Phenomenological Interactions during CVT Synthesis of Large Scale MoS2
Authors: Shendokar Sachin , Hossen Moha Feroz , Mantripragada Shobha , Aravamudhan Shyam 
Published: September 2023

In the Chemical Vapor Transport (CVT), for deposition of MoS2, sulfur and MoO3 powder is evaporated at 200 0C and 650 0C respectively. The Ar flow directs the sulfur atoms to Mo species so as to react chemically as specified in the reactions in Equation-1. During the CVT process there is adsorption of MoS2 on Si/SiO2 substrate associated with the exhuast of SO2 as chemical reaction by-product. The MoS2 is deposited on the substrate by physisorption. Thus, in CVT, the nucleation and growth is a combined effect of chemisorption and physisorption. The three types of nucleation and growth theories for deposition of 2D thin films are presented by a. Volmer–Weber b.Frank–van der Merwe, c. Stranski–Krastanov in Figure 1.
Figure 1
[Equation 1]
The mechanism for MoS2 nucleation and growth during CVT involves the evaporation of powdered precursors at a high temperature which leads to decomposition as well, followed by a chemical reaction. Temperature ramping-up rate, positioning of precursors, type and flow rate of carrier gases, Cooling rate, and pressure simultaneously determine the morphology, thickness, and crystallinity of the physisorbed MoS2. The highly simplified resolution of forces acting during the nucleation process is represented in Figure 2. The σF refers to the forces due to surface tension along the droplet, σS is the force exerted due to the energy associated with the substrate surface, and σFS is the force due to the interface energy between the droplet and the substrate. A little consideration of the comparison of the magnitude of these three forces leads to the determination of Growth Kinetics. When σS is smaller than the sum of σF and σFS, it favors Weber-Volmer theory; when σS is greater than the sum of σF and σFS, it favors Frank van der Merwe theory, and when the balance of this comparison fluctuates or is equal, it favors the Stranski–Krastanov growth model. In practice, the several parameters other than temperature, pressure, flow rate, and precursor flux that influence the nucleation and growth mechanism involve substrate surface texture, functionalization, availability of active cites, steric hindrance, Columbic interactions etc.
Figure 2

Interactions in CVT on the basis of Scientific Theories
:

Considering that CVT involves the gas phase chemical reaction of precursors and physisorption for the MoS2 adsorption on the Si/SiO2 substrate, the modified ideal gas law can be applied more realistically with the introduction of the van der Waals parameters for intermolecular interaction forces ‘a’ and molecular size ‘b’. The modified gas law is stated by van der Waals equation as,
[Equation 2]
a – Constant for Intermolecular forces and b – Constant for Molecular size for the specified gas under consideration. Thus, if studies related to variation in temperature are carried out, Volume being physically constant and significantly large space in case of CVT may be considered as independent parameter. Thus, from relation 2, pressure is directly affected with the change in temperature.
Further, the pressure in accordance with Amonton’s law affects the adsorption and mean free path of the Mo and S atoms that determines the reaction between the chemical species [3].
The mean free path for the atomized precursor is expressed as follows.
[Equation 3]
The dependence of the mean free path λ on T – temperature and P – the pressure is conclusive for the parametric interactions resulting in accordance with the Amonton’s law for constant volume affect the CVT process. In the equation, is the Boltzman’s constant.
As referred to in the beginning, physisorption is the mechanism for depositing 2D thin films in CVT. Physisorption is caused by adsorption and thus, the variation in process parameters will have impact on Langmuir’s adsorption [4]given by
[Equation 4]
Langmuir’s adsorption isotherm explains the interfacial interaction of the gas phase molecules with the substrate. The Figure 3. depicts the variation in corresponding to the KP at a constant temperature. As is evident the Langmuir’s adsorption is derived at isothermal conditions for variation in pressure. Thus, it is implied that during the CVT synthesis of MoS2 if the variation in temperature is studied, it will inherently affect the adsorption.
Arrhenius equation [5] governs the reaction rate based on A- pre-exponent rate factor, Ea – activation energy, R – gas constant and temperature.
[Equation 5]
Considering the van der Waals equation and Amontons law, the temperature is going to affect the pressure. The rate constant will be affected by Ar flow rate. These phenomological interactions occur and influence the nucleation and large scale growth of MoS2 during CVT synthesis.

Figure 1