OSA's Digital Library

Energy Express

Energy Express

  • Editor: Christian Seassal
  • Vol. 22, Iss. S1 — Jan. 13, 2014
  • pp: A53–A67

Analytical solution for haze values of aluminium-induced texture (AIT) glass superstrates for a-Si:H solar cells

Nasim Sahraei, Karen Forberich, Selvaraj Venkataraj, Armin G. Aberle, and Marius Peters  »View Author Affiliations

Optics Express, Vol. 22, Issue S1, pp. A53-A67 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (1888 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Light scattering at randomly textured interfaces is essential to improve the absorption of thin-film silicon solar cells. Aluminium-induced texture (AIT) glass provides suitable scattering for amorphous silicon (a-Si:H) solar cells. The scattering properties of textured surfaces are usually characterised by two properties: the angularly resolved intensity distribution and the haze. However, we find that the commonly used haze equations cannot accurately describe the experimentally observed spectral dependence of the haze of AIT glass. This is particularly the case for surface morphologies with a large rms roughness and small lateral feature sizes. In this paper we present an improved method for haze calculation, based on the power spectral density (PSD) function of the randomly textured surface. To better reproduce the measured haze characteristics, we suggest two improvements: i) inclusion of the average lateral feature size of the textured surface into the haze calculation, and ii) considering the opening angle of the haze measurement. We show that with these two improvements an accurate prediction of the haze of AIT glass is possible. Furthermore, we use the new equation to define optimum morphology parameters for AIT glass to be used for a-Si:H solar cell applications. The autocorrelation length is identified as the critical parameter. For the investigated a-Si:H solar cells, the optimum autocorrelation length is shown to be 320 nm.

© 2013 Optical Society of America

OCIS Codes
(120.6660) Instrumentation, measurement, and metrology : Surface measurements, roughness
(240.5770) Optics at surfaces : Roughness
(290.0290) Scattering : Scattering
(290.5835) Scattering : Scattering, Harvey

ToC Category:
Light Trapping for Photovoltaics

Original Manuscript: September 23, 2013
Revised Manuscript: November 7, 2013
Manuscript Accepted: November 8, 2013
Published: November 27, 2013

