Abstract

A basic upper bound for the efficiency of solar power conversion (generally, from any blackbody source) is derived, generalizing the Landsberg limit to arbitrary solar and sky view factors (e.g., arbitrary concentration or angular confinement), and to coherence-limited devices such as rectifying aperture antennas.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. T. Landsberg and G. Tonge, J. Phys. A 12, 551 (1979).
    [CrossRef]
  2. P. T. Landsberg and G. Tonge, J. Appl. Phys. 51, R1 (1980).
    [CrossRef]
  3. B. Andresen, Angew. Chem. Int. Ed. Engl. 50, 2690 (2011).
    [CrossRef]
  4. J. M. Gordon, Am. J. Phys. 57, 1136 (1989).
    [CrossRef]
  5. J. M. Gordon, Am. J. Phys. 61, 821 (1993).
    [CrossRef]
  6. R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).
  7. R. Petela, J. Heat Transfer 86, 187 (1964).
    [CrossRef]
  8. J. Singh and S. P. Foo, J. Appl. Phys. 59, 1678 (1986).
    [CrossRef]
  9. A. de Vos, P. T. Landsberg, P. Baruch, and J. E. Parrott, J. Appl. Phys. 74, 3631 (1993).
    [CrossRef]
  10. P. Würfel, Physica E 14, 18 (2002).
    [CrossRef]
  11. P. T. Landsberg and P. Baruch, J. Phys. A 22, 1911 (1989).
    [CrossRef]
  12. A. Marti and G. L. Araújo, Sol. Energy Mater. Sol. Cells 43, 203 (1996).
    [CrossRef]
  13. M. A. Green, Third Generation Photovoltaics (Springer, 2006).
  14. M. J. Blanco, J. D. Martin, and D. C. Alarcón-Padilla, Sol. Energy 76, 683 (2004).
    [CrossRef]
  15. R. L. Bailey, J. Eng. Power 94, 73 (1972).
    [CrossRef]
  16. C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
    [CrossRef]
  17. M. Peters, J. C. Goldschmidt, and B. Bläsi, Sol. Energy Mater. Sol. Cells 94, 1393 (2010).
    [CrossRef]
  18. H. Mashaal and J. M. Gordon, Opt. Lett. 36, 900 (2011).
    [CrossRef]
  19. This 1D analysis relates to dual-polarization coherent conversion, e.g., an antenna with a separate feed for each polarization, each connected to its own converter. This is why α=π2(kB)2/(3h) in Eq. (15) is twice the single-polarization value often cited for 1D blackbody radiation.
  20. H. Ries, Appl. Phys. B 32, 153 (1983).
    [CrossRef]
  21. M. A. Green, Nano Lett. 12, 5985 (2012).
    [CrossRef]
  22. Y. Takeda and Y. Motohiro, R&E Rev. Toyota CRDL 43, 77 (2012).
  23. L. C. Hirst and N. J. Ekins-Daukes, Prog. Photovoltaics 19, 286 (2011).
    [CrossRef]
  24. S. Grover, S. Joshi, and G. Moddel, J. Phys. D 46, 135106 (2013).
    [CrossRef]
  25. R. Corkish, M. A. Green, T. Puzzer, and T. Humphrey, in Proceedings of 3rd World Conference on Photovoltaic Energy Conversion (2003), Vol. 3, p. 2682.
  26. P. Bodan, J. Apostolos, W. Mouyos, B. McMahon, P. Gili, and M. Feng, in Clean Technology and Sustainable Industries Conference (2014), pp. 88–91.
  27. Z. Zhu, S. Joshi, S. Grover, and G. Moddel, J. Phys. D 46, 185101 (2013).
    [CrossRef]

2013 (2)

S. Grover, S. Joshi, and G. Moddel, J. Phys. D 46, 135106 (2013).
[CrossRef]

Z. Zhu, S. Joshi, S. Grover, and G. Moddel, J. Phys. D 46, 185101 (2013).
[CrossRef]

2012 (2)

M. A. Green, Nano Lett. 12, 5985 (2012).
[CrossRef]

Y. Takeda and Y. Motohiro, R&E Rev. Toyota CRDL 43, 77 (2012).

2011 (3)

