## Dielectric particle and void resonators for thin film solar cell textures |

Optics Express, Vol. 19, Issue 25, pp. 25729-25740 (2011)

http://dx.doi.org/10.1364/OE.19.025729

Acrobat PDF (1479 KB)

### Abstract

Abstract: Using Mie theory and Rigorous Coupled Wave Analysis (RCWA) we compare the properties of dielectric particle and void resonators. We show that void resonators—low refractive index inclusions within a high index embedding medium—exhibit larger bandwidth resonances, reduced peak scattering intensity, different polarization anisotropies, and enhanced forward scattering when compared to their particle (high index inclusions in a low index medium) counterparts. We evaluate amorphous silicon solar cell textures comprising either arrays of voids or particles. Both designs support substantial absorption enhancements (up to 45%) relative to a flat cell with anti-reflection coating, over a large range of cell thicknesses. By leveraging void-based textures 90% of above-bandgap photons are absorbed in cells with maximal vertical dimension of 100 nm.

© 2011 OSA

## 1. Introduction

1. P. Campbell, “Enhancement of light absorption from randomizing and geometric textures,” J. Opt. Soc. Am. B **10**(12), 2410–2415 (1993). [CrossRef]

2. M. A. Green, “Two new efficient crystalline silicon light-trapping textures,” Prog. Photovolt. Res. Appl. **7**(4), 317–320 (1999). [CrossRef]

4. J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy **77**(6), 917–930 (2004). [CrossRef]

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

7. N. C. Panoiu and R. M. Osgood Jr., “Enhanced optical absorption for photovoltaics via excitation of waveguide and plasmon-polariton modes,” Opt. Lett. **32**(19), 2825–2827 (2007). [CrossRef] [PubMed]

8. Y. A. Akimov, W. S. Koh, S. Y. Sian, and S. Ren, “Nanoparticle-enhanced thin film solar cells: Metallic or dielectric nanoparticles?” Appl. Phys. Lett. **96**(7), 073111 (2010). [CrossRef]

9. J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, “Light absorption enhancement in thin-film solar cells using whispering gallery modes in dielectric nanospheres,” Adv. Mater. (Deerfield Beach Fla.) **23**(10), 1272–1276 (2011). [CrossRef] [PubMed]

10. M. Kroll, S. Fahr, C. Helgert, C. Rockstuhl, F. Lederer, and T. Pertsch, “Employing dielectric diffractive structures in solar cells - a numerical study,” Phys. Status Solidi **205**(12), 2777–2795 (2008). [CrossRef]

12. S. Bandiera, D. Jacob, T. Muller, F. Marquier, M. Laroche, and J. J. Greffet, “Enhanced absorption by nanostructured silicon,” Appl. Phys. Lett. **93**(19), 193103 (2008). [CrossRef]

*particle*resonator geometry, scattering occurs as a result of the dielectric contrast between air and a dielectric or plasmonic nanoparticle (Fig. 1(a) ). For a given choice of material, however, one can also construct a

*void*resonator, wherein light scatters off nanoscale voids within a high-index dielectric (Fig. 1(b)) or plasmonic medium. Such resonators can form the constituent subunits in photonic crystals [13] and metamaterials [14

14. F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. **93**(19), 197401 (2004). [CrossRef] [PubMed]

15. Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, and X. W. Sun, “Enhanced optical absorption in nanopatterned silicon thin films with a nano-cone-hole structure for photovoltaic applications,” Opt. Lett. **36**(9), 1713–1715 (2011). [CrossRef] [PubMed]

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

17. T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics **2**(5), 299–301 (2008). [CrossRef]

18. N. N. Lal, B. F. Soares, J. K. Sinha, F. Huang, S. Mahajan, P. N. Bartlett, N. C. Greenham, and J. J. Baumberg, “Enhancing solar cells with localized plasmons in nanovoids,” Opt. Express **19**(12), 11256–11263 (2011). [CrossRef] [PubMed]

19. T. K. Gaylord, W. E. Baird, and M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. **25**(24), 4562–4567 (1986). [CrossRef] [PubMed]

