Unraveling Mass Transfer and Reaction Processes in CVD-Grown MoS₂ Films: A Multiphysical Field Coupling Study

Abstract

The two-dimensional semiconductor material MoS₂, grown via chemical vapor deposition, has shown significant potential to surpass silicon in advanced electronic technologies. However, the mass transfer and chemical reaction processes critical to the nucleation and growth of MoS₂ grains remain poorly understood. In this study, we conducted an in-depth investigation into the mass transfer and chemical reaction processes during the chemical vapor deposition of MoS₂, employing a novel multi-physics coupling model that integrates flow fields, temperature fields, mass transfer, and chemical reactions. Our findings reveal that the intermediate product Mo₃O₉S₄ not only fails to participate directly in MoS₂ film growth but also hinders the diffusion of MoS₆, limiting the growth process. We demonstrate that increasing the growth temperature accelerates the diffusion rate of MoS₆, mitigates the adverse effects of Mo₃O₉S₄, and promotes the layered growth of MoS₂ films. Additionally, lowering the growth pressure enhances the convective diffusion of reactants, accelerating grain growth. This research significantly advances our understanding of the mass transport and reaction processes in MoS₂ film growth and provides critical insights for optimizing chemical vapor deposition systems.

1. Introduction

With the rapid development of the integrated circuit industry, device density and performance continue to increase, causing channel sizes, which represent the characteristic length of field-effect transistors, to approach physical limits. This makes it difficult for silicon to sustain Moore’s Law, which predicts the doubling of transistor density every two years [1]. As transistors approach atomic scales, alternative materials are needed to overcome challenges in power consumption, heat dissipation, and short-channel effects. Two-dimensional (2D) materials, such as graphene, black phosphorus, and transition metal dichalcogenides (TMDs), have emerged as promising candidates for next-generation electronic devices due to their unique properties [2]. Among 2D materials, MoS₂ stands out due to its semiconducting nature, tunable bandgap, high carrier mobility, and mechanical flexibility, offering unique advantages in short-channel applications [3,4,5,6,7,8,9,10,11]. As a result, achieving the controllable growth of MoS₂ thin films has become an urgent and shared goal in both academic and industrial sectors. Researchers have developed various methods to obtain high-quality MoS₂ thin films, including physical vapor deposition (PVD) [12,13,14,15], metal-organic chemical vapor deposition (MOCVD) [16,17,18], and chemical vapor deposition (CVD) [19,20,21]. Among these methods, CVD has shown great potential for large-scale MoS₂ film production due to its high efficiency, low cost, and ability to produce high-quality films.

During the CVD growth of MoS₂ thin films, various process parameters—such as temperature, pressure, gas flow rate, substrate condition, and precursor type—collectively influence the transport, reaction, and nucleation/growth processes of the reactants [22,23,24,25,26,27,28]. By precisely controlling these parameters, the morphology, size, orientation, and phase structure of the thin films can be effectively tailored, enabling the fabrication of MoS₂ films with tunable properties to meet the demands of different applications. Currently, research on the growth mechanisms of MoS₂ films primarily focuses on the effects of substrate surface properties—such as surface symmetry, step edges, buffer layers, and surface defects—on nucleation and growth [29]. However, the understanding of the growth conditions that directly influence material nucleation and growth remains largely empirical, relying on trial-and-error approaches [19,20,21]. In particular, mass transport and reaction processes, which are directly linked to growth conditions, have not been investigated in depth. Therefore, a systematic study of the flow field, temperature field, mass transfer, and reaction processes during MoS₂ film growth is crucial for a deeper understanding of the growth mechanism and for achieving controlled fabrication of these thin films.

