1. Introduction

High-temperature stable materials with high absorption/emission at short wavelengths and low absorption emission at longer wavelengths are particularly desirable as emitters for thermophotovoltaic (TPV), lighting applications and as absorbers for solar thermal applications [1–4]. These materials should be designed to exhibit required optical properties at high temperatures (>900°C) [3, 4]. Low emissivity in the longer wavelength ranges is critical for TPV to reduce losses due to heat emission at frequencies smaller than those related to the bandgap energy of a photovoltaic cell [5], as such frequencies will not contribute to the photocurrent generation. For lighting applications the longer wavelengths are not observed by the human eye and their emission should thus be avoided as well. Similarly, for selective solar absorbers, low emittance at long wavelengths minimizes the re-radiation of absorbed power.

Numerous selective systems have been proposed for TPV, lighting and solar thermal applications, including one-dimensional (1D) photonic crystals [6] and aperiodic metal-dielectric stacks [7], two-dimensional (2D) and three-dimensional (3D) metallic photonic crystals [8–14], metamaterial-based [15–19] and cermet-based [20] systems. A common feature among all approaches is that the metallic material is nanostructured with feature sizes of the order of 30 nm to 1µm in order to tune the response of the structures in the visible and near-infrared spectral ranges. Compared to flat bulk metallic surfaces, nano- and microstructured metals, however, show significantly reduced thermal stability due to their large surface and hence their susceptibility to chemical reactions as well as mass transport processes [21, 22]. Also, the fabrication of the 2D metallic photonic crystals and the metamaterials requires a lithographic patterning of the metallic surface which is complex, costly and slow [8, 12]. Thus refractory and large-area absorbers/emitters with selective absorption/emission in the near-infrared (NIR) range remains a challenge.

Previously, a low-cost fabrication method based on colloidal monolayers has previously been utilized to produce large area structures with tunable optical properties [23–28]. Particularly, a monolayer of polystyrene spheres on gold substrate was used for narrow-band absorption in visible and in NIR range [23, 24]. Further, the efficiency of a silicon solar cell was enhanced by a colloidal monolayer of dielectric spheres deposited on thin-film silicon layer [28]. A general method for engineering the cooperative electromagnetic interactions in array of nanoparticles was proposed [29].

In this work, we report on a self-assembled refractory absorber/emitter without the necessity to structure the metallic surface itself, still retaining the feature of tailored optical properties for visible light emission and TPV applications. The required selective emission can be obtained by depositing ceramic microspheres on the surface of the flat metal such as tungsten (W) protected by a thin ceramic coating. The obtained spectral response is similar to one obtained with cylindrical microcavities in a tungsten substrate [2]. However, here we use external cavities coupled evanescently to the unstructured metal which poses two important advantages: No need of lithographic processes and higher thermal stability due to avoiding a structured metal with a large reactive surface. Furthermore, an unstructured metallic surface with ceramic microparticles has a lower absorption in the infrared range compared to microcavities in the metallic substrate. This is a very important parameter for the efficiency of the TPV emitter. Highly stable ceramic materials are used such as zirconium oxide (ZrO₂) and hafnium oxide (HfO₂).

2. Simulation results and discussion

As illustrated in the inset in Fig. 1(a), the designed absorber/emitter consists of a two-dimensional (monolayer) hexagonal array of ZrO₂ ceramic microspheres on a tungsten substrate with a HfO₂ nanocoating. The radius of the sphere and the thickness of HfO₂ coating are denoted by R and H, respectively. The thickness of the tungsten substrate is equal to 100 nm for fabrication purposes. The penetration depth of optical fields is below 100 nm and thus such a layer and a bulk tungsten substrate will have the same optical properties. The thickness of the HfO₂ is 20 nm. It fulfills the purposes of protecting the tungsten against oxidation [11] and has almost no effect on the optical properties due to small thickness. We performed numerical computations using the finite-integration-time-domain method with CST Microwave Studio. The relationship between the absorption spectrum and geometric dimensions of the structure was investigated. An accurate model with multiple Lorentzian terms for tungsten was used to describe its dielectric function in the relevant wavelength range. The dispersion of tungsten was taken from [30]. The refractive index of ZrO₂ is assumed as n = 2.12 [31]. ZrO₂ is transparent to IR radiation at temperatures <1200°C [32]. Thus we do expect the complex dielectric function of ZrO₂ to be largely independent of temperature changes in this range. A fine grid (40 points per material wavelength in each direction) together with sufficiently long simulation times (3 ps) were used to take in account coupling to resonant modes.

