## Modal analysis of enhanced absorption in silicon nanowire arrays |

Optics Express, Vol. 19, Issue S5, pp. A1067-A1081 (2011)

http://dx.doi.org/10.1364/OE.19.0A1067

Acrobat PDF (1300 KB)

### Abstract

We analyze the absorption of solar radiation by silicon nanowire arrays, which are being considered for photovoltaic applications. These structures have been shown to have enhanced absorption compared with thin films, however the mechanism responsible for this is not understood. Using a new, semi-analytic model, we show that the enhanced absorption can be attributed to a few modes of the array, which couple well to incident light, overlap well with the nanowires, and exhibit strong Fabry-Pérot resonances. For some wavelengths the absorption is further enhanced by slow light effects. We study the evolution of these modes with wavelength to explain the various features of the absorption spectra, focusing first on a dilute array at normal incidence, before generalizing to a dense array and off-normal angles of incidence. The understanding developed will allow for optimization of simple SiNW arrays, as well as the development of more advanced designs.

© 2011 OSA

## 1. Introduction

1. N. S. Lewis, “Toward cost-effective solar energy use,” Science **315**, 798–801 (2007). [CrossRef] [PubMed]

2. L. Tsakalakos, “Nanostructures for photovoltaics,” Mater. Sci. Eng. R **62**, 175–189 (2008). [CrossRef]

*μ*m thick Si wafers for sufficient absorption. This large thickness necessitates that the silicon be of a high chemical purity, for efficient carrier diffusion across the wafer [2

2. L. Tsakalakos, “Nanostructures for photovoltaics,” Mater. Sci. Eng. R **62**, 175–189 (2008). [CrossRef]

4. K. R. Catchpole and A. Polman, “Plasmonic solar cells,” Opt. Express **16**, 21793–217800 (2008). [CrossRef] [PubMed]

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

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

7. 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**, 16986 (2007). [CrossRef] [PubMed]

8. R. A. Pala, J. S. 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]

7. 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**, 16986 (2007). [CrossRef] [PubMed]

*et al*. for nanostructures in the wave-optics regime [9

9. Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express **18**, 366–380 (2010). [CrossRef]

*n*

^{2}, where

*n*is the refractive index of the material [10

10. E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. **29**, 300–305 (1982). [CrossRef]

11. K. Peng, Y. Xu, Y. Wu, and Y. Yan, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small **1**, 1062–1067 (2005). [CrossRef]

12. C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express **17**, 19371–19381 (2009). [CrossRef] [PubMed]

11. K. Peng, Y. Xu, Y. Wu, and Y. Yan, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small **1**, 1062–1067 (2005). [CrossRef]

13. Z. Fan, H. Razavi, J. Do, A. Moriwaki, O. Ergen, Y.-L. Chueh, P. W. Leu, J. C. Ho, T. Takahashi, L. A. Reichertz, S. Neale, K. Yu, M. Wu, J. W. Ager, and A. Javey, “Three-dimensional nanopillar-array photovoltaics on low-cost and flexible substrates,” Nat. Mater. **8**, 648–53 (2009). [CrossRef] [PubMed]

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

15. B. M. Kayes, M. A. Filler, M. C. Putnam, M. D. Kelzenberg, N. S. Lewis, and H. A. Atwater, “Growth of vertically aligned Si wire arrays over large areas (> 1 cm^{2}) with Au and Cu catalysts,” Appl. Phys. Lett. **91**, 103110 (2007). [CrossRef]

16. M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. **9**, 239–244 (2010). [CrossRef] [PubMed]

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

17. B. M. Kayes, H. A. Atwater, and N. S. Lewis, “Comparison of the device physics principles of planar and radial p-n junction nanorod solar cells,” J. Appl. Phys. **97**, 114302 (2005). [CrossRef]

18. E. C. Garnett and P. Yang, “Silicon nanowire radial p-n junction solar cells.” J. Am. Chem. Soc. **130**, 9224–9225 (2008). [CrossRef] [PubMed]

19. Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, and X. W. Sun, “Broadband absorption enhancement in randomly positioned silicon nanowire arrays for solar cell applications,” Opt. Lett. **36**, 1884–1886 (2011). [CrossRef] [PubMed]

21. J. Li, H. Yu, M. Wong, X. Li, and G. Zhang, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. **95**, 243113 (2009). [CrossRef]