In this study, we established a multiphysics coupling model involving the flow field, temperature field, mass transport, and chemical reactions, and thoroughly analyzed the effects of temperature and pressure on the growth of MoS₂ films. We found that the intermediate product Mo₃O₉S₄ is the key factor limiting the reaction rate, which not only cannot directly participate in the growth of MoS₂ film, but also hinders the diffusion of MoS₆, thus impeding film growth. Increasing the growth temperature can accelerate the diffusion rate of MoS₆ and weaken the influence of Mo₃O₉S₄, enabling the layered growth of MoS₂ thin films. Simultaneously, lowering the growth pressure can accelerate the convective diffusion rate of the reactants, promoting grain growth. When the pressure is reduced from 100 Torr to 10 Torr, the grain size of the MoS₂ film increases from 10 μm to 50 μm. This study deepens our understanding of the mass transport and reaction processes in the CVD growth of MoS₂ films.

2. Experimental Methods

The growth of MoS₂ films was conducted in a low-pressure dual-zone CVD system with an 80 mm diameter tube, as shown in Figure S1a. Elemental S powder (5 g, 99.95%, Aladdin) and MoO₃ powder (60 mg, 99.95%, Aladdin) were placed in two separate quartz crucibles, positioned at the centers of two distinct temperature zones, with a 30 cm distance between them. A 300 nm-thick Si/SiO₂ substrate (1 × 1 cm²) was ultrasonically cleaned with acetone, isopropyl alcohol, and deionized water, followed by nitrogen blow drying. The substrate was placed face-down on the MoO₃ powder, with a distance of approximately 3 mm between the MoO₃ and the substrate. The temperature of the S powder was set to 423 K, while the temperatures of the MoO₃ was set to 1033 K, 1053 K, and 1073 K, respectively. The heating rate was 10 K/min, ensuring that both the S and MoO₃ powders reached their target temperatures simultaneously. Throughout the growth process, a continuous Ar gas flow of 200 sccm was maintained, with the system pressure was set to 10, 40, 70, and 100 Torr via a gate valve.

The optical microscopy images of MoS₂ films were obtained using the BX53M optical microscope from Olympus (Tokyo, Japan). The Raman and photoluminescence (PL) spectra of the samples were measured using the LabRAM Odyssey confocal Raman spectrometer from HORIBA Scientific (Kyoto, Japan) with a ×50 long working distance objective, excited at a wavelength of 532 nm, and a grating density of 600 gr/mm.

3. Construction of Multiphysics Coupling Model

In the CVD system, the entire reaction process involves multiple coupled physical fields, including the flow field, temperature field, mass transfer of trace species, and chemical reactions. The flow field and temperature field are interrelated and form the foundation for mass transfer and chemical reactions. Therefore, we first developed a coupled flow and temperature field model using COMSOL Multiphysics 6.1 software. Based on the results of the flow and temperature fields, we then performed coupled calculations for mass transfer and chemical reactions. The flowchart of the simulation and calculation process is shown in Figure S2. The finite element geometry model is shown in Figure 1, and the detailed modeling process is provided in the Supplementary Information.

The precursor sulfur and MoO₃ source need to undergo a series of elementary reactions to form the final product MoS₂. Previous studies, combining molecular dynamics and first-principles calculations, have outlined the reaction pathway for sulfur and MoO₃. Elemental sulfur evaporates to form S₂ dimers that participate in the reaction, while MoO₃ evaporates to produce the gaseous precursor Mo₃O₉ [30]. The initial gaseous reactants are S₂ and Mo₃O₉, which undergo the following reactions:

$${\mathrm{Mo}}_3{\mathrm{O}}_9+{\mathrm{S}}_2\underset{1.31\mathrm{eV}}{\overset{0.79\mathrm{eV}}{\rightleftharpoons }}{\mathrm{Mo}}_3{\mathrm{O}}_9{S}_2$$

(1)

$${\mathrm{Mo}}_3{\mathrm{O}}_9{\mathrm{S}}_2+{\mathrm{S}}_2\underset{1.11\mathrm{eV}}{\overset{0.81\mathrm{eV}}{\rightleftharpoons }}{\mathrm{Mo}}_3{\mathrm{O}}_9{\mathrm{S}}_4$$

(2)

$${\mathrm{Mo}}_3{\mathrm{O}}_9{\mathrm{S}}_4+{\mathrm{S}}_2\underset{0.42\mathrm{eV}}{\overset{0.95\mathrm{eV}}{\rightleftharpoons }}{\mathrm{Mo}}_2{\mathrm{O}}_6{\mathrm{S}}_4+{\mathrm{MoO}}_3{\mathrm{S}}_2$$

