Probing Polymorphic Stacking Domains in Mechanically Exfoliated Two-Dimensional Nanosheets Using Atomic Force Microscopy and Ultralow-Frequency Raman Spectroscopy

As one of the key features of two-dimensional (2D) layered materials, stacking order has been found to play an important role in modulating the interlayer interactions of 2D materials, potentially affecting their electronic and other properties as a consequence. In this work, ultralow-frequency (ULF) Raman spectroscopy, electrostatic force microscopy (EFM), and high-resolution atomic force microscopy (HR-AFM) were used to systematically study the effect of stacking order on the interlayer interactions as well as electrostatic screening of few-layer polymorphic molybdenum disulfide (MoS2) and molybdenum diselenide (MoSe2) nanosheets. The stacking order difference was first confirmed by measuring the ULF Raman spectrum of the nanosheets with polymorphic stacking domains. The atomic lattice arrangement revealed using HR-AFM also clearly showed a stacking order difference. In addition, EFM phase imaging clearly presented the distribution of the stacking domains in the mechanically exfoliated nanosheets, which could have arisen from electrostatic screening. The results indicate that EFM in combination with ULF Raman spectroscopy could be a simple, fast, and high-resolution method for probing the distribution of polymorphic stacking domains in 2D transition metal dichalcogenide materials. Our work might be promising for correlating the interlayer interactions of TMDC nanosheets with stacking order, a topic of great interest with regard to modulating their optoelectronic properties.


Introduction
In recent years, two-dimensional (2D) layered materials have attracted great interest because of their extensive applications in electrocatalysis, optoelectronics, energy storage, sensing, and other fields [1][2][3][4][5].Among the available 2D materials, the arrangement of adjacent layers, i.e., the stacking order between nanosheets, dominates the polytypes of 2D materials.It is known that the optoelectronic and electrocatalytic properties of 2D materials are highly sensitive to the stacking order [6,7], also termed the crystal phase, along with the size, thickness, and composition [8,9].For instance, the ABA (Bernal) and ABC (rhombohedral) stacking orders have been shown to have a significant influence on the electronic and optical properties of graphene [10][11][12].MoS 2 with a hexagonal phase (2H-MoS 2 ) is the most thermodynamically stable structure and is useful for lowcost photoelectronic applications, while MoS 2 with a trigonal phase (1T-MoS 2 ) has shown promising performance as an electrocatalyst [13,14].It has been reported that MoS 2 with a rhombohedral phase (3R-MoS 2 ) is an excellent material for nonlinear optical devices [15].In addition, robust sliding ferroelectricity has also been demonstrated in a 3R-MoS 2 -based dual-gate FET device [16].
In this work, the polymorphic stacking domains in mechanically exfoliated fewlayer molybdenum disulfide (MoS 2 ) and molybdenum diselenide (MoSe 2 ) nanosheets were directly revealed using electrostatic force microscopy (EFM), high-resolution atomic force microscopy (HR-AFM), and ULF Raman spectroscopy.The distribution of non-2H (including 3R and other types) and 2H stacking orders in the few-layer MoS 2 and MoSe 2 nanosheets was imaged using EFM with a high resolution.The various stacking orders were then confirmed using HR-AFM and ULF Raman spectroscopy.Our results indicate that EFM is a promising and effective method with which to directly identify the stacking order distribution in few-layer TMDCs nanosheets with a mixed crystal phase.

Sample Preparation
A SiO 2 /Si silicon wafer with an oxide layer thickness of 300 nm was cut into 1.2 cm × 1.2 cm square pieces and washed via ultrasonication in a mixture of acetone and deionized water (with a volume ratio of 1:1) for 20 min.Then, the SiO 2 /Si pieces were heated at 110 • C for 30 min in a mixture of concentrated sulfuric acid and hydrogen peroxide (with a volume ratio of 1:1).After that, the SiO 2 /Si pieces were washed with deionized water three times and then dried using purified nitrogen.

Sample Characterization
Optical images were captured using an optical microscope (Axio Scope A1, Zeiss, Jena, Germany).The thickness of the 2D nanosheets on the 300 nm SiO 2 /Si substrates was analyzed using ULF Raman spectroscopy, AFM, and an optical contrast method.The Image J software (https://imagej.net)was used to analyze the contrast difference between the MoS 2 nanosheets and the 300 nm SiO 2 /Si substrate by splitting the grayscale optical image [58].As shown in Figure S1 in the Supporting Information (SI), the red and green channel images could be split from the color channel image.Then, the optical contrast value differences between the MoS 2 nanosheets and the SiO 2 /Si substrate in the red and green channels were obtained by measuring the optical contrast values using Image J. The optical contrast value difference of 1-10L MoS 2 nanosheets is plotted in Figure S2 in the SI as a standard chart for thickness identification.Furthermore, the optical contrast value differences of the MoS 2 nanosheets with an unknown thickness were compared with the standard chart, which could be used to distinguish the layer numbers in the MoS 2 nanosheets.
High-frequency and ultralow-frequency Raman and photoluminescence spectra were obtained using a Raman microscope (LabRAM HR Evolution, Horiba, Kyoto, Japan).A laser of 532 nm was focused through a 100× objective lens at room temperature.A laser power of 8.2 µW and a 60 s accumulation time were chosen to avoid damaging the sample.The Raman band of a Si substrate at 520 cm −1 was used as a reference for calibration.An atomic force microscope (Multimode 8, Bruker, Billerica, MA, USA) was used to obtain the thickness and atomic lattice structures of MoS 2 and MoSe 2 nanosheets.EFM results were collected using the SCM-PIT tip.The cantilever frequency was 75 kHz, and the spring constant was 3 N/m.The scan rate of the EFM test was 1 Hz.The tip bias was applied from −2 V to +2 V, and the lift height was changed from 20 nm to 150 nm.

