Reconfiguring nucleation for CVD growth of twisted bilayer MoS2 with a wide range of twist angles

Twisted bilayer (TB) transition metal dichalcogenides (TMDCs) beyond TB-graphene are considered an ideal platform for investigating condensed matter physics, due to the moiré superlattices-related peculiar band structures and distinct electronic properties. The growth of large-area and high-quality TB-TMDCs with wide twist angles would be significant for exploring twist angle-dependent physics and applications, but remains challenging to implement. Here, we propose a reconfiguring nucleation chemical vapor deposition (CVD) strategy for directly synthesizing TB-MoS2 with twist angles from 0° to 120°. The twist angles-dependent Moiré periodicity can be clearly observed, and the interlayer coupling shows a strong relationship to the twist angles. Moreover, the yield of TB-MoS2 in bilayer MoS2 and density of TB-MoS2 are significantly improved to 17.2% and 28.9 pieces/mm2 by tailoring gas flow rate and molar ratio of NaCl to MoO3. The proposed reconfiguring nucleation approach opens an avenue for the precise growth of TB-TMDCs for both fundamental research and practical applications.

For the triangle with irregular edges, the triangle can be replaced by the external inscribed regular triangle for the twist angle measurement of TB-MoS2 (Supplementary Fig. 1c).The average of six twist angles (with three out θ and three in θ ) is considered to be the twist angle of TB-MoS2.
Here, a TB-MoS2 sample was used to calculate the twisted angle by OM.As shown in Supplementary Fig. 1b, the twist angle can be measured to be 22.0°, 21.5°, and 22.4°.The average value of 22.0° with a standard deviation of about 0.35° was used as the twist angle (Supplementary Fig. 1d).Actually, the error is inevitable when measuring the orientations of each edge (Supplementary Fig. 1f) due to the limited resolution (the minimum resolution σ for an optical microscope is around 200 nm, which responds to the size of fuzzy region) of OM images.The errors ( OM ϕ ) of each edge can be determined as: OM = arctan L σ ϕ (1)  where L is the length of the triangle, σ is the minimum resolution of OM.Here, we can notice that the OM ϕ is dependent on the length of the triangle, thus we use the average length of TB- MoS2 to calculate the error.The average L is calculated to be 28.56 μm (Supplementary Fig. 20) and the error ( OM ϕ ) is 0.4°.Due to the twist angle (θ ) being determined by measuring two edges of the monolayer and bilayer, the OM based error of the twist angle should be twice the value of the error ( OM As shown in Supplementary Fig. 1, the standard deviation is about 0.35°, smaller than the Based on the measurement, the direction of two opposite diffraction points of each MoS2 layer is much higher than the OM method as discussed in Supplementary Note 1. Taking a SAED pattern of 21.9°-TB-MoS2 as an example (as shown Supplementary Fig. 10a), the weight lines connecting the opposite diffraction points intersect with each other at a specific twist angle.
The error ( SAED ϕ ) based on the SAED pattern can be determined by the full width at half maximum (FWHM) of the blurred diffraction points and the distance between each opposite bright point in a single SAED pattern (Supplementary Fig. 10b).

