Introduction

Atomically thin 2D vdW materials have garnered enormous interest since the groundbreaking work on monolayer graphene prepared by mechanical exfoliation, as they not only exhibit distinct properties but also open up a variety of unprecedented functionalities compared to their bulk counterparts1,2,3. Notably, these properties are strongly dependent on stacking order, symmetry, and the presence of defects. MoS2, a prominent member of the 2D vdWs material family, exhibits multiple polytypes, among which the 2H and 3R phases represent the common stacking orders observed in natural and synthetic MoS₂2,4,5. These two phases behave considerably differently because of variations in stacking order and symmetry. For instance, 3R bilayer MoS₂ offers significant potential for piezoelectricity and spin/valley polarization owing to the broken inversion symmetry, while these properties are largely absent in 2H bilayer MoS₂ due to its retained inversion symmetry6,7,8,9. Dislocation, a sort of fundamental topological defect, can readily arise in vdW materials through interlayer sliding due to the inherent weakness of the interlayer vdW forces. The characteristics of dislocation are closely tied to the local atomic stacking configurations. Furthermore, dislocations are increasingly recognized as crucial elements in tuning materials’ properties, such as plasticity and linear magnetoresistance2,10,11. Beyond the properties of intrinsic materials, assembling different layers with a controlled interlayer twist angle provides an exotic platform for exploring fruitful fundamental and novel phenomena in 2D materials. The local stacking orders within domains and domain walls (also referred to as dislocations) in twisted structures are strongly dependent on both the twist angle and the stacking configuration- either parallel (3R) or antiparallel (2H) stacking12,13. The remarkable effect of local stacking arrangement on the electronic structure of twisted bilayers has been extensively addressed, underscoring the potential applications of these materials in the rising field of twistronics14.

Therefore, the reliable identification of the various polytypes and the associated defects is a crucial starting step in comprehending and engineering the structure-dependent properties in 2D vdW materials. Though a wide range of measurement techniques have been developed, the reduced dimensions - being only a few atoms thick, the minute scale of topological defects, the strain and contamination residue in 2D vdW materials require the development of characterization techniques with nanoscale resolution and sensitivity to stacking sequence and symmetry. These stringent requirements limit the effectiveness of individual characterization techniques, emphasizing the necessity for combining different strategies. X-ray diffraction (XRD) is probably one of the most suitable techniques to investigate the crystal structure and quality of materials, but it suffers from complicated data interpretation owing to the atomically thin thickness and the interaction of X-rays with surrounding materials15,16. A broad family of scanning probe microscopy methods can identify local defects (such as vacancies), grain boundaries and qualify their physical properties. However, they are considerably surface- and strain-sensitive and can be influenced by layer number17,18. Optical spectroscopic approaches are promising for wafer-scale inspection and allow nondestructive investigation of the structural characteristics. For instance, both experimental results and theoretical simulations of the low-frequency interlayer modes (rigid-layer vibrations) in Raman spectroscopy enable the distinction between different phases in bilayer MoS219,20. Yet, these methods are also susceptible to strain-induced effects21,22 Most importantly, their spatial resolution is limited by the optical diffraction limit to roughly half a micrometer. This leads to great difficulties in discerning the defects in 2D materials, unless advanced methods like tip-enhanced spectroscopy are applied23,24. TEM excels with its imaging and diffraction capabilities, allowing for the direct observation of stacking orders and defects at the atomic level8,25, probing the crystal structure and symmetry26,27. For instance, the local stacking order in different MoS2 polytypes was directly identified by high-resolution scanning transmission electron microscopy and the electron diffraction patterns from different phases have been comparatively studied8,27. However, TEM is often limited by a small field of view (typically in the micrometer range or less) and local buckling, making it difficult to provide a comprehensive overview of the material. Consequently, it is necessary to integrate the strengths of multiple techniques and devise a correlative strategy to achieve a large-scale (millimeter-scale) identification of stacking sequence while simultaneously resolving the nanoscale dislocations. This is essential not only for the development of 2D material–based devices, but also for gaining a fundamental understanding of the structure and defect-related properties.