21. A. Gombert, K. Rose, A. Heinzel, W. Horbelt, C. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Sol. Energy Mater. Sol. Cells **54**(1-4), 333–342 (1998). [CrossRef]

*single*resonators are manifested as properties of periodic resonator arrays. In particular, we exploit the scattering properties of particle and void resonators in thin film amorphous silicon (a-Si) solar cell textures. Ultimately, we show that these active material textures can enable significant absorption enhancements over equivalent thin film cells with anti-reflection coatings. We demonstrate absorption of 90% of incident solar photons in 100 nm thick a-Si solar cells that take advantage of void resonator geometries.

## 2. Scattering properties of single resonators

*e*. At normal incidence the scattered fields are purely transverse electric (TE) or transverse magnetic (TM) with excitation coefficients

^{imφ}*a*and

_{m}*b*, respectively: where

_{m}*J*and

_{m}*H*are respectively Bessel and Hankel functions of the first kind and primes denote derivatives with respect to the argument. The relative refractive index

_{m}*n*and relative size

_{r}*x*are given by

*n*and

_{emb}*n*are the refractive index of the embedding medium and the resonator respectively,

_{int}*k*is the wavevector,

*r*is the cylinder radius, and

_{0}*λ*is the free space wavelength.

*n*and

_{int}> n_{emb}*n*, whereas for void resonators

_{r}> 1*n*and

_{int}< n_{emb}*n*. In Fig. 2 we plot the lowest order (

_{r}< 1*m*= 0 or 1) Mie coefficients for particle (red) and void (blue) resonators comprising air and a material with refractive index 4—a value that approximates the refractive index of e.g. silicon or germanium (for a discussion of Mie resonances in spherical Si or Ge particles see e.g [23

23. A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express **19**(6), 4815–4826 (2011). [CrossRef] [PubMed]

24. R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, and J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophotonics **5**(1), 053512 (2011). [CrossRef]

_{1}resonance relative to the TE

_{0}resonance. In all other cases resonances shift to higher frequency with increasing mode order (larger

*m*).

25. J. A. Schuller and M. L. Brongersma, “General properties of dielectric optical antennas,” Opt. Express **17**(26), 24084–24095 (2009). [CrossRef] [PubMed]

### 2.1 Simplified resonance conditions

25. J. A. Schuller and M. L. Brongersma, “General properties of dielectric optical antennas,” Opt. Express **17**(26), 24084–24095 (2009). [CrossRef] [PubMed]

*n*≫ 1 and the lowest-order resonances occur for values of

_{r}*x*≪ 1. In the void geometry a large index contrast implies

*n*≪ 1 and the lowest-order resonances occur for values of

_{r}*xn*≪ 1. By taking limits of the Mie coefficients in these respective regimes (see Appendix B for details) we derive simplified resonance conditions, shown in Table 1 .

_{r}*2πr*, where

_{0}n_{H}/λ*n*is the refractive index of the high-index medium, and the relative resonance frequencies are entirely governed by the location of Bessel function zeroes. For instance, the first zeroes of the Bessel functions

_{H}*J*

_{0},

*J*

_{1},

*Y*

_{0},

*Y*

_{1}, and

*Y*

_{2}occur when the arguments equal 2.40, 3.83, 0.89, 2.20, and 3.38, respectively. From a comparison of these values the red-shift of the TE

_{1}void resonance relative to the TE

_{0}void follows directly. Similarly, the derived resonance conditions capture a feature that is evident in comparing the particle and void Mie coefficients in Fig. 2: for a given choice of two materials the void geometry will exhibit a red-shifted TE

_{1}but blue-shifted TE

_{0}, TM

_{0}, and TM

_{1}resonance frequency (

*r*).

