Wrinkling of graphene because of the thermal expansion mismatch between graphene and copper

Omer Tarik Ogurtani, Dogukan Senyildiz, Goknur Cambaz Buke

Research output: Contribution to journalArticlepeer-review


Well‐defined bundles of wrinkles are observed on the graphene‐covered copper by using atomic force microscopy after chemical vapor deposition process. Their numerical analyses are performed by employing a set of formula deduced from classical elasticity theory of bent thin films with clamped boundary conditions. Here they are imposed by the banks of trenches associated with the reconstructed copper substrate surfaces, which suppress lateral movements of graphene monolayers and induce local biaxial stress. The wrinkling wavelength (λ) and amplitude (A) are both measured experimentally (λ = 100‐160 nm and A = 2.5‐3 nm) and calculated numerically (λ = 167 nm and A = 3.0 nm) and found to be in good agreement. Wrinkle formation is attributed to the nonhydrostatic compression stresses induced on the graphene by the linear thermal expan-sion coefficient difference between graphene and copper during cooling. These mismatch stresses, which are varying strongly with the temperature, create temperature‐dependent wrinkling wave formation that decreases in wavelength and increases in amplitude upon cooling below the cross‐ over temperature of 1233 K, at which both values of linear thermal expansion coefficient are equal. KEYWORDS atomic force microscopy, copper, graphene, strain, thermal stresses, wrinkling 1 | INTRODUCTION Wrinkling is a common phenomenon that is seen on graphene grown by the chemical vapor deposition (CVD) method because of the strain induced by the different thermal expansion coefficient mismatch between graphene and the metal substrate. 1 There has been a great interest in understanding the wrinkling of graphene since graphene wrinkles may affect its extraordinary properties such as electrical mobility, 2 band gap opening, 3 local charge accumulation, 4 anticorro-sion degradation, 5 mechanical strength, 6,7 thermal conductivity, 8,9 charge storage enhancement, 10 and strain sensitivity. 11 Hence, under-standing the wrinkling mechanisms of graphene is important for many applications. Moreover, this may shed light to studies in the area of membrane physics and mechanics in ultimate thin films. 2,3,12-17 Basically, periodic ripples in a suspended thin film form by either stretching in the axial direction, which is perpendicular to the fixed boundaries, or compression/displacement of the fixed edges in the lateral direction. 18 When we look at the experimental studies performed related to graphene wrinkling in literature, we see that the compression strain is applied in different ways using either free‐edge suspended or substrate‐supported graphene. In 2009, Bao et al 12 reported the first direct observation of periodic ripples in suspended graphene sheets, using both spontaneously and thermally generated strains by taking into account temperature variation of thermal expan-sion coefficient. In their work, graphene was transferred and suspended across preformed trenches on SiO 2 /Si substrates. By annealing suspended graphene in a furnace, wrinkles formed perpendicularly to the trench direction. Here, the compressive force was applied to the fixed boundaries in the lateral direction from the interface during cooling and the ripple formation was explained by using clasical thin‐ film elasticity theory, 19,20 which was used to analyze the wrinkling of an elastic sheet under tension by using clamped boundary conditions. Following this study, Wang et al 21 investigated the mechanism of wrin-kling of suspended graphene through atomistic simulations. Their results showed that periodic ripples are formed in graphene, when lon-gitudinal compression is applied to the fixed boundaries by thermal effects. They found out that 1/4‐power law formalisms are valid for the wavelength and the out‐of‐plane amplitude as functions of edge strain. In 2012, Tapasztó et al 13 observed periodic graphene ripples, with a wavelength of only 0.7 nm and modulation of only 0.1 nm, over the trenches with widths of about 5 nm on a Cu (111) surface and discussed the application of Cerda model. 20 With respect to the sub-strate‐supported graphene studies, in 2013, Meng et al 17 showed wrin-kling patterns on 10 μm monolayer hexagonal graphene flake grown on liquid copper surfaces. The origin of the anisotropic compression was attributed to the anisotropic surface stress of the Cu substrate, and an
Original languageEnglish
Pages (from-to)547-551
Number of pages5
JournalSurface and Interface Analysis
Issue number5
Publication statusPublished - 1 May 2018


  • atomic force microscopy
  • copper
  • graphene
  • strain
  • thermal stresses
  • wrinkling


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