Abstract

We theoretically demonstrate a novel, efficient and cost effective thermal emitter using a Mie-resonance metamaterial for thermophotovoltaic (TPV) applications. We propose for the first time the design of a thermal emitter which is based on nanoparticle-embedded thin film. The emitter consists of a thin film of SiO2 on the top of tungsten layer deposited on a substrate. The thin film is embedded with tungsten nanoparticles which alter the refractive index of the film. This gives rise to desired emissive properties in the wavelength range of 0.4 μm to 2 μm suitable for GaSb and InGaAs based photovoltaics. Effective dielectric properties are calculated using Maxwell-Garnett-Mie theory. Our calculations indicate this would significantly improve the efficiency of TPV cells. We introduce a new parameter to gauge the efficacy of thermal emitters and use it to compare different designs.

© 2016 Optical Society of America

1. Introduction

Thermophotovoltaics (TPV) is a promising technology for heat recovery and an attractive alternative for existing electricity generation technologies [1–3]. A TPV system consists of a thermal emitter which operates at high temperatures (∼1500 K) [4, 5] and a photovoltaic cell and can directly convert thermal energy into electricity [6]. In principle, TPV systems can achieve an efficiency of Carnot engine for monochromatic radiation [7] and such TPV systems with efficiencies approaching the limit have been discussed in the literature [8–10]. In reality, efficiencies of TPV systems suffer from the mismatch between emission spectrum of emitter and absorption spectrum of PV cell [11]. External quantum efficiency (EQE) of a PV cell is defined as the fraction of incident photons converted into electron-hole pairs [12] and is indicative of the amount of current generated for a given incident photon wavelength. A PV cell has non-zero EQE above the band-gap, i.e. a PV cell can generate electric current only when incident photons have higher energies than the bandgap of semiconductor material [13]. Moreover, absorption of incident photons having wavelength longer than bandgap wavelength is undesirable as it causes thermal leakage and reduces the efficiency [14]. So, in order to achieve high efficiency of a TPV system, goal is to develop a thermal emitter with high emissivity in the region of high external quantum efficiency (EQE) of PV cell and low emissivity in rest of the spectrum. Several studies have focused on using photonics crystals [15, 16], plasmonic metamaterials [17], single micro/nano sized spheres [18], doped materials [19, 20], surface gratings in order to obtain spectrally selective emission [21]. 1-D, 2-D and 3-D photonic crystals and surface gratings have also been developed [22–24]. Numerous works involve use of intermediate filters which reflect the low energy photons back to emitter [25–28].

Metamaterials is another class of nanomaterials/nanostructures which has been the topic of many articles focused on selective thermal emitters. Liu et al [29] have demonstrated a narrow-band mid infrared thermal emitter based on a metamaterial. Plasmonic metamaterials have also been explored for solar TPV applications as in [30, 31]. Woolf et al [32] have presented and also experimentally demonstrated a heterogeneous metasurface for selective emitters and predicted 22% conversion efficiency for InGaAs based TPV system at the operating temperature of 1300 K for the emitter. Use of refractory materials such as tungsten is common in the literature. These studies and several others [33–38], although not specifically focused on TPV applications, involve complex surface patterns which are difficult to fabricate. In this paper, we propose for the first time the use of Mie-metamaterial thin films, i.e., nanoparticle-embedded thin films to design a novel, efficient and low cost thermal emitter suitable for GaSb and InGaAs based TPVs. Mie-metamaterials or Mie-resonance metamaterials are artificial materials which utilize Mie resonances of inclusions for the shaping of emission spectra. Several theoretical studies of nanoparticle inclusions into host materials have been performed [39–41]. However, literature pertaining to optical and emissive properties of nanoparticle embedded thin films is rare. Authors recently published a broad study on the role of polar and metallic nanoparticles on far-field and near-field thermal radiation from thin films by considering different cases of hypothetical Mie-metamaterial thin films [42]. In present study we exploit the idea by using thin films of SiO2 embedded with tungsten (W) nanoparticles to design a novel thermal emitter specifically for GaSb and InGaAs based TPVs.

Schematic of a typical TPV system is shown in Fig. 1(a). Thermal radiation from the heat source is absorbed by the blackbody absorber. This heat is emitted by the selective thermal emitter only in the desired band of wavelengths in which the external quantum efficiency of the PV cell is high. Figure 1(b) depicts an example of 1-D grating structure that could be used to realize wavelength selective radiative properties of thermal emitter. It comprises gratings of SiC and W of period Λ = 50 nm and filling ratio ϕ = 0.55. Grating layer is 50 nm thick. It’s emissive properties along with the emittance of 2-D grating structure considered in Zhao et al [13] will be compared to the Mie-metamaterial based thermal emitter of present study. The prime focus of this paper is the proposed design of thermal emitter shown in Fig. 1(c). It consists of a 0.4 μm thick film of SiO2 on the top of 1 μm thick film of tungsten deposited on a substrate. Thickness of the layer of W makes sure that all the radiation from the substrate is reflected back and the radiative properties of the emitter are dictated by the top two layers alone. The SiO2 film is doped with W nanoparticles of 20 nm radius. Inclusion of W nanoparticles changes the optical properties of the film and results in desired emission spectrum. Volume fraction of W nanoparticles was adjusted to 30% to achieve the best result. While the mixture of SiO2 and W gives rise to spectrally selective emission for the PV, the choice of materials also makes sure that it will withstand high temperatures.

 figure: Fig. 1

Fig. 1 (a) Schematic of a typical TPV system with a thermal emitter/absorber and a PV cell. (b) An example of a thermal emitter based on 1-D grating structure of SiC and W on the top of W base. The grating thickness and period Λ=50 nm, filling ratio ϕ=0.55. (c) A proposed design of thermal emitter consists of 0.4 μm thick SiO2 layer on the top of 1 μm thick W layer deposited on the substrate. SiO2 layer is doped with W nanoparticles of 20 nm radius with a volume fraction of 30%.

