Structural and Multidisciplinary Optimization

, Volume 50, Issue 3, pp 367–382 | Cite as

Topology optimization for light-trapping structure in solar cells

  • Shuangcheng Yu
  • Chen Wang
  • Cheng Sun
  • Wei ChenEmail author


The limitation associated with the low optical absorption remains to be the main technical barrier that constrains the efficiency of thin–film solar cells in energy conversion. Effective design of light-trapping structure is critical to increase light absorption, which is a highly complex phenomenon governed by several competing physical processes, imposing a number of challenges to topology optimization. This paper presents a general, yet systematic approach exploiting topology optimization for designing highly efficient light-trapping structures. We first demonstrate the proposed approach using genetic algorithm (GA) based non-gradient topology optimization (NGTO), which is robust for achieving highly-efficient designs of slot-waveguide based cells with both low-permittivity and high-permittivity scattering material at single wavelength or over a broad spectrum. The optimized light-trapping structure achieves a broadband absorption efficiency of 48.1 % and more than 3-fold increase over the Yablonovitch limit. The fabrication feasibility of the optimized design is also demonstrated. Next, the gradient topology optimization (GTO) approach for designing light-trapping structure is explored based on the Solid Isotropic Material with Penalization (SIMP) method. Similar designs are obtained through both GA based NGTO and SIMP based GTO, which verifies the validity of both approaches. Insights into the application of both approaches for solving the nanophotonic design problem with optimization nonlinearity are provided.


Topology optimization Light-trapping structure Nanophotonic design Genetic algorithm SIMP Solar cell 



This work is supported by the National Science Foundation under Grant number CMMI-1130640 and CMMI-0751621. Shuangcheng Yu would like to thank the International Institute for Nanotechnology for the Ryan Fellowship award. Dr. Fan Zhou at Northwestern University is acknowledged for the fabrication work. The authors would like to thank Prof. Krister Svanberg at KTH Royal Institute of Technology for providing the MMA code. The authors would also thank the reviewers for helpful comments that improved this manuscript.


