Spectroscopic Analysis on Different Stacking Configurations of Multilayered MoSe2

Transition metal dichalcogenides (TMDs) are drawing significant attention due to their intriguing photoelectric properties, and these interesting properties are closely related to the number of layers. Obtaining layer-controlled and high-quality TMD is still a challenge. In this context, we use the salt-assisted chemical vapor deposition to grow multilayered MoSe2 flake and characterize it by Raman spectroscopy, second harmonic generation, and photon luminescence. Spectroscopic analysis is an effective way to characterize the stacking order and optoelectronic properties of two-dimensional materials. Notably, the corresponding mapping reflects the film quality and homogeneity. We found that the grown continuous monolayer, bilayer, and trilayer of MoSe2 sheets with different stacking orders exhibit distinctive features. For bilayer MoSe2, the most stable stacking configurations are the AA’ and AB order. And the uniformity of the spectroscopy maps demonstrates the high quality of the stacked MoSe2 sheets.


Introduction
Molybdenum Diselenide (MoSe 2 ) is a member of the transition metal dichalcogenides (TMD).Compared with the more widely studied MoS 2 , MoSe 2 has received increasing attentions into the preparations and applications due to a number of highly interesting physical properties, such as the narrow bandgap, unique optoelectronics, etc. [1,2].And the various stacking orders further enrich the properties of multilayered MX 2 (M = Mo, W, and X = S, Se) [3,4].Bulk like 2H symmetry and 3R stacking are confirmed to the two stable configurations of bilayer MX 2 [5][6][7][8].In these two configurations, the corresponding electronic, optical, and phonon scattering are significantly modified [4,9].In the lowfrequency Raman spectroscopy, one shear and two breathing vibration modes are detected on 2H and 3R MoSe 2 , and these vibration modes are highly sensitive to the layer numbers and the symmetry [6,[10][11][12][13][14]. From bilayer to trilayer MoSe 2 , the characteristic shear mode of 19.2 cm −1 disappears and two new modes around 13 cm −1 and 24 cm −1 appear, which is attributed to different symmetry as well as Raman tensors.By changing the twisted angle from 60 • to 59.6 • of bilayer MoSe 2 , the breathing B1 mode is observed; when further twisting the angle to 55.3 • , the intensity of the prominent shear mode diminishes to zero instead of a strong B2 mode [13].The symmetry of different stacking configurations can also be demonstrated by the Second harmonic generation (SHG).SHG is a powerful method to characterize the centrosymmetry and inversion symmetry.When the symmetry is broken, a strong SHG signal will be acquired.2H-stacked MoSe 2 is with inversion symmetry without SHG response, but 3R-stacked MoSe 2 is non-centrosymmetric with strong SHG feedback [5,15,16].
In this work, salt-assisted chemical vapor deposition (CVD) is applied to grow the multilayered MoSe 2 .Through controlling the preparation conditions, the thickness (layers) and the stacking order of MoSe 2 are deliberately tuned.We have successfully grown several multilayered MoSe 2 with completely opposite stacking patterns.A series of characterizations includes optical microscopy, low-frequency Raman spectroscopy, SHG, and photoluminescence (PL); in addition, corresponding mappings are performed to investigate their stacking order and properties.Density function theory is carried out to verify the stability of the stack order.Low-frequency Raman spectroscopy is a fingerprint of MX 2 stacking order, and the SHG mapping reflects the uniformity of the sheets.

