Dynamic Modulation of Radiative Heat Transfer beyond the Blackbody

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Dynamic modulation of radiative heat transfer beyond the blackbody limit Kota Ito, Kazutaka Nishikawa, Atsushi Miura, Hiroshi Toshiyoshi, and Hideo Iizuka Nano Lett., Just Accepted Manuscript • Publication Date (Web): 08 Jun 2017 Downloaded from http://pubs.acs.org on June 9, 2017

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Dynamic modulation of radiative heat transfer beyond the blackbody limit Kota Ito,*† Kazutaka Nishikawa, † Atsushi Miura, † Hiroshi Toshiyoshi, ‡ and Hideo Iizuka† *Corresponding author E-mail: [email protected] †

‡

Toyota Central Research and Development Labs.,Inc., Nagakute, Aichi, Japan, 480-1192

Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, Meguro-ku, Tokyo, Japan, 153-8904

TOC

ABSTRACT Dynamic control of electromagnetic heat transfer without changing mechanical configuration opens possibilities in intelligent thermal management in nanoscale systems. We confirmed by experiment that the radiative heat transfer is dynamically modulated beyond the blackbody limit. The near-field electromagnetic heat exchange mediated by phonon-polariton is controlled by the metal-insulator transition of tungsten-doped vanadium dioxide. The

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functionalized heat flux is transferred over an area of 1.6 cm2 across a 370 nm gap, which is maintained by the microfabricated spacers and applied pressure. The uniformity of the gap is validated by optical interferometry, and the measured heat transfer is well modeled as the sum of the radiative and the parasitic conductive components. The presented methodology to form a nanometric gap with functional heat flux paves the way to the smart thermal management in various scenes ranging from highly integrated systems to macroscopic apparatus.

KEYWORDS Near-field radiative heat transfer, Dynamic thermal modulator, Metal-insulator transition, Vanadium dioxide, Uniform nanogap.

TEXT Active control of heat transfer is an important challenge in the fields of the thermal science and thermal engineering. Three modes of thermal transfer are known namely convection with fluids, conduction inside solids governed by electrons and phonons, and radiation mediated by electromagnetic waves. Traditionally, thermal convection has been utilized to tune the heat transport, for instance, by controlling valves in heat pipe systems. On the other hand, the control in solid state systems without moving parts enables thermal management in nanoscale, which opens the possibility of exquisite and sophisticated thermal regulation. Around room temperature, thermal conduction has been modulated by the asymmetric mass loading of nanotubes reconfiguring interfaces in ferroelectrics

(1)

,

(2)

, and profiting from temperature-dependent thermal

conductance(3)-(5), but they commonly fall in relatively low modulation contrasts. Thermal radiation has exhibited a higher contrast (6) by utilizing the metal-insulator transition of vanadium dioxide (VO2)

(7)(8)

, and more functional thermal devices such as thermal transistors(9) and


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thermal memories(10)(11) have been proposed. In these devices(6)(9)-(11), heat flux is below the blackbody limit because electromagnetic coupling is in the far-field regime. Thermal radiation is enhanced when hot and cold bodies are positioned across a nanoscale gap owing to the tunneling of thermal photons. Near-field radiative heat transfer exceeds the blackbody limit particularly when surface polaritons mediate resonant coupling in the evanescent regime, as theoretically modeled by the fluctuational electrodynamics in 1970’s(12). It has recently attracted more interests (13)-(20), and near-field functional thermal devices such as thermal diodes(17)(18) and thermal transistors(19) have been theoretically presented based on the phasechange of materials(17)-(19) or graphene plasmons(20). Near-field coupling has also been experimentally validated by monitoring the thermal exchange between a sphere and a plate(21)-(26). However, heat transport across a uniform gap between parallel plates has more significance in engineering near-field thermal radiation for energy applications such as heat regulation and thermophotovoltaics, because the plate-to-plate heat transfer can be significantly enhanced compared to the sphere-to-plate configuration

(27)

. Uniform gaps have been so far achieved by

using spacers(27)-(32), positioners with angular alignment mechanisms(33)-(36), wafer bonding(37)(38) or integrated-beam-based structures

(39)(40)

. However, none of these preceding studies used

functional materials or demonstrated active modulation of heat transport mostly because no ideal parallelism is maintained when two different materials are used on the plates due to the difference of thermal expansions. It also stems largely to the unoptimized experiment procedures including functional materials preparation and nanogap formation, as both of them are influential to the yield and repeatability of experiments. Amongst various technical requisites, formation of a nanogap between dissimilar materials over a large area exceeding 1 cm2 is the most crucial issue to realize a functional thermal device with large heat transfer.


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In this letter, we demonstrate by experiment a large-amplitude modulation of radiation across a nanometric gap beyond the blackbody limit, not by mechanical reconfiguration but by the change of material properties. Two parallel plates made of fused quartz are placed to form a uniform gap over a 1.6 cm2 area. The plate on the cold side is coated with a functional phase-change material, tungsten (W)-doped vanadium dioxide (VO2). The metal-insulator transition of VO2 modulates resonant near-field radiative transfer across a 370 nm gap, which is maintained by applying a pressure to compensate the bending. An earlier study was performed by van Zwol et al. (41), who observed that near-field radiative heat transfer between SiO2 and VO2 is dependent on the phase of VO2. However, at that time, dynamic modulation based on the phase-change of VO2 was not demonstrated, and the heat flux difference between the phases was not comparable to the blackbody limit because an SiO2 sphere and a plate with VO2 film were used and hence the gap was not uniform. On the other hand, heat transport modulation through mechanically-fixed plates in this work exceeds the blackbody limit and is scalable because no delicate alignments or extra support are needed in parallel with the gap, thereby enlarging the effective area of heat transport. The measured heat transfer is theoretically explained well by the electromagnetic transfer and the parasitic heat conduction so long as the temperature difference across the gap is 50 K or less. Figure 1 (a) shows the schematic representation of our experiment. We have chosen fused quartz as a material of the substrates for the thermal emitter and receiver because it supports surface phonon-polariton, which plays a key role in near-field heat flux enhancement. We have also chosen phase-changing VO2 on the receiver plate to modulate the radiative heat flux by its large change of permittivity (See Supporting Figure S5). Tungsten (W) was doped into the 200nm-thick VO2 film during the sputtering process from a W-V alloy target, in order to lower the phase transition temperature to room temperature (See Supporting Section S1 for the detail of the


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deposition and the characterization). Tungsten inclusion is also beneficial to keep the surface smooth owing to small grain size (See Supporting Figure S2). The nanogap was formed by an array of microfabricated spacer pillars, which are shown in the SEM images in Figure 1 (b) and (c). They were fabricated by photolithography and wet-etching of the fused quartz prior to VO2 deposition (See Supporting Section S2 for details). The wet-etching with buffered hydrofluoric acid (BHF) enables the well-defined spacer height and the pyramidal spacer shape, which facilitate the gap uniformity and the tolerance to the occasional lateral force during the gap formation. A polysilicon hard mask was utilized for the wet-etching to avoid the etchant to sink into the interface between the mask and the fused quartz substrate, thus the size of the spacer top is highly repeatable between fabrication runs. The spacer sizes on the photomask were set differently for each spacer height so as to realize the top size of 3 µm × 3 µm. Spacer pillars are positioned as close as 30 µm from the chip corners and edges as shown in Figure 1 (d) and (e) (See Supporting Section S3 for the detail of the spacer position), not to bring the chip bodies into direct contact as shown in Figure 1 (f). Note that the possibility of the direct contact between the emitter spacer and the receiver spacer is negligible because of the low density of spacers (See Supporting Section S3 for details). The gap formation apparatus was instrumented as shown in Figure 1 (g), which has three features. (1) Force is applied to the chip stack by the compressive spring for the compensation of the intrinsic bending of the chips partially caused by the residual stress of the deposited VO2, while the first soft contact is enabled by the extension springs. By using this feature, the gap has been formed as follows: The intensively cleaned emitter and the receiver chips are stacked and aligned on the pad above the heat flux sensor (See Supporting Section S4 for the detail of the cleaning). Then, the pad on the copper block is slowly pulled down to contact the backside of the