L. C. Hirst and N. J. Ekins-Daukes, Prog. Photovoltaics 19, 286 (2011).
[CrossRef]

H. Mashaal and J. M. Gordon, Opt. Lett. 36, 900 (2011).
[CrossRef]

B. Andresen, Angew. Chem. Int. Ed. Engl. 50, 2690 (2011).
[CrossRef]

2010 (1)

M. Peters, J. C. Goldschmidt, and B. Bläsi, Sol. Energy Mater. Sol. Cells 94, 1393 (2010).
[CrossRef]

2008 (1)

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

2004 (1)

M. J. Blanco, J. D. Martin, and D. C. Alarcón-Padilla, Sol. Energy 76, 683 (2004).
[CrossRef]

2002 (1)

P. Würfel, Physica E 14, 18 (2002).
[CrossRef]

1996 (1)

A. Marti and G. L. Araújo, Sol. Energy Mater. Sol. Cells 43, 203 (1996).
[CrossRef]

1993 (2)

J. M. Gordon, Am. J. Phys. 61, 821 (1993).
[CrossRef]

A. de Vos, P. T. Landsberg, P. Baruch, and J. E. Parrott, J. Appl. Phys. 74, 3631 (1993).
[CrossRef]

1989 (2)

J. M. Gordon, Am. J. Phys. 57, 1136 (1989).
[CrossRef]

P. T. Landsberg and P. Baruch, J. Phys. A 22, 1911 (1989).
[CrossRef]

1986 (1)

J. Singh and S. P. Foo, J. Appl. Phys. 59, 1678 (1986).
[CrossRef]

1983 (1)

H. Ries, Appl. Phys. B 32, 153 (1983).
[CrossRef]

1980 (1)

P. T. Landsberg and G. Tonge, J. Appl. Phys. 51, R1 (1980).
[CrossRef]

1979 (1)

P. T. Landsberg and G. Tonge, J. Phys. A 12, 551 (1979).
[CrossRef]

1972 (1)

R. L. Bailey, J. Eng. Power 94, 73 (1972).
[CrossRef]

1964 (1)

R. Petela, J. Heat Transfer 86, 187 (1964).
[CrossRef]

Alarcón-Padilla, D. C.

M. J. Blanco, J. D. Martin, and D. C. Alarcón-Padilla, Sol. Energy 76, 683 (2004).
[CrossRef]

Andresen, B.

B. Andresen, Angew. Chem. Int. Ed. Engl. 50, 2690 (2011).
[CrossRef]

Apostolos, J.

P. Bodan, J. Apostolos, W. Mouyos, B. McMahon, P. Gili, and M. Feng, in Clean Technology and Sustainable Industries Conference (2014), pp. 88–91.

Araújo, G. L.

A. Marti and G. L. Araújo, Sol. Energy Mater. Sol. Cells 43, 203 (1996).
[CrossRef]

Bailey, R. L.

R. L. Bailey, J. Eng. Power 94, 73 (1972).
[CrossRef]

Baruch, P.

A. de Vos, P. T. Landsberg, P. Baruch, and J. E. Parrott, J. Appl. Phys. 74, 3631 (1993).
[CrossRef]

P. T. Landsberg and P. Baruch, J. Phys. A 22, 1911 (1989).
[CrossRef]

Benítez, P.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

Blanco, M. J.

M. J. Blanco, J. D. Martin, and D. C. Alarcón-Padilla, Sol. Energy 76, 683 (2004).
[CrossRef]

Bläsi, B.

M. Peters, J. C. Goldschmidt, and B. Bläsi, Sol. Energy Mater. Sol. Cells 94, 1393 (2010).
[CrossRef]

Bodan, P.

P. Bodan, J. Apostolos, W. Mouyos, B. McMahon, P. Gili, and M. Feng, in Clean Technology and Sustainable Industries Conference (2014), pp. 88–91.

Corkish, R.

R. Corkish, M. A. Green, T. Puzzer, and T. Humphrey, in Proceedings of 3rd World Conference on Photovoltaic Energy Conversion (2003), Vol. 3, p. 2682.

de Vos, A.

A. de Vos, P. T. Landsberg, P. Baruch, and J. E. Parrott, J. Appl. Phys. 74, 3631 (1993).
[CrossRef]

Ekins-Daukes, N. J.

L. C. Hirst and N. J. Ekins-Daukes, Prog. Photovoltaics 19, 286 (2011).
[CrossRef]

Fahr, S.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

Feng, M.

