Abstract

Significant optical absorption enhancement can be achieved by incorporating optical diffusers in the thin-film silicon photovoltaic (PV) cells. Absorption can be increased further by angular and spectral selective filters. In this work the properties of volume reflection holograms are examined for realizing ultra light-trapping filters for thin film silicon photovoltaic cell applications. The filter properties of reflection volume hologram are evaluated for this application. It is found that variation in the refractive index profile as a function of depth is an important factor. The optimized design is implemented in dichromated gelatin holograms and found to be in good agreement with predicted performance. The enhancement to the conversion efficiency of silicon PV cells are predicted with the PC-1D simulation tool and is found to be similar to that with an optimized Rugate filter. The simulated short circuit current density enhancement was found to be 8.2% for a 50 µm thick silicon PV cell and 15.8% for a 10 µm thick silicon PV cell.

© 2012 OSA

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References

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  1. E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
    [CrossRef]
  2. S. Fahr, C. Ulbrich, T. Kirchartz, U. Rau, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
    [CrossRef] [PubMed]
  3. J. C. Miñano, “Optical confinement in photovoltaics,” Physical Limitations to the Photovoltaic Solar Energy Conversion (Hilger, 1990).
  4. C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
    [CrossRef]
  5. M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap—Improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
    [CrossRef]
  6. P. G. Boj, J. Crespo, and J. A. Quintana, “Broadband reflection holograms in dichromated gelatin,” Appl. Opt. 31(17), 3302–3305 (1992).
    [CrossRef] [PubMed]
  7. T. Jannson, I. Tengara, Y. Qiao, and G. Savant, “Lippmann-Bragg broadband holographic mirrors,” J. Opt. Soc. Am. A 8(1), 201–211 (1991).
    [CrossRef]
  8. C. G. Stojanoff, “Review of the technology for the manufacturing of large-format DCG holograms for technical applications,” Proc. SPIE 3011, 267–278 (1997).
    [CrossRef]
  9. J. Jannson, T. Jannson, and K. H. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mater. 14(3-5), 289–297 (1986).
    [CrossRef]
  10. S. Case and R. Alferness, “Index modulation and spatial harmonic generation in dichromated gelatin films,” Appl. Phys. A-Mater. 10, 41–51 (1976).
  11. T. Kubota, “Control of the reconstruction wavelength of Lippmann holograms recorded in dichromated gelatin,” Appl. Opt. 28(10), 1845–1849 (1989).
    [CrossRef] [PubMed]
  12. W. H. Southwell, “Extended-bandwidth reflector designs by using wavelets,” Appl. Opt. 36(1), 314–318 (1997).
    [CrossRef] [PubMed]
  13. W. H. Southwell, “Using apodization functions to reduce sidelobes in rugate filters,” Appl. Opt. 28(23), 5091–5094 (1989).
    [CrossRef] [PubMed]
  14. Z. N. Kalyashova, E. V. Kalyashov, G. A. Cheremisina, and D. I. Matveeva, “Intensive Bragg harmonics in reflection holograms in dichromated gelatin: II,” Proc. SPIE 3011, 279–284 (1997).
    [CrossRef]
  15. T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985).
    [CrossRef]
  16. M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995).
    [CrossRef]
  17. M. A. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002).
    [CrossRef]
  18. P. A. Basore, “Numerical modeling of textured silicon solar cells using PC-1D,” IEEE Trans. Electron. Dev. 37(2), 337–343 (1990).
    [CrossRef]

2009 (1)

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap—Improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

2008 (2)

S. Fahr, C. Ulbrich, T. Kirchartz, U. Rau, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

2002 (1)

M. A. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002).
[CrossRef]

1997 (3)

W. H. Southwell, “Extended-bandwidth reflector designs by using wavelets,” Appl. Opt. 36(1), 314–318 (1997).
[CrossRef] [PubMed]

Z. N. Kalyashova, E. V. Kalyashov, G. A. Cheremisina, and D. I. Matveeva, “Intensive Bragg harmonics in reflection holograms in dichromated gelatin: II,” Proc. SPIE 3011, 279–284 (1997).
[CrossRef]

C. G. Stojanoff, “Review of the technology for the manufacturing of large-format DCG holograms for technical applications,” Proc. SPIE 3011, 267–278 (1997).
[CrossRef]

1995 (1)

M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995).
[CrossRef]

1992 (1)

1991 (1)

1990 (1)

P. A. Basore, “Numerical modeling of textured silicon solar cells using PC-1D,” IEEE Trans. Electron. Dev. 37(2), 337–343 (1990).
[CrossRef]

1989 (2)

1986 (1)

J. Jannson, T. Jannson, and K. H. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mater. 14(3-5), 289–297 (1986).
[CrossRef]

1985 (1)

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985).
[CrossRef]

1982 (1)

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

1976 (1)

S. Case and R. Alferness, “Index modulation and spatial harmonic generation in dichromated gelatin films,” Appl. Phys. A-Mater. 10, 41–51 (1976).