Results and Discussion
The experimental process is shown in Scheme 1.The few-layer MoS 2 and MoSe 2 nanosheets were exfoliated from the 2H-phase crystals to the 300 nm SiO 2 /Si substrate (Scheme 1a-c).Firstly, the 2H-phase crystal (Scheme 1a) was peeled off using scotch tape (Scheme 1b).After multilayer MoS 2 and MoSe 2 nanosheets were deposited on scotch tape and brought into contact with the SiO 2 /Si substrate, an external force was usually applied to the scotch tape to rub the multilayer nanosheets.Due to the van der Waals interaction between the multilayer nanosheets and the SiO 2 /Si substrate, the monolayer to few-layer nanosheets could remain on the substrate after the scotch tape was removed (Scheme 1c).In this process, the stacking order of the nanosheets could be altered from a 2H phase to a non-2H phase due to the shear force applied between the scotch tape and the SiO 2 /Si substrate (Scheme 1d).Then, AFM was used to measure the surface topography of the nanosheets, and EFM was employed to characterize their stacking domain distribution (Scheme 1e).
Nanomaterials 2024, 14, x FOR PEER REVIEW 3 of 13 thickness identification.Furthermore, the optical contrast value differences of the MoS2 nanosheets with an unknown thickness were compared with the standard chart, which could be used to distinguish the layer numbers in the MoS2 nanosheets.High-frequency and ultralow-frequency Raman and photoluminescence spectra were obtained using a Raman microscope (LabRAM HR Evolution, Horiba, Kyoto, Japan).A laser of 532 nm was focused through a 100× objective lens at room temperature.A laser power of 8.2 µW and a 60 s accumulation time were chosen to avoid damaging the sample.The Raman band of a Si substrate at 520 cm −1 was used as a reference for calibration.An atomic force microscope (Multimode 8, Bruker, Billerica, MA, USA) was used to obtain the thickness and atomic lattice structures of MoS2 and MoSe2 nanosheets.EFM results were collected using the SCM-PIT tip.The cantilever frequency was 75 kHz, and the spring constant was 3 N/m.The scan rate of the EFM test was 1 Hz.The tip bias was applied from −2 V to +2 V, and the lift height was changed from 20 nm to 150 nm.