 

Fig. 1 (a) Calculated absorption of radiation under normal incidence for a flat tungsten substrate (black) and a monolayer hexagonal array of ZrO₂ particles with R = 500 nm deposited on a flat tungsten substrate (blue). Inset: Schematics of the two-dimensional hexagonal array of ceramic microspheres on the tungsten substrate. The electric energy density distributions for (b) λ₁ = 2.14 µm, (c) λ₂ = 1.56 µm, (d) λ₃ = 1.28 µm and (e) λ₄ = 1.06 µm is shown for the cross section parallel to the electric field polarization of the incident light. Arrows in (b) and (c) show the electric field polarization at the position of maximal energy density at the time when this maximum is achieved.

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Under normal incidence we expect an absorption by A(λ) = 1–R(λ)–T(λ), where A(λ) is the absorption, R(λ) is the reflection, and T(λ) is the transmission, where T(λ) = 0 due to the thick layer of tungsten. Emission is equal to absorption of the heated surface because of Kirchhoff’s law [33]. At normal incidence, there is no dependence on the polarization of incident light due to 60° rotational symmetry of the structure. So, we considered the incident electric field (E) polarization parallel to ΓK direction in Brillouin zone of a monolayer photonic crystal for simplicity. We have calculated two absorption spectra: one for the flat tungsten substrate and another for the array of ZrO₂ particles with R = 500 nm deposited on the HfO₂-coated tungsten, as shown in Fig. 1(a). A clear edge of absorption is observed at 1.56 µm for the sample with microspheres coating. The average absorption for flat tungsten substrate and the array of ZrO₂ particles are equal to 44% and 76% for wavelength range from 0.4 µm to 1.5 µm, respectively. Even more important is the sharp transition within 100 nm from high to low absorption observed in the ZrO₂ particle-coated samples, only. The calculated MIR emission of the proposed structure is approximately two times lower than the calculated emission of a structured metal emitter with cylindrical cavities [13]. The estimations in [13] tell that the MIR emission can take up to 50% of the emitter power. This value can be reduced to 25% with our emitter, thus increasing the efficiency of TPV.

We identify four absorption peaks in wavelength range from 1 µm to 2.5 µm. To reveal the physical origin of the absorption in our system, the electromagnetic field distributions for these resonant modes are studied individually. Figures 1(b)-1(e) depict the distributions of the electric energy density of the absorber/emitter with R = 500 nm at the wavelengths λ₁ = 2.14 µm (b), λ₂ = 1.56 µm (c), λ₃ = 1.28 µm (d) and λ₄ = 1.06 µm (e). The spectra indicate the presence of microsphere resonances which are influenced by the substrate and neighbors. The first resonance corresponds to a quadrupole resonance with the electric field horizontal to the substrate [see arrows in Fig. 1(b)]. This resonance is strongly coupled to the incoming plane wave and thus has a very low Q factor. The losses in the tungsten are not sufficient to achieve critical coupling, when coupling to plane wave is equal to absorption loss. Thus, for the resonance at λ₁, absorption at the peak stays very low. The second peak at λ₂ corresponds to the same microparticle resonance, where the quadrupole is rotated by 90 degrees. In this case the electric field is vertical to the substrate [see arrows in Fig. 1(c)] and strong enhancement of electric field is observed in the air gap between the particle and the substrate. As its polarization is vertical to that of the incoming wave this resonance is coupled much weaker to the plane wave. Thus the loss in tungsten is sufficient to achieve critical coupling and thus 100% absorption. The next two resonances correspond to hexapole and octupole modes. This can be derived by counting the number of electric field maxima on the surface of the particle. In Figs. 1(d)-1(e) we did not show the arrows which indicate the electric field polarization due to their complicated spatial distribution. Still the resonances have a large vertical component of electric field close to the substrate, which is expected due to the continuity of the normal component the dielectric displacement function across the interfaces and can be confirmed by the strong enhancement of electric field in the air gap. These resonances at λ₃ and λ₄ are also critically coupled.

In order to evaluate the influence of the refractive index of particles, we calculated the absorption coefficients for the monolayers assuming particles from aluminum oxide (Al₂O₃) [a blue line in Fig. 2(a)], from ZrO₂ [a gray line in Fig. 2(a)] and from titanium dioxide (TiO₂) [a red line in Fig. 2(a)] all with R = 500 nm. The refractive indices of Al₂O₃ and TiO₂ are assumed as 1.62 and 2.41, respectively. The series of critically coupled resonances only occur in the monolayer of ZrO₂ particles on tungsten and provide the band edge absorption with a sharp transition as desired for TPV applications. We do not observe critically coupled resonances for Al₂O₃ and TiO₂ monolayers. This means that for monolayers of particles with 500 nm radius the refractive index of ZrO₂ is crucial to obtain band edge absorption with critically coupled resonances.

 

Fig. 2 (a) Calculated absorption of radiation under normal incidence for monolayers of Al₂O₃ particles (blue), ZrO₂ particles (gray) and TiO₂ particles (red) with R = 500 nm deposited on a flat tungsten substrate. (b) Simulated absorption of the monolayer of ZrO₂ particles with R = 500 nm for unpolarized light at 0°-45° angles of incidence.

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The response of the absorber/emitter has a weak angular dependence. Figure 2(b) presents the simulated absorption of the monolayer of ZrO₂ particles with R = 500 nm for unpolarized light at 0°-45° angles of incidence. The resonances are shifted by only 200 nm to longer wavelengths for 45° incident angle. Larger angles will not contribute significantly to the emitted power due to Lambert’s cosine law. Taking into account the spectral energy density for emission at the envisaged temperatures between 1000°C and 1500°C the edge of the emission can be adjusted such that the 200 nm wavelength shifted emission from oblique angles still matches the sensitivity window of a low band gap photovoltaic cell.

We calculated the absorption coefficients for various sizes of the ceramic spheres as a function of the wavelength λ. We considered the range of radius from 200 to 600 nm in steps of 10 nm as shown in Fig. 3. As the radius becomes larger, the cutoff wavelength also increases. The edge of absorption can be shifted by varying the sphere size. Moreover, we achieved almost perfect absorption for three peaks (λ₂, λ₃, λ₄) independent of the particle radius, despite the strong change of the relative permittivity of tungsten with wavelength. The tungsten substrate influences both the coupling to a plane wave and the absorption loss of the resonance. The absorption loss decreases with larger wavelength, however, the coupling to plane wave also becomes weaker. Thus the resonance stays critically coupled. At the same time the first peak λ₁ disappears for larger radii due to smaller absorption loss. The coupling to plane wave of this resonance is not influenced by tungsten. Thus we can produce spectrally selective emission for a range of wavelengths by adjusting the microsphere radius. This means that the emission spectrum can be tuned with great accuracy to the spectral response of a TPV photodiode.

 

Fig. 3 Simulated absorption for different radii of ceramic microspheres.

