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 grapheme 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.