Measurement of near-field thermal radiation between multilayered metamaterials

Sen Zhang, Yongdi Dang, Xinran Li, Naeem Iqbal, Yi Jin, Pankaj K. Choudhury, Mauro Antezza, Jianbin Xu, and Yungui Ma

Phys. Rev. Applied 21, 024054 – Published 28 February 2024

Abstract

The near-field radiative heat transfer (NFRHT) between one-dimensional metamaterials comprised of phonon dielectric multilayers was investigated experimentally. Large-size (1 × 1 ${cm}^{2}$ ) near-field samples were fabricated using $Si C$ , ${Si O}_{2}$ , and $Ge$ layers at a certain gap distance, and the effects of layer-stacking order and phonon-resonance quality on NFRHT were examined. The measured results show good agreement with the theoretical results obtained by employing the transmission-matrix method. Super-Planckian thermal radiation was observed between emitters and receivers with identical structures. The failure of effective-medium theory (EMT) at predicting the near-field heat flux has been evidenced by measurements, particularly in the presence of bounded surface modes, such as the epsilon-near-zero mode. Additionally, analyses have shown that, in specific scenarios, the EMT can offer reasonable physical insights into the underlying coupling process from the perspective of homogenized media. Furthermore, the conditions for applying the EMT in the near-field regime were also touched upon.

Received 22 October 2023
Revised 29 December 2024
Accepted 5 February 2024

DOI:https://doi.org/10.1103/PhysRevApplied.21.024054

Physics Subject Headings (PhySH)

Heat radiation Metrology Near-field optics Surface & interfacial phenomena

1-dimensional systems Metamaterials Multilayer thin films Optical materials & elements

Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & OpticalEnergy Science & Technology

Authors & Affiliations

Sen Zhang ¹, Yongdi Dang¹, Xinran Li¹, Naeem Iqbal¹, Yi Jin¹, Pankaj K. Choudhury ¹, Mauro Antezza ^2,3, Jianbin Xu ⁴, and Yungui Ma ^1,*

¹State Key Lab of Modern Optical Instrumentation, Centre for Optical and Electromagnetic Research, College of Optical Science and Engineering, International Research Center for Advanced Photonics, Zhejiang University, Hangzhou, China
²Laboratoire Charles Coulomb (L2C), UMR 5221 CNRS-Université de Montpellier, F-34095 Montpellier, France
³Institut Universitaire de France, 1 rue Descartes, F-75231 Paris Cedex 05, France
⁴Department of Electrical and Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, China

^*yungui@zju.edu.cn

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Vol. 21, Iss. 2 — February 2024

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Images

Figure 1
(a) Schematic of the dielectric multilayer structures. Emitter and receiver are separated by photoresist nanopillars with a gap distance of d. (b) NFRHT measurement setup. Two embedded thermistors (not shown here) are used to measure local temperatures of heat spreaders. Right figure is the thermal resistance network of the thermal pathway. T_e, T_r, and T_am represent the temperature of emitter, receiver, and ambient chamber, respectively. R_rad, R_con, and R_rad represent the effective thermal resistance of near-field radiation, conduction through the pillars, and conduction through the heat sink, respectively. (c) SEM images of the cross section of the fabricated multilayer samples. Effective permittivity spectra for (d) bulk materials and (e) $[Si C / Ge]$ and $[{Si O}_{2} / Ge]$ multilayer samples. $ε^{(')}$ corresponds to the real (imaginary) part of the dielectric constant, while the parallel (perpendicular) portion to the surface plane is denoted as $ε_{| | (⊥)}$ . Filling ratios, f, of $Si C$ or ${Si O}_{2}$ are also provided based on the actual thicknesses. Hyperbolic bands are marked by the shaded regions in (e).
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Figure 2
Comparison of NFRHT between (a) I-I and I-II and (b) III-III and III-IV combinations, with ΔT = T_e− T_r. TMM and EMT theoretical predictions (Q_TMM and Q_EMT) are plotted with shaded areas based on uncertainty analyses. Blackbody limit, Q_BB (black dashed line), is also provided. Experimental results, Q_expt., are plotted as dot symbols with error bars (±3%), which are relatively small and indistinguishable in the figure.
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Figure 3
p-Polarized transmission coefficients, τ_p, of $Si C / Ge$ and $[{Si O}_{2} / Ge]$ multilayers in different layer-stacking orders for emitter and receiver calculated by the EMT and TMM approaches. Calculations are conducted at 270-nm gap distance. (a),(d) and (c),(f) correspond to TMM calculations, where the light cone for $Si C$ and ${Si O}_{2}$ are depicted as white lines. EMT results are plotted in (b),(e) for comparison.
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Figure 4
Near-field spectral heat flux for different combinations of (a) $Si C / Ge$ and (b) $[{Si O}_{2} / Ge]$ multilayer samples. Spectral heat flux is normalized to that of the blackbody with H/H_BB. Results of bulk $Si C$ and ${Si O}_{2}$ are also provided for comparison.
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Figure 5
Theoretical investigations of the relative error of EMT in predicting the NFRHT behaviors of (a),(b) $[Si C / Ge]_{3}$ and (c),(d) [ ${Si O}_{2} / Ge$ ]₃ multilayers. (a),(c) Emitter and receiver combination with identical layer-stacking order, and (b),(d) with different layer-stacking order. Quantity d/p depicts the border of 10% deviation, as profiled by the black dashed lines.
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Figure 6
(a) Bending morphology (B_z) of the substrate. Entire surface is divided into two regions by contour lines based on their level of bending, as marked by white arrows. (b) Roughness (R_z) of the multilayer sample. Measuring area is 5 × 5 µm². Average roughness, R_av, is 1.6 nm. (c) Morphology of SU-8 nanopillar. Height of nanopillar is estimated by the average value of vertical distance of red and green measuring bands. (d) Measured total thermal resistance of two adhesion layers of thermal conductive glue. Constant fitting of total thermal resistance is 25.27 K/W, as marked in the figure.
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