(3)

$${\mathrm{MoO}}_3{\mathrm{S}}_2+{\mathrm{S}}_2\underset{1.61\mathrm{eV}}{\overset{0.61\mathrm{eV}}{\rightleftharpoons }}{\mathrm{MoO}}_3{\mathrm{S}}_4$$

(4)

$${\mathrm{MoO}}_3{\mathrm{S}}_4+{\mathrm{S}}_2\underset{1.25\mathrm{eV}}{\overset{0.43\mathrm{eV}}{\rightleftharpoons }}{\mathrm{MoO}}_2{\mathrm{S}}_4+{\mathrm{S}}_2\mathrm{O}$$

(5)

$${\mathrm{MoO}}_2{\mathrm{S}}_4+{\mathrm{S}}_2\underset{0.52\mathrm{eV}}{\overset{0.37\mathrm{eV}}{\rightleftharpoons }}{\mathrm{MoOS}}_4+{\mathrm{S}}_2\mathrm{O}$$

(6)

$${\mathrm{MoOS}}_4+{\mathrm{S}}_2\underset{1.30\mathrm{eV}}{\overset{0.46\mathrm{eV}}{\rightleftharpoons }}{\mathrm{MoOS}}_6$$

(7)

$${\mathrm{MoOS}}_6+{\mathrm{S}}_2\underset{1.30\mathrm{eV}}{\overset{0.46\mathrm{eV}}{\rightleftharpoons }}{\mathrm{MoS}}_6+{\mathrm{S}}_2\mathrm{O}$$

(8)

$${\mathrm{MoS}}_6\to {\mathrm{MoS}}_2\left(\mathrm{monolayer}\right)+{\mathrm{S}}_4$$

(9)

The energy in these equations represents the transition state energy barrier that must be overcome for the reaction to proceed. For most reactions, the forward reaction is more favorable, facilitating the reaction process. However, the reaction between Mo₃O₉S₄ and S₂ limits the overall reaction rate, meaning that modulation of this step can significantly affect the entire process. Finally, MoS₆ serves as the final gaseous intermediate product, which forms monolayer MoS₂ on the substrate.

Based on transition state theory, the reaction rate for these elementary steps can be calculated [31,32]. To model this process, we used the reaction engineering module in the COMSOL software. In a 1 m³ reactor with the temperature set at 1053 K and initial concentrations of S₂ and Mo₃O₉ at 1 mol/m³ and 0.001 mol/m³, respectively, the concentration changes of reactants and intermediate products over time were simulated, as shown in Figure S1b. The results demonstrate that the entire reaction process is essentially completed within 100 ns. The reaction of the intermediate product Mo₃O₉S₄ is identified as the key step that limits the overall reaction rate of the process. Therefore, this study takes S₂ and Mo₃O₉ as the initial reactants, MoS₆ as the product, and further investigates the impact of temperature and flow fields on the reaction dynamics.

4. Results and Discussion

4.1. The Influence of Temperature on MoS₂ Growth

The growth temperature plays a crucial role in influencing the volatility and reactions of precursors, as well as the nucleation and growth processes of MoS₂ films. Figure 2a–c presents optical microscopy images of MoS₂ films grown at 1033 K, 1053 K, and 1073 K under a fixed pressure of 70 Torr. At 1033 K, irregular and fluffy structures are observed on the substrate surface, with no well-defined grains. As the growth temperature increases to 1053 K, triangular-shaped MoS₂ grains appear on the surface, and with further temperature elevation, the grain size gradually increases. Thicker crystal nuclei can be observed at the center of some grains, indicating island-like growth of the MoS₂ films.

