Abstract
Raman spectroscopy is a widely used technique to characterize nanomaterials because of its convenience, nondestructiveness, and sensitivity to materials change. The primary purpose of this work is to determine via Raman spectroscopy the average thickness of MoS_{2} thin films synthesized by direct liquid injection pulsedpressure chemical vapor deposition (DLIPPCVD). Such samples are constituted of nanoflakes (with a lateral size of typically 50 nm, i.e., well below the laser spot size), with possibly a distribution of thicknesses and twist angles between stacked layers. As an essential preliminary, we first reassess the applicability of different Raman criteria to determine the thicknesses (or layer number, N) of MoS_{2} flakes from measurements performed on reference samples, namely wellcharacterized mechanically exfoliated or standard chemical vapor deposition MoS_{2} large flakes deposited on 90 ± 6 nm SiO_{2} on Si substrates. Then, we discuss the applicability of the same criteria for significantly different DLIPPCVD MoS_{2} samples with average thicknesses ranging from submonolayer up to three layers. Finally, an original procedure based on the measurement of the intensity of the layer breathing modes is proposed to evaluate the surface coverage for each N (i.e., the ratio between the surface covered by exactly N layers and the total surface) in DLIPPCVD MoS_{2} samples.
Introduction
The advent of twodimensional (2D) layered materials beyond graphene has initiated a new field of research [13]. In the family of 2D layered structures, transition metal dichalcogenides (TMDs) have attracted considerable attention from academia and regarding potential applications [49] because of a number of remarkable properties [1012]. Particularly, it was found that the properties of layered TMDs drastically change when their thickness is reduced to a monolayer [13,14]. Layered TMD structures have a graphitelike structure with each graphene sheet replaced with an X–M–X or MX_{2} triatomic layer, where X is a chalcogen atom (e.g., sulfur, selenium, or tellurium) and M is a transition metal atom (e.g., molybdenum or tungsten) [10].
Among the layered TMD materials, molybdenum disulfide, MoS_{2}, is of particular interest in optoelectronic applications because of its transition to a direct bandgap semiconductor with very high photoluminescence quantum yield when thinned down to a monolayer [1317]. Its unique electronic and optical properties could provide an edge in many future applications.
The multilayers MoS_{2} structures are of the most common 2Hc type, where atomic layers are arranged in such way that the stacking between two adjacent layers corresponds to a twist angle of θ = 60°, and any Mo atom is sitting on top of two S atoms of the adjacent layers [18,19]. However, during the synthesis process (e.g., chemical vapor deposition (CVD) synthesis) or when using precise transfer or AFM tip manipulation techniques [20], twisted MoS_{2} can be formed with two adjacent layers stacked with a relative twist angle (θ) varying from 0 to 60°. Such twistedlayered MoS_{2} structures can exhibit a variety of interesting physical properties including unconventional super conductivity [21,22], nonlinear optics [23,24], and moiré excitons [25].
Because the properties of MoS_{2} flakes are first a function of their thickness, or layer number (N), it is of a primary importance to determine the N of MoS_{2} flakes, including twisted MoS_{2} flakes and defective MoS_{2} flakes, synthesized by different ways. Independently of the structural organization between adjacent layers, a MoS_{2} flake is usually named NLMoS_{2}, or simply NL, with N being the number of MoS_{2} triatomic layers, which defines the thickness of the flake.
Several optical techniques have been developed to identify the N of MoS_{2} flakes produced by different methods. Among these techniques, Raman spectroscopy is widely used thanks to its convenience, nondestructiveness, and sensitivity to materials change, including strain, temperature, doping, and defects [26]. Concerning the characterization of MoS_{2} flakes, different information can be derived from the measurement of the Raman features (frequencies, linewidths, and intensities) of intralayer phonon modes as well as those of the interlayer modes, the socalled layer breathing (LB) modes and shear (S) modes.
Recently, we have developed the reproducible direct growth of waferscale MoS_{2} thin films on SiO_{2}/Si substrates by direct liquid injection pulsedpressure chemical vapor deposition (DLIPPCVD) using lowtoxicity precursors [27]. Such MoS_{2} thin films showed good stoichiometry (Mo/S = 1.94–1.95) and the potential for high photoluminescence quantum yield. However, atomic force microscopy revealed that they are constituted of nanoflakes (with a lateral size of typically 50 nm) with possibly a distribution of thicknesses. Furthermore, depending on the synthesis conditions, the MoS_{2} surface coverage can be incomplete, and the thin film average thickness can vary. These samples thus have characteristics, especially thickness inhomogeneities smaller than the laser spot size, that differ from the ones used to establish Raman spectroscopybased MoS_{2} layer counting methods [26,2833]. In this context, the primary purpose of this work is to develop and validate an approach for determining the average thickness of such sublaser spot size inhomogeneous MoS_{2} thin films using Raman spectroscopy.
First, we reassess here as a ground work the information that can be derived from the Raman spectra of MoS_{2} flakes for the evaluation of their thickness, N. Different Raman criteria for the determination of the thicknesses of MoS_{2} flakes are first recollected; after the specification of the experimental protocol, domains and limits of application of these criteria are precisely defined from measurements performed on reference samples. These samples are wellcharacterized, either mechanically exfoliated or standard CVD MoS_{2} large flakes deposited on 90 ± 6 nm SiO_{2} on Si substrates. Then, we determine which Raman information is relevant to estimate the average thickness of MoS_{2} samples produced by the DLIPPCVD method, which are constituted of nanoflakes and, thus, significantly different from the reference samples. Finally, an original procedure based on the layer breathing mode intensities is proposed to evaluate the surface coverage for each N, that is, the ratio between the surface covered by exactly N layers and the total surface, in DLIPPCVD samples.
Results and Discussion
Experimental procedure
To define a robust experimental Raman protocol to evaluate the thickness of a MoS_{2} flake (i.e., its number of layers, N), it is first necessary to specify some parameters that can have a direct influence on the quality and accuracy of the results. The first parameter is the wavelength of the incident laser light used in the Raman experiments. As it will be detailed in the following, the measurements of the frequencies, linewidths, and intensity of firstorder Raman active phonon modes of MoS_{2} have to be obtained with good accuracy in order to evaluate the thickness of a MoS_{2} flake. These phonons modes are (i) the inplane phonon mode involving relative motion of Mo and S atoms with E′ symmetry for a monolayer (E^{1}_{2g} for bulk) and (ii) the outofplane phonon mode involving only outofplane motions of S atoms with A′_{1} symmetry for a monolayer (A_{1g} for bulk). These modes are located around 385 and 405 cm^{−1}, respectively, in neutral and defectfree MoS_{2} monolayers [33,34]. More precisely, in MoS_{2} multilayers, the symmetries of these phonon modes are E′ and A′_{1} for an odd number of layers, and E_{g} and A_{1g} for an even number of layers. For simplicity, hereafter when we will discuss the dependence on N of the features of these phonon modes, they will be simply referred to as in the bulk, E^{1}_{2g} and A_{1g}, independently of the number of layers.
A drastic change of the Raman spectra, especially in the frequency range of the A_{1g} and E^{1}_{2g} modes, occurs when the spectra are excited at an energy close to those of the A and B excitons located around 655 nm (1.89 eV) and 601 nm (2.06 eV), respectively, in MoS_{2} monolayers [35,36]. When the incident laser energy is in the range of the A and B exciton energies (the socalled resonance conditions), other bands associated to different secondorder processes are observed in the Raman spectra with a strong intensity, their frequencies, widths, and intensity depending on the excitation energy [36]. In addition, resonance conditions alter the symmetry selection rules of phonons of MoS_{2} [35]. Some of the secondorder bands overlap with the A_{1g} and E^{1}_{2g} modes, complicating the exact determination of the parameters of these modes recorded under resonance conditions. Furthermore, since the MoS_{2} exciton characteristics (energy, width, and spectral weight) can be changed by several factors (e.g., stacking, strain, doping, and defects), the Raman intensities measured with a single laser wavelength close to exciton energies can be affected by external factors and differ for samples elaborated by different methods. For these reasons and in the aim to use Raman spectroscopy to count the number of MoS_{2} layers, one must necessarily work under offresonance conditions, that is, by using incident laser energy far from both exciton resonance energies. In this work, we chose to perform Raman experiments using 532 nm (2.33 eV) laser excitation, because this is sufficiently far from the energy range of A and B excitons [35].
All Raman spectra reported in this paper were recorded on different samples deposited on SiO_{2}/Si(100) substrate. Hence, the second parameter essential to define is the SiO_{2} thickness. Indeed, the multiple reflection interferences that occur in the air/MoS_{2}/SiO_{2}/Si structure influence significantly the intensity of the phonon modes [28,37]. In this work, we chose to focus on substrates with a SiO_{2} thickness around 90 nm, which corresponds to the first optimum value for MoS_{2} monolayer (N = 1) Raman enhancement with a 532 nm excitation energy and also amplifies the signal in the wavelength range of photoluminescence emission (around 650 nm).
The third parameter to define is the power of the 532 nm light, P_{λ}, impinging the sample. Much of the Raman information available to evaluate the thickness of MoS_{2} flakes is based on the following parameters: (i) on precise measurements of frequency of the A_{1g} and E^{1}_{2g} phonon modes of MoS_{2}. These lead to a precise knowledge of the frequency difference Δω_{A−E}. It was established that Δω_{A−E} depends monotonously on the number of layers, and Δω_{A−E} is largely used as criterion to evaluate the thickness of MoS_{2} flakes [26,29,30]; (ii) on the precise evaluation of the integrated intensities of the phonon modes of MoS_{2}, namely A(A_{1g}) and A(E^{1}_{2g}), with respect to the integrated intensity of the 521 cm^{−1} mode from a bare area of the oxidized silicon substrate, A_{0}(Si), used as an intensity reference [31], or from the silicon substrate underneath the MoS_{2} flake, A_{2D}(Si) [28]; (iii) on the precise measurement of the A_{2D}(Si)/A_{0}(Si) intensity ratio [31]; and (iv) on the measurement of ultralowfrequency modes, the socalled breathing modes and shear modes. The frequencies and the number of LB and S modes allow one to identify the number of layers [32,33] and the presence of twist between adjacent layers from the vanishing of the S modes in twisted MoS_{2} flakes [20,3841].
Then, it is essential to determine the limit value of the laser power so that the above measurements are not affected by laser irradiation. Figure 1 shows the evaluation of the temperature of MoS_{2} flakes prepared in different ways and that of the Si substrate as functions of the laser power impinging on the sample through a 100× objective (N.A. 0.9). The power was cycled between ≈5 μW and ≈2 mW. The temperature of MoS_{2} flakes is evaluated from the Stokes/antiStokes intensity ratio of A_{1g} phonon modes (similar results are obtained using E^{1}_{2g}) and that of silicon from the Stokes/antiStokes intensity ratio of the 521 cm^{−1} Si mode (see [42] for method details). While the silicon temperature is quasiinsensitive to P_{λ}, the temperature of MoS_{2} flakes changes monotonically, reversibly, and quasilinearly with P_{λ} (see inset of Figure 1). For MoS_{2}, we found an increase rate of 25–30 °C/mW for monolayers (1LMoS_{2}) and 40–45 °C/mW for bilayers (2LMoS_{2}). Usual effects of sample heating are the frequency shift of the phonon modes and their concomitant broadening. In Supporting Information File 1, the frequency and the linewidth of the Si mode as functions of the laser power are displayed (Figure S2). These two parameters are found to be insensitive to P_{λ} below 0.5 mW. More intriguing is the evolution of the frequency (Figure 2a) and width (Figure 2b) of the phonon modes of 1LMoS_{2} as a function of P_{λ}. For a simple thermal effect [43] and given the 25–30 °C/mW temperature increase rate determined previously, the frequencies of A′_{1} and E′ modes should both downshift by 0.3–0.4 cm^{−1}/mW and the width of A′_{1} should increase by ≈0.2 cm^{−1}/mW (the width of E′ should remain constant) contrary to what is observed in Figure 2a,b. To clarify this point, we present in Figure 2c (filled dots) the relative shift of the frequency of the A′_{1} mode versus that of the E′ mode measured on CVD 1LMoS_{2} at different laser powers. In the same plot the expected shifts of these modes are reported (i) as functions of a pure thermal effect (Figure 2c, red line) [43] and (ii) as functions of the doping state (Figure 2c, magenta curve) [44]. Clearly the relative shift of the A′_{1} mode frequency versus that of the E′ mode frequency as a function of P_{λ} significantly differs from the behavior expected by considering a simple thermal effect. Consequently, the results reported in Figure 2c clearly evidence photodoping of 1LMoS_{2} concomitant with a thermal effect, as already observed for MoS_{2} on SiO_{2}/Si [45] as well as for graphene [42]. Furthermore, the evolution of the A′_{1} and E′ widths with P_{λ} (Figure 2b), that is, the weak change of the E′ width and the significant increase of the A′_{1} width concomitant with the A′_{1} frequency decrease, support this interpretation [44]. For a laser power smaller than 0.3 mW, photodoping remains rather low, but it is the dominant contribution to the shift of the modes. Similar results were obtained on other samples including exfoliated 1LMoS_{2}. The effects were found irreversible in some cases when P_{λ} exceeded 1 mW but remained always reversible if P_{λ} was kept below 1 mW.
