Spectral control of the emissivity of surfaces is essential in applications such as solar thermal and thermophotovoltaic energy conversion in order to achieve the highest conversion efficiencies possible. We investigated the spectral performance of planar aperiodic metal-dielectric multilayer coatings for these applications. The response of the coatings was optimized for a target operational temperature using needle-optimization based on a transfer matrix approach. Excellent spectral selectivity was achieved over a wide angular range. These aperiodic metal-dielectric stacks have the potential to significantly increase the efficiency of thermophotovoltaic and solar thermal conversion systems. Optimal coatings for concentrated solar thermal conversion were modeled to have a thermal emissivity <7% at 720K while absorbing >94% of the incident light. In addition, optimized coatings for solar thermophotovoltaic applications were modeled to have thermal emissivity <16% at 1750K while absorbing >85% of the concentrated solar radiation.
©2009 Optical Society of America
The efficiency of concentrated solar thermal (CST) systems is thermodynamically limited by the Carnot efficiency and is thus strongly dependent on the maximum achievable temperature of the working fluid. Parabolic troughs have concentration ratios of ~80, and operate at temperatures up to 660K [1,2]. The working temperature is currently limited by the long-term thermal stability and the thermal shock-resistance of the available coatings. In addition, cracking of the synthetic oil working fluid also limits the temperature of operation. The hydrogen resulting from the cracking of the oil can permeate through the steel tube. This causes a loss in vacuum and can lead to an accelerated degradation of the absorber coating. Alternative working fluids such as molten salts are being pursued to allow for operation at higher temperatures. To achieve these higher temperatures, an increased spectral selectivity of the absorbing coating on the heat collection element (HCE) is required to prevent re-emission of the absorbed energy as infrared (IR) radiation, while ensuring that solar photons are absorbed.
In solar thermophotovoltaic (STPV) systems, incoming solar radiation is collected on an absorber surface. Due to higher concentration factors (>500), the operation temperature in STPV systems ranges from 1500K to 2000K. Controlling the parasitic thermal emission from the absorber surface is crucial to increasing the overall conversion efficiency [3,4].
Numerous selective coatings have been proposed for the above two applications, including intrinsic absorbers, semiconductor-metal tandems and cermets [5–8]. Recent advances in nanofabrication have led to the exploration of spectral selectivity in one-dimensional (1D) periodic multilayer stacks [9–15], 1D gratings [16–20], two-dimensional (2D) gratings [21–25], photonic cavities  and three-dimensional (3D) photonic crystals [27–29]. A common feature among all approaches is that the absorbing medium is nanostructured with feature sizes of the order of 100nm to 1μm in order to tune the response of the medium in the visible and near-infrared (NIR) spectral ranges.
2. Needle optimization of aperiodic metal-dielectrics multilayer stacks
Periodic multilayer stacks are used as dielectric mirrors and optical filters, in large part because they are easily modeled and fabricated. Another important benefit for high temperature applications is that 1D nanostructured materials (i.e. multilayers) are inherently more stable than 2D or 3D nanostructures. The melting temperatures of nanostructured materials are known to be lower than for the bulk materials . The 2D and 3D nanostructures have larger surface to volume ratios, making them more prone to surface diffusion, especially at sharp edges, such as in gratings. This could lead to a change in shape at temperatures well below the bulk melting temperature, which in turn would lead to a degradation of the spectral properties . Planar stacks are expected to be more stable than 2D and 3D nanostructured materials. Using periodic metal-dielectric multilayer stacks, good spectral selectivity for CST and STPV applications was predicted by Narayanaswamy, et al. [13,14]. The metals inside the stack act as absorbers and the dielectrics as optical spacers, creating interference effects that enhance absorption in a desired spectral range while preserving the reflectivity in the near-infrared spectral range. Here, we consider metal-dielectric stacks in which the periodicity constraint is removed. This significantly boosts the design space available, leading to better performance, at the cost of a more involved optimization procedure.
