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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 13 — Jul. 1, 2013
  • pp: 16043–16055
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Flat-top and patterned-topped cone gratings for visible and mid-infrared antireflective properties

Jean-Baptiste Brückner, Judikaël Le Rouzo, Ludovic Escoubas, Gérard Berginc, Cécile Gourgon, Olivier Desplats, and Jean-Jacques Simon  »View Author Affiliations


Optics Express, Vol. 21, Issue 13, pp. 16043-16055 (2013)
http://dx.doi.org/10.1364/OE.21.016043


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Abstract

Achieving a broadband antireflection property from material surfaces is one of the highest priorities for those who want to improve the efficiency of solar cells or the sensitivity of photo-detectors. To lower the reflectance of a surface, we are concerned with the study of the optical response of flat-top and patterned-topped cone shaped silicon gratings, based on previous work exploring pyramid gratings. Through rigorous numerical methods such as Finite Different Time Domain, we first designed several flat-top structures that theoretically demonstrate an antireflective character within the middle infrared region. From the opto-geometrical parameters such as period, depth and shape of the pattern determined by numerical analysis, these structures have been fabricated using controlled slope plasma etching processes. In order to extend the antireflective properties up to the visible wavelengths, patterned-topped cones have been fabricated as well. Afterwards, optical characterizations of several samples were carried out. Thus, the performances of the flat-top and patterned-topped cones have been compared in the visible and mid infrared range.

© 2013 OSA

1. Introduction

Over the last few years, antireflective gratings have been widely investigated with the emergence of photovoltaics and photosensing. Reducing the reflection losses from incident radiation has become one of the highest priorities for such devices. Controlling the reflection of incident radiation over an interface has then offered numerous applications for a wide range of domains [1

1. S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Anti-reflecting and photonic nanostructures,” Mater. Sci. Engineering: R: Reports 69(1-3), 1–35 (2010). [CrossRef]

]. For instance, optical systems such as lenses need an antireflective treatment to maximize their transmission coefficient [2

2. K. M. Baker, “Highly corrected close-packed microlens arrays and moth-eye structuring on curved surfaces,” Appl. Opt. 38(2), 352–356 (1999). [CrossRef] [PubMed]

]. For a photodetector, reducing reflection is an important matter, since the better the light penetrates into the material, the more it improves its response [3

3. D. M. Braun, “Design of single layer antireflection coatings for InP/In0.53Ga0.47As/InP photodetectors for the 1200-1600-nm wavelength range,” Appl. Opt. 27(10), 2006–2011 (1988). [CrossRef] [PubMed]

]. In photovoltaics, solar cells treated with an antireflective coating see their photon to electron conversion rate increased. Therefore, with the help of antireflective (AR) coatings, the efficiency of these devices has been greatly enhanced over the last few years [4

4. K. T. Park, Z. Guo, H. D. Um, J. Y. Jung, J. M. Yang, S. K. Lim, Y. S. Kim, and J. H. Lee, “Optical properties of Si microwires combined with nanoneedles for flexible thin film photovoltaics,” Opt. Express 19(S1Suppl 1), A41–A50 (2011). [CrossRef] [PubMed]

7

7. K. Forberich, G. Dennler, M. C. Scharber, K. Hingerl, T. Fromherz, and C. J. Brabec, “Performance improvement of organic solar cells with moth eye anti-reflection coating,” Thin Solid Films 516(20), 7167–7170 (2008). [CrossRef]

]. Concerning the stealth domain, reducing the optical signature of a surface is an important matter as well.

2. Numerical analysis

2.1 Computational tools

2.2 Determination of critical parameters and parametric study

2.2.1 Diffracted orders

A critical constraint has to be added to the antireflective grating. No diffracted order may be present in the air, and we have to limit those present in the substrate as much as possible, in order to avoid cross talking situations in the case of imaging sensors such as CCD or CMOS sensors. For recall, a wave encountering a grating of period P with an incident angle θi is diffracted in transmission and in reflection, into a certain number of orders (Fig. 3
Fig. 3 Illustration of a diffraction grating without any orders (a), with orders in the substrate only (b), and with transmitted and reflected orders (c).
).

2.2.2 Variation in the period length

In order to understand the effect of a variation of the period length, FDTD calculations have been carried out. Parameters M and T are fixed (0.375 and 1.57 µm respectively) and the period P is varied from 0.7 to 1.3 µm. The reflectance spectrum is depicted in Fig. 5
Fig. 5 Reflectance spectrum at normal incidence of a flat-top pyramid grating with T = 1.57 µm, M = 0.375 µm and s = 0 µm. The parameter P is varied from 0.7 to 1.3 µm.
and Table 1

Table 1. Ө value for a grating with different length period P, and with M = 0.375 µm, T = 1.5 µm and s = 0 µm.

table-icon
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reports the value of the θangle for different P parameters.