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2. Theoretical fundamentals

The hemispherical emissivity of the thermal emitter can be expressed as [42]

e(ω)=c2ω20ω/cdkρkρμ=s,p(1|R˜h(μ)|2|T˜h(μ)|2)
where c is the speed of light in vacuum, ω is the angular frequency and kρ is the magnitude of inplane wave vector. R˜h(μ) and T˜h(μ) are the polarization dependent effective reflection and transmission coefficients which can be calculated using the recursive relations of Fresnel coefficients of each interface [43]. The dielectric functions can be related to real (n) and imaginary (κ) parts of refractive index as ε=n+jκ. Dielectric functions of the materials (SiO2, W and SiC) considered in this paper are taken from literature [44–46]. Having very low temperature coeffcients, room temperature values of dielectric function are used for SiO2 and SiC [47, 48]. Dielectric properties of tungsten were also assumed to be unchaged as the operating temeprature is much less than the melting point. The top layer of the thermal emitter considered in our calculations is either 1-D grating structure or nanoparticle embedded thin-film. In both cases, it can be approximated as a homogeneous layer of an effective dielectric function.

If the period of grating (Λ) is much smaller than the wavelength of interest such as the case considered here, dielectric function of the grating layer can be approximated using effective medium theory [49]. We use second order effective medium approximation to calculate the effective dielectric function which is given by [49]

εTE,2=εTE,0[1+π23(Λλ)2ϕ2(1ϕ)2(εAεB)2εTE,0]
εTM,2=εTM,0[1+π23(Λλ)2ϕ2(1ϕ)2(εAεB)2εTE,0(εTM,0εAεB)2]
where εA and εB are the dielectric functions of the two materials in surface gratings, Λ is the period and ϕ is the filling ratio. The expressions for zeroth order effective dielectric functions εTE,0 and εTM,0 are given by
εTE,0=ϕεA+(1ϕ)εB
εTM,0=(ϕεA+1ϕεB)1

For calculating the effective dielectric function the Mie-metamaterial, we use Clausius-Mossotti equation. [50, 51].

εeff=εm(r3+2αrfr3αrf)
where εm is the dielectric function of the matrix, αr is the electric dipole polarizability, r and f are the radius and volume fraction of nanoparticles respectively. To consider the size effects of nanoparticle inclusions, we use the Maxwell Garnett formula which employs the expression for electric dipole polarizability using Mie theory [52], αr=3jc3a1,r/2ω3εm3/2, where a1,r is the first electric Mie coefficient given by
a1,r=εnpψ1(xnp)ψ1(xm)εmψ1(xm)ψ1(xnp)εnpψ1(xnp)ξ1(xm)εmξ1(xm)ψ1(xnp)
where ψ1 and ξ1 are Riccati-Bessel functions of the first order given by ψ1(x) = xj1(x) and ξ1(x)=xh1(1)(x) where j1 and h1(1) are first order spherical Bessel functions and spherical Hankel functions of the first kind, respectively. Here, ‘′’ indicates the first derivative. xm=ωrεm/c and xnp=ωrεnp/c are the size parameters of the matrix and the nanoparticles, respectively; εnp being the dielectric function of nanoparticles.

It is worth mentioning that Maxwell-Garnett-Mie theory is applicable when average distance between inclusions is much smaller than the wavelength of interest [53]. This criteria is satisfied in the calculated presented. Also noteworthy is the fact that nanoparticle diameter (40 nm) is much smaller than the thickness of the thin film (0.4 μm) considered. Thus, effective medium theory holds true for the calculations presented in this study.

3. Results

Figure 2(a) illustrates the effect of W nanoparticle inclusions on the refractive indices of SiO2 host. Pure SiO2 has a near constant refractive index (n) ∼ 1.55 and a negligible extinction coefficient (κ). Nano-sized W spheres (2r = 40 nm) much smaller than the operating wavelength are introduced into the SiO2 matrix. This brings about an increased refractive index and extinction coefficient. Although real and imaginary parts of the refractive index have different implications, it is imperative that real and imaginary parts of the mixture depend on both the indices of its constituents. It is essential to point out that change in refractive indices of the mixture is a result of addition of new material as well as the Mie-scattering of electromagnetic waves by spherical nanoparticles. Consequently, refractive indices of the mixture depend on volume fraction and particle size. The resulting changes in the emission spectrum are displayed in Fig. 3(a). Owing to its metallic nature, W is moderately absorptive only at lower wavelengths and highly reflective beyond 2 μm. Although SiO2 bulk has a high absorptivity/emissivity, 0.4 μm thick layer of SiO2 is practically transparent for the entire spectrum. Therefore, both the bare tungsten and the combination of SiO2 layer on tungsten base have low emissivity in the range of 0.4 to 2 μm and negligible emissivity for the majority of spectrum beyond 2 μm. Upon inclusion of W nanoparticles, emissivity is enhanced for spectral region of interest. The geometric parameters available for spectral shaping of the emissivity are thickness of SiO2 film, volume fraction of W nanoparticles and particle radius. If size distribution of nanoparticles is available, it can be incorporated into the extended Maxwell-Garnett formula as in [55]. For the present study, the particle radius is fixed to 20 nm. Figure 3(a) also highlights the effect of volume fraction of W nanoparticles on emission spectra. An increase in volume fraction from 10% to 30% results in higher emissivity and the broadening of the emission spectrum. The final proposed configuration has the SiO2 film thickness of 0.4 μm and 30% volume fraction of W nanoparticles. Note that calculated emissivity of W (black curve in Fig. 3(a)) matches well with high-temperature (1600 K) emissivivty reported in [56]. Also refractive index of SiO2 has a low temeprature coefficient [57]. Therefore these materials are well suited for high temeprature applications.

 figure: Fig. 2

Fig. 2 Refractive indices of W, SiO2 and SiO2 doped with W nanoparticles of volume fraction 30% and 20 nm radius. (a) Real part of refractive index. (b) Imaginary part of refractive index. Imaginary part of refractive index for SiO2 is negligible for the range of wavelengths considered here [46].

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 figure: Fig. 3

Fig. 3 Emission spectra of different configurations. (a) Hemispherical emissivity of W, SiO2 film of 0.4 μm deposited on W base and SiO2 doped with W nanoparticles of 20 nm radius and different volume fractions. (b) Emission spectrum (left y-axis) of the final design is compared to the result presented by Zhao et al [13] and 1-D surface grating discussed in this study. The EQE plots (right y-axis) of PV cells are shown for comparison [54].