In this study, we use diffraction contrast and 3D electron diffraction (3D ED) to differentiate between 2H and 3R polytypes in exfoliated and freestanding bilayer MoS2, along with dislocations present in the respective phases. We observed basal dislocations with distinct Burgers vectors across several bilayer regions, indicating the presence of different polytypes within the same flake. Quantitative evaluation of the relrod derived from 3D ED determines the stacking configuration unambiguously. The 2H and 3R polytypes are further confirmed by correlative low-frequency Raman spectroscopy conducted on the same sample sites. Our findings demonstrate an intuitive and scalable approach for determining stacking order in transition metal dichalcogenides (TMDCs), offering great potential for engineering their properties and applications through phase or defect modification.

Results

Preparation and transfer of bilayer MoS2 flake

We employed a step-by-step approach to prepare and transfer bilayer MoS2 flake onto a TEM grid, as illustrated in Fig. 1. The process starts with the mechanical exfoliation of a bulk MoS2 single crystal using a transparent polydimethylsiloxane (PDMS) gel (Fig. 1a, step 1)28. Individual flakes were identified by light microscopy and transferred onto a 5 mm2 Si substrate with a 300 nm SiO2 layer. The MoS2 flake produced in this way has a lateral size of up to 180 µm, according to the light microscopy image. The specific color and contrast of the flake against the SiO2/Si substrate background offer a straightforward way to determine the number of MoS2 layers annotated in the image. The layer numbers were confirmed afterwards by Raman- and photoluminescence (PL) spectroscopy, see Fig. S10. The 300 nm SiO2 layer displays a purple-colored background, and MoS2 regions with varying numbers of layers exhibit different shades of blue29,30. In some cases, exfoliated flakes were cut by a laser to separate the bilayer part from the thicker part of the flakes, simplifying the transfer of the target flake onto a TEM grid (Fig. 1b, step 2). QUANTIFOIL gold grid with an R1.2/1.3 holey carbon film was coated with a thin gold layer (see Experimental methods) to enhance the transfer efficiency, taking advantage of the strong affinity between gold and sulfur31. The grid was carefully aligned with the target flake under the light microscope, with the gold-coated side pointing towards the flake. A small droplet of isopropanol (IPA) was applied, followed by a small droplet of KOH solution (wt. 3%) after the IPA dried. The KOH solution gradually etched away the SiO2/Si. After several minutes, the target flake was detached from the SiO2/Si substrate and transferred onto the TEM grid (Fig. 1c, step 3). Prior to TEM and Raman spectroscopy investigation, the sample was cleaned with water and an acetone bath, followed by heating on a hot plate (100 °C) for 10 minutes. The example illustrated in Fig. 1 shows a large MoS2 flake that spans two square windows of the TEM grid. TEM, Raman, and PL studies were conducted on the identical holes of the QUANTIFOIL grid, corresponding to the two marked bilayer regions.

Fig. 1: Illustration of the step-by-step approach to prepare and transfer bilayer MoS2 flake onto a gold-coated TEM grid.
Fig. 1: Illustration of the step-by-step approach to prepare and transfer bilayer MoS2 flake onto a gold-coated TEM grid.
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a, b MoS2 flakes were exfoliated using PDMS gel and transferred onto a SiO2/Si substrate (steps 1 and 2). c The gold-coated TEM grid was carefully positioned in relation to the target flakes under the light microscope. The target flake was then transferred to the grid by sequentially applying IPA and KOH solution. Finally, the MoS2 flake was cleaned using water and acetone bath, followed by heating on a hotplate in air. The marked bilayer regions #1 and #2 correspond to 3R and 2H phase, respectively, which are investigated by the following TEM and Raman spectroscopy.

Dislocations and associated polytypes

In 2H and 3R MoS2, the Mo atoms are sandwiched between two S layers in trigonal prismatic coordination, the S-Mo-S prisms of the two layers can be oriented either parallel or antiparallel, i.e., rotated by 180°. In the latter configuration, AA’ also denoted as 2H stacking (Fig. 2a), is the favored stacking arrangement with the lowest ground-state total energy2. In the case of parallel orientation of the prisms, AB (or AC) stacking is the preferred stacking order, with a ground-state total energy only slightly higher than 2H2. AB and AC are energetically equivalent and are commonly referred to as 3R stacking (Fig. 2e), because the layer sequence is part of the ABC (or twinned ACB) stacking of bulk 3R. There are other possible stacking orders with high symmetry (AA, A’B, AB’) but their respective ground-state total energies are considerably higher, in particular those of AA and A’B, where the chalcogen atoms of the two layers directly sit on top of each other2,32. Such stackings are not expected to be formed on large areas upon exfoliation, but may appear locally in defects, moiré lattices, or boundaries14,33,34,35. Various possible stacking sequences in bilayer MoS2 are schematically illustrated in Fig. S4.

