OSA's Digital Library

Energy Express

Energy Express

  • Editor: Christian Seassal
  • Vol. 22, Iss. S2 — Mar. 10, 2014
  • pp: A542–A551

How to assess light trapping structures versus a Lambertian Scatterer for solar cells?

Christian S Schuster, Angelo Bozzola, Lucio C Andreani, and Thomas F Krauss  »View Author Affiliations

Optics Express, Vol. 22, Issue S2, pp. A542-A551 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (1009 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We propose a new figure of merit to assess the performance of light trapping nanostructures for solar cells, which we call the light trapping efficiency (LTE). The LTE has a target value of unity to represent the performance of an ideal Lambertian scatterer, although this is not an absolute limit but rather a benchmark value. Since the LTE aims to assess the nanostructure itself, it is, in principle, independent of the material, fabrication method or technology used. We use the LTE to compare numerous proposals in the literature and to identify the most promising light trapping strategies. We find that different types of photonic structures allow approaching the Lambertian limit, which shows that the light trapping problem can be approached from multiple directions. The LTE of theoretical structures significantly exceeds that of experimental structures, which highlights the need for theoretical descriptions to be more comprehensive and to take all relevant electro-optic effects into account.

© 2014 Optical Society of America

OCIS Codes
(040.5350) Detectors : Photovoltaic
(050.1950) Diffraction and gratings : Diffraction gratings
(350.6050) Other areas of optics : Solar energy
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(050.5298) Diffraction and gratings : Photonic crystals
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Energy Nanotechnology

Original Manuscript: December 4, 2013
Revised Manuscript: January 25, 2014
Manuscript Accepted: January 27, 2014
Published: March 7, 2014

