# Auto-organization of 2H|3R lateral boundaries in bilayer WSe2 grown by chemical vapor deposition

Gaia Di Berardino, Meryem Bouaziz, Gilles Patriarche, Julien Chaste,

Abdelkarim Ouerghi, Fabrice Oehler

► To cite this version:

Gaia Di Berardino, Meryem Bouaziz, Gilles Patriarche, Julien Chaste, Abdelkarim Ouerghi, et al. Auto-organization of 2H|3R lateral boundaries in bilayer WSe2 grown by chemical vapor deposition. Physical Review B, 2025, 111 (12), pp.125403. 10.1103/PhysRevB.111.125403. hal-04984089

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# Auto-organization of 2H|3R lateral boundaries in bilayer WSe₂ grown by chemical vapor deposition

Gaia Di Berardino, Meryem Bouaziz, Gilles Patriarche, Julien Chaste, Abdelkarim Ouerghi, and Fabrice Oehler

Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies, 91120 Palaiseau, France

<figure><img src="image_2.png" /></figure>

(Received 9 October 2024; revised 3 December 2024; accepted 22 January 2025; published 7 March 2025)

Small changes in the structure of thin bidimensional transition metal dichalcogenides (TMDs) can radically alter the overall material properties. Here, we investigate the epitaxial self-organized boundary between two tungsten diselenide domains obtained by chemical vapor deposition: the AB ferroelectric bilayer (noncentrosymmetric, 3R-like) and the conventional AA' bilayer (centrosymmetric, 2H). Several tools are used to isolate and confirm the different polytype signatures, such as micro-Raman, second harmonic generation (SHG) and photoluminescence. Transmission electron microscopy is found to bring complementary information to Raman and SHG in the polytype determination. Finally, we resolve and index a particular sawtooth structure in the experimental 2H|3R boundary wall, whose origin is linked to particular twin boundaries observed in other TMDs.

DOI: 10.1103/PhysRevB.111.125403

## I. INTRODUCTION

The transition metal dichalcogenide (TMD) family is well-known for the direct band gap of several of its members such as MoS₂ [1,2], WS₂ [3], or WSe₂ [4,5] in the monolayer (1ML) form. The evolution from indirect band structure in the bulk to direct transition as few- or monolayer is at the origin of rich physics [6,7] and possible applications in optoelectronic devices [8,9]. Bilayers (2ML) TMDs provide an even richer playground as the in-plane rotation angle between the two layers can be varied continuously, creating a variety of moiré reconstructions which modulate the overall band structure [10–12]. Stepping back from arbitrary misorientation angles, the TMD family already hosts a variety of polytypes in the bulk form, with either 0° or 60° in-plane misorientation angle between adjacent layers [13,14]. This diversity in the bulk is also visible in the bilayers obtained by direct growth using molecular beam epitaxy [15] or chemical vapor deposition (CVD) [16,17], in the form of hexagonal (2H) 2ML polytype or rhombohedral (3R) 2ML arrangement. Note that recent works have also demonstrated the direct CVD growth of 2ML MoS₂ with a wide range of in-plane misorientation angles [18].

The rhombohedral (3R) form of 2ML TMDs exhibits a reduced symmetry, which results in degeneracies being lifted in its electronic structure [19–21], and the existence of permanent ferroelectric polarization [22,23]. This unusual mix of physical characters may find application in CMOS computing [24], optomechanics [25], or resilient ferroelectric memories

[26,27]. However, progress towards these goals requires the controlled growth of single and pure 2ML polytypes, which is a challenge currently being addressed by the community [16,28–33]. Still, more efforts are necessary to ease the identification and to understand the growth mechanism of 2ML TMD polytypes.

In this work, we investigate the stacking order of several 2ML WSe₂ polytypes grown directly by CVD from elemental selenium and tungsten oxide (see Methods). We show that optical methods such as micro-Raman and second harmonic generation (SHG) may be combined to transmission electron microscopy (TEM) to determine particular 2ML polytypes. Selected area diffraction (SAED) using TEM is particularly informative. Details of the epitaxial 2H-3R boundary are investigated by dark-field TEM, indexed with respect to reference crystal directions and compared to existing literature.

## II. NOMENCLATURE

Figure 1 details the six high-symmetry atomic stacking of WSe₂ 2ML stackings. All polytypes can be described using a standard hexagonal basis (a,b,c), with $a = 3.28$ Å and $c = 12.96$ Å for bulk WSe₂ [34]. Tungsten (W), selenium (Se), or an empty site (Ø) are distributed and superposed along the three high-symmetry sites of the hexagonal unit cell.

We adopt here the notation of Dresselhaus et al. [35] associating two letters and a “prime” character to each structure (bold black in Fig. 1) because it has a simple connection with the complete atomic structure of TMDs [13,14] (see Ref. [36] Sec. A). Other variants of the two letters scheme exist [21,37,38], and the atomic superposition registry (X over Y, noted X/Y in the legend of Fig. 1) is presently the only secure definition of the stacking order (see details in Ref. [36] Sec. A).

