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  • Editor: Bernard Kippelen
  • Vol. 20, Iss. S4 — Jul. 2, 2012
  • pp: A545–A553
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Simulation and analysis of the angular response of 1D dielectric nanophotonic light-trapping structures in thin-film photovoltaics

Peng Wang and Rajesh Menon  »View Author Affiliations


Optics Express, Vol. 20, Issue S4, pp. A545-A553 (2012)
http://dx.doi.org/10.1364/OE.20.00A545


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Abstract

Nanophotonics can guide the design of novel structures for light-trapping in ultra-thin photovoltaic cells. Here, we report on the systematic study of the effect of the angle of incidence of sunlight on the performance of such structures. We also conduct a parametric study of a sinusoidal grating and demonstrate that light intensity in the active region averaged over a range of input angles from 0° to 80° can be enhanced by more than 3 times compared to the bare device. Such a broadband light-trapping nanostructure can increase the total daily energy production of a fixed (non-tracking) device by over 60%, compared to a reference device with an anti-reflection coating.

© 2012 OSA

1. Introduction

Photovoltaic devices with ultra-thin active layers have the advantages of lower manufacturing costs [1

1. 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]

], reduced use of expensive material, increased carrier-extraction efficiency [2

2. D. Redfield, “Multiple-pass thin-film silicon solar cell,” Appl. Phys. Lett. 25(11), 647–648 (1974). [CrossRef]

, 3

3. T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. 31(5), 711–716 (1984). [CrossRef]

] and improved open-circuit voltage [4

4. 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]

]. Overall, they show significant potential to decrease solar-power costs such that they are on par with power from non-renewable sources. One major challenge in thin photovoltaic cells is their poor light absorption. Several techniques have been proposed to increase the optical length within the active layer to improve light absorption. These techniques include the use of random textures on the top surface [5

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

, 6

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

], dielectric nanospheres embedded within the active layer [7

7. J. R. Nagel and M. A. Scarpulla, “Enhanced absorption in optically thin solar cells by scattering from embedded dielectric nanoparticles,” Opt. Express 18(S2Suppl 2), A139–A146 (2010). [CrossRef] [PubMed]

], metallic nanostructures on the top [8

8. 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]

, 9

9. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

] or bottom surface [9

9. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

, 10

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

], grating structures in a top layer [11

11. Y. C. Lee, C. F. Huang, J. Y. Chang, and M. L. Wu, “Enhanced light trapping based on guided mode resonance effect for thin-film silicon solar cells with two filling-factor gratings,” Opt. Express 16(11), 7969–7975 (2008). [CrossRef] [PubMed]

13

13. 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]

], and nanophotonic structures [14

14. Z. F. Yu, A. Raman, and S. H. Fan, “Nanophotonic light-trapping theory for solar cells,” Appl. Phys., A Mater. Sci. Process. 105(2), 329–339 (2011). [CrossRef]

]. The last of these hold significant promise due to the ability to excite multiple guided resonances that can couple close-to-normally incident sunlight into modes that can travel within the plane of the active layer, thereby increasing the optical path-length by 2 or more orders of magnitude [14

14. Z. F. Yu, A. Raman, and S. H. Fan, “Nanophotonic light-trapping theory for solar cells,” Appl. Phys., A Mater. Sci. Process. 105(2), 329–339 (2011). [CrossRef]

, 15

15. Z. F. Yu, A. Raman, and S. H. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3Suppl 3), A366–A380 (2010). [CrossRef] [PubMed]

].

2. Effect of the angle of incidence

These results confirm that in order to gain the maximum advantage of nanophotonic light trapping, the photovoltaic device has to track the sun. However, tracking can be expensive. Therefore, it is advantageous to explore nanophotonic designs that can achieve high enhancements over broad angles of incidence. Since the sinusoidal grating shows better performance compared to the square grating, we proceed to use the sinusoidal grating as the default geometry for parametric optimization for broad-angle light trapping.

3. Figures-of-merit for broad-angle light-trapping

We begin by defining the spectrally-cumulative, time-averaged intensity distribution I¯λ(x,z) and the total power per unit grating period within the active layer, S.

I¯λ(x,z,θ)=λI(λ,x,z,θ)dλ
(1)
S(θ)=1ΛactiveI¯λ(x,z,θ)dxdz
(2)

The intensity is averaged over the two orthogonal polarizations of the incident light field. Note that the coordinate system is illustrated in the inset in Fig. 1(A). The overall light-enhancement factor for all incident angles, F is defined as
Fθ=S(θ)Sref(θ)F=0θmaxFθdθ,
(3)
where Sref(θ) is the total power per unit grating period within the active layer of the reference device, in which the nanophotonic structure (cladding and scattering layers) is absent. θmax refers to the maximum angle of incidence under consideration. Normalization with respect to the grating period is necessary to evaluate the effect of varying this period with respect to a reference period. In the case of the reference device, where the nanophotonic structures are absent, Λref is the width of the simulation geometry in the x-direction.

