Abstract

Efficiency of ultrathin flexible solar photovoltaic silicon microcell arrays can be significantly improved using nonimaging solar concentrators. A fluorophore is introduced to match the solar spectrum and the low-reflectivity wavelength range of Si, reduce the escape losses, and allow the nontracking operation. In this paper we optimize our solar concentrators using a luminescent/nonluminescent photon transport model. Key modeling results are compared quantitatively to experiments and are in good agreement with the latter. Our solar concentrator performance is not limited by the dye self-absorption. Bending deformations of the flexible solar collectors do not result in their indirect gain degradation compared to flat solar concentrators with the same projected area.

© 2011 Optical Society of America

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    [CrossRef]
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2010 (1)

2008 (2)

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef] [PubMed]

2004 (1)

A. A. Earp, G. B. Smith, P. D. Swift, and J. Franklin, “Maximising the light output of a luminescent solar concentrator,” Solar Energy 76, 655–667 (2004).
[CrossRef]

2001 (1)

T. Bierhoff, A. Wallrabenstein, A. Himmler, E. Griese, and G. Mrozynski, “Ray tracing technique and its verification for the analysis of highly multimode optical waveguides with rough surfaces,” IEEE Trans. Magn. 37, 3307–3310 (2001).
[CrossRef]

1984 (2)

V. Wittwer, W. Stahl, and A. Goetzberger, “Fluorescent planar concentrators,” Sol. Energy Mater. 11, 187–197 (1984).
[CrossRef]

G. Smestad and P. Hamill, “Concentration of solar radiation by white backed photovoltaic panels,” Appl. Opt. 23, 4394–4402 (1984).
[CrossRef] [PubMed]

1983 (1)

1979 (1)

1977 (1)

A. Goetzberger and W. Greubel, “Solar energy conversion with fluorescent collectors,” Appl. Phys. 14, 123–139 (1977).
[CrossRef]

Ahn, B. Y.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Baca, A. J.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Baldo, M. A.

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef] [PubMed]

Batchelder, J. S.

Bierhoff, T.

T. Bierhoff, A. Wallrabenstein, A. Himmler, E. Griese, and G. Mrozynski, “Ray tracing technique and its verification for the analysis of highly multimode optical waveguides with rough surfaces,” IEEE Trans. Magn. 37, 3307–3310 (2001).
[CrossRef]

T. Bierhoff, E. Griese, and G. Mrozynski, “An efficient Monte Carlo based ray tracing technique for the characterization of highly multimode dielectric waveguides with rough surfaces,” in Proceedings of the 30th European Microwave Conference, 2000, Paris, France, Vol.  1, (Horizon House, 2000), pp. 379–382.

Buslenko, N. P.

N. P. Buslenko, D. I. Golenko, Y. A. Shreider, I. M. Sobol, and V. G. Sragovich, The Monte Carlo Method. The Method of Statistical Trials, Y.A.Shreider, ed. (Pergamon, 1966).

Currie, M. J.

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef] [PubMed]

Cusso, F.

Duoss, E. B.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Earp, A. A.

A. A. Earp, G. B. Smith, P. D. Swift, and J. Franklin, “Maximising the light output of a luminescent solar concentrator,” Solar Energy 76, 655–667 (2004).
[CrossRef]

Elvikis, P.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Ferreira, P. M.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Franklin, J.

A. A. Earp, G. B. Smith, P. D. Swift, and J. Franklin, “Maximising the light output of a luminescent solar concentrator,” Solar Energy 76, 655–667 (2004).
[CrossRef]

Geddes, J. B.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Goetzberger, A.

V. Wittwer, W. Stahl, and A. Goetzberger, “Fluorescent planar concentrators,” Sol. Energy Mater. 11, 187–197 (1984).
[CrossRef]

A. Goetzberger and W. Greubel, “Solar energy conversion with fluorescent collectors,” Appl. Phys. 14, 123–139 (1977).
[CrossRef]

Goffri, S.

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef] [PubMed]

Golenko, D. I.

N. P. Buslenko, D. I. Golenko, Y. A. Shreider, I. M. Sobol, and V. G. Sragovich, The Monte Carlo Method. The Method of Statistical Trials, Y.A.Shreider, ed. (Pergamon, 1966).

Greubel, W.

A. Goetzberger and W. Greubel, “Solar energy conversion with fluorescent collectors,” Appl. Phys. 14, 123–139 (1977).
[CrossRef]

Griese, E.

