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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 7, Iss. 3 — Feb. 29, 2012
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Simulation and optimization of 1-D periodic dielectric nanostructures for light-trapping

Peng Wang and Rajesh Menon  »View Author Affiliations


Optics Express, Vol. 20, Issue 2, pp. 1849-1855 (2012)
http://dx.doi.org/10.1364/OE.20.001849


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Abstract

Light-trapping is essential to improve the performance of thin-film solar cells. In this paper, we perform a parametric optimization of 1-D square and sinusoidal grating structures that act as nanophotonic scatterers to increase light absorption in ultra-thin (10nm) solar cells. Our optimization reveals that the short-circuit current density in a device of active-layer thickness 10nm can be improved by a factor of ~5 in the presence of the scattering structure. More complex geometries allow for increased degrees of design freedom and potentially high enhancement of light absorption.

© 2012 OSA

1. Introduction

Solar energy has the potential to become a significant source of energy in the near future [1

1. L. Fraas and L. Partain, Solar Cells and Their Applications (Wiley, 2010).

]. However, the high cost associated with the active device materials has stymied their wide adoption. The material cost can be contained via the use of thin layers of active materials. In addition, thin-film photovoltaic cells have higher open-circuit voltages due to the lower recombination rates [2

2. A. V. Shah, H. Schade, M. Vanecek, J. Meier, E. Vallat-Sauvain, N. Wyrsch, U. Kroll, C. Droz, and J. Bailat, “Thin-film silicon solar cell technology,” Prog. Photovolt. Res. Appl. 12(23), 113–142 (2004). [CrossRef]

, 3

3. M. A. Green, “Limits on the open-circuit voltage and efficiency of silicon solar cells imposed by intrinsic Auger processes,” IEEE Trans. Electron. Dev. 31(5), 671–678 (1984). [CrossRef]

]. Furthermore, such cells could be manufactured using considerably cheaper processes [2

2. A. V. Shah, H. Schade, M. Vanecek, J. Meier, E. Vallat-Sauvain, N. Wyrsch, U. Kroll, C. Droz, and J. Bailat, “Thin-film silicon solar cell technology,” Prog. Photovolt. Res. Appl. 12(23), 113–142 (2004). [CrossRef]

]. The main drawback of such cells is their poor absorption of sunlight. Light trapping schemes were proposed to increase the light absorption in these thin active layers [2

2. A. V. Shah, H. Schade, M. Vanecek, J. Meier, E. Vallat-Sauvain, N. Wyrsch, U. Kroll, C. Droz, and J. Bailat, “Thin-film silicon solar cell technology,” Prog. Photovolt. Res. Appl. 12(23), 113–142 (2004). [CrossRef]

, 4

4. 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]

, 5

5. R. Dewan and D. Knipp, “Light-trapping in thin-film silicon solar cells with integrated diffractive grating,” J. Appl. Phys. 106(7), 074901 (2009). [CrossRef]

]. Randomly textured surfaces are applied on the top surface. Light scattering from these textures increases the path length within the active material resulting in higher absorption. Such textures are typically applied for devices with thick active layers [6

6. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982). [CrossRef]

8

8. M. A. Green, J. H. Zhao, A. H. Wang, and S. R. Wenham, “Very high efficiency silicon solar cells – science and technology,” IEEE Trans. Electron. Dev. 46(10), 1940–1947 (1999). [CrossRef]

]. Sub-micrometer grating structures on the back surface of the active layer were used to increase light absorption in moderately thick device layers as well [9

9. C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt. 34(14), 2476–2482 (1995). [CrossRef] [PubMed]

].

In order to quantify the impact of the nanophotonic structure, we begin by defining I¯λ(x,z) as the spectrally-cumulative time-averaged intensity distribution and S as the total power per unit grating period within the active layer.
I¯λ(x,z)=λI(λ,x,z)dλ,
(1)
S=1ΛactiveI¯λ(x,z)dxdz,
(2)
where Λ is the grating period. The intensity refers to the total light intensity averaged over the two orthogonal polarizations of the incident light field. The light-enhancement factor, F is defined as the ratio of S in the presence of the nanophotonic structure (cladding and scattering layers) to its value when the structure is absent. Normalization with respect to the grating period is necessary to evaluate the effect of varying this period with respect to a reference period.

In addition to light enhancement, we can also evaluate the effect of light trapping on the device performance by directly computing the short-circuit current density, jsc.
jsc=qtaΛactive(λΦ(λ,x,z)IQE(λ)dλ)dxdz,
(3)
Φ(λ,x,z)=I(λ,x,z)hc/λ,
(4)
where Φ is the local photon flux in the active layer, IQE is the internal quantum efficiency of silicon and c is the velocity of light in silicon. The enhancement in short-circuit current density, J is defined as the ratio of jsc in the presence of the nanophotonic structure to jsc in the absence of the structure.

2. Optimization of the square-grating structure

The active-layer thickness is perhaps the most important parameter in the device since it affects the recombination rate of the light-generated carriers. In addition, the nanophotonic effect is predominant in a thin layer adjacent to the cladding layer. Hence, we calculated both F and J as functions of the active-layer thickness, ta, keeping all the other parameters fixed at ts = 90nm, tc = 30nm, and Λ = 400nm. We also assumed a grating duty cycle of 0.6. The results are shown in Fig. 1(a). As expected, the highest enhancement occurs for the thinnest active layer. The nanophotonic scattering effect is a near-field effect. Hence, the biggest impact will occur in the near field of the cladding structure. Note that as the active-layer thickness becomes larger than about 100nm, the effect of the grating is minimal. In the rest of the simulations, we assume an active-layer thickness of 10nm. The spectral-enhancement factors are defined as

Fλ=1ΛactiveI(λ,x,z)dxdz1ΛrefactiveIref(λ,x,z)dxdzand
(5)
Jλ=qtaΛactiveΦ(λ,x,z)IQE(λ)dxdzqtaΛrefactiveΦref(λ,x,z)IQE(λ)dxdz,where
(6)
Φref(λ,x,z)=Iref(λ,x,z)hc/λ.
(7)

The subscript “ref” indicates the reference cell in the absence of the nanophotonic-trapping stack (scattering and cladding layers). The solid blue line in Fig. 1(b) shows Jλ. The grating scatters strongly for an incident wavelength of 500nm, causing significantly higher light trapping within the active layer. Since the AM1.5 spectrum shows a maximum around 500nm, this grating design provides good light trapping for the entire spectrum as indicated later.

In addition, we also simulated and computed Jλ considering a reference cell with an anti-reflection coating (ARC) comprised of an unpatterned 85nm-thick fused silica layer atop the active layer. This thickness corresponds to λ/4n where λ = 500nm (the approximate peak of AM1.5) and n = 1.47. The results are plotted as a dotted red line in Fig. 1(b). At λ~500nm both TE and TM polarizations excite strong guided resonances in the silica nanostructure. These resonance fields can couple into the active layer directly under it, leading to strong light trapping effects [20

20. S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

, 22

22. Z. F. Yu, A. Raman, and S. H. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3), A366–A380 (2010). [CrossRef] [PubMed]

]. At other wavelengths, weaker resonances are excited leading to lower light trapping. At wavelengths above 1000nm, no resonances are excited but the structure acts as a sub-optimal anti-reflection coating. The highest value for Jλ is 2.3, lower than that compared with the bare reference device (solid blue line). In our following simulations, we utilized the bare device as our reference cell in order to more accurately illustrate the overall performance of the light trapping structure, which includes any anti-reflection effects as well. The incident AM1.5 spectrum is also plotted in Fig. 1(b) for reference.

Figure 2
Fig. 2 Parametric optimization of the square-grating geometry for light and current enhancement. The enhancement factors are plotted as a function of (a) the grating period, Λ, (b) the grating duty-cycle, (c) the cladding thickness, tc and (d) the scattering-layer thickness, ts. The default parameters were Λ = 400nm, duty-cycle = 0.5, tc = 30nm, and ts = 80nm.
shows the parametric analysis of the grating design on the two enhancement factors. The default parameter values were Λ = 400nm, duty-cycle = 0.5, tc = 30nm, and ts = 80nm. In Fig. 2(a), Λ was changed while all the other parameters were kept constant. It was noted that both the enhancement factors peaked sharply at Λ = 400nm. The duty-cycle was defined as the ratio of the width of the scattering layer to the period of the grating. In Fig. 2(b), the duty cycle was varied while all other parameters were fixed at their default values. The enhancement factors peaked at a duty-cycle of 0.6. Similarly, the cladding-layer thickness of 30nm also showed the best enhancement. Finally, the device showed maximum enhancement at a scattering-layer thickness of 90nm.From this simple single-parameter search, we conclude that the grating with the optimized parameters offer good enhancement, with J approaching 5.

3. Optimization of the sinusoidal-grating structure

The sinusoidal grating offers a smoother degree of control on the incident light. In addition, the sinusoidal grating may be fabricated using grayscale lithography. Hence, we explored the potential of this geometry on the enhancement factors. The simulation geometry is illustrated in Fig. 3(a)
Fig. 3 Parametric optimization of the sinusoidal-grating geometry for light and current enhancement. (a) Schematic of the proposed geometry. The enhancement factors are plotted as a function of (b) the grating period, Λ, (c) the cladding thickness, tc and (d) the scattering-layer thickness, ts. The default parameters were Λ = 400nm, tc = 30nm, and ts = 90nm.
. The parametric optimization results are shown in Figs. 3(b)-3(d). Highest enhancement occurs when the period is 400nm and the cladding-layer thickness is 30nm (both similar to the square-grating). This peak is again attributed to the strong resonance at λ ~500nm within the scattering structure. However, the sinusoidal-grating allows for higher enhancement when the scattering-layer thickness is about 120nm. The sinusoidal grating provides a smoother scattering structure, so it would be expected to scatter normally incident light into fewer guided modes in the active layer. However, the broadband behaviour of the sinusoidal grating is similar or even slightly better than that of the square grating. This hints at the possibility of utilizing more complicated geometries for further enhancements.

4. Alternative geometries and materials

5. Conclusions

In this paper, we described the parametric optimization of 1-D square-grating and sinusoidal-grating structures for the enhancement of light absorption and short-circuit-current density in thin silicon solar cells. We note that the enhancement factors can be considerably improved by factors of 5 or more by the judicious choice of the geometric parameters. We have also exploited alternative 1D geometries and potential materials for photonic structures and active absorbers. The performance of such light trapping nanostructures under oblique incidence is another area of future study. The choice of geometric parameters is dependent on the material choices as indicated by our simulations of CdTe and amorphous-silicon solar cells. It is clear that numerical optimization of nanophotonic geometries is advantageous to improve the performance of thin-film solar cells.

Acknowledgments

We thank Lorenzo Bossi for assistance with MEEP, and Ganghun Kim for useful discussion and assistance with the simulations. We also thank Stewart Brock and Mark Ogden for help with the computational facilities. Fruitful discussions with Mike Scarpulla are also gratefully acknowledged. Funding from the Utah Technology Commercialization Grant and USTAR are gratefully acknowledged.

References and links

1.

L. Fraas and L. Partain, Solar Cells and Their Applications (Wiley, 2010).

2.

A. V. Shah, H. Schade, M. Vanecek, J. Meier, E. Vallat-Sauvain, N. Wyrsch, U. Kroll, C. Droz, and J. Bailat, “Thin-film silicon solar cell technology,” Prog. Photovolt. Res. Appl. 12(23), 113–142 (2004). [CrossRef]

3.

M. A. Green, “Limits on the open-circuit voltage and efficiency of silicon solar cells imposed by intrinsic Auger processes,” IEEE Trans. Electron. Dev. 31(5), 671–678 (1984). [CrossRef]

4.

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]

5.

R. Dewan and D. Knipp, “Light-trapping in thin-film silicon solar cells with integrated diffractive grating,” J. Appl. Phys. 106(7), 074901 (2009). [CrossRef]

6.

E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. 72(7), 899–907 (1982). [CrossRef]

7.

P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys. 62(1), 243–249 (1987). [CrossRef]

8.

M. A. Green, J. H. Zhao, A. H. Wang, and S. R. Wenham, “Very high efficiency silicon solar cells – science and technology,” IEEE Trans. Electron. Dev. 46(10), 1940–1947 (1999). [CrossRef]

9.

C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt. 34(14), 2476–2482 (1995). [CrossRef] [PubMed]

10.

K. R. Catchpole, S. Mokkapati, F. Beck, E.-C. Wang, A. McKinley, A. Basch, and J. Lee, “Plasmonics and nanophotonics for photovoltaics,” MRS Bull. 36(06), 461–467 (2011). [CrossRef]

11.

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]

12.

L. L. Yang, Y. M. Xuan, and J. J. Tan, “Efficient optical absorption in thin-film solar cells,” Opt. Express 19(S5), A1165–A1174 (2011). [CrossRef] [PubMed]

13.

J. Gjessing, E. S. Marstein, and A. Sudbø, “2D back-side diffraction grating for improved light trapping in thin silicon solar cells,” Opt. Express 18(6), 5481–5495 (2010). [CrossRef] [PubMed]

14.

