Measuring the size dependence of thermal conductivity of suspended graphene disks using null-point scanning thermal microscopy

Using null-point scanning thermal microscopy (NP SThM), we have measured and analyzed the size dependence of the thermal conductivity of graphene. To do so, we rigorously re-derived the principal equation of NP SThM in terms of thermal property measurements so as to explain how this technique can be effectively used to quantitatively measure the local thermal resistance with nanoscale spatial resolution. This technique has already been proven to resolve the major problems of conventional SThM, and to quantitatively measure the temperature profile. Using NP SThM, we measured the variation in the thermal resistance of suspended chemical vapor deposition (CVD)-grown graphene disks with radii of 50-3680 nm from the center to the edge with respect to the size. By thoroughly analyzing the size dependence of the thermal resistance, we show that, with increasing graphene size, the ballistic resistance becomes more dominant in the thermal resistance experienced by a heat source of finite size and that the thermal conductivity experienced by such a heat source can even decrease. The results of this study reveal that the thermal conductivity of graphene detected by a heat source depends on the size of the heat source relative to that of the suspended graphene and on how the heat source and graphene are connected. As demonstrated in this study, NP SThM will be very useful for quantitative thermal characterization of not only CVD-grown graphene but also various other nanomaterials and nanodevices.