Results and Discussion
The experimental process is shown in Scheme 1.The few-layer MoS2 and MoSe2 nanosheets were exfoliated from the 2H-phase crystals to the 300 nm SiO2/Si substrate (Scheme 1a-c).Firstly, the 2H-phase crystal (Scheme 1a) was peeled off using scotch tape (Scheme 1b).After multilayer MoS2 and MoSe2 nanosheets were deposited on scotch tape and brought into contact with the SiO2/Si substrate, an external force was usually applied to the scotch tape to rub the multilayer nanosheets.Due to the van der Waals interaction between the multilayer nanosheets and the SiO2/Si substrate, the monolayer to few-layer nanosheets could remain on the substrate after the scotch tape was removed (Scheme 1c).In this process, the stacking order of the nanosheets could be altered from a 2H phase to a non-2H phase due to the shear force applied between the scotch tape and the SiO2/Si substrate (Scheme 1d).Then, AFM was used to measure the surface topography of the nanosheets, and EFM was employed to characterize their stacking domain distribution (Scheme 1e).To investigate the origin of the stacking order alternation in the TMDC nanosheets, the few-layer MoS 2 nanosheet was first mechanically exfoliated on the SiO 2 /Si substrate and then transferred onto a flexible polydimethylsiloxane (PDMS) film.Afterward, a Raman microscope was used to monitor the evolution of the ULF and high-frequency Raman peaks of the MoS 2 nanosheets before and after the transfer.As shown in Figure 1a, the MoS 2 nanosheet consisting of 6L and 7L layers was deposited on a 300 nm SiO 2 /Si substrate via mechanical exfoliation.The thickness of the MoS 2 layer was confirmed by measuring the optical contrast and ULF Raman spectra [58,59] To investigate the origin of the stacking order alternation in the TMDC nanosheets the few-layer MoS2 nanosheet was first mechanically exfoliated on the SiO2/Si substrate and then transferred onto a flexible polydimethylsiloxane (PDMS) film.Afterward, a Ra man microscope was used to monitor the evolution of the ULF and high-frequency Raman peaks of the MoS2 nanosheets before and after the transfer.As shown in Figure 1a, th MoS2 nanosheet consisting of 6L and 7L layers was deposited on a 300 nm SiO2/Si substrat via mechanical exfoliation.The thickness of the MoS2 layer was confirmed by measuring the optical contrast and ULF Raman spectra [58,59].The optical contrast difference value in the red and green channels of the upper-left MoS2 nanosheet were −118 and 25, respec tively, which could be assigned to the 6L MoS2 from Figure S2 in the SI.In addition, thes values for the upper-right MoS2 nanosheet were −107 and 30 and could be assigned to the 7L MoS2.Three regions (referred to as P1, P2, and P3 in Figure 1a) on the MoS2 nanosheet were selected to present the change in stacking order by monitoring their ULF Raman spectra before and after being transferred onto the PDMS film (Figure 1b).Regions P1 and P2 wer located on the 6L nanosheet, while region P3 was located on the 7L MoS2 nanosheet.Re gions P1 and P2 showed ULF shear-and breathing-mode peaks located at 31.3 and 14.5 cm −1 , respectively, which were consistent with those of the 6L MoS2 with a 2H phase (Fig ure 1c), indicating that they maintained the 2H phase after being deposited on the 300 nm SiO2/Si substrate.After being transferred onto the PDMS film, regions P1 and P2 showed two new shear-mode peaks at 28.3 (indicated by the purple arrows in Figure 1c) and 16.1 cm −1 (indicated by the green arrow in Figure 1c), indicating the formation of a non-2H Three regions (referred to as P1, P2, and P3 in Figure 1a) on the MoS 2 nanosheet were selected to present the change in stacking order by monitoring their ULF Raman spectra before and after being transferred onto the PDMS film (Figure 1b).Regions P1 and P2 were located on the 6L nanosheet, while region P3 was located on the 7L MoS 2 nanosheet.Regions P1 and P2 showed ULF shear-and breathing-mode peaks located at 31.3 and 14.5 cm −1 , respectively, which were consistent with those of the 6L MoS 2 with a 2H phase (Figure 1c), indicating that they maintained the 2H phase after being deposited on the 300 nm SiO 2 /Si substrate.After being transferred onto the PDMS film, regions P1 and P2 showed two new shear-mode peaks at 28.3 (indicated by the purple arrows in Figure 1c) and 16.1 cm −1 (indicated by the green arrow in Figure 1c), indicating the formation of a non-2H-phase stacking order.As shown in Figure 1c, the 2H-phase 7L MoS 2 showed three characteristic ULF Raman peaks located at 12.3, 25.3, and 31.6 cm −1 , respectively.Region P3 showed additional ULF Raman peaks located at 20.1 (indicated by the yellow arrows in Figure 1c) and 29.3 cm −1 (indicated by the brown arrows in Figure 1c) in addition to the characteristic Raman peaks, implying a stacking order change to a non-2H phase after mechanical exfoliation.Moreover, the intensity ratio of the Raman peaks at 29.3 cm −1 to 31.6 cm −1 changed from 1.38 to 0.54 after the nanosheets were transferred onto the PDMS film, indicating that the stacking order was further changed during the transfer process.
During the mechanical exfoliation process, it is possible to cause a stacking order change due to the shear-force-assisted movement of the constituent layers, thereby forming nanosheets with polymorphic domains.Such a phenomenon has also been reported in relation to the stacking order change in mechanically exfoliated few-layer graphene and 2H-TaS 2 [22,60].The aforementioned phenomena confirmed the stacking order change in the MoS 2 nanosheets during the mechanical exfoliation and transfer processes.
The stacking order change in the few-layer MoS 2 nanosheet was further revealed via HR-AFM and ULF Raman spectroscopy, yielding detailed results.As shown in Figure 2a, the MoS 2 nanosheet consisting of 2L and 5L layers was deposited on a 300 nm SiO 2 /Si substrate via mechanical exfoliation.The thickness of the MoS 2 nanosheet was confirmed through AFM as well as optical contrast measurements.The stacking order was revealed through ULF Raman spectroscopy.As shown in Figure 2b, the 2L MoS 2 layer showed a 2H phase since it had a ULF shear-mode peak at 22.7 cm −1 and a breathing-mode peak at 40.2 cm −1 .The 2H-phase 5L MoS 2 had characteristic ULF Raman shear-and breathing-mode peaks located at 30.9 and 16.9 cm −1 , respectively.Furthermore, besides these characteristic ULF Raman peaks, the 5L MoS 2 layer shown in Figure 2a  phase stacking order.As shown in Figure 1c, the 2H-phase 7L MoS2 showed three characteristic ULF Raman peaks located at 12.3, 25.3, and 31.6 cm −1 , respectively.Region P3 showed additional ULF Raman peaks located at 20.1 (indicated by the yellow arrows in Figure 1c) and 29.3 cm −1 (indicated by the brown arrows in Figure 1c) in addition to the characteristic Raman peaks, implying a stacking order change to a non-2H phase after mechanical exfoliation.Moreover, the intensity ratio of the Raman peaks at 29.3 cm −1 to 31.6 cm −1 changed from 1.38 to 0.54 after the nanosheets were transferred onto the PDMS film, indicating that the stacking order was further changed during the transfer process.
During the mechanical exfoliation process, it is possible to cause a stacking order change due to the shear-force-assisted movement of the constituent layers, thereby forming nanosheets with polymorphic domains.Such a phenomenon has also been reported in relation to the stacking order change in mechanically exfoliated few-layer graphene and 2H-TaS2 [22,60].The aforementioned phenomena confirmed the stacking order change in the MoS2 nanosheets during the mechanical exfoliation and transfer processes.