L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. 89(11), 111111 (2006). [CrossRef]

15.

S. Pillai, K. R. Catchpole, T. Turpke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007). [CrossRef]

16.

J. R. Nagel and M. A. Scarpulla, “Enhanced absorption in optically thin solar cells by scattering from embedded dielectric nanoparticles,” Opt. Express 18(S2), A139–A146 (2010). [CrossRef] [PubMed]

17.

E. Garnett and P. D. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10(3), 1082–1087 (2010). [CrossRef] [PubMed]

18.

J. Zhu, Z. F. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Q. Xu, Q. Wang, M. McGehee, S. H. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009). [CrossRef] [PubMed]

19.

L. Hu and G. Chen, “Analysis of optical absorption in silicon nanowire arrays for photovoltaic applications,” Nano Lett. 7(11), 3249–3252 (2007). [CrossRef] [PubMed]

20.

S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65(23), 235112 (2002). [CrossRef]

21.

S. B. Mallick, N. P. Sergeant, M. Agrawal, J.-Y. Lee, and P. Peumans, “Coherent light trapping in thin-film photovoltaics,” MRS Bull. 36(06), 453–460 (2011). [CrossRef]

22.

Z. F. Yu, A. Raman, and S. H. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3), A366–A380 (2010). [CrossRef] [PubMed]

23.

Z. F. Yu, A. Raman, and S. H. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. 107(41), 17491–17496 (2010). [CrossRef] [PubMed]

24.

J. R. Nagel, S. Blair, and M. A. Scarpulla, “Exact field solution to guided wave propagation in lossy thin films,” Opt. Express 19(21), 20159–20171 (2011). [CrossRef] [PubMed]

25.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010). [CrossRef]

26.

MEEP is a free FDTD simulation software package developed at MIT to model electromagnetic systems: http://ab-initio.mit.edu/wiki/index.php/Meep.

27.

Refractive index database. http://refractiveindex.info/.

28.

American Society for Testing and Materials (ASTM) Terrestrial Reference Spectra for Photovoltaic Performance Evaluation, http://rredc.nrel.gov/solar/spectra/am1.5/.

29.

J. Lu, S. Boyd, and J. Vučković, “Inverse design of a three-dimensional nanophotonic resonator,” Opt. Express 19(11), 10563–10570 (2011). [CrossRef] [PubMed]

30.

S. H. Ahn and L. J. Guo, “High-speed roll-to-roll nanoimprint lithography on flexible plastic substrates,” Adv. Mater. (Deerfield Beach Fla.) 20(11), 2044–2049 (2008). [CrossRef]

31.

A. Romeo, M. Terheggen, D. Abou-Ras, D. L. Batzner, F. J. Haug, M. Kalin, D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt. Res. Appl. 12(23), 93–111 (2004). [CrossRef]

OCIS Codes
(350.4238) Other areas of optics : Nanophotonics and photonic crystals
(310.6188) Thin films : Spectral properties
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Thin Films

History
Original Manuscript: November 11, 2011
Revised Manuscript: December 23, 2011
Manuscript Accepted: December 29, 2011
Published: January 12, 2012

Virtual Issues
Vol. 7, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Peng Wang and Rajesh Menon, "Simulation and optimization of 1-D periodic dielectric nanostructures for light-trapping," Opt. Express 20, 1849-1855 (2012)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-20-2-1849


