## Effect of aperiodicity on the broadband reflection of silicon nanorod structures for photovoltaics |

Optics Express, Vol. 20, Issue S1, pp. A125-A132 (2012)

http://dx.doi.org/10.1364/OE.20.00A125

Acrobat PDF (1650 KB)

### Abstract

We carry out a systematic numerical study of the effects of aperiodicity on silicon nanorod anti-reflection structures. We use the scattering matrix method to calculate the average reflection loss over the solar spectrum for periodic and aperiodic arrangements of nanorods. We find that aperiodicity can either improve or deteriorate the anti-reflection performance, depending on the nanorod diameter. We use a guided random-walk algorithm to design optimal aperiodic structures that exhibit lower reflection loss than both optimal periodic and random aperiodic structures.

© 2011 OSA

1. P. Campbell and M. A. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. **62**(1), 243–249 (1987). [CrossRef]

2. S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Anti-reflecting and photonic nanostructures,” Mater. Sci. Eng. Rep. **69**(1-3), 1–35 (2010). [CrossRef]

3. P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology **8**(2), 53–56 (1997). [CrossRef]

12. H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys. **46**(6A), 3333–3336 (2007). [CrossRef]

9. Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. **2**(12), 770–774 (2007). [CrossRef] [PubMed]

9. Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. **2**(12), 770–774 (2007). [CrossRef] [PubMed]

13. P. Seliger, M. Mahvash, C. Wang, and A. F. J. Levi, “Optimization of aperiodic dielectric structures,” J. Appl. Phys. **100**(3), 034310–034316 (2006). [CrossRef]

*λ*is wavelength,

*I*(

*λ*) is the solar irradiance spectrum, and

*R*(

_{TE}*λ*) and

*R*(

_{TM}*λ*) are the surface reflectance for TE and TM polarization, respectively. This figure of merit gives the ratio between the number of unabsorbed photons due to reflection loss and the total number of available photons above the band gap of crystalline silicon. The band gap corresponds to a wavelength

*λ*= 1127 nm. The solar spectrum is negligible below 310 nm. TE and TM polarized light have electric fields perpendicular or parallel to the incidence plane, respectively. We use a 3D full-vectorial scattering matrix solver (the ISU-TMM simulation package [15

_{g}15. M. Li, X. Hu, Z. Ye, K. M. Ho, J. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. **31**(23), 3498–3500 (2006). [CrossRef] [PubMed]

*d*/

*a*= 0.7). The white dashed line indicates the diffraction limit in air (

*a*=

*λ*). Clearly, for broadband anti-reflection applications, the lattice constant should be kept below the diffraction limit for the lowest wavelength in the spectral range (310 nm in our case); otherwise, the diffuse (high order) reflectance will significantly increase the total reflection loss. On the other hand, below the diffraction limit, the optimal lattice constant is determined by the number and positions of reflection minima in Fig. 2(c). The positions of these minima are determined by the synergy between the propagating optical modes in the nanorod array, Fabry-Perot effects at the nanorod-air and the nanorod-substrate interfaces, as well as the opening of transmission orders. A detailed analysis of these spectral features might be carried out based on the modal method demonstrated in Refs. [16

16. J. Kupec and B. Witzigmann, “Dispersion, wave propagation and efficiency analysis of nanowire solar cells,” Opt. Express **17**(12), 10399–10410 (2009). [CrossRef] [PubMed]

17. B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, C. M. de Sterke, and R. C. McPhedran, “Modal analysis of enhanced absorption in silicon nanowire arrays,” Opt. Express **19**(S5Suppl 5), A1067–A1081 (2011). [CrossRef] [PubMed]

_{3}N

_{4}anti-reflection coating with a thickness of 80 nm are shown by dashed lines. The reflectance spectrum of the pyramid surface texture was calculated by a simple scalar approach, following Ref. [18

18. B. L. Sopori and R. A. Pryor, “Design of antireflection coatings for textured silicon solar cells,” Sol. Cells **8**(3), 249–261 (1983). [CrossRef]

19. M. Schulte, K. Bittkau, K. Jager, M. Ermes, M. Zeman, and B. E. Pieters, “Angular resolved scattering by a nano-textured ZnO/silicon interface,” Appl. Phys. Lett. **99**(11), 111107 (2011). [CrossRef]

20. K. Bittkau, M. Schulte, M. Klein, T. Beckers, and R. Carius, “Modeling of light scattering properties from surface profile in thin-film solar cells by Fourier transform techniques,” Thin Solid Films **519**(19), 6538–6543 (2011). [CrossRef]

