Sample rotation angle dependence of graphene thickness measured using atomic force microscope

A precise measurement of graphene thickness is required for the design and development of nano-devices based on the material. Many factors affect this measurement when using scanning tunneling microscope (STM) and atomic force microscope (AFM), including the interaction between the scanning tip and ripples on graphene; such effects have not previously been explored. To investigate this, we measure the sample rotation angle dependence of graphene thickness as determined by contact mode and tapping mode AFM. The graphene thickness as determined by contact mode AFM follows a cosine modulus function of sample rotation angle, while tapping mode AFM reveals a constant graphene thickness, independent of sample rotation angle. For comparison, the AFM torsion signal is measured and follows a sine function of the sample rotation angle. All the measured sample rotation angle dependences can be explained by the interaction between linearly aligned ripples on graphene and the AFM tip in contact with the graphene.