Wrinkling is a ubiquitous phenomenon in two-dimensional membranes. In particular, in the large-scale growth of graphene on metallic substrates, high densities of wrinkles are commonly observed. Despite their prevalence and potential impact on large-scale graphene electronics, relatively little is known about their structural morphology and electronic properties. Surveying the graphene landscape using atomic force microscopy, we found that wrinkles reach a certain maximum height before folding over. Calculations of the energetics explain the morphological transition, and indicate that the tall ripples are collapsed into narrow standing wrinkles by van der Waals forces, analogous to large-diameter nanotubes. Quantum transport calculations show that conductance through these collapsed wrinkle structures is limited mainly by a density-of-states bottleneck and by interlayer tunneling across the collapsed bilayer region. Also through systematic measurements across large numbers of devices with wide folded wrinkles, we find a distinct anisotropy in their electrical resistivity, consistent with our transport simulations. These results highlight the coupling between morphology and electronic properties, which has important practical implications for large-scale high-speed graphene electronics.
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