Nearfield 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 [1] and if we analyze the light at distances from the emitter large compared to this thermal wavelength [2]. 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 [2]. 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 [5] and so called hyperbolic metamaterials (HMMs) [6]. 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 [7].

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 [8].



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.



Slawa Lang

Alexander Petrov