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emitter chip. Finally, a force ranging from 0.5 N to 3 N is applied to the chip stack to form a uniform nanogap. (2) The uniformity of the gap is optically monitored by the reflective interferometry at the four corners of the chip through an optical fiber with an uncertainty of 10 nm (See Supporting Section S5 for details). (3) The temperatures and are controlled with a heater and a thermoelectric cooler by monitoring the outputs from two thermocouples inserted between the pads and the copper block or the flux sensor. The thermal transport across the gap is monitored by the heat flux sensor based on a thermopile, as schematically illustrated in Figure 1 (h). (See Supporting Section S6 for the detail of the instrumentation and the calibration). The temperature distribution over the emitter and the receiver is negligible according to the finiteelement-method simulation shown in Supporting Figure S11 and S23 (b). An equivalent thermal circuit model was developed as shown in Figure 1 (i), where the temperature drop from the thermocouples to the chip surfaces is modeled by the thermal series resistance RS and a ratio χ. The resistance RS includes the resistance of the pads, that of the chip bodies, and the interfacial thermal resistances, and the ratio χ is set to be 0.5 due to the symmetrical layered structures. The heat transfer across the gap is driven by the temperature gradient ∆ = − , where TE and TR are the temperatures of the emitter and the receiver surfaces, respectively, and flows through the radiative thermal resistance RR and the parasitic conductive resistance RC in parallel. The former varies with temperature conditions because of the phase of VO2 and the temperature-dependent nature of thermal radiation. According to fluctuational electrodynamics, the radiative heat flux

is expressed as:

− 1

= = , − , , , , 4

(1)

!",#


6

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where is the frequency, , = ħ⁄expħ⁄() − 1 the mean energy of the Planck oscillator at the temperature T, ħ the reduced Planck constant, () the Boltzmann constant, the wavenumber parallel to the film surface, and j the polarization. The exchange function , , is written as

, ,

4/6

=

+

4/6

+1 − ,-, , . +1 − ,- , , . ,1 − -, - , / 012 3 ,

4Im-, Im- , / 012 3 ,1 − -, - , / 012 3 ,

,

(2)

where -, and - , are the reflection coefficients of the emitter and the receiver incident from the vacuum in j-polarization, respectively, d the distance between the emitter and the receiver, and ; the wavenumber perpendicular to the film surface. The first and second terms correspond to the far-field and near-field heat transfers, respectively. One can see that the radiative heat flux is modulated beyond the blackbody limit, ? − ? , where is the Stefan-Boltzmann constant, by controlling near-field heat transfer.


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Figure 1. (a) Geometrical configuration of the experiment before the gap formation. (inset) Configuration after the gap formation. (b) SEM image of a spacer on the emitter chip observed at 30° from the normal. (c) SEM image of a spacer on the receiver chip. (d) Spacers around a corner. (e) A spacer around an edge. (f) Schematic illustration of the direct contact between chip bodies in the case that the spacers are not positioned around edges and corners. (g) Photograph of the apparatus. (h) Schematic representation of the heat flux measurement. (i) Equivalent thermal circuit model. Active modulation of radiative heat flux across a 370 nm gap was demonstrated as shown in Figure 2 (a). Initially, TH and TL were set at 355 K and 295 K, respectively, and the VO2 film


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remains as insulator (0 min -100 min). Then, TH and TL were respectively changed to 385 K and 325 K in order to bring the VO2 film into the metallic phase (170 min - 290 min). The temperature difference TH - TL was maintained in both conditions. It is clear that the heat flux across the gap is significantly suppressed when the VO2 is in the metallic phase. One can also see that the heat flux recovers when the temperature profile set back to the original (400 min – 530 min). Note that the bold blue curve corresponds to the steady-state temperature conditions. For the detail of the data analysis, see Supporting Section S7. The amount of the modulation exceeds the blackbody limit of 471 Wm-2, which is the heat transport between blackbodies at temperatures of 355 K and 295 K. The modulation amplitude is underestimated from two perspectives. Firstly, thermal radiation generally increases at higher temperatures when temperature difference is maintained, as expected from the StefanBoltzmann’s law. Such an increase is observed between fused quartz chips positioned across 480 nm, as shown in Supporting Figure S15. The metal-insulator transition of VO2 not only explicitly suppresses the heat flux but also compensates the temperature-dependent nature of electromagnetic heat transfer. Secondary, the temperature difference ∆ = − of two chip surfaces is smaller than two temperatures used for the blackbody calculation because of the thermal series resistance RS. Furthermore, the temperature difference ∆ increases in the metallic state because the heat flux is smaller. In order to further understand the thermal transport, we measured the heat flux in various temperature conditions on another pair of samples having the same nanogap. Temperature TL of the lower thermocouple was kept constant, and temperature TH of the upper thermocouple was swept from TH = TL to TL + 50 K. The background heat flux ΦB was measured by setting TH = TL, and subtracted from the monitored heat flux ΦM in order to obtain the heat flux ΦG across the


