Enhancement of island size by dynamic substrate disorder in simulations of graphene growth

Abstract

We demonstrate a new mechanism in the early stages of sub-monolayer epitaxial island growth, using Monte Carlo simulations motivated by experimental observations on the growth of graphene on copper foil. In our model, the substrate is "dynamically rough", by which we mean (i) the interaction strength between Cu and C varies randomly from site to site, and (ii) these variable strengths themselves migrate from site to site. The dynamic roughness provides a simple representation of the near-molten state of the Cu substrate in the case of real graphene growth. Counterintuitively, the graphene island size increases when dynamic roughness is included, compared to a static and smooth substrate. We attribute this effect to destabilisation of small graphene islands by fluctuations in the substrate, allowing them to break up and join larger islands which are more stable against roughness. In the case of static roughness, when process (ii) is switched off, island growth is strongly inhibited and the scale-free behaviour of island size distributions, present in the smooth-static and rough-dynamic cases, is destroyed. The effects of the dynamic substrate roughness cannot be mimicked by parameter changes in the static cases.

Monte Carlo and Kinetic Monte Carlo Models for Deposition Processes: A Review of Recent Works

“…Graphene growth on a Cu substrate is due to the diffusion of carbon atoms on the Cu surface with the latter having low solubility and catalyst activity. Enstone et al [34] proposed an MC model for graphene growth on a Cu substrate to study the effects of the substrate's roughness on graphene nucleation. They showed that the key factors which determine the island size and formation are roughness amplitude and mobility parameters (Figure 2B).…”

Growth at high substrate coverage can decrease the grain boundary roughness of 2D materials

“…In this work, we introduce a model for the propagation of two grain edges and for the relaxation of the GB formed after the collision of those edges. The aim of the model is to identify the generic consequences of elementary microscopic processes such as adatom surface diffusion, attachment, and detachment from edges and GBs of a variety of 2d materials, in contrast with approaches that focus on particular applications [16,30,31,15]. This modelling approach allows one to investigate the effects of the variations of the rates of those processes over several orders of magnitude using kinetic Monte Carlo (KMC) simulations.…”

Formation of smoother grain boundaries in 2D materials using high deposition rates during the last stages of growth

“…In this work, we introduce a model for the propagation of two grain edges and for the relaxation of the GB formed after the collision of those edges. The aim of the model is to identify the generic consequences of elementary microscopic processes such as adatom surface diffusion, attachment, and detachment from edges and GBs of a variety of 2d materials, in contrast with approaches that focus on particular applications [15,16,25,32,33]. This modelling approach allows one to investigate the effects of the variations of the rates of those processes over several orders of magnitude using kMC simulations.…”