Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Photon management in two-dimensional disordered media

Abstract

Elaborating reliable and versatile strategies for efficient light coupling between free space and thin films is of crucial importance for new technologies in energy efficiency. Nanostructured materials have opened unprecedented opportunities for light management, notably in thin-film solar cells1,2. Efficient coherent light trapping has been accomplished through the careful design of plasmonic nanoparticles and gratings3,4, resonant dielectric particles5,6 and photonic crystals7,8,9,10. Alternative approaches have used randomly textured surfaces11,12,13 as strong light diffusers to benefit from their broadband and wide-angle properties. Here, we propose a new strategy for photon management in thin films that combines both advantages of an efficient trapping due to coherent optical effects and broadband/wide-angle properties due to disorder. Our approach consists of the excitation of electromagnetic modes formed by multiple light scattering and wave interference in two-dimensional random media. We show, by numerical calculations, that the spectral and angular responses of thin films containing disordered photonic patterns are intimately related to the in-plane light transport process and can be tuned through structural correlations. Our findings, which are applicable to all waves, are particularly suited for improving the absorption efficiency of thin-film solar cells and can provide a new approach for high-extraction-efficiency light-emitting diodes.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Light trapping in thin random films.
Figure 2: Distribution of resonances in two-dimensional random media.
Figure 3: Influence of structural correlations.

References

  1. Polman, A. & Atwater, H. A. Photonic design principles for ultrahigh-efficiency photovoltaics. Nature Mater. 11, 174–177 (2012).

    Article  CAS  Google Scholar 

  2. Mallick, S. B., Sergeant, N. P., Agrawal, M., Lee, J-Y. & Peumans, P. Coherent light trapping in thin-film photovoltaics. Mater. Res. Soc. Bull. 36, 453–460 (2011).

    Article  CAS  Google Scholar 

  3. Atwater, H. A. & Polman, A. Plasmonics for improved photovoltaic devices. Nature Mater. 9, 205–213 (2010).

    Article  CAS  Google Scholar 

  4. Pillai, S. & Green, M. A. Plasmonics for photovoltaic applications. Sol. Energy Mater. Sol. Cells 94, 1481–1486 (2010).

    Article  CAS  Google Scholar 

  5. Yao, Y. et al. Broadband light management using low-Q whispering gallery modes in spherical nanoshells. Nature Commun. 3, 664 (2012).

    Article  Google Scholar 

  6. Spinelli, P., Verschuuren, M. & Polman, A. Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators. Nature Commun. 3, 692 (2012).

    Article  CAS  Google Scholar 

  7. Meng, X. et al. Absorbing photonic crystals for silicon thin-film solar cells: Design, fabrication and experimental investigation. Sol. Energy Mater. Sol. Cells 95, S32–S38 (2011).

    Article  CAS  Google Scholar 

  8. Battaglia, C. et al. Nanomoulding of transparent zinc oxide electrodes for efficient light trapping in solar cells. Nature Photon. 5, 535–538 (2011).

    Article  CAS  Google Scholar 

  9. Mallick, S. B. et al. Ultrathin crystalline–silicon solar cells with embedded photonic crystals. Appl. Phys. Lett. 100, 053113 (2012).

    Article  Google Scholar 

  10. Bozzola, A., Liscidini, M. & Andreani, L. C. Photonic light-trapping versus Lambertian limits in thin film silicon solar cells with 1d and 2d periodic patterns. Opt. Express 20, A224–A244 (2012).

    Article  Google Scholar 

  11. Rockstuhl, C. et al. Comparison and optimization of randomly textured surfaces in thin-film solar cells. Opt. Express 18, A335–A341 (2010).

    Article  CAS  Google Scholar 

  12. Ferry, V. E. et al. Optimized spatial correlations for broadband light trapping nanopatterns in high efficiency ultrathin film a-Si:H solar cells. Nano Lett. 11, 4239–4245 (2011).

    Article  CAS  Google Scholar 

  13. Sheng, X., Johnson, S. G., Michel, J. & Kimerling, L. C. Optimization-based design of surface textures for thin-film Si solar cells. Opt. Express 19, A841–A850 (2011).

    Article  CAS  Google Scholar 

  14. Akkermans, E. & Montambaux, G. Mesoscopic Physics of Electrons and Photons 1st edn (Cambridge Univ. Press, 2007).

    Book  Google Scholar 

  15. Lye, J. E. et al. Bose–Einstein condensate in a random potential. Phys. Rev. Lett. 95, 070401 (2005).

    Article  CAS  Google Scholar 

  16. Aspect, A. & Inguscio, M. Anderson localization of ultracold atoms. Phys. Today 62, 30–35 (August, 2009).

    Article  CAS  Google Scholar 

  17. Sheng, P. Introduction to Wave Scattering, Localization and Mesoscopic Phenomena 2nd edn (Springer, 2010).

    Google Scholar 

  18. Wang, J. & Genack, A. Z. Transport through modes in random media. Nature 471, 345–348 (2011).

    Article  CAS  Google Scholar 

  19. Sebbah, P., Sornette, D. & Vanneste, C. Anomalous diffusion in two-dimensional Anderson-localization dynamics. Phys. Rev. B 48, 12506–12510 (1993).

    Article  CAS  Google Scholar 

  20. Sigalas, M. M., Soukoulis, C. M., Chan, C-T. & Turner, D. Localization of electromagnetic waves in two-dimensional disordered systems. Phys. Rev. B 53, 8340–8348 (1996).

    Article  CAS  Google Scholar 

  21. Schwartz, T., Bartal, G., Fishman, S. & Segev, M. Transport and Anderson localization in disordered two-dimensional photonic lattices. Nature 446, 52–55 (2007).