The stacking order change in the few-layer MoS2 nanosheet was further revealed via HR-AFM and ULF Raman spectroscopy, yielding detailed results.As shown in Figure 2a, the MoS2 nanosheet consisting of 2L and 5L layers was deposited on a 300 nm SiO2/Si substrate via mechanical exfoliation.The thickness of the MoS2 nanosheet was confirmed through AFM as well as optical contrast measurements.The stacking order was revealed through ULF Raman spectroscopy.As shown in Figure 2b, the 2L MoS2 layer showed a 2H phase since it had a ULF shear-mode peak at 22.7 cm −1 and a breathing-mode peak at 40.2 cm −1 .The 2H-phase 5L MoS2 had characteristic ULF Raman shear-and breathingmode peaks located at 30.9 and 16.9 cm −1 , respectively.Furthermore, besides these characteristic ULF Raman peaks, the 5L MoS2 layer shown in Figure 2a    In order to reveal the stacking order of the non-2H 5L MoS 2 layer, HR-AFM was performed to image the atomic lattice orientation of the bottom 2H-phase 2L MoS 2 layer and the top non-2H 3L MoS 2 layer, referred to as regions P1, P2, and P3 in Figure 2c.Although regions P2 and P3 were located in the same nanosheet, they showed different ULF Raman peaks (Figure 2c).The ULF Raman peak located at 30.9 cm −1 of region P2 showed a higher intensity than that of region P3, implying that the two might have different stacking orders.Compared to region P1, regions P2 and P3 showed anti-clockwise twist angles of 1 • and 4 • (as shown in the insets in Figure 2c,d), respectively.As shown in Figure 2c, there was a wrinkle between regions P2 and P3, indicating that the origin of the stacking order differed between them.A similar phenomenon was also observed in the non-2H 4L MoS 2 consisting of a 1L MoS 2 layer stacked on top of a 2H-phase 3L MoS 2 layer with a twist angle of 3 • (Figure S3 in SI).
Besides the non-2H stacked 3L MoS 2 , there was another 1L MoS 2 layer stacked on top of the 2H-phase 2L MoS 2 , forming a 3L MoS 2 layer, as shown in Figure S4 in the SI.Although the atomic lattice orientation of the 3L MoS 2 layers (regions P2 and P3, shown in Figure S4c) was the same as that of the bottom 2H-phase 2L MoS 2 layer (region P1, shown in Figure S3c), the ULF Raman spectra indicate that the crystal phases of the 3L MoS 2 layers in regions P2 and P3 were different (Figure S4b).As shown in Figure S4b, the 3L MoS 2 in region P3 showed mixed shear-and breathing-mode peaks around 28.1 cm −1 , which are consistent with those of the 2H-phase 3L MoS 2 (indicated by the bottom black curve in Figure S4b), confirming its 2H phase, while the 3L MoS 2 in region P2 showed a ULF shear-mode peak located at 16.2 cm −1 and a breathing-mode peak (purple arrow in Figure S3b) located at 27.6 cm −1 , respectively, indicating its 3R phase [51].Since the 2L MoS 2 in region P1 was in a 2H phase, the 3R phase of the 3L MoS 2 in region P2 could be attributed to the sliding of the top 1L MoS 2 layer (Figure S4d).
Figure 3a,b show the optical and AFM topography images of a mechanically exfoliated MoS 2 nanosheet on a 300 nm SiO 2 /Si substrate.The height of the MoS 2 nanosheet is 4.6 nm, indicating that its thickness is 6L.Compared to the 2H-phase 6L MoS 2 nanosheet (indicated by the black curve in Figure 3c), the ULF Raman spectra of regions P1 and P2 show new shear-mode peaks at 28.3 cm −1 .In addition, the intensity of the shear-mode peak at 31.3 cm −1 is considerably lower than that of the 2H-phase 6L MoS 2 .Therefore, the 6L MoS 2 nanosheet shown in Figure 3a,b should be in a non-2H phase.Although regions P1 and P2 show similar ULF Raman peaks (indicated by the blue and red curves in Figure 3c), they show different intensity ratios of the peak at 28.3 cm −1 to the peak at 31.3 cm −1 , which were 3.38 and 0.58, respectively.Furthermore, a small shear-mode peak (indicated by the purple arrow) at 16.1 cm −1 appeared in the ULF Raman spectra of region P2.These results indicate that the stacking orders in regions P1 and P2 are different, which was also confirmed by the ULF Raman mapping of regions P1 and P2 in the range of 25.5 to 35.5 cm −1 (Figure 3d).
It is known that there are charged impurities trapped between mechanically exfoliated 2D nanosheets and SiO 2 /Si substrates under ambient conditions [61][62][63].Such charged impurities induce an electric field that can be screened by 2D nanosheets [64][65][66][67].Moreover, the interlayer coupling between MoS 2 layers plays a crucial role in the electrostatic screening of an electric field [63], different from that of graphene.To reveal the electrostatic screening by MoS 2 nanosheets with various stacking orders, EFM was employed.As shown in Figure 3e, there is quite a faint difference between regions P1 and P2 in the EFM amplitude image.Region P1 shows an amplitude difference of 3.15 pm compared to the SiO 2 /Si substrate and that of region P2 shows a slight increase to 5.83 pm, which could be attributed to the low sensitivity of amplitude detection in the EFM test.The cantilever could be considered an oscillator with some damping, while the interaction between the probe and sample would affect the amplitude.However, a certain period of time was required for adjusting the oscillation amplitude, which led to almost no difference in the amplitude profile between regions P1 and P2 (Figure 3e).However, phase detection in the EFM test was instant and sensitive, meaning that the phase shift difference was more obvious than the amplitude change.Regions P1 and P2 show obvious contrast differences (−77 m • and −146 m • ) in the EFM phase image (Figure 3f), implying different forms of electrostatic screening induced by the stacking order.It is known that there are charged impurities trapped between mechanically exfoliated 2D nanosheets and SiO2/Si substrates under ambient conditions [61][62][63].Such charged impurities induce an electric field that can be screened by 2D nanosheets [64][65][66][67].Moreover, the interlayer coupling between MoS2 layers plays a crucial role in the electrostatic screening of an electric field [63], different from that of graphene.To reveal the electrostatic screening by MoS2 nanosheets with various stacking orders, EFM was employed.As shown in Figure 3e, there is quite a faint difference between regions P1 and P2 in the EFM amplitude image.Region P1 shows an amplitude difference of 3.15 pm compared to the SiO2/Si substrate and that of region P2 shows a slight increase to 5.83 pm, which could be attributed to the low sensitivity of amplitude detection in the EFM test.The cantilever could be considered an oscillator with some damping, while the interaction between the probe and sample would affect the amplitude.However, a certain period of time was required for adjusting the oscillation amplitude, which led to almost no difference in the amplitude profile between regions P1 and P2 (Figure 3e).However, phase detection in the EFM test was instant and sensitive, meaning that the phase shift difference was more obvious than the amplitude change.Regions P1 and P2 show obvious contrast differences (−77 m° and −146 m°) in the EFM phase image (Figure 3f), implying different forms of electrostatic screening induced by the stacking order.
To further investigate the influence of stacking order on electrostatic screening, a scanning bias voltage (−2 V to +2 V) was applied to the EFM tip to generate an external electric field with different strengths [68].Firstly, a MoS2 nanosheet consisting of 2L and 3L layers with different stacking orders was deposited on the 300 nm SiO2/Si substrate and imaged using AFM (Figure 4a).As shown in Figure 4b-h, with the change in tip bias volt- To further investigate the influence of stacking order on electrostatic screening, a scanning bias voltage (−2 V to +2 V) was applied to the EFM tip to generate an external electric field with different strengths [68].Firstly, a MoS 2 nanosheet consisting of 2L and 3L layers with different stacking orders was deposited on the 300 nm SiO 2 /Si substrate and imaged using AFM (Figure 4a).As shown in Figure 4b-h, with the change in tip bias voltage, the contrast of different stacking domains (referred to as regions P1, P2, P3, and P4 in Figure 4a) in the EFM phase images was obviously changed, indicating the noticeable electrostatic screening ability of the stacking order.The phase shift results are summarized in Figure 4i.In our EFM test, the resonant frequency shift (∆∅) was larger than the cantilever frequency.Thus, the EFM phase shift is expressed as follows [65]: Here, F is the driving force, i.e., electrostatic force in the EFM test; z is the motion displacement of the AFM tip; k is the spring constant of the cantilever; and Q is the quality factor of the cantilever.If the capacitive interaction between the AFM tip and the sample is considered to be ideal capacitance, the relationship between electrostatic force and applied voltage can be described