12. C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express **17**, 19371–19381 (2009). [CrossRef] [PubMed]

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

12. C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express **17**, 19371–19381 (2009). [CrossRef] [PubMed]

**17**, 19371–19381 (2009). [CrossRef] [PubMed]

16. M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. **9**, 239–244 (2010). [CrossRef] [PubMed]

21. J. Li, H. Yu, M. Wong, X. Li, and G. Zhang, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. **95**, 243113 (2009). [CrossRef]

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

*et al.*[24

24. E. D. Kosten, E. L. Warren, and H. A. Atwater, “Ray optical light trapping in silicon microwires: exceeding the 2n^{2} intensity limit,” Opt. Express **19**, 3316–3331 (2011). [CrossRef] [PubMed]

25. J. Kupec and B. Witzigmann, “Dispersion, wave propagation and efficiency analysis of nanowire solar cells,” Opt. Express **17**, 10399–10410 (2009). [CrossRef] [PubMed]

17. B. M. Kayes, H. A. Atwater, and N. S. Lewis, “Comparison of the device physics principles of planar and radial p-n junction nanorod solar cells,” J. Appl. Phys. **97**, 114302 (2005). [CrossRef]

26. K. R. Catchpole, S. Mokkapati, and F. J. Beck, “Comparing nanowire, multi-junction and single junction solar cells in the presence of light trapping,” J. Appl. Phys. **109**, 084519 (2011). [CrossRef]

## 2. Modal Method

**17**, 19371–19381 (2009). [CrossRef] [PubMed]

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

**17**, 19371–19381 (2009). [CrossRef] [PubMed]

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

*a*, and height

*h*, arranged in a square lattice with lattice constant

*d*(see Fig. 1). The height of the nanowires is set to the standard thin film photovoltaic thickness of

*h*= 2.33

*μ*m. For silicon we use the complex dielectric permittivity of Green and Keevers [28

28. M. A. Green and M. J. Keevers, “Optical properties of intrinsic silicon at 300 K,” Prog. Photovolt. Res. Appl. **3**, 189–192 (1995). [CrossRef]

**, if represented in the plane wave basis, and as**

*f***, if represented in the Bloch mode basis. The advantage of this approach is that the fields are expressed in their natural bases everywhere, greatly reducing the computational cost of the simulations and, critically, providing results in terms of the most intuitive and meaningful basis functions in each domain.**

*c**xy*-plane and is infinite and uniform in

*z*. The Bloch functions satisfy the Maxwell equations and the appropriate continuity conditions at the cylinder boundaries and can be written as the product of a function φ

_{m,k⊥,kz}(

**r**), with the same periodicity as the medium, a phase factor, and a factor representing propagation in the ±

*z*-direction,

*i.e.*Here the Bloch modes are indexed by mode number

*m*, k

*is the*

_{z}*z*-component of the wavevector, and

**r**is the in-plane position vector.

**k**

_{⊥}is the in-plane wavevector that is in the first Brillouin zone, being set by the angle of the incidence. We calculate the Bloch modes using a vectorial FEM routine that discretizes the wave equation to form a generalized eigenvalue problem. The propagation constant k

*and modal field amplitudes are represented by the eigenvalue and eigenvector respectively and are found using standard algebraic techniques. The FEM routine is based on previous work on optical fibers [29*

_{z}29. K. B. Dossou and M. Fontaine, “A high order isoparametric finite element method for the computation of waveguide modes,” Comput. Method Appl. M. **194**, 837–858 (2005). [CrossRef]

**R**

*,*

_{ij}**T**

*, where fields are incident from medium*

_{ij}*i*into medium

*j*. The diagonal matrix

**P**= diag[

*e*

^{ikz,mh}] represents propagation of each of the modes through a layer of thickness

*h*. We then find the total transmission matrix in terms of the scattering and propagation matrices (where free space and the array are labeled as media 1, 2 respectively) as with an analogous expression for the total reflection,

**R**. These matrices express the total transmission through and reflection off the array for each plane wave order. The absorptance A(

*λ*) is found as the difference between unity and the sums of the square magnitudes of the elements of

**T**,

**R**corresponding to propagating waves.

*ultimate efficiencies*,

*η*. The ultimate efficiency, as defined by Shockley and Queisser [32

32. W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. **32**, 510–519 (1961). [CrossRef]

*hc*/

*λ*, where

_{g}*λ*is the wavelength corresponding to the electronic band gap. The ultimate efficiency then represents the fraction of the incident solar energy, I(

