Fluctuational-electrodynamics theory predicts that radiative heat transfer between two parallel, macroscale metallic surfaces is strongly super-Planckian when the vacuum gap is tens of nanometers and the metal is an ultrathin film: for aluminum films of 15-20 nm on 5x5 mm^2 silicon chips, enhancements of roughly 42-123 times the blackbody limit (up to several thousand times the far-field transfer of bulk metal) are predicted at 50-100 nm gaps, arising from non-resonant coupling across the gap plus resonant s-polarized coupling inside the film. The only room-temperature macroscale metallic plate-plate measurement to date (13-79 nm Al films at a fitted 215 nm gap, 6.4 times the blackbody limit) left this regime unverified: the gap was inferred from conductance fitting rather than directly measured, the optical constants of the ultrathin films were not characterized, and spacer-based gap control over macroscopic areas was unproven. The problem is to experimentally confirm or refute these predictions: measure the near-field radiative heat flux between macroscale metallic thin-film surfaces at gaps down to about 50 nm for film thicknesses of roughly 5-20 nm, with independently determined gaps and film optical properties and quantified parasitic heat channels, and compare quantitatively with fluctuational electrodynamics.

Background

Radiative heat transfer between two bodies is bounded, in the far field, by the Stefan-Boltzmann (blackbody) limit of Planck's law. When the vacuum gap dd between the bodies becomes much smaller than the dominant thermal wavelength (about 10 micrometers at room temperature), thermally generated evanescent electromagnetic waves - fields that decay exponentially away from each surface and cannot propagate to the far field - can tunnel across the gap, so that the heat flux can greatly exceed the blackbody limit (so-called super-Planckian transfer). The standard theoretical framework is fluctuational electrodynamics, introduced by Rytov and applied to two parallel half-spaces by Polder and Van Hove in 1971, which computes the thermally fluctuating currents in each body with Maxwell's equations and the fluctuation-dissipation theorem. The enhancement is strongest when the materials support surface polaritons - hybrid electromagnetic-lattice (surface phonon polariton, SPhP) or electromagnetic-electron (surface plasmon polariton, SPP) surface modes - which resonantly exchange energy across the gap. Nearly all experimental progress at sub-100-nm gaps has used polar dielectrics: silica plates have been measured down to a 7 nm gap with 18,000 times the blackbody limit, graphene-covered silica millimeter-scale plates reached about 64 times at 170 nm, and 20-nm-thick silicon carbide membranes at a 100-nm gap showed additional enhancement from corner and edge modes. Metals behave differently: a good metal has a low far-field emissivity, and its near-field response is limited by the skin depth (the depth over which electromagnetic fields penetrate the metal, of order tens of nanometers for aluminum at the mid-infrared and terahertz frequencies that dominate room-temperature transfer). Theory predicts that when the metal layer is made thinner than or comparable to the skin depth, an additional mechanism appears: s-polarized (transverse electric) evanescent waves couple resonantly inside the nanometric film, which behaves like a lossy cavity, so that thinner metallic films transfer more heat than bulk metal. Sabbaghi, Long, Ying, Lambert, Taylor, Messner and Wang (2020) exploited this in the first macroscale metallic experiment: aluminum films of 13, 24, 40 and 79 nm on 5x5 mm^2 silicon chips, separated by polystyrene nanoparticles, with the vacuum gap inferred from the measured conductance with bare silicon reference samples as 215 nm (with a large +55/−50+55/-50 nm uncertainty). At a temperature difference of 65 K they measured a flux 6.4 times the blackbody limit and about 420 times the far-field transfer between bulk aluminum plates, in reasonable agreement with fluctuational electrodynamics using bulk optical constants. A later microdevice experiment by Rincón-García et al. (2022) verified near-field transfer between metallic (platinum and gold) surfaces at gaps below 30 nm down to contact, in excellent agreement with fluctuational electrodynamics, but it used 100-nm-thick (near-bulk) coatings on an 80-micrometer-diameter mesa rather than square-millimeter areas, so the macroscale ultrathin-film regime remained untested. The same calculations as Sabbaghi et al.'s predict much larger enhancements in the unmeasured regime: about 42 times the blackbody limit for 15-nm Al films at a 100 nm gap and about 123 times for 20-nm films at a 50 nm gap (up to about 8060 times the far-field bulk-metal transfer), with the optimum at 215 nm gap occurring near 5-nm film thickness. Confirming this requires solving the practical difficulties that limited the 2020 experiment: direct metrology of the gap and parallelism over square-millimeter areas (the companion capacitance-based approach reached only 190 nm gaps), reliable fabrication and optical characterization of few-nanometer aluminum films (which oxidize natively and whose dielectric function deviates from bulk data through electron scattering at the film boundaries), and separation of the radiative signal from parasitic heat paths (conduction through spacer particles, residual-gas conduction, side radiation, and temperature nonuniformities).