_{0}λ^{−1}### 2.2 Scattering cross section

*a*Mie coefficients with

_{n}*b*. The larger bandwidth of the void Mie coefficients directly leads to broader bandwidth scattering cross sections. However, the cross section is also inversely proportional to the embedding medium refractive index

_{n}*n*, thereby reducing the scattering magnitude. In Fig. 3(a) we plot the scattering cross sections for cylindrical particles and voids. Scattering from particles results from a sequence of narrow resonances, whereas voids have significantly smaller variations with normalized frequency due to strongly overlapping broadband resonant modes. Additionally, very small voids scatter more TE radiation than their particle counterparts, whereas the opposite is true for TM polarization. Regardless, the larger bandwidths of void resonators is offset by the reduction in scattering due to large

_{emb}*n*and the particle resonators have a slightly larger unpolarized scattering cross section over most normalized frequencies.

_{emb}### 2.3 Forward scattering properties

*total*cross section may be slightly weaker for voids, for the solar cell textures in Fig. 1 the principle interest is in

*forward*scattering, where the effect of an interface on scattering properties is very important. Previously, researchers noted that classical dipoles at an interface emit preferentially into the high index material and demonstrated the importance of this phenomenon in plasmon enhanced solar cells [26

26. K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. **93**(19), 191113 (2008). [CrossRef]

*n*= 1, dashed) or high-index (

*n*= 4, solid) medium as a function of distance from the interface. The fraction of forward (into the substrate) emitted radiation decreases rapidly with distance for dipoles sitting above a high-index substrate. This situation approximates scattering in the particle geometry and necessitates careful design of particle resonators that are located within the interface near-field [22] in order to suppress back-scattering. In contrast, a dipole embedded

*within*the high-index substrate emits more than 98% of its radiation in the forward direction regardless of orientation or distance from an interface. This situation is akin to the void geometry, and suggests that void resonators may exhibit substantial preference for forward scattering.

### 2.4 Single particle summary

## 3. Resonator arrays

11. L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. **10**(2), 439–445 (2010). [CrossRef] [PubMed]

28. RSoft Design Group, Inc., http://www.rsoftdesign.com.

29. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A **12**(5), 1068–1076 (1995). [CrossRef]

*a*is the array periodicity,

*n*is the substrate refractive index,

_{s}*k*is the free space wave-vector, and the quantities

_{0}*R*and

_{j}*T*are determined computationally. In Fig. 4(a) we plot the scattering properties of textures based on the designs in Fig. 1 for a substrate index of

_{j}*n =*4 but without an ARC. Simulations are presented for a periodicity 40 times larger than the resonator diameter such that inter-particle coupling is weak and there is a near continuum of diffracted orders

*k*. The sum of the power contained in all diffracted orders is a good approximation to the single resonator scattering cross-sections, and allows for a direct comparison with Fig. 3(a).

_{xj}## 4. Thin film absorption enhancements

30. The algorithm can be found at http://www.lri.fr/~hansen/cmaes_inmatlab.html#python.

*b*, and the simulated absorption spectrum of the cell,

_{AM1.5}(λ)*A(λ)*, for photons with energy larger than the a-Si mobility gap (730nm):

31. J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, “Analytic representations of the dielectric functions of materials for device and structural modeling,” Thin Solid Films **313–314**(1-2), 132–136 (1998). [CrossRef]

_{3}N

_{4}in the optical range. For every value of the

*maximum*a-Si thickness

*t*, we allow the square rod diameter

*d*, the periodicity

*a*, and the ARC coating thickness

*t*to vary (Fig. 6(c) ). The optimized absorption values as a function of

_{ARC}*t*are compared to an equivalent

*maximum*thickness flat cell with optimized ARC and plotted in Figs. 6(a) and 6(b).

## 5. Conclusion

_{1}resonance, which shows an unusual redshift, and have higher bandwidth resonances except for the TM

_{0}mode. Due to the early onset of the TE

_{1}mode ultrasmall voids are more efficient TE scatterers than ultrasmall particles, while for TM polarization the opposite is true. In general, however, the advantages from larger bandwidth resonances in the void configuration are partially offset by an inverse relationship between peak scattering cross-section and embedding medium refractive index.