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(θ)=qtaΛactive(λΦ(λ,x,z,θ)IQE(λ)dλ)dxdz,Φ(λ,x,z,θ)=I(λ,x,z,θ)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 speed of light in silicon. The overall enhancement in short-circuit current-density, J is then defined as

Jθ=jsc(θ)jsc,ref(θ)J=0θmaxJθdθ,
(5)

With these figures-of-merit in place, we can evaluate the effects of various geometric parameters in the nanophotonic structure. Since the sinusoidal grating shows better broad-angle enhancement compared to the square grating, we utilize this as the default design. The default parameters are Λ = 400nm, ta = 10nm, tc = 30nm, ts = 120nm and θmax = 80°. In the following analysis, each parameter is changed while all others are kept constant to elucidate their individual effects.

4. Parametric analysis

The second geometric parameter of interest is the thickness of the cladding layer, tc. As shown in Fig. 3(A)
Fig. 3 Effect of cladding-layer thickness, tc. (A) Overall enhancement factors as a function of tc. (B) Enhancement factor, Fθ as a function of tc. (C)-(F) Spectra of enhancement factor, Fθ for θ = 0°, 20°, 40° and 60°, respectively.
, the overall enhancement factors decrease with increasing tc. This is expected as the closer the scattering layer is to the active layer, the higher the coupling between the incident and the guided modes. Higher coupling will result in larger energy transfer and hence, a stronger resonance. The dependence of Fθ on tc is less strong except at large θ or when tc > ~50nm (Fig. 3(B)). This is borne out in the individual spectra of Fθ, where the location and the strength of the guided-mode resonances are mostly independent of tc (Fig. 3(C)). At oblique angles of incidence, multiple resonances appear as discussed earlier, but their dependence on tc remain weak (Fig. 3(D)). This is also expected since tc << λ and hence, will have little impact on the characteristics of the guided-mode resonance in the active layer. At large θ, the scattering structure mostly serves as an anti-reflection layer and no clear resonances are observed (Fig. 3(E) and 2(F)).

As described earlier [18

18. K. R. Catchpole, “A conceptual model of the diffuse transmittance of lamellar diffraction gratings on solar cells,” J. Appl. Phys. 102(1), 013102 (2007). [CrossRef]

], the scattering-layer thickness, ts has an important impact on the enhancement factors. Figure 4(A)
Fig. 4 Effect of scattering-layer thickness, ts. (A) Overall enhancement factors as a function of ts. (B) Enhancement factor, Fθ as a function of ts. (C)-(F) Spectra of enhancement factor, Fθ for θ = 0°, 20°, 40° and 60°, respectively.
shows that the overall enhancement factors reach a maximum when ts = 120nm. Most of this peak enhancement is achieved due to the sharp increase in the light intensity under normal incidence as illustrated in Fig. 4(B). Significant decrease in Fθ is observed at larger angles, irrespective of ts. The spectra of Fθ clearly illustrate the presence of strong guided-mode resonances (one at normal incidence, two at θ = 20°, and so on). At θ greater than about 40°, the anti-reflection properties seem to dominate and broadband enhancement is achieved, albeit at lower absolute values (Fig. 4(E) and 4(F)).

5. Enhancement of daily energy output

It is well known that the daily energy output from a flat non-tracking photovoltaics panel is determined by the angle that the sun makes with the normal to the panel [19

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

]. Therefore, the panel produces significantly lower power during the early morning and the late afternoon hours. It is illustrative to compare the effect of the subject nanophotonic structure on the total daily energy output of a flat non-tracking thin photovoltaic device. In order to simplify our calculations, we assumed that the device is placed horizontally at the equator. We also assumed that the incident solar spectrum, AM1.5 does not change over the course of the day. Furthermore, we assumed that the azimuthal angle of the sun is 0°. Finally, any effects of the atmosphere including shading due to clouds is ignored. The short-circuit current-density can be calculated by Eq. (4). The incident angle is assumed to vary from −90° to 90°.

Next, we compute the open circuit voltage via a semiconductor-device model [20

20. 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]

, 21

21. A. Chutinan, N. P. Kherani, and S. Zukotynski, “High-efficiency photonic crystal solar cell architecture,” Opt. Express 17(11), 8871–8878 (2009). [CrossRef] [PubMed]

].
voc=Eg+kTln(jsc4π2h3c2q(n2+1)Eg2kT)q,
(7)
where Eg is the bandgap, k is Boltzmann’s constant, T is the absolute temperature, n is the refractive index of the active material and q is the electronic charge. The output power-density for a fixed incident angle θ is then,
p(θ)=jsc(θ)voc(θ)FF,
(8)
where FF is the fill factor. In this paper, we assumed Eg = 1.12eV (c-Si) and FF = 0.6. And θ is a function of time within a day. Finally, the daily output energy-density is given by

E=90o90op(θ)dθ
(9)

For comparison, we computed E for a bare reference device with 10nm-thick active layer, a device with an anti-reflection coating (a uniform 85nm-thick fused silica layer on top of the 10nm-thick active layer) and the designed device with the optimized nanophotonic structure on top of the active layer. The results are summarized in Fig. 5
Fig. 5 Daily energy output per unit area in the non-tracking configuration for a bare device (left), a device with an anti-reflection coating (ARC) (center), and a device with the nanophotonic structure (right).
. The parametric values were ta = 10nm, tc = 10nm, ts = 120nm and Λ = 400nm. The nanophotonic structure increases daily energy output in the non-tracking system by a factor of 2.58X compared to the bare reference device. Even when compared to the standard device with an anti-reflection coating (ARC), the daily energy output is increased by about 1.62X.

6. Conclusions

In this paper, we demonstrated that simple periodic nanostructures could be used to scatter sunlight from a broad range of angles into resonant-guided modes within an underlying active layer resulting in significant increase in broadband light trapping. We performed a preliminary optimization of the geometric factors in a sinusoidal grating and demonstrated that the short-circuit current-density could be increased by a factor of over 3 compared to a bare reference device averaged over incident angles from 0° to 80°. This approach can, therefore increase the daily energy output of a non-tracking PV device by over 60%, compared to the device with the same active layer thickness and an optimal ARC layer. Significant improvements in light-trapping can be expected by considering more complex geometries as well as two-dimensional geometries [13

13. 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]

, 15

15. Z. F. Yu, A. Raman, and S. H. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3Suppl 3), A366–A380 (2010). [CrossRef] [PubMed]

, 16

16. 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]

]. It has been proposed that optimized 2-D nanostructures could overcome the classical Yablonovitch limit for light-trapping [14

14. Z. F. Yu, A. Raman, and S. H. Fan, “Nanophotonic light-trapping theory for solar cells,” Appl. Phys., A Mater. Sci. Process. 105(2), 329–339 (2011). [CrossRef]

16

16. 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]

]. It must be noted that all such nanostructures present significant challenges in fabrication, primarily due to the requirement of large-area coverage. Advances in scalable nanofabrication such as roll-to-roll nanoimprint lithography will be critical for practical implementation of such schemes [22

22. 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]

]. Although, we assumed ultra-thin layers of c-Si for our active layer, it is obvious that the principles apply equally to organic photovoltaic devices as well [23

23. H. Hoppe and N. S. Sariciftci, “Organic solar cells: An overview,” J. Mater. Res. 19(07), 1924–1945 (2004). [CrossRef]

, 24

24. A. Raman, Z. F. Yu, and S. H. Fan, “Dielectric nanostructures for broadband light trapping in organic solar cells,” Opt. Express 19(20), 19015–19026 (2011). [CrossRef] [PubMed]

]. The improvement in electrical performance for such devices is expected to significant at the very small thicknesses as considered here [9

9. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

]. The approach presented here can provide guidance when designing light-trapping nanostructures for ultra-thin devices that need to operate under normal and oblique illumination conditions.

References and links

1.

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]

2.

D. Redfield, “Multiple-pass thin-film silicon solar cell,” Appl. Phys. Lett. 25(11), 647–648 (1974). [CrossRef]

3.

T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev. 31(5), 711–716 (1984). [CrossRef]

4.

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]

5.

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

6.

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

7.

J. R. Nagel and M. A. Scarpulla, “Enhanced absorption in optically thin solar cells by scattering from embedded dielectric nanoparticles,” Opt. Express 18(S2Suppl 2), A139–A146 (2010). [CrossRef] [PubMed]

8.

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]

9.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef] [PubMed]

10.

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

11.

Y. C. Lee, C. F. Huang, J. Y. Chang, and M. L. Wu, “Enhanced light trapping based on guided mode resonance effect for thin-film silicon solar cells with two filling-factor gratings,” Opt. Express 16(11), 7969–7975 (2008). [CrossRef] [PubMed]

12.

S. Zanotto, M. Liscidini, and L. C. Andreani, “Light trapping regimes in thin-film silicon solar cells with a photonic pattern,” Opt. Express 18(5), 4260–4274 (2010). [CrossRef] [PubMed]

13.

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]

14.

Z. F. Yu, A. Raman, and S. H. Fan, “Nanophotonic light-trapping theory for solar cells,” Appl. Phys., A Mater. Sci. Process. 105(2), 329–339 (2011). [CrossRef]

15.

Z. F. Yu, A. Raman, and S. H. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express 18(S3Suppl 3), A366–A380 (2010). [CrossRef] [PubMed]

16.

