## 4 Results and Discussion
### The Influence of Pressure on MoS2 Growth
For Mo\({}_{3}\)O\({}_{9}\), 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 Mo\({}_{3}\)O\({}_{9}\) concentrations at the substrate are 0.025 and 0.004 mol/m\({}^{3}\), respectively. As the pressure increases to 70 and 100 Torr, the Mo\({}_{3}\)O\({}_{9}\) concentration at the substrate becomes 0 mol/m\({}^{3}\). This decrease is partly due to the reduced evaporation rate of Mo\({}_{3}\)O\({}_{9}\) at higher pressures and partly due to the accelerated reaction rate driven by the increased S\({}_{2}\) concentration. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Source** & **Pressure** & **Temperature** & **Mo\({}_{3}\)O\({}_{9}\) Flow** \\ \hline \multirow{4}{*}{MoO\({}_{3}\) powder} & 10 Torr & & 9.4 \(\times\) 10\({}^{-4}\) mol min\({}^{-1}\) cm\({}^{-2}\) \\  & 40 Torr & & 5.5 \(\times\) 10\({}^{-4}\) mol min\({}^{-1}\) cm\({}^{-2}\) \\  & 70 Torr & & 3.9 \(\times\) 10\({}^{-4}\) mol min\({}^{-1}\) cm\({}^{-2}\) \\  & 100 Torr & & 2.4 \(\times\) 10\({}^{-4}\) mol min\({}^{-1}\) cm\({}^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Relationship between the evaporation rate of Mo\({}_{3}\)O\({}_{9}\) and gas pressure. Figure 9 shows the concentration distribution of Mo\({}_{3}\)O\({}_{9}\)S\({}_{4}\) at different pressures. As pressure increases, the concentration of Mo\({}_{3}\)O\({}_{9}\)S\({}_{4}\) 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 Mo\({}_{3}\)O\({}_{9}\)S\({}_{4}\) at the substrate. On the other hand, the increased pressure reduces the volatilization rate of Mo\({}_{3}\)O\({}_{9}\), leading to a decrease in the concentration of the intermediate product Mo\({}_{3}\)O\({}_{9}\)S\({}_{4}\). These two factors compete with each other, resulting in the concentration first increasing and then decreasing with rising pressure. Figure 8: Radial cross-sectional view of the Mo\({}_{3}\)O\({}_{9}\) concentration distribution at the center of the substrate at a set temperature of 1053 K in growth region, with a pressure of (**a**,**b**) 10 Torr, (**c**,**d**) 40 Torr, and (**e**,**f**) 100 Torr. Figure 7: Velocity distribution diagrams of the system at a pressure of (**a**–**c**) 10 Torr, (**d**–**f**) 40 Torr, and (**g**–**i**) 100 Torr when the temperature is set to 1053 K in growth region, where (**b**,**e**,**h**) are radial cross-section diagrams at the center of the substrate and (**c**,**f**,**i**) are corresponding local magnified diagrams. As the pressure increases, the concentration of MoS\({}_{6}\) products within the chamber also increases, as shown in Figure 10. The concentration of MoS\({}_{6}\) at the substrate position rises from 0.03 mol/m\({}^{3}\) at 10 Torr to 0.35 mol/m\({}^{3}\) at 100 Torr. Although the volatilization rate of Mo\({}_{3}\)O\({}_{9}\) 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 MoS\({}_{6}\) 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 MoS\({}_{6}\) at the substrate. On the one hand, the decreased concentration of MoS\({}_{6}\) will slow the nucleation and growth rate of the MoS\({}_{2}\) film; on the other hand, the increased diffusion rate facilitates the diffusion-driven growth of MoS\({}_{6}\) on the substrate.