The morphology of doubly-clamped graphene nanoribbons

Abstract

Understanding the response of micro/nano-patterned graphene to mechanical forces is instrumental for applications such as advanced graphene origami and kirigami. Here, we analyze free-standing nanoribbons milled into single-layer graphene by focused ion beam processing. Using transmission electron microscopy, we show that the length L of the structures determines their morphology. Nanoribbons with L below 300 nm remain mainly flat, whereas longer ribbons exhibit uni-axial crumpling or spontaneous scrolling, a trend that is well reproduced by molecular dynamics simulations. We measure the strain of the ribbons as well as their crystallinity by recording nanometer-resolved convergent beam electron diffraction maps, and show that the beam tails of the focused ion beam cause significant amorphization of the structures adjacent to the cuts. The expansive or compressive strain in the structures remains below 4%. Our measurements provide experimental constraints for the stability of free-standing graphene structures with respect to their geometry, providing guidelines for future applications of patterned graphene.