P. Bodan, J. Apostolos, W. Mouyos, B. McMahon, P. Gili, and M. Feng, in Clean Technology and Sustainable Industries Conference (2014), pp. 88–91.

Foo, S. P.

J. Singh and S. P. Foo, J. Appl. Phys. 59, 1678 (1986).
[CrossRef]

Gili, P.

P. Bodan, J. Apostolos, W. Mouyos, B. McMahon, P. Gili, and M. Feng, in Clean Technology and Sustainable Industries Conference (2014), pp. 88–91.

Goldschmidt, J. C.

M. Peters, J. C. Goldschmidt, and B. Bläsi, Sol. Energy Mater. Sol. Cells 94, 1393 (2010).
[CrossRef]

Gombert, A.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

Gordon, J. M.

H. Mashaal and J. M. Gordon, Opt. Lett. 36, 900 (2011).
[CrossRef]

J. M. Gordon, Am. J. Phys. 61, 821 (1993).
[CrossRef]

J. M. Gordon, Am. J. Phys. 57, 1136 (1989).
[CrossRef]

Green, M. A.

M. A. Green, Nano Lett. 12, 5985 (2012).
[CrossRef]

R. Corkish, M. A. Green, T. Puzzer, and T. Humphrey, in Proceedings of 3rd World Conference on Photovoltaic Energy Conversion (2003), Vol. 3, p. 2682.

M. A. Green, Third Generation Photovoltaics (Springer, 2006).

Grover, S.

S. Grover, S. Joshi, and G. Moddel, J. Phys. D 46, 135106 (2013).
[CrossRef]

Z. Zhu, S. Joshi, S. Grover, and G. Moddel, J. Phys. D 46, 185101 (2013).
[CrossRef]

Hirst, L. C.

L. C. Hirst and N. J. Ekins-Daukes, Prog. Photovoltaics 19, 286 (2011).
[CrossRef]

Humphrey, T.

R. Corkish, M. A. Green, T. Puzzer, and T. Humphrey, in Proceedings of 3rd World Conference on Photovoltaic Energy Conversion (2003), Vol. 3, p. 2682.

Joshi, S.

S. Grover, S. Joshi, and G. Moddel, J. Phys. D 46, 135106 (2013).
[CrossRef]

Z. Zhu, S. Joshi, S. Grover, and G. Moddel, J. Phys. D 46, 185101 (2013).
[CrossRef]

Kirchartz, T.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

Landsberg, P. T.

A. de Vos, P. T. Landsberg, P. Baruch, and J. E. Parrott, J. Appl. Phys. 74, 3631 (1993).
[CrossRef]

P. T. Landsberg and P. Baruch, J. Phys. A 22, 1911 (1989).
[CrossRef]

P. T. Landsberg and G. Tonge, J. Appl. Phys. 51, R1 (1980).
[CrossRef]

P. T. Landsberg and G. Tonge, J. Phys. A 12, 551 (1979).
[CrossRef]

Lederer, F.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

Marti, A.

A. Marti and G. L. Araújo, Sol. Energy Mater. Sol. Cells 43, 203 (1996).
[CrossRef]

Martin, J. D.

M. J. Blanco, J. D. Martin, and D. C. Alarcón-Padilla, Sol. Energy 76, 683 (2004).
[CrossRef]

Mashaal, H.

McMahon, B.

P. Bodan, J. Apostolos, W. Mouyos, B. McMahon, P. Gili, and M. Feng, in Clean Technology and Sustainable Industries Conference (2014), pp. 88–91.

Miñano, J. C.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

Moddel, G.

S. Grover, S. Joshi, and G. Moddel, J. Phys. D 46, 135106 (2013).
[CrossRef]

Z. Zhu, S. Joshi, S. Grover, and G. Moddel, J. Phys. D 46, 185101 (2013).
[CrossRef]

Motohiro, Y.

Y. Takeda and Y. Motohiro, R&E Rev. Toyota CRDL 43, 77 (2012).

Mouyos, W.

P. Bodan, J. Apostolos, W. Mouyos, B. McMahon, P. Gili, and M. Feng, in Clean Technology and Sustainable Industries Conference (2014), pp. 88–91.

Parrott, J. E.

A. de Vos, P. T. Landsberg, P. Baruch, and J. E. Parrott, J. Appl. Phys. 74, 3631 (1993).
[CrossRef]

Petela, R.