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The thermal emitter presented here is suitable for a typical TPV system consisting GaSb or InGaAs based photovoltaics. The EQE of the two PV cells is shown in Fig. 3(b). Both the GaSb and InGaAs based PV cells efficiently generate electricity if the wavelength of incident photons falls in the range of 0.4 μm to 2 μm. Configuration of the proposed design i.e. thickness of the SiO2 layer, radius and volume fraction of W nanoparticles was chosen to achieve best match between the emission spectrum and the EQE curve of the PV cells. Our design exhibits high emissivity (> 0.8) in the wavelength range 0.4 μm to 1.7 μm and very low emissivity (< 0.2) beyond 2 μm. The close match between the emission spectrum of the emitter and EQE curve PV cell ensures high conversion efficiency and minimizes the thermal leakage of long wavelength photons. For comparison, the emission spectrum of 1-D structure (Fig. 1(b)) and that of a 2-D grating structure discussed in Zhao et al [13] is also shown. It is apparent that the emission spectrum of the design presented here is comparable to that of 1-D structure and the 2-D structure presented in [13] for wavelengths below 1.7 μm. Although a substantial part of blackbody radiation at high temepraturs (1000 to 1500 K) exists between 2 to 6 μm, very little energy is emitted by proposed emitter in this region as emissivty is very low. Moreover, the proposed design has lower emissivity beyond 1.7 μm when compared to the 2-D design. This indicates much lower losses due to thermal leakage. It is worth mentioning that, while choice of materials in the present study is same as that used in [13], fabrication of thermal emitter based on tungsten embedded SiO2 thin film is relatively simple. This guarantees low cost of large scale fabrication of such emitters. As refractory materials such as platinum and aluminum oxide (Al2O3) have been tested before for thermal emitter [32], they can also be explored for this new class of emitters.

4. Discussion

While the match between emission spectrum of the emitter and the EQE curve of the PV cell can be a good indicator of TPV system’s performance, the emitter temperature has an equally important role as it decides the dominant wavelength and can dictate the overall efficiency. Therefore, discussion of conversion efficiency cannot be left out in this work. Ideal emitter has an e(ω) = 1 above bandgap and e(ω) = 0 below the bandgap. The conversion efficiency of the TPV system could be defined as the ratio of the power output of the PV cell to the power incident on the PV cell given by

η=PoutPrad
where Prad is the power radiated by the emitter [58]
Prad=0ω24π2c2ω(eω/kBT1)e(ω)dω
The power output, Pout is proportional to the number density of the photons above bandgap and the EQE of PV cell defined as [32]
Pout=qVOCFF0n¯(ω,T)e(ω)ηEQE(ω)dω
where q, VOC, FF and ηEQE are electronic charge, open circuit voltage, fill factor and EQE of PV cell, respectively. (ω, T) is the number density of incident photons
n¯(ω,T)=ω24π2c21(eω/kBT1)
Now consider a hypothetical TPV system with a thermal emitter which has no radiation below the bandgap but covers only a fraction of spectrum above bandgap with e(ω) = 1. Such a system would have lower power output than the one with ideal thermal emitter despite having maximum efficiency with no losses. It is apparent that conversion efficiency of the TPV system alone cannot be regarded as a criterion to gauge the efficacy of a thermal emitter. Therefore we propose a new parameter to calculate the effectiveness of the thermal emitter for a given PV cell and emitter temperature. The parameter termed as effectiveness index is defined as the ratio of the efficiency of the TPV system to the efficiency of the TPV system with ideal thermal emitter at the same temperature and for the given PV cell, βemitter = ηRealIdeal, where subscripts Real and Ideal refer to TPV systems with thermal emitter of consideration and an idealized thermal emitter at the same temperature. So,
βemitter=(PoutPrad)Real×(PradPout)Ideal
While this norm, βemitter doesn’t elaborate anything about the efficiency of the TPV system as a whole, it is a good measure to compare the effectiveness of different thermal emitters for a given PV cell and emitter temperature. Note that if βemitter > 1, it implies that the TPV system is efficient but only a part of the spectrum of the EQE is being utilized and the output power is less than what an ideal emitter would produce. Therefore, the goal is to get βemitter close to 1 but not exceed 1. It is assumed that the emitter has a much higher temperature than the PV cell, which has a negligible reflection coefficient. While calculating effectiveness indices for different thermal emitters and a given PV cell, it is assumed that PV cell temeprature and its EQE do not vary.

We calculate the effectiveness of the thermal emitter for GaSb PV cell and at emitter temperature 1500 K for the designs presented in Fig. 3(b). Our proposed design has an effectiveness index βemitter = 0.72 while its value for the 1-D design and the one considered in [13] is 0.78 and 0.65 respectively. It is important to note that despite having lower emissivity, the 1-D design has higher effectiveness index because it has lower emissivity beyond 2 μm, thermal wavelength at 1500 K being 1.93 μm. Structure discussed in [13] shows lower effectiveness index as it has higher emissivity below the bandgap. Effectiveness index of the aforementioned designs at 1300 K is βemitter = 0.6, 0.68 and 0.58 respectively. As the thermal wavelength shifts to 2.3 μm, losses increase which clearly demonstrates the role of temperature and the dominant thermal wavelength governing the efficiency.

Thus, we have presented for the first time a thermal emitter which consists of Miemetamaterial based thin film. Dielectric properties of SiO2 thin films are influenced by the inclusions of W nanoparticles. This manifests into the spectral shaping of thermal radiation from the surface of the emitter. The best possible emission spectrum is realized by adjusting the thickness of the film, radius and volume fraction of nanoparticles. The emission spectrum of the design matches well with the EQE of GaSb and InGaAs based PV cells that indicates high conversion efficiency. Emission spectrum of the present design is on par with previously proposed design based on 2-D grating structures. Very low emission for λ > 2 μm minimizes the leakage of long wavelength photons below the TPV band-gap. Materials chosen for the design (SiO2 and W) are suitable from fabrication perspective and can withstand high operating temperatures of the TPV system. Moreover, fabrication of the proposed nanostructure is relatively simple as compared to surface gratings making it cost effective. Nanoparticle radius, volume fraction and film thickness offer a good tunability for tailoring of emission spectrum. We also explored a new parameter named as effectiveness index that can be used as a good indicator to compare efficacy of thermal emitter for a given PV cell and operating temperature. This study gives valuable insights into design opportunities for selective thermal emitters that can be applied for TPV systems.