Salt-Assisted CVD Synthesis of MoSe 2
The stacked MoSe 2 sheets were grown by salt-assisted CVD in a two-zone furnace with a 2-inch diameter horizontal quartz tube (OTF-1200X-III-C, Hefei kejing materials technology Co., Ltd., Hefei, China) (Figure 1a).Before putting the 285 nm SiO 2 /Si substrate into the tube, it was cleaned with deionized water, acetone, and isopropyl alcohol consecutively and then dried by N 2 .Two corundum boats filled with excess Se powder (300 mg) and MoO 3 /NaCl mixture (5 mg, with a ratio of 6:1) were placed following the gas stream at the low-temperature and high-temperature zones, respectively.The SiO 2 /Si substrate was directly put above the boat of the MoO 3 /NaCl mixture upside down.During the growth process, a mixed Ar/H 2 carrier with 150 sccm was introduced, and 5% of the H 2 was supposed to create a reducing atmosphere to promote the reaction.The pressure was 0.9 atmospheres.In the high-temperature zone with the MoO 3 /NaCl mixture, it was heated from 25 • C to 600 • C with a heating rate of 30 • C/min for 2 min, and then heated to 760 • C at 20 • C/min for 10 min.For the low-temperature zone, it was heated from 25 • C to 350 • C with 10 • C/min and held over 10 min for a sufficient reaction.After the reaction, both temperature zones were naturally cooled down.
In this work, salt-assisted chemical vapor deposition (CVD) is applied to grow the multilayered MoSe2.Through controlling the preparation conditions, the thickness (layers) and the stacking order of MoSe2 are deliberately tuned.We have successfully grown several multilayered MoSe2 with completely opposite stacking patterns.A series of characterizations includes optical microscopy, low-frequency Raman spectroscopy, SHG, and photoluminescence (PL); in addition, corresponding mappings are performed to investigate their stacking order and properties.Density function theory is carried out to verify the stability of the stack order.Low-frequency Raman spectroscopy is a fingerprint of MX2 stacking order, and the SHG mapping reflects the uniformity of the sheets.

Salt-Assisted CVD Synthesis of MoSe2
The stacked MoSe2 sheets were grown by salt-assisted CVD in a two-zone furnace with a 2-inch diameter horizontal quartz tube (OTF-1200X-III-C, Hefei kejing materials technology co., LTD, Hefei, China) (Figure 1a).Before putting the 285 nm SiO2/Si substrate into the tube, it was cleaned with deionized water, acetone, and isopropyl alcohol consecutively and then dried by N2.Two corundum boats filled with excess Se powder (300 mg) and MoO3/NaCl mixture (5 mg, with a ratio of 6:1) were placed following the gas stream at the low-temperature and high-temperature zones, respectively.The SiO2/Si substrate was directly put above the boat of the MoO3/NaCl mixture upside down.During the growth process, a mixed Ar/H2 carrier with 150 sccm was introduced, and 5% of the H2 was supposed to create a reducing atmosphere to promote the reaction.The pressure was 0.9 atmospheres.In the high-temperature zone with the MoO3/NaCl mixture, it was heated from 25 °C to 600 °C with a heating rate of 30 °C/min for 2 min, and then heated to 760 °C at 20 °C/min for 10 min.For the low-temperature zone, it was heated from 25 °C to 350 °C with 10 °C/min and held over 10 min for a sufficient reaction.After the reaction, both temperature zones were naturally cooled down.

Characterizations of Different Stacked MoSe 2 Sheets
The geometry of different stacked MoSe 2 sheets was identified by an optical microscope (Nikon Ci-Pol, Minato City, Japan).All optical images were captured from the Raman instrument retention.The structure and optoelectronic properties of different stacked MoSe 2 were characterized by Raman spectroscopy and photoluminescence spectroscopy.The measuring instrument is alpha 300 Raman produced by WITEC (Ulm, Germany).For all Raman and PL measurements, a microscope lens of 100× and a laser wavelength of 532 nm were used.In order to prevent thermal effects, the laser power of 1 mW with a spot diameter of 1 µm was chosen to avoid damage to the sample.The grating of 1800 g/mm BLZ = 500 nm was selected for the Raman measurements, and 150 g/mm BLZ = 500 nm was grated for the PL measurements.The SHG measurement was performed with a laser wavelength of 1064 nm and the grating of 150 g/mm BLZ = 500 nm.