18. N. N. Lal, B. F. Soares, J. K. Sinha, F. Huang, S. Mahajan, P. N. Bartlett, N. C. Greenham, and J. J. Baumberg, “Enhancing solar cells with localized plasmons in nanovoids,” Opt. Express **19**(12), 11256–11263 (2011). [CrossRef] [PubMed]

## Appendix A: Bandwidths

*Q*) resonances. This trend becomes more evident as the index contrast between the particle and embedding medium is increased.

*Q*increases exponentially [25

25. J. A. Schuller and M. L. Brongersma, “General properties of dielectric optical antennas,” Opt. Express **17**(26), 24084–24095 (2009). [CrossRef] [PubMed]

*Q*factor is independent of

*n*. This fact can be proven by deriving simplified Mie coefficients in the limit of small

_{r}*n*, as we do in Appendix B. The Mie coefficients depend only on the normalized frequency

_{r}*x,*thus the resonance lineshape of a void resonator looks identical for all values of index contrast where the approximation holds. The possibility to have very small voids with large bandwidths is markedly different than what occurs in the particle geometry for the same choice of materials. In both cases the resonator size

*relative to the free space wavelength*gets smaller with increasing index contrast. However, in the void geometry the size

*relative to the embedding medium wavelength*is constant and it is this normalized size that determines the bandwidth.

*n*. In the void configuration the

*Q*factor is nearly constant with

*m*whereas in the particle configuration the

*Q*factor increases exponentially with

*m*(Fig. 7 ) a scaling which has been observed in low order whispering gallery microcavities [32

32. J. Shainline, S. Elston, Z. Liu, G. Fernandes, R. Zia, and J. Xu, “Subwavelength silicon microcavities,” Opt. Express **17**(25), 23323–23331 (2009). [CrossRef] [PubMed]

*m*the cylindrical boundary looks approximately planar leading to near-total internal reflection and high

*Q*s. In voids, the light-ray approaches the boundary from the low-index side, there is finite transmission even for a planar interface, and bandwidths remain large.

## Appendix B: Simplified Mie coefficients and resonance conditions

*n*→ 0:

_{r}*x = 2πr*and can be solved directly to determine the resonance values in Table 1. The simplified Mie coefficients are reasonably accurate starting from index contrast of approximately 3, and are accurate even up to very high values of the mode index

_{0}n_{emb}/λ*m*. These simplifications highlight the fact that in the high index contrast limit the void resonance lineshapes, and thus bandwidths, are independent of the specific value of

*n*and remain quite large even for resonant voids that are significantly smaller than the freespace wavelength.

_{int}*n*. For particles, we were unable to find a simplified limit of the Mie coefficient as

_{int}*n*→ ∞. To determine the resonance conditions we set the Mie coefficients equal to unity [25

_{r}**17**(26), 24084–24095 (2009). [CrossRef] [PubMed]

*x*and

*n*and the resonances cannot be solved for arbitrary values of

_{r}x*n*. However in the large index contrast limit (

_{r}*n*→ ∞) the resonance condition for TE polarization simplifies to

_{r}*J*= 0. For the lowest order TM resonances, the limit of large index contrast also implies that

_{m}(n_{r}x)*x*→ 0 and with suitable Taylor expansions about

*x*near 0 we can derive simplified resonance conditions:

*n*.

_{r}## Appendix C: Electric field intensity within void resonators

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

*n*) surrounded by a high refractive index medium (

_{L}*n*) they derive a maximal absorption enhancement factor (Eq. (20)) of

_{H}*n*=1 surrounded by a medium of index

_{int}*n*=4 as a function of its normalized frequency (its size relative to the incident wavelength). In addition to recovering the electrostatic result,

_{emb}## Acknowledgments

## References and links

1. | P. Campbell, “Enhancement of light absorption from randomizing and geometric textures,” J. Opt. Soc. Am. B |

2. | M. A. Green, “Two new efficient crystalline silicon light-trapping textures,” Prog. Photovolt. Res. Appl. |

3. | O. Isabella, K. Jager, J. Krč, and M. Zeman, “Light scattering properties of surface-textured substrates for thin-film solar cells,” |