The three noncentrosymmetric 2ML polytypes are {AA, AB, BA}, Fig. 1(a), without in-plane rotation (0°) between the two layers. The opposing vertical polarization between

<footnote>*Contact author: fabrice.oehler@universite-paris-saclay.fr</footnote>

<footnote>Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.</footnote>
<figure><img src="image_3.png" /><figcaption>FIG. 1. (a) Noncentrosymmetric and (b) centrosymmetric 2ML WSe₂ polytypes. Symmetry-related markings (2H) and (3R) are indicated (see caveat in main text). The unit cell is marked as light orange. The superposition registries are AA:(W/W, Se/Se), AB:(W/Ø, Se/W), BA:(W/Se, Ø/W), AA':(W/Se, Se/W), AB':(W/W, Se/Ø), A'B:(W/Ø, Se/Se).</figcaption></figure>

AB and BA is apparent in the chosen notation [22,23,26]. The {AB, BA} stackings are associated to 3R notation in the literature [16,17,26,39], as a hint that these structures are the first two layers of the bulk unit cell of (3R) ABC rhombohedral WSe₂ [13]. Note that (3R) is *not* a Ramsdell notation for 2ML polytypes [40]. Similarly 2ML {AB, BA} do *not* share the same exact symmetry as the bulk R3m (3R) ABC structure but a close variant (see atomic description in Ref. [36] Sec. A and symmetry definition in Ref. [41] or Ref. [36] Sec. B).

All centrosymmetric 2ML polytypes are {AA', AB', BA'}, Fig. 1(b), with a 60° in-plane rotation between the lattice of each layer. The conventional naming (2H) AA' of the hexagonal phase of bulk TMD is retrieved [38]. Although the particular (2H) label is usually associated to bulk hexagonal WSe₂, {AA', AB', BA'} all share the *same* symmetry (*P* − 3*m*1 as bilayers, *P*₆₃/*mmc* as bulk) and the same (2H) Ramsdell notation should apply indiscriminately (see Ref. [36] Secs. A and B).

### III. RESULTS

Assuming a unique dominant zig-zag termination [42], the shape of individual 1ML WSe₂ monocrystals is triangular for growth conditions in excess of chalcogen [16,43], in agreement with our experimental observations in Fig. 2. Due to the strong optical contrast of TMDs over SiO₂(283 nm)/Si(100) substrate [44,45], our 1ML- or 2ML-thin WSe₂ crystals are visible as regular triangles. Changes in WSe₂ thickness are identified by a change in the optical contrast, from 1ML (light) to 2ML (dark).

The WSe₂ monocrystals in Figs. 2(a) and 2(b) present a partial 2ML coverage, which appears as darker triangles over the first layer. In this situation, the relative orientation of the edges of the upper layer gives a hint of the 2ML stacking order, with either 0° or 60° (±120°) rotation angle of the top layer relative to the bottom. Given that 2H (AA') is the

<figure><img src="image_4.png" /><figcaption>FIG. 2. Optical images of WSe₂, as grown on SiO₂/Si(100). [(a) and (b)] Monocrystal WSe₂ of 1ML thickness with partial 2ML coverage of different stacking orders: 2H and 3R. (c) Monocrystal WSe₂ with near complete 2ML coverage, with hint of different stacking order, marked as a proposed 3R main region and 2H inclusions.</figcaption></figure>

lowest energy stacking for 60° rotation stacking and that the two 3R (AB) and (BA) configurations share the lowest energy for 0° rotation [21,46], it is common to assume the simplifying assumption: “60° rotation = 2H (AA’),” “0° rotation = 3R (AB, BA)” as we do ourselves to assign 2ML polytypes in Figs. 2(a) and 2(b). However, this fast sorting technique fails to acknowledge the experimental evidence of other 2ML polytypes [26,47].

Even worse, the assignment of 2H or 3R polytypes from relative orientation of edges becomes difficult in the case of near complete 2ML coverage. In Fig. 2(c), we only see faint morphological hints of the presence of two different stackings. This type of mixed-stacking bilayer makes less than 5% of the total bilayer count in our samples (see Ref. [36] Sec. H) but they are reliably found in our CVD experiments. Here, we propose the *hypothesis* that the main area of the 2ML WSe₂ crystal is 3R (AB or BA stacking) while the three inclusions are 2H AA, even if it is contradictory to the relative edge orientation.