DFT Calculation of Bilayer MoSe 2
We performed first-principles calculations with the software package Vienna Ab initio Simulation Package (VASP4.6)[17] based on density functional theory.The Perdew-Burke-Ernzerhof (PBE) function was selected as the exchange-correlation function [18].To avoid mirror interaction, a 20 Å vacuum layer was adopted.The convergence thresholds for energy and force were set at less than 10 −5 eV and 0.01 eV/Å, respectively.To account for the vdW force between layers of the bilayer structure, we performed the vdW calibration of DFT-D 3 [19].The Brillouin zone (BZ) integration was sampled using a 19 × 19 × 1 kpoint grid.

Results and Discussion
Figure 1a is the schematic diagram of the salt-assisted CVD setup to grow the MoSe 2 sheets with different stacking orders.The details of the growth procedure are described in the Section 2. As already claimed in the previous studies [20,21], adding salts (such as NaCl, KCl, etc.) as promoters in the evaporated oxide powder can effectively reduce the melting point of the reactants, so as to promote the formation of intermediates and increase the reaction speed.Here, NaCl is mixed into the MoO 3 precursor.The optical microscopy image of the product is shown in Figure 1b.Few-layer MoSe 2 sheets are formed by stacking different orientations of typical triangular shapes.The obvious color contrast clearly distinguishes the monolayer-, bilayer-, and trilayer-stacked MoSe 2 , because color variation is a common way to identify the thickness/layers of two-dimensional materials [22].The deepening color is supposed to concomitantly increase the layer number of MoSe 2 .
We also perform Raman spectroscopy to characterize the structural properties of the stacked MoSe 2 sheet.Raman spectroscopy has proven to be a powerful tool for studying the optical response of two-dimensional van der Waals materials as well as the differentiation of layer numbers [23].As shown in Figure 1c, at the high-frequency mode, MoSe 2 mainly has two characteristic Raman modes, out of plane A 1g (240.5 cm −1 ) and in-plane E 1 2g (285.5 cm −1 ).The intensity of these two mode peaks is independent of the MoSe 2 thickness.However, the frequency difference ∆ between A 1g and E 1 2g mode decreases gradually from 47.5 cm −1 of monolayer to 45.6 cm −1 of bilayer and 43.1 cm −1 of trilayer MoSe 2 .This trend is consistent with the previous reports and is ascribed to the strong interface coupling [5].So, the frequency difference is commonly used to define the layer number of TMDs.While at the low-frequency mode, significant changes are observed.For monolayer MoSe 2 , no obvious peak is detected at the low-frequency region.However, a strong peak at 19.2 cm −1 appears on the bilayer MoSe 2 , and this peak further splits into two lessened peaks (at 13.4 cm −1 and 23.2 cm −1 ) on the trilayer MoSe 2 .This indicates that low-frequency Raman spectroscopy is highly sensitive to the sheet layers.Puretzky and Lu et al. attribute the 19.2 cm −1 peak to the shear mode of the bilayer MoSe 2 and explain the split of the shear mode in trilayer MoSe 2 to the interlayer bond polarizability mode [6,11,24].This phenomenon is also observed in the other TMDs, such as MoS 2 and WSe 2 , and is strongly dependent on the stacking orders as well [24,25].We will discuss the stacking configuration below.The intensity and symmetry of the Raman peaks in high/low frequency shows that our MoSe 2 sheet is relatively uniform.
To obtain detailed insights into the stacking order of the MoSe 2 sheets, we studied several bilayer MoSe 2 with completely opposite orientations on the continuous film, as shown in Figure 2a.The 1L of the continuous film is marked by I, and three different orientations of the second triangular MoSe 2 layer are marked by II, III, and IV.Region II and IV have the same orientation and are antiparallel to region III. Figure 2b is the corresponding Raman spectroscopy.On the high-frequency Raman side, the featured vibration modes (240.5 cm −1 ) with a comparable intensity of MoSe 2 are observed in these four regions, and it is similar to the one discussed above.On the low-frequency Raman side, monolayer MoSe 2 in the region I has no signal at all.Bilayer MoSe 2 in regions II, III, and IV all exhibit a shear mode of 19.2 cm −1 , but the intensities of regions II and IV are stronger than region III.The low-frequency mode is strongly dependent on the stack order and layer number of TMDs and is significantly influenced by interface coupling, symmetry, and so on [6,11,24].Therefore, we further conducted the nonlinear