Aperiodic and randomized dielectric mirrors: alternatives to metallic back reflectors for solar cells

Albert Lin; Yan-Kai Zhong; Sze-Ming Fu; Chi Wei Tseng; Sheng Lun Yan

doi:10.1364/OE.22.00A880

Aperiodic and randomized dielectric mirrors: alternatives to metallic back reflectors for solar cells

Albert Lin, Yan-Kai Zhong, Sze-Ming Fu, Chi Wei Tseng, and Sheng Lun Yan

Optics Express
Vol. 22,
Issue S3,
pp. A880-A894
(2014)
•https://doi.org/10.1364/OE.22.00A880

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Albert Lin, Yan-Kai Zhong, Sze-Ming Fu, Chi Wei Tseng, and Sheng Lun Yan, "Aperiodic and randomized dielectric mirrors: alternatives to metallic back reflectors for solar cells," Opt. Express 22, A880-A894 (2014)

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Related Topics
Table of Contents Category
- Light Trapping for Photovoltaics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Photovoltaic (040.5350)
- Diffraction (050.1940)
- Thin film devices and applications (310.6845)

About this Article
History
- Original Manuscript: February 28, 2014
- Revised Manuscript: March 29, 2014
- Manuscript Accepted: March 31, 2014
- Published: April 11, 2014

Accessible

Open Access

Abstract

Dielectric mirrors have recently emerged for solar cells due to the advantages of lower cost, lower temperature processing, higher throughput, and zero plasmonic absorption as compared to conventional metallic counterparts. Nonetheless, in the past, efforts for incorporating dielectric mirrors into photovoltaics were not successful due to limited bandwidth and insufficient light scattering that prevented their wide usage. In this work, it is shown that the key for ultra-broadband dielectric mirrors is aperiodicity, or randomization. In addition, it has been proven that dielectric mirrors can be widely applicable to thin-film and thick wafer-based solar cells to provide for light trapping comparable to conventional metallic back reflectors at their respective optimal geometries. Finally, the near-field angular emission plot of Poynting vectors is conducted, and it further confirms the superior light-scattering property of dielectric mirrors, especially for diffuse medium reflectors, despite the absence of surface plasmon excitation. The preliminary experimental results also confirm the high feasibility of dielectric mirrors for photovoltaics.

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References

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S. Hänni, G. Bugnon, G. Parascandolo, M. Boccard, J. Escarré, M. Despeisse, F. Meillaud, and C. Ballif, “High-efficiency microcrystalline silicon single-junction solar cells,” Prog. Photovolt. Res. Appl. 21, 821–826 (2013).

A. Bozzola, M. Liscidini, and L. C. Andreani, “Broadband light trapping with disordered photonic structures in thin-film silicon solar cells,” Prog. Photovolt. Res. Appl. 21, 2385 (2013).
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E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

A. Lin, Y.-K. Zhong, and S.-M. Fu, “The effect of mode excitations on the absorption enhancement for silicon thin film solar cells,” J. Appl. Phys. 114(23), 233104 (2013).
[Crossref]

M. Burresi, F. Pratesi, K. Vynck, M. Prasciolu, M. Tormen, and D. S. Wiersma, “Two-dimensional disorder for broadband, omnidirectional and polarization-insensitive absorption,” Opt. Express 21(Suppl 2), A268–A275 (2013).
[Crossref] [PubMed]

F. Pratesi, M. Burresi, F. Riboli, K. Vynck, and D. S. Wiersma, “Disordered photonic structures for light harvesting in solar cells,” Opt. Express 21(Suppl 3), A460–A468 (2013).
[Crossref] [PubMed]

2012 (9)

H.-Y. Lin, Y. Kuo, C.-Y. Liao, C. C. Yang, and Y.-W. Kiang, “Surface plasmon effects in the absorption enhancements of amorphous silicon solar cells with periodical metal nanowall and nanopillar structures,” Opt. Express 20(1S1), A104–A118 (2012).
[Crossref] [PubMed]

C. Lin, N. Huang, and M. L. Povinelli, “Effect of aperiodicity on the broadband reflection of silicon nanorod structures for photovoltaics,” Opt. Express 20(1S1), A125–A132 (2012).
[Crossref] [PubMed]