To investigate the proposed stacking assignments, we explore in Fig. 3, the crystal from Fig. 2(c) by various optical means. Figure 3(a) is a Raman intensity map of the integrated spectral window centered around the $A_{1g}$ Raman mode (251 ± 5 cm⁻¹), acquired at room-temperature using a 532 nm laser. The proposed 2H and 3R regions are now clearly distinguished by a major change of the integrated Raman intensity. Figure 3(b) shows that the proposed 2H and 3R regions have similar spectral features and that they mostly differ by intensity of the $A_{1g}$ line.
<figure><img src="image_5.png" /><figcaption>FIG. 3. Room-temperature optical investigations of 2ML WSe$_2$ from Fig. 2(c) with details of the proposed 3R main region (blue) and 2H (orange) inclusions. [(a) and (b)] Integrated Raman intensity map and local Raman spectra near the $A_{1g}$ line. [(c) and (d)] Integrated PL intensity map and local PL spectra. [(e) and (f)] SHG intensity map and polar plot of the local SHG intensity with respect to the laser polarization.</figcaption></figure>

The integrated PL intensity map of Fig. 3(c) (interval $1.57 \pm 0.1$ eV) shows some variations at room temperature, with a larger FWHM and intensity for the proposed 2H region (109 meV, orange color) compared to the proposed 3R region (64 meV, blue color). Intense monolayer contribution is clearly visible on the outer edges. The corresponding PL spectra are shown in Fig. 3(d).

We then investigate the same crystal by second harmonic generation (SHG). The room-temperature SHG signal map [Fig. 3(e)] shows that the proposed 2H inclusions display a constant near zero signal while the proposed 3R central area holds a high and homogeneous SHG response. Long exposure acquisitions reveal that the proposed 2H inclusion has an extremely faint SHG signature [Fig. 3(f)]. Note that both regions display matching angular distributions of the SHG intensity, with sixfold symmetry, as expected from monocrystalline WSe$_2$.

As all the polytypes have slightly different atomic stacking, we may expect that diffraction techniques, such as transmission electron microscopy (TEM), can fingerprint the different

WSe$_2$ stacking orders. In Fig. 4, we investigate by TEM a different 2ML WSe$_2$ crystal, which displays the same morphology and Raman features than Fig. 2(c) (see Ref. [36] Sec. D). Figure 4(a) shows an optical image of the as-grown 2ML WSe$_2$ flake on the silica surface. Morphological hints of the inclusion are visible on the top edge of the triangle. This particular flake is then transferred to a TEM grid by a polymer-assisted technique (see Methods).

Figure 4(b) shows a scanning TEM (STEM) image of the boundary zone between the proposed 2H and 3R regions, obtained in high angle annular dark field mode (STEM-HAADF). As the STEM-HAADF contrast mostly originates from chemical composition (Rutherford scattering), such large-scale HAADF image is mostly sensitive to the thickness of the TMD crystal and it cannot distinguish between polytypes. Consequently, we do not see a clear boundary between the two proposed 3R and 2H regions. However, we remark a small 1ML area (darker) in the center of the image which is used as a spatial reference to image the same zone in subsequent dark field TEM images.

Figures 4(c) and 4(d) are selective area electron diffraction (SAED) patterns collected by restricting the TEM spatial aperture to the two zones marked in Fig. 4(b). We see that both SAED patterns are hexagonal, with matching crystal axes between the two locations. Positions of each spot are identical but the intensity of some diffracting families differs. We quantify in Figs. 4(e) and 4(f) the diffracted intensities of the 100 and 110 families. Due to the hexagonal symmetry, each family holds six members. We normalize all spots intensities with respect to the highest diffracted spot in each pattern (outside of the direct beam), which belongs to the 110 family in our case. In Fig. 4(e), we observe that the intensities from the proposed 2H inclusion are regularly distributed and that the average intensity ratio between the 110 and 100 families is $I_{2H}^{\text{exp}} \sim 0.7$. In the proposed 3R main region, the collected intensities are more dispersed and the average intensity ratio is lower $I_{3R}^{\text{exp}} \sim 0.5$ [Fig. 4(f)].

In Figs. 4(g) and 4(h), we make use of the intensity variations observed in SAED by selecting a unique reflection (either 100 or 110 in reciprocal space) to construct the corresponding dark field TEM (DF-TEM) image in real space. For 110 DF-TEM, there is no contrast difference between the proposed 3R and 2H regions [Fig. 4(g)]. The only visible feature is the small 1ML region, previously identified in STEM-HAADF [Fig. 4(b)]. Images acquired using 100 DF-TEM are more informative: the proposed 2H inclusion appears bright while the proposed 3R main region is darker [Fig. 4(h)].

