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Self-organized twist-heterostructures via aligned van der Waals epitaxy and solid-state transformations

Vertical van der Waals (vdW) heterostructures of 2D crystals with defined interlayer twist are of interest for band-structure engineering via twist moiré superlattice potentials. To date, twist-heterostructures have been realized by micromechanical stacking. Direct synthesis is hindered by the tendency toward equilibrium stacking without interlayer twist. Here, we demonstrate that growing a 2D crystal with fixed azimuthal alignment to the substrate followed by transformation of this intermediate enables a potentially scalable synthesis of twisted heterostructures. Microscopy during growth of ultrathin orthorhombic SnS on trigonal SnS2 shows that vdW epitaxy yields azimuthal order even for non-isotypic 2D crystals. Excess sulfur drives a spontaneous transformation of the few-layer SnS to SnS2, whose orientation – rotated 30° against the underlying SnS2 crystal – is defined by the SnS intermediate rather than the substrate. Preferential nucleation of additional SnS on such twisted domains repeats the process, promising the realization of complex twisted stacks by bottom-up synthesis.

V an der Waals (vdW) heterostructures promise functional materials by integration of two-dimensional (2D) crystal building blocks 1 while largely bypassing conventional structure-and lattice-matching requirements 2,3 . Recently, vertical heterostructures with controlled interlayer twist-a relative inplane (azimuthal) rotation of one 2D crystal against the otherhave attracted particular interest due to emerging electronic phenomena that are defined both by the atomic lattices and a periodic twist-moiré superlattice with substantially larger unit cell. For bilayer graphene with small magic-angle misorientation, this competition causes the emergence of electronic correlations and unconventional superconductivity 4,5 . In 2D semiconductor heterostructures, the interlayer coupling, electronic band structure, and optoelectronic properties depend on the twist angle [6][7][8][9][10][11][12] .
Mechanical stacking [13][14][15] has been the preferred approach for fabricating vdW heterostructures 6,7 , as well as stacks with controlled static [16][17][18] or dynamically adjustable interlayer twist 19 . But factors such as a lack of scalability as well as concerns about uniformity and possible interface contamination are motivating a search for bottom-up synthesis methods for twisted vdW heterostructures. There are two fundamentally interesting regimes for which synthesis approaches need to be developed: (i) Precise small-angle interlayer twists, which cause moiré patterns that give rise to a modulation of the electronic structure within large unit cells whose lateral dimensions can exceed 100 nm; and (ii) high-angle twists. In both cases, the realization of a controlled interlayer orientation during growth is hindered by the strong tendency of 2D crystals to stack in their equilibrium registry, i.e., azimuthally aligned without any twist, both for homo-stacks of the same or hetero-stacks of different but isostructural 2D materials [20][21][22][23][24][25][26][27][28][29] . The affinity toward equilibrium stacking makes it particularly challenging to realize small interlayer twist angles. In recent work, we showed that architectures that depart from the usual 2D vdW heterostructure geometry-specifically layered nanowires with Eshelby twist-can spontaneously yield selforganized twist moirés with small twist angles that are tunable via the nanowire diameter 30 .
For larger interlayer twists, the weak interaction between layered crystals can enable a different avenue toward the bottomup synthesis of twist heterostructures via a two-step process in which the synthesis of an intermediate 2D (or 3D) crystalline phase (B) on a layered substrate (A) is followed by the conversion of the intermediate to a final phase A rot with a defined azimuthal rotation relative to the substrate. Such a two-step process has recently been used for the creation of a dodecagonal quasicrystal in 30°twisted bilayer graphene 31 . In this case, monolayer h-BN served as an intermediate 2D crystal that grows on epitaxial graphene/SiC under 30°rotation, and a high-temperature annealing step replaced this template by a graphene layer with the same orientation, i.e., 30°twist relative to the underlying graphene. While this demonstration was based on a substitution between isostructural 2D honeycomb crystals, a similar strategy could be extended to other 2D/layered materials, such as metal chalcogenide semiconductors as well as intermediates that are not isotypic with the substrate. The viability of this generalized approach depends on two key requirements: Growth of the intermediate B has to involve a fixed azimuthal registry of B relative to the substrate A; and in the final solid-state transformation B → (twisted) A rot , the azimuthal orientation of the resulting crystal should be determined by the lattice structure of the intermediate rather than the substrate.
