Author Correction: Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit.

We would like to correct the sentence in our Letter "However, both our detailed computational analysis (see Supplementary Fig. 2) and past computations13-15 suggest that such enhancements are not anticipated for metallic spheres, and very small increases (by a factor of a few) may be expected for dielectric spheres or metallic cylinders." The work of ref. 13 is not limited to the structures described in this statement but also presents a computational study of radiative heat transfer between rectangular dielectric membranes that is consistent with our experimental and computational analysis, and supports our findings that the blackbody limit can be overcome in the far-field. See accompanying Amendment. The original Letter has not been corrected online.

Hundred-fold enhancement in far-field radiative heat transfer over the blackbody limit.

Radiative heat transfer (RHT) has a central role in entropy generation and energy transfer at length scales ranging from nanometres to light years1. The blackbody limit2, as established in Max Planck's theory of RHT, provides a convenient metric for quantifying rates of RHT because it represents the maximum possible rate of RHT between macroscopic objects in the far field-that is, at separations greater than Wien's wavelength3. Recent experimental work has verified the feasibility of overcoming the blackbody limit in the near field4-7, but heat-transfer rates exceeding the blackbody limit have not previously been demonstrated in the far field. Here we use custom-fabricated calorimetric nanostructures with embedded thermometers to show that RHT between planar membranes with sub-wavelength dimensions can exceed the blackbody limit in the far field by more than two orders of magnitude. The heat-transfer rates that we observe are in good agreement with calculations based on fluctuational electrodynamics. These findings may be directly relevant to various fields, such as energy conversion, atmospheric sciences and astrophysics, in which RHT is important.

Apparatus for combined nanoscale gravimetric, stress, and thermal measurements.

We present an apparatus that allows for the simultaneous measurement of mass change, heat evolution, and stress of thin film samples deposited on quartz crystal microbalances (QCMs). We show device operation at 24.85 ± 0.05 °C under 9.31 ± 0.02 bars of H2 as a reactive gas. Using a 335 nm palladium film, we demonstrate that our apparatus quantifies curvature changes of 0.001 m-1. Using the QCM curvature to account for stress induced frequency changes, we demonstrate the measurement of mass changes of 13 ng/cm2 in material systems exhibiting large stress fluctuations. We use a one-state nonlinear lumped element model to describe our system with thermal potentials measured at discrete positions by three resistance temperature devices lithographically printed on the QCM. By inputting known heat amounts through lithographically defined Cr/Al wires, we demonstrate a 150 µW calorimetric accuracy and 20 µW minimum detectable power. The capabilities of this instrument will allow for a more complete characterization of reactions occurring in nanoscale systems, such as the effects of hydrogenation in various metal films and nanostructures, as well as allow for direct stress compensation in QCM measurements.

Enhancement of near-field radiative heat transfer using polar dielectric thin films.

Thermal radiative emission from a hot surface to a cold surface plays an important role in many applications, including energy conversion, thermal management, lithography, data storage and thermal microscopy. Recent studies on bulk materials have confirmed long-standing theoretical predictions indicating that when the gap between the surfaces is reduced to tens of nanometres, well below the peak wavelength of the blackbody emission spectrum, the radiative heat flux increases by orders of magnitude. However, despite recent attempts, whether such enhancements can be obtained in nanoscale dielectric films thinner than the penetration depth of thermal radiation, as suggested by theory, remains experimentally unknown. Here, using an experimental platform that comprises a heat-flow calorimeter with a resolution of about 100 pW (ref. 7), we experimentally demonstrate a dramatic increase in near-field radiative heat transfer, comparable to that obtained between bulk materials, even for very thin dielectric films (50-100 nm) when the spatial separation between the hot and cold surfaces is comparable to the film thickness. We explain these results by analysing the spectral characteristics and mode shapes of surface phonon polaritons, which dominate near-field radiative heat transport in polar dielectric thin films.

Effect of length and contact chemistry on the electronic structure and thermoelectric properties of molecular junctions.

We present a combined experimental and computational study that probes the thermoelectric and electrical transport properties of molecular junctions. Experiments were performed on junctions created by trapping aromatic molecules between gold electrodes. The end groups (-SH, -NC) of the aromatic molecules were systematically varied to study the effect of contact coupling strength and contact chemistry. When the coupling of the molecule with one of the electrodes was reduced by switching the terminal chemistry from -SH to -H, the electrical conductance of molecular junctions decreased by an order of magnitude, whereas the thermopower varied by only a few percent. This has been predicted computationally in the past and is experimentally demonstrated for the first time. Further, our experiments and computational modeling indicate the prospect of tuning thermoelectric properties at the molecular scale. In particular, the thiol-terminated aromatic molecular junctions revealed a positive thermopower that increased linearly with length. This positive thermopower is associated with charge transport primarily through the highest occupied molecular orbital, as shown by our computational results. In contrast, a negative thermopower was observed for a corresponding molecular junction terminated by an isocyanide group due to charge transport primarily through the lowest unoccupied molecular orbital.

Nanoscale thermometry using point contact thermocouples.

Probing temperature fields with nanometer resolution is critical to understanding nanoscale thermal transport as well as dissipation in nanoscale devices. Here, we demonstrate an atomic force microscope (AFM)-based technique capable of mapping temperature fields in metallic films with approximately 10 mK temperature resolution and <100 nm spatial resolution. A platinum-coated AFM cantilever placed in soft mechanical contact with a metallic (gold) surface is used to sequentially create point contact thermocouples on a grid. The local temperature at each point contact is obtained by measuring the thermoelectric voltage of the platinum-gold point contact and relating it to the local temperature. These results demonstrate a direct measurement of the temperature field of a metallic surface without using specially fabricated scanning temperature-probes.