PHYSICAL REVIEW B 85, 205448 (2012) Computational studies of graphene growth mechanisms Shayesteh Haghighatpanah * and Anders B ¨ orjesson School of Engineering, University of Bor˚ as, SE 501-90 Bor ˚ as, Sweden Hakim Amara Laboratoire d’Etude des Microstructures, ONERA-CNRS, BP 72, 92322 Chˆ atillon Cedex, France Christophe Bichara Centre Interdisciplinaire de Nanoscience de Marseille, CINAM, CNRS and Aix Marseille University, Campus de Luminy, Case 913, 13288 Marseille Cedex 9, France Kim Bolton School of Engineering, University of Bor˚ as, SE 501-90 Bor ˚ as, Sweden (Received 17 March 2012; published 25 May 2012) Density functional theory (DFT) and semiempirical tight-binding (TB) methods have been used to study the mechanism of graphene growth in the presence and absence of a catalytic surface. Both DFT and TB geometry optimized structures relevant to graphene growth show that the minimum energy growth mechanism is via the sequential addition of carbon hexagons at the edge of the graphene sheet. Monte Carlo (MC) simulations based on the TB model show that defect-free graphene sheets can be grown provided one has the proper combination of temperature, chemical potential, and addition rate. In this work, growth of perfect graphene structures has been simulated at the atomic level. Comparison of the growth mechanism in the absence and presence of a nickel catalyst surface shows that the catalyst (i) allows for adsorption of carbon atoms at surface and subsurface sites, (ii) enables formation of long, stable strings of carbon atoms, and (iii) stabilizes small flakes of graphene that can act as precursors to subsequent growth. DOI: 10.1103/PhysRevB.85.205448 PACS number(s): 61.48.Gh, 81.05.ue, 73.22.Pr I. INTRODUCTION Graphene, a monolayer thin carbon material with stable sp 2 hybridization, has attracted a lot of attention in different fields of science. This is because it has unique electrical, mechanical, and optical properties, 1–4 which make it suitable in many applications such as transistors, chemical and biosensors, energy storage devices, and electro-mechanical systems. 5 However, the properties of graphene are highly dependent on its atomic structure, 3,5,6 and it is often desirable that the material contains very few or (if possible) no defects. Various methods are used to synthesize graphene. These include mechanical peeling, reduction of graphene oxide, graphitization of silicon carbide (SiC) substrates and growth of graphene on catalytic metals. 4,7 One of the techniques used for graphene growth on metal surfaces is chemical vapor decomposition (CVD), which can be used to synthesize large graphene sheets of high quality and uniform thickness. 7,8 This is possible for a variety of metal substrates such as Co, Ni, Ir, Ru, and Cu. 4,6,8,9 For example, the Ni(111) surface is considered suitable for CVD growth since there is a good match between its first-neighbor interatomic distance (2.49 ˚ A) with the lattice parameter of graphite (2.46 ˚ A). 10 Previous studies, 4,8,11 indicate that the following stages are involved in the growth of graphene on Ni surfaces: first, carbon atoms from a proper carbon feedstock are adsorbed onto the surface and into subsurface sites where they exist as monomers or dimers. The second stage is graphene nucleation, where the monomers and dimers form longer C chains and small carbon islands on the metal surface. Depending on the C concentration, 12 these islands may be unstable and decompose to chains, monomers and dimers instead of growing into larger structures. The formation of these nucleation sites may occur at defects on the Ni surface such as step edges, 4,11,13 since these sites have higher reactivity than sites on the flat surface. In the third stage, the small graphene flakes increases in size due to the addition of C at the flake edges. The C monomers and dimers that form the graphene island or increase its size may come directly from the decomposed carbon feedstock or from the metal once it is saturated in carbon or when its temperature decreases. 4,8 Details of the growth mechanism, such as the relative abundance of the surface: subsurface adsorption sites for C and the stability and diffusion rate of C species on the substrate, are expected to depend on the metal used for the substrate. 14 It has been seen that the addition of Au to Ni catalyst sub- strates affects the graphene growth mechanism by decreasing the density of graphene nucleation sites. 8 In addition, several groups have grown graphene on low reactivity metals such as Cu and Au, 7 or in the absence of a catalyst. For example, Kim et al. 15 and Zhang et al. 16 have grown graphene on transparent substrates, insulators, and semiconductors without any catalyst, and Yu et al. 17 have grown carbon nanowalls, which are orientated vertically with respect to the substrate, without the addition of a catalyst. In this work, we use a TB model in MC simulations to study the growth of graphene in the absence of a catalyst, and compare this with the growth mechanism on a Ni(111) surface. The TB model has been developed specifically for Ni and C systems, 18–20 and it has been shown that it is valid for graphene growth on a Ni substrate. 1 By comparing to 205448-1 1098-0121/2012/85(20)/205448(9) ©2012 American Physical Society