R. Petela, J. Heat Transfer 86, 187 (1964).
[CrossRef]

Peters, M.

M. Peters, J. C. Goldschmidt, and B. Bläsi, Sol. Energy Mater. Sol. Cells 94, 1393 (2010).
[CrossRef]

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

Puzzer, T.

R. Corkish, M. A. Green, T. Puzzer, and T. Humphrey, in Proceedings of 3rd World Conference on Photovoltaic Energy Conversion (2003), Vol. 3, p. 2682.

Rau, U.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

Ries, H.

H. Ries, Appl. Phys. B 32, 153 (1983).
[CrossRef]

Rockstuhl, C.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

Singh, J.

J. Singh and S. P. Foo, J. Appl. Phys. 59, 1678 (1986).
[CrossRef]

Takeda, Y.

Y. Takeda and Y. Motohiro, R&E Rev. Toyota CRDL 43, 77 (2012).

Tonge, G.

P. T. Landsberg and G. Tonge, J. Appl. Phys. 51, R1 (1980).
[CrossRef]

P. T. Landsberg and G. Tonge, J. Phys. A 12, 551 (1979).
[CrossRef]

Ulbrich, C.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

Üpping, J.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

Wehrspohn, R.

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

Winston, R.

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

Würfel, P.

P. Würfel, Physica E 14, 18 (2002).
[CrossRef]

Zhu, Z.

Z. Zhu, S. Joshi, S. Grover, and G. Moddel, J. Phys. D 46, 185101 (2013).
[CrossRef]

Am. J. Phys. (2)

J. M. Gordon, Am. J. Phys. 57, 1136 (1989).
[CrossRef]

J. M. Gordon, Am. J. Phys. 61, 821 (1993).
[CrossRef]

Angew. Chem. Int. Ed. Engl. (1)

B. Andresen, Angew. Chem. Int. Ed. Engl. 50, 2690 (2011).
[CrossRef]

Appl. Phys. B (1)

H. Ries, Appl. Phys. B 32, 153 (1983).
[CrossRef]

J. Appl. Phys. (3)

J. Singh and S. P. Foo, J. Appl. Phys. 59, 1678 (1986).
[CrossRef]

A. de Vos, P. T. Landsberg, P. Baruch, and J. E. Parrott, J. Appl. Phys. 74, 3631 (1993).
[CrossRef]

P. T. Landsberg and G. Tonge, J. Appl. Phys. 51, R1 (1980).
[CrossRef]

J. Eng. Power (1)

R. L. Bailey, J. Eng. Power 94, 73 (1972).
[CrossRef]

J. Heat Transfer (1)

R. Petela, J. Heat Transfer 86, 187 (1964).
[CrossRef]

J. Phys. A (2)

P. T. Landsberg and G. Tonge, J. Phys. A 12, 551 (1979).
[CrossRef]

P. T. Landsberg and P. Baruch, J. Phys. A 22, 1911 (1989).
[CrossRef]

J. Phys. D (2)

S. Grover, S. Joshi, and G. Moddel, J. Phys. D 46, 135106 (2013).
[CrossRef]

Z. Zhu, S. Joshi, S. Grover, and G. Moddel, J. Phys. D 46, 185101 (2013).
[CrossRef]

Nano Lett. (1)

M. A. Green, Nano Lett. 12, 5985 (2012).
[CrossRef]

Opt. Lett. (1)

Phys. Status Solidi A (1)

C. Ulbrich, S. Fahr, J. Üpping, M. Peters, T. Kirchartz, C. Rockstuhl, R. Wehrspohn, A. Gombert, F. Lederer, and U. Rau, Phys. Status Solidi A 205, 2831 (2008).
[CrossRef]

Physica E (1)

P. Würfel, Physica E 14, 18 (2002).
[CrossRef]

Prog. Photovoltaics (1)

L. C. Hirst and N. J. Ekins-Daukes, Prog. Photovoltaics 19, 286 (2011).
[CrossRef]

R&E Rev. Toyota CRDL (1)

Y. Takeda and Y. Motohiro, R&E Rev. Toyota CRDL 43, 77 (2012).

Sol. Energy (1)

M. J. Blanco, J. D. Martin, and D. C. Alarcón-Padilla, Sol. Energy 76, 683 (2004).
[CrossRef]

Sol. Energy Mater. Sol. Cells (2)

