Radiative heat transfer at the nanoscale Emmanuel Rousseau 1‡ , Alessandro Siria 2,3‡ , Guillaume Jourdan 3 , Sebastian Volz 5† , Fabio Comin 4 , Joe ¨l Chevrier 2 and Jean-Jacques Greffet 1 * Heat can be exchanged between two surfaces through emission and absorption of thermal radiation. It has been predicted theoretically that for distances smaller than the peak wave- length of the blackbody spectrum, radiative heat transfer can be increased by the contribution of evanescent waves 1–8 . This contribution can be viewed as energy tunnelling through the gap between the surfaces. Although these effects have already been observed 9–14 , a detailed quantitative comparison between theory and experiments in the nanometre regime is still lacking. Here, we report an experimental setup that allows measurement of conductance for gaps varying between 30 nm and 2.5 mm. Our measurements pave the way for the design of submicrometre nanoscale heaters that could be used for heat-assisted magnetic recording or heat- assisted lithography. In the late 1960s, an anomalous radiative heat transfer between flat metallic surfaces was reported by Domoto at cryogenic temperatures 15 and by Hargreaves at room temperature 9 . In both cases, an increase of the flux was measured for separation gaps in the micrometre range. A theoretical explanation was given by Polder and Van Hove 1 in the fra- mework of stochastic electrodynamics introduced by Rytov 2 a few years previously. Further theoretical studies are summarized in two recent reviews 5,7 . The theory accounts for both quantum and thermo- dynamic fluctuations and has been successfully applied to model Casimir forces 16 . Although quantum fluctuations yield a force that agrees quantitatively with theory, thermodynamic fluctuations are difficult to observe when measuring forces 17–19 . Instead, heat transfer is only due to thermodynamic fluctuations. The first attempt to quan- titatively detect heat transfer for submicrometre gaps was reported by Xu and colleagues 20 , but was inconclusive. More recently, the Oldenburg group 10,11 has demonstrated unambiguously a heat transfer that increases as the distance decreases in the submicrometre range. They studied heat transfer between a gold-coated scanning tunnelling microscope and a plate of gold or GaN. Unfortunately, the geometry of the experiment was too complex to allow a quantitative comparison with theory. It was predicted that heat transfer between dielectric surfaces is more efficient because of surface-phonon polariton contri- butions 21 . The first measurements between two dielectric materials were reported by the MIT group 13,14 . They measured heat transfer between a sphere and a plate, both made of silica, over a range of 30 nm and 10 mm. The comparison of these results with theoretical calculations based either on the Derjaguin approximation 22 or on sphere–sphere geometry 23 led these authors to the conclusion that the Derjaguin approximation is not valid for near-field radiative heat transfer. To avoid parallelism difficulties in the plane–plane geometry, we used a sphere–plane geometry, as for recent Casimir force measurements 17–19,24 and near-field heat transfer experiments 13,14 . The distance-dependent thermal conductance is given by G(d,T ) ¼ w(d )/DT, where w(d ) is the thermal flux through the gap d and DT is the temperature difference between the sphere and the plate. The plate was heated to produce a temperature differ- ence DT between the sphere and the plate, typically on the order of 10–20 K. Although the radiative resistance of the gap decreased significantly in the near field, it remained much larger than all the other thermal resistances at all distances explored (30 nm– 2.5 mm). Thus, the temperature difference across the gap could be considered to be constant as distance varied (quantitative details are given in the Supplementary Information). The temperatures were measured with a type-K thermocouple. The near-field radiative heat flux was of the order of nanowatts, so conduction through air had to be suppressed by working in a vacuum (10 26 mbar). It was also necessary to use a very sensitive fluxmeter. Following the pro- cedure in ref. 13, we glued the sphere onto a bimorph cantilever based on an atomic force microscope cantilever as proposed by Barnes and colleagues 25,26 . Such fluxmeters can measure fluxes variations in the order of tens of picowatts. We used commercially available cantilevers from Veeco (length ¼ 320 mm, width ¼ 22 mm, thickness ¼ 0.6 mm) made of silicon nitride (thickness 525 nm) with a gold layer (60 nm) deposited on a chromium layer (15 nm). The cantilever bending was measured using a fibre interferometric technique (Fig. 1). A drawback of using an optical readout is that part of the optical beam is absorbed and introduces a spurious flux term. It is therefore fundamental to keep it constant during measurement. A feedback loop keeps the distance between the cantilever and the optical fibre constant. In addition, a thermally stabilized laser is used to reduce the absorption fluctuations by the fluxmeter. The cantilever is perpendicular to the plane (Fig. 1) to avoid bending due to electrostatic or Casimir forces. The displace- ments carried out with the piezoelectric stages from Attocube were calibrated using an interferometric method. The z-displace- ment steps were 7 nm. The raw data were gathered by measuring the bending d of the cantilever in relation to the sphere–plate distance. From Barnes and colleagues 25,26 , the bimorph deformation d is assumed pro- portional to the flux. H is denoted as the proportionality factor. Cantilever bending was detected using the feedback voltage applied to the optical-fibre actuator in constant-distance mode. The contact between the plate and the sphere defined the zero of the z-axis. Note that for distances larger than 10 mm, the thermal conductance tends to its far-field value G ff ¼ 2pR 2 4s1(T )T 3 , where R is the sphere radius, s the Stefan constant and 1(T ) ¼ 0.354 is the silica emissivity evaluated using optical data from ref. 27. We found G ff to be equal to 5.45 nW K 21 . The proportionality 1 Laboratoire Charles Fabry, Institut d Optique, CNRS, Univ Paris-sud, Campus Polytechnique, RD 128, 91127 Palaiseau, France, 2 Institut Ne ´el – CNRS and Universite ´ Joseph Fourier, 38042 Grenoble, France, 3 CEA/LETI MINATEC/DIHS/LCMS, 17 rue des Martyrs, 38054 Grenoble cedex 9, France, 4 ESRF, 6 rue Horowitz 38042 Grenoble Cedex, France, 5 Laboratoire EM2C-CNRS UPR 288, E ´ cole Centrale Paris, Grande voie des vignes 92295 Cha ˆtenay-Malabry France; † Present address: LIMMS, UMI CNRS 2820-IIS, Center for International Research on MicroMechatronics, CIRMM, Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan; ‡ These authors contributed equally to this work. *e-mail: jean-jacques.greffet@institutoptique.fr LETTERS PUBLISHED ONLINE: 23 AUGUST 2009 | DOI: 10.1038/NPHOTON.2009.144 NATURE PHOTONICS | ADVANCE ONLINE PUBLICATION | www.nature.com/naturephotonics 1 © 2009 Macmillan Publishers Limited. All rights reserved.