Equi-biaxial compressive strain in graphene: Grüneisen parameter and buckling ridges

Strain and defects in graphene have critical impact on morphology and properties of graphene. Here we report equi-biaxial compressive strain in monolayer graphene on SiO2 and Si3N4 substrates induced by thermal cycling in vacuum. The equi-biaxial strain is attributed to the mismatch in coefficient of thermal expansion between graphene and the substrate and sliding of graphene on the substrate. The sliding occurs during heating at the temperatures of 390 and 360 K for graphene on SiO2 and Si3N4 substrates, respectively. The biaxial Grüneisen parameter is determined to be 1.95 and 3.15 for G and 2D Raman bands of graphene, respectively. As the heating temperature exceeds a threshold temperature (1040 K for graphene/SiO2 and 640 K for graphene/Si3N4), buckling ridges are observed in graphene after the thermal cycle, from which the biaxial buckling strain of graphene on SiO2 and Si3N4 substrates are obtained as 0.21% and 0.22%, respectively. Importantly, the induced buckling ridges in graphene exhibit a pattern representing the symmetry of graphene crystal structure, which indicates that graphene relieves the compressive stress mainly along its lattice symmetry directions. These thermally induced graphene ridges are also found reminiscent of those in the synthesized graphene, suggesting the same origin of formation of the buckling ridges under biaxial compression.