as follows [63]: Nanomaterials 2024, 14, 339 Here, C is the capacitance between the AFM tip and the sample; V tip is the DC bias voltage; and V s is the effective surface potential of the sample.By combining Equations ( 1) and ( 2), the relationship between the force gradient (∂F/∂z) and bias voltage can be written as ∂F ∂z ment of the AFM tip; k is the spring constant of the cantilever; and Q is the quality factor of the cantilever.If the capacitive interaction between the AFM tip and the sample is considered to be ideal capacitance, the relationship between electrostatic force and applied voltage can be described as follows [63]: Here, C is the capacitance between the AFM tip and the sample; Vtip is the DC bias voltage; and Vs is the effective surface potential of the sample.By combining Equations ( 1) and ( 2), the relationship between the force gradient (əF/əz) and bias voltage can be written as As a result, the phase shift values of regions P1, P2, P3, and P4 in Figure 4a show an obvious parabolic dependence on the voltage applied to the AFM tip, which is similar to that of MoS2 nanosheets with different thicknesses [69].Moreover, the apex of each curve indicates that the applied voltage on the tip is equal to the Vs.The curve of 2H-phase 3L MoS2 reaches its apex at an applied voltage of −0.59 V, indicating the Vs of 2H-phase 3L MoS2, while the Vs of non-2H 3L MoS2 is −0.71V.In addition, the Vs of non-2H-phase 2L MoS2 in region P3 is −0.68 V, while that of non-2H-phase 2L MoS2 in region P4 is −0.44 V. Therefore, the surface potential of MoS2 nanosheets with different stacking orders could also be detected via EFM phase imaging.For the MoS2 nanosheets with the same thicknesses, the apex of the parabola is sensitive to the stacking order, indicating the latter's significant effect on electrostatic screening.The EFM phase shifts of the MoS2 nanosheets with different stacking orders are highly dependent on the lift height during the scanning process.EFM phase measurement on a 15L MoS2 nanosheet was also performed, with the lift height changed from 20 to 150 nm (Figure S5 in SI).The phase shift was about 0.94° when the lift height was set to 20 nm.It decreased rapidly to 0.08° when the lift height increased to 150 nm.By plotting the EFM phase shift as a function of the lift height, it can As a result, the phase shift values of regions P1, P2, P3, and P4 in Figure 4a show an obvious parabolic dependence on the voltage applied to the AFM tip, which is similar to that of MoS 2 nanosheets with different thicknesses [69].Moreover, the apex of each curve indicates that the applied voltage on the tip is equal to the V s .The curve of 2H-phase 3L MoS 2 reaches its apex at an applied voltage of −0.59 V, indicating the V s of 2H-phase 3L MoS 2 , while the V s of non-2H 3L MoS 2 is −0.71V.In addition, the V s of non-2H-phase 2L MoS 2 in region P3 is −0.68 V, while that of non-2H-phase 2L MoS 2 in region P4 is −0.44 V. Therefore, the surface potential of MoS 2 nanosheets with different stacking orders could also be detected via EFM phase imaging.For the MoS 2 nanosheets with the same thicknesses, the apex of the parabola is sensitive to the stacking order, indicating the latter's significant effect on electrostatic screening.The EFM phase shifts of the MoS 2 nanosheets with different stacking orders are highly dependent on the lift height during the scanning process.EFM phase measurement on a 15L MoS 2 nanosheet was also performed, with the lift height changed from 20 to 150 nm (Figure S5 in SI).The phase shift was about 0.94 • when the lift height was set to 20 nm.It decreased rapidly to 0.08 • when the lift height increased to 150 nm.By plotting the EFM phase shift as a function of the lift height, it can be observed that the phase shift of the MoS 2 nanosheets with different stacking domains decreased exponentially as the lift height increased (Figure S5 in SI), a result which aligns with the standard EFM response [70][71][72][73].
EFM phase imaging is also effective in distinguishing the stacking orders of other TMDC nanosheets.As shown in Figure 5a, a MoSe 2 nanosheet with a uniform thickness was deposited on a 300 nm SiO 2 /Si substrate.The thickness of the MoSe 2 nanosheet was 4.6 nm, indicating that it was 6L thick.Three regions (referred to as P1, P2, and P3 in Figure 5a) on the MoSe 2 nanosheet were selected to reveal the stacking order domains using their ULF Raman spectra and EFM phase imaging.Region P3 in Figure 5a has three characteristic ULF Raman peaks at 11.9, 19.0, and 26.2 cm −1 , which are consistent with those of the 2H-6L MoSe 2 nanosheet (indicated by the black curve in Figure 5c), indicating that it was in the 2H phase, while regions P1 and P2 in Figure 5a also show additional Raman peaks at 13.4 and 23.6 cm −1 , respectively, demonstrating that they were in a non-2H phase.In addition, regions P1 and P2 in Figure 5a show the same Raman peaks but different intensities at 11.9 and 13.4 cm −1 , implying that they also have slightly different stacking orders.The Raman mapping result shown in Figure 5d clearly presents the different contrast between regions P2 and P3, while the contrast difference between regions P1 and P2 is almost indistinguishable.
4.6 nm, indicating that it was 6L thick.Three regions (referred to as P1, P2, and P3 in Figure 5a) on the MoSe2 nanosheet were selected to reveal the stacking order domains using their ULF Raman spectra and EFM phase imaging.Region P3 in Figure 5a has three characteristic ULF Raman peaks at 11.9, 19.0, and 26.2 cm −1 , which are consistent with those of the 2H-6L MoSe2 nanosheet (indicated by the black curve in Figure 5c), indicating that it was in the 2H phase, while regions P1 and P2 in Figure 5a also show additional Raman peaks at 13.4 and 23.6 cm −1 , respectively, demonstrating that they were in a non-2H phase.In addition, regions P1 and P2 in Figure 5a show the same Raman peaks but different intensities at 11.9 and 13.4 cm −1 , implying that they also have slightly different stacking orders.The Raman mapping result shown in Figure 5d clearly presents the different contrast between regions P2 and P3, while the contrast difference between regions P1 and P2 is almost indistinguishable.Regions P1, P2, and P3 in Figure 5a show EFM amplitude shifts of 14.6, 5.3, and 11.2 pm, respectively, compared to the SiO2/Si substrate, for which the shifts are difficult to distinguish.Compared to the EFM amplitude image, the EFM phase image clearly shows the contrast differences of regions P1 and P2 with different stacking orders (Figure 5e-f).Regions P1, P2, and P3 show EFM phase shifts of −252, −102, and −142 m° compared to the SiO2/Si substrate, respectively.These results prove that EFM phase imaging is a direct and Regions P1, P2, and P3 in Figure 5a show EFM amplitude shifts of 14.6, 5.3, and 11.2 pm, respectively, compared to the SiO 2 /Si substrate, for which the shifts are difficult to distinguish.Compared to the EFM amplitude image, the EFM phase image clearly shows the contrast differences of regions P1 and P2 with different stacking orders (Figure 5e,f).Regions P1, P2, and P3 show EFM phase shifts of −252, −102, and −142 m • compared to the SiO 2 /Si substrate, respectively.These results prove that EFM phase imaging is a direct and powerful method for visualizing the stacking order distributions of TMDCs on a 300 nm SiO 2 /Si substrate.
Similarly, bias voltage (−2 V to +2 V) was also applied on the same MoSe 2 nanosheet to investigate the electrostatic screening of stacking orders (Figure S6 in SI).As shown in Figure S6, when the tip bias voltage changed from −2 V to +2 V, the EFM phase shifts of different stacking domains (regions P1, P2, and P3) also changed correspondingly, indicating the influence of stacking order on electrostatic screening ability.As shown in Figure S6i, the phase shift values of regions P1, P2, and P3 had a quadratic relation with the applied voltage of the AFM tip, which was similar to that of the MoS 2 nanosheets shown in Figure 4.For the MoSe 2 nanosheets with the same thicknesses, the apex of the parabola was also sensitive to the stacking order.These results show that the stacking order had a greater impact on the electrostatic screening effect than layer thickness.