These DF-TEM 100 imaging conditions are used at a larger scale in Fig. 5(a). The same 100 DF-TEM contrast between the proposed 3R (dark) and 2H (bright) regions is now observed over 0.5 µm distance. Selected locations are investigated in more details in Figs. 5(b) and 5(c). The proposed 2H|3R boundary wall is characterized by jagged edges with near ~90° angle sawtooth. This configuration is observed along two different in-plane orientations [Figs. 5(b) and 5(c)]. The precise orientation (±60°) of the crystallographic axes (a, b) with respect to the observed ‘sawtooth’ boundary is obtained from SAED.
<figure><img src="image_6.png" /><figcaption>FIG. 4. Transmission electron microscopy (TEM) characterization of the 2ML WSe₂ with mixed regions. (a) Optical image. (b) Scanning TEM (STEM) views of the boundary region. [(c) and (d)] Selective area diffraction (SAED) patterns from the areas identified in (b). [(e) and (f)] Corresponding normalized intensity of the sixfold 110 and 100 diffracted intensities from SAED patterns. [(g) and (h)] Dark field TEM (DF-TEM) images obtained by selecting the 110 and 100 spot, respectively. White dotted lines are guides to the eye to mark the 1ML area.</figcaption></figure>

# IV. DISCUSSION

## A. Polytypes sorting using total energy

The first aspect of this discussion is to establish the nature of the observed WSe₂ polytypes. The thickness of the crystal is determined to be 2ML by optical contrast (Fig. 2) and AFM (Ref. [36] Sec. E).

The stability of TMD bilayers (Fig. 1) depends on their atomic structure. The following total energy ordering is found in the literature [21,37,38,47]: AA' ≲ AB (= BA) < AB' ≪ A'B < AA (see notations and atomic details in Ref. [36] Sec. A), so that (2H) AA' and (3R) AB are the most stable 2ML polytypes while AA is the less stable.

In practice, isolated large crystals of (2H) AA' and (3R) AB or BA bilayer have been grown directly by CVD [16,17,39], which confirms that these two configurations have the lowest total energy.

On the opposite end of the formation energy, the 2ML arrangements AA and A'B have the highest total energy due to the vertical superposition of the Se atoms (Se₂/Se₂, see Fig. 1) [21,37,38,47]. In moiré heterostructures, the spatial extension of the AA (near 0° twist) or A'B (near 60° twist) domains is usually reduced to a single point if the lattices are allowed to reconstruct [10,12,22,48,49]. However high energy AA stacking have been recently obtained as ribbons in 2ML MoS₂ grown in metal deficient low-temperature CVD conditions [26].

For the remaining AB' stacking configuration, 2ML WSe₂ AB' has been observed by scanning tunneling microscopy in moiré reconstructions [12], but its surface extension is small [10]. Still, the WSe₂ AB' stacking has been recently grown directly by CVD [47] and it is a stable polytype of other TMDs [14] (see Ref. [36] Sec. A).

Out of the six possible atomic arrangements, we only need to distinguish between four candidates in conventional CVD growth conditions: the three expected low energy configurations (2H) AA', (3R) AB, (3R) BA, and the alternative AB' stacking.

## B. Polytypes sorting using PL, Raman, and SHG

All 2ML WSe₂ polytypes display an indirect character with comparable band gap [17,21,39], so that it is expected to observe comparable room-temperature PL responses. Note that this is not the case at lower temperature [39,50], at which the fine details of the distinct 2ML band structures [17] are expressed through optical transitions of specific character [24,51]. In our case, room-temperature PL is not the most informative technique [Fig. 3(d)] and it would be difficult to draw firm conclusion from these relatively broad PL lines.

All Raman spectra show the characteristic line $B'_{2g}$ (309 cm⁻¹) independently of their location, which indicates that they all originate from 2ML regions [52,53], as expected from the optical contrast (Fig. 2). The Raman spectra of the proposed 2H and 3R regions have similar features near $A_{1g}$ and mostly differ in intensity, in line with the existing WSe₂ literature on 2ML (3R) AB and (2H) AA' polytypes [17,39,51,54].

Additional low-frequency Raman data (see Ref. [36] Sec. D), focused on layer shear and breathing modes [55], points towards the same interpretation [24,54,56,57]. To the best of our knowledge, there are limited Raman references on the alternative WSe₂ AB' polytype beside [47] (or Ref. [35] on MoS₂), so we turn to complementary characterization techniques.
<figure><img src="image_7.png" /><figcaption>FIG. 5. DF-TEM 100 imaging of the boundary region between the proposed 3R and 2H area. (a) Large-scale overview. [(b) and (c)] Details of the boundary at selected locations.</figcaption></figure>

Structures with inversion symmetry theoretically show no SHG response, while the inversionless stackings display a non-zero SHG signal [16,24,58,59]. Therefore SHG provides a simple criteria to distinguish between the two noncentrosymmetric (3R) {AB, BA} stackings (with strong SHG response) and the two other centrosymmetric AB' and (2H) AA' stackings (near-zero SHG signal). The features of Figs. 3(e) and 3(f) show a four order magnitude SHG contrast between the inclusion (SHG poor) and the central area (SHG rich) for the same layer thickness (2ML). Data from SHG and Raman let us conclude that the central area is 3R type (AB or BA) and the inclusion is either AA' or AB'.

