Understanding the competing growth of 2D and 3D transition metal dichalcogenides in a chemical vapor deposition (CVD) reactor

The competing growth of two-dimensional (2D) and three-dimensional (3D) crystals of layered transition metal dichalcogenides (TMDCs) has been reproducibly observed in a large variety of chemical vapor deposition (CVD) reactors and demands a comprehensive understanding in terms of involved energetics. 2D and 3D growth is fundamentally different due to the large difference in the in-plane and out-of-plane binding energies in TMDC materials. Here, an analytical model describing TMDC growth via CVD is developed. The two most common TMDC structures produced via CVD growth (2D triangular flakes and 3D tetrahedra) are considered, and their formation energies are determined as a function of their growth parameters. By calculating the associated energies of 2D triangular or 3D tetrahedral flakes, we predict the minimum sizes of the critical nuclei of 2D triangular and 3D morphologies, and thereby determine the minimum realizable dimensions of TMDC, in the form of quantum dots. Analysis of growth rates shows that CVD favors 2D growth of MoS₂between 820 K and 900 K and 3D growth over 900 K. Our model also suggests that the flow rates of TMDC precursors (metal oxide and sulfur) in a long, cylindrical CVD reactor are important parameters for attaining uniform growth. Our model provides a compressive analysis of TMDC growth via CVD. Therefore, it is a critical tool for helping to achieve reproducible growth of 2D and 3D TMDCs for a variety of applications.