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References

  1. L. Fraas and L. Partain, Solar Cells and Their Applications (Wiley, 2010).
  2. A. V. Shah, H. Schade, M. Vanecek, J. Meier, E. Vallat-Sauvain, N. Wyrsch, U. Kroll, C. Droz, and J. Bailat, “Thin-film silicon solar cell technology,” Prog. Photovolt. Res. Appl.12(23), 113–142 (2004). [CrossRef]
  3. M. A. Green, “Limits on the open-circuit voltage and efficiency of silicon solar cells imposed by intrinsic Auger processes,” IEEE Trans. Electron. Dev.31(5), 671–678 (1984). [CrossRef]
  4. 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. Express15(25), 16986–17000 (2007). [CrossRef] [PubMed]
  5. R. Dewan and D. Knipp, “Light-trapping in thin-film silicon solar cells with integrated diffractive grating,” J. Appl. Phys.106(7), 074901 (2009). [CrossRef]
  6. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am.72(7), 899–907 (1982). [CrossRef]
  7. P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys.62(1), 243–249 (1987). [CrossRef]
  8. M. A. Green, J. H. Zhao, A. H. Wang, and S. R. Wenham, “Very high efficiency silicon solar cells – science and technology,” IEEE Trans. Electron. Dev.46(10), 1940–1947 (1999). [CrossRef]
  9. C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt.34(14), 2476–2482 (1995). [CrossRef] [PubMed]
  10. K. R. Catchpole, S. Mokkapati, F. Beck, E.-C. Wang, A. McKinley, A. Basch, and J. Lee, “Plasmonics and nanophotonics for photovoltaics,” MRS Bull.36(06), 461–467 (2011). [CrossRef]
  11. S. B. Mallick, M. Agrawal, and P. Peumans, “Optimal light trapping in ultra-thin photonic crystal crystalline silicon solar cells,” Opt. Express18(6), 5691–5706 (2010). [CrossRef] [PubMed]
  12. L. L. Yang, Y. M. Xuan, and J. J. Tan, “Efficient optical absorption in thin-film solar cells,” Opt. Express19(S5), A1165–A1174 (2011). [CrossRef] [PubMed]
  13. J. Gjessing, E. S. Marstein, and A. Sudbø, “2D back-side diffraction grating for improved light trapping in thin silicon solar cells,” Opt. Express18(6), 5481–5495 (2010). [CrossRef] [PubMed]
  14. L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, L. C. Kimerling, and B. A. Alamariu, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett.89(11), 111111 (2006). [CrossRef]
  15. S. Pillai, K. R. Catchpole, T. Turpke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys.101(9), 093105 (2007). [CrossRef]
  16. J. R. Nagel and M. A. Scarpulla, “Enhanced absorption in optically thin solar cells by scattering from embedded dielectric nanoparticles,” Opt. Express18(S2), A139–A146 (2010). [CrossRef] [PubMed]
  17. E. Garnett and P. D. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett.10(3), 1082–1087 (2010). [CrossRef] [PubMed]
  18. J. Zhu, Z. F. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Q. Xu, Q. Wang, M. McGehee, S. H. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009). [CrossRef] [PubMed]
  19. L. Hu and G. Chen, “Analysis of optical absorption in silicon nanowire arrays for photovoltaic applications,” Nano Lett.7(11), 3249–3252 (2007). [CrossRef] [PubMed]
  20. S. H. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65(23), 235112 (2002). [CrossRef]
  21. S. B. Mallick, N. P. Sergeant, M. Agrawal, J.-Y. Lee, and P. Peumans, “Coherent light trapping in thin-film photovoltaics,” MRS Bull.36(06), 453–460 (2011). [CrossRef]
  22. Z. F. Yu, A. Raman, and S. H. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express18(S3), A366–A380 (2010). [CrossRef] [PubMed]
  23. Z. F. Yu, A. Raman, and S. H. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A.107(41), 17491–17496 (2010). [CrossRef] [PubMed]
  24. J. R. Nagel, S. Blair, and M. A. Scarpulla, “Exact field solution to guided wave propagation in lossy thin films,” Opt. Express19(21), 20159–20171 (2011). [CrossRef] [PubMed]
  25. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bremel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun.181(3), 687–702 (2010). [CrossRef]
  26. MEEP is a free FDTD simulation software package developed at MIT to model electromagnetic systems: http://ab-initio.mit.edu/wiki/index.php/Meep .
  27. Refractive index database. http://refractiveindex.info/ .
  28. American Society for Testing and Materials (ASTM) Terrestrial Reference Spectra for Photovoltaic Performance Evaluation, http://rredc.nrel.gov/solar/spectra/am1.5/ .
  29. J. Lu, S. Boyd, and J. Vučković, “Inverse design of a three-dimensional nanophotonic resonator,” Opt. Express19(11), 10563–10570 (2011). [CrossRef] [PubMed]
  30. S. H. Ahn and L. J. Guo, “High-speed roll-to-roll nanoimprint lithography on flexible plastic substrates,” Adv. Mater. (Deerfield Beach Fla.)20(11), 2044–2049 (2008). [CrossRef]
  31. A. Romeo, M. Terheggen, D. Abou-Ras, D. L. Batzner, F. J. Haug, M. Kalin, D. Rudmann, and A. N. Tiwari, “Development of thin-film Cu(In,Ga)Se2 and CdTe solar cells,” Prog. Photovolt. Res. Appl.12(23), 93–111 (2004). [CrossRef]

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