Based on the above information, all Raman results reported and discussed in this paper were obtained by using a P_{λ} around 0.1 mW chosen as a good compromise between mitigating laser effects and maintaining measurement efficiency to ensure the accuracy of the Raman criteria discussed in the next part of this paper.
In summary, unless specified otherwise, all Raman spectra reported and discussed in this paper were recorded at an excitation wavelength of 532 nm, with a laser workingpower close to 0.1 mW, and using a 100× objective (N.A. 0.9), on MoS_{2} flakes or thin films deposited on SiO_{2}/Si substrate with a SiO_{2} thickness of 90 ± 6 nm.
Application of Raman criteria to characterize MoS_{2} flakes
In this part, we report and discuss the advantages and limits of some Raman criteria that were found to be efficient to derive the thickness (i.e., the number of layers N) of large MoS_{2} flakes prepared by different ways, namely mechanical exfoliation and standard CVD (including twisted CVD 2LMoS_{2}). Then, we discuss the application of Raman spectroscopy to characterize samples synthesized by DLIPPCVD. In contrast to the first two kinds of MoS_{2} samples, the latter are constituted of nanoflakes with possibly a distribution of thicknesses and twist angles between adjacent layers of multilayer domains as well as a higher number of defects.
Exfoliated MoS_{2} flakes as reference samples
We performed Raman experiments on mechanically exfoliated MoS_{2} [1] that will serve as reference samples. The stacking sequence in exfoliated MoS_{2} flakes is of the 2Hctype [34]. The common feature of all these samples is to have a limited number of defects. Note also that all exfoliated flakes have a lateral size (few micrometers at minimum) significantly larger than the diameter of the laser spot. In such flakes, the exact number of layers, N, is determined by combining optical microscopy, spectral reflectivity, and the measurement of the breathing modes and shear modes in the ultralow frequency (ULF) range of the spectra [3234].
One of the most popular criteria to determine the number of layers of MoS_{2} flakes is the measurement of Δω_{A−E}, that is, the frequency difference between the A_{1g} and E^{1}_{2g} phonon modes [26,29,30]. Figure 3a shows the dependence of Δω_{A−E} on the number of layers measured on exfoliated MoS_{2} flakes deposited on Si/SiO_{2} substrates with four different SiO_{2} thicknesses. As previously well documented in the literature, we confirm that Δω_{A−E} depends monotonously on the number of layers and does not depend on the SiO_{2} thickness (Figure 3a). The separation between N and N + 1 values are larger than the experimental uncertainties (error bars in the graph) up to N = 3. The error bars start to overlap between N = 4 and N = 5. Comparison with data from the literature (see inset in Figure 3a) shows that this overlap occurs even between N = 3 and N = 4 when additional variability due to setup and samples is taken into account. Above N = 4, the separation becomes too small compared to the uncertainty. Thus, the measurement of Δω_{A−E} in exfoliated MoS_{2} flakes allows one to evaluate with good accuracy the number of layers for N ≤ 3. It is then necessary to supplement the Δω_{A−E} criterion with others to reliably count thick multilayers. In addition, we will establish in the following that this criterion has to be taken with care to derive N in MoS_{2} samples other than reference exfoliated MoS_{2}, because the A_{1g} and E^{1}_{2g} frequencies, and thus the value of Δω_{A−E}, can be affected by different factors such as stacking order, strain, doping, and defects which can be present in MoS_{2} flakes prepared by other ways [44,4649].
To evaluate the number of layers, we can also use information associated with the integrated intensity of MoS_{2} phonon modes. Figure 3b and Figure 3d show, respectively, the dependences of the normalized integrated intensities of the A_{1g} and the E^{1}_{2g} mode as functions of N for four values of the SiO_{2} thickness. For normalization, we use here an external reference, which is a bare Si(111) wafer with only native oxide. In the following, A(Si_{111}) stands for the integrated intensity of the Si(111) 521 cm^{−1} mode. This reference is preferred to the Si(100) substrate with 90 ± 6 nm SiO_{2} to avoid the effects of the SiO_{2} thickness variations and crystal orientation. For comparison with other setups or references, the polarization ratio of our setup and the relative values measured on Si(100) with native oxide and 90 nm SiO_{2} are given in Supporting Information File 1. As noted by several authors and predicted by the optical interference model, the normalized integrated intensities of MoS_{2} modes, namely A(A_{1g})/A(Si_{111}) and A(E^{1}_{2g})/A(Si_{111}), increase first with N and then decrease showing a maximum for N = 4–5 for all SiO_{2} thicknesses. Obviously, this nonmonotonous dependence prevents using these measurands alone to evaluate the number of layers for N > 4. Moreover, a significant dependence of the MoS_{2} Raman intensity on the SiO_{2} thickness occurs for N > 2, pointing out the importance to determine precisely this latter parameter.
Another criterion to derive the thickness of MoS_{2} flakes is the A_{2D}(Si)/A_{0}(Si) intensity ratio [31]. For the evaluation of this ratio, it is of great practical advantage to use the same silicon (the silicon below the oxide, which is Si(100) in the present work) in the measurement of A_{2D}(Si) and A_{0}(Si). A necessary precaution is that the Si(100) substrate orientation has to be kept the same for both measurements. Another advantage is to give a common origin to the plots of A_{2D}(Si)/A_{0}(Si) as a function of N (A_{2D}(Si)/A_{0}(Si) = 1 for N = 0) for any SiO_{2} thickness.
Figure 3c displays the A_{2D}(Si)/A_{0}(Si) ratio measured on exfoliated MoS_{2} flakes deposited on SiO_{2}/Si(100) substrates with four different SiO_{2} thicknesses as a function of N. We confirm the monotonous decrease of the A_{2D}(Si)/A_{0}(Si) ratio with increasing N [31]. For each N, the value of this ratio depends on the SiO_{2} thickness (Figure 3c; black, blue, green, and red symbols correspond to a SiO_{2} thickness of 84, 87, 89, and 96 nm, respectively). Despite the monotonous dependence of the A_{2D}(Si)/A_{0}(Si) ratio, its dependence on SiO_{2} thickness combined with experimental errors lead to the conclusion that the measured values for N and N + 1 can overlap for any N if the SiO_{2} thickness is not known with good accuracy. For a given SiO_{2} thickness, the gap between the A_{2D}(Si)/A_{0}(Si) ratio for N and N + 1 is sufficient to ensure a rather good reliability only for N ≤ 5.
In summary, for exfoliated MoS_{2}, considering jointly the three Raman criteria (i) value of Δω_{A−E}, (ii) value of the normalized integrated intensities of the A_{1g} and E^{1}_{2g} modes, and (iii) value of the A_{2D}(Si)/A_{0}(Si) ratio, one can unambiguously derive the number of layers as long as N ≤ 4 and the SiO_{2} thickness is precisely known. It has also been suggested in the literature to use the intensity ratio A(A_{1g})/A_{2D}(Si) (or equivalently A(E^{1}_{2g})/A_{2D}(Si)). As it will be discussed in the following, we see two major problems with this approach. The first is the dependence of the Si signal on the crystal orientation and the SiO_{2} thickness. The second relates to the fact that using this ratio, rather than using each measurand independently and contrasting them, even if more practical, can hide some information.
Finally, we compare in Supporting Information File 1, Figure S3, the dependence on N of A(A_{1g})/A(Si_{111}) and A_{2D}(Si)/A_{0}(Si) for three SiO_{2} thicknesses and two microscope objectives with different numerical apertures, N.A. = 0.9 (blue symbols in Figure S3), and N.A. = 0.5 (red symbols in Figure S3). We observe that the normalized integrated intensity of the A_{1g} mode, A(A_{1g})/A(Si_{111}) (Figure S3a–c), is independent of the value of N.A. Concerning the dependence on N of A_{2D}(Si)/A_{0}(Si) (Figure S3d–f), we found that this ratio is slightly smaller for N.A. = 0.5 than for N.A. = 0.9 and is in a better agreement with the model of Li and coworkers [31] (black solid line in Figure S3d–f). (Note that in this latter work the experimental data on which the model has been adjusted were recorded using a numerical aperture N.A. ≈ 0.45).
MoS_{2} flakes prepared by CVD
In this part, we analyze the pertinence of the previous criteria to derive the thickness of large MoS_{2} flakes synthesized by CVD. In a first part, we probe the effectiveness of these criteria to evaluate the thickness of large standard CVD MoS_{2} flakes. Such flakes have a limited number of defects and, like in exfoliated MoS_{2}, the stacking sequence is of the 2Hc type. In the second part, we examine the relevance of these criteria to evaluate the thickness of twisted CVD MoS_{2} flakes.
Standard CVD MoS_{2} flakes: As derived from the features of the LB and S ultralowfrequency modes, these samples do not show any twist between adjacent layers (presence of S modes for all flakes with N ≥ 2). The flakes are thus characterized by 2Hc stacking (or close to 2Hc stacking) and a low number of defects, and are named standard CVD MoS_{2} flakes. On the basis of the latter features, the structure of these flakes is close to that of exfoliated MoS_{2} flakes. However, the high temperature used in the CVD synthesis and interaction with the substrate can lead to lattice distortion and the presence of vacancies and doping. In the following, we limit our study to a number of layers N ≤ 4.
Figure 4a compares the values of Δω_{A−E} measured on exfoliated (Figure 4a, black symbols) and standard CVD MoS_{2} flakes (Figure 4a, red symbols) for N ≤ 4. As previously, the exact number of layers is obtained by combining optical microscopy, spectral reflectivity, and number and frequencies of LB and S modes. For both kinds of MoS_{2} flakes, Δω_{A−E} increases monotonously with N, but for the same N, the values of Δω_{A−E} are systematically larger in standard CVD MoS_{2} flakes. We attribute this discrepancy mainly to a difference of strain states between the two kinds of samples. Exfoliated samples are mostly found with low or slight compressive strain, while CVD samples are under tension. Other factors such as doping, defects, or stacking were shown to lead to large changes of Δω_{A−E} [44,46,49]. In summary, the value of Δω_{A−E} is clearly and significantly sampledependent. Consequently, Δω_{A−E} cannot be considered as a definitive criterion to derive the number of layers in any of MoS_{2} flakes prepared in different ways. In other words, one cannot define a single master curve, Δω_{A−E} vs N, which would be valid for all the MoS_{2} flakes independently of their preparation method or environment.
The dependencies on N of the normalized integrated intensities of A_{1g} and E^{1}_{2g} modes and the A_{2D}(Si)/A_{0}(Si) ratio measured on standard CVD flakes are compared with the average values of exfoliated samples with the same substrate SiO_{2} thickness (Figure 4b–d). In contrast to Δω_{A−E}, the N dependencies of these intensities are very close in exfoliated and standard CVD MoS_{2} flakes. Only A_{2D}(Si)/A_{0}(Si) and the normalized integrated intensity of the E^{1}_{2g} phonon modes slightly differ for N = 4. However, this may be due to the fact that the statistics is rather poor on this measurement, because this flake is rather small compared to the others. With regards to these results, these measurands give important information to evaluate the number of layers of 2Hcstacked MoS_{2} flakes independently of the elaboration procedure as long as N ≤ 4.
Twisted CVD MoS_{2} flakes: Other interesting samples are large CVD MoS_{2} flakes that present a twist angle, θ, between adjacent layers. We exemplify here the complexity to characterize such samples from the previous Raman criteria with the case of twisted MoS_{2} bilayers. The identification of the bilayer character of the investigated flakes was unambiguously obtained independently from spectral reflectivity and optical contrast.
Figure 5a shows the lowfrequency range of spectra recorded on three types of MoS_{2} bilayer (named 2LMoS_{2} in the following), namely a bilayer with θ ≈ 30° (this sample belongs to the socalled twistedbilayer family for which 0 < θ < 60° and is named in the following as θ2LMoS_{2}), the socalled 2Hc2LMoS_{2} and the socalled 3R2LMoS_{2}. In the latter structure, the stacking between two adjacent layers corresponds to a twist angle of θ = 0°, and it is such that the S atoms of the top monolayer are superimposed on the Mo atoms of the bottom monolayer, and the Mo atoms of the top monolayer are above the hexagon centers of the bottom monolayer [50]. The spectrum in the lowfrequency range is dominated by the contributions of the LB and S modes, the frequencies of these modes depending on the twist angle [20,39]. The LB mode emerges in the Raman spectra of all 2LMoS_{2} samples. In line with previous results [20], the Raman shift of the peak position of the LB mode in 3R2LMoS_{2} is smaller than that of the 2Hc2LMoS_{2}, and the LB mode Raman shift in 30°2LMoS_{2} is even smaller. Also, in agreement with the literature [20,3841], the S mode vanishes in 30°2LMoS_{2}.
In Figure 5b, the 130–240 cm^{−1} range of the Raman spectra recorded on monolayer, 2Hc2LMoS_{2}, and two θ2LMoS_{2} is displayed. As well documented in the literature, this frequency range is dominated by the contributions of secondorder Raman processes [20,26]. The general profile of the spectra is similar in 1LMoS_{2}, 2Hc2LMoS_{2}, and θ2LMoS_{2} with the exception that in the latter flakes, new bands, named FLA and FTA, are superimposed to the secondorder Raman spectra. The FLA and FTA modes in θ2LMoS_{2} are attributed, respectively, to folded longitudinal acoustic phonons and folded transverse acoustic phonons of the monolayer due to the presence of a moiré superlattice [20]. As shown in the literature [20], the frequencies of these modes depend on the twist angle (see Figure 2e in [20]). Unfortunately, these dependencies show a mirror behavior with respect to θ = 30°. This means that from given FLA and FTA positions, two values are possible: θ ∈ [0,30]° or its mirror 60° − θ. As a consequence, θ will be given in the range of 0–30° in all plots in Figure 6 with the possibility that the values attributed to θ2LMoS_{2} could be 60° − θ instead. For instance, the data from both 2Hc2LMoS_{2} and 3R2LMoS_{2} are reported at θ = 0° in these plots. From the positions of the FTA and FLA, we claim that the spectra of the two θ2LMoS_{2} displayed in Figure 5 correspond to 20°2LMoS_{2} (Figure 5b–d, solid green line) and 30°2LMoS_{2} (Figure 5a–d, solid red line), respectively.
The dependence of A_{1g} and E^{1}_{2g} modes on the twist angle (derived from the positions of FTA and FLA modes) is reported in Figure 5c. The frequency of the E^{1}_{2g} mode in 3R, 2Hc, and θ2LMoS_{2} is downshifted with respect to its frequency in 1LMoS_{2}, and it does not show a clear dependence on the twist angle. In contrast, the profile of the A_{1g} mode significantly depends on the twist angle, and a new mode, named FA′_{1}, appears on the highfrequency side of the A_{1g} mode. The FA′_{1} mode is identified as Raman scattering from moiré phonons associated with the A′_{1} dispersion curve of 1LMoS_{2}. It is folded onto the zone center and, consequently, becomes Raman active [20]. Obviously, its frequency depends on the twist angle and the θdependence of the FA′_{1} frequency was recently established both theoretically and experimentally (see Figure 3e in [20]). On the basis of these previous results, we have been able to evaluate the value of θ for each 2LMoS_{2} investigated from the position of the FA′_{1} mode. The values of the angles derived from the position of FTA/FLA and FA′_{1} are in close agreement.
The objective of this work is to characterize the thickness of all MoS_{2} flakes. The relevance of the criteria based on the frequency (Δω_{A−E}) and normalized integrated intensity (A(A_{1g})/A(Si_{111})) of the A_{1g} mode has to be reevaluated in twisted 2LMoS_{2} flakes. As shown in Figure 5d, the normalized intensity of the 521 cm^{−1} Si mode from the substrate underneath MoS_{2} flakes is close in all the 2LMoS_{2} and independent of the twist angle.
Figure 6 summarizes and details the dependence on the twist angle of the four Raman criteria defined above for 2LMoS_{2}. In all plots of Figure 6, the values of angles were derived from the positions of FTA, FLA and FA′_{1}. The values of the different criteria measured for θ2LMoS_{2} are compared with the average values of the same criteria measured on exfoliated 1L, 2L, and 3LMoS_{2} flakes. In θ2LMoS_{2}, the value of Δω_{A−E} strongly depends on the twist angle and significantly differs from the average value measured in 2Hc2LMoS_{2} (Figure 6a). For θ = 30°, the value of Δω_{A−E} is close to the one found in CVD 1LMoS_{2} [51]. In consequence, using Δω_{A−E} alone could lead to a wrong evaluation of the thickness of twisted 2LMoS_{2}.
The normalized integrated intensity A(A_{1g})/A(Si_{111}) significantly decreases when the twist angle increases (Figure 6b, red dots), and in 30°2LMoS_{2}, the value of A(A_{1g})/A(Si_{111}) is close to the average value found in 1LMoS_{2} (Figure 6b, blue solid line). The behavior of A(A_{1g})/A(Si_{111}) is opposite to the one of the normalized integrated intensity of the FA′_{1} mode, A(FA′_{1})/A(Si_{111}), the latter increasing with the twist angle (Figure 6b, gray squares). These results are in qualitative agreement with those reported in [40]. It can be emphasized that the integrated intensity of A_{1g} and FA′_{1} bands taken together (Figure 6b, orange triangles) is close to the average value found for 2Hc2LMoS_{2} (Figure 6b, red solid line). The reason for this compensation between A(A_{1g}) and A(FA′_{1}) is not clear yet, but it could present a practical advantage in the use of the global integrated intensity of the spectral band, located around the position of the A_{1g} mode for the evaluation of the thickness of twisted MoS_{2} flakes.
We also observed a tendency for A(E^{1}_{2g})/A(Si_{111}) to be slightly lower for θ2LMoS_{2} than for 2Hc2LMoS_{2} (or 3R2LMoS_{2}, which is similar), but to a lesser extent compared to A(A_{1g})/A(Si_{111}), that is ca. 20% vs ca. 50% at maximum, respectively (Figure 6d). These results are also in qualitative agreement with those reported in [40]. Finally, only the value of the A_{2D}(Si)/A_{0}(Si) ratio seems to provide a robust/reliable information to characterize the thickness of MoS_{2} flakes, since it is found largely independent of θ in all measured 2LMoS_{2} samples (Figure 6c). Even if further work is needed to complete the data presented here with other values of θ and twisted MoS_{2} samples with N > 2, we anticipate that the value of A_{2D}(Si)/A_{0}(Si) ratio would be close in twisted and 2Hcstacked MoS_{2} multilayers. However, as previously recalled, the sensitivity of this ratio to the SiO_{2} thickness and the gap between the A_{2D}(Si)/A_{0}(Si) ratios for N and N + 1 permit to ensure the determination of N with a rather good reliability only for N ≤ 5.
DLIPPCVD MoS_{2} nanoflakes
The aim of this part is to define which Raman information is relevant to estimate the thickness of MoS_{2} samples produced by DLIPPCVD. These samples are significantly different from the previous ones (exfoliated and standard CVD). Indeed, they are constituted of nanoflakes (with a lateral size of typically 50 nm, i.e., well below the laser spot size) with possibly a distribution of thicknesses and twist angles between adjacent layers of multilayer domains and a higher number of defects (the average interdefect distance ranges from 3 to 6 nm as estimated from the LA and A_{1g} intensity ratio [52]). In addition, the MoS_{2} surface coverage is a priori unknown and can be incomplete. It is then necessary to implement a first check criterion that ensures that the thickness estimation method based on the comparison with results obtained on exfoliated samples is still valid. More generally, this point is critical for the characterization of samples synthesized using new methods or new precursors that can lead to the codeposition of several byproducts (such as carbon, oxides, and metals), which can significantly change the measured Raman intensities. Based on the results presented in the previous sections, we have shown that the value of the A_{2D}(Si)/A_{0}(Si) ratio provides a robust/reliable Raman information to characterize the thickness of MoS_{2} flakes for N ≤ 5. However, this parameter does not rely unambiguously on the presence of MoS_{2}. The deposition of any other material would influence its value and could lead to a wrong estimation. In the most general case, the sample characteristics are not perfectly known and can be significantly different from the reference characteristics. As a consequence, it seems mandatory to compare the thickness estimated from the A_{2D}(Si)/A_{0}(Si) ratio with other measurands directly related to the presence of MoS_{2}. To this aim, we propose to use jointly the normalized integrated intensity of the MoS_{2} phonon modes, namely A(A_{1g})/A(Si_{111}) and/or A(E^{1}_{2g})/A(Si_{111}).
In Figure 7, the values of A(A_{1g})/A(Si_{111}) (Figure 7a) and A(E^{1}_{2g})/A(Si_{111}) (Figure 7b) are plotted as functions of the value of A_{2D}(Si)/A_{0}(Si). In these graphs, the data obtained on DLIPPCVD samples are compared with the average reference measurements established previously on exfoliated MoS_{2} deposited on Si/SiO_{2} substrate with the same SiO_{2} thicknesses, namely 96 nm (red open dots in Figure 7) and 87 nm (blue open dots in Figure 7). Note that in the exfoliated samples, the exact number of layers N is perfectly known and given on the plots of Figure 7 close to corresponding open dots. The idea behind this representation comes from the expectation that the presence of contaminations or deposition of others species would have a different impact on the Raman intensity coming from MoS_{2} in the film and on the one coming from the Si substrate underneath the deposited thin film. It is, thus, expected that the measurements on contaminated or highly defective MoS_{2} thin films will fall off the reference curve. Indeed, data obtained on poorly crystalline MoS_{2} films synthesized by DLI atomic layer deposition (not shown) are found systematically and significantly below the corresponding reference curve. Concerning the DLIPPCVD samples presented in Figure 7, the A(A_{1g})/A(Si_{111}) vs A_{2D}(Si)/A_{0}(Si) dependence is found fully compatible with the respective reference exfoliated curves (Figure 7a). The A(E^{1}_{2g})/A(Si_{111}) vs A_{2D}(Si)/A_{0}(Si) data points mainly agree for thin layers (A_{2D}(Si)/A_{0}(Si) > 0.8) but fall systematically below the corresponding reference exfoliated curves for thicker layers (0.8 > A_{2D}(Si)/A_{0}(Si) > 0.6) as shown in Figure 7b.
Another way to compare the results is estimating the thickness of DLIPPCVD samples by interpolation from exfoliated data of the measured values for A_{2D}(Si)/A_{0}(Si), A(A_{1g})/A(Si_{111}), and A(E^{1}_{2g})/A(Si_{111}). In Figure 8a (respectively 8b), the average number of layers () obtained using A(A_{1g})/A(Si_{111}) (respectively A(E^{1}_{2g})/A(Si_{111})) are plotted as a function of the number derived from A_{2D}(Si)/A_{0}(Si). It can be emphasized that noninteger values are found for , indicating the presence of a mix with unknown proportions of bare substrate (0L), 1LMoS_{2}, 2LMoS_{2}, 3LMoS_{2}, and so on in the investigated DLIPPCVD films. It is also noticeable that the errors of estimated from A(A_{1g})/A(Si_{111}) become larger when is close to 3 as a consequence of the smoother dependence of this parameter with . In agreement with the conclusion drawn above from Figure 7, Figure 8a illustrates the coherence between the values of derived from A(A_{1g})/A(Si_{111}) and A_{2D}(Si)/A_{0}(Si). All data remain close to the red solid line that represents the ideal relation y[ via A(A_{1g})/A(Si_{111})] = x[ via A_{2D}(Si)/A_{0}(Si)]. Figure 8b as well confirms that the values of derived from A(E^{1}_{2g})/A(Si_{111}) and A_{2D}(Si)/A_{0}(Si) agree well for < 1.5, but the values of from A(E^{1}_{2g})/A(Si_{111}) are systematically lower than those obtained from A_{2D}(Si)/A_{0}(Si) when > 1.5. One explanation could the presence of a larger proportion of multilayer regions in the thicker samples, for which, if they are twisted, A(E^{1}_{2g})/A(Si_{111}) has been shown to be attenuated in the previous section. If so, the question then arises why the same behavior is not observed for A(A_{1g})/A(Si_{111}) contrary to what would be expected. A possibility could be that because of the observed broadening of the A_{1g} mode in DLIPPCVD samples (presumably due to local heterogeneities in terms of doping, strain, defects, or thickness), the FA′_{1} mode becomes indistinguishable from the A_{1g} mode. As a consequence, the intensity of FA′_{1} would merge with A(A_{1g}) and compensate its attenuation. Other explanations relying on the presence of defects or strain cannot be disregarded, and further works are needed to fully clarify this point.
In order to further confirm the validity of the estimations of for DLIPPCVD samples, we compare in Figure 8c the values derived from A_{2D}(Si)/A_{0}(Si) with the ones obtained independently from spectral microreflectivity. A very good agreement is found between the two series of data, establishing definitively the relevance of the A_{2D}(Si)/A_{0}(Si) ratio to give with good accuracy the average thickness of DLIPPCVD MoS_{2} samples for ≤ 3. This agreement justifies the use of the values of derived from A_{2D}(Si)/A_{0}(Si) as abscissa axis in the previous plots.
Finally, in Figure 8d the frequency difference between the A_{1g} and E^{1}_{2g} phonons is plotted as a function of estimated from A_{2D}(Si)/A_{0}(Si) for DLIPPCVD samples and compared to the data obtained on exfoliated and CVD MoS_{2}. DLIPPCVD data are distributed between the two curves obtained from the reference samples. This further confirms that this measurand cannot be used to evaluate with good accuracy their average thicknesses. Nevertheless this comparison can be informative, showing that samples with < 1 are most certainly mainly composed of 1LMoS_{2} and suggesting that the proportions of 2LMoS_{2}, 3LMoS_{2}, or more gradually increase with , which is compatible with AFM observations (not shown).
To get further insight on the number of layer distributions in DLIPPCVD samples, we have measured their ULF modes. Representative ULF spectra are shown in Figure 9a for samples with average thicknesses ranging from 0.6 up to 2.8 MoS_{2} layers as estimated from A_{2D}(Si)/A_{0}(Si). Up to = 1.3, only the LB mode of 2LMoS_{2} is observed around 40 cm^{−1} [20,3841], showing that these samples can only be composed of 1LMoS_{2} and twisted 2LMoS_{2} plus possibly uncovered (bare substrate) regions. For thicker samples, the S mode of 2LMoS_{2} around 24 cm^{−1} is additionally visible, as well as a signal between 25 and 30 cm^{−1}, corresponding to the LB and S modes of 3LMoS_{2} [32,33]. For ≥ 2.4, the LB mode of 4LMoS_{2} is also present around 21 cm^{−1}; there may also be a weak signal around 17 cm^{−1} (corresponding to the LB mode of 5LMoS_{2}) reflecting the presence of 5LMoS_{2}. The S mode of 4LMoS_{2} could be present as well around 28 cm^{−1}, but it is hardly distinguishable from the LB and S modes of 3LMoS_{2}. Thus, ULF Raman spectra give valuable qualitative information on the different N present in each sample. Quantitative information relies on the determination of the surface coverages for each N (σ_{N}), that is, the ratio between the surface covered by exactly N layers and the total surface. With N = 0 standing for the bare substrate and N_{max} being the largest number of layers present in the sample, the definition of the average number of layers can be written as
and the total coverage (including bare substrate areas) is obviously 100%:
AFM imaging (see Supporting Information File 1, Figure S4) reveals that for > 1.25, the surface is fully covered by MoS_{2}, that is, σ_{0} = 0, which removes an unknown. In addition, for < 1.3, there is no signature of more than two layers, and we can set σ_{N}_{≥3} = 0 with confidence. Hence, for 1.25 < < 1.3, the set of Equations 1 and 2 simplifies to
This allows one to readily determine the two remaining unknowns σ_{1} and σ_{2}, since is known from A_{2D}(Si)/A_{0}(Si).
Hereafter, a linear relationship between the Raman signal , which is the LB mode peak intensity of 2L (N = 2) areas (the broad but wellidentified 40 cm^{−1} peak), and the surface coverage is assumed, namely σ_{2} = . The ratio α_{2} = is determined from five samples (1.25 < < 1.3) for which we now have both the coverage σ_{2} and the Raman signal .
Because α_{2} is now known and assuming that the linearity between σ_{2} and the Raman signal holds (which should be a good approximation for the thin multilayers considered here), σ_{2} = can be obtained directly for all samples from the Raman spectra, and is thus no longer an unknown.
We now turn to the samples with < 1.25, which may present some bare substrate areas, so σ_{0} and σ_{1} are a priori unknown. Both and σ_{2} are determined as explained above, and σ_{N}_{≥3} = 0 is again a safe estimate. Hence, Equations 1 and 2 reduce to the system
which may be solved trivially for σ_{0} and σ_{1}.
A similar approach can be used for samples with 1.3 < < 2 that are fully covered (σ_{0} = 0) and might present some trilayers but show no trace of thicker layers. We set σ_{N}_{≥4} = 0, and the system of equations reduces to
Both and σ_{2} are determined as explained above. Thus, the system can be trivially solved for the two remaining unknowns σ_{1} and σ_{3}.
At this point it would be natural to get the proportionality between σ_{3} and a Raman signal attributed to 3L areas (N = 3), and proceed recursively to obtain σ_{4} in slightly thicker layers, and so on and so forth. In practice this becomes challenging because of the uncertainty on the 3L (N = 3) Raman signal, which is less clear than the 2L (N = 2) peak. Another approach gave better results.
Three samples with between 2.75 and 2.85 are thick enough to neglect σ_{0} and σ_{1}, yet thin enough for σ_{5} to also be negligible as a first approximation. Equations 1 and 2 then reduce to
where and σ_{2} are known, so σ_{3} and σ_{4} can be determined readily.
The LB mode of 4LMoS_{2}, located around 21 cm^{−1}, is sufficiently separated from other modes to be identified (which was not the case for ), so that can be extracted from the spectra. From the three 2.75 < < 2.85 samples α_{4} = is determined. Then, assuming again a linear relationship σ_{4} = , the coverage by 4L (N = 4) layers can be determined for all samples. This removes another unknown.
Now the last remaining case of 2 < < 2.75 samples can be solved, as
give σ_{1} and σ_{3} directly, since , σ_{2} and σ_{4} are known.
The results obtained using this procedure are shown in Figure 9b where σ_{N} (with N from 0 to 4) is plotted as a function of , the average sample thickness. On this graph, all values of σ_{2} (respectively σ_{4}) are calculated using (respectively ) even for the samples used to derive the proportionality coefficient α_{2} (respectively α_{4}). As shown in Figure 9b for samples with 1.25 < < 1.3 (respectively 2.75 < <2.85), we find by this way −0.03 < σ_{0} < 0.04 (respectively −0.01 < σ_{1} < 0.01) with little fluctuations around the expected value of 0.
Just below the full coverage of the sample surface by MoS_{2} (σ_{0} > 0), both σ_{1} and σ_{2} increase with a slight tendency of σ_{2} to increase faster than σ_{1}. Indeed, 1LMoS_{2} represents 80–90% of the deposited MoS_{2} for = 0.5 and 70–80% for = 1.3. The maximum of σ_{1} is reached around = 1.3 when the sample surface is totally covered by MoS_{2} (σ_{0} = 0), and σ_{1} starts to decrease above this value. Around = 1.6, 1LMoS_{2} only represents 50% of the MoS_{2}. σ_{2} continues to increase and reaches a maximum value of ≈50% around = 2 and then decreases for thicker samples. 3LMoS_{2} starts to appear after the substrate surface is completely covered by MoS_{2} and increases continuously, representing about 50% of the thickest samples ( ≈ 2.8).
In order to verify our approach, we implemented a 2D growth toy model (see Supporting Information File 1 for details). The model results are shown in Figure 9b as full lines and give a good agreement with the experimental results. It should be noted that within this representation (σ_{N} = f()), the results of the model are remarkably robust to any parameter changes (the curves are almost insensitive to either doubling or halving the cell size and, thus, the advance rate, or to multiplying or dividing the growth rate by 5). In other words, this means that this comparison with the experiment cannot be used to validate any model parameters but demonstrates the relevance of the proposed procedure to estimate the σ_{N} from the experiments. Nevertheless, it has to be noted that while for < 1.3 the ULF Raman signature of 2LMoS_{2} remains very similar, it is not the case for thicker samples with the notable appearance of the S mode of 2LMoS_{2} around 24 cm^{−1} [32,33]. This could mean that the stacking order distribution changes. As a consequence, the hypothesis based on the proportionality between and σ_{2} would probably be less valid above = 1.3, and an error on the absolute values deduced can be expected. However, the appearance of the S mode of 2LMoS_{2} around 24 cm^{−1} could also be related to NLMoS_{2} (with N ≥ 3) constituted of a stacking sequence where 2L are not twisted, for example, the socalled t(1+2)L, t(2+2)L, … structures [26,53]. In this case, our hypothesis would remain more appropriate. Despite this unknown as well as the other approximations made, we believe that the main tendencies can still be captured by the proposed analysis. Further works are needed to determine and improve the accuracy of the method.
Conclusion
In this work we have reviewed all Raman information leading to the evaluation of the thickness of MoS_{2} flakes, that is, the layer number N. First, we have analyzed in detail the effects of some experimental parameters, namely the wavelength of the incident laser light used in the experiments, the power of the incident light, and the oxide thickness of the SiO_{2}/Si substrate on which the flakes are deposited, on the quality and accuracy of Raman results. Based on this analysis, an experimental protocol has been defined and systematically applied to large MoS_{2} flakes (i.e., singledomain flakes much larger than the laser spot), including twisted MoS_{2} flakes, prepared by different methods on the one hand and to MoS_{2} thin films composed of nanoflakes prepared by the DLIPPCVD method on the other hand. Special attention was paid to the measurement statistics.
The limits of different Raman criteria which allow one to determine the thicknesses of MoS_{2} flakes, namely (i) the value of Δω_{A−E}, (ii) the value of the normalized integrated intensity of A_{1g} and E^{1}_{2g} MoS_{2} modes, and (iii) the value of the A_{2D}(Si)/A_{0}(Si) ratio, have been precisely studied in the different types of MoS_{2} samples. We definitely confirm that Δω_{A−E} cannot be considered a robust criterion to derive the number of layers in MoS_{2} samples. We found that the value of the A_{2D}(Si)/A_{0}(Si) ratio provides the most robust/reliable information to characterize the thickness of MoS_{2} large flakes, especially since it is found largely independent of the twist angle. The limit of application of this criterion is N ≤ 5, under the condition that the SiO_{2} thickness is precisely known.
We then apply this analysis procedure to DLIPPCVD samples constituted of nanoflakes with a lateral size of typically 50 nm (well below the laser spot size) with possibly a distribution of thicknesses and twist angles between adjacent layers of multilayer domains and a higher number of defects. Our results definitively establish the relevance of the A_{2D}(Si)/A_{0}(Si) ratio to give with good accuracy their average thickness , for ≤ 3. Nevertheless, we emphasize that this criterion is not only related to the presence of MoS_{2} and can be influenced by several factors, such as the codeposition of byproducts or the presence of defects, leading to a wrong estimation of . We propose to combine A_{2D}(Si)/A_{0}(Si) with the normalized integrated intensity of the MoS_{2} phonon modes, namely A(A_{1g}) and/or A(E^{1}_{2g}). Although limiting the application to ≤ 3, this approach enables the validation of the A_{2D}(Si)/A_{0}(Si) ratio to determine in the presented case, and we anticipate that it would avoid possible errors in unfavorable situations.
Finally, to get further insight on the number of layer distributions in DLIPPCVD samples, we have measured their ULF modes. An original procedure based of the measurement of the intensity of the layer breathing modes allows one to evaluate the surface coverage (σ_{N}) for each N. A 2D growth toy model gives a good agreement with the experimental results supporting the proposed procedure to estimate the σ_{N} from the ULF spectra.
Experimental
Samples preparation
Mechanical exfoliation
MoS_{2} flakes were obtained by micromechanical cleavage of a MoS_{2} crystal (HQ graphene) using scotch tape (Nitto) and PDMS slabs (Gelpak). They were then transferred onto Si substrates with SiO_{2} layers of different thicknesses, namely 84, 87, 90, and 96 nm. Flakes were selected by optical microscopy and their thicknesses were determined by optical contrast.
Standard CVD process
MoS_{2} was grown by CVD on 87 nm SiO_{2} on Si substrates using MoO_{3} (SigmaAldrich, 25 mg) and sulfur (SigmaAldrich, 250 mg) powders as solid precursors using a 1 inch quartz tube furnace. MoO_{3} powder was placed in the center of the heating zone of the furnace, while sulfur was placed upstream at the furnace inlet. Prior to growth, air was evacuated by flowing Ar (ultrahigh purity, Linde) for 15 min at 200 sccm, after which the tube was heated to 200 °C for 10 min. The temperature was then increased to 750 °C under Ar (100 sccm), and it was held at this value for 15 min before cooling naturally to room temperature.
Directliquid injection pulsedpressure chemical vapor deposition (DLIPPCVD)
The 12 × 11 mm SiO_{2}/Si (with 87 nm or 96 nm SiO_{2} thicknesses) substrates were cleaned in acetone (C_{3}H_{6}O, technical, Acros Organics), isopropanol (C_{3}H_{7}OH, 99.8%, Höfer Chemie GmbH) and deionized water (H_{2}O, Acros Organics) under ultrasonic agitation for 10 min each, before being blown dry with nitrogen. They were then immediately loaded on the susceptor of the reaction chamber (Annealsys MC050) for deposition. Solutions of 0.001 M molybdenum hexacarbonyl (Mo(CO)_{6}, 98%, Strem Chemicals) and 0.002 M sulfur (S, 99.999%, Acros Organics) in anhydrous toluene (C_{6}H_{5}CH_{3}, 99.8%, SigmaAldrich) were used as precursors. The process is as follows: Following sample installation, the chamber is closed and brought to about 0.02 mbar. For monolayer depositions, it is imperative that the substrate is thoroughly cleaned and free of adsorbates. Therefore, to ensure complete desorption of remaining contaminants, the samples were kept for 30 min under vacuum at room temperature inside the deposition chamber. For the first part of the process, the pumping direction is reversed so that all species are pumped from the deposition chamber to the back of the reactor.
Nitrogen (800 sccm) is flowed through the chamber (200 sccm through the gas line, and 600 sccm through two injection heads) and the substrates are brought to 750 °C at a ramp of 2 °C/s. The reactor is kept in this state for 5 min for homogenization purposes. While still in reverse direction pumping, 0.3 g/min of both precursors are injected and vaporized to prepare the evaporation system for deposition. Then, the Mo(CO)_{6} injection is stopped, the pumping direction is switched back to the deposition direction and hydrogen (40 sccm) is added to the gas mix. For 1 min, sulfur is injected to clean any remaining contaminants, and to prepare the surface of the substrate for MoS_{2} deposition, then the deposition works in 20 s cycles. During one cycle, a single pulse of 3 to 10 ms of Mo(CO)_{6} is injected while the S injection is set to 0.3 g/min. This 20 s cycle is repeated 80 to 160 times. The quantity of MoS_{2} deposited is controlled by the quantity of Mo(CO)_{6} injected, that is, the pulse duration and the number of cycles.
Raman spectroscopy
Raman spectra and maps were recorded using an Acton spectrometer fitted with a Pylon CCD detector and a 1800 grooves/mm grating (≈0.6 cm^{−1} between each CCD pixel). The samples were excited with a 532 nm (2.33 eV) laser (Newport Millennia Prime or Cobolt Samba) throughan Olympus microscope objective either 100× (numerical aperture 0.9) or 50× (numerical aperture 0.5). The full width at halfmaximum (FWHM) of the focused laser spot with the 100× objective is about 380 nm. Optimized focus conditions were checked for each measurement. The samples were mounted on a threeaxis piezoelectric stage (Physik Instrumente) to ensure the precise positioning and focusing of the laser spot. A Si(111) wafer with only native oxide sample was used as a daily reference for the system. The laser power was continuously measured during acquisitions allowing for intensity normalizations of the Raman spectra at each point of the maps. All data presented in this paper, unless specified otherwise, are extracted from Raman maps constituted by hundreds to thousands points (see Supporting Information File 1 for an example), which were analyzed using a custommade software. All reported points are the average values obtained by Gaussian fitting of the data distribution extracted from Raman maps (corresponding to hundreds to several thousands of spectra), and the error bars correspond to 99.7% confidence intervals (±3 standard deviations).
2D growth toy model
The model used the DynamicGrids.jl package, which was part of the Dispersal.jl framework [54], see Supporting Information File 1 for more details.
Supporting Information
Supporting Information File 1 contains additional figures with an example of Raman maps, the Si mode as a function of the laser power, a comparison between two microscope objectives, other intensity references, atomic force microscopy images, and details of the 2D growth toy model. Supporting Information File 2 is a recording of the growth simulation.
Supporting Information File 1: Additional experimental data.  
Format: PDF  Size: 839.3 KB  Download 
Supporting Information File 2: Recording of the growth simulation.  
Format: MP4  Size: 8.9 MB  Download 
References

Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 10451–10453. doi:10.1073/pnas.0502848102
Return to citation in text: [1] [2] 
Gibney, E. Nature 2015, 522, 274–276. doi:10.1038/522274a
Return to citation in text: [1] 
Lin, Z.; McCreary, A.; Briggs, N.; Subramanian, S.; Zhang, K.; Sun, Y.; Li, X.; Borys, N. J.; Yuan, H.; FullertonShirey, S. K.; Chernikov, A.; Zhao, H.; McDonnell, S.; Lindenberg, A. M.; Xiao, K.; LeRoy, B. J.; Drndić, M.; Hwang, J. C. M.; Park, J.; Chhowalla, M.; Schaak, R. E.; Javey, A.; Hersam, M. C.; Robinson, J.; Terrones, M. 2D Mater. 2016, 3, 042001. doi:10.1088/20531583/3/4/042001
Return to citation in text: [1] 
Withers, F.; Del PozoZamudio, O.; Mishchenko, A.; Rooney, A. P.; Gholinia, A.; Watanabe, K.; Taniguchi, T.; Haigh, S. J.; Geim, A. K.; Tartakovskii, A. I.; Novoselov, K. S. Nat. Mater. 2015, 14, 301–306. doi:10.1038/nmat4205
Return to citation in text: [1] 
Jariwala, D.; Sangwan, V. K.; Lauhon, L. J.; Marks, T. J.; Hersam, M. C. ACS Nano 2014, 8, 1102–1120. doi:10.1021/nn500064s
Return to citation in text: [1] 
Georgiou, T.; Jalil, R.; Belle, B. D.; Britnell, L.; Gorbachev, R. V.; Morozov, S. V.; Kim, Y.J.; Gholinia, A.; Haigh, S. J.; Makarovsky, O.; Eaves, L.; Ponomarenko, L. A.; Geim, A. K.; Novoselov, K. S.; Mishchenko, A. Nat. Nanotechnol. 2013, 8, 100–103. doi:10.1038/nnano.2012.224
Return to citation in text: [1] 
Wang, H.; Yu, L.; Lee, Y.H.; Shi, Y.; Hsu, A.; Chin, M. L.; Li, L.J.; Dubey, M.; Kong, J.; Palacios, T. Nano Lett. 2012, 12, 4674–4680. doi:10.1021/nl302015v
Return to citation in text: [1] 
Baugher, B. W. H.; Churchill, H. O. H.; Yang, Y.; JarilloHerrero, P. Nat. Nanotechnol. 2014, 9, 262–267. doi:10.1038/nnano.2014.25
Return to citation in text: [1] 
Zhang, Y. J.; Oka, T.; Suzuki, R.; Ye, J. T.; Iwasa, Y. Science 2014, 344, 725–728. doi:10.1126/science.1251329
Return to citation in text: [1] 
Wang, Q. H.; KalantarZadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. Nat. Nanotechnol. 2012, 7, 699–712. doi:10.1038/nnano.2012.193
Return to citation in text: [1] [2] 
Calman, E. V.; Fogler, M. M.; Butov, L. V.; Hu, S.; Mishchenko, A.; Geim, A. K. Nat. Commun. 2018, 9, 1895. doi:10.1038/s41467018042937
Return to citation in text: [1] 
Rivera, P.; Schaibley, J. R.; Jones, A. M.; Ross, J. S.; Wu, S.; Aivazian, G.; Klement, P.; Seyler, K.; Clark, G.; Ghimire, N. J.; Yan, J.; Mandrus, D. G.; Yao, W.; Xu, X. Nat. Commun. 2015, 6, 6242. doi:10.1038/ncomms7242
Return to citation in text: [1] 
Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Phys. Rev. Lett. 2010, 105, 136805. doi:10.1103/physrevlett.105.136805
Return to citation in text: [1] [2] 
Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C.Y.; Galli, G.; Wang, F. Nano Lett. 2010, 10, 1271–1275. doi:10.1021/nl903868w
Return to citation in text: [1] [2] 
Huang, S.; Ling, X.; Liang, L.; Kong, J.; Terrones, H.; Meunier, V.; Dresselhaus, M. S. Nano Lett. 2014, 14, 5500–5508. doi:10.1021/nl5014597
Return to citation in text: [1] 
Scheuschner, N.; Ochedowski, O.; Kaulitz, A.M.; Gillen, R.; Schleberger, M.; Maultzsch, J. Phys. Rev. B 2014, 89, 125406. doi:10.1103/physrevb.89.125406
Return to citation in text: [1] 
Eda, G.; Yamaguchi, H.; Voiry, D.; Fujita, T.; Chen, M.; Chhowalla, M. Nano Lett. 2011, 11, 5111–5116. doi:10.1021/nl201874w
Return to citation in text: [1] 
RibeiroSoares, J.; Almeida, R. M.; Barros, E. B.; Araujo, P. T.; Dresselhaus, M. S.; Cançado, L. G.; Jorio, A. Phys. Rev. B 2014, 90, 115438. doi:10.1103/physrevb.90.115438
Return to citation in text: [1] 
Wilson, J. A.; Yoffe, A. D. Adv. Phys. 1969, 18, 193–335. doi:10.1080/00018736900101307
Return to citation in text: [1] 
Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006
Return to citation in text: [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] 
Cao, Y.; Fatemi, V.; Fang, S.; Watanabe, K.; Taniguchi, T.; Kaxiras, E.; JarilloHerrero, P. Nature 2018, 556, 43–50. doi:10.1038/nature26160
Return to citation in text: [1] 
Yankowitz, M.; Chen, S.; Polshyn, H.; Zhang, Y.; Watanabe, K.; Taniguchi, T.; Graf, D.; Young, A. F.; Dean, C. R. Science 2019, 363, 1059–1064. doi:10.1126/science.aav1910
Return to citation in text: [1] 
Autere, A.; Jussila, H.; Dai, Y.; Wang, Y.; Lipsanen, H.; Sun, Z. Adv. Mater. (Weinheim, Ger.) 2018, 30, 1705963. doi:10.1002/adma.201705963
Return to citation in text: [1] 
Hsu, W.T.; Zhao, Z.A.; Li, L.J.; Chen, C.H.; Chiu, M.H.; Chang, P.S.; Chou, Y.C.; Chang, W.H. ACS Nano 2014, 8, 2951–2958. doi:10.1021/nn500228r
Return to citation in text: [1] 
Yu, H.; Liu, G.B.; Tang, J.; Xu, X.; Yao, W. Sci. Adv. 2017, 3, e1701696. doi:10.1126/sciadv.1701696
Return to citation in text: [1] 
Zhang, X.; Qiao, X.F.; Shi, W.; Wu, J.B.; Jiang, D.S.; Tan, P.H. Chem. Soc. Rev. 2015, 44, 2757–2785. doi:10.1039/c4cs00282b
Return to citation in text: [1] [2] [3] [4] [5] [6] 
Astié, V.; WasemKlein, F.; Makhlouf, H.; Paillet, M.; Huntzinger, J.R.; Sauvajol, J.L.; Zahab, A.A.; Juillaguet, S.; Contreras, S.; Voiry, D.; Landois, P., in press.