We previously considered aperiodic metal-dielectric stacks as thermal emitters for STPV applications . Here, we consider such aperiodic stacks as solar-selective absorbers for both CST and STPV applications. An ideal absorber coating behaves as a perfect absorber (α = 1) for wavelengths shorter than a cutoff wavelengthto optimize light absorption, and suppresses thermal emission (ε = 0) for wavelengths longer thanto minimize losses through infrared (IR) emission. In accordance to Kirchhoff’s law we assume that the directional spectral absorptivityis equal to the directional spectral emissivity for a system in thermal equilibrium. In order to determineand to evaluate the performance of solar selective coatings, a merit function needs to be defined. Since an ideal absorber has maximized absorptivity in the solar spectrum and has low emissivity for longer wavelengths, the following merit function, F, is proposed:
This merit function F was chosen because it is independent of geometry and operation. Geometry of the design determines the concentration factor, the uniformity and the angular distribution of the solar radiation on the absorber. Operation, such as pumping molten salts through the HCE at night time to avoid solidification, determines the relative importance of thermal emissivity versus solar absorptivity. Therefore a product of thermal emissivity and solar absorptivity is advised when no assumptions are made on geometry and operation. Solar absorptivity at normal incidence was chosen because for relatively low concentration factors, the incidence angle of the solar radiation on the absorber coating will be close to normal. This is in accordance to literature where absorptivity is typically measured and cited for normal incidence . However for thermal emissivity we consider emission over the full hemisphere, as this would lead to a more realistic estimate of the thermal emission losses. When optimizing an absorber for a specific design, a more appropriate merit function can be envisioned, taking both geometry and operation into account.
Based on the merit function introduced above, an ideal cutoff wavelength can be determined. Figure 1a shows the ideal cutoff wavelengthas a function of operational temperature. For the AM1.5 spectrum, the ideal cutoff wavelength is a stepwise function of operation temperature due to atmospheric absorption lines. This indicates that the ideal wavelength cutoff and thus the optimized coating are relatively insensitive to operation temperature within specific temperature ranges. Figure 1b shows the spectral absorptivity of an ideal absorber optimized at 720K or = 2.24 µm and compares it to the solar spectrum and the black body spectrum for T = 720K. This ideal absorber at 720K would absorb 98% of the incident solar radiation and have a spectrally and angularly integrated emissivity that is 3% of that of a black body. In this case, the spectral absorptivity of the ideal absorber was assumed to be identical for all angles of incidence. However, conceptually we can think of an absorber which would be absorbing only inside a limited acceptance cone of incident radiation, and would be a perfect reflector for all angles outside the cone. This would further reduce thermal emissions. Assumptions on concentrator design would be necessary to determine the angular acceptance cone. This was not done in this work to keep the general applicability.
The multilayer stacks are modeled using a standard transfer matrix method . The medium in each layer of the stack is assumed to be linear, isotropic, homogenous and non-magnetic with a spectrally dependent complex relative permittivity. The interface between two media is assumed to be optically flat. Using the Fresnel equations, a 2x2 transfer matrix can then be defined for all layers in the stack. The transfer matrix method offers a computationally efficient means of modeling the optical performance of multilayer stacks. The complex dielectric permittivity data at room-temperature for all media are obtained from the literature [34,35]. Changes in the dielectric constant at elevated temperatures are not considered here due to the lack of appropriate data. Because of their inherent spectral selectivity and stability at elevated temperatures, the optical properties of Molybdenum (Mo) and Tungsten (W) are used for the metal substrate and thin absorber layers. For the dielectric spacer layers, Magnesium Fluoride (MgF2) (n = 1.37 at λ = 1 µm), Titanium Dioxide (TiO2 - Rutile) (n = 2.75 at λ = 1 µm) and Magnesium Oxide (MgO) (n = 1.72 at λ = 1 µm) were used in the optical modeling.
The aperiodic stacks proposed in this work are optimized using the needle optimization method [36,37]. An exhaustive search is performed for the optimal location for insertion of a new layer and its optimal thickness. At each optimization cycle, a thin layer or needle of a selected set of materials is inserted into the stack and its spectral performance is evaluated. Based on merit function evaluations, the optimal needle material and position is then selected. After insertion of the needle, a Nelder-Mead simplex algorithm  is used for a local optimization of all layer thicknesses. Layers with a thicknesses <5nm are automatically removed from the design. This cycle is repeated until a desired spectral selectivity is obtained or a fixed number of layers have been inserted. As explained above, an absorber coating needs to be optimized for a specific operation temperature. In Sections 3 and 4, the absorbers are optimized for CST (~720K) and STPV (~1750K) applications, respectively.