Here, we demonstrate the realization of this concept for layered tin chalcogenide semiconductors. For these materials, several stable layered crystal phases exist with different chalcogen content and prior work has demonstrated the conversion from chalcogen-rich trigonal SnS(e) 2 dichalcogenide phases to orthorhombic SnS(e) monochalcogenides by generation of chalcogen vacancies, either thermally 32 , by electron irradiation 33 , or plasma exposure 34 . For the bottom-up growth of twisted vdW heterostructures, a bulk SnS 2 single crystal plays the role of the layered substrate, A. The intermediate 2D crystal phase, B, is ultrathin SnS grown by vdW epitaxy. In situ low-energy electron microscopy (LEEM) during growth allows us to identify the sequence of azimuthally aligned vdW epitaxy and spontaneous solid-state transformations that ultimately gives rise to self-organized SnS 2 twist heterostructures and incipient complex architectures, such as periodic vertical stacks with multiple twisted vdW interfaces.

Results and discussion
SnS was evaporated by congruent sublimation of intact formula units (i.e., SnS molecules) from a stoichiometric SnS powder precursor 23 onto freshly cleaved SnS 2 single crystals (and other substrates, see below) while imaging the growth process in real time by LEEM. At temperatures below 280°C and between 320-340°C, nucleation and growth produces heterostructures of single-crystalline few-layer SnS with lateral size up to several μm on atomically flat SnS 2 vdW substrates (Fig. 1a). Note that this geometry is the inverse of previously reported SnS 2 /SnS vertical heterostructures 35 . Selected-area low-energy electron diffraction (micro-LEED) was used to analyze the crystal structure and lattice registry. The substrate shows the hexagonal surface mesh of single-crystalline SnS 2 ( Fig. 1b) with two distinct sets of alternating intense and weaker diffraction spots, associated with 10 ð Þ SnS 2 and 01 ð Þ SnS 2 reciprocal lattice vectors 36 . Composite micro-LEED patterns of SnS domains and of the surrounding SnS 2 (Fig. 1c) show monocrystalline few-layer SnS. In contrast to other substrates (graphite, graphene) 23 where SnS grows with random orientation, vdW epitaxy on SnS 2 locks the SnS domains into a well-defined azimuthal alignment, found in all heterostructures reported here. In reciprocal space, the azimuth of the 11 ð Þ SnS reflection of SnS aligns with the 10 ð Þ SnS 2 reflection of SnS 2 . Consistent with a relatively weak interlayer interaction, which can lock the SnS layer into a well-defined azimuthal orientation with the underlying SnS 2 lattice but is not strong enough to force lattice matching, there is no detectable strain and the measured in-plane lattice constants of SnS and SnS 2 coincide with values reported for the respective bulk single crystals 37,38 . Figure 1d, e illustrate the observed real-space azimuthal alignment in the SnS/ SnS 2 heterostructures, where the projected Sn-S bonds in SnS align with one of three bond directions of the SnS 2 lattice. This preferred orientation generates three possible SnS domain orientations, separated by 120°(see Supplementary Fig. 2). The growth process shown in Fig. 1 can be rationalized by densityfunctional theory (DFT) based nudged elastic band calculations ( Supplementary Fig. 3). The DFT results support a picture in which SnS congruently sublimed from precursor powder adsorbs on the SnS 2 surface, diffuses, and nucleates or is incorporated into SnS domains. On-surface SnS dissociation is inhibited by large energy barriers (close to 1 eV), while lower activation energies (0.2-0.4 eV) enable the facile SnS surface diffusion by rotation between different S-sites.
