Interlayer Coupling Limit in Artificially Stacked MoS2 Homojunctions

Interlayer interactions are one of the crucial parameters of two‐dimensional (2D) layered materials‐based junctions. Understanding the limits of interlayer coupling and defining the “maximum building block thickness” in artificially stacked 2D layered materials are key tasks that hold significant importance, not only in fundamental physics, but also in practical applications such as electronics, photonics, and optoelectronics. Here, the interlayer coupling limits are optically investigated of a model 2D layered semiconductor, MoS2, revealing the evolution of distinct interaction mechanisms between layers via artificial stacking. As the total thickness increases, a reduction in the stacking angle influence on the properties of the homojunctions is reflected in the photoluminescence and second harmonic generation responses. The results show that the effective coupling limit for vertically stacked 2D metamaterials resides in three‐layer flakes. The findings pave the way to advanced and complex devices of 2D superlattices for photonics and optoelectronics.


DOI: 10.1002/adfm.202310365
MoS 2 has been extensively studied since 2010, when it was proved experimentally that its monolayer (1L) form is a direct bandgap semiconductor. [26,27][33][34][35][36][37][38][39][40][41][42] These methods build a general picture of various physical changes in 2D materials and their homo-and heterostructures.However, most studies are limited to the effects of stacking 1L flakes . [42]n this work, we study the limit of interlayer coupling by examining complex stacking cases of MoS 2 homojunctions involving different thicknesses, which aims to produce robust devices with enhanced tunability of photonics and optoelectronic properties.We probe the properties of MoS 2 homojunctions with progressively increasing total thicknesses up to 11-layers by characterizing the interlayer coupling via linear and nonlinear optical spectroscopies.We observe a transition in the electronic coupling behavior from stacking-dependent to stacking-independent with increasing thickness.We also study the even-order nonlinear optical response of the artificially stacked systems and the intrinsic flakes to unveil the enhancement efficiency in the stacked homojunctions.The symmetry-breaking effect in the artificially stacked multilayer homojunctions is observed.However, as the total thickness approaches the coupling limit, the nonlinear optical signal drops and can be less than that of the 1L.These results indicate that for effectively-stacked vertically-engineered metamaterials of MoS 2 homojunctions, the "maximum building block thickness" is 3L flakes.For junctions stacked with thicker (> 3L) flakes, the optoelectronic properties of the stacked junctions are dominated by the intrinsic properties of the constituent flakes and the interface interactions at the junction.

Effective Coupling Limit in Stacked 2D TMDs
Figure 1 represents the studied MoS 2 homojunctions.We aim to find the maximum number (m) of layers for constituent flakes in a stacking-dominated vertical structure.These are few-layer homojunctions with optoelectronic properties strongly dependent ) and few-layer (e.g., 2+1, 2+2, 2+3) structures (left panel).We aim to find the maximum thickness limit (i.e., m) for effective interlayer coupling in artificially stacked TMDs.For thicker constituent flakes, the homojunction properties are dictated by the interface interaction between the individual flakes (right panel).
on the stacking parameters. [23,29,32]Bulk-dominated homojunctions, on the other hand, are fabricated by stacking thicker flakes.In this case, the properties of the structure do not show significant changes under different stacking parameters but are dictated by the properties of their component flakes and the interface interaction between them. [20,43]Our measurements are carried out on the most common Si/SiO 2 substrates at room temperature.We fabricate several combinations of flakes with different numbers of layers to identify the individual thickness m where the effective interlayer coupling limit is reached.[46] The homojunctions are labeled with the approximated stacking angle  (detailed in Figure S1, Supporting Information), which is experimentally confirmed by polarization-dependent second harmonic generation (SHG) measurements as presented in Figure S5 (Supporting Information) [37,47] The homojunctions are largely classified into three typical categories: cases with  ˜0°(i.e., AA stacking, 3R-phase),  ˜30°, and  ˜60°(i.e., AB stacking, 2Hphase).