3. Concentrated solar thermal applications
In CST systems, such as parabolic troughs, sunlight is concentrated by mirrors or Fresnel lenses onto a heat collection element (HCE). The HCE absorbs the incoming radiation and heats up the heat transfer fluid (HTF). The HTF is then driven through a heat exchanger to produce steam that can be used in an industrial process or can be converted into electrical energy in a turbine [1,2]. The latter process is thermodynamically limited by the Carnot efficiency and is thus strongly dependent on the maximal achievable temperature of the HTF. To achieve higher temperatures, an increased spectral selectivity of the absorbing coating on the heat collection element (HCE) is required. This prevents re-emission of the absorbed energy as IR radiation, while ensuring that a maximum of solar photons are absorbed. Next-generation solar troughs with molten salts are expected to operate above 660K and up to 820K . Therefore we have optimized the coatings for operation at 720K. A schematic of a HCE is shown in Fig. 2 .
We note that the needle optimization method can be used to optimize stacks for any given operation temperature, and the optimized stacks strongly depend on the targeted application. The absorber coatings are assumed to be deposited on a planar substrate made of Mo (Fig. 3 ) or W (Fig. 4 .). When determining the number of layers L in a stack, the metal substrate also counts as a layer, thus an uncoated stack has L = 1. In Figs. 3 and 4, we show two sets of four stacks optimized at = 720K. In each set, the stacks have respectively L = 5, 7, 9 and 11 layers, made of Mo, MgF2 and TiO2 (Fig. 3) or W, MgF2 and TiO2 (Fig. 4). The combination of MgF2 and TiO2 was selected for the dielectric spacer layers in order to achieve a high refractive index contrast ( = 1.38 at λ = 1 µm) and good high-temperature stability. The stacks all have layer thicknesses varying from 5 to 100 nm.
In Fig. 5 , the spectral hemispherical absorptivity is shown for the Mo- (Fig. 3) and the W-based stacks (Fig. 4), respectively. All these stacks were optimized for operation at 720K and thus for a cutoff wavelength = 2.24 µm. We observe a high hemispherical absorptivity (α> 90%) for wavelengths shorter than 2.24 µm, and a low absorptivity (α< 10%) for longer wavelengths. The spectral absorptivity of uncoated Mo and W are also shown for comparison. It is clear that the spectral selectivity of uncoated metals can be significantly increased by aperiodic metal-dielectric multilayer coatings. In order to compare the performance of the stacks, their merit function F is evaluated at 720K. In Fig. 6 , the merit function F defined by Eq. (1), is shown as a function of the number of layers L in the aperiodic stack. For both the Mo and W coatings, the spectral selectivity and thus the merit function F gradually increases with an increasing number of layers in the stack. This increase in spectral selectivity can also be observed in Fig. 5 as an increasing absorptivity below cutoff when the number of layers in the stacks increases. As the number of layers increases, the spectral response of the multilayer stacks more closely approximates that of the ideal absorber at 720K, also shown in Fig. 5. This result is expected from the theory of needle optimization . The merit function flattens when more than 11 layers are used to F = 0.87 and F = 0.90 for an optimized 21-layer Mo and W coating, respectively. At this point, further increases in absorption beloware compensated by an increased emissivity above. Better results are obtained for W coatings, because W is inherently more spectrally matched than Mo for operation at 720K.
In Fig. 7 , the angular dependence of the absorptivity averaged over the s and p polarization for 11-layer W and Mo coatings is shown. Since there is no azimuthal dependence for the planar stacks, only the polar angle dependence is shown. The optimized aperiodic multilayer stacks show spectrally selective, wide angular absorption, and would therefore be good candidates for solar thermal applications.
Table 1 and 2 list the obtained spectral selectivity of the Mo and W-based coatings, respectively. Both the absorbed solar fraction(see Eq. (2)) as well as the integrated hemispherical thermal emissivity(see Eq. (3)) is listed for all coatings shown in Fig. 5. The aperiodic multilayer coatings optimized at 720K are predicted to have better performance than commercially available cermet coatings, such as PTR70  (see Table 2). Especially the thermal emission from the aperiodic coatings are predicted to be significantly lower than for cermet coatings. Kennedy et al.  have previously modeled complex multilayer coatings with excellent solar absorptivity and relatively low thermal emissivity (NREL 6A). Both the Mo and the W 11-layer coatings with an overall merit F = 0.88 and F = 0.89 respectively are predicted to have spectral performance on par with NREL 6A.