    Article  CAS  Google Scholar 

  22. Riboli, F. et al. Anderson localization of near-visible light in two dimensions. Opt. Lett. 36, 127–129 (2011).

    Article  CAS  Google Scholar 

  23. Vollhardt, D. & Wölfle, P. Diagrammatic, self-consistent treatment of the Anderson localization problem in d<2 dimensions. Phys. Rev. B 22, 4666–4679 (1980).

    Article  Google Scholar 

  24. Sebbah, P. & Vanneste, C. Random laser in the localized regime. Phys. Rev. B 66, 144202 (2002).

    Article  Google Scholar 

  25. Noh, H. et al. Control of lasing in biomimetic structures with short-range order. Phys. Rev. Lett. 106, 183901 (2011).

    Article  Google Scholar 

  26. Brown, G. & Wu, J. Third generation photovoltaics. Laser Photon. Rev. 3, 394–405 (2009).

    Article  CAS  Google Scholar 

  27. Schnitzer, I., Yablonovitch, E., Caneau, C., Gmitter, T. J. & Scherer, A. 30% external quantum efficiency from surface textured, thin film light emitting diodes. Appl. Phys. Lett. 63, 2174–2176 (1993).

    Article  CAS  Google Scholar 

  28. Wiesmann, C., Bergenek, K., Linder, N. & Schwarz, U. Photonic crystal LEDs–designing light extraction. Laser Photon. Rev. 3, 262–286 (2009).

    Article  CAS  Google Scholar 

  29. Yablonovitch, E. & Cody, G. D. Intensity enhancement in textured optical sheets for solar cells. IEEE Trans. Electron Dev. 29, 300–305 (1982).

    Article  Google Scholar 

  30. Green, M. A. Lambertian light trapping in textured solar cells and light- emitting diodes: analytical solutions. Prog. Photovol.: Res. Appl. 10, 235–241 (2002).

    Article  CAS  Google Scholar 

  31. Taflove, A. & Hagness, S. C. Computational Electrodynamics: The Finite-Difference Time-Domain Method 3rd edn (Artech House, 2005).

    Google Scholar 

  32. Palik, E. D. Handbook of Optical Constants of Solids (Academic, 1997).

    Google Scholar 

  33. Yu, Z., Raman, A. & Fan, S. Fundamental limit of nanophotonic light trapping in solar cells. Proc. Natl Acad. Sci. USA 107, 17491–17496 (2010).

    Article  CAS  Google Scholar 

  34. Callahan, D. M., Munday, J. N. & Atwater, H. A. Solar cell light trapping beyond the ray optic limit. Nano Lett. 12, 214–218 (2012).

    Article  CAS  Google Scholar 

  35. Lagendijk, A. & van Tiggelen, B. A. Resonant multiple scattering of light. Phys. Rep. 270, 143–215 (1996).

    Article  CAS  Google Scholar 

  36. Engelen, R. J. P. et al. Ultrafast evolution of photonic eigenstates in k-space. Nature Phys. 3, 401–405 (2007).

    Article  CAS  Google Scholar 

  37. Burresi, M., van Oosten, D., Song, B. S., Noda, S. & Kuipers, L. Ultrafast reciprocal space investigation of cavity–waveguide coupling. Opt. Lett. 36, 1827–1829 (2011).

    Article  CAS  Google Scholar 

  38. Rojas-Ochoa, L. F., Mendez-Alcaraz, J. M., Sáenz, J. J., Schurtenberger, P. & Scheffold, F. Photonic properties of strongly correlated colloidal liquids. Phys. Rev. Lett. 93, 073903 (2004).

    Article  CAS  Google Scholar 

  39. Florescu, M., Torquato, S. & Steinhardt, P. J. Designer disordered materials with large, complete photonic band gaps. Proc. Natl Acad. Sci. USA 106, 20658–20663 (2009).

    Article  CAS  Google Scholar 

  40. Yang, J. et al. Photonic-band-gap effects in two-dimensional polycrystalline and amorphous structures. Phys. Rev. A 82, 053838 (2010).

    Article  Google Scholar 

  41. Joannopoulos, J. D., Johnson, S. G., Winn, J. N. & Meade, R. D. Photonic Crystals: Molding the Flow of Light 2nd edn (Princeton Univ. Press, 2008).

    Google Scholar 

  42. Skoge, M., Donev, A., Stillinger, F. H. & Torquato, S. Packing hyperspheres in high-dimensional Euclidean spaces. Phys. Rev. E 74, 041127 (2006).

    Article  Google Scholar 

  43. Hammer, M. 1-D multilayer slab waveguide mode solver. http://www.home.math.utwente.nl/~hammer/oms.html.

  44. Oskooi, A. F. et al. Meep: A flexible free-software package for electromagnetic simulations by the FDTD method. Comput. Phys. Commun. 181, 687–702 (2010).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work is supported by the Eu NoE Nanophotonics for Energy Efficiency, the Italian CNR project EFOR and ENI S.p.A. We gratefully acknowledge P. Barthelemy, J. Bertolotti and T. Svensson for insightful discussions.

Author information

Authors and Affiliations

Authors

Contributions

All authors developed the concept. K.V. carried out the numerical simulations. K.V. and M.B. performed the data analysis. All authors discussed and interpreted the results. K.V. prepared the manuscript with suggestions from M.B., F.R. and D.S.W.

Corresponding author

Correspondence to Kevin Vynck.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 487 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Vynck, K., Burresi, M., Riboli, F. et al. Photon management in two-dimensional disordered media. Nature Mater 11, 1017–1022 (2012). https://doi.org/10.1038/nmat3442

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nmat3442

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing