The thermal expansion coefficient of monolayer, bilayer, and trilayer graphene derived from the strain induced by cooling to cryogenic temperatures

Abstract

While thermally cycling monolayer, bilayer, and trilayer graphene between 5 K and 300 K, Raman spectroscopy has shown that cooling to 5 K induces a strain in these graphene flakes of - 0.081 ± 0.003 %. This strain was used to measure the graphene thermal expansion coefficient (TEC), which was found to be (- 3.2 ± 0.2) × 10 - 6 K - 1 for monolayers, (- 3.4 ± 0.4) × 10 - 6 K - 1 for bilayers, and (- 3.8 ± 0.6) × 10 - 6 K - 1 for trilayers at room temperature. The TEC showed a similar temperature dependence across all graphene thicknesses and was found to be in good agreement with theoretical predictions. This study, thus, represents the first measurement of the TEC of bilayer and trilayer graphene. Modification of graphene flakes of all thicknesses with various electrical contact designs was found to have no significant impact on the resulting strain, and thus the TEC, compared to the pristine graphene.