Abstract

Diffractive optical structures for increasing the efficiency of crystalline silicon solar cells are discussed. As a consequence of the indirect band gap, light absorption becomes very ineffective near the band edge. This can be remedied by use of optimized diffraction gratings that lead to light trapping. We present blazed gratings that increase the optically effective cell thickness by approximately a factor of 5. In addition we present a wideband antireflection structure for glass that consists of a diffraction grating with a dielectric overcoat, which leads to an average reflection of less than 0.6% in the wavelength range between 300 and 2100 nm.

© 1995 Optical Society of America

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References

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  1. D. Strese, J. Schindler, “Kostendegression Photovoltaik: Fertigung multikristalliner Solarzellen und ihr Einsatz im Kraftwerksbereich,” Rep. 0328830A (Bundesminister für For-schung und Technik, Bonn, Germany, 1988). A short review can be found in Bild Wiss. (July 1988), p. 36.
  2. H. J. Hovel, Solar Cells, Vol. II of the Semiconductor and Semimetals Series (Academic, New York, 1975), p. 97.
  3. P. Campbell, M. A. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62, 243–249 (1987).
    [CrossRef]
  4. D. Redfield, “Multiple-pass thin film silicon solar cell,” Appl. Phys. Lett. 25, 647–648 (1974).
    [CrossRef]
  5. A. Goetzberger, “Optical confinement in thin Si solar cells by diffuse back reflectors,” in Proceedings of the Fifteenth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronic Engineers, New York, 1981), p. 867.
  6. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72, 899–907 (1982).
    [CrossRef]
  7. H. P. Herzig, M. T. Gale, H. W. Lehmann, R. Morf, “Diffractive components: computer generated elements,” in Perspectives for Parallel Optical Interconnects, P. H. Lalanne, P. Chavel, eds. (Springer, New York, 1993) Chap. 5, pp. 71–107.
    [CrossRef]
  8. R. H. Morf, “Exponentially convergent and numerically efficient solution of Maxwell’s equations for lamellar diffraction gratings,” J. Opt. Soc. Am. A (to be published).
  9. R. C. Enger, S. K. Case, “Optical elements with ultrahigh spatial-frequency surface corrugations,” Appl. Opt. 22, 3220–3228 (1983).
    [CrossRef] [PubMed]
  10. D. Raguin, G. M. Morris, “Antireflection structured surfaces for the infrared spectral region,” Appl. Opt. 32, 1154–1167 (1993).
    [CrossRef] [PubMed]
  11. D. Raguin, G. M. Morris, “Analysis of antireflection-structured surfaces with continuous one-dimensional surface profiles,” Appl. Opt. 32, 2582–2598 (1993).
    [CrossRef] [PubMed]
  12. T. K. Gaylord, W. E. Baird, M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. 25, 4562–4567 (1986).
    [CrossRef] [PubMed]
  13. E. N. Glytsis, T. K. Gaylord, “High-spatial frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 32, 4459–4470 (1992).
    [CrossRef]
  14. M. E. Motamedi, W. H. Southwell, W. J. Gunning, “Antireflection surfaces in silicon using binary optics technology,” Appl. Opt. 31, 4371–4376 (1992).
    [CrossRef] [PubMed]
  15. D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
    [CrossRef] [PubMed]
  16. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andreawartha, “The dielectric lamellar grating,” Opt. Acta 28, 413–428 (1981); “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
    [CrossRef]
  17. R. H. Morf, H. Kiess, “Submicron gratings for light trapping in silicon solar cells: a theoretical study,” in Proceedings of the Ninth International Conference on Photovoltaic Solar Energy, W. Palz, ed. (Commission of the European Communities, Brussels, Belgium, 1989), pp. 313–315.
  18. R. Morf, R. E. Kunz, “Dielectric filter optimization by simulated thermal annealing,” in Thin Film Technologies III, K. H. Guenther, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1019, 211–217 (1988).
  19. R. E. Kunz, J. Edlinger, B. J. Curtis, M. T. Gale, L. U. Kempen, H. Rudigier, H. Schütz, “Grating couplers in tapered waveguides for integrated optical sensing,” in Chemical, Biochemical, and Environmental Fiber Sensors V, R. A. Lieberman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2068, 313–325 (1994).