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]

17.

P. Wang and R. Menon, “Simulation and optimization of 1-D periodic dielectric nanostructures for light-trapping,” Opt. Express 20(2), 1849–1855 (2012). [CrossRef] [PubMed]

18.

K. R. Catchpole, “A conceptual model of the diffuse transmittance of lamellar diffraction gratings on solar cells,” J. Appl. Phys. 102(1), 013102 (2007). [CrossRef]

19.

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

20.

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]

21.

A. Chutinan, N. P. Kherani, and S. Zukotynski, “High-efficiency photonic crystal solar cell architecture,” Opt. Express 17(11), 8871–8878 (2009). [CrossRef] [PubMed]

22.

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]

23.

H. Hoppe and N. S. Sariciftci, “Organic solar cells: An overview,” J. Mater. Res. 19(07), 1924–1945 (2004). [CrossRef]

24.

A. Raman, Z. F. Yu, and S. H. Fan, “Dielectric nanostructures for broadband light trapping in organic solar cells,” Opt. Express 19(20), 19015–19026 (2011). [CrossRef] [PubMed]

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:
Photovoltaics

History
Original Manuscript: April 18, 2012
Revised Manuscript: June 6, 2012
Manuscript Accepted: June 12, 2012
Published: June 25, 2012

Citation
Peng Wang and Rajesh Menon, "Simulation and analysis of the angular response of 1D dielectric nanophotonic light-trapping structures in thin-film photovoltaics," Opt. Express 20, A545-A553 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-S4-A545


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References

  1. 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]
  2. D. Redfield, “Multiple-pass thin-film silicon solar cell,” Appl. Phys. Lett.25(11), 647–648 (1974). [CrossRef]
  3. T. Tiedje, E. Yablonovitch, G. D. Cody, and B. G. Brooks, “Limiting efficiency of silicon solar cells,” IEEE Trans. Electron. Dev.31(5), 711–716 (1984). [CrossRef]
  4. 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]
  5. E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am.72(7), 899–907 (1982). [CrossRef]
  6. P. Campbell and M. Green, “Light trapping properties of pyramidally textured surfaces,” J. Appl. Phys.62(1), 243–249 (1987). [CrossRef]
  7. J. R. Nagel and M. A. Scarpulla, “Enhanced absorption in optically thin solar cells by scattering from embedded dielectric nanoparticles,” Opt. Express18(S2Suppl 2), A139–A146 (2010). [CrossRef] [PubMed]
  8. 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]
  9. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010). [CrossRef] [PubMed]
  10. C. Heine and R. H. Morf, “Submicrometer gratings for solar energy applications,” Appl. Opt.34(14), 2476–2482 (1995). [CrossRef] [PubMed]
  11. Y. C. Lee, C. F. Huang, J. Y. Chang, and M. L. Wu, “Enhanced light trapping based on guided mode resonance effect for thin-film silicon solar cells with two filling-factor gratings,” Opt. Express16(11), 7969–7975 (2008). [CrossRef] [PubMed]
  12. S. Zanotto, M. Liscidini, and L. C. Andreani, “Light trapping regimes in thin-film silicon solar cells with a photonic pattern,” Opt. Express18(5), 4260–4274 (2010). [CrossRef] [PubMed]
  13. 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]
  14. Z. F. Yu, A. Raman, and S. H. Fan, “Nanophotonic light-trapping theory for solar cells,” Appl. Phys., A Mater. Sci. Process.105(2), 329–339 (2011). [CrossRef]
  15. Z. F. Yu, A. Raman, and S. H. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express18(S3Suppl 3), A366–A380 (2010). [CrossRef] [PubMed]
  16. 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]
  17. P. Wang and R. Menon, “Simulation and optimization of 1-D periodic dielectric nanostructures for light-trapping,” Opt. Express20(2), 1849–1855 (2012). [CrossRef] [PubMed]
  18. K. R. Catchpole, “A conceptual model of the diffuse transmittance of lamellar diffraction gratings on solar cells,” J. Appl. Phys.102(1), 013102 (2007). [CrossRef]
  19. L. Fraas and L. Partain, Solar Cells and Their Applications (Wiley, 2010).
  20. 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]
  21. A. Chutinan, N. P. Kherani, and S. Zukotynski, “High-efficiency photonic crystal solar cell architecture,” Opt. Express17(11), 8871–8878 (2009). [CrossRef] [PubMed]
  22. 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]
  23. H. Hoppe and N. S. Sariciftci, “Organic solar cells: An overview,” J. Mater. Res.19(07), 1924–1945 (2004). [CrossRef]
  24. A. Raman, Z. F. Yu, and S. H. Fan, “Dielectric nanostructures for broadband light trapping in organic solar cells,” Opt. Express19(20), 19015–19026 (2011). [CrossRef] [PubMed]

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