Fig. 2: Crystal structure and Burgers vector analysis on different types of dislocation, implying the presence of 2H and 3R phases in the exfoliated bilayer MoS2 flake.
Fig. 2: Crystal structure and Burgers vector analysis on different types of dislocation, implying the presence of 2H and 3R phases in the exfoliated bilayer MoS2 flake.
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a, e Top and side views of crystalline structures for bilayer 2H and 3R MoS2. The red and blue arrows in the top views represent the corresponding Burgers vectors of type (1/3)\(\left\langle \bar{2}110\right\rangle\) and (1/3)\(\left\langle 0\bar{1}10\right\rangle\). b LM image of the bilayer MoS2 flake on TEM grid. The yellow rectangles marked the 2H and 3R regions, same as Fig. 1c. The circles in (b) marked the measured holes shown in the DF-TEM images below. c, d Series of \(\left\{\bar{1}100\right\}\) and \(\left\{\bar{2}110\right\}\) DF TEM images acquired from the bilayer region #2, showing a perfect dislocation. f, g Series of \(\left\{\bar{1}100\right\}\) and \(\left\{\bar{2}110\right\}\) DF TEM images acquired from the bilayer region #1, showing a nearly 90° partial dislocation.

Basal-plane dislocations can easily be introduced into the van der Waals gap of bilayer MoS2 due to the weak interlayer bonding. However, the different symmetry and stacking order of 2H and 3R polytypes result in distinct dislocation characteristics. The main characteristic of a dislocation is its Burgers vector b, which describes the total displacement of one layer with respect to the other upon crossing the dislocation. The expected Burgers vectors for 2H and 3R MoS2 are indicated by a red and blue arrow in Fig. 2a and e, respectively. For the 2H phase, the Burgers vector is of type b = (1/3)\(\left\langle \bar{2}110\right\rangle\), which corresponds to a lattice translation vector along a zigzag direction of the crystal. It is therefore a perfect dislocation, which means that the bilayer crystal has the same stacking on both sides of the dislocation. In contrast, the Burgers vector of a dislocation in 3R bilayer MoS2 is of type b = (1/3)\(\left\langle 0\bar{1}10\right\rangle\), oriented along one of the armchair directions of the crystal and is shorter than a lattice translation. Upon crossing the dislocation, the stacking order changes from AB to AC (or vice versa). In dislocation theory, such a dislocation is known as a partial dislocation, but it has also been referred to as a stacking boundary in the 2D materials community36,37. The atomic models of the distinct dislocations are illustrated in Fig. S5. The reason why no perfect but only partial dislocations are expected in 3R bilayer MoS2 is that the two stacking orders, AB and AC, are energetically equivalent, as has been discussed in detail for bilayer graphene38. Line direction u is another characteristic of a dislocation. While the Burgers vector of a dislocation is fixed, the line direction can change along the dislocation, giving the dislocation a screw (u | |b), mixed (u inclined to b), or edge (u ⊥ b) character. Screw dislocations play a particular role in 2D moiré lattices, as they signal the formation of domain boundaries and introduce localized distortions, which ultimately affect the materials’ physical properties12,14.