Virtual Issues
Renewable Energy and the Environment (2014) Optics Express

Christian S Schuster, Angelo Bozzola, Lucio C Andreani, and Thomas F Krauss, "How to assess light trapping structures versus a Lambertian Scatterer for solar cells?," Opt. Express 22, A542-A551 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. Jäger-Waldau, JRC PV Status Report2013, http://iet.jrc.ec.europa.eu/remea/pv-status-report-2013 .
  2. T. Tiedje, E. Yablonovitch, G. Cody, and B. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. 31(5), 711–716 (1984). [CrossRef]
  3. A. Goetzberger, “Optical confinement in thin Si solar cells by diffuse back reflectors,” Proceedings of the 15th IEEE Photovoltaic Specialists Conference, Orlando, 867–870 (1981).
  4. E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. 29(2), 300–305 (1982). [CrossRef]
  5. M. Green, “Lambertian light trapping in textured solar cells and light-emitting diodes: Analytical solutions,” Prog. Photovolt. Res. Appl. 10(4), 235–241 (2002). [CrossRef]
  6. A. Bozzola, M. Liscidini, and L. C. Andreani, “Photonic light-trapping versus Lambertian limits in thin film silicon solar cells with 1D and 2D periodic patterns,” Opt. Express 20(S2Suppl 2), A224–A244 (2012). [CrossRef] [PubMed]
  7. NREL, AM1.5G solar spectrum irradiance data: http://rredc.nrel.gov/solar/spectra/am1.5 .
  8. A. Luque, Solar Cells and Optics for Photovoltaic Concentration (Adam Hilger, Bristol, 1989).
  9. R. Brendel, Thin-Film Crystalline Silicon Solar Cells: Physics and Technology (Wiley-VCH, 2003).
  10. C. Battaglia, M. Boccard, F.-J. Haug, and C. Ballif, “Light trapping in solar cells: When does a Lambertian scatterer scatter Lambertianly?” J. Appl. Phys. 112(9), 094504 (2012). [CrossRef]
  11. H. Sai, K. Saito, N. Hozuki, and M. Kondo, “Relationship between the cell thickness and the optimum period of textured back reflectors in thin-film microcrystalline silicon solar cells,” Appl. Phys. Lett. 102(5), 053509 (2013). [CrossRef]
  12. M. Berginski, J. Hüpkes, A. Gordijn, W. Reetz, T. Wätjen, B. Rech, and M. Wuttig, “Experimental studies and limitations of the light trapping and optical losses in microcrystalline silicon solar cells,” Sol. Energy Mater. Sol. Cells 92(9), 1037–1042 (2008). [CrossRef]
  13. V. Jovanov, U. Planchoke, P. Magnus, H. Stiebig, and D. Knipp, “Influence of back contact morphology on light trapping and plasmonic effects in microcrystalline silicon single junction and micromorph tandem solar cells,” Sol. Energy Mater. Sol. Cells 110, 49–57 (2013). [CrossRef]
  14. V. Depauw, X. Meng, O. El Daif, G. Gomard, L. Lalouat, E. Drouard, C. Trompoukis, A. Fave, C. Seassal, and I. Gordon, “Micrometer-Thin Crystalline-Silicon Solar Cells Integrating Numerically Optimized 2-D Photonic Crystals,” IEEE J Phot., in press (2013).
  15. O. Isabella, A. Ingenito, D. Linssen, and M. Zeman, “Front/Rear Decoupled Texturing in Refractive and Diffractive Regimes for Ultra-Thin Silicon-Based Solar Cells,” Renewable Energy and the Environment, OSA Technical Digest, paper PM4C.2 (2013).
  16. E. R. Martins, J. Li, Y. Liu, V. Depauw, Z. Chen, J. Zhou, and T. F. Krauss, “Deterministic quasi-random nanostructures for photon control,” Nat Commun 4, 2665 (2013). [CrossRef] [PubMed]
  17. E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, 1985).
  18. J. Zhao, A. Wang, P. P. Altermatt, S. R. Wenham, and M. A. Green, “24% Efficient perl silicon solar cell: Recent improvements in high efficiency silicon cell research,” Sol. Energy Mater. Sol. Cells 41-42, 87–99 (1996). [CrossRef]
  19. P. Campbell and M. A. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62(1), 243 (1987). [CrossRef]
  20. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007). [CrossRef] [PubMed]
  21. M. A. Green and M. J. Keevers, “Optical Properties of Intrinsic Silicon at 300 K,” Prog. Photovolt. Res. Appl. 3(3), 189–192 (1995). [CrossRef]
  22. J. Gjessing, A. S. Sudbø, and E. S. Marstein, “Comparison of periodic light-trapping structures in thin crystalline silicon solar cells,” J. Appl. Phys. 110(3), 033104 (2011). [CrossRef]
  23. X. Sheng, L. Z. Broderick, and L. C. Kimerling, “Photonic crystal structures for light trapping in thin-film Si solar cells: Modeling, process and optimizations,” Opt. Commun.in press.
  24. C. Trompoukis, O. El Daif, V. Depauw, I. Gordon, and J. Poortmans, “Photonic assisted light trapping integrated in ultrathin crystalline silicon solar cells by nanoimprint lithography,” Appl. Phys. Lett. 101(10), 103901 (2012). [CrossRef]
  25. F. Feldmann, M. Bivour, C. Reichel, M. Hermle, and S.W. Glunz, “A Passivated Rear Contact for High-Efficiency n-Type Si Solar Cells Enabling High Voc's and FF>82%,” 28th EU PVSEC, 2CO.4.4 (2013).
  26. L. Wang, J. Han, A. Lochtefeld, A. Gerger, M. Carroll, D. Stryker, S. Bengtson, M. Curtin, H. Li, Y. Yao, D. Lin, J. Ji, A.J. Lennon, R.L. Opila, and A. Barnett, “16.8% Efficient Ultra-Thin Silicon Solar Cells on Steel,” 28th EU PVSEC, 3DV.1.12 (2013).
  27. J. H. Petermann, D. Zielke, J. Schmidt, F. Haase, E. G. Rojas, and R. Brendel, “19% efficient and 43μm thick crystalline Si solar cell from layer transfer using porous silicon,” Prog. Photovolt. Res. Appl. 20(1), 1–5 (2012). [CrossRef]
  28. J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy 77(6), 917–930 (2004). [CrossRef]
  29. C. Haase and H. Stiebig, “Optical Properties of Thin-film Silicon Solar Cells with Grating Couplers,” Prog. Photovolt. Res. Appl. 14(7), 629–641 (2006). [CrossRef]
  30. S. E. Han and G. Chen, “Toward the Lambertian limit of light trapping in thin nanostructured silicon solar cells,” Nano Lett. 10(11), 4692–4696 (2010). [CrossRef] [PubMed]
  31. K. X. Wang, Z. Yu, V. Liu, Y. Cui, and S. Fan, “Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings,” Nano Lett. 12(3), 1616–1619 (2012). [CrossRef] [PubMed]
  32. S. B. Mallick, M. Agrawal, and P. Peumans, “Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells,” Opt. Express 18(6), 5691–5706 (2010). [CrossRef] [PubMed]
  33. A. Mellor, I. Tobias, A. Marti, and A. Luque, “A numerical study of Bi-periodic binary diffraction gratings for solar cell applications,” Sol. Energy Mater. Sol. Cells 95(12), 3527–3535 (2011). [CrossRef]
  34. A. Mellor, H. Hauser, C. Wellens, J. Benick, J. Eisenlohr, M. Peters, A. Guttowski, I. Tobías, A. Martí, A. Luque, and B. Bläsi, “Nanoimprinted diffraction gratings for crystalline silicon solar cells: implementation, characterization and simulation,” Opt. Express 21(S2), A295–A304 (2013). [CrossRef] [PubMed]
  35. R. Dewan and D. Knipp, “Light trapping in thin-film silicon solar cells with integrated diffraction grating,” J. Appl. Phys. 106(7), 074901 (2009). [CrossRef]
  36. N. T. Fofang, T. S. Luk, M. Okandan, G. N. Nielson, and I. Brener, “Substrate-modified scattering properties of silicon nanostructures for solar energy applications,” Opt. Express 21(4), 4774–4782 (2013). [CrossRef] [PubMed]
  37. D. Lockau, T. Sontheimer, C. Becker, E. Rudigier-Voigt, F. Schmidt, and B. Rech, “Nanophotonic light trapping in 3-dimensional thin-film silicon architectures,” Opt. Express 21(S1), A42–A52 (2013). [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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited