**10. Growth Mechanisms**

The synthesis of MoS<sup>2</sup> by CVD is the result of several steps, which can be summarized as follows: (i) transport of precursors to the substrate by a carrier gas; (ii) diffusion through the boundary layer from the gas phase to the substrate surface; (iii) adsorption of molecules to the substrate surface; (iv) diffusion of adsorbed molecules on the surface; (v) heterogeneous reactions on the surface resulting in TMD growth; (vi) desorption of by-products. In order to control the process and obtain a monolayer or few-layer material as an outcome, a high degree of control of the heterogeneous reactions should be pursued [35]. The exact evolution and progress of the synthesis and its mechanisms depend, of course, on the chosen precursors. The "holy grail" of MoS<sup>2</sup> CVD would be to develop a precise, controllable, and reproducible process to uniformly deposit large-area monodimensional flakes over a large area without grain boundaries and with a low density of defects. Understanding the growth mechanisms for the different available precursors and considering the possible presence of growth promoters could help to recognize the strengths and weaknesses of these precursors.

Considering the experience gathered on graphene, but at the same keeping in mind that the synthesis of MoS<sup>2</sup> proceeds through completely different mechanisms, in order to promote the growth of large 2D flakes, it is important to decrease the density of the nuclei and to increase the lateral growth rate while at the same time suppressing 3D nucleation [112]. Nucleation of MoO3−<sup>x</sup> species at the beginning of growth is the first step to allow the formation of MoS<sup>2</sup> nanoparticles and large flakes in the later stage of the synthesis [113]. It was suggested that this growth mode is essentially controlled by the deposition rate, which should be kept below a certain threshold to avoid the formation of thicker islands. Kang et al. [32] observed that this occurred when a low partial pressure of Mo vapour was used. With a higher Mo partial pressure, the layer-by-layer growth mode was abandoned in favour of the nucleation of a mixture of monolayer, multilayer, and no-growth regions. To obtain uniform monolayer growth, potentially on a large substrate, a precise and constant Mo partial pressure for the entire duration of growth is necessary. This requirement is not straightforward when Mo powders are used as precursors, since they deplete and are consumed as the growth proceeds, but is more easily obtained using metal-organic-like precursors such as Mo(CO)6.

The competition between the precursor mass flow towards the substrate and the reactions occurring at the surface determines the ultimate evolution of the growth. Zhou et al. [114] presented a general growth model for the deposition of a wide variety of TMDs, combining 12 transition metals and 3 chalcogens to synthesize up to 47 different 2D materials. They suggested that the mass flow supply determines the amount of metal precursors involved in the formation of the nucleus and the growth of domains, while the growth rate, essentially

determined by the temperature, dominates the grain size of the layer. The interplay between growth rate and mass flow determines the formation of continuous monolayers, small flakes, atomic clusters, or large 2D single crystals. The two contradictory statements presented in [32,114] may be interpreted as a sign that the deposition of MoS<sup>2</sup> with powders is very dependent on the used growth system and setup, and finding a unifying explanation of the experimental observation is not straightforward.

The main reason for the lateral enlargement of MoS<sup>2</sup> flakes is the high chemical reactivity of the atoms at the edge of the flakes and in the presence of preferred nucleation sites, with high chemical reactivity, compared to the absence of dangling bonds in the vertical direction. A low and constant Mo precursor partial pressure may help in growing uniform monolayer thin films over a large area [32]. However, the growth of vertically standing MoS<sup>2</sup> nanosheets was also reported [115]. They were supposed to be caused by the reduction in the elastic strain energy that forms during the horizontal growth of MoS<sup>2</sup> nanosheets. The transition from 2D to 3D structure was achieved by controlling the quantity and distribution of the precursor concentration, placing the substrate in different orientations and positions with respect to the source powders [107]

when using Mo powders, the proposed reactions for MoS<sup>2</sup> synthesis are:

$$2\text{ MoO}\_3 + \text{S} \to 2\text{ MoO}\_{3-\text{x}} + \text{SO}\_2$$

$$2\text{ MoO}\_{3-x} + (7-x)\text{ S} \to 2\text{ MoS}\_2 + (3-x)\text{ SO}\_2$$

MoO<sup>3</sup> is first reduced to suboxides (MoO3−x) by S vapours, further reduced to oxisulfides, and then transported to the substrate, where a further reaction with S vapour to form MoS<sup>2</sup> occurs [116]. Since a MoO<sup>3</sup> suboxide is involved in the growth reaction, the use of MoO<sup>2</sup> instead of MoO<sup>3</sup> was proposed in order to obtain better control of the flakes [117]. In this case, the synthesis reaction would proceed by the mechanism:

$$\text{MoO}\_2 + 3\text{ S} \rightarrow \text{MoS}\_2 + \text{O}\_2$$

This reaction avoids intermediate chemistry and permits obtaining higher-quality flakes on different substrates such as SiO2, Si, quartz, and SiN. The quantity of starting Mo powders greatly influences the reaction process. In [118], a comprehensive summary of typical powder weights, along with growth temperature and setup, was presented.

In order to have a detailed outlook on the growth process of MoS2, Cain et al. [119] deposited MoS<sup>2</sup> using S and MoO<sup>3</sup> powders on ultrathin SiO<sup>2</sup> membranes to allow investigation of the nucleation mechanism with aberration-corrected STEM and elemental EDS mapping. They confirmed the presence of nucleation centres (10–30 nm) only at the centres of triangular flakes, representing the early stages of TMD growth. The second or third layer of the flakes also started at this site. Moreover, the nuclei showed a nanoscale core–shell structure, similar to that of inorganic TMD fullerenes, with inhomogeneous distribution of Mo and S. The growth process was essentially defined by the concentration of the chalcogen vapour: if the atmosphere was weakly reducing (sulfur poor), oxi-chalcogenide particles with an orthorhombic crystal structure were formed. In a moderately reducing sulfur-rich atmosphere, MoS<sup>2</sup> formation was favoured. These experimental observations confirm the importance of promoting the formation of nucleation sites.

A convenient and empirical method to tune growth parameters towards the optimal growth conditions is to observe the flake shape at the optical microscope. Yang et al. [120] studied the morphological evolution of MoS<sup>2</sup> flakes for various Mo–S ratios, using MoO<sup>3</sup> and S powders as reagents at different temperatures. Obtaining a continuous film with large triangular MoS<sup>2</sup> flakes should be possible at higher temperature and with a high S content (Figure 7).

**Figure 7.** Schematic illustration of the evolution of the morphology of MoS<sup>2</sup> flakes for changing Mo–S ratios and temperatures. Marker represents a flake size of 100 µm. Derived from data from [120].

Obtaining large flakes, by preventing the cohesion of smaller flakes, would also limit the presence of grain boundaries at flake coalescence regions, which may limit electrical transport in the layer [16]. Moreover, it was observed that the MoS<sup>2</sup> bandgap could be tuned by controlling the distance from a grain boundary [121], so it is important to achieve good control over the flakes' size over the substrate area in order to avoid undesired modulations of the bandgap. Nevertheless, it was demonstrated that MoS<sup>2</sup> grain boundaries could exhibit a memristor behaviour [122], which may open new applications for this material.

An important source of carrier scattering in devices is defects and charged particles at the interface (Coulomb scattering). These defects are usually introduced in postprocessing fabrication steps, and it was suggested that proper passivation with a suitable dielectric could help mitigating the issue, increasing the performance of the device [123].

In general, point defects in MoS<sup>2</sup> act as important electron scattering centres and may be categorized as vacancies or antisite defects [124,125]. Sulfur vacancies behave as deep donors and induce midgap defect states, making the material n-type. Furthermore, vacancies and antisites induce a modification in the electrical properties of MoS2, resulting in n-type doping and introducing localized states in the band gap, lowering the carrier mobility. They can cause Fermi level pinning and high contact resistance in electrical devices. Inclusion of other elements related to promoters (Na, Au) can also cause unintentional doping effects. These states also reduce the emission efficiency for photonic devices based on this material.

On the other hand, control of defect density and nature can be an effective tool to engineer material properties. It was shown that the electrical properties of MoS<sup>2</sup> could be changed by exposing the samples to oxygen plasma, going from the semiconducting to the insulating regime [50]. A recent method to reduce sulfur vacancies was introduced by Durairaj et al. [126]; in this study, a SiO2/Si wafer was placed next to the growth substrate, providing oxygen and effectively enabling oxygen passivation of sulfur-vacancy defects in monolayer flakes. The authors observed a threefold increase in the PL efficiency due to the elimination of defect-related bound exciton emission.

In Figure 8, the reaction pathways that lead to the formation of MoS<sup>2</sup> through intermediate species are summarized [118,127].

**Figure 8.** Ternary phase diagram for Mo-S-O, showing the possible reactions to produce MoS<sup>2</sup> . Adapted from [127]; reprinted with permission from AAAS.

If MoCl<sup>5</sup> is used instead of MoO<sup>3</sup> powders, the proposed reactions are different from those reported above. Since the ratio between S and MoCl<sup>5</sup> is very high (>1000), the conversion of MoCl<sup>5</sup> to MoS<sup>2</sup> is supposed to be completed in the gas phase, with a negligible concentration of intermediate suboxides. By precisely controlling the amounts of MoCl<sup>5</sup> and S powders, their flow in the growth environment, and the total pressure in the growth chamber, Yu et al. [69] were able to control the number of MoS<sup>2</sup> layers, with good uniformity over an area of several cm<sup>2</sup> . The key role was suggested to be the self-limiting nature of the layer-by-layer process, which could be controlled by tuning the flow of the precursors as well as the total pressure of the system: increasing the amount of precursors (from 1 mg of MoCl<sup>5</sup> to 25 mg) and the total pressure (from 2 to 750 torr) resulted in the deposition of thicker films.

One could argue that the use of powder Mo precursors, because of their timedependent evaporation and the necessity of precise and continuous flow control, would lead to worse and less reproducible results with respect to the sulfurization of a thin Mo layer predeposited on the substrate [118]. In the latter case, the resulting MoS<sup>2</sup> layer would depend only on the starting conditions, which in principle could be precisely optimized by thermal evaporation or sputtering of the thin Mo or MoO<sup>x</sup> layer. However, starting with a Mo film deposited on the substrate, the sulfurization process should occur at very high temperature to be efficient. This results in undesired surface evaporation of the starting material and leads to inhomogeneities, since the balance between the surface mobility and surface evaporation leads to limited grain sizes and/or limited yields of monolayer films. Moreover, it is still difficult to obtain an optimal starting film density and uniformity. However, one of the advantages of this approach is the ease of saturating the

growth chamber with sulfur vapours (either from powders or from H2S), so this is not the process-limiting factor.

To promote bilayer growth, the interactions between the adatoms and the surface should be larger than the adatom–adatom interactions. If these conditions are not met, the deposition evolves towards a 3D growth. It was suggested that by increasing the intermolecular acid–base interactions between admolecules and the substrate surface, it should be possible to increase the adsorption. This can be done by selecting precursors and substrates with complementary acid/base properties [35]. A convenient way to increase the surface forces is to use growth promoters or seed molecules to change the surface energy, reduce the free energy barrier, and lower the nucleation energy necessary to obtain monolayer MoS2. It was argued that the best promoters are aromatic or graphene-like molecules that enhance the wettability of the substrate, lowering the free energy for the nucleation. In this way, better control of nucleation can be achieved [91]. Thus, an optimal concentration of the seeding promoter is essential for MoS<sup>2</sup> monolayer deposition [128]. One important factor to be considered is the polarity of the growth promoter molecule, as pointed out by Ko et al. [93]. With density function theory calculations coupled to experimental evidence, they suggested that the polar part of the crystal violet molecule used as a promoter provides a preferred site for S adsorption, initiating the MoS<sup>2</sup> nucleation. The orientation of the molecule during the spinning on the substrate, mediated by appropriate solvents, can effectively promote monolayer growth instead of multilayer MoS<sup>2</sup> deposition.

It has been shown that the use of alkali-based promoters allows for larger flakes [98], but their excess might result in loss of MoS<sup>2</sup> crystallinity, with the creation of additional defects [128]. Extensive work is currently underway on controlling defects in MoS<sup>2</sup> flakes acting on growth parameters, not only to reduce their deleterious effects on devices, but also to take advantage of some of their features. For example, Na cations coming from promoters can cure interface defects to achieve low intrinsic defect levels and enhance electrical properties [129]. The use of liquid precursors spun in a controllable way on the substrate could overcome the problems due to the limited supply control of powder precursors. Spinning SMD and/or AMT with a density gradient medium and a growth promoter such as NaOH or NaCl could permit obtaining a reproducible layer that could be sulfurized in a controllable way. Kang et al. [130] presented a comprehensive study on the role of the different growth parameters in the synthesis of MoS<sup>2</sup> flakes using liquid precursor, including the roles of temperature, S pressure, gas carrier flow, composition of the initial spun solution, and time. By an optimization of the process, MoS<sup>2</sup> flakes with dimensions up to 100 µm were obtained in a reproducible way. AFM analysis of the MoS<sup>2</sup> surface revealed the presence of precursor and promoter residues, particularly at the interfaces between different flakes. AMT is converted to MoO<sup>3</sup> at about 300 ◦C. Using Na as a promoter, if further reacts with NaOH to produce sodium molybdate (Na6MoO4), which finally converts to MoS<sup>2</sup> thanks to the presence of S vapour. Using SiO<sup>2</sup> as a substrate, in this case, permits the reaction between Na2MoO<sup>4</sup> and the oxide substrate to form sodium silicon oxide, promoting the lateral growth of the MoS<sup>2</sup> layer [97].