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3. Experimental results and discussion

The substrates for monolayer deposition of the spheres were fabricated using a magnetron sputtering technique. The tungsten layer (100 nm thickness) and hafnium oxide (HfO₂) layer (20 nm thickness) were deposited on planar and polished silicon substrates in an ultrahigh-vacuum chamber by direct current (for W) and medium frequency (for HfO₂) magnetron sputtering. The deposition rates of W and HfO₂ were 0.08 and 0.21 nm/s, respectively. A thin coating of HfO₂ was used, which shows excellent stability at high temperature and typically serves as a thermal barrier coating and surface protection for tungsten substrates [11]. Monodisperse ZrO₂ particles with a radius of 371 nm were fabricated by a modified sol-gel approach [34, 35]. This modified process reproducibly leads to monodisperse particles with virtually no agglomeration and secondary nucleation. Particle sizes were determined from SEM images by counting 200 particles per batch. The standard deviation (SD) of the size distribution was determined to be 7%. The ‘as synthesized’ particles are amorphous. Before a spin-coating deposition process the ZrO₂ particles were calcined at 600 °C in order to stabilize the particles sizes [35], leading to an average radius of 330 nm with a slightly larger SD of 8%. Also, the transformation from amorphous into tetragonal crystalline phase takes place during calcination [34, 35]. The radius of 330 nm is not optimal for sharp edge absorption due to large peak at λ₁, as can be seen from Fig. 3. But it was used to demonstrate the effect.

A suspension was prepared by mixing the pre-calcined zirconia particles with a mixture of ethylene glycol and ethanol (1:1 in volume), leading to a final concentration of 14 vol.% of particles. The mixture was ultrasonicated for 5 min for homogenization. Before deposition the substrate was oxygen-plasma cleaned to render the surface hydrophilic. The monolayers of ZrO₂ particles on tungsten substrates were then formed by spin coating the suspension at 2000 rpm rotation speed for 200 s. After spin coating the substrates were cleaned by oxygen plasma to eliminate the ethylene glycol. We deposited a ZrO₂ monolayer over an area of ~1.5 cm x 1.5 cm, but island-wise with the size of islands ~100 µm x 100 µm. These islands were larger than the area used for the reflection measurements. For the complete coverage of larger substrates, the fabrication process needs optimization. The SEM pictures in Fig. 4 show higher and lower magnification of the surface of the deposited monolayer of ZrO₂ particles. The lower magnification image shows that large area coverage with domains of hexagonal lattice ordering was achieved. The fact that we do not achieve ideal crystalline layers, however, polycrystalline layers, does not pose a problem as the optical properties presented above are governed by the resonances of the single particles in conjunction with the neighbour particles and the tungsten substrate.

 

Fig. 4 SEM images of the monolayer of ZrO₂ microparticles on the tungsten substrate deposited from spheres with radius 330 nm.

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The optical properties of the absorber/emitter were probed by collecting reflection in spectral range 0.9-2.7 µm using a FTIR microscope (Bruker Hyperion 2000) with 15x objective that is coupled to the FTIR spectrometer (Bruker Vertex 70). The measuring spot was defined as ~100 µm x 100 µm by an integrated knife-edge aperture. The incidence beam is ~16.7° off-normal to the surface of the sample and the cone has an apex angle of ~14°. At this small incident angles the reflection spectra only slightly deviate from normal incidence spectra. The reflection spectrum was measured by using a gold mirror as reference. The absorption spectrum was obtained as 1-R(λ). Figure 5(a) presents an experimental absorption of the monolayer of ZrO₂ microparticles (blue) and the tungsten substrate with 20 nm HfO₂ coating (red). The calculated absorption for a monolayer of particles with 8% SD in size is shown in black. The effect of the particles’ size distribution is approximated by averaging the simulated spectra for eight different particle radii taking into account the relative fractions according to a Gaussian size distribution function with 8% SD. As deposited, the monolayer of ZrO₂ microparticles exhibits two absorption peaks at 1 µm and 1.4 µm and low absorption in the NIR range with the same level as experimentally observed for the substrate alone. The experiment does not show multiple peaks due to the limited spectral window of the FTIR microscope. We expect that the selectivity of absorption can be further increased if particles with radius R = 450-600 nm are used. The measured absorption is higher than the calculated absorption, in particular in the 1-1.5 µm wavelength range. The reflection in the experiment can be increased by scattering on crystal boundaries and lattice defects due to the size distribution of the particles. This missing reflection can lead to larger measured absorption. Also, we expect the absorption of the tungsten substrate will increase especially at longer wavelengths at high operating temperatures (> 900°C) [2].