4. | J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy |

5. | H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. |

6. | V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express |

7. | N. C. Panoiu and R. M. Osgood Jr., “Enhanced optical absorption for photovoltaics via excitation of waveguide and plasmon-polariton modes,” Opt. Lett. |

8. | Y. A. Akimov, W. S. Koh, S. Y. Sian, and S. Ren, “Nanoparticle-enhanced thin film solar cells: Metallic or dielectric nanoparticles?” Appl. Phys. Lett. |

9. | J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, “Light absorption enhancement in thin-film solar cells using whispering gallery modes in dielectric nanospheres,” Adv. Mater. (Deerfield Beach Fla.) |

10. | M. Kroll, S. Fahr, C. Helgert, C. Rockstuhl, F. Lederer, and T. Pertsch, “Employing dielectric diffractive structures in solar cells - a numerical study,” Phys. Status Solidi |

11. | L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett. |

12. | S. Bandiera, D. Jacob, T. Muller, F. Marquier, M. Laroche, and J. J. Greffet, “Enhanced absorption by nanostructured silicon,” Appl. Phys. Lett. |

13. | J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, |

14. | F. Falcone, T. Lopetegi, M. A. G. Laso, J. D. Baena, J. Bonache, M. Beruete, R. Marqués, F. Martín, and M. Sorolla, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. |

15. | Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, and X. W. Sun, “Enhanced optical absorption in nanopatterned silicon thin films with a nano-cone-hole structure for photovoltaic applications,” Opt. Lett. |

16. | Z. Yu, A. Raman, and S. Fan, “Fundamental limit of nanophotonic light trapping in solar cells,” Proc. Natl. Acad. Sci. U.S.A. |

17. | T. V. Teperik, F. J. García de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics |

18. | N. N. Lal, B. F. Soares, J. K. Sinha, F. Huang, S. Mahajan, P. N. Bartlett, N. C. Greenham, and J. J. Baumberg, “Enhancing solar cells with localized plasmons in nanovoids,” Opt. Express |

19. | T. K. Gaylord, W. E. Baird, and M. G. Moharam, “Zero-reflectivity high spatial-frequency rectangular-groove dielectric surface-relief gratings,” Appl. Opt. |

20. | M. E. Motamedi, W. H. Southwell, and W. J. Gunning, “Antireflection surfaces in silicon using binary optics technology,” Appl. Opt. |

21. | A. Gombert, K. Rose, A. Heinzel, W. Horbelt, C. Zanke, B. Bläsi, and V. Wittwer, “Antireflective submicrometer surface-relief gratings for solar applications,” Sol. Energy Mater. Sol. Cells |

22. | C. F. Bohren and D. R. Huffman, |

23. | A. García-Etxarri, R. Gómez-Medina, L. S. Froufe-Pérez, C. López, L. Chantada, F. Scheffold, J. Aizpurua, M. Nieto-Vesperinas, and J. J. Sáenz, “Strong magnetic response of submicron silicon particles in the infrared,” Opt. Express |

24. | R. Gómez-Medina, B. García-Cámara, I. Suárez-Lacalle, F. González, F. Moreno, M. Nieto-Vesperinas, and J. J. Sáenz, “Electric and magnetic dipolar response of germanium nanospheres: interference effects, scattering anisotropy, and optical forces,” J. Nanophotonics |

25. | J. A. Schuller and M. L. Brongersma, “General properties of dielectric optical antennas,” Opt. Express |

26. | K. R. Catchpole and A. Polman, “Design principles for particle plasmon enhanced solar cells,” Appl. Phys. Lett. |

27. | A.B. Evlyukhin, C. Reinhardt, A. Seidel, B.S. Luk’yanchuk, and B.N. Chichkov, “Optical response features of Si-nanoparticle arrays,” Phys. Rev. Lett. B |

28. | RSoft Design Group, Inc., http://www.rsoftdesign.com. |

29. | M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A |

30. | The algorithm can be found at http://www.lri.fr/~hansen/cmaes_inmatlab.html#python. |

31. | J. Leng, J. Opsal, H. Chu, M. Senko, and D. E. Aspnes, “Analytic representations of the dielectric functions of materials for device and structural modeling,” Thin Solid Films |