The XPS data for the sample grown at 1053 K and 70 Torr are shown in Figure S3. The Mo 3d_3/2 and Mo 3d_5/2 peaks appear at 233.0 eV and 229.9 eV, suggesting the 4+ oxidation state of Mo. An additional peak at 227.1 eV corresponds to the S 2s state. Figure S3b shows that S 2p_3/2 and S 2p_1/2 peaks appear at 163.9 eV and 162.7 eV, indicating the 2-oxidation state of sulfur. This provides confirmation of the formation of MoS₂.

The interlayer interactions in MoS₂ films are influenced by the film thickness, resulting in a thickness-dependent characteristic of the vibrational mode frequencies. Figure 2d presents the Raman spectra of MoS₂ films grown at different temperatures. The Raman frequency difference between the E_2g¹ and A_1g modes for the MoS₂ films grown at 1053 K and 1073 K are 21.1 cm⁻¹ and 21.4 cm⁻¹, respectively, which corresponds to the bilayer MoS₂ films, indicating the presence of small crystallites on top of the monolayer MoS₂. For the MoS₂ film grown at 1033 K, the frequency difference is 26.3 cm⁻¹, suggesting that the film thickness has exceeded four layers [33]. Figure 2e presents the PL spectra of MoS₂ films grown at different temperatures. It includes a strong A-excitonic peak around 681 nm and a weak B-excitonic peak around 632 nm. The A-excitonic peak is highly sensitive to the film’s quality and thickness [34]. As the film thickness increases, the intensity of the A-excitonic peak undergoes quenching.

The following section focuses on analyzing the impact of temperature on the reaction process. First, temperature affects the evaporation rates of S₂ and Mo₃O₉. In this study, the evaporation rates of S₂ and Mo₃O₉ were obtained by measuring the consumption of sulfur (S) and MoO₃. At a pressure of 70 Torr and a temperature of 423 K, the evaporation rate of S₂ was 1.26 × 10⁻³ mol min⁻¹ cm⁻². Additionally, the evaporation rate of MoO₃ was tested at different temperatures under a pressure of 70 Torr, as shown in

Table 1. Relationship between the evaporation rate of Mo₃O₉ and temperature.

Source	Pressure	Temperature	Mo3O9 Flow
MoO3 powder	70 Torr	1033 K	1.9 × 10−4 mol min−1 cm−2
		1053 K	3.9 × 10−4 mol min−1 cm−2
		1073 K	6.6 × 10−4 mol min−1 cm−2

. As the temperature increased, the evaporation rate of Mo₃O₉ rapidly increased from 1.9 × 10⁻⁴ mol min⁻¹ cm⁻² at 1033 K to 6.6 × 10⁻⁴ mol min⁻¹ cm⁻² at 1073 K.

Based on the experimental conditions, the finite element model was set up with the temperatures of the IV region at 1033 K, 1053 K, and 1073 K for calculation. Figure S4 shows the temperature distribution in the CVD system along with the cross-sectional temperature distribution at the center of the substrate. At a set temperature of 1033 K, the substrate temperature is only 884 K. This is because the gas flow carries away additional heat as it passes over the substrate. As the set temperature increases, the substrate temperature also rises, but the temperature difference between the set temperature and the substrate temperature gradually becomes larger. At a set temperature of 1073 K, the substrate temperature increases to 915 K, with a temperature difference of 158 K.

Figure S5 present the velocity distribution and the cross-sectional velocity distribution at the center of the substrate under different set temperatures. Since the gas is in a laminar flow state, the flow velocity is higher at the center of the chamber. At a set temperature of 1033 K, the gas velocity at the inlet reaches a maximum of approximately 4.6 m/s. After entering the chamber, the velocity quickly decreases, with the flow velocity at the rear of the first temperature zone dropping to 0.03 m/s. When the gas transitions from the low-temperature zone to the high-temperature zone, the velocity increases rapidly, reaching 0.07 m/s at the center. This is due to the reduced gas density caused by the higher temperature. However, it is noteworthy that as the set temperature increases, the change in gas velocity is minimal. Inside the crucible, the maximum gas velocity at the center is only about 0.001 m/s. Moreover, since the gas is in laminar flow, the gas velocity at the surface of the substrate is nearly zero, which helps create a relatively stable growth environment. This reduces the interference of the carrier gas on the nucleation and growth processes.

