Large-Scale Spontaneous Wrinkling of Polycrystalline Atomically Thin Films

Wafer-scale atomically thin films are inherently polycrystalline, and therefore criss-crossed by defect laden grain boundaries. It is well understood that a single, isolated crystalline defect creates long range deformations in a thin film, much like an electron that sources an electric field. Yet, unlike Maxwell's equations, the elasticity governing a buckled sheet is nonlinear. Thus, when multiple defects are present, superimposing their undulations will not give the sheet's final shape. This poses a challenge for understanding the shape of atomically thin films when they are not confined to a substrate. Here we perform spatially resolved measurements of the wrinkling of monolayer MoS₂ in a relatively force free environement. In doing so, we directly investigate the relationship between grain size and emergent corrugations of single layer polycrystalline MoS₂. We show that polycrystallinity, even with free boundaries, gives rise to micron scale wrinkles. Using universal scaling properties of thin sheets, we rationalize the large-scale features of the topography, including wrinkle wavelength and amplitude. Though the wrinkles we observe originate from a network of topological defects, our continuum arguments depend only on average strain and grain size, and not on atomistic details. The scaling relations we obtain suggest guidelines for tailoring grain size for specific application requirements.