Phase imaging and nanoscale energy dissipation of supported graphene using amplitude modulation atomic force microscopy.

We investigate the phase imaging of supported graphene using amplitude modulation atomic force microscopy (AFM), the so-called tapping mode. The phase contrast between graphene and the neighboring substrate grows in hard tapping conditions and the contrast is enhanced compared to the topographic one. Therefore, phase measurements could enable the high-contrast imaging of graphene and related two-dimensional materials and heterostructures, which is not achievable with conventional AFM based topographic measurements. Obtained phase maps are then transformed into energy dissipation maps, which are important for graphene applications in various nano-mechanical systems. From a fundamental point of view, energy dissipation gives further insight into mechanical properties. Reliable measurements, obtained in the repulsive regime, show that the energy dissipation on a graphene-covered substrate is lower than that on a bare one, so graphene provides certain shielding in tip-substrate interaction. Based on the obtained phase curves and their derivatives, as well as on correlation measurements based on AFM nanoindentation and force modulation microscopy, we conclude that the main dissipation channels in graphene-substrate systems are short-range hysteresis and long-range interfacial forces.