Near-field radiative heat transfer
The worldwide increase in energy consumption, accompanied by the effort to use more and more green technologies, has placed emphasis on thermophotovoltaics (TPV), among other technologies. In TPV heat is transformed into electrical energy. The heat can be taken from industrial processes where it is a byproduct and would be wasted otherwise. On the other hand sunlight can be used to heat up an emitter.
The hot emitter radiates electromagnetic waves mainly in the infrared. That radiation is absorbed in a photovoltaic cell creating usable electrical energy. The cells used for TPV are similar to solar cells. The difference is the material. To absorb infrared radiation semiconductors with smaller band gaps are needed than for visible light. Heat transfer mechanisms other than radiation will decrease the efficiency and must be suppressed, e.g. by having vacuum between emitter and PV cell.
Due to the band structure of semiconductors the most efficient way to use a photovoltaic cell is to illuminate it with light having the same energy as the band gap. Light with smaller energies is not absorbed at all. Light with larger energy is absorbed but the energy difference is lost as heat. Naturally, the radiation of a hot body is broadband and not narrowband as desired. To get an efficient TPV system one can use a filter which lets pass radiation with the correct wavelength and reflects everything else back to the emitter, or one can structure the emitter to emit narrowband light.
According to Kirchhoff's law absorption and emission of a body are linked. The best absorber, which is thus also the best emitter, is a black body, a theoretical entity which absorbs all incident electromagnetic radiation. The emission of a black body, derived by Max Planck, is commonly assumed to be the upper limit. But this is only true if the emitter is larger than the thermal wavelength  and if we analyze the light at distances from the emitter large compared to this thermal wavelength . This far-field zone starts at distances of a few thermal wavelengths. The thermal wavelength is about 10 µm at 300 K and scales with the inverse of the temperature.
In the near field besides the normal propagating modes there are also evanescent modes. Evanescent modes are light that propagates along the surface and exponentially decays into the space. If a cold second body is brought closely to the hot first one these evanescent modes will contribute to the heat transfer from hot to cold body. The near-field radiative heat transfer can be orders of magnitude larger than the far-field transfer . For TPV applications it means an increase in total power, together with a high efficiency if designed narrowband [3,4].
Several mechanisms are known to lead to good near-field heat transfers, e.g. surface polaritons  and so called hyperbolic metamaterials (HMMs) . Hyperbolic corresponds to the isofrequency surfaces in k-space. They are hyperboloids instead of ellipsoids as for natural materials.
Two realizations of HMMs exist. One is metallic wires in a dielectric membrane, the other one is a layered system consisting of alternating metallic and dielectric layers. The feature sizes of the structures must be below the wavelength to be able to treat them as an effective homogeneous material, so in the nanometer range .
Hyperbolic metamaterials in the context of near-field radiative heat transfer shall be analyzed in this subproject of the Collaborative Research Centre 986. Besides thermophotovoltaics other applications are conceivable, e.g. touchless cooling .
The main goal of the project is to measure the enhanced near-field radiative heat transfer between HMMs.
Concrete goals are:
- Identify HMMs with desired properties
- Fabricate those HMMs
- Confirm HMM properties with different characterization techniques
- Measure near-field heat flux between and through HMMs
- Clarify advantages and disadvantages of HMMs in comparison to other concepts
Depending on the purpose the HMMs should have different properties:
- For TPV systems the metamaterials must be hyperbolic in near infrared (NIR)
- For e.g. touchless cooling the metamaterials may be hyperbolic in mid infrared (MIR)
- For TPV systems the hyperbolic frequency band must be narrowband
- For e.g. touchless cooling the hyperbolic frequency band must be broadband
Such studies, if successful, could be followed by design and characterization studies on concrete TPV systems.
HMMs are simulated and then produced and measured. The different simulation tasks are:
- Reflection, transmission and absorption with MATLAB using effective medium theory (EMT) and transfer matrix method (TMM)
- Near-field heat transfer with MATLAB using EMT and TMM
The production is done by colleagues from Helmholtz-Zentrum Geesthacht (HZG) and Hamburg University. Fabrication tasks are:
- Layered HMMs using magnetron sputtering
- Nanowire HMMs using a combination of laser interference lithography (LIL) and hard anodization followed by electrodeposition
Characterization tasks are:
- Reflection, transmission and absorption measured with UV/Vis and Fourier transform infrared (FTIR) spectroscopy
- Structure analyzed by scanning electron microscopy (SEM) and X-ray reflection (XRR)
- Near-field heat transfer measured with a guarded hot plate like setup
Furthermore, theoretical considerations are undertaken together with colleagues from Carl von Ossietzky Universität, Oldenburg, to compare hyperbolic modes to other mechanisms providing large radiative heat fluxes. For this purpose mainly numerical calculations are performed with MATLAB.
A layered hyperbolic metamaterial was produced and characterized . The alternating layers consist of silicon (Si) and gold (Au). XRR and SEM measurements (Fig. 1(a)) provided the structural parameters. Fitting simulations to measured reflection and transmission resulted in the confirmation of hyperbolic properties (Fig. 1(b)). In addition, a significantly increased gold collision frequency was observed. Due to the high refractive index of Si and a high Si volume fraction, the transition from purely dielectric to hyperbolic behavior is in the near infrared, as can be seen in Fig. 1(b).
Fig. 1(a). XRR measurement together with a ﬁtted simulation. Both coincide well. Inset: SEM picture of fabricated sample. The multilayer stack located on a silicon substrate is featured here. Because of charging effects the upper surface seems rough. 
(b). Real part of effective permittivities of our HMM calculated with effective medium theory. For comparison, not only the values for thin ﬁlm gold (“ﬁt 3”) but also values for bulk gold (“bulk”) are displayed. 
To emphasize the advantage of hyperbolic metamaterials over materials supporting surface modes, the penetration depth of thermal photons into the different materials was calculated . Fig. 2(a) shows the analyzed systems. Gallium nitride (GaN) has a band in the mid infrared where its permittivity is negative and hence it supports surface modes there. The near-field heat flux supported by surface waves is normally slightly higher than that supported by hyperbolic modes. But the hyperbolic modes have one big advantage. They are propagating bulk modes and are not constrained to the surface. Their penetration depth is only limited by material losses and is more than one order of magnitude larger in the near-field regime (Fig. 2(b)). Having larger penetration depths is advantageous for TPV and touchless cooling, because photons transport heat much faster than phonons and the energy densities are smaller.
Figure 2 (a). Systems to be analyzed. Two identical half spaces of (i) bulk GaN, of (ii) GaN/Ge layer HMMs and of (iii) GaN/Ge wire HMMs separated by a vacuum gap. The HMMs are modeled as effective media. The GaN ﬁlling factor of the layer HMM is 50%, the one of the wire HMM is 30%. The gap width is l. 
(b). Thermal penetration depth at T = 300 K for different vacuum gap widths. 
List of publications
Lang, S., Lee, H. S., Petrov, A. Y., Störmer, M., Ritter, M., & Eich, M., “Gold-silicon metamaterial with hyperbolic transition in near infrared,” Appl. Phys. Lett. 103, 021905 (2013).
Lang, S., Tschikin, M., Biehs, S.-A., Petrov, A. Y., & Eich, M., “Large penetration depth of near-field heat flux in hyperbolic media,” Appl. Phys. Lett. 104, 121903 (2014).
Dr. Michael Störmer, Helmholtz-Zentrum Geesthacht Centre for Materials and Coastal Research, Institute of Materials Research
Prof. Dr. Kornelius Nielsch, University of Hamburg, Institute of Applied Physics
Dr. Svend-Age Biehs, Carl von Ossietzky Universität, Institut für Physik
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