T. Bierhoff, A. Wallrabenstein, A. Himmler, E. Griese, and G. Mrozynski, “Ray tracing technique and its verification for the analysis of highly multimode optical waveguides with rough surfaces,” IEEE Trans. Magn. 37, 3307–3310 (2001).
[CrossRef]

T. Bierhoff, E. Griese, and G. Mrozynski, “An efficient Monte Carlo based ray tracing technique for the characterization of highly multimode dielectric waveguides with rough surfaces,” in Proceedings of the 30th European Microwave Conference, 2000, Paris, France, Vol.  1, (Horizon House, 2000), pp. 379–382.

Hamill, P.

Heidel, T. D.

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef] [PubMed]

Himmler, A.

T. Bierhoff, A. Wallrabenstein, A. Himmler, E. Griese, and G. Mrozynski, “Ray tracing technique and its verification for the analysis of highly multimode optical waveguides with rough surfaces,” IEEE Trans. Magn. 37, 3307–3310 (2001).
[CrossRef]

Huang, Y.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Jaque, F.

Johnson, H. T.

J. Yoon, L. Li, A. V. Semichaevsky, H. T. Johnson, R. Nuzzo, and J. A. Rogers, “Flexible luminescent concentrator photovoltaics based on sparse, embedded arrays of microscale silicon solar cells,” Nat. Comm. (in press).

Jones, A. C.

Kim, R. H.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Kim, T.-H.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Lewis, J. A.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Li, L.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

J. Yoon, L. Li, A. V. Semichaevsky, H. T. Johnson, R. Nuzzo, and J. A. Rogers, “Flexible luminescent concentrator photovoltaics based on sparse, embedded arrays of microscale silicon solar cells,” Nat. Comm. (in press).

Lifante, G.

Mapel, J. K.

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef] [PubMed]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides(Academic, 1991).

Meseguer, F.

Motala, M. J.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Moudam, O.

Mrozynski, G.

T. Bierhoff, A. Wallrabenstein, A. Himmler, E. Griese, and G. Mrozynski, “Ray tracing technique and its verification for the analysis of highly multimode optical waveguides with rough surfaces,” IEEE Trans. Magn. 37, 3307–3310 (2001).
[CrossRef]

T. Bierhoff, E. Griese, and G. Mrozynski, “An efficient Monte Carlo based ray tracing technique for the characterization of highly multimode dielectric waveguides with rough surfaces,” in Proceedings of the 30th European Microwave Conference, 2000, Paris, France, Vol.  1, (Horizon House, 2000), pp. 379–382.

Nuzzo, R.

J. Yoon, L. Li, A. V. Semichaevsky, H. T. Johnson, R. Nuzzo, and J. A. Rogers, “Flexible luminescent concentrator photovoltaics based on sparse, embedded arrays of microscale silicon solar cells,” Nat. Comm. (in press).

Nuzzo, R. G.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Park, S.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Richards, B. S.

Robertson, N.

Rockett, A.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Rogers, J. A.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

J. Yoon, L. Li, A. V. Semichaevsky, H. T. Johnson, R. Nuzzo, and J. A. Rogers, “Flexible luminescent concentrator photovoltaics based on sparse, embedded arrays of microscale silicon solar cells,” Nat. Comm. (in press).

Rowan, B. C.

Semichaevsky, A. V.

J. Yoon, L. Li, A. V. Semichaevsky, H. T. Johnson, R. Nuzzo, and J. A. Rogers, “Flexible luminescent concentrator photovoltaics based on sparse, embedded arrays of microscale silicon solar cells,” Nat. Comm. (in press).

Shreider, Y. A.

N. P. Buslenko, D. I. Golenko, Y. A. Shreider, I. M. Sobol, and V. G. Sragovich, The Monte Carlo Method. The Method of Statistical Trials, Y.A.Shreider, ed. (Pergamon, 1966).

Smestad, G.

Smith, G. B.

A. A. Earp, G. B. Smith, P. D. Swift, and J. Franklin, “Maximising the light output of a luminescent solar concentrator,” Solar Energy 76, 655–667 (2004).
[CrossRef]

Sobol, I. M.

N. P. Buslenko, D. I. Golenko, Y. A. Shreider, I. M. Sobol, and V. G. Sragovich, The Monte Carlo Method. The Method of Statistical Trials, Y.A.Shreider, ed. (Pergamon, 1966).

Sragovich, V. G.

N. P. Buslenko, D. I. Golenko, Y. A. Shreider, I. M. Sobol, and V. G. Sragovich, The Monte Carlo Method. The Method of Statistical Trials, Y.A.Shreider, ed. (Pergamon, 1966).

Stahl, W.