Problem Statement

Determine experimentally whether the fluctuational-electrodynamics predictions for near-field radiative heat transfer between macroscale parallel metallic surfaces coated with ultrathin films are realized. The single objective is a quantitative measurement campaign on face-to-face metallic thin-film surfaces of macroscopic (square-millimeter) area, and it comprises jointly linked components: (1) measure the radiative heat flux as a function of vacuum gap over the range from the present 215 nm regime down to about 50 nm, where the predicted enhancements over the blackbody limit rise from about 6 times to about 42-123 times (and to thousands of times over the far-field transfer of bulk metal); (2) measure the flux as a function of metal-film thickness over the roughly 5-20 nm range, where the resonant thin-film contribution is predicted to peak and where the flux should exceed that of thicker and bulk films; (3) determine the vacuum gap and parallelism directly rather than by fitting the measured conductance, and characterize the actual optical constants of the ultrathin films (including native oxide and boundary-scattering modifications of the bulk dielectric function); and (4) quantify the nonideal contributions - conduction through spacer particles or posts, residual-gas conduction, side radiation, and temperature nonuniformities - so that the radiative flux is isolated with a stated uncertainty budget. The measured flux-versus-gap and flux-versus-thickness data are to be compared with fluctuational-electrodynamics calculations using the characterized film properties; a result that either confirms the predicted enhancements within uncertainties, or refutes or quantitatively revises them with a defensible error analysis, resolves the problem. A partial resolution restricted to near-bulk film thicknesses, to non-metallic surfaces, or to sub-millimeter active areas (as in existing microdevice experiments) does not, by itself, resolve it.