The distribution of the flow field and temperature field determines the convective and diffusive rates of S₂ and Mo₃O₉, which in turn influences their concentration distribution after evaporation. Under different growth temperatures, the concentration distribution of S₂ is shown in Figure S6. In the heated evaporation region, S₂ exhibits an uneven concentration distribution. Upon entering the high-temperature zone, the concentration of S₂ becomes uniformly distributed due to the high diffusion rate induced by the elevated temperature, reaching approximately 2.60 mol/m³. As S₂ reaches the precursor MoO₃, it begins to react with the gaseous precursor Mo₃O₉ and intermediate products, leading to a decrease in S₂ concentration. At growth temperatures of 1033 K, 1053 K, and 1073 K, the concentrations of S₂ at the substrate position are 1.32, 0.40, and 0.48 mol/m³, respectively.

The increase in temperature leads to a rise in the evaporation rate of Mo₃O₉, which causes its concentration to increase inside the crucible, primarily concentrated above the precursor, as shown in Figure 3. At growth temperatures of 1033 K and 1053 K, the concentration of Mo₃O₉ at the substrate position is 0 mol/m³, indicating that the reaction between Mo₃O₉ and S₂ is completed rapidly. However, when the growth temperature is increased to 1073 K, the concentration of Mo₃O₉ at the substrate position rises to 0.03 mol/m³. This is mainly due to the fact that with the further increase in temperature, the reverse reaction rates of the intermediate products Mo₂O₆S₄ and MoO₃S₂ are accelerated, which limits the progression of the reaction, preventing the complete reaction of Mo₃O₉ and S₂ and causing an increase in their concentrations at the substrate position.

After the reaction of Mo₃O₉ with S₂, intermediate products are rapidly formed. Figure 4 shows the concentration distribution of Mo₃O₉S₄ under different growth temperatures at a pressure of 70 Torr. As the set temperature increases from 1033 K to 1073 K, the concentration of Mo₃O₉S₄ at the substrate position increases significantly from 0.006 mol/m³ to 0.24 mol/m³. This can be attributed to both the increased evaporation rate of Mo₃O₉ and the accelerated reverse reaction rates of Mo₂O₆S₄ and MoO₃S₂. The concentration distributions of other intermediate products at a pressure of 70 Torr and a temperature of 1053 K are shown in Figure S7. The concentrations of all intermediate products are concentrated above the precursor inside the crucible, and the concentrations at the substrate position are significantly lower, indicating that the reaction proceeds rapidly. The concentration of Mo₃O₉S₄ is approximately 0.09 mol/m³, much higher than that of other intermediate products (e.g., the concentration of MoO₃S₂ is 1 × 10⁻⁴ mol/m³). This suggests that the reaction involving Mo₃O₉S₄ is the rate-limiting step for the entire reaction.

Figure 5 shows the concentration distribution of MoS₆ products at different growth temperatures. At 1033 K, 1053 K, and 1073 K, the concentration of MoS₆ at the substrate position is 0.19 mol/m³, 0.31 mol/m³, and 0.24 mol/m³, respectively. As the temperature increases, the evaporation rate of Mo₃O₉ rises, while the reverse reaction rates of Mo₂O₆S₄ and MoO₃S₂ accelerate, resulting in a non-monotonic change in the concentration of MoS₆. Figure 5c,f,i shows a symmetric distribution of MoS₆ concentration along the center of the substrate inside the crucible, indicating that the diffusion of reactants is the dominant factor in the mass transfer process within the crucible. This is mainly due to the relatively low gas flow rate inside the crucible.