The structures with period P = 0.7 µm is too reflective in the 3-5 µm and will not be retained. For structures with periods P = 1 µm and P = 1.3 µm, the reflection coefficient is less than 2% in the 3-5 µm region. The latter one, with a slope angle of 73.5 °, shows the lowest reflectivity. However, as we want to restrain the efficiency of the diffracted orders (see section 2.2.1), we do not retain either of the structures with a period P = 1.3 µm.

2.2.3 Variation of the thickness

The M and P parameters are fixed (0.375 µm and 1 µm respectively) while the thickness T is varied. The reflectance spectrum is depicted in Fig. 6
Fig. 6 Reflectance spectrum at normal incidence of a flat-top pyramid grating with P = 1 µm, M = 0.375 µm and s = 0 µm. The parameter T is varied from 1.1 to 2 µm.
and Table 2

Table 2. Ө value for a grating with different thicknesses T, and with P = 1 µm, M = 0.375 µm and s = 0 µm.

table-icon
View This Table
| View All Tables
reports the values of the angle θ for different T.

It can be observed that the slope has a minor effect compared to the height of the pyramid. Indeed, the best efficiency is achieved for a 2 µm flat-top pyramid, showing a slope of the order of 81°. In terms of height, a too small pyramid (1.1 µm) cannot yield less than 2% reflectivity. On the other hand, objectives are achieved with structures with T = 1.57 µm and higher.

2.2.4 Variation in the flat-top length

Figure 7
Fig. 7 Reflectance spectrum at normal incidence of a flat-top pyramid grating with T = 1.57 µm, P = 1 µm and s = 0 µm. The parameter M is varied from 0.1 to 0.6 µm.
gives the reflectance of three structures with the following parameters: P = 1 µm, T = 1.57 µm and s = 0 µm. M is equal to 0.1, 0.375 or 0.6 µm.

Table 3

Table 3. Ө value for a grating with different length of the flat-top M, and with P = 1 µm, T = 1.5 µm and s = 0 µm.

table-icon
View This Table
| View All Tables
reports the value of the angleθ for different M value.

It can be observed that a 10° change in the slope can have a dramatic influence on the efficiency of the grating. The best efficiency is obtained for a slope angle of 73.9°. Structures having a flat-top smaller than 0.4 µm will demonstrate an average reflectivity coefficient R less than 2% in the 3-5 µm region. Structures with larger flat-top will then not be acceptable. It can be seen as well, that the best efficiency is achieved with M = 0.1 µm. However, structures with a flat-top smaller than 0.2 µm are hard to fabricate (see section 3.1).

2.2.5 Variation of the spacing

Simulations have been made to determine how much the spacing “s” at the bottom end of the structures [Fig. 8(a)
Fig. 8 Schematic view of the spacing between the structures (a) and reflectance spectra at normal incidence of flat -top pyramid grating with P = 1 µm, M = 0.375 µm and T = 1.5 µm. The spacing s is varied from 0 to 1 µm (b).
] would be detrimental to the efficiency of the grating [Fig. 8(b)]. The parameters used are those of the reference structure: P = 1 µm, T = 1.57 µm and M = 0.375 µm. The spacing s is varied from 0 to 1 µm. Results show that, as expected, even a small spacing of 0.2 µm is sufficient to increase the average reflectivity to a value higher than 2%. Therefore, gratings with spacing between the structures will not be accepted.

2.2.6 Geometrical specifications

This study has permitted us to define realistic parameters for the flat-top grating, in order to fabricate efficient antireflective silicon gratings. A set of parameters has been fixed. For less than 2% reflectance in the 3-5 µm region, the retained flat-top pyramids have to show the following parameters:

  • Length of the flat-top M: 0.2-0.4 µm
  • Length of the period P: 1 µm
  • Thickness of the pyramid T: greater than 1.57 µm
  • Slope must be comprised between 70 and 80 °
  • No spacing between the structures

Also, the fabrication of a patterned-topped pyramid is considered as well. With the aim of broadening the antireflective range down to the visible region, adding another flat-top pyramidal pattern on top of a classical flat-top pyramid allows to demonstrate two antireflective bands. While the first level is efficient for the 3-5 µm wavelength range, by scaling down the geometric parameters of the second level of periodicity following a ratio of M/2P, it is possible to decrease the reflection in the visible region [Fig. 9
Fig. 9 Calculated reflectance spectra at normal incidence of flat-top and patterned-topped pyramids. Parameters of the flat-top pyramids are P = 1 µm, M = 0.375 µm, T = 1.5625 µm and spacing s = 0 µm. Parameters of the patterned-topped pyramids' first level are P = 1 µm, T = 1.25 µm and M = 0.5 µm. Parameters of the second level are p = 0.25 µm, t = 0.3125 µm, m = 0.125 µm.
]. Therefore the parameters of the second level are: p = M/2P × P, t = M/2P × T and M = M/2P × M (see Fig. 1(b)). As the second level of periodicity is proportional to the first one, geometric specifications detailed above are still valid for the patterned-topped structures.