Coupling Limits Detected by Photoluminescence (PL)
The carrier transitions in the stacked homostructures can be identified by monitoring their PL spectra since the direct and indirect radiative excitonic recombination processes emit photons with significantly different energies [19,41] (Figure 2a).The absolute PL intensity may significantly differ in two flakes with the same thickness due to slight variations in the conditions of the transfer process or the quality of the flakes.Therefore, the PL signal of a homojunction is evaluated relatively to the signal of its component flakes and to the signal of an intrinsic 2H flake of similar to-tal thickness present in the same sample (Figures S2 and S3, Supporting Information).In this fashion, the PL signal from a 2+3 homojunction is assessed relative to the signal of the 2H 2L, 2H 3L and 2H 5-layer (5L) MoS 2 .
The PL intensities of various artificially-stacked MoS 2 homojunctions and their constituent flakes (i.e., bottom and top flakes) are presented in Figure 2b.In homojunctions with constituent flakes of less than 3 layers the PL intensity largely depends on the stacking angle.This phenomenon is more pronounced in 1+1 homojunctions and diminishes as the total number of layers in the homojunction n increases toward the coupling limit.Studied homojunctions in this range show strong stacking angledependent modulation of PL.Their peak intensities can be lower than the signal of both constituent flakes, or close to the one of the 2H equivalent (e.g., the case 1+1 (0°)), or higher than both constituent flakes (e.g., the case of 3+3 (0°)).The tendency, however, in most cases is for the signal to lay in between the signals of its component flakes until the coupling limit is reached at n = 6.Further, in homojunctions with more than 6-layers, the PL intensity is quenched, emulating intrinsic 2H-MoS 2 .In this case (i.e., n > 6), the PL also shows no significant intensity variations at different stacking angles.
PL originating from the IE is also observed in multilayer MoS 2 and several homojunctions, confirming interlayer indirect band transitions and quasiparticle population. [29,32,36,38]50][51][52] A stacking angle-dependent shift of the IE peak is present in the PL spectra of homojunctions with constituent flakes of three or fewer layers, evidencing flake-to-flake coupling and perturbation of indirect interlayer transitions [29,32] as shown in Figures S2 and S3 (Supporting Information).This shift in the IE energy (E IE ) reflects the tunability of interlayer electronic interactions as a function of interflake coupling (Figure 2d).In cases with thicker (> 3L, Figures 2c right and Figure S3, Supporting Information) constituent flakes, the IE PL peak broadens and eventually disappears, marking the transition between stackingdominated and bulk-dominated homojunctions (Figure 1).Therefore, it is feasible to effectively manipulate the electronic coupling via stacking angles in homojunctions with constituent flakes of up to 3L of thickness for future MoS 2 -based electronic and optoelectronic applications.

Coupling Limits Detected by SHG
To characterize the nonlinear optical response from our artificially constructed homojunctions, we use SHG micrographs (Figure 3c).Typical optical microscope images from 9 of the 22 studied homojunctions and their corresponding SHG micrographs are presented in Figure 3b,c, respectively.Note that polymer residues, defects, and strain during the transfer process can produce undesired localized enhancement of SHG, which can be excluded from the optical images for better analysis.
As expected, areas with an even number of layers have no SHG signal in the intrinsic individual 2H-phase flakes. [18,40,54]However, artificially stacked homojunctions with an even number of layers present SHG only if their constituent flakes are odd number-layered due to the interference of the signals from individual flakes (as shown in Figure 3a bottom panel).A strong SHG signal modulation by stacking angle is observed in the studied homojunctions that decreases as the total thickness increases.The homojunctions with constituent 1L, 2H 3L, and 2H 5L show a reduction in signal modulation according to our theoretical calculations, [42,47,49,55] as the total thickness of the structure approaches the interlayer coupling limit (inset in Figure 3d).Theoretical calculations consider a single stacking symmetry along the surface, variations between the experimental and theoretical values support the influence of interlayer coupling on the SHG of homojunctions.
The thickness of the bottom flake in a homojunction influences the SHG signal enhancement as shown in the SHG micrographs in Figure 3c; Figures S4 and S6 (Supporting Information).The substrate effect is less evident as the homojunction thickness increases.In cases with constituent flakes of 4-layers (4L) and 5L, this phenomenon is not visible, as the homojunction becomes bulk-dominated, and its SHG signal significantly losses its modulation by stacking efficiency.Consequently, the SHG signals from these homojunctions are very close to the ones of their nonlinear optically active constituent flakes independently of the stacking angle.