 

Fig. 5 1-R(λ) spectra measured from monolayer of ZrO₂ microparticles with 330 nm radius (blue), measured from tungsten substrate with 20 nm HfO₂ coating (red) and averaged for simulated monolayers with varying particle sizes (black). (b) 1-R(λ) measurements of the monolayer of ZrO₂ microparticles before annealing (black) and after heat cycling to 800°C (blue), 900°C (green), 1000°C (red) and 1100°C (brown).

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At high operating temperatures (> 900°C), thermal stability of nanostructures is an important issue. We therefore investigated the thermal stability of our fabricated structures by experimentally determining the absorption at room temperature before and after annealing the samples at different temperatures for the duration of 3 h. The samples were heat treated under vacuum (~2x10⁻² mbar) in a high temperature heating stage (TS1500, Linkam) with a heating rate of 10 °C min⁻¹. After reaching the final temperature the samples were kept at this temperature for 3 h before cooling down with a cooling rate of 10 °C min⁻¹. In this heating stage, the sample is heated with a ceramic crucible heating element and a type S Rh/Pt thermocouple is used as a temperature sensor.

Figure 5(b) compares the absorption spectra of the sample before annealing (black) and after heat cycling to 800°C for 3 h under vacuum (blue), 900°C for 3 h (green), 1000°C for 3 h (red) and 1100°C for 3 h (brown). As can be seen, the optical performance is unchanged up to 1000°C. The sample was destroyed when annealed at 1100°C. After this annealing the spectrum loses selectivity due to additional absorption and scattering in the sample. In order to understand the degradation mechanism we recorded SEM images of the sample before annealing [Fig. 6(a)] and after annealing at 1000°C [Fig. 6(b)] and 1100°C [Fig. 6(c)]. The ceramic particles are still stable but the substrate consisting of silicon and the tungsten coating was destroyed by a chemical reaction between the silicon substrate and the tungsten nanolayer. We expect the thermal stability of the system will be improved by changing the substrate to bulk tungsten, avoiding the silicon. This is a topic of current investigations.

 

Fig. 6 SEM images of the edge of monolayers of ZrO₂ microparticles on silicon/tungsten/HfO₂ substrates before annealing (a) and after annealing at 1000°C for 3 h (b) and 1100°C for 3 h (c).

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4. Conclusion

We have demonstrated theoretically and experimentally that monolayers of ZrO₂ microparticles on a tungsten layer can be used as thermally stable selective absorbers/emitters for high-temperature applications. The amount of the change in the spectral selectivity due to temperature dependent optical properties of metal will be a topic of future investigation. The high refractive index of ZrO₂ is crucial to obtain band edge absorption with critically coupled resonances. We demonstrated the optical functionality of the structure after annealing up to temperatures of 1000°C under vacuum conditions. We expect that the stability can be further increased if a bulk tungsten substrate is used and zirconia particles are phase stabilized by yttrium. The selectivity of the sample absorption/emission can be improved if microspheres with radius 450-600 nm are used. These tasks will be the addressed in future work. This concept for selective absorbers/emitters can be potentially used for large scale and robust absorbers for solar TPV systems or emitters for lighting applications or solar TPV. In particular it opens up the route towards high efficiency TPV systems with emission matched to the photovoltaic cell.