Figure 5: Computational prediction of the radiative thermal conductance.

(a) Tip-substrate geometry employed in our numerical simulations. Following the SEM images of our thermal probes, the tip was modelled as an irregular cone that ends in a hemisphere, while the substrate was modelled as a thick disk. The height of the cone was chosen to be 3 μm and the radius of its base was 1.9 μm. The radius of the disk was 4 μm and its thickness was 2 μm. The solid black lines depict the triangular mesh employed in the boundary element method (BEM) calculations. The right inset shows a blow-up of the tip apex region. (b) The computed total radiative thermal conductance as a function of the gap size between the Au tip and substrate. The red solid line corresponds to the ideal tip (no roughness) and the blue line to the average obtained for 15 different tips with stochastically chosen roughness profiles (RMS roughness ∼2–3 nm), while the shaded region indicate the s.d. The black dashed line is the computed thermal conductance from the proximity approximation for the case of no roughness. The tip diameter in these calculations is 300 nm, while the temperature of the probe and substrate were chosen to be 303 and 343 K, respectively. Inset, similar to the main panel except that the probe and substrate temperatures are 315 and 445 K, respectively.