Conclusions
In summary, we investigated few-layer MoS 2 and MoSe 2 nanosheets with various stacking orders using ULF Raman spectroscopy, HR-AFM, and EFM.The correlation between stacking order and interlayer interaction as well as the electrostatic screening of 2D materials were explored in detail.In the TMDC nanosheets with different stacking orders, the electrostatic screening contrast was consistent with the stacking domain distribution.Through EFM characterization, phase mapping with higher contrast and resolution could be obtained.Therefore, EFM phase imaging was proposed to be a direct and accurate method for characterizing polymorphic domain distribution in mechanically exfoliated 2D materials.Compared to thickness, the stacking order had a more significant impact on electrostatic screening.Our work could be helpful for studying the influence of stacking order on the optical and electronic properties of polymorphic TMDC samples.
Author Contributions: H.L. conceived the project; C.P. and J.Z. prepared the samples and carried out the experimental measurements; H.L., C.P. and J.Z. analyzed the data; H.L., C.P. and J.Z. wrote the manuscript.All authors discussed the results and commented on the paper.All authors have read and agreed to the published version of the manuscript.

Scheme 1 .
Scheme 1. Scheme depicting the preparation and characterization of mechanically exfoliated MoS2 and MoSe2 with different stacking orders.(a,b) Peeling off of the multilayer nanosheets from the Scheme 1. Scheme depicting the preparation and characterization of mechanically exfoliated MoS 2 and MoSe 2 with different stacking orders.(a,b) Peeling off of the multilayer nanosheets from the 2H-phase crystal using scotch tape.(c,d) Deposition of the 2H-and non-2H-phase MoS 2 or MoSe 2 nanosheets from the bulk 2H crystal via mechanical exfoliation.(e) EFM characterization of 2H-and non-2H-phase MoS 2 or MoSe 2 nanosheets.
. The optical contrast difference values in the red and green channels of the upper-left MoS 2 nanosheet were −118 and 25, respectively, which could be assigned to the 6L MoS 2 from Figure S2 in the SI.In addition, these values for the upper-right MoS 2 nanosheet were −107 and 30 and could be assigned to the 7L MoS 2 .2H-phase crystal using scotch tape.(c,d) Deposition of the 2H-and non-2H-phase MoS2 or MoSe nanosheets from the bulk 2H crystal via mechanical exfoliation.(e) EFM characterization of 2H-and non-2H-phase MoS2 or MoSe2 nanosheets.