Figure 2 summarizes the investigation of isolated dislocations in the exfoliated bilayer MoS2 using centered dark-field TEM (DF TEM) imaging and careful Burgers vector analysis. The stacking orders of the two regions in the bilayer MoS2 were unknown at the time of the investigation but will be confirmed later through correlative electron diffraction, Raman, and PL spectroscopy. Figure 2c and d depict a series of \(\left\{\bar{1}100\right\}\) and \(\left\{\bar{2}110\right\}\) DF TEM images, revealing the dislocation in bilayer region #2 (Fig. 2b). The corresponding diffraction pattern is shown in Fig. S6 (Supplementary information) and the diffraction vector g used for dark-field imaging is indicated in each DF TEM image. The invisibility of the dislocation in the \((\bar{1}100)\) DF image suggests that the Burgers vector b is perpendicular to the diffraction vector g (according to the g·b = 0 invisibility criterion11,38) and thus parallel to \(\left[\bar{1}\bar{1}20\right]\), as indicated by the red arrow in Fig. S7b. The sign of the Burgers vector is determined by investigating the dislocation contrast variation under different tilting angles (see details in Fig. S7). The only crystallographically meaningful Burgers vector in this direction is b = (1/3) \(\left[\bar{1}\bar{1}20\right]\), confirming a perfect dislocation as discussed above. These findings also (indirectly) indicate a 2H stacking of the bilayer MoS2 in region #2. As expected, all other dark-field images in Fig. 2c and d exhibit dislocation contrast, as no other g vector fulfills the invisibility criterion. Notably, the dislocation is seen with double line contrast in the \((\bar{1}\bar{1}20)\) DF image. This phenomenon is well known and results from the fact that |g·b | = 2 for this particular g vector39. In fact, the g vector is oriented parallel to the Burgers vector b, resulting in maximum scalar product g·b = (1/3)\(\left(\bar{1}\bar{1}20\right)\cdot\left[\bar{1}\bar{1}20\right]\) = 2. For all the other g vectors, |g·b | = 1, in accordance with the observed single-line contrast. Observing that the MoS2 exhibits identical contrast on both sides of the dislocation further supports the conclusion that the dislocation in region #2 is a perfect dislocation. The angle between the Burgers vector b and the dislocation line direction u indicates the dislocation has a mixed character with a larger edge component than the screw component. All pieces of evidence are pointing to the conclusion that the bilayer MoS2 in region #2 has 2H stacking and that the dislocation is a perfect dislocation with Burgers vector b = (1/3) \(\left[\bar{1}\bar{1}20\right]\) and mixed character.

Figures 2f and g presents the corresponding DF TEM images and analysis for a dislocation located in region #1 (Fig. 2b). The dislocation contrast is clearly different from that observed in region #2. The invisibility of the dislocation is achieved with the \((\bar{2}110)\) reflection, thus the Burgers vector of the dislocation is parallel to \(\left[0\bar{1}10\right]\), as indicated by the blue arrow in Fig. S7e. The dislocation is almost a pure edge dislocation since the Burgers vector is approximately perpendicular to the dislocation line direction u. Taking crystallographic considerations into account again, the only meaningful Burgers vector is b = (1/3) \(\left[0\bar{1}10\right]\), confirming the dislocation is a partial dislocation associated with 3R stacking. The stacking order changes from AB to AC (or vice versa) when moving from one side of the dislocation to the other. This change in stacking sequence is also consistent with the distinct contrast across the dislocation in the three \(\left\{\bar{1}100\right\}\) DF TEM images (Fig. 2f). The degree of contrast asymmetry depends on the exact orientation of the MoS2 with respect to the incident electron beam. Even a slight deviation from the exact Bragg condition introduces a contrast difference that increases with increasing excitation error39. No contrast asymmetry is observed in the \(\left\{\bar{2}110\right\}\) DF images (Fig. 2g), as these reflections are insensitive to the change in stacking order from AB to AC. Apart from the \((\bar{2}110)\) DF image, all other DF images in Figs. 2f and g show pronounced dislocation contrast, as expected for g·b ≠ 0. The dislocation contrast in the \((0\bar{1}10)\) DF image is particularly strong (and bright) compared to the dislocation contrast in the other two \(\left\{\bar{1}100\right\}\) DF images. This is attributed to the fact that g is oriented parallel to b, resulting in a larger magnitude of the scalar product |g·b | = 2/3 than |g·b | = 1/3 for the other two \(\left\{\bar{1}100\right\}\) DF images. For the \((\bar{1}\bar{1}20)\) and \((1\bar{2}10)\) DF images, |g·b | = 1, resulting in equally strong dislocation contrast. In summary, the DF TEM analysis in Figs. 2f and g strongly suggests that the bilayer MoS2 in region #1 has 3R stacking and that the dislocation is a partial dislocation with Burgers vector b = (1/3) \(\left[0\bar{1}10\right]\) and nearly pure edge character.

