Accurate determination of stiffness and strength of graphene via AFM-based membrane deflection

The Young’s modulus and fracture strength of single and bilayer graphene (BLGr) grown by chemical vapour deposition (CVD) were determined using atomic force microscopy-based membrane deflection experiments. The uncertainty resulting from instrument calibration and the errors due to the experimental conditions like tip wear, loading position, and sample preparation were investigated to estimate the accuracy of the method. The theoretical estimation of the uncertainty on the Young’s modulus linked to the calibration is around 16%. Finite element simulations were performed to determine the effects of membrane shape and loading position on the extraction of the Young’s modulus. Off-centre loading results in the overestimation of the Young’s modulus while deviation from the circular shape leads to an underestimation of the stiffness. The simulated results were compared with experiments. With all these sources of errors taken into account, the Young’s modulus and fracture strength of CVD-grown single layer graphene are found equal to 0.88 ± 0.14 TPa and 134 ± 16 GPa, respectively. For CVD BLGr, the mean values of the Young’s modulus and fracture strength are equal to 0.70 ± 0.11 TPa and 95 ± 11 GPa, respectively.