3. Fabrication

After setting the parameter range necessary to achieve an efficient antireflective grating, several samples have been fabricated by plasma etching on a silicon surface. However, as it has not been possible to fabricate a silicon flat-top pyramids grating, a flat-top cone one was made instead. In this section, the fabrication process is first described, then a discussion will be dedicated to the fabricated samples.

3.1 Process

The flat-top cones were fabricated using DeepUV lithography and plasma etching processes. The photoresist was exposed with a 248 nm laser beam of a DUV stepper on 200 mm silicon wafers in order to define 300 nm dots. Nominal features are squares but since their dimension is close to the equipment resolution, circular structures have been obtained. The transfer into silicon was performed through a 100 nm thick SiO2 hardmask with a Centura 300 plasma etching cluster from Applied Materials. A specific etching process was developed to control the cone slope with high accuracy from 70° to 80°. Moreover this patented process allows a perfect control of the sharp profile at the bottom of the patterns. It has been demonstrated that this process is reproducible. The patterned-topped cones were fabricated by e-beam lithography and the same plasma etching processes. The main advantage of this process is that the cones exhibit no spaces and a sharp profile at the bottom of the features for both structuration levels. Once again this process is reproducible and geometrical parameters can be controlled with the top cone diameter defined by E-beam lithography.

3.2 Fabricated samples

Figures 10(a)
Fig. 10 SEM picture of flat-topped (a) and patterned-topped (b) silicon cones gratings.
and 10(b) present flat-top cones and patterned-topped cones respectively, characterized using Scanning Electron Microscopy. The patterns dimensions are listed: M = 310 nm, P = 1 µm and T = 1.6 µm for flat-top patterns and m = 125 nm, t = 325 nm, p = 250 nm, M = 500 nm, T = 1.25 µm and P = 1 µm for patterned-topped cones.

Figure 11(a)
Fig. 11 Calculated reflectance spectra at normal incidence of a flat-top pyramid and a flat-top cone grating with P = 1 µm, T = 1.5 µm, M = 0.375 µm and s = 0 µm (a), schematic top view of flat-top pyramid and cone gratings and their parameters (b).
shows that for the same P, M and T parameters, a flat-top cone grating is roughly 1% less efficient as an antireflective grating than a pyramid one. This is mostly due to the fact that the cone structures are not totally joined (as it has been seen for the pyramids grating), letting appear a small flat surface contributing to increase the reflectivity [Fig. 11(b)]. Although the first simulations were meant for pyramids, we decided to keep the same geometrical specifications for the cone grating.

4. Optical measurements

Performances of the fabricated samples in the visible and mid infrared regions have been measured with an integrating sphere and a Fourier Transform Infrared (FTIR) spectrometer. In the first place, the reflectance of the flat-top cone gratings has been measured in the 3-5 µm region. Following the good results, patterned-topped cone gratings have been fabricated. From there, a comparison of the optical responses in the visible and mid infrared regions with the two types of gratings has been made.

4.1 Flat-top cones gratings

Most of the samples present M and P parameters close to those specified (around 0.32 and 1 µm for M and P parameters respectively). The height T of the flat-top cone is rather variable and goes from 1.21 up to 1.97 µm. Some of the samples present no spacing between the structures. Geometric parameters of the series of samples are reported in Table 4

Table 4. Parameters of the fabricated flat top cone gratings

table-icon
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. FTIR measurements are depicted in Fig. 12
Fig. 12 Reflectance measurements of the fabricated silicon flat-top cone gratings.
.

As expected, the structuration strongly decreased the reflectivity when compared to a polished silicon surface (R = 30% in the 3-5 µm region). Best performances are then obtained by samples showing small or even zero spaces between the structures and high thicknesses (samples G25, G31, G37 and G39). Those samples demonstrate an average reflection coefficient less than 2% in the 3-5 µm region. The performances displayed are satisfying since we are considering flat-top cone gratings.

4.1 Extending the antireflective properties to the visible

After having successfully demonstrated a less than 2% reflectivity in the mid infrared with flat-top cone gratings, elaboration of patterned-topped cone gratings have been carried out (see section 3). As described in section 2.2.6, the patterning of the top of the cones has the goal of extending the antireflective properties up to the visible band.