  1. Almeida VR et al. (2004) Guiding and confining light in void nanostructure. Opt Lett 29(11):1209–1211CrossRefMathSciNetGoogle Scholar
  2. Atwater HA, Polman A (2010) Plasmonics for improved photovoltaic devices. Nat Mater 9(3):205–213CrossRefGoogle Scholar
  3. Aydin K et al. (2011) Broadband polarization-independent resonant light absorption using ultrathin plasmonic super absorbers. Nat Commun 2Google Scholar
  4. Andkjaer J, Sigmund O (2011) Topology optimized low-contrast all-dielectric optical cloak. Appl Phys Lett 98(2)Google Scholar
  5. Bendsoe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224CrossRefMathSciNetGoogle Scholar
  6. Bendsøe M (1989) Optimal shape design as a material distribution problem. Struct Multidiscip Optim 1:193–202CrossRefGoogle Scholar
  7. Bensoe M, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9–10):635–654Google Scholar
  8. Bellido JC, Donoso A (2007) An optimal design problem in wave propagation. J Optim Theory Appl 134(2):339–352CrossRefzbMATHMathSciNetGoogle Scholar
  9. Bermel P et al. (2007) Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals. Opt Express 15(25):16986–17000CrossRefGoogle Scholar
  10. Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. 2nd ed. SpringerGoogle Scholar
  11. Cheng DK (1989) Field and wave electromagnetics. Addison-Wesley, New YorkGoogle Scholar
  12. Chen X et al (2012) Broadband enhancement in thin-film amorphous silicon solar cells enabled by nucleated silver nanoparticles. Nano Lett 12(5):2187-2192CrossRefGoogle Scholar
  13. Callahan DM et al. (2012) Solar cell light trapping beyond the ray optic limit. Nano Lett 12(1):214–218CrossRefGoogle Scholar
  14. Dewan R et al. (2009) Light trapping in thin-film silicon solar cells with submicron surface texture. Opt Express 17(25):23058–23065CrossRefGoogle Scholar
  15. Feng NN et al. (2007) Design of highly efficient light-trapping structures for thin-film crystalline silicon solar cells. Ieee Trans Electr Devices 54(8):1926–1933CrossRefGoogle Scholar
  16. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley ProfessionalGoogle Scholar
  17. Goldberg DE, Deb K (1991) A comparative analysis of selection schemes used in genetic algorithm. In: foundations of Genetic Algorithms. Morgan Kaufmann, San Francisco, pp 69–93Google Scholar
  18. Guest J et al (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61:238–254CrossRefzbMATHMathSciNetGoogle Scholar
  19. Gondarenko A et al (2006) Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures. Phys Rev Lett 96(14):143904CrossRefGoogle Scholar
  20. Garnett E, Yang PD (2010) Light Trapping in Silicon Nanowire Solar Cells. Nano Lett 10(3):1082–1087CrossRefGoogle Scholar
  21. Guest JK et al. (2011) Eliminating beta-continuation from Heaviside projection and density filter algorithms. Struct Multidiscip Optim 44(4):443–453CrossRefzbMATHMathSciNetGoogle Scholar
  22. Holland JH (1975) Adaptation in natural and artificial systems. The University of Michigan Press, Ann ArborGoogle Scholar
  23. Jensen JS, Sigmund O (2004) Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends. Appl Phys Lett 84(12):2022–2024CrossRefGoogle Scholar
  24. Jensen JS, Sigmund O (2005) Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide. J Opt Soc Am B Opt Phys 22(6):1191–1198CrossRefGoogle Scholar
  25. Jensen JS, Sigmund O (2011) Topology optimization for nano-photonics. Laser Photonics Rev 5(2):308–321CrossRefGoogle Scholar
  26. Kao CY et al. (2005) Maximizing band gaps in two-dimensional photonic crystals by using level set methods. Appl Phys B Lasers Opt 81(2–3):235–244CrossRefGoogle Scholar
  27. Li LF (1997) New formulation of the Fourier modal method for crossed surface-relief gratings. J Opt Soc Am A Opt Image Sci Vis 14(10):2758–2767CrossRefGoogle Scholar
  28. Li LF (2003) Note on the S-matrix propagation algorithm. J Opt Soc Am A Opt Image Sci Vis 20(4):655–660CrossRefGoogle Scholar
  29. Luh GC, Lin CY (2009) Structural topology optimization using ant colony optimization algorithm. Appl Soft Comput 9(4):1343–1353CrossRefGoogle Scholar
  30. Moharam MG et al. (1995a) Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings - enhanced transmittance matrix approach. J Opt Soc Am A Opt Image Sci Vis 12(5):1077–1086CrossRefGoogle Scholar
  31. Moharam MG et al. (1995b) Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings. J Opt Soc Am A Opt Image Sci Vis 12(5):1068–1076CrossRefGoogle Scholar
  32. Mallick SB et al (2010) Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells. Opt Express 18(6):5691–5706CrossRefGoogle Scholar
  33. Mallick SB et al (2011) Coherent light trapping in thin-film photovoltaics. Mrs Bull 36(6):453–460CrossRefGoogle Scholar
  34. Miller OD et al (2012) Inverse design of a nano-scale surface texture for light trapping. In: 2012 Conference on lasers and electro-optics (Cleo)Google Scholar