Acknowledgments

This work is partially funded by the Rhode Island STAC Research Grant and the Start-up Grant through the College of Engineering at the University of Rhode Island.

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48. C. Xu, S. Wang, G. Wang, J. Liang, S. Wang, L. Bai, J. Yang, and X. Chen, “Temperature dependence of refractive indices for 4h-and 6h-sic,” Journal of Applied Physics 115, 113501 (2014). [CrossRef]  

49. Y.-B. Chen, Z. Zhang, and P. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129, 79–90 (2007). [CrossRef]  

50. V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. G. de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008). [CrossRef]   [PubMed]  

51. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, vol. 25 (SpringerBerlin, 1995). [CrossRef]  

52. W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39, 9852 (1989). [CrossRef]  

53. M. S. Wheeler, “A scattering-based approach to the design, analysis, and experimental verification of magnetic metamaterials made from dielectrics,” Ph.D. thesis (2010).

54. O. V. Sulima, A. W. Bett, and P. S. Dutta, “Proc. 5th TPV Conf., Rome, Italy, September 2002 (AIP, New York, 1999),” p. p 402.

55. Y. Battie, A. Resano-Garcia, N. Chaoui, Y. Zhang, and A. E. Naciri, “Extended maxwell-garnett-mie formulation applied to size dispersion of metallic nanoparticles embedded in host liquid matrix,” J. Chem. Phys. 140, 044705 (2014). [CrossRef]  

56. S. Roberts, “Optical properties of nickel and tungsten and their interpretation according to drude’s formula,” Phys. Rev. 114, 104 (1959). [CrossRef]  

57. P. Timans, “The thermal radiative properties of semiconductors,” in “Advances in Rapid Thermal and Integrated Processing,” (Springer, 1996), pp. 35–101. [CrossRef]  

58. M. Planck, The Theory of Heat Radiation (Dover Publications, 2011).

References

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  29. X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107, 045901 (2011).
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  48. C. Xu, S. Wang, G. Wang, J. Liang, S. Wang, L. Bai, J. Yang, and X. Chen, “Temperature dependence of refractive indices for 4h-and 6h-sic,” Journal of Applied Physics 115, 113501 (2014).
    [Crossref]
  49. Y.-B. Chen, Z. Zhang, and P. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129, 79–90 (2007).
    [Crossref]
  50. V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. G. de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
    [Crossref] [PubMed]
  51. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters, vol. 25 (SpringerBerlin, 1995).
    [Crossref]
  52. W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39, 9852 (1989).
    [Crossref]
  53. M. S. Wheeler, “A scattering-based approach to the design, analysis, and experimental verification of magnetic metamaterials made from dielectrics,” Ph.D. thesis (2010).
  54. M. G. M., Y. B. B., O. V. Sulima, A. W. Bett, and P. S. Dutta, “Proc. 5th TPV Conf., Rome, Italy, September 2002 (AIP, New York, 1999),” p. p 402.
  55. Y. Battie, A. Resano-Garcia, N. Chaoui, Y. Zhang, and A. E. Naciri, “Extended maxwell-garnett-mie formulation applied to size dispersion of metallic nanoparticles embedded in host liquid matrix,” J. Chem. Phys. 140, 044705 (2014).
    [Crossref]
  56. S. Roberts, “Optical properties of nickel and tungsten and their interpretation according to drude’s formula,” Phys. Rev. 114, 104 (1959).
    [Crossref]
  57. P. Timans, “The thermal radiative properties of semiconductors,” in “Advances in Rapid Thermal and Integrated Processing,” (Springer, 1996), pp. 35–101.
    [Crossref]
  58. M. Planck, The Theory of Heat Radiation (Dover Publications, 2011).

2015 (3)

J. K. Tong, W.-C. Hsu, Y. Huang, S. V. Boriskina, and G. Chen, “Thin-film’thermal well’emitters and absorbers for high-efficiency thermophotovoltaics,” arXiv preprint arXiv:1502.02061 (2015).

Y. Zheng and A. Ghanekar, “Radiative energy and momentum transfer for various spherical shapes: a single sphere, a bubble, a spherical shell and a coated sphere,” J. Appl. Phys. 117, 064314 (2015).
[Crossref]

A. Ghanekar, L. Lin, J. Su, H. Sun, and Y. Zheng, “Role of nanoparticles in wavelength selectivity of multilayered structures in the far-field and near-field regimes,” Opt. Express 23, A1129–A1139 (2015).
[Crossref] [PubMed]

2014 (5)

C. Xu, S. Wang, G. Wang, J. Liang, S. Wang, L. Bai, J. Yang, and X. Chen, “Temperature dependence of refractive indices for 4h-and 6h-sic,” Journal of Applied Physics 115, 113501 (2014).
[Crossref]

Y. Battie, A. Resano-Garcia, N. Chaoui, Y. Zhang, and A. E. Naciri, “Extended maxwell-garnett-mie formulation applied to size dispersion of metallic nanoparticles embedded in host liquid matrix,” J. Chem. Phys. 140, 044705 (2014).
[Crossref]

Y. Nam, Y. X. Yeng, A. Lenert, P. Bermel, I. Celanovic, M. Soljačić, and E. N. Wang, “Solar thermophotovoltaic energy conversion systems with two-dimensional tantalum photonic crystal absorbers and emitters,” Solar Sol. Energy Mater. Sol. Cells 122, 287–296 (2014).
[Crossref]

D. Woolf, J. Hensley, J. Cederberg, D. Bethke, A. Grine, and E. Shaner, “Heterogeneous metasurface for high temperature selective emission,” Appl. Phys. Lett. 105, 081110 (2014).
[Crossref]

C. Wu, N. Arju, G. Kelp, J. A. Fan, J. Dominguez, E. Gonzales, E. Tutuc, I. Brener, and G. Shvets, “Spectrally selective chiral silicon metasurfaces based on infrared fano resonances,” Nat. Commun. 5, 3892 (2014).
[Crossref] [PubMed]

2013 (7)

H. Wang and L. Wang, “Perfect selective metamaterial solar absorbers,” Opt. Express 21, A1078–A1093 (2013).
[Crossref]

C. Argyropoulos, K. Q. Le, N. Mattiucci, G. DAguanno, and A. Alu, “Broadband absorbers and selective emitters based on plasmonic brewster metasurfaces,” Phys. Rev. B 87, 205112 (2013).
[Crossref]

