title: 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.
authors.affiliation: Centre for Complexity Science, University of Warwick, Coventry, CV4 7AL, UK. g.t.enstone@warwick.ac.uk.
authors.forename: Gwilym
authors.initials: G
authors.lastname: Enstone
authors.affiliation: Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, UK and Warwick Centre for Predictive Modelling, School of Engineering, University of Warwick, Coventry, CV4 7AL, UK.
authors.forename: Peter
authors.initials: P
authors.lastname: Brommer
authors.affiliation: Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, UK and Department of Physics, University of Warwick, Coventry, CV4 7AL, UK.
authors.forename: David
authors.initials: D
authors.lastname: Quigley
authors.affiliation: Department of Physics, University of Warwick, Coventry, CV4 7AL, UK.
authors.forename: Gavin
authors.initials: G
authors.lastname: R Bell