Comparative study of defects in graphene flake grown on amorphous and crystalline copper surfaces

Abstract Experimentally, it has been determined that at large scales graphene sheets grown on amorphous or liquid copper have less defects than graphene sheets grown on crystalline copper. No information has been obtained however for small-scale graphene flakes. Understanding defects in flakes is crucial as they serve as intermediates in large-scale graphene growth. Our goal in this work is to quantify defects in graphene flakes grown on different copper substrates. We performed a computational study using Density Functional Theory calculations on a copper-graphene system. A global minima search was performed using the Minima Hopping algorithm to find multiple graphene isomers that can appear on different substrates. As a model of copper substrate, we used a 112 copper atom cluster and as a model of graphene flake, we used 40 carbon atoms on top of the copper surface. The system was placed in vacuum to guarantee no interaction between images. The global minima search identified multiple graphene isomers on crystalline and amorphous substrates with dangling bonds and with all defects located on the edge. However, graphene on amorphous copper exhibits a higher frequency and greater variety of polygon defects than on crystalline copper. To estimate inner defects, a Stone-Wales defect was introduced, showing higher formation energy on amorphous surfaces than crystalline ones. These findings show that substrate type influences defect formation in graphene isomers. As a result, we propose that in the growth of graphene sheets the flakes on amorphous surfaces will have much lower inner defects (because of higher energy formation) while the edge defects will reconstruct more easily (having more available isomers and relaxation paths). The combination of both mechanisms could then be a contributing factor to the final formation of a more pristine graphene sheet in the amorphous surface.