_{g}*λ*), (taken as the ASTM Air Mass 1.5 direct and circum-solar spectrum [33

33. ASTM, “Reference Solar Spectral Irradiance: Air Mass 1.5 Spectra,” http://rredc.nreal.gov/solar/spectra/am1.5.

*λ*= 310 nm is where the solar irradiance is negligibly small,

_{l}*λ*= 4000 nm is the upper limit of the available data for the solar spectrum and

_{u}*λ*= 1127 nm is the band edge of bulk silicon.

_{g}## 3. Analysis of a Dilute Array

*dilute*array, consisting of nanowires of 60 nm radius, spaced with a 600 nm period, such that the silicon fill fraction is

*πa*

^{2}/

*d*

^{2}= 3.1% (with 96.9% air background). The absorption spectrum of this array is shown in Fig. 2(a) for normally incident light, where

**k**

_{⊥}= 0 at the center of the Brillouin zone. For normally incident light the absorption spectrum is polarization independent [34

34. G. H. Derrick and R. C. McPhedran, “Coated crossed gratings,” J. Opt. **15**, 69–81 (1984). [CrossRef]

### 3.1. Absorbing Modes

*key*modes of the array, and we find that these modes often feature slow light regions that complement criteria (i)–(iii) to enhance their absorption further. In addition to the key modes, the fundamental mode, which is roughly equivalent to that of a single nanowire (

*i.e.*, an optical fiber), contributes moderately to the absorption at longer wavelengths. The fundamental and key modes evolve distinctly with wavelength and we explain the absorption spectrum fully in terms of how the modes fulfill the absorption criteria (i)–(iii) across the wavelength range. We first examine the criteria (i) through (iii) and then investigate the properties of the key modes as expressed in the dispersion diagram of the array.

### 3.2. Coupling

### 3.3. Resonances

**R**

_{21}. These occur as a valid solution of the continuity requirements at the top and bottom interfaces. Such resonances further enhance light trapping and absorption in region III, where they involve the fundamental and key modes.

### 3.4. Energy Concentration

*𝒞*as, where dispersive effects are neglected. Figure 5(a) shows

*𝒞*for the fundamental mode (blue) and for the key mode (red), overlaid on the absorption spectrum.

35. K. Seo, M. Wober, P. Steinvurzel, E. Schonbrun, Y. Dan, T. Ellenbogen, and K. B. Crozier, “Multicolored Vertical Silicon Nanowires.” Nano Lett. **11**, 1851–1856 (2011). [CrossRef] [PubMed]

### 3.5. Dispersion Diagram

_{z}*d*), the real part of the normalized propagation constant, plotted in blue for all but the key mode (red) versus wavelength. The black curve shown in Fig. 5(b) is the light line, where

*n*

_{eff}= 1.

36. T. Baba, “Slow light in photonic crystals,” Nat. Photonics **2**, 465–473 (2008). [CrossRef]

_{g}, is inversely proportional to the gradient: Thus a large gradient of a mode’s dispersion curve represents a region of slow energy transport through the array, whilst a small gradient indicates a group velocity close to

*c*, the speed of light in vacuum. The latter occurs when the dispersion curves approach the light line, where most of the mode’s energy is in the air (

*n*

_{eff}= 1), resulting in weak absorption. For the key mode the group velocity corresponds directly to the energy concentration fraction and inversely to the absorption spectrum; when the group velocity is low (as in regions I, III) the absorption is high (strengthened by Fabry-Pérot resonances) whilst in region II the velocity is high but the absorption is low. The group velocity of the key mode also determines the resonance spacings, with the free spectral range given as Δ

*f*= v

_{g}/2

*h*. Thus the resonances in slow light regions lie close together, overlapping to form the major absorption peak of region III.

*) = 0, well below the light line. Their existence here is made possible by the presence of the array, which removes the restriction on modes to decay to zero at infinity. Importantly we see that the absorption peak above 595 nm occurs when the key mode is below the light line.*

_{z}d### 3.6. Ultimate Efficiency

*η*= 13.8%) [12

**17**, 19371–19381 (2009). [CrossRef] [PubMed]

## 4. Analysis of a Dense Array

*a*= 125 nm,

*d*= 495 nm (20% fill fraction), which has an ultimate efficiency of 15.8%, exceeding that of the thin film. The absorption spectrum of this array, shown in Fig. 6(a), features many sharp, irregularly spaced peaks and a broad peak between 500–600 nm. Although the spectrum is significantly more complex than that of the dilute array, it can be understood using the same concepts.