optics SHG measurements to investigate the stack order of the bilayer, as shown in Figure 2c.SHG signals are highly affected by the centrosymmetry and inversion symmetry of materials [26].Monolayer MoSe 2 belongs to the non-centrosymmetric D 1 3h group, so region I presents a strong SHG signal [5].In region III, the SHG signal is strengthened.We speculate the second layer of MoSe 2 possesses the same orientation as the first layer, so the accumulation of the noncentrosymmetry enhances the SHG intensity.On the contrary, the SHG signal in regions II and IV is highly suppressed.The stack order of these bilayers is supposed to be antiparallel and inversion symmetry.This phenomenon is also reported in the literature.The bilayer without twist (θ = 0 • ) exhibits a strong SHG signal, while the SHG disappears both in twisted (θ = 60 • ) bilayer MoSe 2 and MoS 2 [5,[26][27][28].We propose the bilayer MoSe 2 in region III and regions II, IV have a completely different stacking pattern with the twist angle of θ = 0 • and θ = 60 • , respectively.However, the twist angle has minor effects on the PL spectroscopy of this bilayer MoSe 2 , which displays a similarly weaker intensity compared to the monolayer, as shown in Figure 2d.The monolayer in region I has a main peak at 815 nm converting to a band gap of 1.52 eV.The PL intensity of stacked bilayer MoSe 2 in three different regions is significantly suppressed due to the indirect-to-direct bandgap transition [5].DFT calculations are carried out to further confirm the stability of different stacking orders of bilayer MoSe 2 .According to the previous studies [4,8], five typical stacking configurations (AA, AA', A'B, AB', and AB) are calculated.We found that the AA' configuration has the lowest total energy and AB configuration with 2.9 meV/formula unit higher.This result agrees well with ref. [8].The crystal structure of AA' and AB configurations are displayed in Figure 2e,f.In the AA' configuration, the Mo (Se) atom is over the Se (Mo) atom with a twisted angle of 60 • , while in AB configuration with θ = 0 • , Mo over Se and the other Mo and Se are over the center of the hexagons.To sum up, bilayer MoSe 2 in region III is stacked by AB configuration, while in regions II and IV, they are stacked by AA' configuration.
In order to investigate the natural properties of different stacking MoSe 2 , we perform the Raman, PL, and SHG mappings on a separate AA' and AB bilayer.Figure 3a,e are the optical microscopy images of AA'-and AB-stacked MoSe 2 .As mentioned above, lowfrequency Raman spectroscopy is an efficient method to characterize the stacking order of the TMDs.A strong shear mode of AA'-stacked MoSe 2 is detected at 19.2 cm −1 (Figure 2c of region III), so a Raman mapping with a low wavenumber of 19.2 cm −1 is acquired, as shown in Figure 3b of the AA' stack and Figure 3f of the AB stack.The AA'-stacked MoSe 2 shows an exceptionally strong and uniform Raman response, while AB-stacked MoSe 2 displays only a visible contour signal.This evident distinction is ascribed to the change of symmetry and demonstrated by the DFT calculations [6].However, there is a strong Raman response in the middle of AB-stacked MoSe 2 .This may be explained by the non-uniformity of the MoSe 2 sheet or defects.Minor deviation of the orientation of bilayer MoSe 2 leads to great change in the low-frequency vibration mode.Puretzky et al. show that there is a small change of the twisted angle from 60 • to 55.3 • , the shear mode of bilayer MoSe 2 has completely disappeared, and the two breathing modes are also highly influenced by the twisted angles [13].In order to investigate the natural properties of different stacking MoSe2, we perform the Raman, PL, and SHG mappings on a separate AA' and AB bilayer.Figure 3a,e are the optical microscopy images of AA'-and AB-stacked MoSe2.As mentioned above, low-frequency Raman spectroscopy is an efficient method to characterize the stacking order of the TMDs.A strong shear mode of AA'-stacked MoSe2 is detected at 19.2 cm −1 (Figure 2c of region III), so a Raman mapping with a low wavenumber of 19.2 cm −1 is acquired, as shown in Figure 3b of the AA' stack and Figure 3f of the AB stack.The AA'-stacked MoSe2 shows an exceptionally strong and uniform Raman response, while AB-stacked MoSe2 displays only a visible contour signal.This evident distinction is ascribed to the change of symmetry and demonstrated by the DFT calculations [6].However, there is a strong Raman response in the middle of AB-stacked MoSe2.This may be explained by the non-uniformity of the MoSe2 sheet