Study of radiative heat transfer in Ångström- and nanometre-sized gaps

Abstract

Radiative heat transfer in Ångström- and nanometre-sized gaps is of great interest because of both its technological importance and open questions regarding the physics of energy transfer in this regime. Here we report studies of radiative heat transfer in few Å to 5 nm gap sizes, performed under ultrahigh vacuum conditions between a Au-coated probe featuring embedded nanoscale thermocouples and a heated planar Au substrate that were both subjected to various surface-cleaning procedures. By drawing on the apparent tunnelling barrier height as a signature of cleanliness, we found that upon systematically cleaning via a plasma or locally pushing the tip into the substrate by a few nanometres, the observed radiative conductances decreased from unexpectedly large values to extremely small ones-below the detection limit of our probe-as expected from our computational results. Our results show that it is possible to avoid the confounding effects of surface contamination and systematically study thermal radiation in Ångström- and nanometre-sized gaps.

Figure 1. Experimental set-up and SEM images of the SThM probes and gold-coated tips.

(a) Schematic of the experimental set-up, in which a Au-coated SThM probe (cross-sectional view) is brought into close proximity of a heated Au substrate. The tunnelling current across the nanogap is monitored by applying d.c. or a.c. voltages. Simultaneously, the thermoelectric voltage (V_th) generated by the Au–Cr thermocouple is recorded to monitor the temperature of the probe’s tip. The diagram on the right shows the thermal resistance network representing the heat flow from the substrate, through the nanogap, to the probe. (b) SEM image showing the top view of a SThM probe. (c,d) SEM images of the probe and its tip, which has a diameter of ∼300 nm.

Figure 2. Measured gap size-dependent thermal conductance and tunnelling current.

Each thermal conductance (pink) and tunnelling current (blue) curve is averaged over 15 repeated measurements. The shaded region represents the s.d. The first three panels show representative experimental results from (a) organic solvent-cleaned, (b) oxygen plasma-cleaned and (c) repeated oxygen plasma-cleaned probes. The gold sample is heated while the probe is maintained at a lower temperature to create a temperature difference ΔT=40 K. (d) The measurement results obtained in experiments where a large temperature differential (ΔT) of 130 K was applied. The thermal conductance data in the subnanometre region is shown on an expanded scale in the inset to facilitate visualization. The green line in the inset panel corresponds to the near-field radiative thermal conductance calculated from fluctuational electrodynamics. Further, the measured tunnelling currents versus displacement are shown in insets for each of the plots and were used in the analysis of the apparent tunnelling barrier height φ_ap. The estimated values of φ_ap are 1.1, 1.6, 1.7 and 1.9 eV for a–d, respectively.

Figure 3. Apparent tunnelling barrier and thermal conductance by controlled-crashing cleaning.

Solvent and plasma-cleaned probes were used in experiments where the probe was intentionally indented into the substrate by a few nanometres to create a direct point contact between the probe and the sample. This procedure resulted in gaps that featured larger apparent tunnelling barrier heights. Specifically, φ_ap was found from tunnelling current versus displacement curves (a) to monotonically increase from 1 eV (dark blue dots, for the probe in initial condition) to 1.4 eV, to 2.2 eV and finally to 2.5 eV in consecutive experiments where the tip was displaced into the substrate by 1 nm (light blue dots), 2 nm (red dots) and 5 nm (green dots), respectively. The thermal conductance corresponding to each of these scenarios is shown in b–e. It can be seen that the apparent near-field thermal conductance is systematically reduced as the apparent tunnelling barrier height increases.

Figure 4. Time-dependent thermal conductance for probes subjected to different cleaning procedures.

(a–c) Thermal conductance as a function of time for probes subjected to the cleaning procedures as described for Fig. 2a–c, respectively.

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.