Toward a Mechanistic Understanding of Vertical Growth of van der Waals Stacked 2D Materials: A Multiscale Model and Experiments.

Vertical stacking of monolayers via van der Waals (vdW) interaction opens promising routes toward engineering physical properties of two-dimensional (2D) materials and designing atomically thin devices. However, due to the lack of mechanistic understanding, challenges remain in the controlled fabrication of these structures via scalable methods such as chemical vapor deposition (CVD) onto substrates. In this paper, we develop a general multiscale model to describe the size evolution of 2D layers and predict the necessary growth conditions for vertical (initial + subsequent layers) versus in-plane lateral (monolayer) growth. An analytic thermodynamic criterion is established for subsequent layer growth that depends on the sizes of both layers, the vdW interaction energies, and the edge energy of 2D layers. Considering the time-dependent growth process, we find that temperature and adatom flux from vapor are the primary criteria affecting the self-assembled growth. The proposed model clearly demonstrates the distinct roles of thermodynamic and kinetic mechanisms governing the final structure. Our model agrees with experimental observations of various monolayer and bilayer transition metal dichalcogenides grown by CVD and provides a predictive framework to guide the fabrication of vertically stacked 2D materials.