Abstract
Upon cooling, branched line defects develop in epitaxial graphene grown at high temperature on Pt(111) and Ir(111). Using atomically resolved scanning tunneling microscopy, we demonstrate that these defects are wrinkles in the graphene layer, i.e. stripes of partially delaminated graphene. With low energy electron microscopy (LEEM), we investigate the wrinkling phenomenon in situ. Upon temperature cycling, we observe hysteresis in the appearance and disappearance of the wrinkles. Simultaneously with wrinkle formation a change in bright field imaging intensity of adjacent areas and a shift in the moiré spot positions for micro diffraction of such areas takes place. The stress relieved by wrinkle formation results from the mismatch in thermal expansion coefficients of graphene and the substrate. A simple one-dimensional model taking into account the energies related to strain, delamination and bending of graphene is in qualitative agreement with our observations.
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GENERAL SCIENTIFIC SUMMARY Introduction and background. Graphene is one atomic layer of carbon as it occurs naturally in graphite. Graphene has properties which promise a broad range of applications including post-silicon electronic devices. Such a graphene layer can be grown on various substrates including metal surfaces in a high temperature (ca. 1000°C) process. For applications it is desirable to grow perfectly flat and extended graphene layers.
Main results. After the high temperature growth process, the graphene layer and the substrate cool down. Graphene does barely contract when the temperature is reduced, but the substrate shrinks upon cooling and compresses the graphene layer laterally. If the compression exceeds a few tenths of a percent, the graphene layer partly evades the compression by forming wrinkles. More and more wrinkles are formed until the sample reaches room temperature. After cooling, wrinkles and inhomogeneous compression are present in the graphene layer. We have observed this process on a scale from nanometers to micrometers and developed a model to describe the wrinkle formation.
Wider implications. The principle of wrinkle formation during graphene growth is simple. Yet, if one wants to grow perfect graphene (e.g. for electronics) the wrinkle formation and the strain have to be accounted for. This paper helps to understand the mechanism the formation of wrinkles and inhomogeneous residual strain and may help to find ways to avoid them.
Figure. A graphene flake (blue) grown on an iridium crystal (red). During cooling to room temperature strain has led to dark wrinkles on the flake. (Low energy electron microscopy image, false colors.)