Atomic force microscopy (AFM) has been used to further analyze the vertical tin chalcogenide heterostructures. Figure 2 shows AFM images of the SnS 2 substrate prior to SnS growth, and of a SnS/SnS 2 heterostructure. The freshly cleaved SnS 2 substrate is flat, with atomic terraces separated by single-layer high steps (Fig. 2a). Following SnS deposition, AFM shows ultrathin fewlayer SnS domains with lateral dimensions up to several μm, consistent with the LEEM results of Fig. 1 and evidence that synthesis on SnS 2 avoids the strong tendency toward vertical growth of thicker SnS found for other vdW substrates 23 . The domain shown in Fig. 2b, for example, varies in thickness between 3-4 SnS layers (1L SnS % 0:56 nm) 38 and its vdW interface lies 1L SnS 2 below the average substrate surface. SnS flakes in this thickness range should allow the experimental realization of phenomena such as in-plane ferroelectric ordering [39][40][41] and photostriction 42 predicted for few-layer group IV monochalcogenides with odd number of layers. Surface potential measurements using Kelvin probe force microscopy (KPFM, see below) indeed show clear thickness-dependent properties (Fig. 2c, Supplementary Fig. 4). Such ultrathin SnS domains generally crystallize in a rounded shape bounded by micro-facets 43 . Also evident is the transformation of the atomically flat SnS 2 surface into a patchwork of single-layer deep pits, where SnS 2 was apparently removed during SnS growth (Fig. 2b, inset). Analysis shows that these single-layer deep vacancy islands cover about 20% of the SnS 2 surface after SnS growth (see Supplementary The product of the transformation is identified in Fig. 4. Imaging at different electron energy, E, shows the SnS 2 substrate coexisting with two types of μm-scale domains with different Edependent contrast (Fig. 4a). The analysis of these phases by micro-diffraction is shown in Fig. 4b-e. The diffraction patterns of hexagonal SnS 2 (Fig. 4c) and orthorhombic SnS (Fig. 4d) are identical to Fig. 1, including the fixed azimuthal alignment of SnS on SnS 2 . Figure 4e shows diffraction from one of the domains transformed from SnS. The pattern is a superposition of two sets of hexagonal reflections, rotated relative to each other by 30°. From this result, we conclude that the converted domains consist of twisted t-SnS 2 , rotated in-plane by 30°relative to the substrate lattice; and the t-SnS 2 is ultrathin, so that it contributes jointly with the underlying SnS 2 to surface-sensitive diffraction. A further diffraction analysis provides evidence for superlattice reflections that arise from the twist moiré pattern of the hexagonal SnS 2 crystals ( Supplementary Fig. 6). Micro-LEED patterns on domains of 30°twisted t-SnS 2 /SnS 2 show superlattice spots centered around the zone center and the first-order  Fig. 6a-d). Fast-Fourier transforms of such diffraction patterns reflect the emerging dodecahedral structural motifs associated with a Stampfli-tiling quasicrystal 45 (Supplementary Fig. 6e, f) as realized recently in 30°twisted bilayer graphene 31 . The mechanism identified here, involving a solid-state transformation of a SnS intermediate, can also explain previously observed moiré patterns in SnS 2 crystals synthesized by co-evaporation of Sn and S 46 . Consistent with previous work on twisted bilayer MoS 2 7 , calculations show modifications of several key properties for 30°twisted SnS 2 . The twisted vdW gap of 6.22 Å is much larger than in equilibriumstacked bilayer (5.87 Å) or bulk (5.82 Å) SnS 2 , and the interlayer binding energy decreases from 0.22 eV/unit cell in the aligned bilayer to 0.16 eV/unit cell in the twisted bilayer. Electronically, the twist decouples the layers at the vdW gap in t-SnS 2 so that in a twisted bilayer they behave much like two monolayers, except for a few states around the Γ-point (Fig. 4g).
