Crossover from ballistic to diffusive thermal transport in suspended graphene membranes

We report heat transport measurements on suspended single-layer graphene disks with radius of 150-1600 nm using a high-vacuum scanning thermal microscope. The results of this study revealed a radius-dependent thermal contact resistance between tip and graphene, with values between 1.15 and 1.52 × 10 KW. The observed scaling of thermal resistance with radius is interpreted in terms of ballistic phonon transport in suspended graphene discs with radius smaller than 775 nm. In larger suspended graphene discs (radius >775 nm), the thermal resistance increases with radius, which is attributed to in-plane heat transport being limited by phonon-phonon resistive scattering processes, which resulted in a transition from ballistic to diffusive thermal transport. In addition, by simultaneously mapping topography and steady-state heat flux signals between a self-heated scanning probe sensor and graphene with 17 nm thermal spatial resolution, we demonstrated that the surface quality of the suspended graphene and its connectivity with the Si/SiO substrate play a determining role in thermal transport. Our approach allows the investigation of heat transport in suspended graphene at sub-micrometre length scales and overcomes major limitations of conventional experimental methods usually caused by extrinsic thermal contact resistances, assumptions on the value of the graphene's optical absorbance and limited thermal spatial resolution