Return to citation in text: [1] 
Li, S.L.; Miyazaki, H.; Song, H.; Kuramochi, H.; Nakaharai, S.; Tsukagoshi, K. ACS Nano 2012, 6, 7381–7388. doi:10.1021/nn3025173
Return to citation in text: [1] [2] [3] 
Lee, C.; Yan, H.; Brus, L. E.; Heinz, T. F.; Hone, J.; Ryu, S. ACS Nano 2010, 4, 2695–2700. doi:10.1021/nn1003937
Return to citation in text: [1] [2] [3] 
MolinaSanchez, A.; Wirtz, L. Phys. Rev. B 2011, 84, 155413. doi:10.1103/physrevb.84.155413
Return to citation in text: [1] [2] [3] 
Li, X.L.; Qiao, X.F.; Han, W.P.; Zhang, X.; Tan, Q.H.; Chen, T.; Tan, P.H. Nanotechnology 2016, 27, 145704. doi:10.1088/09574484/27/14/145704
Return to citation in text: [1] [2] [3] [4] [5] [6] 
Zhao, Y.; Luo, X.; Li, H.; Zhang, J.; Araujo, P. T.; Gan, C. K.; Wu, J.; Zhang, H.; Quek, S. Y.; Dresselhaus, M. S.; Xiong, Q. Nano Lett. 2013, 13, 1007–1015. doi:10.1021/nl304169w
Return to citation in text: [1] [2] [3] [4] [5] 
Zhang, X.; Han, W. P.; Wu, J. B.; Milana, S.; Lu, Y.; Li, Q. Q.; Ferrari, A. C.; Tan, P. H. Phys. Rev. B 2013, 87, 115413. doi:10.1103/physrevb.87.115413
Return to citation in text: [1] [2] [3] [4] [5] [6] 
Lee, J.U.; Cheong, H. J. Raman Spectrosc. 2018, 49, 66–75. doi:10.1002/jrs.5200
Return to citation in text: [1] [2] [3] 
Drapcho, S. G.; Kim, J.; Hong, X.; Jin, C.; Shi, S.; Tongay, S.; Wu, J.; Wang, F. Phys. Rev. B 2017, 95, 165417. doi:10.1103/physrevb.95.165417
Return to citation in text: [1] [2] [3] 
Carvalho, B. R.; Malard, L. M.; Alves, J. M.; Fantini, C.; Pimenta, M. A. Phys. Rev. Lett. 2016, 116, 089904. doi:10.1103/physrevlett.116.089904
Return to citation in text: [1] [2] 
Nemanich, R. J.; Tsai, C. C.; Connell, G. A. N. Phys. Rev. Lett. 1980, 44, 273–276. doi:10.1103/physrevlett.44.273
Return to citation in text: [1] 
Lui, C. H.; Ye, Z.; Ji, C.; Chiu, K.C.; Chou, C.T.; Andersen, T. I.; MeansShively, C.; Anderson, H.; Wu, J.M.; Kidd, T.; Lee, Y.H.; He, R. Phys. Rev. B 2015, 91, 165403. doi:10.1103/physrevb.91.165403
Return to citation in text: [1] [2] [3] 
Huang, S.; Liang, L.; Ling, X.; Puretzky, A. A.; Geohegan, D. B.; Sumpter, B. G.; Kong, J.; Meunier, V.; Dresselhaus, M. S. Nano Lett. 2016, 16, 1435–1444. doi:10.1021/acs.nanolett.5b05015
Return to citation in text: [1] [2] [3] [4] 
Liao, M.; Wei, Z.; Du, L.; Wang, Q.; Tang, J.; Yu, H.; Wu, F.; Zhao, J.; Xu, X.; Han, B.; Liu, K.; Gao, P.; Polcar, T.; Sun, Z.; Shi, D.; Yang, R.; Zhang, G. Nat. Commun. 2020, 11, 2153. doi:10.1038/s41467020160564
Return to citation in text: [1] [2] [3] [4] [5] 
Quan, J.; Linhart, L.; Lin, M.L.; Lee, D.; Zhu, J.; Wang, C.Y.; Hsu, W.T.; Choi, J.; Embley, J.; Young, C.; Taniguchi, T.; Watanabe, K.; Shih, C.K.; Lai, K.; MacDonald, A. H.; Tan, P.H.; Libisch, F.; Li, X. Nat. Mater. 2021, 20, 1100–1105. doi:10.1038/s41563021009601
Return to citation in text: [1] [2] [3] 
Tiberj, A.; RubioRoy, M.; Paillet, M.; Huntzinger, J.R.; Landois, P.; Mikolasek, M.; Contreras, S.; Sauvajol, J.L.; Dujardin, E.; Zahab, A.A. Sci. Rep. 2013, 3, 2355. doi:10.1038/srep02355
Return to citation in text: [1] [2] 
Yan, R.; Simpson, J. R.; Bertolazzi, S.; Brivio, J.; Watson, M.; Wu, X.; Kis, A.; Luo, T.; Hight Walker, A. R.; Xing, H. G. ACS Nano 2014, 8, 986–993. doi:10.1021/nn405826k
Return to citation in text: [1] [2] [3] 
MelnikovaKominkova, Z.; Jurkova, K.; Vales, V.; DrogowskaHorná, K.; Frank, O.; Kalbac, M. Phys. Chem. Chem. Phys. 2019, 21, 25700–25706. doi:10.1039/c9cp04993b
Return to citation in text: [1] [2] [3] [4] [5] 
Lee, T.; Choi, J.H.; Ahn, J.H.; Yoon, Y.G.; Rho, H. Appl. Surf. Sci. 2022, 579, 152208. doi:10.1016/j.apsusc.2021.152208
Return to citation in text: [1] 
Liu, K.; Zhang, L.; Cao, T.; Jin, C.; Qiu, D.; Zhou, Q.; Zettl, A.; Yang, P.; Louie, S. G.; Wang, F. Nat. Commun. 2014, 5, 4966. doi:10.1038/ncomms5966
Return to citation in text: [1] [2] 
Rice, C.; Young, R. J.; Zan, R.; Bangert, U.; Wolverson, D.; Georgiou, T.; Jalil, R.; Novoselov, K. S. Phys. Rev. B 2013, 87, 081307. doi:10.1103/physrevb.87.081307
Return to citation in text: [1] 
Li, Z.; Lv, Y.; Ren, L.; Li, J.; Kong, L.; Zeng, Y.; Tao, Q.; Wu, R.; Ma, H.; Zhao, B.; Wang, D.; Dang, W.; Chen, K.; Liao, L.; Duan, X.; Duan, X.; Liu, Y. Nat. Commun. 2020, 11, 1151. doi:10.1038/s41467020150233
Return to citation in text: [1] 
CortijoCampos, S.; Prieto, C.; De Andrés, A. Nanomaterials 2022, 12, 1330. doi:10.3390/nano12081330
Return to citation in text: [1] [2] 
Liu, Q.; Li, L.; Li, Y.; Gao, Z.; Chen, Z.; Lu, J. J. Phys. Chem. C 2012, 116, 21556–21562. doi:10.1021/jp307124d
Return to citation in text: [1] 
Debnath, R.; Maity, I.; Biswas, R.; Raghunathan, V.; Jain, M.; Ghosh, A. Nanoscale 2020, 12, 17272–17280. doi:10.1039/c9nr09897f
Return to citation in text: [1] 
Mignuzzi, S.; Pollard, A. J.; Bonini, N.; Brennan, B.; Gilmore, I. S.; Pimenta, M. A.; Richards, D.; Roy, D. Phys. Rev. B 2015, 91, 195411. doi:10.1103/physrevb.91.195411
Return to citation in text: [1] 
Zhou, X.; Jin, K.; Cong, X.; Tan, Q.; Li, J.; Liu, D.; Luo, J. J. Colloid Interface Sci. 2019, 538, 159–164. doi:10.1016/j.jcis.2018.11.032
Return to citation in text: [1] 
Maino, J. L.; Schouten, R.; Umina, P. J. Appl. Ecol. 2021, 58, 789–800. doi:10.1111/13652664.13812
Return to citation in text: [1]
43.  Yan, R.; Simpson, J. R.; Bertolazzi, S.; Brivio, J.; Watson, M.; Wu, X.; Kis, A.; Luo, T.; Hight Walker, A. R.; Xing, H. G. ACS Nano 2014, 8, 986–993. doi:10.1021/nn405826k 
43.  Yan, R.; Simpson, J. R.; Bertolazzi, S.; Brivio, J.; Watson, M.; Wu, X.; Kis, A.; Luo, T.; Hight Walker, A. R.; Xing, H. G. ACS Nano 2014, 8, 986–993. doi:10.1021/nn405826k 
44.  MelnikovaKominkova, Z.; Jurkova, K.; Vales, V.; DrogowskaHorná, K.; Frank, O.; Kalbac, M. Phys. Chem. Chem. Phys. 2019, 21, 25700–25706. doi:10.1039/c9cp04993b 
34.  Lee, J.U.; Cheong, H. J. Raman Spectrosc. 2018, 49, 66–75. doi:10.1002/jrs.5200 
32.  Zhao, Y.; Luo, X.; Li, H.; Zhang, J.; Araujo, P. T.; Gan, C. K.; Wu, J.; Zhang, H.; Quek, S. Y.; Dresselhaus, M. S.; Xiong, Q. Nano Lett. 2013, 13, 1007–1015. doi:10.1021/nl304169w 
33.  Zhang, X.; Han, W. P.; Wu, J. B.; Milana, S.; Lu, Y.; Li, Q. Q.; Ferrari, A. C.; Tan, P. H. Phys. Rev. B 2013, 87, 115413. doi:10.1103/physrevb.87.115413 
34.  Lee, J.U.; Cheong, H. J. Raman Spectrosc. 2018, 49, 66–75. doi:10.1002/jrs.5200 
44.  MelnikovaKominkova, Z.; Jurkova, K.; Vales, V.; DrogowskaHorná, K.; Frank, O.; Kalbac, M. Phys. Chem. Chem. Phys. 2019, 21, 25700–25706. doi:10.1039/c9cp04993b 
1.  Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 10451–10453. doi:10.1073/pnas.0502848102 
44.  MelnikovaKominkova, Z.; Jurkova, K.; Vales, V.; DrogowskaHorná, K.; Frank, O.; Kalbac, M. Phys. Chem. Chem. Phys. 2019, 21, 25700–25706. doi:10.1039/c9cp04993b 
43.  Yan, R.; Simpson, J. R.; Bertolazzi, S.; Brivio, J.; Watson, M.; Wu, X.; Kis, A.; Luo, T.; Hight Walker, A. R.; Xing, H. G. ACS Nano 2014, 8, 986–993. doi:10.1021/nn405826k 
45.  Lee, T.; Choi, J.H.; Ahn, J.H.; Yoon, Y.G.; Rho, H. Appl. Surf. Sci. 2022, 579, 152208. doi:10.1016/j.apsusc.2021.152208 
