Radiative heat conductances between dielectric and metallic parallel plates with nanoscale gaps

A nanoscale photonic thermal transistor for sub-second heat flow switching

Control of heat flow is critical for thermal logic devices and thermal management and has been explored theoretically. However, experimental progress on active control of heat flow has been limited. Here, we describe a nanoscale radiative thermal transistor that comprises of a hot source and a cold drain (both are ~250 nm-thick silicon nitride membranes), which are analogous to the source and drain electrodes of a transistor. The source and drain are in close proximity to a vanadium oxide (VOx)-based planar gate electrode, whose dielectric properties can be adjusted by changing its temperature. We demonstrate that when the gate is located close ( < ~1 µm) to the source-drain device and undergoes a metal-insulator transition, the radiative heat transfer between the source and drain can be changed by a factor of three. More importantly, our nanomembrane-based thermal transistor features fast switching times ( ~ 500 ms as opposed to minutes for past three-terminal thermal transistors) due to its small thermal mass. Our experiments are supported by detailed calculations that highlight the mechanism of thermal modulation. We anticipate that the advances reported here will open new opportunities for designing thermal circuits or thermal logic devices for advanced thermal management.

Long Propagating Polaritonic Heat Transfer: Shaping Radiation to Conduction

Surface phonon polaritons (SPhPs) originate from the coupling of mid-IR photons and optical phonons, generating evanescent waves along the polar dielectric surface. The emergence of SPhPs gives rise to a phase of quantum matter that facilitates long-range energy transfer (100s μm-scale). Albeit of the recent experimental progress to observe the enhanced thermal conductivity of polar dielectric nanostructures mediated by SPhPs, the potential mechanism to present the high thermal conductivity beyond the Landauer limit has not been addressed. Here, we revisit the comprehensive theoretical framework to unify the distinct pictures of two heat transfer mechanisms by conduction and radiation. We first designed our experimental platform to distinguish contributions of two distinct fundamental modes of SPhPs, resulting in far-field radiation and long propagating conduction, respectively, by tuning the configuration of a nanostructured heat channel integrated into the thermometer. We could effectively control the transmission of long-propagating SPhPs to influence the apparent thermal conductivity of the nanostructure. This study reveals the high thermal conductance of 1.63 nW/K by a fast SPhP mode comparable to that by classical phonons, with measurements showing apparent conductivity values of up to 2 W/m·K at 515 K. The origin of the enhanced thermal conductivity was exploited by observing the interference of dispersive evanescent waves by double heat channels. Furthermore, our experimental observations of length-dependent thermal conductance by SPhPs are in good agreement with the revisited Landauer formula to illustrate a polaritonic mode of heat conduction, considering the dispersive nature of radiation not limited to the physical boundaries of a solid object yet directionally guided along the surface.

Enhanced Far-Field Thermal Radiation through a Polaritonic Waveguide

We experimentally demonstrate the enhancement of the far-field thermal radiation between two nonabsorbent Si microplates coated with energy-absorbent silicon dioxide (SiO_{2}) nanolayers supporting the propagation of surface phonon polaritons. By measuring the radiative thermal conductance between two coated Si plates, we find that its values are twice those obtained without the SiO_{2} coating. This twofold increase results from the hybridization of polaritons with guided modes inside Si and is well predicted by fluctuational electrodynamics and an analytical model based on a two-dimensional density of polariton states. These findings could be applied to thermal management in microelectronics, silicon photonics, energy conversion, atmospheric sciences, and astrophysics.

Corner- and edge-mode enhancement of near-field radiative heat transfer

It is well established that near-field radiative heat transfer (NFRHT) can exceed Planck's blackbody limit1 by orders of magnitude owing to the tunnelling of evanescent electromagnetic frustrated and surface modes2-4, as has been demonstrated experimentally for NFRHT between two large parallel surfaces5-7 and between two subwavelength membranes8,9. However, although nanostructures can also sustain a much richer variety of localized electromagnetic modes at their corners and edges10,11, the contributions of such additional modes to further enhancing NFRHT remain unexplored. Here we demonstrate both theoretically and experimentally a physical mechanism of NFRHT mediated by the corner and edge modes, and show that it can dominate the NFRHT in the 'dual nanoscale regime' in which both the thickness of the emitter and receiver, and their gap spacing, are much smaller than the thermal photon wavelengths. For two coplanar 20-nm-thick silicon carbide membranes separated by a 100-nm vacuum gap, the NFRHT coefficient at room temperature is both predicted and measured to be 830 W m-2 K-1, which is 5.5 times larger than that for two infinite silicon carbide surfaces separated by the same gap, and 1,400 times larger than the corresponding blackbody limit accounting for the geometric view factor between two coplanar membranes. This enhancement is dominated by the electromagnetic corner and edge modes, which account for 81% of the NFRHT between the silicon carbide membranes. These findings are important for future NFRHT applications in thermal management and energy conversion.

Nanophotonic Heat Exchanger for Enhanced Near-Field Radiative Heat Transfer

Increasing near-field radiative heat transfer between two bodies separated by a vacuum gap is crucial for enhancing the power density in radiative energy transport and conversion devices. However, the largest radiative heat transfer coefficient between two realistic materials at room temperature is limited to around 2000 W/(m2·K) for a gap of 100 nm. Here, analogous to conventional plate-fin heat exchangers based on convection, we introduce the concept of a nanophotonic heat exchanger, which enhances near-field radiative heat transfer using two bodies with interpenetrating gratings. Our calculations, based on rigorous fluctuational electrodynamics, show that the radiative heat transfer coefficient between the bodies separated by a 100 nm gap can significantly exceed 2000 W/(m2·K) by increasing the aspect ratios of the gratings. We develop a semianalytical heat transfer model that agrees well with the rigorous calculations for design optimization. Our work opens new opportunities for enhancing near-field radiative heat transfer between any materials.