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, and G. S. Girolami, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[Crossref] [PubMed]

W. R. Chan, P. Bermel, R. C. Pilawa-Podgurski, C. H. Marton, K. F. Jensen, J. J. Senkevich, J. D. Joannopoulos, M. Soljačić, and I. Celanovic, “Toward high-energy-density, high-efficiency, and moderate-temperature chip-scale thermophotovoltaics,” Proc. Natl. Acad. Sci. U. S. A. 110, 5309–5314 (2013).
[Crossref] [PubMed]

B. Zhao, L. Wang, Y. Shuai, and Z. M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transfer 67, 637–645 (2013).
[Crossref]

S. Molesky, C. J. Dewalt, and Z. Jacob, “High temperature epsilon-near-zero and epsilon-near-pole metamaterial emitters for thermophotovoltaics,” Opt. Express 21, A96–A110 (2013).
[Crossref] [PubMed]

L. Gao, F. Lemarchand, and M. Lequime, “Refractive index determination of sio2 layer in the uv/vis/nir range: spectrophotometric reverse engineering on single and bi-layer designs,” Journal of the European Optical Society-Rapid publications 8 (2013).
[Crossref]

2012 (3)

L. Wang and Z. Zhang, “Wavelength-selective and diffuse emitter enhanced by magnetic polaritons for thermophotovoltaics,” Appl. Phys. Lett. 100, 063902 (2012).
[Crossref]

C.-W. Cheng, M. N. Abbas, C.-W. Chiu, K.-T. Lai, M.-H. Shih, and Y.-C. Chang, “Wide-angle polarization independent infrared broadband absorbers based on metallic multi-sized disk arrays,” Opt. Express 20, 10376–10381 (2012).
[Crossref] [PubMed]

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).
[Crossref]

2011 (3)

X. Liu, T. Tyler, T. Starr, A. F. Starr, N. M. Jokerst, and W. J. Padilla, “Taming the blackbody with infrared metamaterials as selective thermal emitters,” Phys. Rev. Lett. 107, 045901 (2011).
[Crossref] [PubMed]

P.-E. Chang, Y.-W. Jiang, H.-H. Chen, Y.-T. Chang, Y.-T. Wu, L. D.-C. Tzuang, Y.-H. Ye, and S.-C. Lee, “Wavelength selective plasmonic thermal emitter by polarization utilizing fabry-pérot type resonances,” Appl. Phys. Lett. 98, 073111 (2011).
[Crossref]

M. Francoeur, S. Basu, and S. J. Petersen, “Electric and magnetic surface polariton mediated near-field radiative heat transfer between metamaterials made of silicon carbide particles,” Opt. Express 19, 18774–18788 (2011).
[Crossref] [PubMed]

2010 (2)

2009 (2)

2008 (3)

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. G. de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
[Crossref] [PubMed]

P. Nagpal, S. E. Han, A. Stein, and D. J. Norris, “Efficient low-temperature thermophotovoltaic emitters from metallic photonic crystals,” Nano Lett. 8, 3238–3243 (2008).
[Crossref] [PubMed]

G. Liu, Y. Xuan, Y. Han, and Q. Li, “Investigation of one-dimensional si/sio2 hotonic crystals for thermophotovoltaic filter,” Science in China Series E: Technological Sciences 51, 2031–2039 (2008).
[Crossref]

2007 (2)

S. Basu, Y. Chen, and Z. Zhang, “Microscale radiation in thermophotovoltaic devices-a review,” Int. J. Energy Res. 31, 689–716 (2007).
[Crossref]

Y.-B. Chen, Z. Zhang, and P. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129, 79–90 (2007).
[Crossref]

2006 (2)

G. Colangelo, A. De Risi, and D. Laforgia, “Experimental study of a burner with high temperature heat recovery system for tpv applications,” Energy Convers. Manage. 47, 1192–1206 (2006).
[Crossref]

M.-W. Tsai, T.-H. Chuang, C.-Y. Meng, Y.-T. Chang, and S.-C. Lee, “High performance midinfrared narrow-band plasmonic thermal emitter,” Appl. Phys. Lett. 89, 173116 (2006).
[Crossref]

2005 (3)

H. Sai, Y. Kanamori, and H. Yugami, “Tuning of the thermal radiation spectrum in the near-infrared region by metallic surface microstructures,” J. Micromech. Microeng. 15, S243 (2005).
[Crossref]

G. Kiziltas, J. L. Volakis, and N. Kikuchi, “Design of a frequency selective structure with inhomogeneous substrates as a thermophotovoltaic filter,” IEEE Trans. Antennas Propagation 53, 2282–2289 (2005).
[Crossref]

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[Crossref]

2004 (1)

B. Wernsman, R. R. Siergiej, S. D. Link, R. G. Mahorter, M. N. Palmisiano, R. J. Wehrer, R. W. Schultz, G. P. Schmuck, R. L. Messham, S. Murray, and C. S. Murray, “Greater than 20% radiant heat conversion efficiency of a thermophotovoltaic radiator/module system using reflective spectral control,” IEEE Trans. Electron. Dev. 51, 512–515 (2004).
[Crossref]

2003 (2)

N.-P. Harder and P. Würfel, “Theoretical limits of thermophotovoltaic solar energy conversion,” Semicond. Sci. Technol. 18, S151 (2003).
[Crossref]

A. Licciulli, D. Diso, G. Torsello, S. Tundo, A. Maffezzoli, M. Lomascolo, and M. Mazzer, “The challenge of high-performance selective emitters for thermophotovoltaic applications,” Semicond. Sci. Technol. 18, S174 (2003).
[Crossref]

2002 (2)

J. Fleming, S. Lin, I. El-Kady, R. Biswas, and K. Ho, “All-metallic three-dimensional photonic crystals with a large infrared bandgap,” Nature 417, 52–55 (2002).
[Crossref] [PubMed]

L. Ferguson and F. Dogan, “Spectral analysis of transition metal-doped mgo ‘matched emitters’ for thermophotovoltaic energy conversion,” J. Mater. Sci. 37, 1301–1308 (2002).
[Crossref]

2000 (1)

A. Heinzel, V. Boerner, A. Gombert, B. Bläsi, V. Wittwer, and J. Luther, “Radiation filters and emitters for the nir based on periodically structured metal surfaces,” J. Mod. Opt. 47, 2399–2419 (2000).
[Crossref]

1999 (1)

T. Coutts, “A review of progress in thermophotovoltaic generation of electricity,” Renewable Sustainable Energy Rev. 3, 77–184 (1999).
[Crossref]

1998 (1)

1989 (1)

W. T. Doyle, “Optical properties of a suspension of metal spheres,” Phys. Rev. B 39, 9852 (1989).
[Crossref]

1983 (1)

H. Höfler, H. Paul, W. Ruppel, and P. Würfel, “Interference filters for thermophotovoltaic solar energy conversion,” Solar Cells 10, 273–286 (1983).
[Crossref]

1980 (1)

P. Wurfel and W. Ruppel, “Upper limit of thermophotovoltaic solar-energy conversion,” IEEE Trans. Electron. Dev. 27, 745–750 (1980).
[Crossref]

1959 (1)

S. Roberts, “Optical properties of nickel and tungsten and their interpretation according to drude’s formula,” Phys. Rev. 114, 104 (1959).
[Crossref]

Abbas, M. N.

Aitchison, J. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[Crossref]

Alu, A.

C. Argyropoulos, K. Q. Le, N. Mattiucci, G. DAguanno, and A. Alu, “Broadband absorbers and selective emitters based on plasmonic brewster metasurfaces,” Phys. Rev. B 87, 205112 (2013).
[Crossref]

Araghchini, M.

Argyropoulos, C.

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C. Xu, S. Wang, G. Wang, J. Liang, S. Wang, L. Bai, J. Yang, and X. Chen, “Temperature dependence of refractive indices for 4h-and 6h-sic,” Journal of Applied Physics 115, 113501 (2014).
[Crossref]

C. Xu, S. Wang, G. Wang, J. Liang, S. Wang, L. Bai, J. Yang, and X. Chen, “Temperature dependence of refractive indices for 4h-and 6h-sic,” Journal of Applied Physics 115, 113501 (2014).
[Crossref]

Wang, Z.

B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagn. Res. 101, 231–239 (2010).
[Crossref]

Wedlock, B. D.

D. C. White, B. D. Wedlock, and J. Blair, “Recent advances in thermal energy conversion,” in “15th Annual Proceedings, Power Sources Conference,” (1961), pp. 125–132.

Wehrer, R. J.

B. Wernsman, R. R. Siergiej, S. D. Link, R. G. Mahorter, M. N. Palmisiano, R. J. Wehrer, R. W. Schultz, G. P. Schmuck, R. L. Messham, S. Murray, and C. S. Murray, “Greater than 20% radiant heat conversion efficiency of a thermophotovoltaic radiator/module system using reflective spectral control,” IEEE Trans. Electron. Dev. 51, 512–515 (2004).
[Crossref]

Wernsman, B.

B. Wernsman, R. R. Siergiej, S. D. Link, R. G. Mahorter, M. N. Palmisiano, R. J. Wehrer, R. W. Schultz, G. P. Schmuck, R. L. Messham, S. Murray, and C. S. Murray, “Greater than 20% radiant heat conversion efficiency of a thermophotovoltaic radiator/module system using reflective spectral control,” IEEE Trans. Electron. Dev. 51, 512–515 (2004).
[Crossref]

Wheeler, M. S.

M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005).
[Crossref]

M. S. Wheeler, “A scattering-based approach to the design, analysis, and experimental verification of magnetic metamaterials made from dielectrics,” Ph.D. thesis (2010).

White, D. C.

D. C. White, B. D. Wedlock, and J. Blair, “Recent advances in thermal energy conversion,” in “15th Annual Proceedings, Power Sources Conference,” (1961), pp. 125–132.

Wittwer, V.

A. Heinzel, V. Boerner, A. Gombert, B. Bläsi, V. Wittwer, and J. Luther, “Radiation filters and emitters for the nir based on periodically structured metal surfaces,” J. Mod. Opt. 47, 2399–2419 (2000).
[Crossref]

Woolf, D.

D. Woolf, J. Hensley, J. Cederberg, D. Bethke, A. Grine, and E. Shaner, “Heterogeneous metasurface for high temperature selective emission,” Appl. Phys. Lett. 105, 081110 (2014).
[Crossref]

Wu, C.

C. Wu, N. Arju, G. Kelp, J. A. Fan, J. Dominguez, E. Gonzales, E. Tutuc, I. Brener, and G. Shvets, “Spectrally selective chiral silicon metasurfaces based on infrared fano resonances,” Nat. Commun. 5, 3892 (2014).
[Crossref] [PubMed]

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).
[Crossref]

Wu, Y.-T.

P.-E. Chang, Y.-W. Jiang, H.-H. Chen, Y.-T. Chang, Y.-T. Wu, L. D.-C. Tzuang, Y.-H. Ye, and S.-C. Lee, “Wavelength selective plasmonic thermal emitter by polarization utilizing fabry-pérot type resonances,” Appl. Phys. Lett. 98, 073111 (2011).
[Crossref]

Wurfel, P.

P. Wurfel and W. Ruppel, “Upper limit of thermophotovoltaic solar-energy conversion,” IEEE Trans. Electron. Dev. 27, 745–750 (1980).
[Crossref]

Würfel, P.

N.-P. Harder and P. Würfel, “Theoretical limits of thermophotovoltaic solar energy conversion,” Semicond. Sci. Technol. 18, S151 (2003).
[Crossref]

H. Höfler, H. Paul, W. Ruppel, and P. Würfel, “Interference filters for thermophotovoltaic solar energy conversion,” Solar Cells 10, 273–286 (1983).
[Crossref]

Xu, C.

C. Xu, S. Wang, G. Wang, J. Liang, S. Wang, L. Bai, J. Yang, and X. Chen, “Temperature dependence of refractive indices for 4h-and 6h-sic,” Journal of Applied Physics 115, 113501 (2014).
[Crossref]

Xuan, Y.

G. Liu, Y. Xuan, Y. Han, and Q. Li, “Investigation of one-dimensional si/sio2 hotonic crystals for thermophotovoltaic filter,” Science in China Series E: Technological Sciences 51, 2031–2039 (2008).
[Crossref]

Yang, J.

C. Xu, S. Wang, G. Wang, J. Liang, S. Wang, L. Bai, J. Yang, and X. Chen, “Temperature dependence of refractive indices for 4h-and 6h-sic,” Journal of Applied Physics 115, 113501 (2014).
[Crossref]

Ye, Y.-H.

P.-E. Chang, Y.-W. Jiang, H.-H. Chen, Y.-T. Chang, Y.-T. Wu, L. D.-C. Tzuang, Y.-H. Ye, and S.-C. Lee, “Wavelength selective plasmonic thermal emitter by polarization utilizing fabry-pérot type resonances,” Appl. Phys. Lett. 98, 073111 (2011).
[Crossref]

Yeng, Y. X.

Y. Nam, Y. X. Yeng, A. Lenert, P. Bermel, I. Celanovic, M. Soljačić, and E. N. Wang, “Solar thermophotovoltaic energy conversion systems with two-dimensional tantalum photonic crystal absorbers and emitters,” Solar Sol. Energy Mater. Sol. Cells 122, 287–296 (2014).
[Crossref]

P. Bermel, M. Ghebrebrhan, W. Chan, Y. X. Yeng, M. Araghchini, R. Hamam, C. H. Marton, K. F. Jensen, M. Soljačić, J. D. Joannopoulos, and S. G. Johnson, “Design and global optimization of high-efficiency thermophotovoltaic systems,” Opt. Express 18, A314–A334 (2010).
[Crossref] [PubMed]

Yu, Z.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, and G. S. Girolami, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[Crossref] [PubMed]

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H. Sai, Y. Kanamori, and H. Yugami, “Tuning of the thermal radiation spectrum in the near-infrared region by metallic surface microstructures,” J. Micromech. Microeng. 15, S243 (2005).
[Crossref]

Zhang, F.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Materials Today 12, 60–69 (2009).
[Crossref]

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Y. Battie, A. Resano-Garcia, N. Chaoui, Y. Zhang, and A. E. Naciri, “Extended maxwell-garnett-mie formulation applied to size dispersion of metallic nanoparticles embedded in host liquid matrix,” J. Chem. Phys. 140, 044705 (2014).
[Crossref]

Zhang, Z.

L. Wang and Z. Zhang, “Wavelength-selective and diffuse emitter enhanced by magnetic polaritons for thermophotovoltaics,” Appl. Phys. Lett. 100, 063902 (2012).
[Crossref]

S. Basu, Y. Chen, and Z. Zhang, “Microscale radiation in thermophotovoltaic devices-a review,” Int. J. Energy Res. 31, 689–716 (2007).
[Crossref]

Y.-B. Chen, Z. Zhang, and P. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129, 79–90 (2007).
[Crossref]

Zhang, Z. M.

B. Zhao, L. Wang, Y. Shuai, and Z. M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transfer 67, 637–645 (2013).
[Crossref]

Zhao, B.

B. Zhao, L. Wang, Y. Shuai, and Z. M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transfer 67, 637–645 (2013).
[Crossref]

Zhao, J.

B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagn. Res. 101, 231–239 (2010).
[Crossref]

Zhao, Q.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Materials Today 12, 60–69 (2009).
[Crossref]

Zheng, Y.

A. Ghanekar, L. Lin, J. Su, H. Sun, and Y. Zheng, “Role of nanoparticles in wavelength selectivity of multilayered structures in the far-field and near-field regimes,” Opt. Express 23, A1129–A1139 (2015).
[Crossref] [PubMed]

Y. Zheng and A. Ghanekar, “Radiative energy and momentum transfer for various spherical shapes: a single sphere, a bubble, a spherical shell and a coated sphere,” J. Appl. Phys. 117, 064314 (2015).
[Crossref]

Zhou, J.

Q. Zhao, J. Zhou, F. Zhang, and D. Lippens, “Mie resonance-based dielectric metamaterials,” Materials Today 12, 60–69 (2009).
[Crossref]

Zhu, B.

B. Zhu, Z. Wang, C. Huang, Y. Feng, J. Zhao, and T. Jiang, “Polarization insensitive metamaterial absorber with wide incident angle,” Prog. Electromagn. Res. 101, 231–239 (2010).
[Crossref]

Zhu, L.

K. A. Arpin, M. D. Losego, A. N. Cloud, H. Ning, J. Mallek, N. P. Sergeant, L. Zhu, Z. Yu, B. Kalanyan, G. N. Parsons, and G. S. Girolami, “Three-dimensional self-assembled photonic crystals with high temperature stability for thermal emission modification,” Nat. Commun. 4, 2630 (2013).
[Crossref] [PubMed]

Zollars, B.

C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).
[Crossref]

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Appl. Phys. Lett. (4)

P.-E. Chang, Y.-W. Jiang, H.-H. Chen, Y.-T. Chang, Y.-T. Wu, L. D.-C. Tzuang, Y.-H. Ye, and S.-C. Lee, “Wavelength selective plasmonic thermal emitter by polarization utilizing fabry-pérot type resonances,” Appl. Phys. Lett. 98, 073111 (2011).
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M.-W. Tsai, T.-H. Chuang, C.-Y. Meng, Y.-T. Chang, and S.-C. Lee, “High performance midinfrared narrow-band plasmonic thermal emitter,” Appl. Phys. Lett. 89, 173116 (2006).
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L. Wang and Z. Zhang, “Wavelength-selective and diffuse emitter enhanced by magnetic polaritons for thermophotovoltaics,” Appl. Phys. Lett. 100, 063902 (2012).
[Crossref]

D. Woolf, J. Hensley, J. Cederberg, D. Bethke, A. Grine, and E. Shaner, “Heterogeneous metasurface for high temperature selective emission,” Appl. Phys. Lett. 105, 081110 (2014).
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Chem. Soc. Rev. (1)

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. G. de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37, 1792–1805 (2008).
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B. Wernsman, R. R. Siergiej, S. D. Link, R. G. Mahorter, M. N. Palmisiano, R. J. Wehrer, R. W. Schultz, G. P. Schmuck, R. L. Messham, S. Murray, and C. S. Murray, “Greater than 20% radiant heat conversion efficiency of a thermophotovoltaic radiator/module system using reflective spectral control,” IEEE Trans. Electron. Dev. 51, 512–515 (2004).
[Crossref]

P. Wurfel and W. Ruppel, “Upper limit of thermophotovoltaic solar-energy conversion,” IEEE Trans. Electron. Dev. 27, 745–750 (1980).
[Crossref]

Int. J. Energy Res. (1)

S. Basu, Y. Chen, and Z. Zhang, “Microscale radiation in thermophotovoltaic devices-a review,” Int. J. Energy Res. 31, 689–716 (2007).
[Crossref]

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B. Zhao, L. Wang, Y. Shuai, and Z. M. Zhang, “Thermophotovoltaic emitters based on a two-dimensional grating/thin-film nanostructure,” Int. J. Heat Mass Transfer 67, 637–645 (2013).
[Crossref]

J. Appl. Phys. (1)

Y. Zheng and A. Ghanekar, “Radiative energy and momentum transfer for various spherical shapes: a single sphere, a bubble, a spherical shell and a coated sphere,” J. Appl. Phys. 117, 064314 (2015).
[Crossref]

J. Chem. Phys. (1)

Y. Battie, A. Resano-Garcia, N. Chaoui, Y. Zhang, and A. E. Naciri, “Extended maxwell-garnett-mie formulation applied to size dispersion of metallic nanoparticles embedded in host liquid matrix,” J. Chem. Phys. 140, 044705 (2014).
[Crossref]

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Y.-B. Chen, Z. Zhang, and P. Timans, “Radiative properties of patterned wafers with nanoscale linewidth,” J. Heat Transfer 129, 79–90 (2007).
[Crossref]

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H. Sai, Y. Kanamori, and H. Yugami, “Tuning of the thermal radiation spectrum in the near-infrared region by metallic surface microstructures,” J. Micromech. Microeng. 15, S243 (2005).
[Crossref]

J. Mod. Opt. (1)

A. Heinzel, V. Boerner, A. Gombert, B. Bläsi, V. Wittwer, and J. Luther, “Radiation filters and emitters for the nir based on periodically structured metal surfaces,” J. Mod. Opt. 47, 2399–2419 (2000).
[Crossref]

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C. Wu, B. Neuner, J. John, A. Milder, B. Zollars, S. Savoy, and G. Shvets, “Metamaterial-based integrated plasmonic absorber/emitter for solar thermo-photovoltaic systems,” J. Opt. 14, 024005 (2012).
[Crossref]

Journal of Applied Physics (1)

C. Xu, S. Wang, G. Wang, J. Liang, S. Wang, L. Bai, J. Yang, and X. Chen, “Temperature dependence of refractive indices for 4h-and 6h-sic,” Journal of Applied Physics 115, 113501 (2014).
[Crossref]

Journal of the European Optical Society-Rapid publications (1)

L. Gao, F. Lemarchand, and M. Lequime, “Refractive index determination of sio2 layer in the uv/vis/nir range: spectrophotometric reverse engineering on single and bi-layer designs,” Journal of the European Optical Society-Rapid publications 8 (2013).
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C. Wu, N. Arju, G. Kelp, J. A. Fan, J. Dominguez, E. Gonzales, E. Tutuc, I. Brener, and G. Shvets, “Spectrally selective chiral silicon metasurfaces based on infrared fano resonances,” Nat. Commun. 5, 3892 (2014).
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A. Ghanekar, L. Lin, J. Su, H. Sun, and Y. Zheng, “Role of nanoparticles in wavelength selectivity of multilayered structures in the far-field and near-field regimes,” Opt. Express 23, A1129–A1139 (2015).
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Figures (3)

Fig. 1
Fig. 1 (a) Schematic of a typical TPV system with a thermal emitter/absorber and a PV cell. (b) An example of a thermal emitter based on 1-D grating structure of SiC and W on the top of W base. The grating thickness and period Λ=50 nm, filling ratio ϕ=0.55. (c) A proposed design of thermal emitter consists of 0.4 μm thick SiO2 layer on the top of 1 μm thick W layer deposited on the substrate. SiO2 layer is doped with W nanoparticles of 20 nm radius with a volume fraction of 30%.
Fig. 2
Fig. 2 Refractive indices of W, SiO2 and SiO2 doped with W nanoparticles of volume fraction 30% and 20 nm radius. (a) Real part of refractive index. (b) Imaginary part of refractive index. Imaginary part of refractive index for SiO2 is negligible for the range of wavelengths considered here [46].
Fig. 3
Fig. 3 Emission spectra of different configurations. (a) Hemispherical emissivity of W, SiO2 film of 0.4 μm deposited on W base and SiO2 doped with W nanoparticles of 20 nm radius and different volume fractions. (b) Emission spectrum (left y-axis) of the final design is compared to the result presented by Zhao et al [13] and 1-D surface grating discussed in this study. The EQE plots (right y-axis) of PV cells are shown for comparison [54].

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

e ( ω ) = c 2 ω 2 0 ω / c d k ρ k ρ μ = s , p ( 1 | R ˜ h ( μ ) | 2 | T ˜ h ( μ ) | 2 )
ε TE , 2 = ε TE , 0 [ 1 + π 2 3 ( Λ λ ) 2 ϕ 2 ( 1 ϕ ) 2 ( ε A ε B ) 2 ε TE , 0 ]
ε TM , 2 = ε TM , 0 [ 1 + π 2 3 ( Λ λ ) 2 ϕ 2 ( 1 ϕ ) 2 ( ε A ε B ) 2 ε TE , 0 ( ε TM , 0 ε A ε B ) 2 ]
ε TE , 0 = ϕ ε A + ( 1 ϕ ) ε B
ε TM , 0 = ( ϕ ε A + 1 ϕ ε B ) 1
ε eff = ε m ( r 3 + 2 α r f r 3 α r f )
a 1 , r = ε np ψ 1 ( x np ) ψ 1 ( x m ) ε m ψ 1 ( x m ) ψ 1 ( x np ) ε np ψ 1 ( x np ) ξ 1 ( x m ) ε m ξ 1 ( x m ) ψ 1 ( x np )
η = P out P rad
P rad = 0 ω 2 4 π 2 c 2 ω ( e ω / k B T 1 ) e ( ω ) d ω
P out = q V OC F F 0 n ¯ ( ω , T ) e ( ω ) η EQE ( ω ) d ω
n ¯ ( ω , T ) = ω 2 4 π 2 c 2 1 ( e ω / k B T 1 )
β emitter = ( P out P rad ) Real × ( P rad P out ) Ideal

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