Fractal etching of graphene

An anisotropic etching mode is commonly known for perfect crystalline materials, generally leading to simple Euclidean geometric patterns. This principle has also proved to apply to the etching of the thinnest crystalline material, graphene, resulting in hexagonal holes with zigzag edge structures. Here we demonstrate for the first time that the graphene etching mode can deviate significantly from simple anisotropic etching. Using an as-grown graphene film on a liquid copper surface as a model system, we show that the etched graphene pattern can be modulated from a simple hexagonal pattern to complex fractal geometric patterns with sixfold symmetry by varying the Ar/H2 flow rate ratio. The etched fractal patterns are formed by the repeated construction of a basic identical motif, and the physical origin of the pattern formation is consistent with a diffusion-controlled process. The fractal etching mode of graphene presents an intriguing case for the fundamental study of material etching.