Lateral Versus Vertical Growth of Two-Dimensional Layered Transition-Metal Dichalcogenides: Thermodynamic Insight into MoS₂

Unprecedented interest has been spurred recently in two-dimensional (2D) layered transition metal dichalcogenides (TMDs) that possess tunable electronic and optical properties. However, synthesis of a wafer-scale TMD thin film with controlled layers and homogeneity remains highly challenging due mainly to the lack of thermodynamic and diffusion knowledge, which can be used to understand and design process conditions, but falls far behind the rapidly growing TMD field. Here, an integrated density functional theory (DFT) and calculation of phase diagram (CALPHAD) modeling approach is employed to provide thermodynamic insight into lateral versus vertical growth of the prototypical 2D material MoS₂. Various DFT energies are predicted from the layer-dependent MoS₂, 2D flake-size related mono- and bilayer MoS₂, to Mo and S migrations with and without graphene and sapphire substrates, thus shedding light on the factors that control lateral versus vertical growth of 2D islands. For example, the monolayer MoS₂ flake in a small 2D lateral size is thermodynamically favorable with respect to the bilayer counterpart, indicating the monolayer preference during the initial stage of nucleation; while the bilayer MoS₂ flake becomes stable with increasing 2D lateral size. The critical 2D flake-size of phase stability between mono- and bilayer MoS₂ is adjustable via the choice of substrate. In terms of DFT energies and CALPHAD modeling, the size dependent pressure-temperature-composition (P-T-x) growth windows are predicted for MoS₂, indicating that the formation of MoS₂ flake with reduced size appears in the middle but close to the lower T and higher P "Gas + MoS₂" phase region. It further suggests that Mo diffusion is a controlling factor for MoS₂ growth owing to its extremely low diffusivity compared to that of sulfur. Calculated MoS₂ energies, Mo and S diffusivities, and size-dependent P-T-x growth windows are in good accord with available experiments, and the present data provide quantitative insight into the controlled growth of 2D layered MoS₂.