Figure 1 .
Figure 1.Optical images of the MoS2 nanosheets consisting of 2H 6L and non-2H 7L layers (a) befor and (b) after their transfer onto a PDMS film.(c) The ULF Raman spectra of regions P1, P2, and P in the 6L and 7L MoS2 layers before and after the transfer.The red dashed lines are referred to th breathing-mode peak, the blue and green dashed lines are referred to the shear-mode peaks.

Figure 1 .
Figure 1.Optical images of the MoS 2 nanosheets consisting of 2H 6L and non-2H 7L layers (a) before and (b) after their transfer onto a PDMS film.(c) The ULF Raman spectra of regions P1, P2, and P3 in the 6L and 7L MoS 2 layers before and after the transfer.The red dashed lines are referred to the breathing-mode peak, the blue and green dashed lines are referred to the shear-mode peaks.
exhibited an additional ULF shear-mode peak at 26.0 cm −1 (indicated by the purple arrows in Figure 2b), indicating that it had a non-2H phase.The non-2H 5L MoS 2 layer could have been formed through the stacking of another 3L MoS 2 layer on top of the 2H-phase 2L MoS 2 layer, as indicated by the AFM height image shown in Figure 2c.Since the bottom 2L MoS 2 layer has a 2H-phase and the as-stacked 5L MoS 2 layer has a non-2H phase, the top 3L MoS 2 layer should be stacked in a non-2H manner.
exhibited an additional ULF shear-mode peak at 26.0 cm −1 (indicated by the purple arrows in Figure 2b), indicating that it had a non-2H phase.The non-2H 5L MoS2 layer could have been formed through the stacking of another 3L MoS2 layer on top of the 2H-phase 2L MoS2 layer, as indicated by the AFM height image shown in Figure 2c.Since the bottom 2L MoS2 layer has a 2H-phase and the as-stacked 5L MoS2 layer has a non-2H phase, the top 3L MoS2 layer should be stacked in a non-2H manner.