Correlative identification of polytypism

The careful dislocation analysis described above provides indirect evidence of the stacking order - 2H in region #2 and 3R in region #1, through the specific dislocations associated with the respective bilayer MoS2 polytype. To validate the stacking configuration and number of layers in the two sample regions, we performed correlative rocking curve analyses in TEM, followed by Raman and PL spectroscopy at the two marked regions in Fig. 1c, which included the identical locations as the TEM investigation. We initially investigated the intensity oscillation of the relrods (rocking curves along qz direction, qz is defined at the origin along reciprocal lattice along the c* direction. The c* direction in hexagonal symmetry coincident with c lattice, and the zero position intersects the plane defined by the real space lattice basis vectors a and b) extracted from reconstructed 3D ED datacubes (complete 3D data visualizations are shown as insets in Fig. 3a, b, and in Fig. S8). These results are compared with simulated kinematic rocking curves for bilayer MoS₂ with various stacking sequences, including the low-energy configurations of 2H and 3R phases, as well as other theoretically possible, high-energy configurations (Fig. S9)2,32. Two key pieces of information are yielded: I) layer number; II) symmetry and structure, reflected by first-order relrods40. As shown in Fig. 3a and b, apart from the deviation, the experimental data aligns well with the simulations in terms of peak positions and widths of the \(\{1\bar{1}00\}\) and \(\{11\bar{2}0\}\) relrods. The observed deviation can be attributed to two aspects: 1) the corrugated nature of the flake41,42 and the contamination growth during data acquisition growth; 2) the normal incidence electron diffraction pattern of MoS2 calculated by the kinematical theory exhibits systematic violation of the Friedel law (which means dynamic effects take place), with the difference in the intensities of 10 − 20%43. The \(\{11\bar{2}0\}\) relrods for both polytypes exhibit symmetric intensity oscillations and confirm the bilayer thickness. In contrast, the \(\{1\bar{1}00\}\) intensity profiles vary dramatically between the 2H and 3R stacking configurations, owing to the differences in stacking sequence and crystal symmetry. For the intensity profile of \(\left(1\bar{1}00\right)\) relrod in 2H stacking, the central peak nearly appears at the reciprocal lattice point qz = 0, but the whole profile exhibits a pronounced asymmetry, with a first intense peak on one side at −0.25 Å−1 and a much smaller peak on the other side at 0.14 Å−1 (red scattered dots and line in Fig. 3a). For 3R bilayer, the \(\left(1\bar{1}00\right)\) relrod intensity shows similar oscillations, but the central peak shifts to qz = −0.07 Å−1. This shift originates from the phase shift of the scattering wave that interacts with the atoms in the lower and upper layers, which are vertically separated by a definite amount (which is implicitly acknowledged in the bilayer systems), and the lateral shift of these atoms towards the \(\left[1\bar{1}00\right]\) crystalline orientation within the unit cell. Additional simulated rocking curves for theoretically high-energy configurations (AB’ and A’B stacking, Fig. S9) reveal first-order relrod intensity profiles that clearly deviate from experimental observations. As a result, by comparing quantitative rocking curve evaluation to simulation, we unambiguously discriminate between the 2H and 3R polymorphs while ruling out additional high-energy configurations in bilayer MoS2.

Fig. 3: Correlative determination of 2H and 3R polytypes within the bilayer MoS2 flake using 3D ED, Raman and PL spectroscopy.
Fig. 3: Correlative determination of 2H and 3R polytypes within the bilayer MoS2 flake using 3D ED, Raman and PL spectroscopy.
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a, b Rocking curves of \(\left(1\bar{1}00\right)\) (red dots) and \(\left(11\bar{2}0\right)\) (black dots) reflections, extracted from 3D ED datasets (insets), which were acquired from dislocation-free areas of bilayer MoS2. Solid lines are the simulated rocking curves. The rocking curves confirm the layer numbers as well as the different atomic staking orders (i.e., polymorphism). c, e Low-frequency Raman and PL spectra of the 2H and 3R bilayer MoS2; the peaks were fit by Lorentzians (dashed lines). d The amplitude ratio and frequency difference between LB and S modes in 2H and 3R bilayer MoS2. The inset in (e) highlights the average value of the A exciton and B exciton energy differences between 2H and 3R bilayer MoS2. The error bars in (d) and inset in (e) represent the standard deviation derived from three independent Raman and PL spectra measured from three different sample regions (holes on the TEM grid). The inset (e) confirms that the A and B exciton positions vary between different measurement points (as indicated by the error bars). The shift of the B exciton is slightly larger than that of the A exciton from 2H to 3R, with both exciton energies showing a redshift.