4. Solar thermophotovoltaics
In solar thermophotovoltaic (STPV) systems, solar radiation is concentrated onto an absorber surface. The absorber surface should maximize the absorbed fraction of the solar irradiation, while keeping parasitic thermal emission from the surface as low as possible. In a typical STPV design, the absorber surface is in thermal contact with a selective emitter. The emitter surface emits photons in a preferably narrow spectral range tuned to the bandgap of a photovoltaic cell. The photovoltaic cell, typically with a narrow bandgap around 0.7eV, converts the emitted photons into electrical energy. A schematic of a STPV system is shown if Fig. 8 . STPV systems have theoretical conversion efficiencies that are significantly higher (up to 85.4% under full concentration) than that of traditional PV systems (up to 40.8% under full concentration)  because they make use of the full solar spectrum.
In order to optimize the performance of STPV systems, spectral tuning of both the emitter as well as the absorber surface is needed . We have previously reported on the former , and therefore focus on the latter here. Similar to the case of CST, we have optimized aperiodic multilayer stacks as a selective absorber for STPV applications. Since in STPV systems, concentration ratios >500 are used, typical operation temperatures for TPV systems vary from 1500K to 2000K. We focus on absorber coatings optimized at 1750K, equivalent to a cutoff wavelength of = 1.3µm. The ideal absorber with a cutoff at 1.3µm would absorb 88% of the normal incident solar radiation and have a spectrally and angularly integrated emissivity that is 12% of that of a black body. This would result in an optimal merit F = 0.78. In Fig. 9a and b , 4-layer periodic stacks optimized at = 1750K are shown, with Mo and W as the metallic absorber layers, respectively. MgO was chosen for optical modeling of the spacer layers because of its high thermal stability ( = 3125K).
In Fig. 10 , the spectral hemispherical absorptivity is shown for a 2 and 4-layer Mo and MgO coating (a) and a 2 and 4-layer W and MgO coating (b), optimized at 1750K. In addition, the spectral absorptivity of uncoated Mo and W are shown, as well as the spectral absorptivity of an ideal absorber at 1750K with a cutoff wavelength = 1.3µm. For the 4-layer stacks, illustrated in Fig. 9, significant higher spectral selectivity can be obtained compared to bare metal.
In Fig. 11 , the merit function F is shown as a function of the number of layers L in the aperiodic stack. As expected, the spectral selectivity gradually increases with increasing number of layers in the stack. This is mainly caused by the increase in absorptivity for wavelengths below = 1.3µm, as observed in Fig. 10. As the number of layers increases, the spectral absorptivity of the multilayer stack more closely approximates the ideal absorber for operation at 1750K. For > 6 layers, the merit function flattens to F = 0.72 and F = 0.69 for an optimized 6-layer Mo coating and W coating, respectively. In contrast to the CST case discussed above, better results are now obtained for the Mo-based coatings. This is explained by the lower spectral absorptivity of bare Mo for wavelengthsλ>1.3µm, as can be seen in Fig. 10a. In contrast, the absorption tail of the W coatings forλ>1.3µm is more pronounced in Fig. 10b.
In Fig. 12 the angular dependence of the absorptivity for the two 4-layer coatings is illustrated. Similar to the CST case, the optimized aperiodic absorbers exhibit good spectral selectivity over a wide angular range.
In Table 3 and 4 , the spectral selectivity data is summarized for the Mo and W coatings optimized for operation at 1750K. The Mo-MgO 4-layer coating has an absorbed solar fraction = 0.86, an integrated thermal emissivity = 0.16 and an overall merit F = 0.72. The solar fraction absorbed is slightly better for the W-MgO 4-layer coating, however the thermal emissivity at 1750K is significantly higher, leading to a lower overall merit of F = 0.69.
We investigated the spectral performance of planar aperiodic metal-dielectric multilayer coatings. These coatings were optimized using needle-optimization based upon a transfer matrix approach. This technique allows for the optimization of the absorber coating at a selected operational temperature, depending on the application. We defined a merit function to analyze and compare the spectral performance of the aperiodic stacks. We have shown excellent spectral selectivity over a wide angular range. Optimal coatings for CST applications are predicted to have thermal emissivity below 7% at 720K while absorbing >94% of the incident light. In addition, optimized coatings for STPV applications are predicted to have thermal emissivity below 16% at 1750K while absorbing >85% of the concentrated solar irradiation. These aperiodic metal-dielectric stacks may significantly increase the efficiency of both STPV and CST systems if they prove to be thermally stable.
The authors gratefully acknowledge the financial support from GCEP at Stanford University. N.P.S. acknowledges financial support as a Francqui Foundation Fellow from the Belgian American Educational Foundation.
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