Evidently, a source of sulfur is required for the transformation of SnS to t-SnS 2 . The large SnS bond dissociation energy (467 kJ mol −1 ) 47 , congruent SnS sublimation 23 , and large on-surface dissociation energy (Supplementary Fig. 3; Supplementary  Table 1) rule out SnS dissociation as the primary source of S, which instead comes from the slow thermal decomposition of the SnS 2 substrate, explaining the formation of vacancy islands on the SnS 2 surface (Fig. 2). An alternative source of excess sulfur is the presence of S-rich minority phases in the nominally pure SnS precursor powder, shown in recent work to spontaneously produce layered SnS-SnS 2 core-shell heterostructures on mica vdW substrates 48 . Both the release of S from the SnS 2 substrate and the supply of excess S from the precursor are consistent with the limited T-range in which the spontaneous SnS → t-SnS 2 conversion is observed, as supported by DFT ( Supplementary Fig. 3, Supplementary Fig. 7, Supplementary Fig. 8 (Supplementary Fig. 9). Note that the decomposition of the SnS 2 surface layer via the thermally activated reaction SnS 2 → SnS + S produces SnS and sulfur that are both mobile on the surface ( Supplementary Fig. 3, Supplementary Fig. 7). Whereas the former adds to the deposited SnS, the adsorbed S contributes to the transformation of some of the SnS flakes into twisted t-SnS 2 . The limited amount of sulfur released from the substrate implies that only a small fraction of the SnS flakes can be converted to t-SnS 2 , as is indeed observed in Fig. 4. A higher yield of twisted SnS 2 flakes may be obtained by supplying additional S from an external source. In this way, twisted dichalcogenide heterostructures can also realized on substrates that do not release substantial amounts of chalcogens (e.g., MoS 2 , WS 2 ; see below). AFM imaging confirms that the converted t-SnS 2 is indeed ultrathin. Figure 5a shows coexisting SnS and t-SnS 2 domains, where the latter are merely two atomic layers 2L SnS 2 À Á thick (Fig. 5b). SnS and t-SnS 2 /SnS 2 are clearly distinguished via their surface potential, measured by KPFM (Fig. 5c, d). Generally, the potential ϕ SnS of SnS is higher than that of the surrounding SnS 2 substrate, with Δϕ ¼ ϕ SnS À ϕ SnS 2 ffi þ400 mV measured by KPFM in air. Twisted t-SnS 2 domains show the same potential as the SnS 2 substrate as expected due to their identical chemical nature and minimal potential shift due to twisted stacking. These findings are confirmed by local LEEM I-V measurements of the surface potential in ultrahigh vacuum (UHV, see Supplementary Fig. 10) 49 . Pristine samples again show a large positive potential of SnS relative to the surrounding SnS 2 but a negligible difference between t-SnS 2 and SnS 2 . For pristine SnS domains in UHV, Δϕ> þ 1:0 V ( Supplementary Fig. 10, Supplementary Fig. 11). Air exposure changes both ϕ SnS and ϕ SnS 2 , reducing Δϕ to~380 mV, consistent with the KPFM results. Annealing in UHV essentially recovers the pristine Δϕ $ þ1:0 V, consistent with adsorption of ambient species, strongly bound on SnS but weaker on SnS 2 (as shown by T for recovery of pristine potentials, SnS 2 :~200°C; SnS:~300°C).
We find a strong preference for SnS nucleation on ultrathin t-SnS 2 domains during continued growth, which can give rise to a cyclic sequence of SnS growth and transformation to twisted SnS 2 . In situ microscopy illustrates this effect (Fig. 6). Starting with a 30°-rotated t-SnS 2 /SnS 2 twist heterostructure, further SnS deposition causes the t-SnS 2 domain to expand laterally, implying a continued reaction of SnS to SnS 2 (Fig. 6a, b). This suggests that the t-SnS 2 domains represent efficient sinks for adsorbed SnS, which attaches to the edges, captures S, and rapidly reacts to SnS 2 at the microscopic level so that no SnS is detectable during realtime microscopy of the t-SnS 2 domain expansion. Ultimately, SnS nucleates either homogeneously or, as shown here, heterogeneously near the coalescence point of two t-SnS 2 domains ( Fig. 6c; 450 s). The subsequent evolution involves the spreading of SnS confined to t-SnS 2 , followed by a renewed transformation to SnS 2 ( Fig. 6c; 490-530 s). Based on the characteristic contrast of SnS 2 , SnS, and t-SnS 2 , we find that SnS confined to t-SnS 2 again undergoes a 30°azimuthal rotation relative to the underlying lattice as it transforms to SnS 2 . As illustrated in Fig. 6d, this additional twist brings this new SnS 2 layer back into azimuthal alignment with the substrate. In this way, alternating ultrathin SnS 2 with 0°and 30°twist is formed, suggesting that complex heterostructures, e.g., periodic vertical vdW superlattices with multiple twisted interfaces, may be realized by direct growth.
