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In this paper, an energy harvesting/re-radiating device is proposed to realize high efficiency energy conversion in the solar thermo-photovoltaic system. Such device consists of double-sided metamaterials which are assembled by a broadband absorber working in the major solar spectrum, and a back-by-back narrowband emitter working in the infrared band. It is theoretically proved that most of solar light (from 0.28 μm to 4 μm) can be collected, and then, converted to a sharp emission at the maximal response energy level (~0.4 eV) of photovoltaic cells in thermal equilibrium state. The impact of high temperature (as large as 966 K) and the parasitic radiation on the performance is discussed and compensated by geometric optimization.
© 2013 Optical Society of America
1. Introduction
The fact that every object with temperature above absolute zero radiates electromagnetic wave has been known for many years. Nowadays the desire to control radiated energy effectively has been focused on. According to Kirchhoff’s law, the emissivity of a material equals its absorbance at equilibrium [1,2]. Thus one can obtain the emissivity of the material by characterizing its corresponding absorption coefficients. In the last decade, metamaterial absorber has attracted much attention due to its potential applications in bolo-meters, photo-detectors and solar thermophotovoltaic (STPV) cells [1–16]. The realization of such applications lies in the capacity of the metamaterials to tune the resonant characteristics by changing the size and shape of the structure.
For applications such as STPV converters, it is essential to control the spectral properties to make sure the emitter has a sharp emission peak and corresponds to the band gap of solar cells [3,4]. In STPV system, efficiency of the energy conversion is dominated by the Shockly-Queisser limit [1], which is strongly connected with the mismatch between the energy of incident electromagnetic wave and the band gap of the STPV cells [17]. One effective method to increase STPV efficiency is to use selective emitter whose emissivity is nearly unity in a band corresponding to the STPV cell’s sensitive region and much lower outside it.
In 2011, Padilla et al. demonstrated the blackbody emission can be independently controlled in both magnitude and wavelength by properly designing the metallic structure [1]. Quite recently, Xiong et al. report a layer of continuous metal film coating on a three-dimensional microstructure to solve the problem of surface melting and reshaping caused by ultrafast heating [18].
The metamaterial selective emitters have some advantages over traditional emitters. For example, luminescent bands of rare earth oxides have been used for selective emission, but the realization of the perfect emissivity is limited by the lack of such materials [1]. Photonic crystals are considered as another candidate for selective emitters in energy conversion system. However the emitters usually do not have very high emittance because of their nonresonant nature [11]. With metamaterial selective emitter, the loss caused by non-adequate photon energies and radiative recombination can be avoided [3].
In the energy harvesting of STPV, broadband absorbers are also very important, which have been researched by various groups [19–28]. In particular, Sai et al., theoretically and experimentally demonstrated that subwavelength structure based on tungsten can be utilized for the control of thermal radiation in the visible and near infrared frequency bands [2]. In 2011, we used truncated spherical voids to realize a broadband absorber at visible and near-infrared frequencies [24]. However, the influence of high temperature on the absorption properties is rarely discussed.
In this paper, the broadband absorber is composed of a periodic array of tungsten-fused silica multilayered truncated pyramids [28] which exhibits polarization-independent and wide-angle absorption. The narrowband absorber consists of a tungsten cylinder cavity with a tungsten cylinder embedded. Such design can harvest solar energy (from 0.28 μm to 1.5 μm) efficiently through the broadband absorber with absorbance of 99% and emit the thermal radiation at about 3.1 μm with emittance of 99.75% according to the energy gap of the solar cells (the maximal response energy level is 0.4 eV [17]).
2. Principle and simulation
Figure 1 shows the principle geometry. This is a harvesting/re-radiating system by combining a broadband absorber with a perfect selective emitter in the opposite surface separated by a tungsten cylinder contained in a silica substrate. This design assures the conduction of the thermal energy and possesses little parasitic radiation emitted from the connecting component. Since the energy gap of the STPV cell is typically larger than 0.3 eV [17], the operating temperature of STPV systems should be at least 750 K according to Planck’s law. As the temperature is so high, selecting a kind of thermal resistive material to avoid material melting is very important [18].Characteristics of withstanding high temperature (as high as 3650 K) makes tungsten and fused silica suited candidates for this system. The absorber is heated through absorbing solar radiation and the radiation emitted by the emitter converts to electrical energy through a solar cell. The temperature at equilibrium state is set to be 966 K, corresponding to solar cell with energy gap of 0.4 eV. Thus the emission peak for narrowband absorber is 3.1 μm.
2.1 Design of the broadband absorber
For the broadband absorber, the absorption spectrum should cover the entire solar spectrum and vanish at 3.1 μm in order to suppress parasitic radiation. Although various broadband absorber based on tungsten has been designed in recent years [2,4,24,25], the influence of high temperature is rarely discussed. In fact, the refractive index as well as the absorption spectrum of tungsten changes obviously since the collision frequency of the electrons increases with temperature [29–31]. According to experiments data of the fused silica [32] and the tungsten at different temperatures (300K~1777 K) [29–31], the permittivity of the fused silica and the tungsten at 966 K was fitted by interpolation. This method remedied the errors caused by the estimations considering a linearly dependence of the collision frequency of the Drude model [9].
As shown in Figs. 2(a) and 2(b), the structure of the broadband absorber considered here consists of a periodic array of tungsten-fused silica multilayered truncated pyramids with the period l and height t. We performed simulations and optimizations of above structure by using commercial software Microwave Studios CST 2012. The absorbance can be obtained through the equation A = 1-R-Tr, where R stands for the reflectance and Tr stands for the transmission. For this structure, absorption is only relative to reflectance since the tungsten substrate is thick enough.
Fig. 2 Design of the broadband absorber. (a) Three dimensional model of the broadband absorber, (b) The illustration of the broadband absorber unit cell.
The absorption at 966 K is optimized with geometrical parameters l = 0.15 μm, tm = 0.02 μm, td = 0.03 μm and w = 0.044 μm. For comparison, the absorption of the absorber at 300 K is also depicted (the black dot curve). We also compared the absorption of traditional truncated pyramids with the multilayered structure. In the simulations, the shapes of the two structures kept the same. The absorption spectrum is depicted by blue dashed curve in Fig. 3. Evidently, the absorption as well as the parasitic radiation at 3.1 μm becomes larger. Figure 4(a) shows the electric field amplitude distributions on the central cross section of a tungsten-fused silica truncated pyramid unit cell at several wavelengths. Compared with truncated pyramids made of tungsten only, this structure absorbs electromagnetic wave at different parts of the truncated pyramids. The localized electric field moves towards the top as the wavelength decreases. Figure 4(b) shows electric field distributions of the tungsten truncated pyramid unit cell at several wavelengths. The electric field mostly exists on the surface of the structure and there is no obvious connection between field distributions and wavelength. As a result, a periodic array of tungsten-silica multilayered truncated pyramids has been chosen to absorb the solar radiation and suppress parasitic radiation.
Fig. 3 Absorption spectrums of the broadband absorber at different temperatures and transmissivity of the borofloat. The blue dashed curve describes the absorption of the absorber made of tungsten only. The black dot curve shows absorption of the broadband absorber at 300 K and the red dashed curve stands for absorption of the absorber at 966 K. The green solid curve describes transmission of the borofloat, which possesses characteristics of infrared suppression. The gray curve is solar irradiance spectrum.
Fig. 4 (a) Simulated electric amplitude along z direction (Ez) distributions on the central cross section of a tungsten-fused silica multilayered truncated pyramid unit cell at some wavelengths. (b) Simulated electric amplitude distributions on the central cross section of a tungsten truncated pyramid unit cell at some wavelengths.
Nevertheless, the absorption as well as the parasitic radiation at 3.1 μm become as large as 22%. In order to solve this problem, an infrared suppression filter can be used, which works as the borofloat with thickness 5 mm [33]. This borofloat was put in front of the broadband absorber to reflect the radiation at 3.1 μm. As depicted in Fig. 3, the transmissivity spectrums exceed 92% in the wavelengths ranging from 0.24 μm to 2.1 μm. If anti-reflection films are coated on the borofloat, the transmissivity will be higher. But at 3.1 μm, only 8% radiation from the broadband absorber at 966 K (parasitic radiation) can pass through the borofloat. It is obvious that the use of the borofloat can suppress the parasitic radiation effectively.