Based on the above observations, the state of the substrate can be summarized as follows: During the early stages of growth, the substrate surface is characterized by the coexistence of both MoS₆ and Mo₃O₉S₄. MoS₆, as the final reactant before MoS₂ film growth, directly contributes to the formation of the MoS₂ film after diffusing to the edges of the MoS₂ grains. In contrast, the intermediate product Mo₃O₉S₄ not only fails to directly participate in the MoS₂ film growth but also obstructs the diffusion of MoS₆, hindering overall film growth, as shown in Figure S8. At low substrate temperatures, the diffusion rate of MoS₆ is also low, and Mo₃O₉S₄ severely restricts its diffusion. This results in a thicker film with a substrate surface covered by irregular and fluffy MoS₂, which prevents the MoS₂ from growing layer by layer. As the substrate temperature increases, although the concentration of Mo₃O₉S₄ rises, the diffusion rate of MoS₆ increases and the hindrance caused by Mo₃O₉S₄ decreases. This enables MoS₆ to diffuse more effectively to the vicinity of the nucleus, promoting the growth of a well-ordered MoS₂ film. It is important to note that the MoS₆ precursor undergoes an exothermic reaction on the substrate, forming MoS₂ and releasing S₄, without involving a transition state. As a result, we believe that temperature has a minimal effect on the growth rate.

4.2. The Influence of Pressure on MoS₂ Growth

Since pressure can significantly alter the flow field, thereby affecting the concentration of reactants and the reaction rate, we further investigate the influence of pressure. In this section, the growth temperature is fixed at 1053 K, and the impact of different pressures (10 Torr, 40 Torr, 70 Torr, and 100 Torr) on the growth of MoS₂ films is explored, with results at 70 Torr presented in the above section. Figure 2b and Figure 6a–c show optical micrographs of samples grown under different pressures. As the pressure increases, the grain size gradually decreases. At 10 Torr, the grain size can reach up to 50 μm, whereas at 100 Torr, it shrinks to approximately 10 μm. Additionally, at both 10 Torr and 100 Torr, some grain centers exhibit distinctly thicker nuclei.

Figure 6d presents the Raman spectra of MoS₂ films grown under different pressures. For films grown at pressures below 70 Torr, the wavenumber difference between the E_2g¹ and A_1g peaks is less than 22 cm⁻¹, indicating the presence of bilayer MoS₂ films. However, when the pressure increases to 100 Torr, this wavenumber difference rises to 23.5 cm⁻¹, corresponding to the Raman wavenumber difference of trilayer MoS₂. Figure 6e shows the PL spectra of the samples grown at different pressures. As the film thickness increases, the PL intensity significantly decreases, accompanied by a slight red shift. This is due to the stronger interlayer interactions caused by the increased thickness, which leads to a reduction in the bandgap.

Not only does temperature affect the volatility rate of Mo₃O₉, but pressure also plays a crucial role in influencing its volatility rate.

Table 2. Relationship between the evaporation rate of Mo₃O₉ and gas pressure.

Source	Pressure	Temperature	Mo3O9 Flow
MoO3 powder	10 Torr	1053 K	9.4 × 10−4 mol min−1 cm−2
	40 Torr		5.5 × 10−4 mol min−1 cm−2
	70 Torr		3.9 × 10−4 mol min−1 cm−2
	100 Torr		2.4 × 10−4 mol min−1 cm−2

shows the volatility rate of Mo₃O₉ at different pressures when the temperature is 1053 K. As the pressure increases from 10 Torr to 100 Torr, the volatility rate of Mo₃O₉ rapidly decreases from 9.4 × 10⁻⁴ mol min⁻¹ cm⁻² to 2.4 × 10⁻⁴ mol min⁻¹ cm⁻². In contrast, the pressure has little effect on the volatility rate of S₂, which remains relatively stable at 1.26 × 10⁻³ mol min⁻¹ cm⁻². Finite element simulations were then conducted based on these volatility rates.

Figure S9 illustrates the temperature distribution in the CVD system at different pressures, along with the cross-sectional temperature distribution at the center of the substrate. The results indicate that pressure has a minimal impact on the temperature. Although additional heat is carried away by the gas flowing through the substrate, varying the pressure does not affect the temperature distribution at the substrate when the gas flow rate remains constant. Figure 7 shows the flow velocity distribution in the CVD system at different pressures, as well as the cross-sectional flow velocity distribution at the center of the substrate. As pressure increases, the gas velocity rises significantly. At 10 Torr, the maximum gas velocities in the IV region and inside the crucible are 0.48 m/s and 0.008 m/s, respectively, while at 100 Torr, these values decrease to 0.05 m/s and 0.0008 m/s.