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gap. The temperature difference ∆T between the emitter and the receiver surfaces was calculated from the measured thermal series resistance RS. (See Supporting Figure S12) We monitored the output of the heat flux sensor for 9.5 hours as shown in Supporting Figure S16. The heat flux ΦG across a 370 nm gap was derived as a function of the temperature difference ∆T between the surfaces as shown in Figure 2 (b). For the detail of the measurement, see Supporting Section S8. The optical interferometry through the optical fiber was performed at the four corners of the chip as shown in Figure 2 (e), by which we confirmed a sufficient uniformity. Additionally, we also measured the intrinsic bending of the chips and simulated the bending compensation by a pressure. The spacers after the gap formation were also visually inspected. These results support the gap uniformity as discussed in Supporting Section S9. We first focus on the heat transfer coefficient around ∆T = 0 K. As shown in Figure 2 (c), the coefficient at the high temperature is smaller than that at the low temperature. The slopes are 25.1 Wm-2K-1 and 16.9 Wm-2K-1 at TL = 295 K and TL = 325 K, respectively. The difference of the coefficients is 8.2 Wm-2K-1, which is larger than the coefficient of the blackbody at 300 K (6.1 Wm-2K-1). As previously discussed, this comparison underestimates the capability of the heat flux modulator because the temperature dependence of the radiation is not considered. Instead, we compare the slopes between TH = 325 K and 345 K, as shown in Figure 2 (d). The values are 30.2 Wm-2K-1 and 17.0 Wm-2K-1, respectively, and we defined the difference as the modulation amplitude in the following discussion. In Figure 2 (d), the modulation amplitude of 13.2 Wm-2K-1 clearly overcomes the blackbody limit of 8.5 Wm-2K-1.


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Figure 2. Heat transfer across a 370 nm gap. (a) Measured transient heat flux. Bold blue curves denote the heat flux measured in the steady-state. The distance between the upper and the lower dashed lines denotes the blackbody limit transferred across two surfaces whose temperatures are 355 K and 295 K, which is 471 Wm-2. (b) Measured heat transfer as a function of the temperature difference ∆ between the substrate surfaces. Red and blue markers denote the case of = 325 K and = 295 K, respectively. The plus signs and the circles are the data utilized to derive heat transfer coefficients. The modeled heat transfer is also shown as curves. (c) Heat transfer coefficient around ∆ = 0 K calculated from the plus signs in (b), which are shown at the top of the bar for reference. The coefficients at = 325 K and = 295 K are shown. The coefficient of the blackbody at 300 K is stacked on the case of = 325 K, as the black bar. (d) Heat transfer coefficient around = 335 K. The coefficients are calculated from the data


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between = 345 K and = 325 K, which corresponds to the circles in (b). The coefficients at = 325 K and = 295 K are shown. The corresponding coefficient of the blackbody is also shown by the black bars. The definition of the modulation amplitude is also shown. (e) Optical reflectance spectra measured at the four points of the chips. Red and blue curves denote the measured and the calculated spectra. In this gap range, half the dip of the spectra indicates the gap. The corresponding gap values are shown with the curves. We have repeated the gap formation with different nominal spacer heights of 350 nm, 500 nm, 1000 nm, and 2000 nm. We also have formed gaps without depositing VO2 films on the receiver surfaces. Such repetitive measurements are possible by the well-designed gap formation methodology developed in this work. The modulation amplitude is plotted in Figure 3 (a), which visibly exceeds the blackbody limit when the gap is in the submicron regime, where the strong near-field coupling is significantly modulated by the metal-insulator transition of VO2. The modulation amplitude decreases to a level smaller than the blackbody limit when the distance is large and the near-field transfer is small. The measured modulation amplitude is slightly smaller than the calculated value, which can be explained by the temperature-dependent thermal conductivity of VO2 and the contact thermal resistance between the spacer top and the opposing substrate, as discussed in detail later. Without VO2 film on the receiver, the modulation amplitude is close to null. The small negative values of the modulation amplitude are explained by the temperature drop across RS and ratio χ; when the actual χ is greater than 0.5 due to the cuts on the pad for the optical fiber access, the temperature drops more between the thermocouple and the emitter surface in the case that TL is 295 K. The total heat transfer coefficients when TL = 295 K are shown in Figure 3 (b), and they show that the near-field coupling is largely enhanced as the gap becomes small. The measured heat transport is slightly


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larger than the modeled radiative heat transfer because of the parasitic heat conduction through the spacer pillars. The transfer coefficient variation observed between runs is partially explained by the different spacer contact conditions around the edges.

