Abstract:

Controllable synthesis of MoS₂ with desired number of layers via chemical vapor deposition (CVD) remains challenging. Hence, it is highly desirable to develop a theoretical model that can be used to predict the single- and multilayer growth of MoS₂ quantitatively, and provide guidelines for experimental fabrication. Herein we have established a kinetic Monte Carlo (kMC) model to predict the CVD growth of mono- and bilayer MoS₂. First, we proposed that the growth rates of layer 1 and layer 2 were governed by the distribution of the adatom concentration, and the growth kinetics of compact triangular MoS₂ followed the kink nucleation-propagation mechanism. The adatom concentration was formulated in terms of adatom flux, effective lifetime of adatoms, growth temperature, binding energies, edge energies, and nucleation criterion. The kink nucleation and propagation were determined by energy barriers of the adatom attachments to the zigzag and armchair edges. We then employed an analytic thermodynamic criterion to extract these parameters. Using the calibrated model, we found that the growth rate of layer 2 strongly depended on the size of layer 1 and decreased monotonically with increasing size of layer 1, and might even become prohibited at the maximum size of layer 1. Furthermore, we analyzed the size and morphology evolutions of bilayer MoS₂ at different growth temperatures and adatom fluxes. Throughout the growth processes of bilayer MoS₂, the morphologies of layers 1 and 2 maintained triangular shapes with compact edges, consistent with the kink nucleation-propagation growth mechanism. Our simulations revealed that the growth of bilayer MoS₂ was promoted by increasing the growth temperature or decreasing the adatom flux, which corroborated the experimental observations. The increase in growth temperature led to reduced adatom concentration at the edge of layer 2 in accordance with the adatom concentration far from the edge of layer 2, resulting in a consistent difference in the adatom concentration to promote the growth of bilayer MoS₂. Similarly, the decrease in adatom flux lowered the difference between the adatom concentrations far from the edge and at the edge of layer 1, decelerating the growth of layer 1. The decelerated growth of layer 1 reduced the difference between the adatom concentrations far from the edge and at the edge of layer 2 to zero, permitting the growth of bilayer MoS₂. To guide the experimental synthesis, we constructed a phase diagram to delineate the permitted or prohibited growth of bilayer MoS₂ at different growth temperatures and adatom fluxes. Hence, this work not only unveils the conditions for the growth of mono- and bi-layer MoS₂, but also provides guidelines for controllable synthesis of MoS₂ with the desired number of layers.

Key words: MoS₂, Monolayer growth, Bilayer growth, Chemical vapor deposition, Kinetic Monte Carlo