Dynamic growth/etching model for the synthesis of two-dimensional transition metal dichalcogenides via chemical vapour deposition

The preparation of two-dimensional transition metal dichalcogenides on an industrially relevant scale will rely heavily on bottom-up methods such as chemical vapour deposition. In order to obtain sufficiently large quantities of high-quality material, a knowledge-based optimization strategy for the synthesis process must be developed. A major problem that has not yet been considered is the degradation of materials by etching during synthesis due to the high growth temperatures. To address this problem, we introduce a mathematical model that accounts for both growth and, for the first time, etching to describe the synthesis of two-dimensional transition metal dichalcogenides. We consider several experimental observations that lead to a differential equation based on several terms corresponding to different supply mechanisms, describing the time-dependent change in flake size. By solving this equation and fitting two independently obtained experimental data sets, we find that the flake area is the leading term in our model. We show that the differential equation can be solved analytically when only this term is considered, and that this solution provides a general description of complex growth and shrinkage phenomena. Physically, the dominance suggests that the supply of material via the flake itself contributes most to its net growth. This finding also implies a predominant interplay between insertion and release of atoms and their motion in the form of a highly dynamic process within the flake. In contrast to previous assumptions, we show that the flake edges do not play an important role in the actual size change of the two-dimensional transition metal dichalcogenide flakes during chemical vapour deposition.