Coupling Limits Detected by Raman Spectroscopy
The optical contrast in samples with different numbers of layers , [44] and the low-frequency (LF) Raman modes [39,44,56] are widely implemented to The enhancement from the case 1+1 (0°) is taken from the data presented in Figure S7 (Supporting Information).The SHG signal normalized to the SHG of a 1L MoS 2 flake is presented in the inset for the homojunctions that show the maximum EF SHG relative to intrinsic 1L, 2H 3L and 2H 5L.determine the 2D material thicknesses.Atomic force microscopy profiles from intrinsic flakes are included in Figure S12 (Supporting Information) to corroborate the thicknesses identified by LF Raman measurements.The collective oscillations from our homojunctions are also assessed with Raman spectroscopy.LF vibrational modes reveal low-symmetry features from the lattice mismatch [29,40,52] and remnants from the 2H vibrational modes in thicker cases (Figures S88 and S10, Supporting Information).Vibrational modes are schematized in Figure 4a,b.By comparing the LF Raman peaks between homojunctions and intrinsic 2H-phase flakes, we observe the presence of breathing modes (BM) at the positions corresponding to the BM of their 2H equivalents in each homojunction with n > 2. Two examples are presented in Figure 4c,d, where the BM of 2H 5L and 2H 7-layer (7L) MoS 2 are also observed in the 2+3 (30°) and 5+2 (0°) homojunctions at ≈16.55 and ≈11.86 cm −1 respectively.This matching mode varies its intensity at the different stacking orientations (Figure 4c; Figures S8 and S10, Supporting Information).Shearing modes (SM) strongly depend on the stacking symmetry . [40]These modes shift toward the position of its intrinsic 2H equivalent as the  angle approaches 0°or 60°, and in cases with n > 3, they are located in-between the positions of the SM of their constituent flakes.In the special case of 1+1 homojunctions, the SM is out of our measurement range unless the stacking is close to match the AA or AB arranges, while the BM is present but shifting, giving an estimate of the twisting angle and the presence of different symmetries along the stacked area. [28,40]The high-frequency (HF) modes presented in Figure 4d, and Figures S7 and S11 (Supporting Information) are not as sensitive to the stacking angle as the LF modes . [40]More detailed results from the Raman spectroscopy are provided in Figures S8-S11 in the supporting information.