Figure 2 .
Figure 2. (a) Optical and (c) AFM topography images.(b) ULF Raman spectra of the MoS2 nanosheet on the 300 nm SiO2/Si substrate.The red and blue dashed lines are referred to the shear-and breathing-mode peaks of 2H 2L MoS2, the orange and green dashed lines are referred to the shear-and breathing-mode peaks of 2H 5L MoS2.The purple arrows are referred to the new shear-mode peaks of non-2H 5L MoS2.(d) Simulated atomic lattice images of regions P2 and P3 shown in (c) and according to the measured twist angle.

Figure 2 .
Figure 2. (a) Optical and (c) AFM topography images.(b) ULF Raman spectra of the MoS 2 nanosheet on the 300 nm SiO 2 /Si substrate.The red and blue dashed lines are referred to the shear-and breathing-mode peaks of 2H 2L MoS 2 , the orange and green dashed lines are referred to the shearand breathing-mode peaks of 2H 5L MoS 2 .The purple arrows are referred to the new shear-mode peaks of non-2H 5L MoS 2 .(d) Simulated atomic lattice images of regions P2 and P3 shown in (c) and according to the measured twist angle.

Nanomaterials 2024 , 13 Figure 3 .
Figure 3. (a) Optical image, (b) AFM topography image, (c) ULF Raman spectra, the red and blue dashed lines are referred to the shear-mode peaks of non-2H 6L MoS2, (d) Raman mapping in the range of 25.5 to 35.5 cm −1 , (e) EFM amplitude image, and (f) EFM phase image of the 6L MoS2 sample with different stacking orders.

Figure 3 .
Figure 3. (a) Optical image, (b) AFM topography image, (c) ULF Raman spectra, the red and blue dashed lines are referred to the shear-mode peaks of non-2H 6L MoS 2 , (d) Raman mapping in the range of 25.5 to 35.5 cm −1 , (e) EFM amplitude image, and (f) EFM phase image of the 6L MoS 2 sample with different stacking orders.

Figure 4 .
Figure 4. (a) AFM topography image.(b-h) EFM phase images of 2L and 3L MoS2 nanosheets shown in (a), with the tip bias changed from −2 V to +2 V. (i) EFM phase shift as a function of the applied tip bias.

Figure 4 .
Figure 4. (a) AFM topography image.(b-h) EFM phase images of 2L and 3L MoS 2 nanosheets shown in (a), with the tip bias changed from −2 V to +2 V. (i) EFM phase shift as a function of the applied tip bias.

Figure 5 .
Figure 5. (a) Optical image, (b) AFM topography image, (c) ULF Raman spectra, the green and blue dashed lines are referred to the shear-mode peaks of non-2H 6L MoSe2, (d) Raman mapping in the range of 12.4 to 14.4 cm −1 and 17.1 to 20.7 cm −1 , (e) EFM amplitude image, and (f) EFM phase image of the 6L MoSe2 sample with different stacking orders.

Figure 5 .
Figure 5. (a) Optical image, (b) AFM topography image, (c) ULF Raman spectra, the green and blue dashed lines are referred to the shear-mode peaks of non-2H 6L MoSe 2 , (d) Raman mapping in the range of 12.4 to 14.4 cm −1 and 17.1 to 20.7 cm −1 , (e) EFM amplitude image, and (f) EFM phase image of the 6L MoSe 2 sample with different stacking orders.

Funding:
This work was supported by the National Natural Science Foundation of China (Grant No. 21571101), the Natural Science Foundation of the Jiangsu Province in China (Grant No. BK20161543), and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 15KJB430016).