To further validate these findings on a large scale, Raman and PL measurements were conducted not only at the identical sample locations as in the TEM study but also at additional regions (the laser spots during Raman and PL measurements are indicated in Fig. S10, determined by carefully aligning the TEM and light microscopy images). Figure 3c shows the Raman spectra of MoS2 in the low-frequency range, with the shear mode (S) at a frequency of ~23 cm−1 and the layer-breathing mode (LB) at ~40 cm−1. The positions and shapes of the low-frequency modes are consistent with those of bilayer MoS244. Significantly, as shown in the top panel of Fig. 3d, the amplitude ratio of LB/S in 2H stacking (~0.4) is smaller than that in 3R stacking (~1.4), due to the difference in the interlayer coupling between the two polytypes. A frequency shift in the S and LB modes from the 2H to the 3R polytype is also observed, leading to a slight increase in the frequency difference (~1.9 cm−1) between the two modes (bottom panel in Fig. 3d). Figures S10 c and g show additional Raman spectra of MoS2 in the high-frequency region (Eg and A1g modes), which further validate the bilayer thickness. The findings of the PL measurement results are displayed in Fig. 3e, revealing two distinct peaks corresponding to the A and B excitons of bilayer MoS2 with energies of ~ 1.81 eV and ~ 1.95 eV, respectively. The A and B exciton peak positions in 3R MoS2 are red-shifted by 15.1 meV and 24.6 meV, respectively, compared to those in the 2H polytype, as seen in the inset of Fig. 3e. Additionally, the B exciton appears more pronounced in the 3R structure. Both MoS2 polytypes are therefore effectively distinguished using Raman and PL spectroscopy. In addition, comparative measurements reveal the splitting of Eg mode in Raman spectra and considerable quenching in PL spectra for the measured regions with dislocations, regardless of stacking orders (Figs. S10 c-d, g-h), indicating the presence of dislocations. However, it should be noted that not all holes containing dislocations exhibit such differences or signals in the Raman or PL spectra. Therefore, we believe a systematic investigation on the effects of dislocation on Raman and PL spectroscopy would be of great interest using tip-enhanced spectroscopy which exhibits spatial resolution on the scale of ~10 nm.

Discussion

The correlative TEM – Raman spectroscopy methodology effectively integrates the benefits of these two techniques, while their individual limitations are largely mitigated. This approach allows for the reliable identification of stacking configurations in 2D materials across a broad range of length scales—from the nanoscale to the millimeter scale, along with the ability to investigate the distinct dislocations. As a result, it overcomes the limited field of view inherent to TEM studies, the strain-induced effects and limited spatial resolution in Raman and PL spectroscopy. This capability is particularly significant for the development of future 2D material–based devices, which demand high sample uniformity over large areas. Furthermore, nanoscale dislocations are clearly resolved and analyzed, and their impact on spectroscopy is explored through the correlative method. While the effects of dislocation are not yet fully established, our findings offer valuable insights and pave the way for future research on the role of defects in tuning the properties of 2D materials. Notably, it is surprising to observe the occurrence of the 3R phase in the MoS2 flake, despite starting with the hexagonal bulk crystal (confirmed by XRD results, Fig. S1). Theoretical calculations of the energy landscape for different stacking orders in bilayer MoS2 indicate that the 3R phase (AB stacking) exhibits a slightly higher ground-state energy than that in 2H phase (AA’ stacking), implying that an external stimulus is required to trigger the 2H to 3R phase transition. Previous studies have demonstrated that the phase transition in 2D materials can be induced by pressure45,46, heating47,48, electric-field49, and alkali metal intercalation50. Particularly, a phase transition from 2H to 3R in bulk MoS2 has been achieved with a pressure above 20 GPa45. Considering the overall sample preparation process, we highly suspect that the strain introduced during exfoliation and transfer may have played a role in promoting the formation of the 3R phase. Though we are currently unable to validate this hypothesis due to a lack of precise control or quantification of the stress or strain, this unexpected finding opens up new thoughts for exploring the phase transition in atomically thin 2D materials.

