superlattices were fabricated with additional steps of depositing a Al2O3 layer by ALD after each wet-chemical transfer of the TMDC layer. The topmost TMDCs layer in all superlattices were not coated with either Al2O3 or h-BN.

Rabi splitting and energy calculation:
We modelled the exciton-polaritons in WS2-based superlattices using a coupled oscillator model which is based on the Jaynes-Cummings Model Hamiltonian 3 = ( ( 2 3 ) ) ……. (1) Where Ex and Ec are the uncoupled energies of the exciton and cavity modes, respectively, and g is the coupling parameter which is related to the Rabi splitting as = ℏΩ 2 . Ec was determined to be linearly dependent on the thickness of the bottom alumina layer, tAl2O3.
Assuming the damping factor of the cavity mode is much larger than the damping factor of the exciton, the splitting of the exciton-polaritons is in the strong coupling regime when > 4 4 where is the damping factor of the cavity mode which is related to the Q factor of the mode by = . We found that our superlattices were all in the strong coupling regime as the incident angle approached 90 o , and strong coupling occurred at lower incident angles as N increased (see Figure S24A).
The model was fitted to the simulated values using g and the linear dependence of the cavity mode on the bottom alumina thickness (Ec = mtAl2O3 + b) as the fit parameters and by using a least squares optimization method. Figure S19A shows that our model and the simulated energies of the UEP and LEP agree. The energy difference between the A and B excitons in MoS2 is smaller than in WS2 allowing the cavity mode to interact with the A and B excitons simultaneously in MoS2. This is reflected in the model as we used a three-coupled oscillator for MoS2 where two of the oscillators are excitons while the third is the cavity. The Hamiltonian of this system can be written as 5 = ( 0 0 ( 2 3 ) ) ……. (2) Similar to the coupled oscillator model, the diagonal terms (EA, EB, and EC) are the uncoupled energies of the A exciton, B exciton, and cavity mode, respectively, while the off-diagonal terms determine the coupling strength between oscillators. gA is the coupling parameter between the A exciton and the cavity mode while gB is the coupling parameter between the B exciton and the cavity mode. The 0 terms are due to the assumption that the A and B excitons do not couple with one another. This assumption was checked by allowing the terms to vary when fitting the model, but this approached gave the coupling between the excitons to be 5 orders of magnitude smaller than gA and gB. The model was fitted to the simulated values using gA, gB, and the linear dependence of the cavity mode on the bottom alumina thickness as the fit parameters and a least square optimization approach.