Two-dimensional hexagonal boron nitride (h-BN) has appeared as a promising material in diverse areas of applications, including as an excellent substrate for graphene devices, deep-ultraviolet emitters, and tunneling barriers, thanks to its outstanding stability, flat surface, and wide-bandgap. However, for achieving such exciting applications, controllable mass synthesis of high-quality and large-scale h-BN is a precondition. The synthesis of h-BN on metal surfaces using chemical vapor deposition (CVD) has been extensively studied, aiming to obtain large-scale and high-quality materials. The atomic-scale growth process, which is a prerequisite for rationally optimizing growth circumstances, is a key topic in these investigations. Although theoretical investigations on h-BN growth mechanisms are expected to reveal numerous new insights and understandings, different growth methods have completely dissimilar mechanisms, making theoretical research extremely challenging. In this article, we have summarized the recent cutting-edge theoretical research on the growth mechanisms of h-BN on different metal substrates. On the frequently utilized Cu substrate, h-BN development was shown to be more challenging than a simple adsorption-dehydrogenation-growth scenario. Controlling the number of surface layers is also an important challenge. Growth on the Ni surface is controlled by precipitation. An unusual reaction-limited aggregation growth behavior has been seen on interfaces having a significant lattice mismatch to h-BN. With intensive theoretical investigations employing advanced simulation approaches, further progress in understanding h-BN growth processes is predicted, paving the way for guided growth protocol design.
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