Thermally induced mechanical strain of graphene on copper and other substrates

Raman spectroscopy is employed to investigate the temperature dependence of the phonon frequencies of the G and 2D modes of monolayer graphene grown on copper foil by chemical vapor deposition. Both the G and 2D modes exhibit significant red shift as temperature increases, and the extracted values of the temperature coefficients of the G and 2D modes are about -0.07 cm- 1K-1 and -0.15 cm- 1K-1, respectively. In addition, we extracted the intrinsic Raman shift of the G mode by determining the thermally induced mechanical strain that is transmitted from the copper substrate to graphene. The extracted intrinsic G mode frequency shift is in very good agreement with earlier reported first principles calculations. Finally, we have calculated the temperature dependence of the substrate-induced strain on graphene when it is deposited or grown to various technologically important substrates, showing that strains as high as 1.1% can be imparted to graphene within a temperature range of 500 K.