21. C. Lin and M. L. Povinelli, “Optimal design of aperiodic, vertical silicon nanowire structures for photovoltaics,” Opt. Express **19**(S5Suppl 5), A1148–A1154 (2011). [CrossRef] [PubMed]

## Acknowledgment

## References and links

1. | P. Campbell and M. A. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. |

2. | S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Anti-reflecting and photonic nanostructures,” Mater. Sci. Eng. Rep. |

3. | P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology |

4. | Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. |

5. | K. Hadobás, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotechnology |

6. | H. Sai, H. Fujii, K. Arafune, Y. Ohshita, M. Yamaguchi, Y. Kanamori, and H. Yugami, “Antireflective subwavelength structures on crystalline Si fabricated using directly formed anodic porous alumina masks,” Appl. Phys. Lett. |

7. | S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett. |

8. | Y.-H. Pai, Y.-C. Lin, J.-L. Tsai, and G.-R. Lin, “Nonlinear dependence between the surface reflectance and the duty-cycle of semiconductor nanorod array,” Opt. Express |

9. | Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. |

10. | H. Sai, Y. Kanamori, K. Arafune, Y. Ohshita, and M. Yamaguchi, “Light trapping effect of submicron surface textures in crystalline Si solar cells,” Prog. Photovolt. Res. Appl. |

11. | S. A. Boden and D. M. Bagnall, “Optimization of moth-eye antireflection schemes for silicon solar cells,” Prog. Photovolt. Res. Appl. |

12. | H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys. |

13. | P. Seliger, M. Mahvash, C. Wang, and A. F. J. Levi, “Optimization of aperiodic dielectric structures,” J. Appl. Phys. |

14. | D. F. Edwards, “Silicon (Si),” in |

15. | M. Li, X. Hu, Z. Ye, K. M. Ho, J. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. |

16. | J. Kupec and B. Witzigmann, “Dispersion, wave propagation and efficiency analysis of nanowire solar cells,” Opt. Express |

17. | B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, C. M. de Sterke, and R. C. McPhedran, “Modal analysis of enhanced absorption in silicon nanowire arrays,” Opt. Express |

18. | B. L. Sopori and R. A. Pryor, “Design of antireflection coatings for textured silicon solar cells,” Sol. Cells |

19. | M. Schulte, K. Bittkau, K. Jager, M. Ermes, M. Zeman, and B. E. Pieters, “Angular resolved scattering by a nano-textured ZnO/silicon interface,” Appl. Phys. Lett. |

20. | K. Bittkau, M. Schulte, M. Klein, T. Beckers, and R. Carius, “Modeling of light scattering properties from surface profile in thin-film solar cells by Fourier transform techniques,” Thin Solid Films |

21. | C. Lin and M. L. Povinelli, “Optimal design of aperiodic, vertical silicon nanowire structures for photovoltaics,” Opt. Express |

22. | T. C. Choy, |

23. | H. Bao and X. Ruan, “Optical absorption enhancement in disordered vertical silicon nanowire arrays for photovoltaic applications,” Opt. Lett. |

24. | D. Shir, J. Yoon, D. Chanda, J.-H. Ryu, and J. A. Rogers, “Performance of ultrathin silicon solar microcells with nanostructures of relief formed by soft imprint lithography for broad band absorption enhancement,” Nano Lett. |

**OCIS Codes**

(350.6050) Other areas of optics : Solar energy

(310.6628) Thin films : Subwavelength structures, nanostructures

**ToC Category:**

Photovoltaics

**History**

Original Manuscript: October 24, 2011

Revised Manuscript: December 5, 2011

Manuscript Accepted: December 8, 2011

Published: December 22, 2011

**Citation**

Chenxi Lin, Ningfeng Huang, and Michelle L. Povinelli, "Effect of aperiodicity on the broadband reflection of silicon nanorod structures for photovoltaics," Opt. Express **20**, A125-A132 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-S1-A125