Machine Learning Aided Design and Optimization of Thermal Metamaterials

Artificial Intelligence (AI) has advanced material research that were previously intractable, for example, the machine learning (ML) has been able to predict some unprecedented thermal properties. In this review, we first elucidate the methodologies underpinning discriminative and generative models, as well as the paradigm of optimization approaches. Then, we present a series of case studies showcasing the application of machine learning in thermal metamaterial design. Finally, we give a brief discussion on the challenges and opportunities in this fast developing field. In particular, this review provides: (1) Optimization of thermal metamaterials using optimization algorithms to achieve specific target properties. (2) Integration of discriminative models with optimization algorithms to enhance computational efficiency. (3) Generative models for the structural design and optimization of thermal metamaterials.

Observation of Near-Field Thermal Radiation between Coplanar Nanodevices with Subwavelength Dimensions

With the continuous advancement of nanotechnology, nanodevices have become crucial components in computing, sensing, and energy conversion applications. The structures of nanodevices typically possess subwavelength dimensions and separations, which pose significant challenges for understanding energy transport phenomena in nanodevices. Here, on the basis of a judiciously designed thermal photonic nanodevice, we report the first measurement of near-field energy transport between two coplanar subwavelength structures over temperature bias up to ∼190 K. Our experimental results demonstrate a 20-fold enhancement in energy transfer beyond blackbody radiation. In contrast with the well-established near-field interactions between two semi-infinite bodies, the subwavelength confinements in nanodevices lead to increased polariton scattering and reduction of supporting photonic modes and, therefore, a lower energy flow at a given separation. Our work unveils exciting opportunities for the rational design of nanodevices, particularly for coplanar near-field energy transport, with important implications for the development of efficient nanodevices for energy harvesting and thermal management.

Transient measurement of near-field thermal radiation between macroscopic objects

The involvement of evanescent waves in the near-field regime could greatly enhance spontaneous thermal radiation, offering a unique opportunity to study nanoscale photon-phonon interaction. However, accurately characterizing this subtle phenomenon is very challenging. This paper proposes a transient all-optical method for rapidly characterizing near-field radiative heat transfer (NFRHT) between macroscopic objects, using the first law of thermodynamics. Significantly, a full measurement at a fixed gap distance is completed within tens of seconds. By simplifying the configuration, the transient all-optical method achieves high measurement accuracy and reliable reproducibility. The proposed method can effectively analyze the NFRHT in various material systems, including SiO2, SiC, and Si, which involve different phonon or plasmon polaritons. Experimental observations demonstrate significant super-Planckian radiation, which arises from the near-field coupling of bounded surface modes. Furthermore, the method achieves excellent agreement with theory, with a minimal discrepancy of less than 2.7% across a wide temperature range. This wireless method could accurately characterize the NFRHT for objects with different sizes or optical properties, enabling the exploration of both fundamental interests and practical applications.

Surface Phonon Polariton-Mediated Near-Field Radiative Heat Transfer at Cryogenic Temperatures

Recent experiments, at room temperature, have shown that near-field radiative heat transfer (NFRHT) via surface phonon polaritons (SPhPs) exceeds the blackbody limit by several orders of magnitude. Yet, SPhP-mediated NFRHT at cryogenic temperatures remains experimentally unexplored. Here, we probe thermal transport in nanoscale gaps between a silica sphere and a planar silica surface from 77-300 K. These experiments reveal that cryogenic NFRHT has strong contributions from SPhPs and does not follow the T^{3} temperature (T) dependence of far-field thermal radiation. Our modeling based on fluctuational electrodynamics shows that the temperature dependence of NFRHT can be related to the confinement of heat transfer to two narrow frequency ranges and is well accounted for by a simple analytical model. These advances enable detailed NFRHT studies at cryogenic temperatures that are relevant to thermal management and solid-state cooling applications.

Enhanced far-field coherent thermal emission using mid-infrared bilayer metasurfaces

A classical thermal source, such as an incandescent filament, radiates according to Planck's law. The feasibility of super-Planckian radiation has been investigated with sub-wavelength-sized sources in the last decade. In such sources, a crystal-dependent coupling of photons and optical phonons is possible at thermal energies corresponding to that at room temperature. This interaction can be used to tailor the far-field thermal emission in a coherent manner; however, understanding heat transfer during this process is still nascent. Here, we used a novel measurement platform to quantify thermal signals in a Ge2Sb2Te5/SiO2 nanoribbon structure. We were able to separate and quantify the radiated and conducted heat transfer mechanisms. The thermal emission from the Ge2Sb2Te5/SiO2 nanoribbons was enhanced by 3.5× compared to that of a bare SiO2 nanoribbon. Our model revealed that this enhancement was directly due to polaritonic heat transfer, which was possible due to the large and lossless dielectric permittivity of Ge2Sb2Te5 at mid-IR frequencies. This study directly probes the far-field emission with a thermal gradient stimulated by Joule heating in temperature ranges from 100 to 400 K, which bridges the gap between mid-IR optics and thermal engineering.

Spectrally Sharp Near-Field Thermal Emission: Revealing Some Disagreements between a Casimir-Polder Sensor and Predictions from Far-Field Emittance

Near-field thermal emission largely exceeds blackbody radiation, owing to spectrally sharp emission in surface polaritons. We turn the Casimir-Polder interaction between Cs(7P_{1/2}) and a sapphire interface into a sensor sharply filtering, at 24.687 THz, the near-field sapphire emission at ∼24.5  THz. The temperature evolution of the sapphire mode is demonstrated. The Cs sensor, sensitive to both dispersion and dissipation, suggests the polariton to be redshifted and sharper, as compared, up to 1100 K, to predictions from far-field sapphire emission, affected by birefringence and multiple resonances.