Figure 3. (a) Modulation amplitudes measured in runs. The modulation amplitude is defined in Figure 2 (d). The error bars in the x-direction denote the maximum and the minimum gaps at four points, while the marker positions denote the average gap distance. The error bars in the ydirection denote the uncertainty of the heat transfer coefficients. Calculated radiative modulation amplitude is also shown as a blue curve. (b) Heat transfer coefficients derived from the data between TH = 325 K and 345 K at TL = 295 K. Calculated radiative heat transfer coefficient with VO2 film is also shown as a blue curve.


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Next, the theoretical model for the heat transfer across the gap is described. The calculated exchange functions across a 370 nm gap with insulating and metallic VO2 are shown in Figure 4 (a) and (b), and also in Supporting Figure S21. As shown in Figure 4 (a), insulating VO2 allows several resonant couplings owing to the phonon-polaritons of fused quartz (See Supporting Figure S22). These resonant couplings lie in the evanescent regime, thus enhancing the heat flux considerably. Noteworthy, the non-resonant coupling also contributes to the enhancements in the insulating case. On the other hand, metallic VO2 hampers the heat flux to be transmitted as shown in Figure 4 (b), because the real part of the permittivity becomes negative as plotted in Supporting Figure S5 (b). In this condition, the resonant couplings lose their amplitude, and the non-resonant couplings are weakened. The exchange function is multiplied by the Planck oscillator to give a spectral heat flux as shown in Figure 4 (c). The spectral heat flux in the insulating state surpasses that in the metallic state, compensating the positive correlation between the blackbody spectra and absolute temperature. For the detail of the theoretical modelling, see Supporting Section S10. The conductive thermal resistance is expressed as the series of the resistance from the emitter body to the spacer, the resistance of the spacer body, the contact resistance between the spacer and the receiver, and the resistance from the receiver surface to the body. In the commercial software COMSOL Multiphysics, we built a finite-element-method (FEM) model that includes all of these components except for the contact resistance, as shown in Figure 4 (d) and Supporting Figure S23 (a). Hereafter, we call the simulated resistance as the geometrical thermal resistance. The temperature change in the emitter body indicates that the resistance from the emitter body to the spacer contributes to the geometrical thermal resistance. From the simulated relationship between the overall heat flux and the applied temperature gradient, we have


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calculated the geometrical thermal resistance as 0.11 W-1m2K and 0.10 W-1m2K for the insulating and the metallic cases, respectively. The different resistances reflect the temperature dependent thermal conductivities of VO2, which have been reported to be 3.5 Wm-1K-1 and 6.0 Wm-1K-1, respectively

(42)

. In contrast to radiation, metallic VO2 facilitates thermal conduction

due to the large number of free electrons, while insulating VO2 suppresses. Such a temperaturedependent thermal conductivity also affects the contact resistance between the spacer top and the VO2 film. Thermal contact resistances are found to be 1.9 × 10DE W-1m2K and 1.1× 10DE W1

m2K for the insulating and the metallic cases, respectively, and they quantitatively explain well

the overall heat transfer across the nanogap, as shown in Figure 2 (b). The developed theoretical model is also applicable to larger gaps, as shown in Figure S24. Thermal transport can be broken down to the sum of the radiative and conductive components, as shown in Figure 4 (e). The radiative heat flux dominates the overall thermal transport especially in the insulating state, and it stems to the suppression of the heat conduction through spacers. The radiative modulation is large enough to surpass the blackbody limit, and it compensates the change of the parasitic thermal conduction. The temperature-dependent parasitic conduction can be reduced by further process optimization in future so as to maximize the modulation amplitude. The thermal resistance of the conductive transfer is also broken down to the sum of the geometrical resistance and the contact resistance, as shown in Figure 4 (f). It reveals that the geometrical thermal resistance and the contact thermal resistance equally contribute to the suppression of the parasitic transport through the spacers.


