Lattice mismatch induced nonlinear growth of graphene.

As a two-dimensional material, graphene can be obtained via epitaxial growth on a suitable substrate. Recently, an interesting nonlinear behavior of graphene growth has been observed on some metal surfaces, but the underlying mechanism is still elusive. Taking the Ir(111) surface as an example, we perform a mechanistic study on graphene growth using a combined approach of first-principles calculations and kinetic Monte Carlo (kMC) simulations. Small carbon clusters on the terrace or at step sites are studied first. Then, we investigate how these small carbon species are attached to graphene edges. Generally, attachment of carbon atoms is thermodynamically favorable. However, due to substrate effect, there are also some edge sites where graphene growth must proceed via cluster attachment. The overall growth rate is determined by these cluster attachment processes, which have a much lower chance of happening compared to the monomer attachment. On the basis of such an inhomogeneous growth picture, kMC simulations are performed by separating different time scales, and the experimentally found quintic-like behavior is well reproduced. Different nonlinear growth behaviors are predicted for different graphene orientations, which is consistent with previous experiments. Inhomogeneity induced by lattice mismatch revealed in this study is expected to be a universal phenomenon and will play an important role in the growth of many other heteroepitaxial systems.