V. Wittwer, W. Stahl, and A. Goetzberger, “Fluorescent planar concentrators,” Sol. Energy Mater. 11, 187–197 (1984).
[CrossRef]

Swift, P. D.

A. A. Earp, G. B. Smith, P. D. Swift, and J. Franklin, “Maximising the light output of a luminescent solar concentrator,” Solar Energy 76, 655–667 (2004).
[CrossRef]

Wallrabenstein, A.

T. Bierhoff, A. Wallrabenstein, A. Himmler, E. Griese, and G. Mrozynski, “Ray tracing technique and its verification for the analysis of highly multimode optical waveguides with rough surfaces,” IEEE Trans. Magn. 37, 3307–3310 (2001).
[CrossRef]

Wang, S.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Wilson, L. R.

Wittwer, V.

V. Wittwer, W. Stahl, and A. Goetzberger, “Fluorescent planar concentrators,” Sol. Energy Mater. 11, 187–197 (1984).
[CrossRef]

Xiao, J.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Yoon, J.

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

J. Yoon, L. Li, A. V. Semichaevsky, H. T. Johnson, R. Nuzzo, and J. A. Rogers, “Flexible luminescent concentrator photovoltaics based on sparse, embedded arrays of microscale silicon solar cells,” Nat. Comm. (in press).

Appl. Opt. (4)

Appl. Phys. (1)

A. Goetzberger and W. Greubel, “Solar energy conversion with fluorescent collectors,” Appl. Phys. 14, 123–139 (1977).
[CrossRef]

IEEE Trans. Magn. (1)

T. Bierhoff, A. Wallrabenstein, A. Himmler, E. Griese, and G. Mrozynski, “Ray tracing technique and its verification for the analysis of highly multimode optical waveguides with rough surfaces,” IEEE Trans. Magn. 37, 3307–3310 (2001).
[CrossRef]

Nat. Mater. (1)

J. Yoon, A. J. Baca, S. Park, P. Elvikis, J. B. Geddes, L. Li, R. H. Kim, J. Xiao, S. Wang, T.-H. Kim, M. J. Motala, B. Y. Ahn, E. B. Duoss, J. A. Lewis, R. G. Nuzzo, P. M. Ferreira, Y. Huang, A. Rockett, and J. A. Rogers, “Ultrathin silicon solar microcells for semitransparent, mechanically flexible and microconcentrator module designs,” Nat. Mater. 7, 907–915 (2008).
[CrossRef] [PubMed]

Science (1)

M. J. Currie, J. K. Mapel, T. D. Heidel, S. Goffri, and M. A. Baldo, “High-efficiency organic solar concentrators for photovoltaics,” Science 321, 226–228 (2008).
[CrossRef] [PubMed]

Sol. Energy Mater. (1)

V. Wittwer, W. Stahl, and A. Goetzberger, “Fluorescent planar concentrators,” Sol. Energy Mater. 11, 187–197 (1984).
[CrossRef]

Solar Energy (1)

A. A. Earp, G. B. Smith, P. D. Swift, and J. Franklin, “Maximising the light output of a luminescent solar concentrator,” Solar Energy 76, 655–667 (2004).
[CrossRef]

Other (7)

D. Marcuse, Theory of Dielectric Optical Waveguides(Academic, 1991).

T. Bierhoff, E. Griese, and G. Mrozynski, “An efficient Monte Carlo based ray tracing technique for the characterization of highly multimode dielectric waveguides with rough surfaces,” in Proceedings of the 30th European Microwave Conference, 2000, Paris, France, Vol.  1, (Horizon House, 2000), pp. 379–382.

Norland Optical Adhesive 61, https://www.norlandprod.com/adhesives/NOA%2061.html.

ASTM G173-03, http://rredc.nrel.gov/solar/spectra/am1.5/.

N. P. Buslenko, D. I. Golenko, Y. A. Shreider, I. M. Sobol, and V. G. Sragovich, The Monte Carlo Method. The Method of Statistical Trials, Y.A.Shreider, ed. (Pergamon, 1966).

Virginia Semiconductor, Inc., Optical properties of silicon(2004).

J. Yoon, L. Li, A. V. Semichaevsky, H. T. Johnson, R. Nuzzo, and J. A. Rogers, “Flexible luminescent concentrator photovoltaics based on sparse, embedded arrays of microscale silicon solar cells,” Nat. Comm. (in press).

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Figures (7)

Fig. 1
Fig. 1

Cross section of the solar concentrator for ultrathin Si microcells.

Fig. 2
Fig. 2

Optical properties. (a) Si normal reflectance in NOA and 15 μm Si slab normalized absorbance, Si properties from [13], (b) absorption and emission spectra for DCM.