O. Deparis and O. El Daif, “Optimization of slow light one-dimensional Bragg structures for photocurrent enhancement in solar cells,” Opt. Lett. 37(20), 4230–4232 (2012).
[Crossref] [PubMed]

C. Battaglia, C.-M. Hsu, K. Söderström, J. Escarré, F.-J. Haug, M. Charrière, M. Boccard, M. Despeisse, D. T. L. Alexander, M. Cantoni, Y. Cui, and C. Ballif, “Light trapping in solar cells: can periodic beat random?” ACS Nano 6(3), 2790–2797 (2012).
[Crossref] [PubMed]

X. Sheng, S. G. Johnson, L. Z. Broderick, J. Michel, and L. C. Kimerling, “Integrated photonic structures for light trapping in thin-film Si solar cells,” Appl. Phys. Lett. 100(11), 111110 (2012).
[Crossref]

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: the supercell concept,” Phys. Rev. B 86(4), 041404 (2012).
[Crossref]

A. Oskooi, P. A. Favuzzi, Y. Tanaka, H. Shigeta, Y. Kawakami, and S. Noda, “Partially disordered photonic-crystal thin films for enhanced and robust photovoltaics,” Appl. Phys. Lett. 100(18), 181110 (2012).
[Crossref]

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012).
[PubMed]

2011 (4)

S. Pillai, F. J. Beck, K. R. Catchpole, Z. Ouyang, and M. A. Green, “The effect of dielectric spacer thickness on surface plasmon enhanced solar cells for front and rear side depositions,” J. Appl. Phys. 109(7), 073105 (2011).
[Crossref]

U. W. Paetzold, E. Moulin, D. Michaelis, W. Bottler, C. Wächter, V. Hagemann, M. Meier, R. Carius, and U. Rau, “Plasmonic reflection grating back contacts for microcrystalline silicon solar cells,” Appl. Phys. Lett. 99(18), 181105 (2011).
[Crossref]

C. Lin and M. L. Povinelli, “Optimal design of aperiodic, vertical silicon nanowire structures for photovoltaics,” Opt. Express 19(Suppl 5), A1148–A1154 (2011).
[Crossref] [PubMed]

U. W. Paetzold, E. Moulin, B. E. Pieters, R. Carius, and U. Rau, “Design of nanostructured plasmonic back contacts for thin-film silicon solar cells,” Opt. Express 19(Suppl 6), A1219–A1230 (2011).
[Crossref] [PubMed]

2010 (2)

K. Söderström, F.-J. Haug, J. Escarré, O. Cubero, and C. Ballif, “Photocurrent increase in n-i-p thin film silicon solar cells by guided mode excitation via grating coupler,” Appl. Phys. Lett. 96(21), 213508 (2010).
[Crossref]

B. Lipovšek, J. Krč, O. Isabella, M. Zeman, and M. Topič, “Modeling and optimization of white paint back reflectors for thin-film silicon solar cells,” J. Appl. Phys. 108(10), 103115 (2010).
[Crossref]

2008 (1)

Y.-C. Lee, C.-F. Huang, J.-Y. Chang, and M.-L. Wu, “Enhanced light trapping based on guided mode resonance effect for thin-film silicon solar cells with two filling-factor gratings,” Opt. Express 16(11), 7969–7975 (2008).
[Crossref] [PubMed]

2007 (1)

P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007).
[Crossref] [PubMed]

2006 (2)

W. E. Vargas, A. Amador, and G. A. Niklasson, “Diffuse reflectance of TiO2 pigmented paints: spectral dependence of the average path length parameter and the forward scattering ratio,” Opt. Commun. 261(1), 71–78 (2006).
[Crossref]

B. Deken, S. Pekarek, and F. Dogan, “Minimization of field enhancement in multilayer capacitors,” Comput. Mater. Sci. 37(3), 401–409 (2006).
[Crossref]

2005 (1)

S. Preble, M. Lipson, and H. Lipson, “Two-dimensional photonic crystals designed by evolutionary algorithms,” Appl. Phys. Lett. 86, 061111 (2005).

