Abstract

Nontransparent contact fingers on the sun-facing side of solar cells represent optically dead regions which reduce the energy conversion per area. We consider two approaches for guiding the incident light around the contacts onto the active area. The first approach uses graded-index metamaterials designed by two-dimensional Schwarz–Christoffel conformal maps, and the second uses freeform surfaces designed by one-dimensional coordinate transformations of a point to an interval. We provide proof-of-principle demonstrators using direct laser writing of polymer structures on silicon wafers with opaque contacts. Freeform surfaces are amenable to mass fabrication and allow for complete recovery of the shadowing effect for all relevant incidence angles.

© 2015 Optical Society of America

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References

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  1. H. Booth, J. Laser Micro/Nanoeng. 5, 183 (2010).
    [Crossref]
  2. A. Meulenberg, J. Energy 1, 151 (1977).
    [Crossref]
  3. C. Vogeli and P. Nath, “Photovoltaic device with decreased gridline shading and method for its manufacture,” U.S. patent5, 110, 370 (May5, 1992).
  4. J. Schneider, M. Turek, M. Dyrba, I. Baumann, B. Koll, and T. Booz, Prog. Photovoltaics 22, 830 (2014).
    [Crossref]
  5. J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
    [Crossref]
  6. U. Leonhardt, Science 312, 1777 (2006).
    [Crossref]
  7. R. Schmied, J. C. Halimeh, and M. Wegener, Opt. Express 18, 24361 (2010).
    [Crossref]
  8. J. C. Halimeh and M. Wegener, Opt. Express 21, 9457 (2013).
    [Crossref]
  9. T. A. Driscoll and L. N. Trefethen, Schwarz-Christoffel Mapping (Cambridge University, 2002).
  10. N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
    [Crossref]
  11. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
    [Crossref]
  12. J. Fischer, T. Ergin, and M. Wegener, Opt. Lett. 36, 2059 (2011).
    [Crossref]

2014 (2)

J. Schneider, M. Turek, M. Dyrba, I. Baumann, B. Koll, and T. Booz, Prog. Photovoltaics 22, 830 (2014).
[Crossref]

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[Crossref]

2013 (1)

2011 (1)

2010 (3)

R. Schmied, J. C. Halimeh, and M. Wegener, Opt. Express 18, 24361 (2010).
[Crossref]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[Crossref]

H. Booth, J. Laser Micro/Nanoeng. 5, 183 (2010).
[Crossref]

2006 (2)

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[Crossref]

U. Leonhardt, Science 312, 1777 (2006).
[Crossref]

1977 (1)

A. Meulenberg, J. Energy 1, 151 (1977).
[Crossref]

Baumann, I.

J. Schneider, M. Turek, M. Dyrba, I. Baumann, B. Koll, and T. Booz, Prog. Photovoltaics 22, 830 (2014).
[Crossref]

Booth, H.

H. Booth, J. Laser Micro/Nanoeng. 5, 183 (2010).
[Crossref]

Booz, T.

J. Schneider, M. Turek, M. Dyrba, I. Baumann, B. Koll, and T. Booz, Prog. Photovoltaics 22, 830 (2014).
[Crossref]

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[Crossref]

Capasso, F.

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[Crossref]

Driscoll, T. A.

T. A. Driscoll and L. N. Trefethen, Schwarz-Christoffel Mapping (Cambridge University, 2002).

Dyrba, M.

J. Schneider, M. Turek, M. Dyrba, I. Baumann, B. Koll, and T. Booz, Prog. Photovoltaics 22, 830 (2014).
[Crossref]

Ergin, T.

J. Fischer, T. Ergin, and M. Wegener, Opt. Lett. 36, 2059 (2011).
[Crossref]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[Crossref]

Fischer, J.

Halimeh, J. C.

Koll, B.

J. Schneider, M. Turek, M. Dyrba, I. Baumann, B. Koll, and T. Booz, Prog. Photovoltaics 22, 830 (2014).
[Crossref]

Leonhardt, U.

U. Leonhardt, Science 312, 1777 (2006).
[Crossref]

Meulenberg, A.

A. Meulenberg, J. Energy 1, 151 (1977).
[Crossref]

Nath, P.

C. Vogeli and P. Nath, “Photovoltaic device with decreased gridline shading and method for its manufacture,” U.S. patent5, 110, 370 (May5, 1992).