To demonstrate the generality of the concepts identified here, i.e., a strong tendency toward azimuthally aligned vdW epitaxy in nonisotypic 2D chalcogenide semiconductors and the ability of transforming an aligned intermediate to realize twisted vdW stacks-we performed additional growth experiments involving SnS vdW epitaxy on MoS 2 (Fig. 7, Supplementary Fig. 12) and WS 2 (Supplementary Fig. 13) substrates. On MoS 2 , SnS growth at 300°C produces ensembles of high-quality few-layer SnS flakes that expand to several μm lateral size (Supplementary Fig. 12) and exhibit a well-ordered layered morphology (Fig. 7a). Micro-LEED shows single-crystal diffraction patterns for both the MoS 2 substrate (Fig. 7b) and the SnS flakes (Fig. 7c). Importantly, diffraction analysis shows the same azimuthal alignment for SnS on MoS 2 as found for SnS on SnS 2 , namely the 11 ð Þ SnS reflection of SnS aligns with the 10 ð Þ MoS 2 reflection of the MoS 2 substrate. Likewise, growth on WS 2 again locks the SnS into the same azimuthal registry with the substrate (Supplementary Fig. 13). While the in-plane orientation is fixed, the SnS flakes grow unstrained with their native inplane lattice parameters on the different substrates.
In contrast to growth on SnS 2 , where some of the SnS flakes transform to t-SnS 2 , such a spontaneous transformation is not observed during growth on MoS 2 or WS 2 , consistent with the absence of their thermal decomposition into stable Mo or W intense E 1 2g and A 1g peaks of the MoS 2 substrate (Fig. 7f, g) 50 . In the as-grown flakes, the most intense vibrational mode of SnS 2 (A 1g ,~311 cm −1 ) 36 is not detectable. Figure 7h, i shows Raman spectra from flakes on the same sample following a 2-hour exposure to sulfur vapor at 370°C. After sulfurization, few-layer flakes show the appearance of the SnS 2 A 1g peak with intensity similar to that of the SnS modes (Fig. 7h), indicating a partial In contrast to SnS, which shows a large potential difference, ϕ SnS À ϕ SnS 2 ffi þ400 mV, relative to the surrounding SnS 2 , the surface potential of the 30°twisted t-SnS 2 is indistinguishable from that of the SnS 2 substrate. Surface potential measurements can thus unambiguously distinguish t-SnS 2 from SnS.

Conclusions
From our combined findings, we can draw several conclusions. Firstly, azimuthally aligned vdW growth appears to be widespread, even for non-isotypic crystals such as orthorhombic SnS on trigonal SnS 2 , MoS 2 , and WS 2 substrates. In cases where the support can release significant amounts of sulfur at the growth temperature, as is the case for SnS 2 substrates, ultrathin aligned intermediate crystals can spontaneously transform to form twisted heterostructures. On substrates with limited sulfur release, a two-step process with post-growth sulfurization can achieve the same result. Our observations also suggest that exposure to additional sulfur may be used to increase the fraction of SnS flakes that transform to t-SnS 2 during growth on SnS 2 substrates. Finally, we found indications that the nucleation and transformation of an azimuthally aligned intermediate crystal phase may also govern the growth on non-chalcogenide substrates, if sulfur is provided in the vapor phase. As shown in Supplementary  Figure 14, vapor transport growth of SnS on mica substrates with exposure to sulfur gives rise to two populations of oriented SnS 2 flakes: A majority phase (~82% of all flakes) and a minority phase (~18%) rotated by 30°. This again supports a growth mechanism in which aligned SnS crystals ultimately transform into 30°rotated t-SnS 2 . While the work reported here focused on transformations between 2D SnS and t-SnS 2 crystals to realize the bottom-up synthesis of twisted vdW heterostructures, our results raise the possibility of using the sulfurization of 3D crystals, e.g., thin metal or metal oxide templates for forming twisted chalcogenide heterostructures. Future work needs to show if such 3D intermediates can be grown in a fixed azimuthal orientation with a vdW substrate, and if the azimuthal orientation of the final chalcogenide phase after transformation with sulfur will again be defined by the intermediate rather than the substrate.