Discussion
We discuss now the abovementioned PL, SHG and Raman results of various homojunctions.The observed reduction of the PL intensity is an indicator of interlayer coupling.It is caused by the transition of the bandgap from the direct type to the indirect type with increasing thickness. [26,27]The results show a dependence of the PL intensity and the position of the IE PL peak on the constituent flakes thicknesses and the stacking angle of the homojunction.As 1L MoS 2 is a direct bandgap semiconductor, any 1+1 homojunction relatively reduces its PL signal as the indirect recombination processes significantly increase. [26,27]This is confirmed after observing the presence of the IE PL peak in all the 1+1 cases, absent from the 1L MoS 2 PL spectrum.In homojunctions with n > 2, where the indirect transitions happen in one or both constituent flakes intrinsically, the stacking angle changes the direct and indirect recombination probability by allowing or blocking interlayer electronic transitions, as can be observed in 2+2 (0°) and 2+2 (30°) cases.The results show that homojunctions stacked at ∼30°have the highest relative PL signal.This can be attributed to the low symmetry of the stacking allowing the interlayer direct recombination of carriers intrinsically blocked by the potential related to the crystalline structure of the flakes.However, with increasing thickness, the effect of the stacking angle is reduced until the coupling limit is reached at n = 6 (i.e., a homojunction of two 3L flakes), meaning that the recombination processes become dominated by the intrinsic nature of the constituent flakes and not by the stacking (bulkdominated).The IE PL peak is modulated in intensity and position in samples with constituent layers of 3L or less.This peak red-shifts relative to the IE PL positions of constituent flakes as the indirect bandgap decreases.The PL signal in homojunctions with n from 7 to 11 quenches and the IE PL peak is absent, showing the same tendency as their intrinsic 2H equivalents.In these cases, the stacking orientation shows little effect in the homojunction signal independently of the combination of flakes used (Figure 2b).
Further, we observe a nonlinear optical response dependence on the stacking angle in all the studied homojunctions that involve at least one odd number-layered flake.SHG from homojunctions with n = 3 shows a strong signal dependence on the stacking order; however, it is not strongly influenced by the stack-ing orientation.In this case, the SHG signal intensity is similar to that of its equivalent 2H 3L MoS 2 .This is not the case when n is between 4 and 6 (Figure S4, Supporting Information).In these homojunctions, the SHG significantly differs, while the stacking angle changes mainly due to a change in the interlayer distance between contacting layers at the interface and their corresponding flakes.This can be explained as the interlayer forces at the stacking interface suffer from less influence from the substrate in cases with thicker bottom flakes, showing a more pronounced inversion symmetry-breaking effect.Therefore, cases with thicker bottom flakes present stronger interlayer coupling . [57]This can be observed by comparing cases 1+2 (60°) and 2+1 (60°), where the latter presents not only a stronger EF SHG, but also significantly better-defined Raman features (Figure S8, Supporting Information) and a lower PL signal.The same behavior can be observed in homojunctions with n = 5 (i.e., in the case 3+2 compared to the case 2+3).46] The efficient stacking limit for optical applications is also identified by comparing the SHG enhancement efficiency relative to the 1L MoS 2 signal of the homojunctions with the highest EF SHG : While the SHG signal from the 3+3 (0°) homojunction is ≈211% of the 1L MoS 2 signal, for the 5+5 (0°) case it is only ≈89%, as shown in the inset in Figure 3d.Additionally, the contrast between the ≈400% EF SHG from cases 1+1 (0°) and 3+3 (0°), and the ≈203% EF SHG from the 5+5 (0°) case, indicates that the measured SHG signal from the last one comes from the individual constituent flakes interacting at the interface and not from the homojunction as a system.It is also worth mentioning that despite showing an SHG signal of ≈62% and ≈64% of the 1L MoS 2 signal, the homojunctions 2+3 (30°) and 3+2 (30°) present EF SHG relative to the intrinsic 3L of ≈121% and ≈125% respectively.This shows that it is possible to enhance the SHG signal in 2D vertically-stacked van der Waals materials by stacking even and odd number-layered 2H-MoS 2 flakes.For the cases with diminished SHG signal, the high absorption of MoS 2 for 400 nm light [58] was discarded as an explanation (Figure S13, Supporting Information).Even though the SHG photon energy is around the C exciton energy (i.e., ≈2.8 eV for 1L, ≈2.7 eV for 2L and up to ≈2.6 eV for thicker flakes) , [59] thicker samples with 5L bottom flakes present quite close signal intensities after stacking 4L and 5L flakes on top.Additionally, the electrostatic coupling (Figure 2), the polarization-dependent SHG results (Figure S5, Supporting Information), and the enhanced SHG signals observed in several 30°and 0°stacked samples provide clear evidence that the SHG signal is a product of the interaction of light with the stacked system.The results mark the effective limit for nonlinear optical signal enhancement engineered via 2D-TMDs vertical stacking at 3L flakes.
Homojunctions with constant n but varying stacking angles, show the progressive appearance of Raman modes from their equivalent 2H-MoS 2 as the stacking angles approach to a highly symmetrical configuration (AA or AB stacking).The coupling of the individual layer oscillations strictly depends on the stacking angle, and it is reflected in the relative intensity between SM from constituent flakes and BM from the whole homojunction (i.e., BM corresponding to the equivalent n-layered 2H-MoS 2 ) si-multaneously present in the measured Raman spectra (Figure 4c; Figures S8 and S10, Supporting Information).In homojunctions with stacking angles close to 30°, the intensity of the 2H equivalent BM is reduced as the signals from the SM of the constituent flakes increase.In this case, the oscillations of the flakes are partially synchronized, as the interlayer distances along the stacking are not constant [30,32,40] (Figure 4b,c).Even though HF modes are not as sensitive to the stacking angle as the LF modes, the peak position shifting follows the thickness dependence of the intrinsic 2H flakes.Results show that Raman spectroscopy can identify the stacking angle in homojunctions with values of n up to 11.However, for larger n, the characteristic BM of the junction will shift towards the 0 cm −1 position and the SM towards the bulk position at ≈33.5 cm −1 , making it indistinguishable from the signal of bulk MoS 2 .Note that the results of the coupling effects probed by different spectroscopies are summarized in Table Figure S1 (Supporting Information).The coupling effects of artificially-stacked MoS 2 homojunctions under different environmental conditions (e.g., substrates, temperatures, electrical doping and pressure) might differ, which is out of this manuscript's scope but deserves further study.