2004 (2)

L. Dal Negro, M. Stolfi, Y. Yi, J. Michel, X. Duan, L. C. Kimerling, J. LeBlanc, and J. Haavisto, “Photon band gap properties and omnidirectional reflectance in Si/SiO 2 Thue–Morse quasicrystals,” Appl. Phys. Lett. 84(25), 5186 (2004).
[Crossref]

L. Miao, S. Tanemura, S. Toh, K. Kaneko, and M. Tanemura, “Preparation and characterization of rutile TiO2 nanorods,” J. Mater. Sci. Technol. 20, 59–62 (2004).

2003 (2)

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68, 035109 (2003).

L. Dal Negro, C. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003).
[Crossref] [PubMed]

2000 (2)

W. E. Vargas, P. Greenwood, J. E. Otterstedt, and G. A. Niklasson, “Light scattering in pigmented coatings: experiment and theory,” Sol. Energy 68(6), 553–561 (2000).
[Crossref]

J. B. Pollack and H. Lipson, “Automatic design and manufacture of robotic life forms,” Nature 406(6799), 974–978 (2000).
[Crossref] [PubMed]

1998 (2)

J. E. Cotter, “Optical intensity of light in layers of silicon with rear diffuse reflectors,” J. Appl. Phys. 84(1), 618–624 (1998).
[Crossref]

P. Nitz, J. Ferber, R. Stangl, H. R. Wilson, and V. Wittwer, “Simulation of multiply scattering media,” Sol. Energ. Mat. Sol. Cells 54(1-4), 297–307 (1998).
[Crossref]

1994 (1)

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[Crossref] [PubMed]

1951 (1)

J. R. Devore, “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am. 41(6), 416–419 (1951).
[Crossref]

Alexander, D. T. L.

Amador, A.

Andreani, L. C.

Ballif, C.

Battaglia, C.

Beck, F. J.

Bermel, P.

Boccard, M.

Bottler, W.

Bozzola, A.

Broderick, L. Z.

Bugnon, G.

Burresi, M.

K. Vynck, M. Burresi, F. Riboli, and D. S. Wiersma, “Photon management in two-dimensional disordered media,” Nat. Mater. 11(12), 1017–1022 (2012).
[PubMed]

Cantoni, M.

Carius, R.

Catchpole, K. R.

Chang, J.-Y.

Charrière, M.

Chen, Z.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

Colocci, M.

Cotter, J. E.

J. E. Cotter, “Optical intensity of light in layers of silicon with rear diffuse reflectors,” J. Appl. Phys. 84(1), 618–624 (1998).
[Crossref]

Cubero, O.

Cui, Y.

Dal Negro, L.

Deken, B.

B. Deken, S. Pekarek, and F. Dogan, “Minimization of field enhancement in multilayer capacitors,” Comput. Mater. Sci. 37(3), 401–409 (2006).
[Crossref]

Deparis, O.

O. Deparis and O. El Daif, “Optimization of slow light one-dimensional Bragg structures for photocurrent enhancement in solar cells,” Opt. Lett. 37(20), 4230–4232 (2012).
[Crossref] [PubMed]

Depauw, V.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

Despeisse, M.

Devore, J. R.

J. R. Devore, “Refractive indices of rutile and sphalerite,” J. Opt. Soc. Am. 41(6), 416–419 (1951).
[Crossref]

Dogan, F.

B. Deken, S. Pekarek, and F. Dogan, “Minimization of field enhancement in multilayer capacitors,” Comput. Mater. Sci. 37(3), 401–409 (2006).
[Crossref]

Duan, X.

El Daif, O.

O. Deparis and O. El Daif, “Optimization of slow light one-dimensional Bragg structures for photocurrent enhancement in solar cells,” Opt. Lett. 37(20), 4230–4232 (2012).
[Crossref] [PubMed]

Escarré, J.

Favuzzi, P. A.

Ferber, J.

P. Nitz, J. Ferber, R. Stangl, H. R. Wilson, and V. Wittwer, “Simulation of multiply scattering media,” Sol. Energ. Mat. Sol. Cells 54(1-4), 297–307 (1998).
[Crossref]

Fu, S.-M.

