Understanding thermal properties at the nanoscale is of fundamental importance for the development of next generation nanodevices, where ballistic transport is expected to dominate bulk-like diffusive and convective transport and may, indeed, be quantised. Here we report the exploration of the thermal properties of graphene, MoS2 and other 2D materials from monolayer to bulk using experimental nanoscale scanning thermal microscopy (SThM) correlated with finite elements (FE) simulations.

SThM is a modification of the more well-known Atomic Force Microscope employing a self-heated probe which is used to scan the sample; during probe-sample contact the corresponding drop in probe temperature can be electronically monitored and directly related to changes in the thermal properties. FE simulations and analytical calculations were performed to correlate the measured properties of our systems with variations of graphene’s isotropy and anisoptropy as well as substrate interactions.

We have investigated how these 2D materials thermal properties change as a function of sample thickness on substrates of both high and low thermal conductivities. We observe well defined values of thermal conductance for monolayer and near monolayer thicknesses, however unlike graphene where thermal conductance decreases with layer number other materials do not show this monotonic behaviours – for example MoS2 demonstrates a drop in thermal conductance ~10% from mono- to tri-layer. We discuss and compare experimental considerations and simulation outputs in order to construct a thermal conductance models to explain these interesting results which takes into account the competing lateral and normal conductance pathways.