Alferness, R.

S. Case and R. Alferness, “Index modulation and spatial harmonic generation in dichromated gelatin films,” Appl. Phys. A-Mater. 10, 41–51 (1976).

Basore, P. A.

P. A. Basore, “Numerical modeling of textured silicon solar cells using PC-1D,” IEEE Trans. Electron. Dev. 37(2), 337–343 (1990).
[CrossRef]

Bläsi, B.

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap—Improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

Boj, P. G.

Case, S.

S. Case and R. Alferness, “Index modulation and spatial harmonic generation in dichromated gelatin films,” Appl. Phys. A-Mater. 10, 41–51 (1976).

Cheremisina, G. A.

Z. N. Kalyashova, E. V. Kalyashov, G. A. Cheremisina, and D. I. Matveeva, “Intensive Bragg harmonics in reflection holograms in dichromated gelatin: II,” Proc. SPIE 3011, 279–284 (1997).
[CrossRef]

Cody, G. D.

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

Crespo, J.

Fahr, S.

S. Fahr, C. Ulbrich, T. Kirchartz, U. Rau, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

Gaylord, T. K.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985).
[CrossRef]

Goldschmidt, J. C.

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap—Improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

Gombert, A.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

Green, M. A.

M. A. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002).
[CrossRef]

M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995).
[CrossRef]

Jannson, J.

J. Jannson, T. Jannson, and K. H. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mater. 14(3-5), 289–297 (1986).
[CrossRef]

Jannson, T.

T. Jannson, I. Tengara, Y. Qiao, and G. Savant, “Lippmann-Bragg broadband holographic mirrors,” J. Opt. Soc. Am. A 8(1), 201–211 (1991).
[CrossRef]

J. Jannson, T. Jannson, and K. H. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mater. 14(3-5), 289–297 (1986).
[CrossRef]

Kalyashov, E. V.

Z. N. Kalyashova, E. V. Kalyashov, G. A. Cheremisina, and D. I. Matveeva, “Intensive Bragg harmonics in reflection holograms in dichromated gelatin: II,” Proc. SPIE 3011, 279–284 (1997).
[CrossRef]

Kalyashova, Z. N.

Z. N. Kalyashova, E. V. Kalyashov, G. A. Cheremisina, and D. I. Matveeva, “Intensive Bragg harmonics in reflection holograms in dichromated gelatin: II,” Proc. SPIE 3011, 279–284 (1997).
[CrossRef]

Keevers, M. J.

M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995).
[CrossRef]

Kirchartz, T.

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap—Improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

S. Fahr, C. Ulbrich, T. Kirchartz, U. Rau, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

Kubota, T.

Lederer, F.

S. Fahr, C. Ulbrich, T. Kirchartz, U. Rau, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

Matveeva, D. I.

Z. N. Kalyashova, E. V. Kalyashov, G. A. Cheremisina, and D. I. Matveeva, “Intensive Bragg harmonics in reflection holograms in dichromated gelatin: II,” Proc. SPIE 3011, 279–284 (1997).
[CrossRef]

Moharam, M. G.

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985).
[CrossRef]

Peters, M.

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap—Improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

Qiao, Y.

Quintana, J. A.

Rau, U.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

S. Fahr, C. Ulbrich, T. Kirchartz, U. Rau, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

Rockstuhl, C.

S. Fahr, C. Ulbrich, T. Kirchartz, U. Rau, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

Savant, G.

Southwell, W. H.

Stojanoff, C. G.

C. G. Stojanoff, “Review of the technology for the manufacturing of large-format DCG holograms for technical applications,” Proc. SPIE 3011, 267–278 (1997).
[CrossRef]

Tengara, I.

Ulbrich, C.

S. Fahr, C. Ulbrich, T. Kirchartz, U. Rau, C. Rockstuhl, and F. Lederer, “Rugate filter for light-trapping in solar cells,” Opt. Express 16(13), 9332–9343 (2008).
[CrossRef] [PubMed]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

Üpping, J.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

Wehrspohn, R.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

Yu, K. H.

J. Jannson, T. Jannson, and K. H. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mater. 14(3-5), 289–297 (1986).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. A-Mater. (1)

S. Case and R. Alferness, “Index modulation and spatial harmonic generation in dichromated gelatin films,” Appl. Phys. A-Mater. 10, 41–51 (1976).

