Abstract

Surface textures are widely used to enhance absorption in an optical sheet by scattering weakly absorbed light into totally internally reflected modes. This study, which is based on ray-tracing studies of crystalline silicon solar cells with periodic geometric textures, investigates how the distribution of scatter influences absorption enhancement. The distribution of scatter is found to depend on the topology of texture facets as well as on the direction of incident light. Examples of the scatter characteristics in sheets textured with inverted pyramids, grooves, and perpendicular grooves are given. Broadly scattering textures are found to develop random scatter consistently only when exposed to isotropically incident band-gap wavelengths. Although broadband absorption enhancement from a geometric texture is affected by whether scatter is two or three dimensional, the fraction of rays blocked by the texture at early scatter stages is more important. Reasons are given as to why there may be geometric textures that enhance broadband absorption more than the randomizing texture under isotropic incidence.

© 1993 Optical Society of America

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References

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  1. E. Yablonovitch, J. Opt. Soc. Am. 72, 899–907 (1982).
    [CrossRef]
  2. T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, IEEE Trans. Electron. Devices ED-37, 711–716 (1984).
    [CrossRef]
  3. H. Deckman and J. Dunsmuir, Appl. Phys. Lett. 36, 727–730 (1980).
    [CrossRef]
  4. A. Goetzberger, in Proceedings of the Fifteenth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 867–870.
  5. Ping Sheng, IEEE Trans. Electron. Devices ED-31, 634–636 (1984).
    [CrossRef]
  6. P. Campbell and M. A. Green, J. Appl. Phys. 62, 243–249 (1987).
    [CrossRef]
  7. B. Sopori and R. Pryor, in Proceedings of the Fifteenth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 466–472.
  8. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 121.
  9. P. Campbell and M. A. Green, IEEE Trans. Electron. Devices ED-31, 1834–1835 (1986).
    [CrossRef]
  10. P. Campbell, S. R. Wenham, and M. A. Green, in Fourth Photovoltaic Science and Engineering Conference Proceedings (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), pp. 615–620.
  11. R. Morf and H. Kiess, in Eighth European Community Photovoltaic Solar Energy Conference Proceedings (Kluwer, Dordrecht, The Netherlands, 1989), pp. 313–316.
  12. P. Campbell, in Sixth Photovoltaic Science and Engineering Conference Proceedings (Oxford, New Delhi, 1989), pp. 759–764.
  13. M. A. Green, in Tenth European Community Photovoltaic Solar Energy Conference Proceedings (Kluwer, Dordrecht, The Netherlands, 1989), pp. 250–253.
  14. G. Landis, in Twentieth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 708–711. G. Landis suggested this design in 1984 to a colleague, M. A. Green, who later passed it on to the author.
    [CrossRef]
  15. P. Campbell, Solar Energy Mat. 21, 165–172 (1990).
    [CrossRef]
  16. AM1.5 global spectrum (97 mW/cm2): R. Matson, K. A. Emery, and R. E. Bird, Solar Cells 11, 105–145 (1984). This does not need correction to 100 mW/cm2 when used to compare current collection from different textures.
    [CrossRef]
  17. J. Rand and P. Basore, in 22nd IEEE Conference Proceedings (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 192–197.
  18. P. Campbell, S. R. Wenham, and M. A. Green, “Light trapping and reflection control in solar cells using tilted crystallographic surface textures,” Sol. Energy Mater. Solar Cells (to be published).
  19. P. Campbell, “Light trapping and reflection control in a crystalline silicon solar cell,” Ph.D. dissertation (University of New South Wales, Sydney, Australia, 1989), App. C.

1990 (1)

P. Campbell, Solar Energy Mat. 21, 165–172 (1990).
[CrossRef]

1987 (1)

P. Campbell and M. A. Green, J. Appl. Phys. 62, 243–249 (1987).
[CrossRef]

1986 (1)

P. Campbell and M. A. Green, IEEE Trans. Electron. Devices ED-31, 1834–1835 (1986).
[CrossRef]

1984 (3)

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, IEEE Trans. Electron. Devices ED-37, 711–716 (1984).
[CrossRef]

AM1.5 global spectrum (97 mW/cm2): R. Matson, K. A. Emery, and R. E. Bird, Solar Cells 11, 105–145 (1984). This does not need correction to 100 mW/cm2 when used to compare current collection from different textures.
[CrossRef]

Ping Sheng, IEEE Trans. Electron. Devices ED-31, 634–636 (1984).
[CrossRef]

1982 (1)

1980 (1)

H. Deckman and J. Dunsmuir, Appl. Phys. Lett. 36, 727–730 (1980).
[CrossRef]

Basore, P.

J. Rand and P. Basore, in 22nd IEEE Conference Proceedings (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 192–197.

Bird, R. E.

AM1.5 global spectrum (97 mW/cm2): R. Matson, K. A. Emery, and R. E. Bird, Solar Cells 11, 105–145 (1984). This does not need correction to 100 mW/cm2 when used to compare current collection from different textures.
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 121.

Brooks, B. G.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, IEEE Trans. Electron. Devices ED-37, 711–716 (1984).
[CrossRef]

Campbell, P.