Conclusion
We have artificially stacked MoS 2 homojunctions to explore the coupling limits between flakes up to 11-layers.The results show that a flake thickness of 3L is the "maximum building unit" in TMD-based vertically stacked optoelectronic devices.The results of this work demonstrate an effective interaction between contacting layers from each flake, breaking the inversion symmetry of the system while maintaining strong interlayer coupling in >1L systems.We show that engineering stacked TMD crystals is a robust approach for 2D materials integration for a wide range of applications, including integrated photonics, laser gain mediums, all-optical communications, and quantum technologies.

Experimental Section
Sample Fabrication: The studied samples were prepared by artificially stacking mechanically exfoliated 2H-phase MoS 2 flakes.The flakes were exfoliated using the scotch tape technique and a substrate of polydimethylsiloxane.The flakes were then transferred on top of a Si substrate with 285 nm thermally grown SiO 2 .For the deterministic transfer, a sacrificial layer of polypropylene carbonate on top of a polydimethylsiloxane substrate allows for the manipulation and precise deposition of the top flakes.The deterministic dry-transfer process allows the characterization of intrinsic layers and stacked areas under the same conditions.Each sample was annealed for 60 mins in forming gas at 300 °C in an ATV PEO-601 (EPFL) furnace to increase the flake adhesion.
SHG Mapping: The SHG mapping was carried out using a laser scanning setup with a galvanometric scanner and pumped with an 800 nm femtosecond laser at ≈84.4 MHz repetition rate from a Ti:Sapphire laser (Solstice-Ace, Spectra-physics).The light was directed to the objective lens (40X Olympus Plan N, 0.65 NA) through a 550 nm long pass dichroic mirror.The signal was collected in reflection geometry and filtered with a 400-440 nm band pass filter (Thorlabs) before a photomultiplier tube (H7844, Hamamatsu) . [53]aman and PL Spectroscopies: Linear optical characterizations were carried out with a 532 nm continuous wave laser at ≈0.7 mW input power.The Raman signals were detected by a WITEC alpha 300 RA+ system equipped with a Newton Andor EMCCD and a 100X CF Plan Nikon objective (NA = 0.95).The PL signals were measured using a WITEC alpha 300 system, an iVac Andor OEM CCD camera and a 100X ZEISS Epiplan neofluar objective (NA = 0.9).