Measurement of Near-Field Radiative Heat Transfer at Deep Sub-Wavelength Distances using Nanomechanical Resonators

Near-field radiative heat transfer (NFRHT) measurements often rely on custom microdevices that can be difficult to reproduce after their original demonstration. Here we study NFRHT using plain silicon nitride (SiN) membrane nanomechanical resonators─a widely available substrate used in applications such as electron microscopy and optomechanics─and on which other materials can easily be deposited. We report measurements down to a minimal distance of 180 nm between a large radius of curvature (15.5 mm) glass radiator and a SiN membrane resonator. At such deep sub-wavelength distance, heat transfer is dominated by surface polariton resonances over a (0.25 mm)2 effective area, which is comparable to plane-plane experiments employing custom microfabricated devices. We also discuss how measurements using nanomechanical resonators create opportunities for simultaneously measuring near-field radiative heat transfer and thermal radiation forces (e.g., thermal corrections to Casimir forces).

Nonlocal Near-Field Radiative Heat Transfer by Transdimensional Plasmonics

Using transdimensional plasmonic materials (TDPM) within the framework of fluctuational electrodynamics, we demonstrate nonlocality in dielectric response alters near-field heat transfer at gap sizes on the order of hundreds of nanometers. Our theoretical study reveals that, opposite to the local model prediction, propagating waves can transport energy through the TDPM. However, energy transport by polaritons at shorter separations is reduced due to the metallic response of TDPM stronger than that predicted by the local model. Our experiments conducted for a configuration with a silica sphere and a doped silicon plate coated with an ultrathin layer of platinum as the TDPM show good agreement with the nonlocal near-field radiation theory. Our experimental work in conjunction with the nonlocal theory has important implications in thermophotovoltaic energy conversion, thermal management applications with metal coatings, and quantum-optical structures.

Ultrafast and Nanoscale Energy Transduction Mechanisms and Coupled Thermal Transport across Interfaces

The coupled interactions among the fundamental carriers of charge, heat, and electromagnetic fields at interfaces and boundaries give rise to energetic processes that enable a wide array of technologies. The energy transduction among these coupled carriers results in thermal dissipation at these surfaces, often quantified by the thermal boundary resistance, thus driving the functionalities of the modern nanotechnologies that are continuing to provide transformational benefits in computing, communication, health care, clean energy, power recycling, sensing, and manufacturing, to name a few. It is the purpose of this Review to summarize recent works that have been reported on ultrafast and nanoscale energy transduction and heat transfer mechanisms across interfaces when different thermal carriers couple near or across interfaces. We review coupled heat transfer mechanisms at interfaces of solids, liquids, gasses, and plasmas that drive the resulting interfacial heat transfer and temperature gradients due to energy and momentum coupling among various combinations of electrons, vibrons, photons, polaritons (plasmon polaritons and phonon polaritons), and molecules. These interfacial thermal transport processes with coupled energy carriers involve relatively recent research, and thus, several opportunities exist to further develop these nascent fields, which we comment on throughout the course of this Review.

Probing the Limits to Near-Field Heat Transfer Enhancements in Phonon-Polaritonic Materials

Near-field radiative heat transfer (NFRHT) arises between objects separated by nanoscale gaps and leads to dramatic enhancements in heat transfer rates compared to the far-field. Recent experiments have provided first insights into these enhancements, especially using silicon dioxide (SiO₂) surfaces, which support surface phonon polaritons (SPhP). Yet, theoretical analysis suggests that SPhPs in SiO₂ occur at frequencies far higher than optimal. Here, we first show theoretically that SPhP-mediated NFRHT, at room temperature, can be 5-fold larger than that of SiO₂, for materials that support SPhPs closer to an optimal frequency of 67 meV. Next, we experimentally demonstrate that MgF₂ and Al₂O₃ closely approach this limit. Specifically, we demonstrate that near-field thermal conductance between MgF₂ plates separated by 50 nm approaches within nearly 50% of the global SPhP bound. These findings lay the foundation for exploring the limits to radiative heat transfer rates at the nanoscale.

Breakdown of Detailed Balance for Thermal Radiation by Synthetic Fields

In recent times the possibility of nonreciprocity in heat transfer between two bodies has been extensively studied. In particular the role of strong magnetic fields has been investigated. A much simpler approach with considerable flexibility would be to consider heat transfer in synthetic electric and magnetic fields that are easily applied. We demonstrate the breakdown of detailed balance for the heat transfer function T(ω), i.e., the spectrum of heat transfer between two objects due to the presence of synthetic electric and magnetic fields. The spectral measurements carry much more physical information and are the reason for the quantum theory of radiation. We demonstrate explicitly the synthetic field induced nonreciprocity in the heat transfer transmission function between two graphene flakes and for the Casimir coupling between two objects. Unlike many other cases of heat transfer, the latter case has interesting features of the strong coupling. Further the presence of synthetic fields affects the mean occupation numbers of two membranes and we propose this system for the experimental verification of the breakdown of detailed balance.

Highly-efficient radiative thermal rectifiers based on near-field gap variations

Near-field radiative thermal rectifiers (NFRTRs) enabling directional heat transport hold great promise for various applications, including thermal logic computing, thermal management, and energy conversion. Current NFRTR designs rely on dissimilar terminal materials with high contrasts in their temperature-dependent dielectric properties, which in turn hinders the spectral match for radiative heat transfer and thus limits the device's efficiency. Herein, this dilemma is solved by designing heterostructures where a pair of polaritonic layers are separately stacked on a thermally-expanding layer and a rigid substrate, spaced by a vacuum gap. In this scheme, the symmetric polaritonic layers can provide stable near-field radiative channels for heat transfer, while the thermally-expanding layer can modulate the gap size with flipped temperature bias to allow high contrasts in heat flux. In exemplified implementations, the hBN-based design has achieved a record-high thermal rectification factor (TRF, ∼10⁴) even under small thermal gradients (∼20 K), which can be further boosted by polaritonic hybridizations in the graphene/hBN-based design. This study paves the way to design novel NFRTRs with 2D materials, thus providing enriched polaritons to realize higher TRFs.

