Generalized Mechanistic Model for the Chemical Vapor Deposition of 2D Transition Metal Dichalcogenide Monolayers

Transition metal dichalcogenides (TMDs) like molybdenum disulfide (MoS<sub>2</sub>) and tungsten disulfide (WS<sub>2</sub>) are layered materials capable of growth to one monolayer thickness <i>via</i> chemical vapor deposition (CVD). Such CVD methods, while powerful, are notoriously difficult to extend across different reactor types and conditions, with subtle variations often confounding reproducibility, particularly for 2D TMD growth. In this work, we formulate the first generalized TMD synthetic theory by constructing a thermodynamic and kinetic growth mechanism linked to CVD reactor parameters that is predictive of specific geometric shape, size, and aspect ratio from triangular to hexagonal growth, depending on specific CVD reactor conditions. We validate our model using experimental data from Wang <i>et al.</i> (<i>Chem. Mater.</i> <b>2014</b>, <i>26</i>, 6371−6379) that demonstrate the systemic evolution of MoS<sub>2</sub> morphology down the length of a flow CVD reactor where variations in gas phase concentrations can be accurately estimated using a transport model (<i>C</i><sub>Sulfur</sub> = 9–965 μmol/m<sup>3</sup>; <i>C</i><sub>MoO3</sub> = 15–16 mmol/m<sup>3</sup>) under otherwise isothermal conditions (700 °C). A stochastic model which utilizes a site-dependent activation energy barrier based on the intrinsic TMD bond energies and a series of Evans–Polanyi relations leads to remarkable, quantitative agreement with both shape and size evolution along the reactor. The model is shown to extend to the growth of WS<sub>2</sub> at 800 °C and MoS<sub>2</sub> under varied process conditions. Finally, a simplified theory is developed to translate the model into a “kinetic phase diagram” of the growth process. The predictive capability of this model and its extension to other TMD systems promise to significantly increase the controlled synthesis of such materials.