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Figure 4. Theoretical modeling for the heat transfer across 370 nm shown in Figure 2 (b). Exchange functions with the (a) insulating and (b) metallic VO2 in p-polarization. The blue line denotes the light line. (c) Spectral heat flux when ∆ = 50 K. (d) Finite-element-method result of the parasitic heat conductance through a spacer. Color represents the temperature distribution. Red arrows visualize heat flux. (e) Heat transfer breakdown. (f) Thermal resistance breakdown of parasitic heat conduction. We would like to stress the advantage of the gap formation methodology developed in this work, which is fully disclosed in Supporting Information. Firstly, we have formed the gap between the parallel plates without the need of delicate alignment system or mechanical supports in the direction parallel to the gap. The gap formation methodology is therefore scalable in terms of the effective area, which would have been impossible in the sphere-plate, wafer-bonding-


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based or integrated-beam-based configuration with large mechanical supports. The power modulation over the nanogap is demonstrated to be around 98 mW as shown in Figure 2 (a), which is comparable to the highest total radiative transfer across a nanogap ever measured (134 mW(32) and 250 mW(38)). This proves the lateral scalability as well as the tolerance to the temperature difference of the heat flux modulator in this work. The authors believe that the scalability helps us bring the near-field radiative heat transfer toward energy applications. Secondary, the yield of the gap formation was as high as 50 % in 40 trials, owing to the properly designed spacers and the optimized experimental procedures. In particular, the arrangement of the spacers near the edges of the chip is useful to avoid the direct contact between chip edges. The spacer design employed in this study would promote further experimental investigation in near-field thermal management and thermophotovoltaics. Finally, the applied pressure compensates the bending of the plates, which is especially crucial in the case that thin-film coating or nanostructure is utilized to functionalize near-field thermal radiation. In summary, we have demonstrated by experiment the functional control of near-field radiative heat transfer for the first time to the best of our knowledge. The combination of nanogap and the metal-insulator transition of VO2 has modulated the near-field thermal radiation beyond the blackbody limit in an active manner. Such a modulation was enabled by a simple and scalable but well-designed gap formation methodology utilizing microfabricated spacers. Numbers of trials have verified the repeatability of the gap formation methodology and the modulation, and the theoretical explanation supports the modulated heat flux. This approach enables various intelligent radiative thermal management systems exceeding the blackbody limit. Supporting Information Available: (1) Deposition and characterization of the vanadium dioxide film. (2) Fabrication of emitter and receiver chips. (3) Spacer design. (4) Chip cleaning


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before gap formation. (5) Detail of the optical measurement. (6) Instrumentation and calibration of the heat transfer measurement. (7) Transient modulation of the heat flux. (8) Heat flux measurement. (9) Gap uniformity. (10) Theoretical modeling. This material is available free of charge via the Internet at http://pubs.acs.org. Notes: The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work was supported by JSPS KAKENHI Grant Number JP16K17538. We thank cleanroom staffs of Toyota CRDL including I. Takahashi and S. Iwasaki for technical support. We also thank T. Ikeda for fruitful discussions.

REFERENCES (1) Chang, C. W.; Okawa, D.; Majumdar, A.; Zettl, Science 2006, 314, 1121-1124. (2) Ihlefeld, J. F.; Foley, B. M.; Scrymgeour, D. A.; Michael, J. R.; McKenzie, B. B.; Medlin, D. L.; Wallace, M.; Trolier-McKinstry, S.; Hopkins, P. E. Nano Lett. 2015, 15, 1791-1795. (3) Kobayashi, W.; Teraoka, Y.; Terasaki, I. Appl. Phys. Lett. 2009, 95, 171905. (4) Takeuchi, T.; Goto, H.; Nakayama, R.S.; Terazawa, Y.I.; Ogawa, K.; Yamamoto, A.; Itoh, T.; Mikami, M. J. Appl. Phys. 2012, 111, 093517. (5) Zhu, J.; Hippalgaonkar, K.; Shen, S.; Wang, K.; Abate, Y.; Lee, S.; Wu, J.; Yin, X.; Majumdar, A.; Zhang, X. Nano Lett. 2014, 14, 4867-4872. (6) Ito, K.; Nishikawa, K.; Iizuka, H.; Toshiyoshi, H. Appl. Phys. Lett. 2014, 105, 253503. (7) Barker Jr, A.S.; Verleur, H.W.; Guggenheim, H.J. Phys. Rev. Lett. 1966, 17, 1286. (8) Kats, M.A.; Blanchard, R.; Zhang, S.; Genevet, P.; Ko, C.; Ramanathan, S.; Capasso, F.; Phys. Rev. X 2013, 3, 041004. (9) Joulain, K.; Ezzahri, Y.; Drevillon, J.; Ben-Abdallah, P. Appl. Phys. Lett. 2015, 106, 133505.


18

Page 19 of 26

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(10)

Kubytskyi, V.; Biehs, S.A.; Ben-Abdallah, P. Phys. Rev. Lett. 2014, 113, 074301.