The variation in flow velocity has a significant impact on the convection process of mass transport, leading to a notable increase in the concentration of S₂ within the chamber as pressure rises, as shown in Figure S10. At pressures of 10, 40, 70, and 100 Torr, the S₂ concentrations at the substrate are 0.08, 0.17, 0.40, and 1.40 mol/m³, respectively. For Mo₃O₉, the concentration in both the crucible and substrate regions decreases as pressure increases, as shown in Figure 8. At pressures of 10 and 40 Torr, the Mo₃O₉ concentrations at the substrate are 0.025 and 0.004 mol/m³, respectively. As the pressure increases to 70 and 100 Torr, the Mo₃O₉ concentration at the substrate becomes 0 mol/m³. This decrease is partly due to the reduced evaporation rate of Mo₃O₉ at higher pressures and partly due to the accelerated reaction rate driven by the increased S₂ concentration.

Figure 9 shows the concentration distribution of Mo₃O₉S₄ at different pressures. As pressure increases, the concentration of Mo₃O₉S₄ in the substrate region first increases and then decreases. On the one hand, the increase in pressure slows down the convection diffusion rate of the dilute species, causing the reaction in the substrate region to reach completion more quickly and raising the equilibrium concentration of Mo₃O₉S₄ at the substrate. On the other hand, the increased pressure reduces the volatilization rate of Mo₃O₉, leading to a decrease in the concentration of the intermediate product Mo₃O₉S₄. These two factors compete with each other, resulting in the concentration first increasing and then decreasing with rising pressure.

As the pressure increases, the concentration of MoS₆ products within the chamber also increases, as shown in Figure 10. The concentration of MoS₆ at the substrate position rises from 0.03 mol/m³ at 10 Torr to 0.35 mol/m³ at 100 Torr. Although the volatilization rate of Mo₃O₉ is faster at lower pressures, the higher diffusion rate at these pressures causes the reaction products to diffuse rapidly, thereby diluting the product concentration. Figure 10c,f,i demonstrates that the MoS₆ concentration is symmetrically distributed along the substrate center at different pressures. Despite the accelerated gas flow at lower pressures, the diffusion process of dilute species within the crucible region still dominates mass transfer.

Therefore, reducing the pressure to increase the flow velocity accelerates the convective diffusion rate of dilute species and decreases the concentration of MoS₆ at the substrate. On the one hand, the decreased concentration of MoS₆ will slow the nucleation and growth rate of the MoS₂ film; on the other hand, the increased diffusion rate facilitates the diffusion-driven growth of MoS₆ on the substrate. Consequently, reducing the pressure promotes grain growth but inhibits nucleation. This explains why, at 100 Torr, MoS₂ films have thicker layers and smaller grains, while at 10 Torr, the films exhibit significantly larger grains.

5. Conclusions

In summary, this study provides a comprehensive analysis of the dual-temperature CVD growth process of MoS₂ films, integrating both experimental and simulated approaches to systematically examine the impact of various growth parameters on mass transfer, reaction dynamics, and film growth. The results reveal that during the growth process, the substrate surface exhibits a coexistence of MoS₆ and Mo₃O₉S₄. The intermediate product Mo₃O₉S₄ not only fails to directly contribute to MoS₂ film growth but also obstructs the diffusion of MoS₆, hindering film formation. When the growth temperature is increased from 1033 K to 1053 K, the diffusion rate of MoS₆ increases, and the inhibitory effect of Mo₃O₉S₄ on MoS₆ diffusion decreases, enabling the layered growth of MoS₂ films. Furthermore, lowering the pressure accelerates the convective diffusion rate of dilute species, significantly influencing the location of chemical reactions and the distribution of reaction products, which promotes grain diffusion and growth. This study not only deepens our understanding of mass transfer and reaction processes during MoS₂ growth but also provides valuable insights for the design and optimization of CVD systems.