Anisotropic Strain Relaxation of Graphene by Corrugation on Copper Crystal Surfaces

Abstract

Corrugation is a ubiquitous phenomenon for graphene grown on metal substrates by chemical vapor deposition, which greatly affects the electrical, mechanical, and chemical properties. Recent years have witnessed great progress in controlled growth of large graphene single crystals; however, the issue of surface roughness is far from being addressed. Here, the corrugation at the interface of copper (Cu) and graphene, including Cu step bunches (CuSB) and graphene wrinkles, are investigated and ascribed to the anisotropic strain relaxation. It is found that the corrugation is strongly dependent on Cu crystallographic orientations, specifically, the packed density and anisotropic atomic configuration. Dense Cu step bunches are prone to form on loose packed faces due to the instability of surface dynamics. On an anisotropic Cu crystal surface, Cu step bunches and graphene wrinkles are formed in two perpendicular directions to release the anisotropic interfacial stress, as revealed by morphology imaging and vibrational analysis. Cu(111) is a suitable crystal face for growth of ultraflat graphene with roughness as low as 0.20 nm. It is believed the findings will contribute to clarifying the interplay between graphene and Cu crystal faces, and reducing surface roughness of graphene by engineering the crystallographic orientation of Cu substrates.

Crystal Orientation Dependent Oxidation Modes at the Buried Graphene–Cu Interface

“…These surface corrugation have previously been described as Cu step bunches. 86 The existence of such Cu step bunches, wrinkle formation and variations in strain are commonly rationalized via a thermal expansion coefficient mismatch between graphene and Cu. The thermal expansion coefficient mismatch causes the graphene film to be under compressive stress and the Cu surface layer to be under tensile stress.…”

“… 91 Upon cooling the tensile stress in the Cu surface layer is relaxed by the formation of step bunches. 86 The compressive strain in graphene is relaxed by out of plane wrinkle formation, which again is dependent on the Cu crystallographic interaction strength of the graphene–Cu interface. 43 , 86 − 90 This is consistent with our measurements in Figure 5 (d) (see also Figures S11 and S12 ), where we observe reduced strain along a graphene wrinkle.…”

“… 86 The compressive strain in graphene is relaxed by out of plane wrinkle formation, which again is dependent on the Cu crystallographic interaction strength of the graphene–Cu interface. 43 , 86 − 90 This is consistent with our measurements in Figure 5 (d) (see also Figures S11 and S12 ), where we observe reduced strain along a graphene wrinkle. Upon intercalation and interface oxidation there is a volume expansion due to Cu oxidation and thus the compressive strain in graphene is released and graphene is under tensile strain (see Figure 5 ).…”

Possible pair-graphene structures govern the thermodynamic properties of arbitrarily stacked few-layer graphene

“…It is also necessary to transfer the resulting graphene layer to a substrate in order to fabricate electronic devices. Several types of crystal defects such as point defects 10 , one-dimensional dislocations 11 grain boundaries 12 , and wrinkles 2 , 13 – 15 formed during growth and ripple defects from the transfer process can be introduced into the graphene layer. Defects can form during in growth due to both crystal imperfections of the catalyst substrate and large temperature differences during cooling from the growth temperature to room temperature.…”

Silicon- and Graphene-based FETs for THz technology

“…This leads to a considerable degradation of the carrier mobility [114]. Similar effects can be observed on different substrates as graphene growth on copper by epitaxial growth and CVD [115] or graphene growth on SiC by Epitaxial growth [116] among other substrates [117].…”