(11)

Ito, K.; Nishikawa, K.; Iizuka, H. Appl. Phys. Lett. 2016, 108, 053507.

(12)

Polder, D.; Van Hove, M. Phys. Rev. B 1971, 4, 3303.

(13)

Otey, C.R.; Lau, W.T.; Fan, S. Phys. Rev. Lett. 2010, 104, 154301.

(14)

Basu, S.; Francoeur, M. Appl. Phys. Lett. 2011, 98, 113106.

(15)

Wang, L.P.; Zhang, Z.M. Nanosc. Microsc. Thermophys. Eng. 2013, 17, 337-348.

(16)

Van Zwol, P.J.; Joulain, K.; Ben-Abdallah, P.; Chevrier, J. Phys. Rev. B 2011, 84,

161413. (17)

Yang, Y.; Basu, S.; Wang, L. Appl. Phys. Lett. 2013, 103, 163101.

(18)

Ghanekar, A.; Ji, J.; Zheng, Y. Appl. Phys. Lett. 2016, 109, 123106.

(19)

Ben-Abdallah, P.; Biehs, S.A. Phys. Rev. Lett. 2014, 112, 044301.

(20)

Ilic, O.; Jablan, M.; Joannopoulos, J.D.; Celanovic, I.; Buljan, H.; Soljačić, M. Phys. Rev.

B 2012, 85, 155422. (21)

Shen, S.; Narayanaswamy, A.; Chen, G. Nano Lett. 2009, 9, 2909-2913.

(22)

Rousseau, E.; Siria, A.; Jourdan, G.; Volz, S.; Comin, F.; Chevrier, J.; Greffet, J.J. 2009.

Nat. Photon. 2009, 3, 514-517. (23)

Guha, B.; Otey, C.; Poitras, C.B.; Fan, S.; Lipson, M. Nano Lett. 2012, 12, 4546-4550.

(24)

Shi, J.; Liu, B.; Li, P.; Ng, L.Y.; Shen, S. Nano Lett. 2015, 15, 1217-1221.

(25)

Song, B.; Ganjeh, Y.; Sadat, S.; Thompson, D.; Fiorino, A.; Fernández-Hurtado, V.; Feist,

J., Garcia-Vidal, F.J.; Cuevas, J.C.; Reddy, P.; Meyhofer, E. Nat. Nanotech. 2015, 10, 253258. (26)

Kim, K.; Song, B.; Fernández-Hurtado, V.; Lee, W.; Jeong, W.; Cui, L.; Thompson, D.;

Feist, J.; Reid, M.H.; García-Vidal, F.J.; Cuevas, J.C.; Meyhofer, E.; Reddy, P. Nature 2015, 528, 387-391. (27)

Ito, K.; Miura, A.; Iizuka, H.; Toshiyoshi, H., Appl. Phys. Lett. 2015, 106, 083504.

(28)

Hargreaves, C.M., 1969. Phys. Lett. A 1969, 30, 491-492.

(29)

DiMatteo, R.S.; Greiff, P.; Finberg, S.L.; Young-Waithe, K.A.; Choy, H.K.H.; Masaki,

M.M.; Fonstad, C.G.; Appl. Phys. Lett. 2001, 79, 1894-1896. (30)

DiMatteo, R.; Greiff, P.; Seltzer, D.; Meulenberg, D.; Brown, E.; Carlen, E.; Kaiser, K.;

Finberg, S.; Nguyen, H.; Azarkevich, J.; Baldasaro, P. AIP Conf. Proc. 2004, 738, 42-51.


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(31)

Page 20 of 26

Hu, L.; Narayanaswamy, A.; Chen, X.; Chen, G. 2008. Appl. Phys. Lett. 2008, 92,

133106. (32)

Watjen, J.I.; Zhao, B.; Zhang, Z.M. Appl. Phys. Lett. 2016, 109, 203112.

(33)

Ottens, R.S.; Quetschke, V.; Wise, S.; Alemi, A.A.; Lundock, R.; Mueller, G.; Reitze,

D.H.; Tanner D.B.; Whiting, B.F. Phys. Rev. Lett. 2011, 107, 014301. (34)

Kralik, T.; Hanzelka, P.; Zobac, M.; Musilova, V.; Fort, T.; Horak, M. Phys. Rev. Lett.

2012, 109, 224302. (35)

Ijiro, T.; Yamada, N. Appl. Phys. Lett. 2015, 106, 023103.