1994 (1)

1993 (2)

1992 (2)

E. N. Glytsis, T. K. Gaylord, “High-spatial frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 32, 4459–4470 (1992).
[CrossRef]

M. E. Motamedi, W. H. Southwell, W. J. Gunning, “Antireflection surfaces in silicon using binary optics technology,” Appl. Opt. 31, 4371–4376 (1992).
[CrossRef] [PubMed]

1987 (1)

P. Campbell, M. A. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62, 243–249 (1987).
[CrossRef]

1986 (1)

1983 (1)

1982 (1)

1981 (1)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andreawartha, “The dielectric lamellar grating,” Opt. Acta 28, 413–428 (1981); “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

1974 (1)

D. Redfield, “Multiple-pass thin film silicon solar cell,” Appl. Phys. Lett. 25, 647–648 (1974).
[CrossRef]

Adams, J. L.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andreawartha, “The dielectric lamellar grating,” Opt. Acta 28, 413–428 (1981); “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Andreawartha, J. R.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andreawartha, “The dielectric lamellar grating,” Opt. Acta 28, 413–428 (1981); “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Baird, W. E.

Botten, L. C.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andreawartha, “The dielectric lamellar grating,” Opt. Acta 28, 413–428 (1981); “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Brundrett, D. L.

Campbell, P.

P. Campbell, M. A. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62, 243–249 (1987).
[CrossRef]

Case, S. K.

Craig, M. S.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andreawartha, “The dielectric lamellar grating,” Opt. Acta 28, 413–428 (1981); “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Curtis, B. J.

R. E. Kunz, J. Edlinger, B. J. Curtis, M. T. Gale, L. U. Kempen, H. Rudigier, H. Schütz, “Grating couplers in tapered waveguides for integrated optical sensing,” in Chemical, Biochemical, and Environmental Fiber Sensors V, R. A. Lieberman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2068, 313–325 (1994).

Edlinger, J.

R. E. Kunz, J. Edlinger, B. J. Curtis, M. T. Gale, L. U. Kempen, H. Rudigier, H. Schütz, “Grating couplers in tapered waveguides for integrated optical sensing,” in Chemical, Biochemical, and Environmental Fiber Sensors V, R. A. Lieberman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2068, 313–325 (1994).

Enger, R. C.

Gale, M. T.

H. P. Herzig, M. T. Gale, H. W. Lehmann, R. Morf, “Diffractive components: computer generated elements,” in Perspectives for Parallel Optical Interconnects, P. H. Lalanne, P. Chavel, eds. (Springer, New York, 1993) Chap. 5, pp. 71–107.
[CrossRef]

R. E. Kunz, J. Edlinger, B. J. Curtis, M. T. Gale, L. U. Kempen, H. Rudigier, H. Schütz, “Grating couplers in tapered waveguides for integrated optical sensing,” in Chemical, Biochemical, and Environmental Fiber Sensors V, R. A. Lieberman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2068, 313–325 (1994).

Gaylord, T. K.

Glytsis, E. N.

D. L. Brundrett, E. N. Glytsis, T. K. Gaylord, “Homogeneous layer models for high-spatial-frequency dielectric surface-relief gratings: conical diffraction and antireflection designs,” Appl. Opt. 33, 2695–2706 (1994).
[CrossRef] [PubMed]

E. N. Glytsis, T. K. Gaylord, “High-spatial frequency binary and multilevel stairstep gratings: polarization-selective mirrors and broadband antireflection surfaces,” Appl. Opt. 32, 4459–4470 (1992).
[CrossRef]

Goetzberger, A.

A. Goetzberger, “Optical confinement in thin Si solar cells by diffuse back reflectors,” in Proceedings of the Fifteenth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronic Engineers, New York, 1981), p. 867.

Green, M. A.

P. Campbell, M. A. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62, 243–249 (1987).
[CrossRef]

Gunning, W. J.

Herzig, H. P.

H. P. Herzig, M. T. Gale, H. W. Lehmann, R. Morf, “Diffractive components: computer generated elements,” in Perspectives for Parallel Optical Interconnects, P. H. Lalanne, P. Chavel, eds. (Springer, New York, 1993) Chap. 5, pp. 71–107.
[CrossRef]

Hovel, H. J.

H. J. Hovel, Solar Cells, Vol. II of the Semiconductor and Semimetals Series (Academic, New York, 1975), p. 97.

Kempen, L. U.

R. E. Kunz, J. Edlinger, B. J. Curtis, M. T. Gale, L. U. Kempen, H. Rudigier, H. Schütz, “Grating couplers in tapered waveguides for integrated optical sensing,” in Chemical, Biochemical, and Environmental Fiber Sensors V, R. A. Lieberman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2068, 313–325 (1994).

Kiess, H.

R. H. Morf, H. Kiess, “Submicron gratings for light trapping in silicon solar cells: a theoretical study,” in Proceedings of the Ninth International Conference on Photovoltaic Solar Energy, W. Palz, ed. (Commission of the European Communities, Brussels, Belgium, 1989), pp. 313–315.

Kunz, R. E.

