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A model for direct laser interference patterning of ZnO:Al - predicting possible sample topographies to optimize light trapping in thin-film silicon solar cells

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We present a novel approach to obtaining a quick prediction of a sample’s topography after the treatment with direct laser interference patterning (DLIP) . The underlying model uses the parameters of the experimental setup as input, calculates the laser intensity distribution in the interference volume and determines the corresponding heat intake into the material as well as the subsequent heat diffusion within the material. The resulting heat distribution is used to determine the topography of the sample after the DLIP treatment . This output topography is in good agreement with corresponding experiments. The model can be applied in optimization algorithms in which a sample topography needs to be engineered in order to suit the needs of a given device. A prominent example for such an application is the optimization of the light scattering properties of the textured interfaces in a solar cell.

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  1. Mu Plus Lambda evolutionary algorithm implemented in DEAP [16].


  1. S. Ring, B. Stannowski, F. Fink, R. Schlatmann, Micro gratings written in ZnO:Al thin films using picosecond UV-laser interference patterning. Phys. Status Solidi RRL 7, 635–638 (2013)

    Article  ADS  Google Scholar 

  2. S. Ring, S. Neubert, C. Schultz, S.S. Schmidt, F. Ruske, B. Stannowski, F. Fink, R. Schlatmann, Light trapping for a-Si:H/c-Si:H tandem solar cells using direct pulsed laser interference texturing. Phys. Status Solidi RRL 9(1), 3640 (2014)

    Google Scholar 

  3. S. Eckhardt, C. Sachse, A.F. Lasagni, Light management in transparent conducting oxides by direct fabrication of periodic surface arrays. Phys. Proc. 41, 552–557 (2013)

    Article  ADS  Google Scholar 

  4. L. Müller-Meskamp, Y.H. Kim, T. Roch, S. Hofmann, R. Scholz, S. Eckardt, K. Leo, A.F. Lasagni, Efficiency enhancement of organic solar cells by fabricating periodic surface textures using direct laser interference patterning. Adv. Mater. 24(7), 906–910 (2012)

    Article  Google Scholar 

  5. D.Y. Kim, S.K. Tripathy, L. Li, J. Kumar, Laserinduced holographic surface relief gratings on nonlinear optical polymer films. Appl. Phys. Lett. 66(10), 1166–1168 (1995)

    Article  ADS  Google Scholar 

  6. F. Mücklich, A. Lasagni, C. Daniel, Laser interference metallurgy—periodic surface patterning and formation of intermetallics. Intermetallics 13, 437–442 (2005)

    Article  Google Scholar 

  7. A. Lasagni, C. Holzapfel, F. Mücklich, Periodic pattern formation of intermetallic phases with long range order by laser interference metallurgy. Adv. Eng. Mater. 7(6), 487–492 (2005)

    Article  Google Scholar 

  8. A. Lasagni, F. Mücklich, M. Nejati, R. Clasen, Periodical surface structuring of metals by laser interference metallurgy as a new fabrication method of textured solar selective absorbers. Adv. Eng. Mater. 8, 580–584 (2006)

    Article  Google Scholar 

  9. A. Lasagni, T. Roch, M. Bieda, D. Benke, E. Beyer, High speed surface functionalization using direct laser interference patterning, towards 1 m2/min fabrication speed with sub-μm resolution. In: Proc. SPIE 8968, Laser-based Micro- and Nanoprocessing VIII. (2014), p. 89680A. doi: 10.1117/12.2041215

  10. S. Beckemper, Generation of periodic micro- and nano-structures by parameter-controlled three-beam laser interference technique. J. Laser Micro/Nanoeng. 6(1), 49–53 (2011)

    Article  Google Scholar 

  11. J. Huang, S. Beckemper, A. Gillner, K. Wang, Tunable surface texturing by polarization-controlled three-beam interference. J. Micromech. Microeng. 20(9), 095004 (2010)