### 4.1. Effects of Radius and Period

*a*/

*λ*. Similarly, we find that increasing the spacing between nanowires of constant radius (thereby decreasing the fill fraction) also shifts the dispersion relation to longer wavelengths.

*B*

_{1}, and a higher order mode,

*B*

_{2}. In Fig. 6(b) these are seen to cut-off at 1099 nm (

*B*

_{1}, red) and 585 nm (

*B*

_{2}, green). As the number of key modes increases with radius and fill fraction, modal analysis becomes increasingly complicated, however the same physical mechanisms still drive the absorption of SiNW arrays.

*B*

_{1}versus lattice constant, for various radii nanowires. Shown are results from our FEM calculation of the Bloch modes (as in Sect. 2) as well as an analytic calculation of just the key modes, which shows excellent agreement and will be discussed in Sect. 4.3.

### 4.2. Dense Array Absorption Spectrum

*B*

_{2}is beyond cut-off, so that

*B*

_{1}alone determines the absorption (see Fig. 6(b)). At wavelengths below the absorption edge at 1010 nm (above which Im(

*n*) = 0) the Fabry-Pérot resonances of

*B*

_{1}produce absorption spikes, which are sharp because the mode is only slightly lossy and they are irregularly spaced due to geometric and material dispersion. The low loss of key mode

*B*

_{1}is a product of its moderate energy concentration in silicon and the small values of Im(

*n*), whilst the increased spacing between resonances is due to the larger group velocity of

*B*

_{1}, see Sect. 3.5.

*B*

_{1}increases around 600 nm the mode becomes increasingly lossy, which broadens its resonances. Although the modes of the dense array reach higher energy concentration fractions than in the dilute array, this does not suppress coupling until the fraction exceeds 0.95, as the fields are confined within a larger nanowire. This suppresses the coupling of the incident fields to the fundamental mode throughout the wavelength range (see the blue curve in Fig. 6(a)).

*B*

_{2}cuts off with a high energy concentration and low group velocity, and so together with

*B*

_{1}creates the broad absorption peak via lossy Fabry-Pérot resonances. The short wavelength side of the absorption peak is marked by the energy concentration of

*B*

_{2}going through a trough, in so doing contributing significantly to the transmission through the array, at the cost of the absorption. This reduction is not as large as in the dilute case because there is still a well absorbing key mode, and the minimum concentration fraction of

*B*

_{2}is higher. As for the dilute array the real and imaginary components of silicon’s refractive index increase around 400 nm and light is efficiently absorbed.

### 4.3. Dipole Model for Key Mode Cutoff

*z*-components of both electric and magnetic fields are predominantly dipolar. This suggests that the fields can be written to a good approximation as where

*ε*

_{1}and

*ε*

_{2}are the permittivities of the nanowire and background respectively, and

*J*

_{1},

*H*

_{1}are the Bessel and Hankel functions of the first kind [37

37. A. Movchan, N. Movchan, and C. Poulton, *Asymptotic Models of Fields in Dilute and Densely Packed Composites* (Imperial College Press, 2002), Chap. 3. [CrossRef]

*a/d*≪ 1) that higher-order multipoles are not necessary for a true representation of the field contributions from the other cylinders in the array. The coefficients

*A*,

*B*and

*C*can be eliminated from the expansion by enforcing the appropriate field continuity conditions at the cylinder boundaries. The effect of the lattice can be taken into account using the Rayleigh identity (including only dipole terms) to find where

*S*

_{0}is the zero-th order lattice sum [37

37. A. Movchan, N. Movchan, and C. Poulton, *Asymptotic Models of Fields in Dilute and Densely Packed Composites* (Imperial College Press, 2002), Chap. 3. [CrossRef]

**R**

*in the array Fast techniques for summing this slowly-converging series are given in [38*

_{p}38. R. C. McPhedran, N. A. Nicorovici, L. C. Botten, and K. A. Grubits, “Lattice sums for gratings and arrays,” J. Math. Phys. **41**, 7808–16 (2000). [CrossRef]

*i.e.*the wavelength at which k

*= 0 for the key modes, where primes denote derivatives with respect to the argument. The simple dependence on the lattice sum*

_{z}*S*

_{0}allows for easy variation of the lattice type by exchanging

*S*

_{0}. For a single isolated wire

*S*

_{0}= 0; in this case there are no real solutions to Eq. (10). This reiterates the finding of Sect. 3.5 that the existence of the key modes is supported by the lattice geometry.

