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Energy Express

Energy Express

  • Editor: Bernard Kippelen
  • Vol. 20, Iss. S1 — Jan. 2, 2012
  • pp: A141–A156

Transmission line equivalent circuit model applied to a plasmonic grating nanosurface for light trapping

Alessia Polemi and Kevin L. Shuford  »View Author Affiliations

Optics Express, Vol. 20, Issue S1, pp. A141-A156 (2012)

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In this paper, we show how light absorption in a plasmonic grating nanosurface can be calculated by means of a simple, analytical model based on a transmission line equivalent circuit. The nanosurface is a one-dimensional grating etched into a silver metal film covered by a silicon slab. The transmission line model is specified for both transverse electric and transverse magnetic polarizations of the incident light, and it incorporates the effect of the plasmonic modes diffracted by the ridges of the grating. Under the assumption that the adjacent ridges are weakly interacting in terms of diffracted waves, we show that the approximate, closed form expression for the reflection coefficient at the air-silicon interface can be used to evaluate light absorption of the solar cell. The weak-coupling assumption is valid if the grating structure is not closely packed and the excitation direction is close to normal incidence. Also, we show the utility of the circuit theory for understanding how the peaks in the absorption coefficient are related to the resonances of the equivalent transmission model and how this can help in designing more efficient structures.

© 2011 OSA

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(160.4760) Materials : Optical properties
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:

Original Manuscript: October 28, 2011
Revised Manuscript: December 13, 2011
Manuscript Accepted: December 16, 2011
Published: January 2, 2012

Alessia Polemi and Kevin L. Shuford, "Transmission line equivalent circuit model applied to a plasmonic grating nanosurface for light trapping," Opt. Express 20, A141-A156 (2012)

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  1. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nature Mater.9, 205–213 (2010). [CrossRef]
  2. A. Tiwari, A. Romeo, D. Bätzner, and H. Zogg, “Flexible CdTe solar cells on polymer films,” Prog. Photovolt: Res. Appl.9, 211–215 (2001). [CrossRef]
  3. A. Romeo, A. Terheggen, D. Abou-Ras, D. L. Bätzner, F.-J. Haug, M. K. D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt: Res. Appl.12, 93–111 (2004). [CrossRef]
  4. W. Koch, A. Endrös, D. Franke, C. Häbler, J. P. Kaleis, and H.-J. Möller, “Bulk crystal growth and wavering for PV,” Handbook of Photovoltaic Science and Engineering, pp. 205–255 (John Wiley2003).
  5. V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater.22, 4794–4808 (2010). [CrossRef] [PubMed]
  6. P. N. Saeta, V. E. Ferry, D. Pacifici, J. N. Munday, and H. A. Atwater, “How much can guided modes enhance absorption in thin solar cells?” Opt. Express17, 975–20, (2009). [CrossRef]
  7. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett.8, 4391–4397 (2008). [CrossRef]
  8. M. Green, Third generation photovoltaics: advanced solar energy conversion, Springer series in photonics (Springer, 2003). URL http://books.google.com/books?id=TimK46htCMoC .
  9. D. Madzharov, R. Dewan, and D. Knipp, “Influence of front and back grating on light trapping in microcrystalline thin-film silicon solar cells,” Opt. Express19, 95–107 (2011). [CrossRef]
  10. R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater.21, 3504–3509 (2009). [CrossRef]
  11. A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” Appl. Phys. Lett.98, 104–107 (2011). [CrossRef]
  12. C. Haase and H. Stiebig, “Optical properties of thin-film silicon solar cells with grating couplers,” Prog. Photovolt: Res. Appl.14, 629–641 (2006). [CrossRef]
  13. K. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag.14, 302–307 (1966). [CrossRef]
  14. T. Weiland, “A discretization method for the solution of Maxwell’s equations for six-component fields,” Electron. Commun.31, 116–120 (1977).
  15. N.-N. Feng, J. Michel, L. Zeng, J. Liu, C.-Y. Hong, L. C. Kimerling, and X. Duan, “Design of Highly Efficient Light-Trapping Structures for Thin-Film Crystalline Silicon Solar Cells,” IEEE Trans. Electron Devices54, 1926–1933 (2007). [CrossRef]
  16. J. Chen, Q. Wang, and H. Li, “Microstructured design of metallic diffraction gratings for light trapping in thin-film silicon solar cells,” Opt. Commun.283, 5236–5244 (2010). [CrossRef]
  17. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. A71, 811–818 (1981). [CrossRef]
  18. T. Tamir and S. Zhang, “Modal transmission-line theory of multilayered grating structures,” J. Lightwave Technol.14, 914–927 (1996). [CrossRef]
  19. A. Chutinan and S. John, “Light trapping and absorption optimization in certain thin-film photonic crystal architectures,” Phys. Rev. A78, 023,825 (2008). [CrossRef]
  20. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express18, 366–380 (2010). [CrossRef]
  21. I. T. A. Luque and A. Marti, “Light intensity enhancement by diffracting structures in solar cells,” J. Appl. Phys.104, 502–034, (2008).
  22. L. Felsen and N. Markuvitz, Radiation and scattering of waves, 1st ed. (Prentice-Hall, Englewood Cliffs, NJ, 1973).
  23. www.cst.com (2011 CST Computer Simulation Technology AG).
  24. E. Palik, Handbook of optical constants of solids, 1st ed. (Academic Press, Orlando, 1985).
  25. A. Polemi, A. Toccafondi, and S. Maci, “High-frequency Green’s function for a semi-infinite array of electric dipoles on a grounded slab. Part I: formulation,” IEEE Trans. Antennas Propag.49, 1667–1677 (2001). [CrossRef]
  26. B. Davies, “Locating the zeros of an analytic function,” J. Comput. Phys.66, 36–49 (1986). [CrossRef]

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