    Article  ADS  Google Scholar 

  12. Y. Nakata, K. Murakawa, K. Sonoda, K. Momoo, N. Miyanaga, Design of interference using coherent beams configured as a six-sided pyramid. Appl. Opt. 51(21), 5004–5010 (2012)

    Article  ADS  Google Scholar 

  13. T. Knüttel, S. Bergfeld, S. Haas, Laser texturing of surfaces in thin-film silicon photovoltaics—a comparison of potential processes. J. Laser Micro/Nanoeng. 8(3), 222–229 (2013)

    Article  Google Scholar 

  14. M. Berginski, J. Hüpkes, M. Schulte, G. Schöpe, H. Stiebig, B. Rech, M. Wuttig, The effect of front ZnO:Al surface texture and optical transparency on efficient light trapping in silicon thin-film solar cells. J. Appl. Phys. 101(7), 074903 (2007)

    Article  ADS  Google Scholar 

  15. J.L. Stay, T.K. Gaylord, Three-beam-interference lithography: contrast and crystallography. Appl. Opt. 47, 3221–3230 (2008)

    Article  ADS  Google Scholar 

  16. C. Gagn, DEAP: evolutionary algorithms made easy. J. Mach. Learn. Res. 13, 2171–2175 (2012)

    MathSciNet  MATH  Google Scholar 

  17. R. Poprawe, Lasertechnik für die Fertigung, ch. 4 (Springer, New York, 2005), p. 41

    Google Scholar 

  18. D. Bäuerle, Laser Processing and Chemistry, ch. 2 (Springer, New York, 2011), pp. 19–24

    Book  Google Scholar 

  19. K. Ellmer, A. Klein, B. Rech, Transparent Conductive Zinc Oxide: Basics and Applications in Thin Film Solar Cells, ch. 1 (Springer, New York, 2007), p. 6

    Google Scholar 

  20. D. Dufft, A. Rosenfeld, S.K. Das, R. Grunwald, J. Bonse, Femtosecond laser-induced periodic surface structures revisited: a comparative study on ZnO. J. Appl. Phys. 105(3), 034908 (2009)

    Article  ADS  Google Scholar 

  21. A. Sarkar, S. Ghosh, S. Chaudhuri, A. Pal, Studies on electron transport properties and the Burstein–Moss shift in indium-doped ZnO films. Thin Solid Films 204(2), 255–264 (1991)

    Article  ADS  Google Scholar 

  22. J.M. Liu, Simple technique for measurements of pulsed Gaussian-beam spot sizes. Opt. Lett. 7(5), 196–198 (1982)

    Article  ADS  Google Scholar 

  23. D.F. Anthrop, A.W. Searcy, Sublimation and thermodynamic properties of zinc oxide. J. Phys. Chem. 68(8), 2335–2342 (1964)

    Article  Google Scholar 

  24. C. Chan, J. Mazumder, M. Chen, Three-dimensional axisymmetric model for convection in laser-melted pools. Mater. Sci. Technol. 3(4), 306–311 (1987)

    Article  Google Scholar 

  25. R. Poprawe, Lasertechnik für die Fertigung, ch. 11 (Springer, New York, 2005), p. 176

    Google Scholar 

  26. D. Bäuerle, Laser Processing and Chemistry, ch. 10 (Springer, New York, 2011)

    Book  Google Scholar 

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The authors want to thank Gunnar Schöpe, Andreas Bauer and Pascal Foucart for technical assistance, Bugra Turan, Nicolas Sommer and Uwe Rau for fruitful discussions and the European Union as well as the state of North Rhine-Westphalia for financial funding (Project LATEXT EN3003/B).

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Correspondence to Tobias Dyck.

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Dyck, T., Haas, S. A model for direct laser interference patterning of ZnO:Al - predicting possible sample topographies to optimize light trapping in thin-film silicon solar cells. Appl. Phys. A 122, 445 (2016).

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