32. | J. Shainline, S. Elston, Z. Liu, G. Fernandes, R. Zia, and J. Xu, “Subwavelength silicon microcavities,” Opt. Express |

33. | H. C. van der Hulst, |

**OCIS Codes**

(050.1950) Diffraction and gratings : Diffraction gratings

(140.4780) Lasers and laser optics : Optical resonators

(290.4020) Scattering : Mie theory

(350.6050) Other areas of optics : Solar energy

(050.6624) Diffraction and gratings : Subwavelength structures

(310.6845) Thin films : Thin film devices and applications

**ToC Category:**

Solar Energy

**History**

Original Manuscript: September 30, 2011

Revised Manuscript: November 17, 2011

Manuscript Accepted: November 17, 2011

Published: December 1, 2011

**Citation**

Sander A. Mann, Richard R. Grote, Richard M. Osgood, and Jon A. Schuller, "Dielectric particle and void resonators for thin film solar cell textures," Opt. Express **19**, 25729-25740 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-25-25729

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### References

- P. Campbell, “Enhancement of light absorption from randomizing and geometric textures,” J. Opt. Soc. Am. B10(12), 2410–2415 (1993). [CrossRef]
- M. A. Green, “Two new efficient crystalline silicon light-trapping textures,” Prog. Photovolt. Res. Appl.7(4), 317–320 (1999). [CrossRef]
- O. Isabella, K. Jager, J. Krč, and M. Zeman, “Light scattering properties of surface-textured substrates for thin-film solar cells,” Proceedings of the 23rd European Photovoltaic Solar Energy Conference and Exhibition (EU PVSEC), (2008), Session 3AV 1, pp. 476–481.
- J. Müller, B. Rech, J. Springer, and M. Vanecek, “TCO and light trapping in silicon thin film solar cells,” Sol. Energy77(6), 917–930 (2004). [CrossRef]
- H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater.9(3), 205–213 (2010). [CrossRef] [PubMed]
- V. E. Ferry, M. A. Verschuuren, H. B. T. Li, E. Verhagen, R. J. Walters, R. E. I. Schropp, H. A. Atwater, and A. Polman, “Light trapping in ultrathin plasmonic solar cells,” Opt. Express18(S2Suppl 2), A237–A245 (2010). [CrossRef] [PubMed]
- N. C. Panoiu and R. M. Osgood., “Enhanced optical absorption for photovoltaics via excitation of waveguide and plasmon-polariton modes,” Opt. Lett.32(19), 2825–2827 (2007). [CrossRef] [PubMed]
- Y. A. Akimov, W. S. Koh, S. Y. Sian, and S. Ren, “Nanoparticle-enhanced thin film solar cells: Metallic or dielectric nanoparticles?” Appl. Phys. Lett.96(7), 073111 (2010). [CrossRef]
- J. Grandidier, D. M. Callahan, J. N. Munday, and H. A. Atwater, “Light absorption enhancement in thin-film solar cells using whispering gallery modes in dielectric nanospheres,” Adv. Mater. (Deerfield Beach Fla.)23(10), 1272–1276 (2011). [CrossRef] [PubMed]
- M. Kroll, S. Fahr, C. Helgert, C. Rockstuhl, F. Lederer, and T. Pertsch, “Employing dielectric diffractive structures in solar cells - a numerical study,” Phys. Status Solidi205(12), 2777–2795 (2008). [CrossRef]
- L. Cao, P. Fan, A. P. Vasudev, J. S. White, Z. Yu, W. Cai, J. A. Schuller, S. Fan, and M. L. Brongersma, “Semiconductor nanowire optical antenna solar absorbers,” Nano Lett.10(2), 439–445 (2010). [CrossRef] [PubMed]
- S. Bandiera, D. Jacob, T. Muller, F. Marquier, M. Laroche, and J. J. Greffet, “Enhanced absorption by nanostructured silicon,” Appl. Phys. Lett.93(19), 193103 (2008). [CrossRef]
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