Figure 1 .
Figure 1.Schematic of the coupling limit in artificially stacked MoS 2 homojunctions.The middle inset in the left panel shows schematic examples of the stacking cases studied with different building blocks.The first (second) number in each case corresponds to the thickness of the bottom (top) flake in the junction.The current state-of-the-art results mainly focus on 2L (e.g., 1+1) and few-layer (e.g., 2+1, 2+2, 2+3) structures (left panel).We aim to find the maximum thickness limit (i.e., m) for effective interlayer coupling in artificially stacked TMDs.For thicker constituent flakes, the homojunction properties are dictated by the interface interaction between the individual flakes (right panel).

Figure 2 .
Figure 2. Interlayer coupling characterized with PL spectroscopy.a).Simplified schematics of radiative recombination processes in MoS 2 homojunctions.A-( A ) and B-( B ) exciton (blue) and indirect bandgap exciton (IE) ( IE , orange) recombination processes and their corresponding photons generated at different frequencies (ℏ A/B/IE respectively) are depicted.The inset shows the schematics of the interlayer IE in a 1+1 stacking case.b).PL peak intensities from 22 studied cases.Signals of top and bottom constituent flakes are given as a reference to indicate the relative change in the signal at the homojunction.The thickness limit where the PL intensity and E IE modulations are insignificant relative to the equivalent 2H signal is denoted with a dashed line.c).PL spectra from homojunctions 3+3 (0°), left panel, 4+2 (60°) and 5+2 (0°), right panel; and their top and bottom constituent flakes.The positions of the peaks corresponding to IE, A and B excitons are indicated on the left panel.IE peaks present in the spectral region between ≈720 and 950 nm are enhanced 7 times for representation purposes.d).IE PL peak positions corresponding to different E IE for different stacking cases (circles).IE PL peak positions of intrinsic 2H 2L and 3L MoS 2 are placed as a reference (stars).Results are grouped by total stacking layers in b) and d).

Figure 3 .
Figure 3. Interlayer coupling characterized by SHG.a).Schematic of the SHG process (Top panel) from a 1+1 stacking showing the individual contributions from each flake (Bottom panel).b).Optical microscope images from artificially stacked samples.The bottom and top flakes are highlighted in orange and white, respectively.Different homojunction regions are separated in red and indicated with white arrows.The scale bars correspond to 10 μm.c).Normalized SHG mappings corresponding to the samples shown in b).The SHG micrographs of all 22 homojunctions are presented in Figure S4 (Supporting Information).d).EF SHG as a function of stacking layer numbers and angles.Homojunctions are grouped by total stacking layers.The enhancement from the case 1+1 (0°) is taken from the data presented in FigureS7(Supporting Information).The SHG signal normalized to the SHG of a 1L MoS 2 flake is presented in the inset for the homojunctions that show the maximum EF SHG relative to intrinsic 1L, 2H 3L and 2H 5L.

Figure 4 .
Figure 4. Interlayer coupling measured with Raman spectroscopy.a).Representation of the MoS 2 interlayer BM (circles) and SM (triangles) on the left and intralayer E 1 2 g (pentagons) and A 1g (diamonds) vibrational modes on the right.b).Schematic of Raman modes of the 1+1 (30°) stacking case.The lattice mismatch creates zones with inconsistent stacking symmetries and different interlayer distances (exaggerated for better representation).Vibrational modes from zones with different interlayer distances are illustrated in the inset.c).LF Raman modes from 2+3 (30°) (left panel) and 5+2 (0°) (right panel) homojunctions and their constituent flakes.d).HF Raman modes from the samples studied in c).Spectra from intrinsic 5L and 7L MoS 2 are included as references in c) and d).Modes are labeled with the same symbol in a), c) and d).