Fig. 3
Fig. 3

Indirect gain (a) as a function of the microcell fill factor and microcell width, predicted for with a nonluminescent concentrator, t = 15 μm , a = 1000 μm (glass substrate), (b) predicted for luminescent concentrators with DCM dye (specular, R 0 = 0.98 , and diffuse reflectors, R 0 = 0.93 ), W = 50 μm , a = 1000 μm (glass substrate), (c) measured for luminescent concentrators with DCM dye (specular, R 0 = 0.98 , and diffuse reflectors, R 0 = 0.93 ), W = 50 μm , a = 1000 μm (glass substrate), as in [15].

Fig. 4
Fig. 4

(a) Dependence of the indirect gain on the distance between the microcells and the backside reflector for the nonluminescent and luminescent solar concentrators ( W = 50 μm , microcell fill factor is 0.11). The optimal value of an a / W is approximately 10. (b) Effect of microcell thickness on the light absorption relative to a very thick Si slab, in the presence of the diffuse BSR, with a / W = 20 , W = 50 μm , and constant microcell fill factor = 0.126 . In both cases, glass substrates are assumed.

Fig. 5
Fig. 5

Indirect gain of a Si microcell array with a nonluminescent concentrator as a function of the microcell fill factor and microcell thickness. W = 50 μm , a = 1000 μm , glass substrate, ideal Lambertian reflector.

Fig. 6
Fig. 6

Indirect gain of a deformed Si microcell array, W = 50 μm , s = 100 μm , a = 30 μm with luminescent and nonluminescent concentrators, specular reflector, R = 0.98 , as a function of the bending radius normalized to the width of substrate. Curves labeled “projected area” show indirect gains calculated with the normalization to a flat system with the same projected area.

Fig. 7
Fig. 7

Indirect gain of a microcell array with and without ideal AR surfaces as a function of separation between microcells, W = 50 μm , a = 1000 μm , glass substrate, luminescent solar concentrator, specular reflector, and R 0 = 0.98 .

Equations (15)

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f TIR , n l = 1 π π π θ TIR π / 2 cos θ sin θ d θ d ϕ ,
f TIR , l = π π θ TIR π / 2 1 4 π sin θ d θ d ϕ + 1 2 π π π θ TIR π / 2 cos θ sin θ d θ d ϕ .
P in = A S ( λ ) d λ ,
η = P out P in ,
P out = q V oc FF h c 0 λ g , Si η q ( λ ) ( A exp Φ 0 ( r , λ ) d A + A ind Φ ind ( r , λ ) d A ) λ d λ ,
k Φ = 0 λ g { A exp Φ 0 ( r , λ ) d A + A ind Φ ind ( r , λ ) d A } d λ A Φ 0 ( λ ) d λ ,
k Φ , m = h c 0 λ g { i = 1 N A exp Φ 0 , i ( r , λ ) d A + A ind Φ ind , i ( r , λ ) d A } d λ 0 λ g { A exp S ( λ ) ( 1 R ( λ ) ) } λ d λ ,
F θ ( λ ) = F θ 0 ( λ , ϕ ) exp ( α ( λ ) d ( θ , ϕ ) ) ϕ ,
R rp ( θ , ϕ ) = 1 2 ( R TM ( θ , ϕ ) + R TE ( θ , ϕ ) ) ,
T rp ( θ , ϕ ) = 1 2 ( T TM ( θ , ϕ ) + T TE ( θ , ϕ ) ) ,
F θ ( λ ) = F θ ( λ ) R ( λ , θ , θ , ϕ ) ϕ ,
Φ abs , k = 1 h c 0 λ g i = 1 M n = 1 N F 0 , i ( λ , θ n , ϕ ) ( 1 exp ( α ( λ ) d ( θ n , ϕ ) ) ) ϕ λ d λ ,
d F l ( x , λ ) d r i = α ( λ ) F l ( r i , λ ) + η q ( λ ) ε 0 ( λ ) 0 λ α ( λ ) ( F l ( r j , λ ) + F n l ( r j , λ ) ) λ d λ / 0 λ λ d λ ,
d F n l ( r i , λ ) d r i = α ( λ ) F n l ( r i , λ ) ,
F l ( λ , θ , ϕ , L ( θ ) ) = η q ε 0 ( λ ) exp ( α ( λ ) Δ L ( θ , ϕ ) ) × ( 1 exp ( α ( λ ) Δ L ( θ ) ) ) ( F l ( λ , θ , ϕ , Δ L ( θ ) ) + F n l ( λ , θ , ϕ , Δ L ( θ ) ) ) λ d λ λ d λ , λ < λ ,

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