Modeling of the self-limited growth in catalytic chemical vapor deposition of graphene

The development of wafer-scale continuous single-crystal graphene layers is key in view of its prospective applications. To this end, here we pave the way for a graphene growth model in the framework of the Langmuir adsorption theory and two dimensional crystallization. In specific, we model the nucleation and growth of graphene on copper using methane as carbon precursor. The model leads to identification of the range of growth parameters (temperature and gas pressures) that uniquely entails the final surface coverage of graphene. This becomes an invaluable tool to address the fundamental problems of continuity of polycrystalline graphene layers, and crystalline grain dimensions. The model shows agreement with the existing experimental data in the literature. On the basis of the "contour map" for graphene growth developed here and existing evidence of optimized growth of large graphene grains, novel insights for engineering wafer-scale continuous graphene films are provided.