A. Marti and G. L. Araújo, Sol. Energy Mater. Sol. Cells 43, 203 (1996).
[CrossRef]

M. Peters, J. C. Goldschmidt, and B. Bläsi, Sol. Energy Mater. Sol. Cells 94, 1393 (2010).
[CrossRef]

Other (5)

This 1D analysis relates to dual-polarization coherent conversion, e.g., an antenna with a separate feed for each polarization, each connected to its own converter. This is why α=π2(kB)2/(3h) in Eq. (15) is twice the single-polarization value often cited for 1D blackbody radiation.

M. A. Green, Third Generation Photovoltaics (Springer, 2006).

R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics (Elsevier, 2005).

R. Corkish, M. A. Green, T. Puzzer, and T. Humphrey, in Proceedings of 3rd World Conference on Photovoltaic Energy Conversion (2003), Vol. 3, p. 2682.

P. Bodan, J. Apostolos, W. Mouyos, B. McMahon, P. Gili, and M. Feng, in Clean Technology and Sustainable Industries Conference (2014), pp. 88–91.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

System schematic. The converter is internally reversible. The energy exchange between the converter and the infinite cold reservoir at temperature Tc is reversible (isothermal). At the converter’s entry, the blackbody hot source at Ts subtends a view factor fs. fc is the view factor at the converter’s entry for incident radiation that can be collected by the converter with fsfc1. The view factor to the blackbody sky at Tsky is fcfs.

Fig. 2.
Fig. 2.

ηoverall (solid black curve) for solar conversion, as the product of ηconv (solid red curve) and ηcoherence (dotted blue curve), plotted against aperture radius R, with Th=5780K and Tc=300K. ηconv—which ηoverall approaches in the limit of small R—is bounded from above by the 3D limit of 0.93, and from below by the 1D limit of 0.90 (indicated by dashed horizontal lines).

Fig. 3.
Fig. 3.

Aperture radius as a function of normalized Ωaperture (relative to the hemisphere) for spectrum-integrated solar.

Equations (21)

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

ηL=143TcTh+13(TcTh)4.
W=QhQc.
Sh=Sc=Qc/TcorQc=TcSh.
Qh=Qfss+QfcfsskyQfcc.
Sh=Sfss+SfcfsskySfcc.
W=Qfss+QfcfsskyQfccTc(Sfss+SfcfsskySfcc).
W=QfssQfscTc(SfssSfsc)Wsource+QfcfsskyQfcfscTc(SfcfsskySfcfsc)Wsky.
ηconv=QfssQfscTc(SfssSfsc)Qfss.
Qfss=AfsσTh4,Qfsc=AfsσTc4Sfss=Afs43σTh3,Sfsc=Afs43σTc3.
ηoverallincoherent=143TCTH+13(TCTH),4
Qfss=0λ2B(λ,Th)ε(ksinθsR)dλ=ηcoherence(θs,R,Th)AfsσTh4Qfsc=0λ2B(λ,Tc)ε(ksinθsR)dλ=ηcoherence(θs,R,Tc)AfsσTc4whereB(λ,T)=2hc2λ5(ehckBTλ1)withε(ksinθsR)=1J02(ksinθsR)J12(ksinθsR).
ηcoherence=0λ2B(λ,Th)ε(ksinθsR)dλAfsσTh4.
dS=dQT=1T0dB(λ,T)dT·λ2ε(ksinθsR)dλS(θs,R,T)=0T1T·ddT[0B(λ,T)·λ2ε(ksinθsR)dλ]dT,
Sfss=0(0Th1T·dB(λ,T)dT·dT)·λ2·ε(ksinθsR)dλ,Sfsc=0(0Tc1T·dB(λ,T)dT·dT)·λ2·ε(ksinθsR)dλ.
Qfss=αTh2,Qfsc=αTc2,Sfss=2αTh,Sfsc=2αTc,
ηconvcoherent=(1TcTh)2.
AcoherentΩaperture=λ2.
Acoherent(λ)Ωs=λ2ε(ksinθsR).
Ωaperture(λ)=Ωsε(ksinθsR).
Ωaperture=0πB(λ,Th)σTh4·Ωsε(ksinθsR)dλ.
Ωaperture=απσT2R2,

Metrics