Menezes L, Tittl A, Ren H, Maier SA. Optical Metasurfaces for Energy Conversion

Nanostructured surfaces with designed optical functionalities, such as metasurfaces, allow efficient harvesting of light at the nanoscale, enhancing light-matter interactions for a wide variety of material combinations. Exploiting light-driven matter excitations in these artificial materials opens up a new dimension in the conversion and management of energy at the nanoscale. In this review, we outline the impact, opportunities, applications, and challenges of optical metasurfaces in converting the energy of incoming photons into frequency-shifted photons, phonons, and energetic charge carriers. A myriad of opportunities await for the utilization of the converted energy. Here we cover the most pertinent aspects from a fundamental nanoscopic viewpoint all the way to applications.

Near-Field Radiative Heat Transfer Modulation with an Ultrahigh Dynamic Range through Mode Mismatching

Modulating near-field radiative heat transfer (NFRHT) with a high dynamic range is challenging in nanoscale thermal science and engineering. Modulation depths [(maximum value - minimum value)/(maximum value + minimum value) × 100%] of ≈2% to ≈15.7% have been reported with matched modes, but breaking the constraint of mode matching theoretically allows for higher modulation depth. We demonstrate a modulation depth of ≈32.2% by a pair of graphene-covered SU8 heterostructures at a gap distance of ≈80 nm. Dissimilar Fermi levels tuned by bias voltages enable mismatched surface plasmon polaritons which improves the modulation. The modulation depth when switching from a matched mode to a mismatched mode is ≈4.4-fold compared to that when switching between matched modes. This work shows the importance of symmetry in polariton-mediated NFRHT and represents the largest modulation depth to date in a two-body system with fixed gap distance and temperature.

Enhancement and Saturation of Near-Field Radiative Heat Transfer in Nanogaps between Metallic Surfaces

Near-field radiative heat transfer (NFRHT) between planar metallic surfaces was computationally explored over five decades ago by Polder and van Hove [Phys. Rev. B 4, 3303 (1971)PLRBAQ0556-280510.1103/PhysRevB.4.3303]. These studies predicted that, as the gap size (d) between the surfaces decreased, the radiative heat flux first increases by several orders of magnitude until d is ∼100  nm after which the heat flux saturates. However, despite both the fundamental and practical importance of these predictions, the combined enhancement and saturation of NFRHT at small gaps in metallic surfaces remains experimentally unverified. Here, we probe NFRHT between planar metallic (Pt, Au) surfaces and show that RHT rates can exceed the far-field rate by over a thousand times when d is reduced to ∼25  nm. More importantly, we show that for small values of d RHT saturates due to the dominant contributions from transverse electric evanescent modes. Our results are in excellent agreement with the predictions of fluctuational electrodynamics and are expected to inform the development of technologies such as near-field thermophotovoltaics, radiative heat-assisted magnetic recording, and nanolithography.

Scaling Planck's law: a unified approach to the Casimir effect and radiative heat-conductance in nanogaps

Using Planck's law from an innovative point of view brings about the possibility to understand the common origin of the repulsive Casimir thermal pressure and the heat exchange in nanogaps. Based on a scale transformation, a procedure that removes divergences of the energy density, we prove the validity of Planck's law to describe confined thermal radiation properties in nanoscale gaps. This scaling involves a configurational temperature obtained from Wien's displacement law and having an entropic origin. We derive analytical expressions for the Casimir thermal pressure as well as for the heat conductance. Comparison of our results with experimental data shows a remarkable agreement.

Effective Approximation Method for Nanogratings-induced Near-Field Radiative Heat Transfer

Nanoscale radiative thermal transport between a pair of metamaterial gratings is studied within this work. The effective medium theory (EMT), a traditional method to calculate the near-field radiative heat transfer (NFRHT) between nanograting structures, does not account for the surface pattern effects of nanostructures. Here, we introduce the effective approximation NFRHT method that considers the effects of surface patterns on the NFRHT. Meanwhile, we calculate the heat flux between a pair of silica (SiO₂) nanogratings with various separation distances, lateral displacements, and grating heights with respect to one another. Numerical calculations show that when compared with the EMT method, here the effective approximation method is more suitable for analyzing the NFRHT between a pair of relatively displaced nanogratings. Furthermore, it is demonstrated that compared with the result based on the EMT method, it is possible to realize an inverse heat flux trend with respect to the nanograting height between nanogratings without modifying the vacuum gap calculated by this effective approximation NFRHT method, which verifies that the NFRHT between the side faces of gratings greatly affects the NFRHT between a pair of nanogratings. By taking advantage of this effective approximation NFRHT method, the NFRHT in complex micro/nano-electromechanical devices can be accurately predicted and analyzed.

Quasi-Casimir coupling can induce thermal resonance of adsorbed liquid layers in a nanogap

In a vacuum nanogap, phonon heat transfer can be induced by quasi-Casimir coupling in the absence of electromagnetic fields. However, it is unknown whether phonons can be transmitted across a...

Optimized Colossal Near-Field Thermal Radiation Enabled by Manipulating Coupled Plasmon Polariton Geometry

Collective optoelectronic phenomena such as plasmons and phonon polaritons can drive processes in many branches of nanoscale science. Classical physics predicts that a perfect thermal emitter operates at the black body limit. Numerous experiments have shown that surface phonon polaritons allow emission two orders of magnitude above the limit at a gap distance of ≈50 nm. This work shows that a supported multilayer graphene structure improves the state of the art by around one order of magnitude with a ≈1129-fold-enhancement at a gap distance of ≈55 nm. Coupled surface plasmon polaritons at mid- and far-infrared frequencies allow for near-unity photon tunneling across a broad swath of k-space enabling the improved result. Electric tuning of the Fermi-level allows for the detailed characterization and optimization of the colossal nanoscale heat transfer.

Graphene-based autonomous pyroelectric system for near-field energy conversion

In the close vicinity of a hot solid, at distances smaller than the thermal wavelength, a strong electromagnetic energy density exists because of the presence of evanescent field. Here we introduce a many-body conversion principle to harvest this energy using graphene-based pyroelectric conversion devices made with an active layer encapsulated between two graphene field-effect transistors which are deposited on the source and on the cold sink. By tuning the bias voltage applied to the gates of these transistors, the thermal state and the spontaneous polarization of the active layer can be controlled at kHz frequencies. We demonstrate that the power density generated by these conversion systems can reach [Formula: see text] using pyroelectric Ericsson cycles, a value which surpasses the current production capacity of near-field thermophotovoltaic conversion devices by more than three orders of magnitude with low grade heat sources ([Formula: see text]) and small temperature differences ([Formula: see text]).

Toward applications of near-field radiative heat transfer with micro-hotplates

Bringing bodies close together at sub-micron distances can drastically enhance radiative heat transfer, leading to heat fluxes greater than the blackbody limit set by Stefan–Boltzmann law. This effect, known as near-field radiative heat transfer (NFRHT), has wide implications for thermal management in microsystems, as well as technological applications such as direct heat to electricity conversion in thermophotovoltaic cells. Here, we demonstrate NFRHT from microfabricated hotplates made by surface micromachining of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {SiO}_2$$\end{document}SiO2/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {SiN}$$\end{document}SiN thin films deposited on a sacrificial amorphous Si layer. The sacrificial layer is dry etched to form wide membranes (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${100}\,\upmu \hbox {m} \times {100}\,\upmu \hbox {m}$$\end{document}100μm×100μm) separated from the substrate by nanometric distances. Nickel traces allow both resistive heating and temperature measurement on the micro-hotplates. We report on two samples with measured gaps of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${610}\,\hbox {nm}$$\end{document}610nm and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${280}\,\hbox {nm}$$\end{document}280nm. The membranes can be heated up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${250}\,^{\circ }\hbox {C}$$\end{document}250∘C under vacuum with no mechanical damage. At \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${120}\,^{\circ }\hbox {C}$$\end{document}120∘C we observed a 6.4-fold enhancement of radiative heat transfer compared to far-field emission for the smallest gap and a 3.5-fold enhancement for the larger gap. Furthermore, the measured transmitted power exhibits an exponential dependence with respect to gap size, a clear signature of NFRHT. Calculations of photon transmission probabilities indicate that the observed increase in heat transfer can be attributed to near-field coupling by surface phonon-polaritons supported by the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {SiO}_2$$\end{document}SiO2 films. The fabrication process presented here, relying solely on well-established surface micromachining technology, is a key step toward integration of NFRHT in industrial applications.

Near-Field Radiative Heat Transfer Eigenmodes

The near-field electromagnetic interaction between nanoscale objects produces enhanced radiative heat transfer that can greatly surpass the limits established by far-field blackbody radiation. Here, we present a theoretical framework to describe the temporal dynamics of the radiative heat transfer in ensembles of nanostructures, which is based on the use of an eigenmode expansion of the equations that govern this process. Using this formalism, we identify the fundamental principles that determine the thermalization of collections of nanostructures, revealing general but often unintuitive dynamics. Our results provide an elegant and precise approach to efficiently analyze the temporal dynamics of the near-field radiative heat transfer in systems containing a large number of nanoparticles.

Progress Toward High Power Output in Thermionic Energy Converters

Thermionic energy converters are solid-state heat engines that have the potential to produce electricity with efficiencies of over 30% and area-specific power densities of 100 Wcm-2. Despite this prospect, no prototypes reported in the literature have achieved true efficiencies close to this target, and many of the most recent investigations report power densities on the order of mWcm-2 or less. These discrepancies stem in part from the low-temperature (<1300 K) test conditions used to evaluate these devices, the large vacuum gap distances (25-100 µm) employed by these devices, and material challenges related to these devices' electrodes. This review will argue that, for feasible electrode work functions available today, efficient performance requires generating output power densities of >1 Wcm-2 and employing emitter temperatures of 1300 K or higher. With this result in mind, this review provides an overview of historical and current design architectures and comments on their capacity to realize the efficiency and power potential of thermionic energy converters. Also emphasized is the importance of using standardized efficiency metrics to report thermionic energy converter performance data.

Many-body near-field radiative heat transfer: methods, functionalities and applications

Near-field radiative heat transfer (NFRHT) governed by evanescent waves, provides a platform to thoroughly understand the transport behavior of nonradiative photons, and also has great potential in high-efficiency energy harvesting and thermal management at the nanoscale. It is more usual in nature that objects participate in heat transfer process in many-body form rather than the frequently-considered two-body scenarios, and the inborn mutual interactions among objects are important to be understood and utilized for practical applications. The last decade has witnessed considerable achievements on many-body NFRHT, ranging from the establishment of different calculation methods to various unprecedented heat transport phenomena that are distinct from two-body systems. In this invited review, we introduce concisely the basic physics of NFRHT, lay out various theoretical methods to deal with many-body NFRHT, and highlight unique functionalities realized in many-body systems and the resulting applications. At last, the key challenges and opportunities of many-body NFRHT in terms of fundamental physics, experimental validations, and potential applications are outlined and discussed.

Radiative heat transfer at the nanoscale: experimental trends and challenges

Energy transport theories are being revisited at the nanoscale, as macroscopic laws known for a century are broken at dimensions smaller than those associated with energy carriers. For thermal radiation, where the typical dimension is provided by Wien's wavelength, Planck's law and associated concepts describing surface-to-surface radiative transfer have to be replaced by a full electromagnetic framework capturing near-field radiative heat transfer (photon tunnelling between close bodies), interference effects and sub-wavelength thermal emission (emitting body of small size). It is only during the last decade that nanotechnology has allowed for many experimental verifications - with a recent boom - of the large increase of radiative heat transfer at the nanoscale. In this minireview, we highlight the parameter space that has been investigated until now, showing that it is limited in terms of inter-body distance, temperature and object size, and provide clues about possible thermal-energy harvesting, sensing and management applications. We also provide an outlook on open topics, underlining some difficulties in applying single-wavelength approaches to broadband thermal emitters while acknowledging the promise of thermal nanophotonics and observing that molecular/chemical viewpoints have been hardly addressed.

Design of a calorimeter for near-field heat transfer measurements and thermal scanning probe microscopy

Multilayer cantilever beams are used in the measurement of near-field radiative heat transfer. The materials and dimensions of the cantilever probe are chosen in order to improve system performance in terms of sensitivity and noise. This is done using an analytical model that describes the thermo-mechanical and mechanical behavior of the cantilever and its influences at the system level. In the design, the optical reflectance and the sensitivity of cantilever rotation to the heat input are maximized under constraints for thermal noise, temperature drift, and a lower bound for the spring constant. The analytical model is verified using finite element analysis, which shows that the effects of radiative losses to the environment are insignificant for design purposes, while the effects of ignoring three-dimensional heat flow introduces larger errors. Moreover, the finite element analysis shows that the designed probes are up to 41 times more sensitive than the often used commercial-of-the-shelf benchmark and have a four times lower thermal noise. Experimental validation of the designed probes shows good agreement with the theoretical values for sensitivity. However, the most sensitive designs were found to be susceptible to damage due to overheating and carbon contamination.

Near-field radiative heat transfer between high-temperature superconductors

Near-field radiative heat transfer (NFRHT) management can be achieved using high-temperature superconductors. In this work, we present a theoretical study of the radiative heat transfer between two [Formula: see text] (YBCO) slabs in three different scenarios: Both slabs either in the normal or superconducting state, and only one of them below the superconductor critical temperature [Formula: see text]. The radiative heat transfer is calculated using Rytov's theory of fluctuating electrodynamics, while a two-fluid model describes the dielectric function of the superconducting materials. Our main result is the significant suppression of the NFRHT when one or both of the slabs are superconducting, which is explained in terms of the detailed balance of the charge carriers density together with the sudden reduction of the free electron scattering rate. A critical and unique feature affecting the radiative heat transfer between high-temperature superconductors is the large damping of the mid-infrared carriers which screens the surface plasmon excitation.

Near-Field Thermal Radiation between Two Plates with Sub-10 nm Vacuum Separation

Radiation greatly exceeding blackbody between two objects separated by microscale distances has attracted great interest. However, challenges in reaching such a small separation between two plates have so far prevented studies below a separation distance of about 25 nm. Here, we report a study of radiation enhancement in the near-field regime of less than 10 nm between two parallel plates. We make use of bulk, rigid plates to approach small separation distances without the adverse snap-in effect, develop embedded temperature sensors to allow near-zero separation, and employ advanced sensing method to level the plates and approach and maintain small separations. Our findings agree with theoretical predictions between parallel surfaces with separations down to 7 nm where an 18000 times enhancement in radiation between two quartz plates is observed. Our method can also be used to explore heat transfer between other materials and can possibly be extended to smaller separation gaps.

Wrong expectation of superinsulation behavior from largely-expanded nanocellular foams

This work aims to predict the thermal conductivity of microcellular and nanocellular thermal insulation foams to explore the correlation between the cellular structure and the thermal insulating properties. Closed-cell foam consisting of cell walls and struts was used as the base geometry for modeling. The mathematical correlations to calculate the thickness of cell walls and the diameter of struts for a given cell size, the void fraction and the volume fraction of polymer located in struts were investigated. Then, a mathematical model for the conductive thermal conductivity including the dependency on the void fraction, the strut fraction and the Knudsen effect for gas was introduced. The radiative thermal conductivity was determined by analyzing the attenuation of radiative energy by absorption and scattering based on Mie's theory together with electromagnetic wave interference, as well as interference of propagating waves and tunneling of the radiative energy by evanescent waves in the cells. The thermal conductivity model was validated by experimental data and used to predict the thermal conductivity of polystyrene (PS) and poly(methyl methacrylate) (PMMA) foams at various cell sizes and volume expansion ratios. It was found that the radiative thermal conductivity plays a crucial role in nanocellular foam. The trade-off between the cell size and cell wall thickness when cell walls become thinner and highly transparent to thermal radiation was demonstrated, leading to the optimal volume expansion ratio at which the thermal conductivities were minimized. Perspectives for the manufacture of high-performance thermal insulation foams are also discussed.

NanoThermoMechanical AND and OR Logic Gates

Today’s electronics cannot perform in harsh environments (e.g., elevated temperatures and ionizing radiation environments) found in many engineering applications. Based on the coupling between near-field thermal radiation and MEMS thermal actuation, we presented the design and modeling of NanoThermoMechanical AND, OR, and NOT logic gates as an alternative, and showed their ability to be combined into a full thermal adder to perform complex operations. In this work, we introduce the fabrication and characterization of the first ever documented Thermal AND and OR logic gates. The results show thermal logic operations can be achieved successfully through demonstrated and easy-to-manufacture NanoThermoMechanical logic gates.

Nanoscale radiative thermal switching via multi-body effects

Control of thermal transport at the nanoscale is of great current interest for creating novel thermal logic and energy conversion devices. Recent experimental studies have demonstrated that radiative heat transfer between macroscopic objects separated by nanogaps, or between nanostructures located in the far-field of each other, can exceed the blackbody limit. Here, we show that the radiative heat transfer between two coplanar SiN membranes can be modulated by factors as large as five by bringing a third planar object into close proximity of the membranes. Numerical modelling reveals that this modulation is due to a modification of guided modes (supported in the SiN nanomembranes) by evanescent interactions with the third object. This multi-body effect could offer an efficient pathway for active control of heat currents at the nanoscale.

Colossal Enhancement of Near-Field Thermal Radiation Across Hundreds of Nanometers between Millimeter-Scale Plates through Surface Plasmon and Phonon Polaritons Coupling

Coupling modes between surface plasmon polaritons (SPPs) and surface phonon polaritons (SPhPs) play a vital role in enhancing near-field thermal radiation but are relatively unexplored, and no experimental result is available. Here, we consider the NFTR enhancement between two identical graphene-covered SiO₂ heterostructures with millimeter-scale surface area and report an experimentally record-breaking ∼64-fold enhancement compared to blackbody (BB) limit at a gap distance of 170 nm. The energy transmission coefficient and radiation spectra show that the physical mechanism behind the colossal enhancement is the coupling between the surface plasmon and phonon polaritons.

Adiabatic Thermal Radiation Pumps for Thermal Photonics

We control the direction and magnitude of thermal radiation, between two bodies at equal temperature (in thermal equilibrium), by invoking the concept of adiabatic pumping. Specifically, within a resonant near-field electromagnetic heat transfer framework, we utilize an instantaneous scattering matrix approach to unveil the critical role of wave interference in radiative heat transfer. We find that appropriately designed adiabatic pumping cycling near diabolic singularities can dramatically enhance the efficiency of the directional energy transfer. We confirm our results using a realistic electronic circuit setup.

A near-field radiative heat transfer device

Recently, several reports have experimentally shown near-field radiative heat transfer (NFRHT) exceeding the far-field blackbody limit between planar surfaces^1-5. However, owing to the difficulties associated with maintaining the nanosized gap required for measuring a near-field enhancement, these demonstrations have been limited to experiments that cannot be implemented in large-scale devices. This poses a bottleneck to the deployment of NFRHT concepts in practical applications. Here, we describe a device bridging laboratory-scale measurements and potential NFRHT engineering applications in energy conversion^6,7 and thermal management^8-10. We report a maximum NFRHT enhancement of approximately 28.5 over the blackbody limit with devices made of millimetre-sized doped Si surfaces separated by vacuum gap spacings down to approximately 110 nm. The devices use micropillars, separating the high-temperature emitter and low-temperature receiver, manufactured within micrometre-deep pits. These micropillars, which are about 4.5 to 45 times longer than the nanosize vacuum spacing at which radiation transfer takes place, minimize parasitic heat conduction without sacrificing the structural integrity of the device. The robustness of our devices enables gap spacing visualization by scanning electron microscopy (SEM) before performing NFRHT measurements.

Electronic Modulation of Near-Field Radiative Transfer in Graphene Field Effect Heterostructures

Manipulating heat flow in a controllable and reversible manner is a topic of fundamental and practical interest. Numerous approaches to perform thermal switching have been reported, but they typically suffer from various limitations, for instance requiring mechanical modulation of a submicron gap spacing or only operating in a narrow temperature window. Here, we report the experimental modulation of radiative heat flow by electronic gating of a graphene field effect heterostructure without any moving elements. We measure a maximum heat flux modulation of 4 ± 3% and an absolute modulation depth of 24 ± 7 mW m^-2 V^-1 in samples with vacuum gap distances ranging from 1 to 3 μm. The active area in the samples through which heat is transferred is ∼1 cm², indicating the scalable nature of these structures. A clear experimental path exists to realize switching ratios as large as 100%, laying the foundation for electronic control of near-field thermal radiation using 2D materials.

Harvesting the Electromagnetic Energy Confined Close to a Hot Body

In the close vicinity of a hot body, at distances smaller than the thermal wavelength, a high electromagnetic energy density exists due to the presence of evanescent fields radiated by the partial charges in thermal motion around its surface. This energy density can surpass the energy density in vacuum by several orders of magnitude. By approaching a photovoltaic (PV) cell with a band gap in the infrared frequency range, this nonradiative energy can be transferred to it by photon tunnelling and surface mode coupling. Here we review the basic ideas and recent progress in near-field energy harvesting.

Far-field coherent thermal emission from polaritonic resonance in individual anisotropic nanoribbons

Coherent thermal emission deviates from the Planckian blackbody emission with a narrow spectrum and strong directionality. While far-field thermal emission from polaritonic resonance has shown the deviation through modelling and optical characterizations, an approach to achieve and directly measure dominant coherent thermal emission has not materialised. By exploiting the large disparity in the skin depth and wavelength of surface phonon polaritons, we design anisotropic SiO₂ nanoribbons to enable independent control of the incoherent and coherent behaviours, which exhibit over 8.5-fold enhancement in the emissivity compared with the thin-film limit. Importantly, this enhancement is attributed to the coherent polaritonic resonant effect, hence, was found to be stronger at lower temperature. A thermometry platform is devised to extract, for the first time, the thermal emissivity from such dielectric nanoemitters with nanowatt-level emitting power. The result provides new insight into the realisation of spatial and spectral distribution control for far-field thermal emission.

Near-field photonic cooling through control of the chemical potential of photons

Photonic cooling of matter has enabled both access to unexplored states of matter, such as Bose-Einstein condensates, and novel approaches to solid-state refrigeration^1-3. Critical to these photonic cooling approaches is the use of low-entropy coherent radiation from lasers, which makes the cooling process thermodynamically feasible^4-6. Recent theoretical work^7-9 has suggested that photonic solid-state cooling may be accomplished by tuning the chemical potential of photons without using coherent laser radiation, but such cooling has not been experimentally realized. Here we report an experimental demonstration of photonic cooling without laser light using a custom-fabricated nanocalorimetric device and a photodiode. We show that when they are in each other's near-field-that is, when the size of the vacuum gap between the planar surfaces of the calorimetric device and a reverse-biased photodiode is reduced to tens of nanometres-solid-state cooling of the calorimetric device can be accomplished via a combination of photon tunnelling, which enhances the transport of photons across nanoscale gaps, and suppression of photon emission from the photodiode due to a change in the chemical potential of the photons under an applied reverse bias. This demonstration of active nanophotonic cooling-without the use of coherent laser radiation-lays the experimental foundation for systematic exploration of nanoscale photonics and optoelectronics for solid-state refrigeration and on-chip device cooling.