References

  1. Payam Sabbaghi, Linshuang Long, Xiaoyan Ying, Lee Lambert, Sydney Taylor, Christian Messner, Liping Wang, 'Super-Planckian radiative heat transfer between macroscale metallic surfaces due to near-field and thin-film effects', Journal of Applied Physics 128, 025305 (2020). DOI: 10.1063/5.0008259, https://doi.org/10.1063/5.0008259 (accepted preprint arXiv:1907.09638, https://arxiv.org/abs/1907.09638)
  2. Xiaoyan Ying, Payam Sabbaghi, Nicole Sluder, Liping Wang, 'Super-Planckian Radiative Heat Transfer between Macroscale Surfaces with Vacuum Gaps Down to 190 nm Directly Created by SU-8 Posts and Characterized by Capacitance Method', ACS Photonics 7, 190-196 (2020). DOI: 10.1021/acsphotonics.9b01360, https://doi.org/10.1021/acsphotonics.9b01360
  3. D. Polder, M. Van Hove, 'Theory of Radiative Heat Transfer between Closely Spaced Bodies', Physical Review B 4, 3303-3314 (1971). DOI: 10.1103/PhysRevB.4.3303, https://doi.org/10.1103/PhysRevB.4.3303
  4. Laura Rincón-García, Dakotah Thompson, Rohith Mittapally, Nicolás Agraït, Edgar Meyhofer, Pramod Reddy, 'Enhancement and Saturation of Near-Field Radiative Heat Transfer in Nanogaps between Metallic Surfaces', Physical Review Letters 129, 145901 (2022). DOI: 10.1103/PhysRevLett.129.145901, https://doi.org/10.1103/PhysRevLett.129.145901 (accepted manuscript at https://www.osti.gov/servlets/purl/1980328)
  5. Hakan Salihoglu, Woongsik Nam, Luis Traverso, Mauricio Segovia, Prabhu K. Venuthurumilli, Wen Liu, Yu Wei, Wenjuan Li, Xianfan Xu, 'Near-Field Thermal Radiation between Two Plates with Sub-10 nm Vacuum Separation', Nano Letters 20, 6091-6096 (2020). DOI: 10.1021/acs.nanolett.0c02137, https://doi.org/10.1021/acs.nanolett.0c02137
  6. Mariano Pascale, Maxime Giteau, Georgia T. Papadakis, 'Perspective on near-field radiative heat transfer', Applied Physics Letters 122, 100501 (2023). DOI: 10.1063/5.0142651, https://doi.org/10.1063/5.0142651 (preprint arXiv:2210.00929, https://arxiv.org/abs/2210.00929)
  7. Tomáš Králík, Pavel Hanzelka, Věra Musilová, Aleš Srnka, Pavel Urban, 'Near field radiative heat transfer between macro-scale metallic surfaces at cryogenic temperatures', Cryogenics 113, 103156 (2021). DOI: 10.1016/j.cryogenics.2020.103156, https://doi.org/10.1016/j.cryogenics.2020.103156
  8. Rohith Mittapally, Ju Won Lim, Edgar Meyhofer, Pramod Reddy, Bai Song, 'Quantifying the Effect of Nanofilms on Near-Field Radiative Heat Transfer', ACS Photonics 10, 2474-2480 (2023). DOI: 10.1021/acsphotonics.3c00638, https://doi.org/10.1021/acsphotonics.3c00638
  9. Song Li, Deyu Xu, Chengxin Hou, Junming Zhao, Linhua Liu, 'Experimental study of near-field radiative heat transfer between large-area polar dielectric films', Journal of Quantitative Spectroscopy and Radiative Transfer 324, 109077 (2024). DOI: 10.1016/j.jqsrt.2024.109077, https://doi.org/10.1016/j.jqsrt.2024.109077
  10. Mathieu Giroux, Michel Stephan, Maxime Brazeau, Sean Molesky, Alejandro W. Rodriguez, Jacob J. Krich, Karin Hinzer, Raphael St-Gelais, 'Measurement of Near-Field Radiative Heat Transfer at Deep Sub-Wavelength Distances using Nanomechanical Resonators', Nano Letters 23, 8490-8497 (2023). DOI: 10.1021/acs.nanolett.3c02049, https://doi.org/10.1021/acs.nanolett.3c02049
  11. Ali Rajabpour, Julien El Hajj, Mauricio Gómez Viloria, Riccardo Messina, Philippe Ben-Abdallah, Yangyu Guo, Samy Merabia, 'Extreme near-field heat transfer between silica surfaces', Applied Physics Letters 124, 192203 (2024). DOI: 10.1063/5.0203074, https://doi.org/10.1063/5.0203074
  12. Kezhang Shi, Yongcheng Sun, Zhaoyang Chen, Nan He, Fanglin Bao, Julian Evans, Sailing He, 'Colossal Enhancement of Near-Field Thermal Radiation Across Hundreds of Nanometers between Millimeter-Scale Plates through Surface Plasmon and Phonon Polaritons Coupling', Nano Letters 19, 8082-8088 (2019). DOI: 10.1021/acs.nanolett.9b03269, https://doi.org/10.1021/acs.nanolett.9b03269
  13. Lei Tang, Lívia M. Corrêa, Mathieu Francoeur, Chris Dames, 'Corner- and edge-mode enhancement of near-field radiative heat transfer', Nature 629, 67-73 (2024). DOI: 10.1038/s41586-024-07279-2, https://doi.org/10.1038/s41586-024-07279-2
  14. Zexiao Wang, Renwen Yu, Hakan Salihoglu, Xiao Luo, Zhuo Li, Hyeonggyun Kim, Xiu Liu, Tianyi Huang, Yibai Zhong, Shanhui Fan, Sheng Shen, 'Metamaterial-enhanced near-field radiative heat transfer', Nature 654, 64-68 (2026). DOI: 10.1038/s41586-026-10595-4, https://doi.org/10.1038/s41586-026-10595-4