### C. Polytypes sorting using SAED

To lift the ambiguity between (2H) AA' and AB', we turn to yet another technique to differentiate between these particular 2ML WSe₂ polytypes. In Figs. 4 and 5, we use SAED and DF-TEM to separate the domains based on the intensity ratio $I_{100}/I_{110}$ in SAED or the absolute value of $I_{100}$ in DF-TEM.

A similar SAED analysis was already proposed in Pan et al. [16], with a focus on (2H) AA', (3R) AB and AA polytypes of increasing thickness. It is here extended to all six

<table><caption>TABLE I. Analytical expression of TEM diffracted intensities $I_{HK0}$ in the zero-order Laue zone using the kinematic approximation, with *n* a natural integer. The atomic electron diffusion factors $f_W$ and $f_{Se}$ depend on the chosen HK0. Numerical values are normalized to $I_{110}$ for bilayers.</caption><thead><tr><th rowspan="2">WSe<sub>2</sub></th><th colspan="2">I<sub>HK0</sub></th><th rowspan="2">I<sub>110</sub></th><th rowspan="2">I<sub>100</sub>/I<sub>110</sub></th></tr><tr><th>H - K = 3n</th><th>H - K = 3n ± 1</th></tr></thead><tbody><tr><td>A (1ML)</td><td>(f<sub>W</sub> + 2f<sub>Se</sub>)<sup>2</sup></td><td>(f<sub>W</sub> - f<sub>Se</sub>)<sup>2</sup> + 3f<sub>Se</sub><sup>2</sup></td><td>0.25</td><td>0.90</td></tr><tr><td>AA</td><td>4(f<sub>W</sub> + 2f<sub>Se</sub>)<sup>2</sup></td><td>4((f<sub>W</sub> - f<sub>Se</sub>)<sup>2</sup> + 3f<sub>Se</sub><sup>2</sup>)</td><td>1</td><td>0.90</td></tr><tr><td>AB (3R)</td><td>4(f<sub>W</sub> + 2f<sub>Se</sub>)<sup>2</sup></td><td>(f<sub>W</sub> - f<sub>Se</sub>)<sup>2</sup> + 3f<sub>Se</sub><sup>2</sup></td><td>1</td><td>0.23</td></tr><tr><td>BA (3R)</td><td>4(f<sub>W</sub> + 2f<sub>Se</sub>)<sup>2</sup></td><td>(f<sub>W</sub> - f<sub>Se</sub>)<sup>2</sup> + 3f<sub>Se</sub><sup>2</sup></td><td>1</td><td>0.23</td></tr><tr><td>AA' (2H)</td><td>4(f<sub>W</sub> + 2f<sub>Se</sub>)<sup>2</sup></td><td>(f<sub>W</sub> + 2f<sub>Se</sub>)<sup>2</sup></td><td>1</td><td>0.89</td></tr><tr><td>AB'</td><td>4(f<sub>W</sub> + 2f<sub>Se</sub>)<sup>2</sup></td><td>4(f<sub>W</sub> - f<sub>Se</sub>)<sup>2</sup></td><td>1</td><td>0.15</td></tr><tr><td>A'B</td><td>4(f<sub>W</sub> + 2f<sub>Se</sub>)<sup>2</sup></td><td>(f<sub>W</sub> - 4f<sub>Se</sub>)<sup>2</sup></td><td>1</td><td>0.31</td></tr><tr><td>AA'A (2H)</td><td>9(f<sub>W</sub> + 2f<sub>Se</sub>)<sup>2</sup></td><td>3((f<sub>W</sub> + f<sub>Se</sub>)<sup>2</sup> + 3f<sub>Se</sub><sup>2</sup>)</td><td>2.25</td><td>0.89</td></tr><tr><td>ABC (3R)</td><td>9(f<sub>W</sub> + 2f<sub>Se</sub>)<sup>2</sup></td><td>0</td><td>2.25</td><td>0</td></tr><tr><td>AAA</td><td>9(f<sub>W</sub> + 2f<sub>Se</sub>)<sup>2</sup></td><td>9((f<sub>W</sub> - f<sub>Se</sub>)<sup>2</sup> + 3f<sub>Se</sub><sup>2</sup>)</td><td>2.25</td><td>0.90</td></tr></tbody></table>

high-symmetry 2ML polytypes, with a more analytical approach. We compute a different result than [16] for AA-type stackings (see Ref. [36] Sec. G) but our results are in line for the AA' or AB cases.

SAED was also used by Lan et al. [26] to investigate the AA, AB and BA stackings of ferroelectric (3R) 2ML MoS₂, but with little details on the physical origin of the DF-TEM contrasts and SAED intensities. Our calculations (detailed below) are in line with the SAED in [26].