Methods
Low-energy electron microscopy and micro-LEED of SnS growth on vdW substrates. High-quality SnS 2 single crystals synthesized by the vertical Bridgman method were used as substrates. Additional layered supports included bulk MoS 2 (extracted from natural minerals) and WS 2 (synthetic, 2D Semiconductors). Prior to growth the layered substrates were mechanically cleaved and degassed at 300°C in ultrahigh vacuum (UHV). SnS was congruently evaporated from SnS powder (99.99%, Sigma-Aldrich) using a custom-built miniature Knudsen cell heated to 400-450°C while observing the resulting surface processes in real time by bright-field LEEM. In situ LEEM, Micro-LEED, and other complementary measurements were performed in a modified Elmitec LEEM III microscope that allows observations at variable temperature in UHV (base pressure 2 × 10 −10 Torr) and during sample exposure to gases or vapors (notably chalcogens or chalcogenides) with~6 nm lateral and monolayer height resolution. Sample temperatures in LEEM were measured using a W-Re thermocouple spot-welded onto the sample support. Real-time image sequences were acquired at a rate of 1 frame per second and recorded at 1024 × 1024 pixels. Micro-LEED was performed in selected areas with~1 μm lateral size. LEEM I-V data were acquired in real space with the full spatial resolution of the microscope; reported curves represent averages over areas with 200-400 nm lateral size.
Post-growth sulfurization. SnS samples grown on MoS 2 substrates were exposed to sulfur vapor in a separate quartz reactor implemented in a single-zone tube furnace with an additional external heating zone for sulfur. Sulfur powder (99.9995%, Alfa Aesar) was loaded into a quartz boat and as-grown SnS flakes on MoS 2 were positioned in the center of the heating zone of the furnace. Following evacuation of the reactor a carrier gas mixture of Ar and H 2 (ratio 98:2) was introduced at a flow rate of 50 sccm and a pressure of 76 Torr. The sulfur reservoir was heated to 80°C (vapor pressure~4 × 10 −4 Torr) and sulfurization was carried out at a sample temperature of 370°C for 2 h, followed by natural cooling to room temperature. f Raman spectra of the few-layer SnS flake (red) and of the nearby MoS 2 substrate (green), extracted at locations shown in d. g Raman spectra of the ultrathin SnS flake (red) and of the nearby MoS 2 substrate (green), extracted at locations shown in e. h Raman spectra of a few-layer SnS flake (red) and of the MoS 2 substrate (green), following reaction with sulfur at 370°C for 2 h. The inset shows the intensity of the main SnS Raman modes, along with an additional peak at 311 cm −1 due to the A 1g mode of SnS 2 . i Raman spectra of an ultrathin SnS flake (red) and of the MoS 2 substrate (green), following reaction with sulfur at 370°C for 2 h. The inset shows the absence of SnS Raman modes and a peak at 311 cm −1 due to the A 1g mode of SnS 2 , indicating complete conversion of the ultrathin SnS to SnS 2 .
Ex-situ measurements. AFM, phase mapping, and KPFM were carried out in tapping mode in air using a Veeco Multimode microscope with commercial SiN cantilevers or probes coated with thin metallic (Ru,~10 nm) films. Raman spectroscopy was performed at room temperature in air in a Horiba Xplora Plus Raman microscope using a 100x objective at excitation wavelength of 532 nm and laser power of 0.168 μW. Computational methods are reported in the Supplementary Methods.

Data availability
All relevant data are available upon reasonable request from the corresponding author. The source data underlying Figs. 2c and 2e are provided as a Source Data file.