Estimating the thermal expansion coefficient of graphene: the role of graphene-substrate interactions

The temperature-dependent thermal expansion coefficient of graphene is estimated for as-grown chemical vapor deposited graphene using temperature-dependent Raman spectroscopy. For as-grown graphene on copper, the extent of thermal expansion mismatch between substrate and the graphene layer is significant across the entire measured temperature interval, T  =  90-300 K. This mismatch induces lattice strain in graphene. However, graphene grown on copper substrates has a unique morphology in the form of quasi-periodic nanoripples. This crucially influences the profile of the strain in the graphene membrane, which is uniaxial. An estimate of the thermal expansion coefficient of graphene α (T) is obtained after consideration of this strain profile and after incorporating temperature-dependent Grüneisen parameter corrections. The value of α (T) , is found to be negative (average value, -3.75  ×  10^-6 K^-1) for the entire temperature range and it approaches close to zero for T  <  150 K. For graphene wet-transferred to three kinds of substrates: copper, poly-dimethylsiloxane, and SiO₂/Si, the Raman shifts can largely be modeled with lattice expansion and anharmonic contributions, and the data suggests limited interfacial interaction with the substrate.