A. Lin, Y.-K. Zhong, and S.-M. Fu, “The effect of mode excitations on the absorption enhancement for silicon thin film solar cells,” J. Appl. Phys. 114(23), 233104 (2013).
[Crossref]

Gaburro, Z.

Gellermann, W.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[Crossref] [PubMed]

Green, M. A.

Greenwood, P.

W. E. Vargas, P. Greenwood, J. E. Otterstedt, and G. A. Niklasson, “Light scattering in pigmented coatings: experiment and theory,” Sol. Energy 68(6), 553–561 (2000).
[Crossref]

Haavisto, J.

Hagemann, V.

Hänni, S.

Haug, F.-J.

He, S.

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68, 035109 (2003).

Hsu, C.-M.

Huang, C.-F.

Huang, N.

Isabella, O.

Joannopoulos, J. D.

Johnson, P.

Johnson, S. G.

Kaneko, K.

L. Miao, S. Tanemura, S. Toh, K. Kaneko, and M. Tanemura, “Preparation and characterization of rutile TiO2 nanorods,” J. Mater. Sci. Technol. 20, 59–62 (2004).

Kawakami, Y.

Kiang, Y.-W.

Kimerling, L. C.

Kohmoto, M.

W. Gellermann, M. Kohmoto, B. Sutherland, and P. C. Taylor, “Localization of light waves in Fibonacci dielectric multilayers,” Phys. Rev. Lett. 72(5), 633–636 (1994).
[Crossref] [PubMed]

Krauss, T. F.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: the supercell concept,” Phys. Rev. B 86(4), 041404 (2012).
[Crossref]

Krc, J.

Kuo, Y.

Lagendijk, A.

LeBlanc, J.

Lee, Y.-C.

Li, J.

E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat. Commun. 4, 2665 (2013).
[Crossref] [PubMed]

E. R. Martins, J. Li, Y. Liu, J. Zhou, and T. F. Krauss, “Engineering gratings for light trapping in photovoltaics: the supercell concept,” Phys. Rev. B 86(4), 041404 (2012).
[Crossref]

Liao, C.-Y.

Lin, A.

A. Lin, Y.-K. Zhong, and S.-M. Fu, “The effect of mode excitations on the absorption enhancement for silicon thin film solar cells,” J. Appl. Phys. 114(23), 233104 (2013).
[Crossref]

Lin, C.

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Fig. 1 Illustration of the solar cell stack in this study and the front surface structure. The Mie resonator-based design [21], or equivalent photonic-crystal circular grating arranged in a square lattice, is selected to be the solar cell front surface nanostructure.

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Fig. 2 Illustration of the solar cell structure with an A-DBR. Layer thickness of an A-DBR can be optimized individually. Randomly determined layer thickness is also possible, and it can still lead to high reflectance.

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Fig. 3 (Left) Spectral absorbance of the solar cell with an A-DBR, N=10 for A-DBR. (Right) reflectance for regular periodic DBR and A-DBR, N=100 for A-DBR.

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Fig. 4 Illustration of the solar cell structure with white paint diffuse medium reflector. The TiO₂ scatterers are cylindrical in shape to enhance the reflectance.

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Fig. 5 (Left) Spectral absorbance of the solar cell with a white paint diffuse medium reflector. (Right) Reflectance for the white paint diffuse medium reflector.

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Fig. 6 Different configurations of metallic back reflectors for solar cells. (a) Planar metallic mirror with grating on the dielectric spacer. (b) Bare metallic mirror with grating. (c) Grated metallic mirror wrapped by a dielectric spacer. (d) Bare planar metallic mirror.

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Fig. 7 Illustration of the solar cell structure with a metallic mirror. The selection of the metal back reflector configuration here is the best trade-off between plasmonic light scattering and metal absorption.

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Fig. 8 (Left) Spectral absorbance of the solar cell with a metallic mirror. (Right) Reflectance and metallic absorbance for the metallic mirror.