R. Morf, R. E. Kunz, “Dielectric filter optimization by simulated thermal annealing,” in Thin Film Technologies III, K. H. Guenther, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1019, 211–217 (1988).

R. E. Kunz, J. Edlinger, B. J. Curtis, M. T. Gale, L. U. Kempen, H. Rudigier, H. Schütz, “Grating couplers in tapered waveguides for integrated optical sensing,” in Chemical, Biochemical, and Environmental Fiber Sensors V, R. A. Lieberman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2068, 313–325 (1994).

Lehmann, H. W.

H. P. Herzig, M. T. Gale, H. W. Lehmann, R. Morf, “Diffractive components: computer generated elements,” in Perspectives for Parallel Optical Interconnects, P. H. Lalanne, P. Chavel, eds. (Springer, New York, 1993) Chap. 5, pp. 71–107.
[CrossRef]

McPhedran, R. C.

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andreawartha, “The dielectric lamellar grating,” Opt. Acta 28, 413–428 (1981); “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Moharam, M. G.

Morf, R.

H. P. Herzig, M. T. Gale, H. W. Lehmann, R. Morf, “Diffractive components: computer generated elements,” in Perspectives for Parallel Optical Interconnects, P. H. Lalanne, P. Chavel, eds. (Springer, New York, 1993) Chap. 5, pp. 71–107.
[CrossRef]

R. Morf, R. E. Kunz, “Dielectric filter optimization by simulated thermal annealing,” in Thin Film Technologies III, K. H. Guenther, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1019, 211–217 (1988).

Morf, R. H.

R. H. Morf, “Exponentially convergent and numerically efficient solution of Maxwell’s equations for lamellar diffraction gratings,” J. Opt. Soc. Am. A (to be published).

R. H. Morf, H. Kiess, “Submicron gratings for light trapping in silicon solar cells: a theoretical study,” in Proceedings of the Ninth International Conference on Photovoltaic Solar Energy, W. Palz, ed. (Commission of the European Communities, Brussels, Belgium, 1989), pp. 313–315.

Morris, G. M.

Motamedi, M. E.

Raguin, D.

Redfield, D.

D. Redfield, “Multiple-pass thin film silicon solar cell,” Appl. Phys. Lett. 25, 647–648 (1974).
[CrossRef]

Rudigier, H.

R. E. Kunz, J. Edlinger, B. J. Curtis, M. T. Gale, L. U. Kempen, H. Rudigier, H. Schütz, “Grating couplers in tapered waveguides for integrated optical sensing,” in Chemical, Biochemical, and Environmental Fiber Sensors V, R. A. Lieberman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2068, 313–325 (1994).

Schindler, J.

D. Strese, J. Schindler, “Kostendegression Photovoltaik: Fertigung multikristalliner Solarzellen und ihr Einsatz im Kraftwerksbereich,” Rep. 0328830A (Bundesminister für For-schung und Technik, Bonn, Germany, 1988). A short review can be found in Bild Wiss. (July 1988), p. 36.

Schütz, H.

R. E. Kunz, J. Edlinger, B. J. Curtis, M. T. Gale, L. U. Kempen, H. Rudigier, H. Schütz, “Grating couplers in tapered waveguides for integrated optical sensing,” in Chemical, Biochemical, and Environmental Fiber Sensors V, R. A. Lieberman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2068, 313–325 (1994).

Southwell, W. H.

Strese, D.

D. Strese, J. Schindler, “Kostendegression Photovoltaik: Fertigung multikristalliner Solarzellen und ihr Einsatz im Kraftwerksbereich,” Rep. 0328830A (Bundesminister für For-schung und Technik, Bonn, Germany, 1988). A short review can be found in Bild Wiss. (July 1988), p. 36.

Yablonovitch, E.

Appl. Opt. (7)

Appl. Phys. Lett. (1)

D. Redfield, “Multiple-pass thin film silicon solar cell,” Appl. Phys. Lett. 25, 647–648 (1974).
[CrossRef]

J. Appl. Phys. (1)

P. Campbell, M. A. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62, 243–249 (1987).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Acta (1)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andreawartha, “The dielectric lamellar grating,” Opt. Acta 28, 413–428 (1981); “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981).
[CrossRef]

Other (8)

R. H. Morf, H. Kiess, “Submicron gratings for light trapping in silicon solar cells: a theoretical study,” in Proceedings of the Ninth International Conference on Photovoltaic Solar Energy, W. Palz, ed. (Commission of the European Communities, Brussels, Belgium, 1989), pp. 313–315.

R. Morf, R. E. Kunz, “Dielectric filter optimization by simulated thermal annealing,” in Thin Film Technologies III, K. H. Guenther, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1019, 211–217 (1988).