Nasim Sahraei, Karen Forberich, Selvaraj Venkataraj, Armin G. Aberle, and Marius Peters, "Analytical solution for haze values of aluminium-induced texture (AIT) glass superstrates for a-Si:H solar cells," Opt. Express 22, A53-A67 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. T. Tiedje, B. Abeles, J. M. Cebulka, and J. Pelz, “Photoconductivity enhancement by light trapping in rough amorphous silicon,” Appl. Phys. Lett. 42(8), 712–714 (1983). [CrossRef]
  2. H. W. Deckman, C. R. Wronski, H. Witzke, and E. Yablonovitch, “Optically enhanced amorphous-silicon solar-cells,” Appl. Phys. Lett. 42(11), 968–970 (1983). [CrossRef]
  3. H. Sakai, T. Yoshida, S. Fujikake, Y. Ichikawa, A. Ueda, O. Ishiwata, and M. Nagano, “Effects of the surface morphology of transparent electrode on film deposition and photovoltaic performance of a-Si:H solar cells,” J. Non-Cryst. Solids 115(1–3), 198–200 (1989). [CrossRef]
  4. C. Battaglia, K. Söderström, J. Escarré, F.-J. Haug, D. Dominé, P. Cuony, M. Boccard, G. Bugnon, C. Denizot, M. Despeisse, A. Feltrin, and C. Ballif, “Efficient light management scheme for thin film silicon solar cells via transparent random nanostructures fabricated by nanoimprinting,” Appl. Phys. Lett. 96(21), 213504 (2010). [CrossRef]
  5. M. Zeman, O. Isabella, K. Jager, R. Santbergen, S. Solntsev, M. Topic, and J. Krc, “Advanced light management approaches for thin-film silicon solar cells,” Energy Procedia 15, 189–199 (2012). [CrossRef]
  6. A. Hongsingthong, A. Aino, P. Sichanugrist, M. Konagai, H. Kuramochi, R. Akiike, H. Iigusa, K. Utsumi, and T. Shibutami, “Development of novel Al-doped zinc oxide films fabricated on etched glass and their application to solar cells,” Jpn. J. Appl. Phys. 51, 10NB09 (2012). [CrossRef]
  7. J. Krč, M. Zeman, O. Kluth, F. Smole, and M. Topic, “Effect of surface roughness of ZnO:Al films on light scattering in hydrogenated amorphous silicon solar cells,” Thin Solid Films 426(1–2), 296–304 (2003). [CrossRef]
  8. M. Zeman, R. van Swaaij, J. W. Metselaar, and R. E. I. Schropp, “Optical modeling of a-Si: H solar cells with rough interfaces: Effect of back contact and interface roughness,” J. Appl. Phys. 88(11), 6436–6443 (2000). [CrossRef]
  9. O. Isabella, J. Krc, and M. Zeman, “Modulated surface textures for enhanced light trapping in thin-film silicon solar cells,” Appl. Phys. Lett. 97(10), 101106 (2010). [CrossRef]
  10. A. G. Aberle, P. I. Widenborg, and N. Chuangsuwanich, “Glass texturing,” European patent, EP1613562 B1, 2011.
  11. J. Wang, S. Venkataraj, C. Battaglia, P. Vayalakkara, and A. G. Aberle, “Analysis of optical and morphological properties of aluminium induced texture glass superstrates,” Jpn. J. Appl. Phys. 51, 10NB08 (2012). [CrossRef]
  12. P. I. Widenborg and A. G. Aberle, “Polycrystalline silicon thin-film solar cells on AIT-textured glass superstrates,” Adv. OptoElectronics. 2007, 1–7 (2007).
  13. N. Sahraei, S. Venkataraj, A. G. Aberle, and I. M. Peters, “Investigation of the optical absorption of a-Si:H solar cells on micro- and nano-textured surfaces,” Energy Procedia 33, 166–172 (2013). [CrossRef]
  14. K. Jäger, M. Fischer, R. A. C. M. M. van Swaaij, and M. Zeman, “A scattering model for nano-textured interfaces and its application in opto-electrical simulations of thin-film silicon solar cells,” J. Appl. Phys. 111(8), 083108 (2012). [CrossRef]
  15. D. Dominé, F. J. Haug, C. Battaglia, and C. Ballif, “Modeling of light scattering from micro- and nanotextured surfaces,” J. Appl. Phys. 107(4), 044504 (2010). [CrossRef]
  16. M. Boccard, P. Cuony, C. Battaglia, M. Despeisse, and C. Ballif, “Unlinking absorption and haze in thin film silicon solar cells front electrodes,” Phys. Status Solidi 4, 326–328 (2010).
  17. J. O. Porteus, “Relation between the height distribution of a rough surface and the reflectance at normal incidence,” J. Opt. Soc. Am. 53(12), 1394–1402 (1963). [CrossRef]
  18. I. Simonsen, A. Larsen, E. Andreassen, E. Ommundsen, and K. Nord-Varhaug, “Haze of surface random systems: An approximate analytic approach,” Phys. Rev. A 79(6), 063813 (2009). [CrossRef]
  19. J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51(1), 013402 (2012). [CrossRef]
  20. J. M. Bennett and L. Mattsson, Introduction to Surface Roughness and Scattering (Optical Society of America, 1989).
  21. V. Premachandran, S. Venkataraj, J. Wang, J. Long, Z. Ren, Y. Yin, P. I. Widenborg, and A. G. Aberle, “Aluminium induced glass texturing process on borosilicate and soda- lime glass superstrate for thin-film solar cells,” in Proc. 37th IEEE Photovoltaic Specialist Conference (Seattle, 2011), pp. L28–871.
  22. D. Domine, “The role of front electrodes and intermediate reflectors in the optoelectronic properties of high-efficiency micromorph solar cells,” PhD thesis (Faculté des Sciences, Institut de Microtechnique, Université de Neuchâtel, 2009), p. 179.
  23. S. Schröder, A. Duparré, L. Coriand, A. Tünnermann, D. H. Penalver, and J. E. Harvey, “Modeling of light scattering in different regimes of surface roughness,” Opt. Express 19(10), 9820–9835 (2011). [CrossRef] [PubMed]
  24. H. L. Yu and C. C. Hsaio, “Comparison of different measurement methods for transmittance haze,” Metrologia 46(4), S233–S237 (2009). [CrossRef]
  25. C. K. Carniglia, “Scalar scattering theory for multilayer optical coatings,” Opt. Eng. 18(2), 104–115 (1979). [CrossRef]
  26. A. Poruba, A. Fejfar, Z. Remeš, J. Špringer, M. Vaněček, J. Kočka, J. Meier, P. Torres, and A. Shah, “Optical absorption and light scattering in microcrystalline silicon thin films and solar cells,” J. Appl. Phys. 88(1), 148–160 (2000). [CrossRef]
  27. J. Springer, A. Poruba, and M. Vanecek, “Improved three-dimensional optical model for thin-film silicon solar cells,” J. Appl. Phys. 96(9), 5329–5337 (2004). [CrossRef]
  28. H. Stiebig, T. Brammer, T. Repmann, O. Kluth, N. Senoussaoui, A. Lambertz, and H. Wagner, “Light scattering in microcrystalline silicon thin-film solar cells,” in Proc. of the 16th EU-PVSEC (Glasgow, 2000), pp. 549–552.
  29. J. Krč, M. Zeman, F. Smole, and M. Topič, “Optical modeling of a-Si:H solar cells deposited on textured glass/SnO2 substrates,” J. Appl. Phys. 92(2), 749–755 (2002). [CrossRef]
  30. E. Sidick, H. Bosse, B. Bodermann, and R. M. Silver, eds., “Power spectral density specification and analysis of large optical surfaces,” in Modeling Aspects in Optical Metrology II, H. Bosse, B. Bodermann, and R. M. Silver, eds. (Proceedings of SPIE, Munich, Germany, 2009), pp. 73009L. [CrossRef]
  31. E. L. Church and P. Z. Takacs, “Light scattering from non-Gaussian surfaces,” in Optical Scattering in the Optics, Semiconductor, and Computer Disk Industries, J. C. Stover, ed. (SPIE, 1995), pp. 91–107.

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.

CrossCheck Deposited