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Fig. 9 Long-wavelength angular emission plot at λ=1 μm for metallic mirrors. (a) Planar metallic mirror with grating on the dielectric spacer. (b) Metallic grating mirror wrapped by a dielectric spacer. (c) Bare metallic mirror with grating. Larger θ_scatt, or equivalently smaller θ_avg, indicates stronger light scattering.

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Fig. 10 Long-wavelength angular emission plot λ=1 μm for dielectric mirrors. (a) White paint diffuse medium reflector. (b) A-DBR. Larger θ_scatt, or equivalently smaller θ_avg, indicates stronger light scattering.

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Fig. 11 (a) J-V with and without an aluminum back reflector. (b) J-V with and without a white paint back reflector. In these measurements, the light comes from the indium tin oxide (ITO) side.

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Tables (2)

Table 1 Comparison of AM 1.5 Weighted Integrated Absorbance A_Int

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Table 2 Comparison of Long-wavelength Scattering Angles for Different Dielectric and Metallic Mirrors at λ = 1μm^*

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Equations (4)

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A (λ) = \frac{\frac{1}{2} \int_{V} ω ε_{0} ε^{″} (λ) {| \overset{⇀}{E} (\overset{⇀}{r}) |}^{2} d v}{\frac{1}{2} \int_{S} Re {\overset{⇀}{E} (\overset{⇀}{r}) \times {\overset{⇀}{H}}^{*} (\overset{⇀}{r})} \cdot d \overset{⇀}{s}},

A_{Int} = \frac{\int \frac{λ}{h c} Ω (λ) A (λ) d λ}{\int \frac{λ}{h c} Ω (λ) d λ},

\begin{array}{l} {\overset{⇀}{P}}_{poynting, avg} = P_{poynting, avg, x} + P_{poynting, avg, y} \\ = \frac{1}{2} Re {E_{y} (\overset{⇀}{r}) * H_{z}^{*} (\overset{⇀}{r})} - \frac{1}{2} Re {E_{x} (\overset{⇀}{r}) * H_{z}^{*} (\overset{⇀}{r})} . \end{array}

\begin{array}{l} \overset{⇀}{E} (x, y, z) = \sum_{n} \sum_{m} a_{n, m} \exp (j k_{z} z) \exp (j k_{n} x) \exp (j k_{m} y) \\ = \sum_{n} \sum_{m} a_{n, m} \exp (j k_{z} z) \exp (j \frac{2 π n}{Λ_{n}} x) \exp (j \frac{2 π m}{Λ_{m}} y), \\ k_{z} = \sqrt{k_{0}^{2} - {(\frac{2 π n}{Λ_{n}})}^{2} - {(\frac{2 π m}{Λ_{m}})}^{2}}, \end{array}

Mirror Type	Periodic-DBR (300nm)	A-DBR (300nm)	WP Mirror (300nm)	Metallic (300nm)
A_Int	0.525	0.563	0.588	0.543
Mirror Type	Periodic-DBR (30μm)	A-DBR (30μm)	WP Mirror (30μm)	Metallic (30μm)
A_Int	0.984	0.984	0.971	0.988

Mirror Type	A-DBR	WP mirror	Planar Metallic with Grated Dielectric Spacer	Grated Metallic Wrapped by a Dielectric Spacer	Bare Metallic with Grating
θ_scatt	35.3°	42.8°	26.5°	32.5°	39.2°
Metallic Absorbance(%)	0	0	1.4	12.3	23.3

Mirror Type	Periodic-DBR (300nm)	A-DBR (300nm)	WP Mirror (300nm)	Metallic (300nm)
A_Int	0.525	0.563	0.588	0.543
Mirror Type	Periodic-DBR (30μm)	A-DBR (30μm)	WP Mirror (30μm)	Metallic (30μm)
A_Int	0.984	0.984	0.971	0.988

Mirror Type	A-DBR	WP mirror	Planar Metallic with Grated Dielectric Spacer	Grated Metallic Wrapped by a Dielectric Spacer	Bare Metallic with Grating
θ_scatt	35.3°	42.8°	26.5°	32.5°	39.2°
Metallic Absorbance(%)	0	0	1.4	12.3	23.3