SAED = arctan
where i is the diffraction order ( 1, 2,3, 4... i = ), i D is the distance from the two opposite bright points under the diffraction order of i .In order to calculate the error based on the SAED method, we measure FWHMs of four groups of the position dependent diffraction intensity plot (1 st , 2 nd , 3 rd , and 5 th , Supplementary Fig. 10c-f) with the average FWHMs of 0.0049 nm -1 .
While the distance from the two opposite bright point with the diffraction order i can be measured to be ( 1 D = 7.356 nm -1 , 2 D =12.542 nm -1 , 3 D =14.666 nm -1 , and 5 D =21.986 nm -1 ), indicating that the error will be smaller if higher order diffraction points are selected.Thus, the error of twist angle ( SAED Error θ − ) should be the twice of the value of SAEDi ϕ due to the measurement for two times.In our work, the 2 nd diffraction point is selected, and the SAED Error θ − is calculated to be 0.44°, which is more accurate than the OM Error θ − of 0.8°.
Supplementary Note 4. The density and yield calculation of TB-MoS2.
The OM under the 20X objective was selected due to the TB-MoS2 can be easily identified under the 20X objective.The number of TB-MoS2 and bilayer MoS2 based on the OM under the 20X objective was calculated.The density ( TB D ) and yield ( TB Y ) can be calculated by the total number of TB-MoS2 samples ( TB N ), the total number of bilayer MoS2 samples ( BL N ), and the total area ( S ). 100% To make the results more accurate, five samples were adopted under the same growth conditions.The average density ( D ), standard deviation ( D δ , density error), yield ( Y ), and corresponding standard deviation ( Y δ , yield error)were canulated by the following equations.
In our previous works, we have discussed the effects of salt on the CVD growth of TMDCs via thermodynamics and kinetics 1,2 .In terms of affecting thermodynamics, NaCl can be reacted From this equation, we can find that the partial pressure i P is the dominate factor for the nucleation rate.As we mentioned before 1 , the vapor pressure of NaCl is much higher than that of MoO3 precursors.Besides, the formation of MoOxCly induces a high i P due to the high volatility nature of MoOxCly.Therefore, the NaCl will result in a higher nucleation rate.The vapor pressure of NaCl and MoO3 can be found to be around ~10 Pa and ~10 -9 Pa under 780 °201 C (1053 K), respectively.Considering that the solubility of metal oxide is at the order of ppm, the metal oxide and salt will dramatically increase the vapor pressure of metal precursors of a few orders.
example, large-area monolayer MoS2 is synthesized under a reaction temperature of 760 °C.
Temperature is the key to affect the thermodynamics and dynamics of the reaction system.Here, we have carried out the simulation on the temperature in the tube, as shown in Supplementary Fig. 27c-d.As noticed, due to the effect of the gas flow rate, the temperature shows an uneven distribution.However, with the introduction of the confined space, there is a uniform temperature distribution near the SiO2/Si substrate.The inner tube serves as a "heat insulation layer" to prevent the heat diffusion.Thus, we believe that the confined space plays the key role to stabilize the substrate temperature.
In most cases, laminar gas flow is desirable, but some local areas of turbulent flow may exist.
Generally, conventional CVD that uses tubular horizontal reactors possesses laminar flow under any conditions.A high pressure or flow rate is required to produce turbulent flow in the reactor, which exceeds the flow rate used in CVD.To induce turbulent flow, some form of physical disturbance of the gas flow is needed in the CVD setup.In this work, we introduce the confined space to CVD to induce the turbulent flow in the inner tube.This design creates a circumfluent flow, wherein the gas flows around the chamber and backflows toward the substrate.This significantly reduces the gas flow velocity on the substrate to create an unsteady gas flow.
It is reported that the turbulent flow indeed causes the different growth conditions in CVD process.The turbulent flow has been adopted for the synthesis of 2D materials, such as graphene and TMDCs, which effectively changes the morphology of the products [8][9][10] .The supposed to enhance the MoS2 twisted nucleation in the carrier gas because backflows increase the collision rate of molecules to molecules and molecules to substrate by producing enough energy for the twist nucleation, resulting in an alteration of the synthesis conditions.We believe that the introduced backflow gas through the inner tube drives the entire inner tube out of equilibrium to reduce the chance to form more stable 0°-and 60°-TB-MoS2, which is expected to be the most important reason for the synthesis of TB-MoS2.( ) ( ) a-f The typical OM synthesized under different gas flow rates without confined space.g-l The typical OM synthesized under different gas flow rates with confined space.Scale bars: 100 μm for the OM under 20X objective, 10 μm for the small area under 50X objective.The TB-MoS2 was synthesized with fixed NaCl to MoO3 of 20.

with
MoO3 for the synthesis of MoOxCly in first step.Notably, the degrees of freedom changed by reacting with MoOxCly results in the change of entropy.Compared with the CVD system without NaCl, the participation of MoOxCly may affect the Gibbs free energy ( G H T S ∆ = ∆ − ∆ ) by neglecting the change of pressure and volume.For the kinetics process, NaCl will affect the nucleation process and dominate the geometries of MoS2 layers.The nucleation rate with and without NaCl can be roughly written as:

1 3hD symmetry of monolayer MoS2 and the 3 3dD
area 30.0° and 90.0°-TB-MoS2 with different zigzag-Mo and zigzag-S edge of top and bottom layer, respectively.As we know, Raman and PL are micro-area analysis methods, wherein only an area of hundreds of nanometers can be detected under a 532 nm laser.Due to the symmetry of bilayer MoS2, the twist angle is optimized from 0°~120° to 0°~60°.As shown in Supplementary Fig.13a, the triangle MoS2 shows a three-fold symmetry both in macroscopic OM and hundreds of nanometers area.Three-fold symmetry can also be observed for the macroscopic OM of 30° and 90°-TB-MoS2 (Supplementary Fig.13b).It should be noted that the triangle morphology might own the zigzag-S or zigzag-Mo edges, which means eight different combinations (Supplementary Fig.13c) can be obtained with 30° and 90° twist angle and different zigzag-Mo and zigzag-S edge in bottom and top-layer, respectively.Eight combinations can be classified into two groups with different atom structures.Besides, the two groups of atom structure show mirror symmetry, which indicates that all the 30° and 90°-TB-MoS2 show the same atom structure or mirror symmetry.Although only 30° and 90°-TB-MoS2 were discussed, the mirror symmetry can be observed in all the micro-areas of the TB-MoS2 samples due to the crystal symmetry.Therefore, considering the Raman and PL were measured under the micro-area, the twist angle ( Raman-PL θ ) under the Raman and PL can be reduced to 0°~60° based on the following equations by the twist angle ( OM θ ) measured from OM.

600 sccm for 10 min before heating, 50 sccm Ar for ramping to 780 °C at a rate of 30 °C/min, growing for 5 minutes
The proportion of bilayer TMDCs in all obtained TMDCs domains.