In the limit of atomically thin samples such as monolayer TMDs, simple kinematical scattering [60] seems the most straightforward theory for the computation of the diffracted intensities. The intensity $I_{HKL}$ of the diffracted beam at position HKL in reciprocal space is simply the squared modulus of the summed atomic contributions from the 2ML unit cell. With $f_i$ the atomic diffusion factor of atom *i* at the position $\mathbf{x}_i$, we find the following (see details in Ref. [36] Sec. G).

$$I_{HKL} = \left\| \sum_i f_i \cdot \exp(\mathbf{HKL} \cdot \mathbf{x}_i) \right\|^2 \quad (1)$$

Kinematical scattering is a very simple approximation and it has been reported that TMDs are not weak phase objects for TEM, not even single monolayer [61,62]. Yet the numerical deviations are about 10% for WSe₂ [62], so that kinematical scattering remains a good starting point to understand how to distinguish TMD bilayer polytypes from SAED or DF-TEM contrast. Here, analytical results for all diffracted intensities $I_{HK0}$ in the zero-order Laue zone are summarized in Table I. Depending on its symmetry and $(H - K)$ being or not a multiple of 3, we distinguish only two cases.

When (H-K) is a multiple of 3, we see that all 2ML high-symmetry polytypes have the exact same $I_{HK0}$. This particular value is the maximum diffracted intensity for which all atomic contributions are positive. In the kinematical approximation, the value of $I_{110}$ scales as $n^2$ with *n* the number of layers.
Nearly all $I_{HK0}$ are different when (H-K) is *not* a multiple of 3. Therefore we may expect to distinguish the polytypes using $I_{100}$. Note that (3R) AB and BA are always indistinguishable in the kinematical approximation and that they accidentally have the same analytical formula of single monolayer A.

Within non-centrosymmetric polytypes, AA stands out as the only 2ML stacking with a high $I_{100}/I_{110}$ ratio. Similarly (2H) AA' is the only 2ML polytype with high $I_{100}/I_{110}$ ratio for the centro-symmetric polytypes, showing that SHG and SAED are very complementary.

The histogram of the SAED intensities in Figs. 4(e) and 4(f) and the corresponding DF-TEM 100 contrast of Figs. 4(h) allows us to assign the inclusion to (2H) AA' or high-energy AA. If we exclude high-energy AA for stability reasons (see Sec. IV A), SAED would be enough to unambiguously determine the nature of 2ML polytype, but recent work points out that the AA stacking may exist experimentally [26]. Therefore SAED must be complemented by other techniques.

Using Raman, we observe that the proposed 2H inclusion investigated by TEM in Fig. 4 has comparable Raman and LF-Raman signatures with that from Fig. 2(c) (see Ref. [36] Sec. D), which itself shows a clear centro-symmetric character by SHG. This centro-symmetric character is not compatible with the AA stacking. This combination of Raman/SHG/SAED finally confirms our base hypothesis so we can conclude that the central area is (3R) AB or BA, while the inclusion is (2H) AA' for the crystal of Fig. 4.

The two domains thus form a lateral 2H|3R structure, which true nature cannot be determined from the outer edge alignment in optical micrograph. It is interesting that our (2H) AA' | (3R) AB WSe₂ bilayer [Fig. 2(c)] is optically similar to the AA | (3R) AB MoS₂ bilayer from Lan *et al.* [26]. However, the present combination of SHG (Fig. 3) and SAED (Fig. 5) clearly disambiguates AA from AA' so that we can establish our particular 2H|3R polytype combination.

### D. Epitaxial origin of 2H|3R structure

A defining characteristic of our 2H|3R region is that both angle-resolved SHG [Fig. 3(f)] and SAED data [Figs. 4(c) and 4(d)] indicate that the 3R central area and the 2H inclusions share the *exact same* crystalline axes (±60° in-plane rotation). As our substrate is amorphous silica, we expect no epitaxial alignment between the underlying SiO₂ and WSe₂. Therefore the only possibility for the 2H inclusions and the 3R central area to precisely align their main crystal axes is to be epitaxially related.

Still, Ref. [36] Sec. F enumerates no less than twelve atomic combinations of 2H|3R domains with matching hexagonal crystal axes. Additional characterization by AFM (Ref. [36] Sec. F) restricts this count to six, using particular surface defects.

During CVD growth, we expect the top layer to grow after the bottom. From Figs. 2(a) and 2(b), we see that a likely scenario consists in the nucleation of second layer, of various stacking order, over an existing monolayer. Figure 6 extends this growth model with the simultaneous nucleation of two 3R and 2H seeds at different locations on the initial WSe₂ monolayer. The subsequent lateral expansion of these two

<figure><img src="image_8.png" /><figcaption>FIG. 6. Growth model of the particular 2H|3R bilayer WSe₂ during our CVD experiment.</figcaption></figure>

non-equivalent seeds will create a 2H|3R boundary in the upper layer only.