IEEE Trans. Electron. Dev. (2)

P. A. Basore, “Numerical modeling of textured silicon solar cells using PC-1D,” IEEE Trans. Electron. Dev. 37(2), 337–343 (1990).
[CrossRef]

E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Express (1)

Phys. Status Solidi (1)

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, “Directional selectivity and ultra-light-trapping in solar cells,” Phys. Status Solidi 205(12), 2831–2843 (2008) (a).
[CrossRef]

Proc. IEEE (1)

T. K. Gaylord and M. G. Moharam, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73(5), 894–937 (1985).
[CrossRef]

Proc. SPIE (2)

Z. N. Kalyashova, E. V. Kalyashov, G. A. Cheremisina, and D. I. Matveeva, “Intensive Bragg harmonics in reflection holograms in dichromated gelatin: II,” Proc. SPIE 3011, 279–284 (1997).
[CrossRef]

C. G. Stojanoff, “Review of the technology for the manufacturing of large-format DCG holograms for technical applications,” Proc. SPIE 3011, 267–278 (1997).
[CrossRef]

Prog. Photovolt. Res. Appl. (2)

M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995).
[CrossRef]

M. A. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: analytical solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002).
[CrossRef]

Sol. Energy Mater. (1)

J. Jannson, T. Jannson, and K. H. Yu, “Solar control tunable Lippmann holowindows,” Sol. Energy Mater. 14(3-5), 289–297 (1986).
[CrossRef]

Sol. Energy Mater. Sol. Cells (1)

M. Peters, J. C. Goldschmidt, T. Kirchartz, and B. Bläsi, “The photonic light trap—Improved light trapping in solar cells by angularly selective filters,” Sol. Energy Mater. Sol. Cells 93(10), 1721–1727 (2009).
[CrossRef]

Other (1)

J. C. Miñano, “Optical confinement in photovoltaics,” Physical Limitations to the Photovoltaic Solar Energy Conversion (Hilger, 1990).

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Figures (10)

Fig. 1
Fig. 1

Typical light-trapping structure. A DCG holographic filter is included in a regular PV encapsulation. The escape cone in air has half-angle of θ a and the corresponding half-angle in the encapsulation medium is θ a ' .

Fig. 2
Fig. 2

Optical transmittance of an ideal Bragg light-trapping filter: (a) the high reflection spectral bands at different ray angles in air; (b) diagram of ray transmission and reflection.

Fig. 3
Fig. 3

Exposure geometry for reflection DCG holographic filter.

Fig. 4
Fig. 4

Measured specular transmittance of an experimental DCG filter at normal incidence.

Fig. 5
Fig. 5

Measured (blue) and simulated (red) diffraction efficiency characteristics.

Fig. 6
Fig. 6

Simulated diffraction efficiency for a range of angle of incidence and wavelength. The angle of incidence is evaluated in the grating medium (n = 1.53). Parameters used for the simulation are listed in Table 2.

Fig. 7
Fig. 7

Absorption enhancement factor calculated numerically using DE properties shown in Fig. 6.

Fig. 8
Fig. 8

Simulated absorptance for silicon solar cells with thickness of 50µm (left) and 10µm (right).

Fig. 9
Fig. 9

The total carrier generation rate for a 10 µm thick specular thin-film silicon PV cell, cell with Lambertian diffuser and with both diffuser and holographic filter.

Fig. 10
Fig. 10

Simulated IV curves for 10µm and 50µm Si PV cells with different light trapping configurations.

Tables (3)

Tables Icon

Table 1 DCG Development Procedure

Tables Icon

Table 2 Best-Fit Parameters for the Experimental DCG Holographic Filter

Tables Icon

Table 3 Parameters of Thin-Film Silicon Solar Cell used in PC-1D Simulation

Equations (14)

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

λ p ( θ ) = 2 Λ ( n 2 sin 2 θ )
n 1 (z)= n 1 (d)Δ n 1 (1 z d ) r
Λ(z)=Λ(0)ΔΛ ( z d ) s
k= 2T(0°,λ) 0 π/2 T(θ,λ) cosθsinθdθ
A(λ)= z=0 d g(λ,z)dz
g 0 (λ,z)=α(λ)( e α(λ)z + e α(λ)(z2d) )
A 0 (λ)=1 e 2α(λ)d
g 1 (λ,z)=2α(λ) E i 2 (α(λ)z)+E i 2 (α(λ)(2dz)) 1 t cell [1 t diffuser (λ)]
t cell (λ)= 1α(λ)2d e α(λ)2d + [α(λ)2d] 2 Ei(α(λ)2d)
A 1 (λ)= 1 t cell (λ) 1 t cell (λ)[1 t diffuser (λ)]
g 2 (λ,z)=2α(λ) E i 2 (α(λ)z)+E i 2 (α(λ)(2dz)) 1 t cell (1 t diffuser,filter )
A 2 (λ)= 1 t cell (λ) 1 t cell (λ)[1 t diffuser,filter (λ)]
t diffuser,filter (λ)= 0 π/2 [1DE(λ,θ)]sinθcosθdθ 0 π/2 sinθcosθdθ
G(z)= λ=400nm 1200nm N p,AM1.5 (λ)g(λ,z)dλ

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