  35. Preble S et al (2005) Two-dimensional photonic crystals designed by evolutionary algorithms. Appl Phys Lett 86(6)Google Scholar
  36. Park SH et al. (2009) Bulk heterojunction solar cells with internal quantum efficiency approaching 100%. Nat Photonics 3(5):297–U5CrossRefGoogle Scholar
  37. Polman A, Atwater HA (2012) Photonic design principles for ultrahigh-efficiency photovoltaics. Nat Mater 11(3):174–177CrossRefGoogle Scholar
  38. Rozvany GIN (1992) Shape and layout optimization of structural systems and optimality criteria methods. SpringerGoogle Scholar
  39. Rai-Choudhury P (1997) Handbook of microlithography, micromachining and microfabrication. SPIE Optical Engineering PressGoogle Scholar
  40. Reed P et al. (2000) Designing a competent simple genetic algorithm for search and optimization. Water Resour Res 36(12):3757–3761CrossRefGoogle Scholar
  41. Raman A et al. (2011) Dielectric nanostructures for broadband light trapping in organic solar cells. Opt Express 19(20):19015–19026CrossRefGoogle Scholar
  42. Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373CrossRefzbMATHMathSciNetGoogle Scholar
  43. Shim PY, Manoochehri S (1997) Generating optimal configurations in structural design using simulated annealing. Int J Numer Methods Eng 40(6):1053–1069CrossRefzbMATHGoogle Scholar
  44. Sigmund O (1997) On the design of compliant mechanisms using topology optimization. Mech Struct Mach 25(4):493–524CrossRefGoogle Scholar
  45. Sigmund O, Peterson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Multidiscip Optim 16(1):68–75CrossRefGoogle Scholar
  46. Shah A et al. (1999) Photovoltaic technology: the case for thin-film solar cells. Sci 285(5428):692–698CrossRefGoogle Scholar
  47. Shen LF et al (2003) Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm. Phys Rev B 68(3):035109CrossRefGoogle Scholar
  48. Svanberg K (2004) Some modelling aspects for the Matlab implementation of MMA. KTH Royal Institute of Technology, StockholmGoogle Scholar
  49. Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33(4–5):401–424CrossRefGoogle Scholar
  50. Shaw PE et al (2008) Exciton diffusion measurements in poly(3-hexylthiophene). Adv Mater 20(18): 3516–+CrossRefGoogle Scholar
  51. Sigmund O, Hougaard K (2008) Geometric properties of optimal photonic crystals. Phys Rev Lett 100(15)CrossRefGoogle Scholar
  52. Schuller JA et al (2010) Plasmonics for extreme light concentration and manipulation. Nat Mater 9(4):193CrossRefGoogle Scholar
  53. Sigmund O (2011) On the usefulness of non-gradient approaches in topology optimization. Struct Multidiscip Optim 43(5):589–596CrossRefzbMATHMathSciNetGoogle Scholar
  54. Soh HJ, Yoo J (2012) Texturing design for a light trapping system using topology optimization. Ieee Trans Magn 48(2):227–230CrossRefGoogle Scholar
  55. Soh HJ et al (2012) Optimal design of the light absorbing layer in thin film silicon solar cells. Sol Energy 86(7):2095–2105CrossRefGoogle Scholar
  56. van der Aa NP, Mattheij RMM (2007) Computing shape parameter sensitivity of the field of one-dimensional surface-relief gratings by using an analytical approach based on RCWA. J Opt Soc Am A Opt Image Sci Vis 24(9):2692–2700CrossRefGoogle Scholar
  57. Wang M et al (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246CrossRefzbMATHGoogle Scholar
  58. Wang SY, Tai K (2005) Structural topology design optimization using Genetic Algorithms with a bit-array representation. Comput Methods Appl Mech Eng 194(36–38):3749–3770CrossRefzbMATHGoogle Scholar
  59. Wang SY et al (2006) An enhanced genetic algorithm for structural topology optimization. Int J Numer Methods Eng 65(1):18–44CrossRefzbMATHGoogle Scholar
  60. Wang W et al (2010) Broadband light absorption enhancement in thin-film silicon solar cells. Nano Lett 10(6):2012–2018CrossRefGoogle Scholar
  61. Wang FW et al (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767–784CrossRefzbMATHGoogle Scholar
  62. Wang KXZ et al (2012) Absorption enhancement in ultrathin crystalline silicon solar cells with antireflection and light-trapping nanocone gratings. Nano Lett 12(3):1616–1619CrossRefGoogle Scholar
  63. Wang C et al (2013) Highly Efficient Light-Trapping Structure Design Inspired By Natural Evolution. Scientific Reports 3Google Scholar
  64. Yablonovitch E (1982) Statistical ray optics. J Opt Soc Am 72(7):899–907CrossRefGoogle Scholar
  65. Yu ZF et al (2010) Fundamental limit of nanophotonic light trapping in solar cells. Proc Natl Acad Sci USA 107(41):17491–17496CrossRefGoogle Scholar
  66. Zhou M, Rozvany GIN (1991) The COC algorithm, Part II: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89(1–3):309–336CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Shuangcheng Yu
    • 1
  • Chen Wang
    • 1
  • Cheng Sun
    • 1
  • Wei Chen
    • 1
    Email author
  1. 1.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA

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