(36)

Song, B.; Thompson, D.; Fiorino, A.; Ganjeh, Y.; Reddy, P.; Meyhofer, E. Nat. Nanotech.

2016, 11, 509-514. (37)

Lim, M.; Lee, S.S.; Lee, B.J. Phys. Rev. B 2015, 91, 195136.

(38)

Bernardi, M.P.; Milovich, D.; Francoeur, M. Nat. Comm. 2016, 7, 12900.

(39)

St-Gelais, R.; Guha, B.; Zhu, L.; Fan, S.; Lipson, M. Nano Lett. 2014, 14, 6971-6975.

(40)

St-Gelais, R.; Zhu, L.; Fan, S.; Lipson, M. Nat. Nanotech. 2016, 11, 515-519.

(41)

van Zwol, P.J.; Ranno, L.; Chevrier, J. Phys. Rev. Lett. 2012, 108, 234301.

(42)

Oh, D.W.; Ko, C.; Ramanathan, S.; Cahill, D.G. Appl. Phys. Lett. 2010, 96, 151906.


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Table of Contents Graphics with a size of 9 cm by 3.5 cm 179x70mm (150 x 150 DPI)


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Figure 1. (a) Geometrical configuration of the experiment before the gap formation. (inset) Configuration after the gap formation. (b) SEM image of a spacer on the emitter chip observed at 30° from the normal. (c) SEM image of a spacer on the receiver chip. (d) Spacers around a corner. (e) A spacer around an edge. (f) Schematic illustration of the direct contact between chip bodies in the case that the spacers are not positioned around edges and corners. (g) Photograph of the apparatus. (h) Schematic representation of the heat flux measurement. (i) Equivalent thermal circuit model.

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Figure 2. Heat transfer across a 370 nm gap. (a) Measured transient heat flux. Bold blue curves denote the heat flux measured in the steady-state. The distance between the upper and the lower dashed lines denotes the blackbody limit transferred across two surfaces whose temperatures are 355 K and 295 K, which is 471 Wm-2. (b) Measured heat transfer as a function of the temperature difference ∆T between the substrate surfaces. Red and blue markers denote the case of T_L = 325 K and T_L = 295 K, respectively. The plus signs and the circles are the data utilized to derive heat transfer coefficients. The modeled heat transfer is also shown as curves. (c) Heat transfer coefficient around ∆T = 0 K calculated from the plus signs in (b), which are shown at the top of the bar for reference. The coefficients at T_L = 325 K and T_L = 295 K are shown. The coefficient of the blackbody at 300 K is stacked on the case of T_L = 325 K, as the black bar. (d) Heat transfer coefficient around T_H = 335 K. The coefficients are calculated from the data between T_H = 345 K and T_H = 325 K, which corresponds to the circles in (b). The coefficients at T_L = 325 K and T_L = 295 K are shown. The corresponding coefficient of the blackbody is also shown by the black bars. The definition of the modulation amplitude is also shown. (e) Optical reflectance spectra measured at the four points of the chips. Red and blue curves denote the measured and the calculated spectra. In this gap range, half the dip of the spectra indicates the gap. The corresponding gap values are shown with the curves. 335x218mm (150 x 150 DPI)


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Figure 3. (a) Modulation amplitudes measured in runs. The modulation amplitude is defined in Figure 2 (d). The error bars in the x-direction denote the maximum and the minimum gap at four points, while the marker positions denote the average gap distance. The error bars in the y-direction denote the uncertainty of the heat transfer coefficients. Calculated radiative modulation amplitude is also shown as a blue curve. (b) Heat transfer coefficients derived from the data between TH = 325 K and 345 K at TL = 295 K. Calculated radiative heat transfer coefficient with VO2 film is also shown as a blue curve. 168x230mm (150 x 150 DPI)


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Figure 4. Theoretical modeling for the heat transfer across 370 nm shown in Figure 2 (b). Exchange functions with the (a) insulating and (b) metallic VO2 in p-polarization. The blue line denotes the light line. (c) Spectral heat flux when ∆T = 50 K. (d) Finite-element-method result of the parasitic heat conductance through a spacer. Color represents the temperature distribution. Red arrows visualize heat flux. (e) Heat transfer breakdown. (f) Thermal resistance breakdown of parasitic heat conduction. 337x220mm (150 x 150 DPI)


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Dynamic Modulation of Radiative Heat Transfer beyond the Blackbody

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