42.  Tiberj, A.; RubioRoy, M.; Paillet, M.; Huntzinger, J.R.; Landois, P.; Mikolasek, M.; Contreras, S.; Sauvajol, J.L.; Dujardin, E.; Zahab, A.A. Sci. Rep. 2013, 3, 2355. doi:10.1038/srep02355 
26.  Zhang, X.; Qiao, X.F.; Shi, W.; Wu, J.B.; Jiang, D.S.; Tan, P.H. Chem. Soc. Rev. 2015, 44, 2757–2785. doi:10.1039/c4cs00282b 
29.  Lee, C.; Yan, H.; Brus, L. E.; Heinz, T. F.; Hone, J.; Ryu, S. ACS Nano 2010, 4, 2695–2700. doi:10.1021/nn1003937 
30.  MolinaSanchez, A.; Wirtz, L. Phys. Rev. B 2011, 84, 155413. doi:10.1103/physrevb.84.155413 
44.  MelnikovaKominkova, Z.; Jurkova, K.; Vales, V.; DrogowskaHorná, K.; Frank, O.; Kalbac, M. Phys. Chem. Chem. Phys. 2019, 21, 25700–25706. doi:10.1039/c9cp04993b 
46.  Liu, K.; Zhang, L.; Cao, T.; Jin, C.; Qiu, D.; Zhou, Q.; Zettl, A.; Yang, P.; Louie, S. G.; Wang, F. Nat. Commun. 2014, 5, 4966. doi:10.1038/ncomms5966 
47.  Rice, C.; Young, R. J.; Zan, R.; Bangert, U.; Wolverson, D.; Georgiou, T.; Jalil, R.; Novoselov, K. S. Phys. Rev. B 2013, 87, 081307. doi:10.1103/physrevb.87.081307 
48.  Li, Z.; Lv, Y.; Ren, L.; Li, J.; Kong, L.; Zeng, Y.; Tao, Q.; Wu, R.; Ma, H.; Zhao, B.; Wang, D.; Dang, W.; Chen, K.; Liao, L.; Duan, X.; Duan, X.; Liu, Y. Nat. Commun. 2020, 11, 1151. doi:10.1038/s41467020150233 
49.  CortijoCampos, S.; Prieto, C.; De Andrés, A. Nanomaterials 2022, 12, 1330. doi:10.3390/nano12081330 
31.  Li, X.L.; Qiao, X.F.; Han, W.P.; Zhang, X.; Tan, Q.H.; Chen, T.; Tan, P.H. Nanotechnology 2016, 27, 145704. doi:10.1088/09574484/27/14/145704 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
38.  Lui, C. H.; Ye, Z.; Ji, C.; Chiu, K.C.; Chou, C.T.; Andersen, T. I.; MeansShively, C.; Anderson, H.; Wu, J.M.; Kidd, T.; Lee, Y.H.; He, R. Phys. Rev. B 2015, 91, 165403. doi:10.1103/physrevb.91.165403 
39.  Huang, S.; Liang, L.; Ling, X.; Puretzky, A. A.; Geohegan, D. B.; Sumpter, B. G.; Kong, J.; Meunier, V.; Dresselhaus, M. S. Nano Lett. 2016, 16, 1435–1444. doi:10.1021/acs.nanolett.5b05015 
40.  Liao, M.; Wei, Z.; Du, L.; Wang, Q.; Tang, J.; Yu, H.; Wu, F.; Zhao, J.; Xu, X.; Han, B.; Liu, K.; Gao, P.; Polcar, T.; Sun, Z.; Shi, D.; Yang, R.; Zhang, G. Nat. Commun. 2020, 11, 2153. doi:10.1038/s41467020160564 
41.  Quan, J.; Linhart, L.; Lin, M.L.; Lee, D.; Zhu, J.; Wang, C.Y.; Hsu, W.T.; Choi, J.; Embley, J.; Young, C.; Taniguchi, T.; Watanabe, K.; Shih, C.K.; Lai, K.; MacDonald, A. H.; Tan, P.H.; Libisch, F.; Li, X. Nat. Mater. 2021, 20, 1100–1105. doi:10.1038/s41563021009601 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
26.  Zhang, X.; Qiao, X.F.; Shi, W.; Wu, J.B.; Jiang, D.S.; Tan, P.H. Chem. Soc. Rev. 2015, 44, 2757–2785. doi:10.1039/c4cs00282b 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
39.  Huang, S.; Liang, L.; Ling, X.; Puretzky, A. A.; Geohegan, D. B.; Sumpter, B. G.; Kong, J.; Meunier, V.; Dresselhaus, M. S. Nano Lett. 2016, 16, 1435–1444. doi:10.1021/acs.nanolett.5b05015 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
44.  MelnikovaKominkova, Z.; Jurkova, K.; Vales, V.; DrogowskaHorná, K.; Frank, O.; Kalbac, M. Phys. Chem. Chem. Phys. 2019, 21, 25700–25706. doi:10.1039/c9cp04993b 
46.  Liu, K.; Zhang, L.; Cao, T.; Jin, C.; Qiu, D.; Zhou, Q.; Zettl, A.; Yang, P.; Louie, S. G.; Wang, F. Nat. Commun. 2014, 5, 4966. doi:10.1038/ncomms5966 
49.  CortijoCampos, S.; Prieto, C.; De Andrés, A. Nanomaterials 2022, 12, 1330. doi:10.3390/nano12081330 
50.  Liu, Q.; Li, L.; Li, Y.; Gao, Z.; Chen, Z.; Lu, J. J. Phys. Chem. C 2012, 116, 21556–21562. doi:10.1021/jp307124d 
31.  Li, X.L.; Qiao, X.F.; Han, W.P.; Zhang, X.; Tan, Q.H.; Chen, T.; Tan, P.H. Nanotechnology 2016, 27, 145704. doi:10.1088/09574484/27/14/145704 
31.  Li, X.L.; Qiao, X.F.; Han, W.P.; Zhang, X.; Tan, Q.H.; Chen, T.; Tan, P.H. Nanotechnology 2016, 27, 145704. doi:10.1088/09574484/27/14/145704 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
1.  Novoselov, K. S.; Jiang, D.; Schedin, F.; Booth, T. J.; Khotkevich, V. V.; Morozov, S. V.; Geim, A. K. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 10451–10453. doi:10.1073/pnas.0502848102 
2.  Gibney, E. Nature 2015, 522, 274–276. doi:10.1038/522274a 
3.  Lin, Z.; McCreary, A.; Briggs, N.; Subramanian, S.; Zhang, K.; Sun, Y.; Li, X.; Borys, N. J.; Yuan, H.; FullertonShirey, S. K.; Chernikov, A.; Zhao, H.; McDonnell, S.; Lindenberg, A. M.; Xiao, K.; LeRoy, B. J.; Drndić, M.; Hwang, J. C. M.; Park, J.; Chhowalla, M.; Schaak, R. E.; Javey, A.; Hersam, M. C.; Robinson, J.; Terrones, M. 2D Mater. 2016, 3, 042001. doi:10.1088/20531583/3/4/042001 
10.  Wang, Q. H.; KalantarZadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. Nat. Nanotechnol. 2012, 7, 699–712. doi:10.1038/nnano.2012.193 
33.  Zhang, X.; Han, W. P.; Wu, J. B.; Milana, S.; Lu, Y.; Li, Q. Q.; Ferrari, A. C.; Tan, P. H. Phys. Rev. B 2013, 87, 115413. doi:10.1103/physrevb.87.115413 
34.  Lee, J.U.; Cheong, H. J. Raman Spectrosc. 2018, 49, 66–75. doi:10.1002/jrs.5200 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
38.  Lui, C. H.; Ye, Z.; Ji, C.; Chiu, K.C.; Chou, C.T.; Andersen, T. I.; MeansShively, C.; Anderson, H.; Wu, J.M.; Kidd, T.; Lee, Y.H.; He, R. Phys. Rev. B 2015, 91, 165403. doi:10.1103/physrevb.91.165403 
39.  Huang, S.; Liang, L.; Ling, X.; Puretzky, A. A.; Geohegan, D. B.; Sumpter, B. G.; Kong, J.; Meunier, V.; Dresselhaus, M. S. Nano Lett. 2016, 16, 1435–1444. doi:10.1021/acs.nanolett.5b05015 
40.  Liao, M.; Wei, Z.; Du, L.; Wang, Q.; Tang, J.; Yu, H.; Wu, F.; Zhao, J.; Xu, X.; Han, B.; Liu, K.; Gao, P.; Polcar, T.; Sun, Z.; Shi, D.; Yang, R.; Zhang, G. Nat. Commun. 2020, 11, 2153. doi:10.1038/s41467020160564 
41.  Quan, J.; Linhart, L.; Lin, M.L.; Lee, D.; Zhu, J.; Wang, C.Y.; Hsu, W.T.; Choi, J.; Embley, J.; Young, C.; Taniguchi, T.; Watanabe, K.; Shih, C.K.; Lai, K.; MacDonald, A. H.; Tan, P.H.; Libisch, F.; Li, X. Nat. Mater. 2021, 20, 1100–1105. doi:10.1038/s41563021009601 
13.  Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Phys. Rev. Lett. 2010, 105, 136805. doi:10.1103/physrevlett.105.136805 
14.  Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C.Y.; Galli, G.; Wang, F. Nano Lett. 2010, 10, 1271–1275. doi:10.1021/nl903868w 
35.  Drapcho, S. G.; Kim, J.; Hong, X.; Jin, C.; Shi, S.; Tongay, S.; Wu, J.; Wang, F. Phys. Rev. B 2017, 95, 165417. doi:10.1103/physrevb.95.165417 
36.  Carvalho, B. R.; Malard, L. M.; Alves, J. M.; Fantini, C.; Pimenta, M. A. Phys. Rev. Lett. 2016, 116, 089904. doi:10.1103/physrevlett.116.089904 
10.  Wang, Q. H.; KalantarZadeh, K.; Kis, A.; Coleman, J. N.; Strano, M. S. Nat. Nanotechnol. 2012, 7, 699–712. doi:10.1038/nnano.2012.193 
11.  Calman, E. V.; Fogler, M. M.; Butov, L. V.; Hu, S.; Mishchenko, A.; Geim, A. K. Nat. Commun. 2018, 9, 1895. doi:10.1038/s41467018042937 
12.  Rivera, P.; Schaibley, J. R.; Jones, A. M.; Ross, J. S.; Wu, S.; Aivazian, G.; Klement, P.; Seyler, K.; Clark, G.; Ghimire, N. J.; Yan, J.; Mandrus, D. G.; Yao, W.; Xu, X. Nat. Commun. 2015, 6, 6242. doi:10.1038/ncomms7242 
27.  Astié, V.; WasemKlein, F.; Makhlouf, H.; Paillet, M.; Huntzinger, J.R.; Sauvajol, J.L.; Zahab, A.A.; Juillaguet, S.; Contreras, S.; Voiry, D.; Landois, P., in press. 