Due to the incident angle of the solar radiation changes with the time, it is necessary to make the broadband absorber possess wide angle operation range. Figures 5(a) and 5(b) show the absorption of TE and TM polarizations with different incident angles at 966K, respectively. For the case of the TE polarizations, a high absorption of 85% from 0.25 μm to 1.5 μm is still achieved when θ = 70 deg. For the TM polarizations, a little reduction of the absorption peak as the incident angle increases till 70 deg from 1 μm to 1.5 μm. Beyond 1 μm, the absorbance spectrums for 0-70 deg all exceed 90%. The results demonstrate the broadband absorber possesses wide angels operation range.
Fig. 5 (a) Absorbance of the broadband absorber as a function of incidence angle and frequency for TE polarizations (b) Absorbance of the broadband absorber as a function of incidence angle and frequency for TM polarizations.
2.2 Design of the selective emitter
For the narrowband absorber/emitter, we set the emission peak at about 3.1 μm corresponding to the maximum response energy level 0.4 eV of solar cell.
Typically, narrowband absorber/emitter can be realized by a metal-insulator-metal triple layered metamaterial [7, 34,35]. As illustrated in Fig. 6(a), the top layer is a tungsten circle plate and is separated from the bottom tungsten substrate by a fused silica interlayer. The optimized absorption spectrum is plotted as the black dot curve as shown in Fig. 6(g). The corresponding electromagnetic fields distribution is shown in Fig. 6(e), which is characterized by the anti-parallel currents excited on the two separated tungsten layers.
Fig. 6 Design of the selective emitter. (a) Perspective view of the traditional trilayer structure unit cell. (b) Perspective view of the flat selective emitter unit cell. (c) Front view of the emitter unit cell. (d) Top view of the emitter unit cell. (e) The electric field distribution of the traditional trilayer structure, (f) The electric field distribution of the flat selective structure. (g) The emittance of the traditional trilayer structure and the flat selective structure at different temperatures.
Unfortunately, the trilayer structure cannot form a sharp absorption peak since the electron scattering rate of tungsten at 966 K is quite large. In order to solve this problem, the top layer is flattened to decrease surface scattering. Meanwhile, the resonant cavity is preserved as shown in Figs. 6(b)-6(d). The geometrical parameters are optimized for T = 966 K: h = 0.9 μm, hd = 0.72 μm, hm = 0.27 μm, p = 1.17 μm, rs = 0.495 μm, ri = 0.225 μm. Figure 6(f) describes the distribution of the electric fields, which implies the local resonance is almost unchanged compared to traditional trilayer structure. Since the electron scattering at the upper surface becomes much weaker, the absorption bandwidth becomes narrower as indicated in Fig. 6(g).
Figures 7(a) and 7(b) show the emittance of the selective emitter plotted for θ = 0-70 deg with φ fixed at 0 deg for TE polarizations and TM polarizations, respectively. The emittance for varying φ (0-180 deg) with θ fixed at 20 deg is described in Figs. 7(c) and 7(d). The wide angle operation characteristics can be ascribed to the localized electromagnetic resonance excited in the cavity as shown in Fig. 6(f).
Fig. 7 (a) and (b) Simulated emissivity for various polar angles of incidence for TE polarizations and TM polarizations, respectively. (c) and (d) Simulated emissivity for θ = 20 deg and various azimuthal angles for TE polarizations and TM polarizations, respectively.
Since the sensitivity of the emission peak to fabrication tolerances is very important to ensure the high conversion efficiency, we performed several simulations to compare the effects of fabrication errors. For example, rs, ri, hd and hm have been varied by ± 50 nm individually. The different results caused by the variation have been compared as shown in Figs. 8(a)-8(d), respectively. Also, the tungsten cylinder embedded in the fused silica cannot be assumed in the center. Interestingly, this eccentricity has little influence on the absorption property as indicated in Fig. 8(e).
Fig. 8 Emission spectrums for different fabrication tolerances. (a) (b) Emission spectrums for different radius of the fused silica rs and the tungsten cylinder ri inside, respectively. (c) (d) Emission spectrums for different thickness of the fused silica hd and the tungsten cylinder hm, respectively. (e) Emission spectrums for Δc = 0 and 50 nm.
For all kinds of fabrication errors considered above, a good emission can be achieved. Longer radius of fused silica leads to a small increase (less than 0.01 μm) in the center wavelength. For thicker fused silica and tungsten cylinder, the emission spectrum keeps almost the same. If the tungsten cylinder has a Δc = 50 nm deviation from the center, the emission spectrum also keeps unchanged. Changes in the radius of tungsten cylinder cause the strongest change in the emission spectrum, shifting the center wavelength of the peak by about ± 0.4 μm. Thus it is very important to control the size of the tungsten cylinders embedded precisely in the fabrication process.
2.3 Discussion of thermal radiation
In this STPV system, the thermal equilibrium temperature is set as 966 K, where the absorption of the system equals the emission. As Fig. 6(g) described, the emitter has an emission peak at 3.1 μm with emittance of 99.75%. Figure 3 shows that the absorbance of the broadband absorber at 3.1 μm is about 22%. The use of the borofloat makes the transmission at 3.1 μm decrease to 8%. That means the broadband absorber only emits a very little part of energy (1.76%) through parasitic radiation.
It is assumed that the solar constant is 1366 W/m2 and the atmospheric transmissivity is 75% under normal condition. Since the average absorption of the broadband absorber from 0.28 μm to 1.5 μm where the solar spectrum mainly distribute is about 99% and the transmissivity of the borofloat is about 92%. The power of the incoming solar radiation collected on the broadband absorber surface is 1366*75%*99%*92% = 933.1 W/m2. For the selective emitter, Planck’s Radiation Law gives the spectral radiant emittance of the blackbody as a function of wavelength and temperature:
where, c1 is the first radiation constant (3.7415*104 W*μm4/cm2),The radiant emittance is obtained through integrating Mbb (λ, T) over the wavelength band. For the 2 μm-10 μm band, the formula is shown below:
The final spectral radiation is calculated as:where E(λ, T) is the emissivity of the selective emitter. The product of emissivity and the blackbody radiation has been plotted as the blue solid curve in Fig. 9 and the above integration has been calculated through MATLAB. The energy emitted by the selective emitter is 16278 W/m2. In order to realize the equilibrium, the sizes should be satisfied with the equation below: 16278*An + 933.1*1.76%*Ab = 933.1*Ab, namely Ab = 17.7*An. where, An and Ab stand for the area of the selective emitter and the area of the broadband absorber, respectively.Fig. 9 Blackbody radiation (black dashed curve) and radiative power of the selective emitter (blue solid curve). If the temperature is adjusted, the maximum of the blackbody spectra and the emission peak coincide using Wien Displacement Law (T = 966 K).
3. Conclusions
In summary, we have designed an efficiency energy conversion system by combining a broadband and narrowband metamaterial absorbers. The broadband absorber is made up of a periodic array of multilayered truncated pyramids. The absorbance is about 99% from 0.28 μm to 1.5 μm for both TE and TM polarizations for both room temperature and high temperature (966 K). Meanwhile, a narrowband absorber works as a selective emitter with emission peak at 3.1 μm and emissivity of 99.75% at 966 K. The effect of deviations in the size caused by fabrication is also investigated. From above consideration, the high conversion efficiency can be assured and this structure can be realized with planar fabrication technology. We have also calculated the absorption and the radiation from room temperature to 966 K to explain the whole thermal transfer process. We believe the conversion of broadband energy to narrowband emission through the double-sided metamaterial is promising in high-temperature energy conversion applications.
Acknowledgments
This work was supported by 973 Program of China (No. 2013CBA01700), National Natural Science Funds (No. 61138002).
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