Keeping in mind that there are other alternatives, a likely hypothesis consists in a common base monolayer A hosting monolithic 2H AA' and 3R AB (or AC) regions. In this context, the domain wall occurs in the top layer only, between the A' and B (or C) lattices, and it is akin to a twin boundary.

### E. Structure of the 2H|3R domain wall

Even if we cannot determine the full atomic details of the lateral 2H|3R boundary, we are certain of the matching sixfold symmetry between the two regions. The near-90° angle observed at the sawtooth-like boundary in Fig. 4(h) is thus most curious for hexagonal crystals.

We report in Fig. 7(a) the precise orientation of the domain walls with respect to the crystallographic orientation determined by SAED. The red and blue pairs of near orthogonal planes are directly taken from Figs. 5(b) and 5(c). These two sets of planes are related by a 120° rotation, so that we construct a third pair of domain walls (green) by assuming a threefold symmetry (±120°).

We find that these boundaries can be conveniently described as the intersection of (H, K, L) crystallographic planes with (0,0,1) basal plane. Two sets of planes are necessary: the {3,1,0} and {-1, -3, 0} plane families, with each family consisting in three planes related by the threefold symmetry axis along *c*.

We see that the boundaries are not positioned along the usual zigzag or armchair directions. Instead, they align between the closest armchair direction and a single type of zigzag, exclusively metal (M) or chalcogen (X) zigzag. Given atomically-resolved data obtained by others on monolayer
<figure><img src="image_9.png" /><figcaption>FIG. 7. (a) Alignments of the experimentally derived 2H|3R boundary with respect to crystal structure of the upper 2H layer. (b) Details of armchair and zigzag boundaries in the upper layer depending on the 2H|3R configurations: AA' | AB or AA' | AC. (c) Details of selected boundaries in the AA' | AC configuration, off-axis from the X-zigzag direction. The experimental angles match the Θ(3, 1) boundary.</figcaption></figure>

TMD twin boundaries [63,64], we choose a X-zigzag as the reference in Fig. 7(a).

For TMD monolayer [65], the X- and M-zigzag walls between twinned domains are expected to hold a different atomic structure and total energy. We retrieve this diversity in Fig. 7(b) in our 2H|3R bilayer. Along the twin boundary in upper layer, we consider single (cyan) and double (yellow) tetragonal defects [65], along with octahedral rings (grey), guided by experimental observations from literature [63].

The armchair boundary may be constructed using a particular (1,1) repeat alternating an octahedral ring and a single tetragonal defect. Other combinations are possible but this form is closer to experiments (see later). Note that the armchair boundary structure is independent of the 2H|3R configurations (AA' | AB or AA' | AC).

Conversely, the structure of the zigzag boundaries depends both on the AA' | AB or AA' | AC configurations and the zigzag type (X- or M-). For a given 2H|3R configuration, only one zigzag can be constructed using a continuous string of single tetragonal defects. This string of tetragonal defects closes exclusively on M atoms in the AA' | AB configuration and exclusively on X atoms for AA' | AC.

Experiments by others [61,63,64] reveal that boundaries in twinned TMD monolayers host a significant fraction of single tetragonal defects which run preferentially through X atoms. Applied to our 2H|3R bilayers, the only approaching configuration is the X-zigzag AA' | AC configuration [red rectangle Fig. 7(b)].

In Fig. 7(c), we detail selected off-axis boundaries from this particular configuration (X-zigzag, AA' | AC). We describe the boundary using the Θ(*M*, *N*) notation introduced by Alem *et al.* [66], where *M* and *N* are respectively the number of single tetragonal and octagonal defects in the repeating unit along the boundary. The armchair boundary can be described as Θ(1, 1). Any addition of tetragonal defects in the repeat, Θ(*M*, 1) with *M* > 1, pushes the boundary closer to the X-zigzag Θ(1, 0). For symmetry reason, there are always two equivalent boundaries which run at a given off-axis angle *ζ* from the X zigzag.

Our crystallographic description [Fig. 7(a)], based on the {3,1,0} and {-1, -3, 0} plane families, matches the Θ(3, 1) configuration described by Alem *et al.* [66] [Fig. 7(c)]. We see in Table II the simple connection between these two notations for any arbitrary Θ(*M*, 1).

In this framework, Warner *et al.* [63] describes a complex twin boundary in a MoS₂ monolayer, which mixes Θ(2, 1), Θ(3, 1) and Θ(4, 1) characters. Alternatively the twin boundaries observed by Hone *et al.* [61] are only of the Θ(2, 1) type, with both positive and negative offsets to X zigzag. Here, the 2H|3R twin boundary running in the upper layer is of a single type, comparable to Hone *et al.* [61], but it belongs to Θ(3, 1) exclusively. We observe Θ(3, 1) boundaries at positive and negative offsets from several X-zigzag directions, so that the overall domain wall appears to break into a succession of near orthogonal segments. The existence of such “sawtooth” boundary over several tens of nanometer points toward a stabilization of the particular Θ(3, 1) configuration during growth, possibly favored by our experimental conditions.