R. E. Kunz, J. Edlinger, B. J. Curtis, M. T. Gale, L. U. Kempen, H. Rudigier, H. Schütz, “Grating couplers in tapered waveguides for integrated optical sensing,” in Chemical, Biochemical, and Environmental Fiber Sensors V, R. A. Lieberman, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2068, 313–325 (1994).

H. P. Herzig, M. T. Gale, H. W. Lehmann, R. Morf, “Diffractive components: computer generated elements,” in Perspectives for Parallel Optical Interconnects, P. H. Lalanne, P. Chavel, eds. (Springer, New York, 1993) Chap. 5, pp. 71–107.
[CrossRef]

R. H. Morf, “Exponentially convergent and numerically efficient solution of Maxwell’s equations for lamellar diffraction gratings,” J. Opt. Soc. Am. A (to be published).

A. Goetzberger, “Optical confinement in thin Si solar cells by diffuse back reflectors,” in Proceedings of the Fifteenth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronic Engineers, New York, 1981), p. 867.

D. Strese, J. Schindler, “Kostendegression Photovoltaik: Fertigung multikristalliner Solarzellen und ihr Einsatz im Kraftwerksbereich,” Rep. 0328830A (Bundesminister für For-schung und Technik, Bonn, Germany, 1988). A short review can be found in Bild Wiss. (July 1988), p. 36.

H. J. Hovel, Solar Cells, Vol. II of the Semiconductor and Semimetals Series (Academic, New York, 1975), p. 97.

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Figures (12)

Fig. 1
Fig. 1

Rectangular grating optimized for use with thin Si solar cells. Λ is the grating period, f is the duty cycle, and h is the grating depth.

Fig. 2
Fig. 2

In a symmetric grating structure ±nth-order modes are excited with equal strength. According to the reciprocity theorem the minus first order (−1) impinging on the grating excites the zero-order outgoing wave (out) in the same way the zero-order incident (inc) couples to the plus first order (+1).

Fig. 3
Fig. 3

Structure is optimized such that the zero-order incident wave generates only plus first- or plus second-order (right-moving) waves. The minus first-order wave therefore does not necessarily couple to the zero-order outgoing wave.

Fig. 4
Fig. 4

Optimized staircase approximation to a blazed grating for a thin Si solar cell.

Fig. 5
Fig. 5

Reflection loss as a function of Si cell thickness for a cell with a planar reflector (no grating), with a rectangular grating (Fig. 3) and with the staircase grating (blazed grating) of Fig. 4. Note that the reflection loss of the Si surface with a two-layer AR coat is ~2.5%.

Fig. 6
Fig. 6

(a) Scanning electron micrograph picture of a blazed grating in Si with a 660-nm period fabricated by ion-beam etching. (b) Reflection spectrum measured for the grating of (a). The total reflection is the sum of specular reflected (R) and diffuse scattered light (R streu) resulting from surface roughness effects. Note the absence of an AR coating, which leads to a reflection of ≈35% for λ ≈ 900 nm. The blazed grating leads to an optically effective thickness that lies between that of a 177-μm and a 760-μm cell with a planar reflector.

Fig. 7
Fig. 7

Geometry of a BAR structure: a lamellar surface relief grating embossed in a substrate with diffraction index n s . A dielectric coating n c < n s is deposited on and between the grating grooves. The period of the grating is Λ, h is the grating groove depth, f is the duty cycle, and d is the thickness of the coating. Calculations were made for normally incident light with wavelength λ between 300 and 2100 nm.

Fig. 8
Fig. 8

Effect of a dielectric coating on a lamellar grating for (a) E polarization, (b) H polarization. We also show the incident solar energy flux in arbitrary units as a function of wavelength.

Fig. 9
Fig. 9

Average reflectivity of a BAR as a function of the duty cycle for E and H polarizations and unpolarized light. The grating depth is 170 nm, and the coating thickness is 100 nm.

Fig. 10
Fig. 10

Average reflectivity of a BAR as a function of the grating depth. The duty cycle is 0.45, and the coating thickness is 100 nm.

Fig. 11
Fig. 11

Average reflectivity of a BAR as a function of coating thickness d. The duty cycle is 0.45, and the grating depth is 170 nm.

Fig. 12
Fig. 12

Average reflectivity as a function of the angle of incidence. The BAR optimized for normal incidence reflects up to ±40° less than 1% of the incoming solar flux.

Equations (5)

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sin ( Ө m ) = m λ / Λ n Si .
sin θ m = m λ n i Λ sin θ i ,
| sin θ m | = | m λ Λ sin θ i | > 1 .
( λ / Λ ) > 1 + sin θ i .
Λ < ( λ min / 2 ) = 150 nm .

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