Tailoring near-field thermal radiation between metallo-dielectric multilayers using coupled surface plasmon polaritons

Several experiments have shown a huge enhancement in thermal radiation over the blackbody limit when two objects are separated by nanoscale gaps. Although those measurements only demonstrated enhanced radiation between homogeneous materials, theoretical studies now focus on controlling the near-field radiation by tuning surface polaritons supported in nanomaterials. Here, we experimentally demonstrate near-field thermal radiation between metallo-dielectric multilayers at nanoscale gaps. Significant enhancement in heat transfer is achieved due to the coupling of surface plasmon polaritons (SPPs) supported at multiple metal-dielectric interfaces. This enables the metallo-dielectric multilayers at a 160-nm vacuum gap to have the same heat transfer rate as that between semi-infinite metal surfaces separated by only 75 nm. We also demonstrate that near-field thermal radiation can be readily tuned by modifying the resonance condition of coupled SPPs. This study will provide a new direction for exploiting surface-polariton-mediated near-field thermal radiation between planar structures.

Observing of the super-Planckian near-field thermal radiation between graphene sheets

Thermal radiation can be substantially enhanced in the near-field scenario due to the tunneling of evanescent waves. Monolayer graphene could play a vital role in this process owing to its strong infrared plasmonic response, however, which still lacks an experimental verification due to the technical challenges. Here, we manage to make a direct measurement about plasmon-mediated thermal radiation between two macroscopic graphene sheets using a custom-made setup. Super-Planckian radiation with efficiency 4.5 times larger than the blackbody limit is observed at a 430-nm vacuum gap on insulating silicon hosting substrates. The positive role of graphene plasmons is further confirmed on conductive silicon substrates which have strong infrared loss and thermal emittance. Based on these, a thermophotovoltaic cell made of the graphene–silicon heterostructure is lastly discussed. The current work validates the classic thermodynamical theory in treating graphene and also paves a way to pursue the application of near-field thermal management.

Though monolayer graphene has the potential to be used in near-field thermal management applications, no experimental verification has been provided to date. Here, the authors directly measure plasmon-enhanced near-field heat transfer between graphene sheets on intrinsic silicon substrates.

Dynamic optical control of near-field radiative transfer

Dynamic control of radiative heat transfer is of fundamental interest as well as for applications in thermal management and energy conversion. However, realizing high contrast control of heat flow without moving parts and with high temporal frequencies remains a challenge. Here, we propose a thermal modulation scheme based on optical pumping of semiconductors in near-field radiative contact. External photo-excitation of the semiconductor emitters leads to increases in the free carrier concentration that in turn alters the plasma frequency, resulting in modulation of near-field thermal radiation. The temporal frequency of the modulation can reach hundreds of kHz limited only by the recombination lifetime, greatly exceeding the bandwidth of methods based on temperature modulcation. Calculations based on fluctuational electrodynamics show that the heat transfer coefficient between two silicon films can be tuned from near zero to 600 Wm^-2K^-1 with a gap distance of 100 nm at room temperature.

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 field^4-7, 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.

Nanogap near-field thermophotovoltaics

Conversion of heat to electricity via solid-state devices is of great interest and has led to intense research of thermoelectric materials^1,2. Alternative approaches for solid-state heat-to-electricity conversion include thermophotovoltaic (TPV) systems where photons from a hot emitter traverse a vacuum gap and are absorbed by a photovoltaic (PV) cell to generate electrical power. In principle, such systems may also achieve higher efficiencies and offer more versatility in use. However, the typical temperature of the hot emitter remains too low (<1,000 K) to achieve a sufficient photon flux to the PV cell, limiting practical applications. Theoretical proposals^3-12 suggest that near-field (NF) effects^13-18 that arise in nanoscale gaps may be leveraged to increase the photon flux to the PV cell and significantly enhance the power output. Here, we describe functional NFTPV devices consisting of a microfabricated system and a custom-built nanopositioner and demonstrate an ~40-fold enhancement in the power output at nominally 60 nm gaps relative to the far field. We systematically characterize this enhancement over a range of gap sizes and emitter temperatures, and for PV cells with two different bandgap energies. We anticipate that this technology, once optimized, will be viable for waste heat recovery applications.

Coulomb-force-mediated heat transfer in the near field: Geometric effect

It has been shown recently that the Coulomb part of electromagnetic interactions is more important than the transverse propagation waves for the near-field enhancement of heat transfer between metal objects at a distance of order nanometers. Here we present a theory focusing solely on the Coulomb potential between electrons hopping among tight-binding sites. When the relevant systems are reduced to very small geometry, for example, a single site, the enhancement is much higher compared to a collection of them packed within a distance of a few Å. We credit this to the screening effect. This result may be useful in designing metal-based metamaterials to enhance heat transfer much higher.

A Thermal Diode Based on Nanoscale Thermal Radiation

In this work we demonstrate thermal rectification at the nanoscale between doped Si and VO₂ surfaces. Specifically, we show that the metal-insulator transition of VO₂ makes it possible to achieve large differences in the heat flow between Si and VO₂ when the direction of the temperature gradient is reversed. We further show that this rectification increases at nanoscale separations, with a maximum rectification coefficient exceeding 50% at ∼140 nm gaps and a temperature difference of 70 K. Our modeling indicates that this high rectification coefficient arises due to broadband enhancement of heat transfer between metallic VO₂ and doped Si surfaces, as compared to narrower-band exchange that occurs when VO₂ is in its insulating state. This work demonstrates the feasibility of accomplishing near-field-based rectification of heat, which is a key component for creating nanoscale radiation-based information processing devices and thermal management approaches.