P. Campbell, Solar Energy Mat. 21, 165–172 (1990).
[CrossRef]

P. Campbell and M. A. Green, J. Appl. Phys. 62, 243–249 (1987).
[CrossRef]

P. Campbell and M. A. Green, IEEE Trans. Electron. Devices ED-31, 1834–1835 (1986).
[CrossRef]

P. Campbell, S. R. Wenham, and M. A. Green, in Fourth Photovoltaic Science and Engineering Conference Proceedings (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), pp. 615–620.

P. Campbell, in Sixth Photovoltaic Science and Engineering Conference Proceedings (Oxford, New Delhi, 1989), pp. 759–764.

P. Campbell, S. R. Wenham, and M. A. Green, “Light trapping and reflection control in solar cells using tilted crystallographic surface textures,” Sol. Energy Mater. Solar Cells (to be published).

P. Campbell, “Light trapping and reflection control in a crystalline silicon solar cell,” Ph.D. dissertation (University of New South Wales, Sydney, Australia, 1989), App. C.

Cody, G. D.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, IEEE Trans. Electron. Devices ED-37, 711–716 (1984).
[CrossRef]

Deckman, H.

H. Deckman and J. Dunsmuir, Appl. Phys. Lett. 36, 727–730 (1980).
[CrossRef]

Dunsmuir, J.

H. Deckman and J. Dunsmuir, Appl. Phys. Lett. 36, 727–730 (1980).
[CrossRef]

Emery, K. A.

AM1.5 global spectrum (97 mW/cm2): R. Matson, K. A. Emery, and R. E. Bird, Solar Cells 11, 105–145 (1984). This does not need correction to 100 mW/cm2 when used to compare current collection from different textures.
[CrossRef]

Goetzberger, A.

A. Goetzberger, in Proceedings of the Fifteenth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 867–870.

Green, M. A.

P. Campbell and M. A. Green, J. Appl. Phys. 62, 243–249 (1987).
[CrossRef]

P. Campbell and M. A. Green, IEEE Trans. Electron. Devices ED-31, 1834–1835 (1986).
[CrossRef]

M. A. Green, in Tenth European Community Photovoltaic Solar Energy Conference Proceedings (Kluwer, Dordrecht, The Netherlands, 1989), pp. 250–253.

P. Campbell, S. R. Wenham, and M. A. Green, in Fourth Photovoltaic Science and Engineering Conference Proceedings (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), pp. 615–620.

P. Campbell, S. R. Wenham, and M. A. Green, “Light trapping and reflection control in solar cells using tilted crystallographic surface textures,” Sol. Energy Mater. Solar Cells (to be published).

Kiess, H.

R. Morf and H. Kiess, in Eighth European Community Photovoltaic Solar Energy Conference Proceedings (Kluwer, Dordrecht, The Netherlands, 1989), pp. 313–316.

Landis, G.

G. Landis, in Twentieth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 708–711. G. Landis suggested this design in 1984 to a colleague, M. A. Green, who later passed it on to the author.
[CrossRef]

Matson, R.

AM1.5 global spectrum (97 mW/cm2): R. Matson, K. A. Emery, and R. E. Bird, Solar Cells 11, 105–145 (1984). This does not need correction to 100 mW/cm2 when used to compare current collection from different textures.
[CrossRef]

Morf, R.

R. Morf and H. Kiess, in Eighth European Community Photovoltaic Solar Energy Conference Proceedings (Kluwer, Dordrecht, The Netherlands, 1989), pp. 313–316.

Pryor, R.

B. Sopori and R. Pryor, in Proceedings of the Fifteenth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 466–472.

Rand, J.

J. Rand and P. Basore, in 22nd IEEE Conference Proceedings (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 192–197.

Sheng, Ping

Ping Sheng, IEEE Trans. Electron. Devices ED-31, 634–636 (1984).
[CrossRef]

Sopori, B.

B. Sopori and R. Pryor, in Proceedings of the Fifteenth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 466–472.

Tiedje, T.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, IEEE Trans. Electron. Devices ED-37, 711–716 (1984).
[CrossRef]

Wenham, S. R.

P. Campbell, S. R. Wenham, and M. A. Green, in Fourth Photovoltaic Science and Engineering Conference Proceedings (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), pp. 615–620.

P. Campbell, S. R. Wenham, and M. A. Green, “Light trapping and reflection control in solar cells using tilted crystallographic surface textures,” Sol. Energy Mater. Solar Cells (to be published).

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 121.

Yablonovitch, E.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, IEEE Trans. Electron. Devices ED-37, 711–716 (1984).
[CrossRef]

E. Yablonovitch, J. Opt. Soc. Am. 72, 899–907 (1982).
[CrossRef]

Appl. Phys. Lett. (1)

H. Deckman and J. Dunsmuir, Appl. Phys. Lett. 36, 727–730 (1980).
[CrossRef]

IEEE Trans. Electron. Devices (3)

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, IEEE Trans. Electron. Devices ED-37, 711–716 (1984).
[CrossRef]

Ping Sheng, IEEE Trans. Electron. Devices ED-31, 634–636 (1984).
[CrossRef]

P. Campbell and M. A. Green, IEEE Trans. Electron. Devices ED-31, 1834–1835 (1986).
[CrossRef]

J. Appl. Phys. (1)

P. Campbell and M. A. Green, J. Appl. Phys. 62, 243–249 (1987).
[CrossRef]

J. Opt. Soc. Am. (1)

Solar Cells (1)

AM1.5 global spectrum (97 mW/cm2): R. Matson, K. A. Emery, and R. E. Bird, Solar Cells 11, 105–145 (1984). This does not need correction to 100 mW/cm2 when used to compare current collection from different textures.
[CrossRef]

Solar Energy Mat. (1)

P. Campbell, Solar Energy Mat. 21, 165–172 (1990).
[CrossRef]

Other (11)

J. Rand and P. Basore, in 22nd IEEE Conference Proceedings (Institute of Electrical and Electronics Engineers, New York, 1991), pp. 192–197.

P. Campbell, S. R. Wenham, and M. A. Green, “Light trapping and reflection control in solar cells using tilted crystallographic surface textures,” Sol. Energy Mater. Solar Cells (to be published).

P. Campbell, “Light trapping and reflection control in a crystalline silicon solar cell,” Ph.D. dissertation (University of New South Wales, Sydney, Australia, 1989), App. C.

P. Campbell, S. R. Wenham, and M. A. Green, in Fourth Photovoltaic Science and Engineering Conference Proceedings (Institution of Radio and Electronics Engineers, Sydney, Australia, 1989), pp. 615–620.

R. Morf and H. Kiess, in Eighth European Community Photovoltaic Solar Energy Conference Proceedings (Kluwer, Dordrecht, The Netherlands, 1989), pp. 313–316.

P. Campbell, in Sixth Photovoltaic Science and Engineering Conference Proceedings (Oxford, New Delhi, 1989), pp. 759–764.

M. A. Green, in Tenth European Community Photovoltaic Solar Energy Conference Proceedings (Kluwer, Dordrecht, The Netherlands, 1989), pp. 250–253.

G. Landis, in Twentieth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronics Engineers, New York, 1988), pp. 708–711. G. Landis suggested this design in 1984 to a colleague, M. A. Green, who later passed it on to the author.
[CrossRef]

A. Goetzberger, in Proceedings of the Fifteenth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 867–870.

B. Sopori and R. Pryor, in Proceedings of the Fifteenth IEEE Photovoltaic Specialists’ Conference (Institute of Electrical and Electronics Engineers, New York, 1981), pp. 466–472.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 121.

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Figures (7)

Fig. 1
Fig. 1

Examples of class I texturing that can be readily fabricated on silicon with 〈111〉 facet orientations: (a) inverted pyramids and (b) perpendicular grooves.

Fig. 2
Fig. 2

Examples of class II texturing that can be readily fabricated on silicon with 〈111〉 facet orientations: (a) one-sided grooves and (b) two-sided parallel grooves.

Fig. 3
Fig. 3

Ray passage in (a) a single-sided grooved sheet with a fully reflective rear is, by symmetry, identical to that in (b) a double-sided, conformally grooved sheet with twice the substrate thickness and no reflector.

Fig. 4
Fig. 4

Generation of an additional scatter orientation from the splitting of a trapped ray on reflection.

Fig. 5
Fig. 5

Relative distribution of radiance (intensity per unit solid angle), weighted by sec θ, with respect to the angle from the macroscopic surface normal, from normal (diamonds) and isotropic (squares) incidence for (a) inverted pyramids top, planar rear; (b) perpendicular grooves. Random scatter produces a unity level of radiance with this weighting.

Fig. 6
Fig. 6

Scatter categories A, B, and C produced by a symmetrically grooved texture: (a) A, B produced at normal incidence when groove angle β > βp, such as with 〈111〉 grooves; (b) A, C produced at normal incidence when β < βp (groove angle βp refracts normally incident light parallel to the opposite face of each groove).

Fig. 7
Fig. 7

Schematic of a grooved surface showing the refraction R of a ray that is steeply incident in the direction z along the grooves. The angle α between R and its projection P in the plane xy containing the profile of grooves is always less than θc.

Tables (2)

Tables Icon

Table 1 Variation of Path-Length Enhancement with Incident Angle for a Class I Texturea

Tables Icon

Table 2 Variation of Path-Length Enhancement with Incident Angle for a Class II Texturea

Equations (7)

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

f = 0 θ c sin θ cos θ d θ 0 π / 2 sin θ cos θ d θ = 1 n 2 .
p = 0 W cos θ sin θ cos θ d θ 0 π / 2 sin θ cos θ d θ = 2 W ,
f = 0 θ c cos θ d θ 0 π / 2 cos θ d θ = 1 n ,
p = 0 π / 2 W cos θ cos θ d θ 0 π / 2 cos θ d θ = π W 2 ,
a [ α ( λ ) W ] = 1 exp [ α ( λ ) P W ] ,
P ( λ ) = 1 α ( λ ) W In { 1 a [ α ( λ ) W ] } ,
J sc = a ( λ ) S ( λ ) d λ .

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