Formation of Ripples in Graphene as a Result of Interfacial Instabilities

Abstract

Formation of ripples on a supported graphene sheet involves interfacial interaction with the substrate. In this work, graphene was grown on a copper foil by chemical vapor deposition from methane. On thermal quenching from elevated temperatures, we observed the formation of ripples in grown graphene, developing a peculiar topographic pattern in the form of wavy grooves and single/double rolls, roughly honeycomb cells, or their combinations. Studies on pure copper foil under corresponding conditions but without the presence of hydrocarbon revealed the appearance of peculiar patterns on the foil surface, such as dendritic structures that are distinctive not of equilibrium solidified phases but arise from planar and/or convective instabilities driven by solutal and thermal capillary forces. We propose a new origin for the formation of ripples in the course of graphene growth at elevated temperatures, where the topographic pattern formation is governed by dynamic instabilities on the interface of a carbon-catalyst binary system. These non-equilibrium processes can be described based on Mullins-Sekerka and Benard-Marangoni instabilities in diluted binary alloys, which offer control over the ripple texturing through synthesis parameters such as temperature, imposed temperature gradient, quenching rate, diffusion coefficients of carbon in the metal catalyst, and the miscibility gap of the metal catalyst-carbon system.

A first principles study on the CVD graphene growth on copper surfaces: A carbon atom incorporation to graphene edges

“…Molecular dynamical approach was adopted since copper surface is active dynamically in typical CVD graphene growth experiments at ~1000 °C [30]. Since carbon atom bonding takes place rarely in plain MD simulations, constrained MD calculations were performed to force C-C bonding.…”

“…These findings are valuable but should be verified well, since they are mostly based on static geometry calculations where the copper surface is assumed to be ordered. Our concern is that such static modelling may not be appropriate for Cu-CVD systems, since the copper surface is thought to be dynamically active in typical graphene growth experiments at ~1000 °C (note that the melting point of copper is 1084 °C) [30].…”

Graphene as transparent conducting layer for high temperature thin film device applications

“…5(b)) is attributed to the transfer process, which is known to introduce wrinkles and discontinuities that cause an increase of the macroscopic resistivity of G membranes [27][28][29][30][31]. Interestingly, similar results have been obtained for both catalysts, in spite of the presence of a high density of grain boundaries in the Cu-film grown membranes, associated to the smaller Cu grain size [32][33][34].…”

Growth Study and Characterization of Single-Layer Graphene Structures Deposited on Copper Substrate by Chemical Vapour Deposition

“…This gives rise to the surface reconstruction and to the formation of nano-ripples. While cooling down to room temperature, the copper substrate contracts, whereas the graphene which is on top tries to expand according to its negative thermal expansion coefficient [59]. In the areas where graphene is pinned to the copper, it is displayed to a strong compressive stress, whereas in the areas where the graphene is suspended above the nano-ripples it is allowed to relax some amount of the compressive strain through out-ofplane deformation (rippling) [60][61].…”