Pendry, J. B.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[Crossref]

Schmied, R.

Schneider, J.

J. Schneider, M. Turek, M. Dyrba, I. Baumann, B. Koll, and T. Booz, Prog. Photovoltaics 22, 830 (2014).
[Crossref]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[Crossref]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[Crossref]

Stenger, N.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[Crossref]

Trefethen, L. N.

T. A. Driscoll and L. N. Trefethen, Schwarz-Christoffel Mapping (Cambridge University, 2002).

Turek, M.

J. Schneider, M. Turek, M. Dyrba, I. Baumann, B. Koll, and T. Booz, Prog. Photovoltaics 22, 830 (2014).
[Crossref]

Vogeli, C.

C. Vogeli and P. Nath, “Photovoltaic device with decreased gridline shading and method for its manufacture,” U.S. patent5, 110, 370 (May5, 1992).

Wegener, M.

Yu, N.

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[Crossref]

J. Energy (1)

A. Meulenberg, J. Energy 1, 151 (1977).
[Crossref]

J. Laser Micro/Nanoeng. (1)

H. Booth, J. Laser Micro/Nanoeng. 5, 183 (2010).
[Crossref]

Nat. Mater. (1)

N. Yu and F. Capasso, Nat. Mater. 13, 139 (2014).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Prog. Photovoltaics (1)

J. Schneider, M. Turek, M. Dyrba, I. Baumann, B. Koll, and T. Booz, Prog. Photovoltaics 22, 830 (2014).
[Crossref]

Science (3)

J. B. Pendry, D. Schurig, and D. R. Smith, Science 312, 1780 (2006).
[Crossref]

U. Leonhardt, Science 312, 1777 (2006).
[Crossref]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, Science 328, 337 (2010).
[Crossref]

Other (2)

T. A. Driscoll and L. N. Trefethen, Schwarz-Christoffel Mapping (Cambridge University, 2002).

C. Vogeli and P. Nath, “Photovoltaic device with decreased gridline shading and method for its manufacture,” U.S. patent5, 110, 370 (May5, 1992).

Supplementary Material (1)

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Figures (4)

Fig. 1.
Fig. 1.

Coordinate transformations enabling invisible contacts on solar cells. The elongated metal contact to be made invisible can be arbitrarily shaped within the black region. (a) Transformation of a point to a circle with diameter 2R1 leading to anisotropic magnetodielectric material distributions (white region). (b) Schwarz–Christoffel conformal map leading to an isotropic graded-index structure with n(x,y)[0,[ (color-coded). For the realization, we truncate the refractive index to the interval [1.0, 1.5] and fill the forbidden region (black) with full material (n=1.5).

Fig. 2.
Fig. 2.

One-dimensional linear coordinate transformation xx of a point to a finite interval with width 2R1 leading to an angle distribution α(x). This distribution can be realized by a freeform surface y(x) of a dielectric with constant refractive index, n, on top of the solar cell. The local surface inclination angle is denoted by β(x).

Fig. 3.
Fig. 3.

Electron micrographs of fabricated polymer structures (left) and measured detector signals with metal contact, with (red curve) and without (blue curve) invisibility structure on top (right). The detector signal, I, is normalized to the value far away from the contact, I0. (a) Graded-index structure following Fig. 1(b). (b) Freeform surface following Fig. 2, with y(0)=12μm, R1=12μm, and R2=100μm.

Fig. 4.
Fig. 4.

(a) Calculated relative improvement ζ=(NNref)/Nref due to the invisibility structure on top of the periodic arrangement of metal contacts with width w=R1/0.6 versus ray angle of incidence with respect to the surface normal, neglecting partial reflections. Here, N is the number of light rays hitting the silicon surface with invisibility structure and Nref is that without this structure. As an example, we assume 10% area coverage of the metal contacts, leading to a maximum possible relative improvement ζmax=0.1/0.911%. Graded-index structure as in Fig. 1(b) with polymer core (red curve), air core (gray curve), and transformed freeform surface (blue curve) as in Fig. 2 (with R2/w=5, y(0)/R1=1, and n=1.5). (b) Calculated average annual relative improvement due to the freeform surface, ζ, versus areal fraction covered by the contact (blue curve). The dashed curve represents the maximum possible relative improvement ζmax.

Equations (2)

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rr=R2R1R2r+R1,
x=R2R1R2x+R1,

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