In summary, we have overcome the limitations of single-characterization techniques by implementing a correlative TEM-Raman approach to differentiate 2H and 3R polytypes in bilayer MoS2. The different intensity oscillation and structural features in the first-order relrod, reconstructed through 3D ED construction, along with the variations in shear and layer breathing modes detected by Raman spectroscopy, allow for a comprehensive determination of the stacking orders in MoS2. Furthermore, we identified perfect dislocation with Burgers vector of type b = (1/3)\(\left\langle \bar{2}110\right\rangle\) in the 2H phase and partial dislocation with Burgers vector of type b = (1/3)\(\left\langle 0\bar{1}10\right\rangle\) in the 3R phase. These dislocations are closely related to their respective stacking arrangements. Interestingly, both polytypes were found within the same bilayer flake that was exfoliated from a parental 2H bulk crystal, implying a possible phase transition during exfoliation or transfer of the flake. Our study of stacking arrangements and dislocations in MoS2 emphasizes the importance of correlative electron microscopy and optical-spectroscopy methods in investigating the structural and functional properties in 2D vdW materials.

Methods

Sputter deposition of gold film on TEM Grids

Standard QUANTIFOIL Holey carbon R1.2/1.3 foils on 200 mesh gold grid is fixed onto the customized holder and placed into the HEX thin film sputter coater (Korvus Technology), with the carbon support film facing the gold source. After the evacuation of the sputter coater chamber, gold depositing starts along with the rotation of the grid (rotation speed, 5 rpm) to ensure uniform deposition. Eventually, a nominal thickness of 20 nm gold was deposited onto the gold TEM grids.

Samples

Hexagonal MoS2 bulk crystal was purchased from HQ Graphene. The 2H polytype was confirmed by X-ray diffraction, which showed well-developed pole figures of the 2H reflection (103)2H, whereas no intensity was detected for the expected Bragg angle of the 3R reflection (104)3R (see Fig. S1). Although this does not represent a full quantitative analysis of phase purity, the measurement demonstrates that the 2H phase is strongly dominant, and the presence of 3R stacking is negligible. Bilayer MoS2 flakes were prepared by mechanical exfoliation of the bulk crystal using PDMS gel. Flakes with bilayer thickness were identified by light microscopy (LM, Zeiss Axio Scope) and then transferred to the gold TEM grid. Further details of the preparation procedure for correlative TEM, Raman and PL spectroscopy are described in the Results and discussion section.

Transmission electron microscopy and diffraction rocking curves

TEM experiments were carried out using a Thermo Fisher Scientific (TFS) Spectra 200 microscope operated at 200 kV. The TEM is equipped with a cold field emission gun (X-CFEG), a Probe Cs-corrector, a high-resolution CMOS camera Ceta-S with ultra-sensitive scintillator (for TEM dark-field imaging), and a fast hybrid pixel detector Destris ARINA (for 4D scanning transmission electron microscopy, 4D STEM). For centered dark-field imaging (exposure time, 15 s), an objective aperture with size of 10 µm was used. The rocking curves were extracted from the 3D electron diffraction (3D ED) data, which were reconstructed based on nano-beam 4D STEM tilt series experiment. We have developed 4D STEM tilt automation workflow (see details below), along with a 3D ED data reconstruction routine based on simple polar transformation (see details in Supplementary information and Fig. S2). Further experimental conditions include: Fishione Model 2021 analytical tomography holder, probe current of ~ 150 pA, calibrated convergence of 0.45 mrad (quasi-parallel illumination and the diffraction-limited probe size is estimated to be ~ 2.8 nm), camera length of 155 mm, dwell time of 100 µs, tilt range from −60° to 60° at 1° interval, which allows the rocking curve of \(\{1\bar{1}00\}\) reflections to reach ± 0.6 Å−1 before cutting by the missing wedge. The spatially resolved 4D STEM datasets assure (via the virtual dark-field images) that diffraction patterns for 3D ED reconstruction are extracted from identical locations in each tilt angle, which can be critical given the known sample buckling. In particular, we have applied a background noise subtraction as implemented in PETS software51 prior to 3D volume reconstruction. Alternatively, the rocking curves of selected reflection of interest were also acquired via dark-field imaging and tilt series experiment using a normal double tile holder (tilt range ± 25°). While the results are consistent, the limited tilt range is not sufficient to differentiate the theoretically possible high-energy stacking phases (see details in Fig. S3).

