Temperature-induced strain release via rugae on the nanometer and micrometer scale in graphene monolayer

Abstract

Wrinkles are one possible rugae phase that can be observed in two-dimensional crystals. Those topographic features, with dimensions ranging from nanometers to micrometers, can be identified in single-layer graphene transferred onto various substrates. When the temperature of the sample is varied, the different thermal expansion coefficients of graphene and its supporting substrate lead to reconstruction of the graphene's topography, which results in spatially inhomogeneous strain and doping. Using Raman spectral mapping, we investigated in situ the temperature dependence (50–300 K) of topographic features in a graphene monolayer grown by chemical vapor deposition (CVD) and transferred onto a Si/SiO2 substrate. We find that the temperature-induced strain follows the temperature variation of the cubic lattice parameter of the Si substrate. Furthermore, the temperature-induced strain has an unambiguous relation to the topographic reconstruction of the graphene monolayer. We focused on the behavior of two types of rugae: 1) large wrinkles with dimensions that are larger than the laser spot size and can be traced directly and 2) nanoscale wrinkles and ripples, which can be identified by changes in the parameters of the principal Raman active bands of the graphene monolayer. In addition, we observed that temperature-induced reconstructions are accompanied by local variation of doping.