In conclusion, we report the CVD growth of bilayer WSe₂ crystals on SiO₂/Si substrate using the salt-assisted method. Some of the 2ML crystals have a mixed-phase structure with a main 3R region and some 2H inclusions. The exact nature of the WSe₂ polytype, which cannot be guessed from optical micrograph, is established by a combination of Raman, SHG, AFM and TEM-SAED. The specifics of SAED are detailed for all 2ML high-symmetry WSe₂ polytypes, calculated in the simple kinematical framework. Dark-field TEM 100 imaging reveals a peculiar sawtooth structure at the 2H|3R boundary wall, which shares common crystallographic features with
<table><caption>TABLE II. $Θ(M, N)$ boundary and their equivalent HKL crystallographic orientations. $ζ$ is the angle from the closest X-zigzag direction. $ξ$ is the angle between boundaries [see Fig. 7(a)]. $Θ(3, 1)$ matches our experimental observations.</caption><thead><tr><th></th><th>Θ(1, 1) armchair</th><th>Θ(2, 1)</th><th>Θ(3, 1)</th><th>Θ(4, 1)</th><th>Θ(M, 1)</th><th>Θ(1, 0) X-zigzag</th></tr></thead><tbody><tr><td>ζ</td><td>±30°</td><td>±19.1°</td><td>±13.9°</td><td>±10.9°</td><td></td><td>0°</td></tr><tr><td>ξ</td><td>120°</td><td>98.2°</td><td>87.8°</td><td>81.8°</td><td></td><td>60°</td></tr><tr><td>HKL</td><td>{1,1,0}</td><td>{2,1,0}</td><td>{3,1,0}</td><td>{4,1,0}</td><td>{M, 1, 0}</td><td>{1,0,0}</td></tr><tr><td>sets</td><td>{-1, -1, 0}</td><td>{-1, -2, 0}</td><td>{-1, -3, 0}</td><td>{-1, 4, 0}</td><td>{-1, M, 0}</td><td></td></tr></tbody></table>

other experimental twin boundaries observed in monolayer TMDs.

## V. METHODS

**CVD growth.** $WSe_2$ crystals are grown by chemical vapor deposition (CVD) in a 4" customized Nabertherm (RST 120) horizontal reactor in the hot-wall configuration. Source materials are elemental Se (Neyco 99.9%), heated to 330 °C, and tungsten oxide $H_2WO_4$ (Acros Organics, 99%), mixed with KCl (Alfa Aeasar, 99.9%) and heated to 900 °C. The halide salt is used as promoter for the growth reaction [67,68]. The tungsten precursor is positioned close to the $SiO_2$/Si substrate (283 nm thick $SiO_2$ on Si(100), Nova Wafers). Ar (60 sccm) and $H_2$ (40 sccm) are used as carrier gas during 30 minutes growth at the constant pressure of 2.5 mbar. The whole process, considering temperature ramps for heating and cooling, takes 4 hours.

**Transfer.** $WSe_2$ crystals are transferred from the $SiO_2$/Si substrate to the TEM grid thanks to a polymer-assisted dry transfer technique [69,70]. The crystal on its original substrate is first immersed for 13 minutes in liquid $N_2$ to favor its detachment [71]. A pickup is performed at 35 °C with a polydimethylsiloxane (PDMS) stamp covered by a polypropylene carbonate (PPC) thin foil. The $WSe_2$ is then transferred on the host substrate by heating (90 °C). The remaining PPC is removed by thermal evaporation in vacuum.

**TEM.** Transmission electron microscopy (TEM) is performed using a FEI ThermoFisher TEM/STEM Titan Themis 200 microscope operating at 200 keV. Diffraction patterns are measured by selective area electron diffraction (SAED) with an aperture of 200 nm. Dark-field TEM imaging is used to distinguish the 2H and 3R crystal phases by filtering on the 100 and 110 diffraction peaks respectively, in addition to high-angle annular dark field (HAADF).

**Raman and photoluminescence.** Micro-Raman and microphotoluminescence are performed at room temperature using a commercial Horiba Labram Evolution spectrometer (532 nm laser excitation). The laser width on the sample is about 0.5 µm diameter.

**SHG.** Second harmonic generation is performed on a comparable platform at room temperature using a 1040 nm laser. The angular resolution of the polarization-resolved SHG measurements is 2°.

## ACKNOWLEDGMENTS

We acknowledge the financial support by Optitaste (ANR-21-CE24-0002), DEEP2D (ANR-22-CE09-0013), 2D-on-Demand (ANR-20-CE09-0026), MixDferro (ANR-21-CE09-0029), and FastNano (ANR-22-PEXD-0006), as well as the French technological network RENATECH. The authors acknowledge Aurélien Thieffry for his help in setting up the SHG measurements, performed at the HORIBA platform.

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