## 5. Off-Normal Incidence

*s*and

*p*polarizations and unlike previous studies [12

**17**, 19371–19381 (2009). [CrossRef] [PubMed]

**7**, 3249–3252 (2007). [CrossRef] [PubMed]

*B*

_{2}shifts to around 805 nm, where it has a high energy concentration, thus producing an additional broad peak. The characteristic evolution of key modes follows, with an absorption low between 600–700 nm, before another broad peak below this, once

*B*

_{2}passes through the light line.

*θ*, where the reduced projection of the sunlight to the arrays surface is incorporated by a scaling of cos(

*θ*), and the average of the polarizations and orientations is shown in black. We find the average efficiency to remain high across the angular range, dropping by less than cos(

*θ*) for both arrays. For the dense array the additional broad peak increases the efficiency above the normal incidence value for angles up to 30° off-normal. Consistent with previous studies [12

**17**, 19371–19381 (2009). [CrossRef] [PubMed]

*p*polarized light to be in general higher than

*s*polarized light, due to higher absorption at short wavelengths.

## 6. Conclusion

## Acknowledgments

## References and links

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6. | L. Zeng, Y. Yi, C. Hong, J. Liu, N. Feng, X. Duan, and L. C. Kimerling, “Efficiency enhancement in Si solar cells by textured photonic crystal back reflector,” Appl. Phys. Lett. |

7. | 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 |

8. | R. A. Pala, J. S. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film Solar cells with broadband absorption enhancements,” Adv. Mater. |

9. | Z. Yu, A. Raman, and S. Fan, “Fundamental limit of light trapping in grating structures,” Opt. Express |

10. | E. Yablonovitch and G. D. Cody, “Intensity enhancement in textured optical sheets for solar cells,” IEEE Trans. Electron. Dev. |

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16. | M. D. Kelzenberg, S. W. Boettcher, J. A. Petykiewicz, D. B. Turner-Evans, M. C. Putnam, E. L. Warren, J. M. Spurgeon, R. M. Briggs, N. S. Lewis, and H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. |

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23. | E. Yablonovitch, “Statistical ray optics,” J. Opt. Soc. Am. |

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25. | J. Kupec and B. Witzigmann, “Dispersion, wave propagation and efficiency analysis of nanowire solar cells,” Opt. Express |

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34. | G. H. Derrick and R. C. McPhedran, “Coated crossed gratings,” J. Opt. |

35. | K. Seo, M. Wober, P. Steinvurzel, E. Schonbrun, Y. Dan, T. Ellenbogen, and K. B. Crozier, “Multicolored Vertical Silicon Nanowires.” Nano Lett. |

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38. | R. C. McPhedran, N. A. Nicorovici, L. C. Botten, and K. A. Grubits, “Lattice sums for gratings and arrays,” J. Math. Phys. |

39. | S. E. Han and G. Chen, “Optical absorption enhancement in silicon nanohole arrays for solar photovoltaics,” Nano Lett. |

40. | R. C. McPhedran and W. T. Perrins, “Electrostatic and optical resonances of cylinder pairs,” Appl. Phys. |

**OCIS Codes**

(040.5350) Detectors : Photovoltaic

(050.0050) Diffraction and gratings : Diffraction and gratings

(350.6050) Other areas of optics : Solar energy

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

(310.6628) Thin films : Subwavelength structures, nanostructures

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: May 26, 2011

Revised Manuscript: June 29, 2011

Manuscript Accepted: July 1, 2011

Published: July 19, 2011

**Citation**

Björn C. P. Sturmberg, Kokou B. Dossou, Lindsay C. Botten, Ara A. Asatryan, Christopher G. Poulton, C. Martijn de Sterke, and Ross C. McPhedran, "Modal analysis of enhanced absorption in silicon nanowire arrays," Opt. Express **19**, A1067-A1081 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S5-A1067

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