or defects.Minor deviation of the orientation of bilayer MoSe2 leads to great change in the low-frequency vibration mode.Puretzky et al. show that there is a small change of the twisted angle from 60° to 55.3°, the shear mode of bilayer MoSe2 has completely disappeared, and the two breathing modes are also highly influenced by the twisted angles [13].In the SHG mapping, for the AA' stack, two layers of MoSe 2 with a twisted angle of 60 • belong to an inversion symmetry, so a suppressed SHG signal is observed in Figure 3c.For the AB stack, compared to the monolayer MoSe 2 , a stronger SHG signal is captured due to the enhanced non-centrosymmetry.This discovery of non-uniformity is consistent with the low-frequency Raman mapping of the AB stack.In the PL mapping, as shown in Figure 3d-h, both the AA' and AB stacks exhibit weaker and even PL properties than the monolayer ones, without the influence of a grain boundary or twisted angle.From these mapping results, the stacking order, uniformity, and quality of the MoSe 2 layer are revealed.
By further optimizing the growth parameters, we also successfully obtain the perfect trilayer MoSe 2 with AA'A stack and AA'B stack, respectively, as shown in Figure 4a-e.This complies with the fact that AA' stack is the most stable configuration.The corresponding Raman mapping is shown in Figure 4b,f.it can be seen that the second layer has strong vibration at 19.2 cm −1 in both the AA'A and AA'B stacks, while the intensity is diminished on the third layer.This might be due to the split of the vibration mode into 13.4 cm −1 and 23.2 cm −1 of the trilayer MoSe 2 , as we mentioned in Figure 1c.Two vibration modes of 13.7 cm −1 and 23.1 cm −1 are reported in trilayer MoSe 2 [6,11].Figure 4c,g shows the SHG mappings.As discussed above, the AA' stack possesses a suppressed SHG due to the forming of inversion symmetry.But a similar result is not expected in the AA'A stack.The strong SHG of the AA'A stack might have originated from the interaction between the first and third layers.Shinde et al. present a similar result in MoS 2 [27].For the PL mapping shown in Figure 4d,h, the intensity is highly affected by the thickness due to the transition of the direct-indirect band gap.In the Raman and SHG mappings, both the AA'A and AA'B stacks appear with shape edges; this indicates a uniform high quality of our trilayer MoSe 2 .But in the AA'B stack, the PL vanishes at three angles.This may need further investigation.In the SHG mapping, for the AA' stack, two layers of MoSe2 with a twisted angle of 60° belong to an inversion symmetry, so a suppressed SHG signal is observed in Figure 3c.For the AB stack, compared to the monolayer MoSe2, a stronger SHG signal is captured due to the enhanced non-centrosymmetry.This discovery of non-uniformity is consistent with the low-frequency Raman mapping of the AB stack.In the PL mapping, as shown in Figure 3d-h, both the AA' and AB stacks exhibit weaker and even PL properties than the monolayer ones, without the influence of a grain boundary or twisted angle.From these mapping results, the stacking order, uniformity, and quality of the MoSe2 layer are revealed.
By further optimizing the growth parameters, we also successfully obtain the perfect trilayer MoSe2 with AA'A stack and AA'B stack, respectively, as shown in Figure 4a-e.This complies with the fact that AA' stack is the most stable configuration.The corresponding Raman mapping is shown in Figure 4b,f.it can be seen that the second layer has strong vibration at 19.2 cm −1 in both the AA'A and AA'B stacks, while the intensity is diminished on the third layer.This might be due to the split of the vibration mode into 13.4 cm −1 and 23.2 cm −1 of the trilayer MoSe2, as we mentioned in Figure 1c.Two vibration modes of 13.7 cm −1 and 23.1 cm −1 are reported in trilayer MoSe2 [6,11].Figure 4c,g shows the SHG mappings.As discussed above, the AA' stack possesses a suppressed SHG due to the forming of inversion symmetry.But a similar result is not expected in the AA'A stack.The strong SHG of the AA'A stack might have originated from the interaction between the first and third layers.Shinde et al. present a similar result in MoS2 [27].For the PL mapping shown in Figure 4d,h, the intensity is highly affected by the thickness due to the transition of the direct-indirect band gap.In the Raman and SHG mappings, both the AA'A and AA'B stacks appear with shape edges; this indicates a uniform high quality of our trilayer MoSe2.But in the AA'B stack, the PL vanishes at three angles.This may need further investigation.