Sort: Year | Journal | Reset

### References

- P. Campbell and M. A. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys.62(1), 243–249 (1987). [CrossRef]
- S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Anti-reflecting and photonic nanostructures,” Mater. Sci. Eng. Rep.69(1-3), 1–35 (2010). [CrossRef]
- P. Lalanne and G. M. Morris, “Antireflection behavior of silicon subwavelength periodic structures for visible light,” Nanotechnology8(2), 53–56 (1997). [CrossRef]
- Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett.24(20), 1422–1424 (1999). [CrossRef] [PubMed]
- K. Hadobás, S. Kirsch, A. Carl, M. Acet, and E. F. Wassermann, “Reflection properties of nanostructure-arrayed silicon surfaces,” Nanotechnology11(3), 161–164 (2000). [CrossRef]
- H. Sai, H. Fujii, K. Arafune, Y. Ohshita, M. Yamaguchi, Y. Kanamori, and H. Yugami, “Antireflective subwavelength structures on crystalline Si fabricated using directly formed anodic porous alumina masks,” Appl. Phys. Lett.88(20), 201116 (2006). [CrossRef]
- S. A. Boden and D. M. Bagnall, “Tunable reflection minima of nanostructured antireflective surfaces,” Appl. Phys. Lett.93(13), 133108 (2008). [CrossRef]
- Y.-H. Pai, Y.-C. Lin, J.-L. Tsai, and G.-R. Lin, “Nonlinear dependence between the surface reflectance and the duty-cycle of semiconductor nanorod array,” Opt. Express19(3), 1680–1690 (2011). [CrossRef] [PubMed]
- Y.-F. Huang, S. Chattopadhyay, Y.-J. Jen, C.-Y. Peng, T.-A. Liu, Y.-K. Hsu, C.-L. Pan, H.-C. Lo, C.-H. Hsu, Y.-H. Chang, C.-S. Lee, K.-H. Chen, and L.-C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol.2(12), 770–774 (2007). [CrossRef] [PubMed]
- H. Sai, Y. Kanamori, K. Arafune, Y. Ohshita, and M. Yamaguchi, “Light trapping effect of submicron surface textures in crystalline Si solar cells,” Prog. Photovolt. Res. Appl.15(5), 415–423 (2007). [CrossRef]
- S. A. Boden and D. M. Bagnall, “Optimization of moth-eye antireflection schemes for silicon solar cells,” Prog. Photovolt. Res. Appl.18(3), 195–203 (2010). [CrossRef]
- H. Sai, H. Fujii, K. Arafune, Y. Ohshita, Y. Kanamori, H. Yugami, and M. Yamaguchi, “Wide-angle antireflection effect of subwavelength structures for solar cells,” Jpn. J. Appl. Phys.46(6A), 3333–3336 (2007). [CrossRef]
- P. Seliger, M. Mahvash, C. Wang, and A. F. J. Levi, “Optimization of aperiodic dielectric structures,” J. Appl. Phys.100(3), 034310–034316 (2006). [CrossRef]
- D. F. Edwards, “Silicon (Si),” in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, Orlando, Fla., 1985).
- M. Li, X. Hu, Z. Ye, K. M. Ho, J. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett.31(23), 3498–3500 (2006). [CrossRef] [PubMed]
- J. Kupec and B. Witzigmann, “Dispersion, wave propagation and efficiency analysis of nanowire solar cells,” Opt. Express17(12), 10399–10410 (2009). [CrossRef] [PubMed]
- B. C. P. Sturmberg, K. B. Dossou, L. C. Botten, A. A. Asatryan, C. G. Poulton, C. M. de Sterke, and R. C. McPhedran, “Modal analysis of enhanced absorption in silicon nanowire arrays,” Opt. Express19(S5Suppl 5), A1067–A1081 (2011). [CrossRef] [PubMed]
- B. L. Sopori and R. A. Pryor, “Design of antireflection coatings for textured silicon solar cells,” Sol. Cells8(3), 249–261 (1983). [CrossRef]
- M. Schulte, K. Bittkau, K. Jager, M. Ermes, M. Zeman, and B. E. Pieters, “Angular resolved scattering by a nano-textured ZnO/silicon interface,” Appl. Phys. Lett.99(11), 111107 (2011). [CrossRef]
- K. Bittkau, M. Schulte, M. Klein, T. Beckers, and R. Carius, “Modeling of light scattering properties from surface profile in thin-film solar cells by Fourier transform techniques,” Thin Solid Films519(19), 6538–6543 (2011). [CrossRef]
- C. Lin and M. L. Povinelli, “Optimal design of aperiodic, vertical silicon nanowire structures for photovoltaics,” Opt. Express19(S5Suppl 5), A1148–A1154 (2011). [CrossRef] [PubMed]
- T. C. Choy, Effective Medium Theory: Principles and Applications (Calrendon, 1999).
- H. Bao and X. Ruan, “Optical absorption enhancement in disordered vertical silicon nanowire arrays for photovoltaic applications,” Opt. Lett.35(20), 3378–3380 (2010). [CrossRef] [PubMed]
- D. Shir, J. Yoon, D. Chanda, J.-H. Ryu, and J. A. Rogers, “Performance of ultrathin silicon solar microcells with nanostructures of relief formed by soft imprint lithography for broad band absorption enhancement,” Nano Lett.10(8), 3041–3046 (2010). [CrossRef] [PubMed]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.