Theoretical rocking curves for an equilibrium interlayer distance of 3.370 Å were calculated according to kinematic diffraction theory. We defined the lattice parameters as a = b = 3.161 Å, c = 12.295 Å for the 2H phase, and a = b = 3.163 Å, c = 18.37 Å for the 3R phase52. Supercells by extending c to be 200 Å, but containing only two layers of MoS2 (thus only 6 atoms in the supercells) placed in the middle of the cells are constructed. Structure factor (F(q)),

$$F\left({\boldsymbol{q}}\right)={\sum }_{i}{f}_{i}\left(q\right){e}^{2\pi i\left({\boldsymbol{q}}\cdot {{\boldsymbol{r}}}_{{\boldsymbol{i}}}\right)}$$

of the supercells are calculated using the ACOM module in the py4DSTEM package, where q is the scattering vector, fi is the atomic scattering factor, ri is the atomic position in the real space53,54. Since the bilayers are only 6 atoms thick, the diffracted intensity (I(q)) can be well described by kinematic diffraction theory, i.e.,

$${\rm{I}}\left({\boldsymbol{q}}\right)\propto {|F}\left({\boldsymbol{q}}\right){|}^{2}$$

The intensity of reflections of interest (i.e., {1100} and {2110}) are calculated by the square of the respective structure factors extracted from the full list of the calculated structure factor data. When comparing the experimental and simulation data, the intensity of the experimental data was scaled where the scaling factor is determined via least square fitting.

Automated workflow for acquiring tomographic 4D STEM datasets

The automated tomographic 4D STEM data collection workflow is based on SerialEM scripts55 and SavvyScan external scan generator plug-in56. SerialEM is an open-source program that includes a variety of functions to control the electron microscope, including tilting the sample, performing stage shift and image shift, etc. SavvyScan connects SerialEM with our external scan generator DISS6 (Digital Imaging Scanning System generation 6, Point Electronic), which then controls the 4D STEM camera (ARINA, DECTRIS). SavvyScan integrates the two main functions, image acquisition for general purposes such as finding the target, which is mainly done by a high-angle annular dark-field (HAADF) detector, and 4D STEM data acquisition, which is done by ARINA detector, onto one scan generator. Hence, switching between scan generators is no longer needed and the automated workflow is possible.The automated workflow is described as follows. The electron microscope (Thermo Fisher Spectra 200 TEM) is controlled by the microscope PC using SerialEM. Two targets are selected under low magnification. The exact stage positions of these two targets are recorded, and an image of each target is taken under high magnification for tracking in the future. A set of hyper-parameters including tilt range, tilt steps, convergence semi-angle, and scan parameters, are defined in a custom SerialEM script. This custom SerialEM script performs an automated tilt series. At each tilt angle, the script will use stage shift to move to the recorded target position and then perform cross-correlation with the stored target image to move the beam to the exact target area. Then, a message including the current tilt angle, scan size, dwell time, acceleration voltage, and pixel size is sent to the workstation. Once the workstation receives the message, it will control the DISS6 scan generator to perform the 4D STEM data collection accordingly. After the data is collected, a confirm message will be sent back to the SerialEM, so the SerialEM will move to the next tilt angle and repeat the process.

Raman and photoluminescence spectroscopy

Raman and PL spectroscopy measurements on the bilayer MoS2 flakes supported on the TEM grid were performed with a HORIBA LabRam HR Evolution spectrometer with laser excitation at λ = 532 nm and an 1800 lines/mm grating (300 lines/mm grating for PL measurements). The incident laser power was set to 30 µW to avoid heating effects and damage to the sample; the diameter of the laser spot on the sample was approximately 0.5 µm. Within the 500 nm laser spot size, it is able to differentiate 2H and 3R polytypes in the Raman spectrum in terms of the peak position and intensity. The Raman and PL spectra were calibrated by neon lines. We performed a thorough DF TEM investigation on the entire bilayer MoS2 flake and carefully aligned the TEM images with the LM images, so that TEM, Raman, and PL results are correlatively collected from the identical measured regions.

X-ray diffraction

X-ray characterization of MoS2 bulk flakes was conducted using a Rigaku SmarLab 9 kW diffractometer operating at 45 kV and 160 mA. A Johansson monochromator is utilized to monochromatized to the Cu-Kα1 wavelength of 1.54 Å. The beam is further parallelized to 0.05° and collimated to 5° by a Goebel mirror and Soller slits for Θ/2Θ measurements, respectively. For pole figure measurements the beam was further collimated towards 0.5°, which were then performed with a beam width and height of 2 and 1 mm, respectively.