Conclusions
In conclusion, we have successfully grown the multilayered MoSe2 sheets with different stacking orders by salt-assisted CVD.After a series of spectroscopic characterizations and DFT calculations, we have discovered that the AA' (θ = 60°) and AB (θ = 0°) stacks are stable configurations of bilayer MoSe2.These two stack configurations exhibit quite different low-frequency Raman modes and SHG signals due to the change in symmetry.Compared to the bilayer MoSe2, the featured Raman mode at 19.2 cm −1 splits into

Conclusions
In conclusion, we have successfully grown the multilayered MoSe 2 sheets with different stacking orders by salt-assisted CVD.After a series of spectroscopic characterizations and DFT calculations, we have discovered that the AA' (θ = 60 • ) and AB (θ = 0 • ) stacks are stable configurations of bilayer MoSe 2 .These two stack configurations exhibit quite different low-frequency Raman modes and SHG signals due to the change in symmetry.Compared to the bilayer MoSe 2 , the featured Raman mode at 19.2 cm −1 splits into two peaks at 13.4 cm −1 and 23.2 cm −1 of trilayer MoSe 2 and can be well explained by the interlayer bond polarizability model.So, the low-frequency Raman and SHG are efficient ways to differentiate the stack order and the layer number of MoSe 2 .Moreover, the low-frequency Raman, SHG, and PL mappings obviously reflect the homogeneity and distribution of the bilayer and trilayer MoSe 2 , which provide references to the future optimization of CVD growth.

Materials 2024 , 9 Figure 2 .
Figure 2. (a) Optical microscopy image of bilayer MoSe2 with different orientations marked by I, II, III, and IV.The corresponding (b) Raman spectroscopy, (c) SHG, and (d) PL spectra of the four regions.Crystal structure of (e) AA' and (f) AB stack configuration of bilayer MoSe2.

Figure 2 .
Figure 2. (a) Optical microscopy image of bilayer MoSe 2 with different orientations marked by I, II, III, and IV.The corresponding (b) Raman spectroscopy, (c) SHG, and (d) PL spectra of the four regions.Crystal structure of (e) AA' and (f) AB stack configuration of bilayer MoSe 2 .