40.  Liao, M.; Wei, Z.; Du, L.; Wang, Q.; Tang, J.; Yu, H.; Wu, F.; Zhao, J.; Xu, X.; Han, B.; Liu, K.; Gao, P.; Polcar, T.; Sun, Z.; Shi, D.; Yang, R.; Zhang, G. Nat. Commun. 2020, 11, 2153. doi:10.1038/s41467020160564 
4.  Withers, F.; Del PozoZamudio, O.; Mishchenko, A.; Rooney, A. P.; Gholinia, A.; Watanabe, K.; Taniguchi, T.; Haigh, S. J.; Geim, A. K.; Tartakovskii, A. I.; Novoselov, K. S. Nat. Mater. 2015, 14, 301–306. doi:10.1038/nmat4205 
5.  Jariwala, D.; Sangwan, V. K.; Lauhon, L. J.; Marks, T. J.; Hersam, M. C. ACS Nano 2014, 8, 1102–1120. doi:10.1021/nn500064s 
6.  Georgiou, T.; Jalil, R.; Belle, B. D.; Britnell, L.; Gorbachev, R. V.; Morozov, S. V.; Kim, Y.J.; Gholinia, A.; Haigh, S. J.; Makarovsky, O.; Eaves, L.; Ponomarenko, L. A.; Geim, A. K.; Novoselov, K. S.; Mishchenko, A. Nat. Nanotechnol. 2013, 8, 100–103. doi:10.1038/nnano.2012.224 
7.  Wang, H.; Yu, L.; Lee, Y.H.; Shi, Y.; Hsu, A.; Chin, M. L.; Li, L.J.; Dubey, M.; Kong, J.; Palacios, T. Nano Lett. 2012, 12, 4674–4680. doi:10.1021/nl302015v 
8.  Baugher, B. W. H.; Churchill, H. O. H.; Yang, Y.; JarilloHerrero, P. Nat. Nanotechnol. 2014, 9, 262–267. doi:10.1038/nnano.2014.25 
9.  Zhang, Y. J.; Oka, T.; Suzuki, R.; Ye, J. T.; Iwasa, Y. Science 2014, 344, 725–728. doi:10.1126/science.1251329 
26.  Zhang, X.; Qiao, X.F.; Shi, W.; Wu, J.B.; Jiang, D.S.; Tan, P.H. Chem. Soc. Rev. 2015, 44, 2757–2785. doi:10.1039/c4cs00282b 
28.  Li, S.L.; Miyazaki, H.; Song, H.; Kuramochi, H.; Nakaharai, S.; Tsukagoshi, K. ACS Nano 2012, 6, 7381–7388. doi:10.1021/nn3025173 
29.  Lee, C.; Yan, H.; Brus, L. E.; Heinz, T. F.; Hone, J.; Ryu, S. ACS Nano 2010, 4, 2695–2700. doi:10.1021/nn1003937 
30.  MolinaSanchez, A.; Wirtz, L. Phys. Rev. B 2011, 84, 155413. doi:10.1103/physrevb.84.155413 
31.  Li, X.L.; Qiao, X.F.; Han, W.P.; Zhang, X.; Tan, Q.H.; Chen, T.; Tan, P.H. Nanotechnology 2016, 27, 145704. doi:10.1088/09574484/27/14/145704 
32.  Zhao, Y.; Luo, X.; Li, H.; Zhang, J.; Araujo, P. T.; Gan, C. K.; Wu, J.; Zhang, H.; Quek, S. Y.; Dresselhaus, M. S.; Xiong, Q. Nano Lett. 2013, 13, 1007–1015. doi:10.1021/nl304169w 
33.  Zhang, X.; Han, W. P.; Wu, J. B.; Milana, S.; Lu, Y.; Li, Q. Q.; Ferrari, A. C.; Tan, P. H. Phys. Rev. B 2013, 87, 115413. doi:10.1103/physrevb.87.115413 
52.  Mignuzzi, S.; Pollard, A. J.; Bonini, N.; Brennan, B.; Gilmore, I. S.; Pimenta, M. A.; Richards, D.; Roy, D. Phys. Rev. B 2015, 91, 195411. doi:10.1103/physrevb.91.195411 
21.  Cao, Y.; Fatemi, V.; Fang, S.; Watanabe, K.; Taniguchi, T.; Kaxiras, E.; JarilloHerrero, P. Nature 2018, 556, 43–50. doi:10.1038/nature26160 
22.  Yankowitz, M.; Chen, S.; Polshyn, H.; Zhang, Y.; Watanabe, K.; Taniguchi, T.; Graf, D.; Young, A. F.; Dean, C. R. Science 2019, 363, 1059–1064. doi:10.1126/science.aav1910 
25.  Yu, H.; Liu, G.B.; Tang, J.; Xu, X.; Yao, W. Sci. Adv. 2017, 3, e1701696. doi:10.1126/sciadv.1701696 
51.  Debnath, R.; Maity, I.; Biswas, R.; Raghunathan, V.; Jain, M.; Ghosh, A. Nanoscale 2020, 12, 17272–17280. doi:10.1039/c9nr09897f 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
26.  Zhang, X.; Qiao, X.F.; Shi, W.; Wu, J.B.; Jiang, D.S.; Tan, P.H. Chem. Soc. Rev. 2015, 44, 2757–2785. doi:10.1039/c4cs00282b 
40.  Liao, M.; Wei, Z.; Du, L.; Wang, Q.; Tang, J.; Yu, H.; Wu, F.; Zhao, J.; Xu, X.; Han, B.; Liu, K.; Gao, P.; Polcar, T.; Sun, Z.; Shi, D.; Yang, R.; Zhang, G. Nat. Commun. 2020, 11, 2153. doi:10.1038/s41467020160564 
18.  RibeiroSoares, J.; Almeida, R. M.; Barros, E. B.; Araujo, P. T.; Dresselhaus, M. S.; Cançado, L. G.; Jorio, A. Phys. Rev. B 2014, 90, 115438. doi:10.1103/physrevb.90.115438 
19.  Wilson, J. A.; Yoffe, A. D. Adv. Phys. 1969, 18, 193–335. doi:10.1080/00018736900101307 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
13.  Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Phys. Rev. Lett. 2010, 105, 136805. doi:10.1103/physrevlett.105.136805 
14.  Splendiani, A.; Sun, L.; Zhang, Y.; Li, T.; Kim, J.; Chim, C.Y.; Galli, G.; Wang, F. Nano Lett. 2010, 10, 1271–1275. doi:10.1021/nl903868w 
15.  Huang, S.; Ling, X.; Liang, L.; Kong, J.; Terrones, H.; Meunier, V.; Dresselhaus, M. S. Nano Lett. 2014, 14, 5500–5508. doi:10.1021/nl5014597 
16.  Scheuschner, N.; Ochedowski, O.; Kaulitz, A.M.; Gillen, R.; Schleberger, M.; Maultzsch, J. Phys. Rev. B 2014, 89, 125406. doi:10.1103/physrevb.89.125406 
17.  Eda, G.; Yamaguchi, H.; Voiry, D.; Fujita, T.; Chen, M.; Chhowalla, M. Nano Lett. 2011, 11, 5111–5116. doi:10.1021/nl201874w 
23.  Autere, A.; Jussila, H.; Dai, Y.; Wang, Y.; Lipsanen, H.; Sun, Z. Adv. Mater. (Weinheim, Ger.) 2018, 30, 1705963. doi:10.1002/adma.201705963 
24.  Hsu, W.T.; Zhao, Z.A.; Li, L.J.; Chen, C.H.; Chiu, M.H.; Chang, P.S.; Chou, Y.C.; Chang, W.H. ACS Nano 2014, 8, 2951–2958. doi:10.1021/nn500228r 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
35.  Drapcho, S. G.; Kim, J.; Hong, X.; Jin, C.; Shi, S.; Tongay, S.; Wu, J.; Wang, F. Phys. Rev. B 2017, 95, 165417. doi:10.1103/physrevb.95.165417 
36.  Carvalho, B. R.; Malard, L. M.; Alves, J. M.; Fantini, C.; Pimenta, M. A. Phys. Rev. Lett. 2016, 116, 089904. doi:10.1103/physrevlett.116.089904 
35.  Drapcho, S. G.; Kim, J.; Hong, X.; Jin, C.; Shi, S.; Tongay, S.; Wu, J.; Wang, F. Phys. Rev. B 2017, 95, 165417. doi:10.1103/physrevb.95.165417 
26.  Zhang, X.; Qiao, X.F.; Shi, W.; Wu, J.B.; Jiang, D.S.; Tan, P.H. Chem. Soc. Rev. 2015, 44, 2757–2785. doi:10.1039/c4cs00282b 
53.  Zhou, X.; Jin, K.; Cong, X.; Tan, Q.; Li, J.; Liu, D.; Luo, J. J. Colloid Interface Sci. 2019, 538, 159–164. doi:10.1016/j.jcis.2018.11.032 
54.  Maino, J. L.; Schouten, R.; Umina, P. J. Appl. Ecol. 2021, 58, 789–800. doi:10.1111/13652664.13812 
32.  Zhao, Y.; Luo, X.; Li, H.; Zhang, J.; Araujo, P. T.; Gan, C. K.; Wu, J.; Zhang, H.; Quek, S. Y.; Dresselhaus, M. S.; Xiong, Q. Nano Lett. 2013, 13, 1007–1015. doi:10.1021/nl304169w 
33.  Zhang, X.; Han, W. P.; Wu, J. B.; Milana, S.; Lu, Y.; Li, Q. Q.; Ferrari, A. C.; Tan, P. H. Phys. Rev. B 2013, 87, 115413. doi:10.1103/physrevb.87.115413 
32.  Zhao, Y.; Luo, X.; Li, H.; Zhang, J.; Araujo, P. T.; Gan, C. K.; Wu, J.; Zhang, H.; Quek, S. Y.; Dresselhaus, M. S.; Xiong, Q. Nano Lett. 2013, 13, 1007–1015. doi:10.1021/nl304169w 
33.  Zhang, X.; Han, W. P.; Wu, J. B.; Milana, S.; Lu, Y.; Li, Q. Q.; Ferrari, A. C.; Tan, P. H. Phys. Rev. B 2013, 87, 115413. doi:10.1103/physrevb.87.115413 
20.  Lin, M.L.; Tan, Q.H.; Wu, J.B.; Chen, X.S.; Wang, J.H.; Pan, Y.H.; Zhang, X.; Cong, X.; Zhang, J.; Ji, W.; Hu, P.A.; Liu, K.H.; Tan, P.H. ACS Nano 2018, 12, 8770–8780. doi:10.1021/acsnano.8b05006 
38.  Lui, C. H.; Ye, Z.; Ji, C.; Chiu, K.C.; Chou, C.T.; Andersen, T. I.; MeansShively, C.; Anderson, H.; Wu, J.M.; Kidd, T.; Lee, Y.H.; He, R. Phys. Rev. B 2015, 91, 165403. doi:10.1103/physrevb.91.165403 
39.  Huang, S.; Liang, L.; Ling, X.; Puretzky, A. A.; Geohegan, D. B.; Sumpter, B. G.; Kong, J.; Meunier, V.; Dresselhaus, M. S. Nano Lett. 2016, 16, 1435–1444. doi:10.1021/acs.nanolett.5b05015 
40.  Liao, M.; Wei, Z.; Du, L.; Wang, Q.; Tang, J.; Yu, H.; Wu, F.; Zhao, J.; Xu, X.; Han, B.; Liu, K.; Gao, P.; Polcar, T.; Sun, Z.; Shi, D.; Yang, R.; Zhang, G. Nat. Commun. 2020, 11, 2153. doi:10.1038/s41467020160564 
41.  Quan, J.; Linhart, L.; Lin, M.L.; Lee, D.; Zhu, J.; Wang, C.Y.; Hsu, W.T.; Choi, J.; Embley, J.; Young, C.; Taniguchi, T.; Watanabe, K.; Shih, C.K.; Lai, K.; MacDonald, A. H.; Tan, P.H.; Libisch, F.; Li, X. Nat. Mater. 2021, 20, 1100–1105. doi:10.1038/s41563021009601 
42.  Tiberj, A.; RubioRoy, M.; Paillet, M.; Huntzinger, J.R.; Landois, P.; Mikolasek, M.; Contreras, S.; Sauvajol, J.L.; Dujardin, E.; Zahab, A.A. Sci. Rep. 2013, 3, 2355. doi:10.1038/srep02355 
31.  Li, X.L.; Qiao, X.F.; Han, W.P.; Zhang, X.; Tan, Q.H.; Chen, T.; Tan, P.H. Nanotechnology 2016, 27, 145704. doi:10.1088/09574484/27/14/145704 
32.  Zhao, Y.; Luo, X.; Li, H.; Zhang, J.; Araujo, P. T.; Gan, C. K.; Wu, J.; Zhang, H.; Quek, S. Y.; Dresselhaus, M. S.; Xiong, Q. Nano Lett. 2013, 13, 1007–1015. doi:10.1021/nl304169w 
33.  Zhang, X.; Han, W. P.; Wu, J. B.; Milana, S.; Lu, Y.; Li, Q. Q.; Ferrari, A. C.; Tan, P. H. Phys. Rev. B 2013, 87, 115413. doi:10.1103/physrevb.87.115413 
31.  Li, X.L.; Qiao, X.F.; Han, W.P.; Zhang, X.; Tan, Q.H.; Chen, T.; Tan, P.H. Nanotechnology 2016, 27, 145704. doi:10.1088/09574484/27/14/145704 
28.  Li, S.L.; Miyazaki, H.; Song, H.; Kuramochi, H.; Nakaharai, S.; Tsukagoshi, K. ACS Nano 2012, 6, 7381–7388. doi:10.1021/nn3025173 
28.  Li, S.L.; Miyazaki, H.; Song, H.; Kuramochi, H.; Nakaharai, S.; Tsukagoshi, K. ACS Nano 2012, 6, 7381–7388. doi:10.1021/nn3025173 
37.  Nemanich, R. J.; Tsai, C. C.; Connell, G. A. N. Phys. Rev. Lett. 1980, 44, 273–276. doi:10.1103/physrevlett.44.273 
26.  Zhang, X.; Qiao, X.F.; Shi, W.; Wu, J.B.; Jiang, D.S.; Tan, P.H. Chem. Soc. Rev. 2015, 44, 2757–2785. doi:10.1039/c4cs00282b 
29.  Lee, C.; Yan, H.; Brus, L. E.; Heinz, T. F.; Hone, J.; Ryu, S. ACS Nano 2010, 4, 2695–2700. doi:10.1021/nn1003937 
30.  MolinaSanchez, A.; Wirtz, L. Phys. Rev. B 2011, 84, 155413. doi:10.1103/physrevb.84.155413 
© 2024 Wasem Klein et al.; licensee BeilsteinInstitut.
This is an open access article licensed under the terms of the BeilsteinInstitut Open Access License Agreement (https://www.beilsteinjournals.org/bjnano/terms), which is identical to the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0). The reuse of material under this license requires that the author(s), source and license are credited. Thirdparty material in this article could be subject to other licenses (typically indicated in the credit line), and in this case, users are required to obtain permission from the license holder to reuse the material.