The complementary graphene growth and etching revealed by large-scale kinetic Monte Carlo simulation

To fully understand the kinetics of graphene growth, large-scale atomic simulations of graphene islands evolution up to macro sizes (i.e., graphene islands of a few micrometers or with billions of carbon atoms) during growth and etching is essential, but remains a great challenge. In this paper, we developed a low computational cost large-scale kinetic Monte Carlo (KMC) algorithm, which includes all possible events of carbon attachments and detachments on various edge sites of graphene islands. Such a method allows us to simulate the evolution of graphene islands with sizes up to tens of micrometers during either growth or etching with a single CPU core. With this approach and the carefully fitted parameters, we have reproduced the experimentally observed evolution of graphene islands during both growth or etching on Pt(111) surface, and revealed more atomic details of graphene growth and etching. Based on the atomic simulations, we discovered a complementary relationship of graphene growth and etching—the route of graphene island shape evolution during growth is exactly the same as that of the etching of a hole in graphene and that of graphene island etching is exactly same as that of hole growth. The complementary relation brings us a basic principle to understand the growth and etching of graphene, and other 2D materials from atomic scale to macro size and the KMC algorithm is expected to be further developed into a standard simulation package for investigating the growth mechanism of 2D materials on various substrates.