Integrating sphere measurements [Fig. 13(a)
Fig. 13 Reflectance spectra of flat-and patterned-topped cones gratings measured in the visible by integrating sphere (a) and in Infrared by FTIR spectrometry (b).
] clearly shows that, due to the second periodicity level, the reflectivity of the patterned-topped cone (named G80 here, parameters are P = 967 nm, T = 1.368 µm and M = 502 nm for the first level, p = 251 nm, t = 342 nm and m = 119 nm for the second level) in the visible region has been lowered. However, as the index profile has been changed by patterning the top of the cones, performances of the patterned-topped structures have been slightly degraded as well in the 3-5 µm range [Fig. 13(b)] as it has already been demonstrated in another regime of wavelength [20

20. Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007). [CrossRef] [PubMed]

]. Nonetheless those results are very promising and with a little more optimization, improvements in the mid infrared are yet to be expected.

5. Conclusion

References and links

1.

S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Anti-reflecting and photonic nanostructures,” Mater. Sci. Engineering: R: Reports 69(1-3), 1–35 (2010). [CrossRef]

2.

K. M. Baker, “Highly corrected close-packed microlens arrays and moth-eye structuring on curved surfaces,” Appl. Opt. 38(2), 352–356 (1999). [CrossRef] [PubMed]

3.

D. M. Braun, “Design of single layer antireflection coatings for InP/In0.53Ga0.47As/InP photodetectors for the 1200-1600-nm wavelength range,” Appl. Opt. 27(10), 2006–2011 (1988). [CrossRef] [PubMed]

4.

K. T. Park, Z. Guo, H. D. Um, J. Y. Jung, J. M. Yang, S. K. Lim, Y. S. Kim, and J. H. Lee, “Optical properties of Si microwires combined with nanoneedles for flexible thin film photovoltaics,” Opt. Express 19(S1Suppl 1), A41–A50 (2011). [CrossRef] [PubMed]

5.

N. Yamada, T. Ijiro, E. Okamoto, K. Hayashi, and H. Masuda, “Characterization of antireflection moth-eye film on crystalline silicon photovoltaic module,” Opt. Express 19(S2Suppl 2), A118–A125 (2011). [CrossRef] [PubMed]

6.

J. Oh, H. C. Yuan, and H. M. Branz, “An 18.2%-efficient black-silicon solar cell achieved through control of carrier recombination in nanostructures,” Nat. Nanotechnol. 7(11), 743–748 (2012). [CrossRef] [PubMed]

7.

K. Forberich, G. Dennler, M. C. Scharber, K. Hingerl, T. Fromherz, and C. J. Brabec, “Performance improvement of organic solar cells with moth eye anti-reflection coating,” Thin Solid Films 516(20), 7167–7170 (2008). [CrossRef]

8.

H. A. MacLeod, Thin-Film Optical Filters (Taylor & Francis Ed. IV, (2010) p. 668.

9.

P. B. Clapham and M. C. Hutley, “Reduction of lens reflection by the ‘moth eye’ principle,” Nature 244(5414), 281–282 (1973). [CrossRef]

10.

M. Born and E. Wolf, in Principle of Optics (Pergamon, 1980) pp. 705–708.

11.

E. Grann, M. G. Varga, and D. Pommet, “Optimal design for antireflective tapered two dimensional subwavelength grating structures,” J. Opt. Soc. Am. A 12(2), 333–339 (1995). [CrossRef]

12.

S. K. Srivastava, D. Kumar, K. Singh, M. Kar, V. Kumar, and M. Husain, “Excellent antireflection properties of vertical nanowire arrays,” Sol. Energy Mater. Sol. Cells 94(9), 1506–1511 (2010). [CrossRef]

13.

J. Zhou, M. Hildebrandt, and M. Lu, “Self-organized antireflecting nano-cone arrays on Si (100) induced by ion bombardment,” J. Appl. Phys. 109(5), 053513 (2011). [CrossRef]

14.

H. Yuan, V. E. Yost, M. R. Page, P. Stradins, D. L. Meier, and H. M. Branz, “Efficient black silicon solar cell with a density-graded nanoporous surface: Optical properties, performance limitations, and design rules,” Appl. Phys. Lett. 95(12), 123501 (2009). [CrossRef]

15.

L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for near infrared spectral region,” Opt. Commun. 226(1-6), 81–88 (2003). [CrossRef]

16.

R. Bouffaron, L. Escoubas, J. J. Simon, P. Torchio, F. Flory, G. Berginc, and P. Masclet, “Enhanced antireflecting properties of microstructured flat-top pyramids,” J. Opt. Soc. Am. A 16, 19304–19309 (2008).

17.

L. Escoubas, R. Bouffaron, V. Brissonneau, J. J. Simon, G. Berginc, F. Flory, and P. Torchio, “Sand-castle biperiodic pattern for spectral and angular broadening of antireflective properties,” Opt. Lett. 35(9), 1455–1457 (2010). [CrossRef] [PubMed]

18.

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]

19.

E. D. Palik, in Handbook of Optical Constants, (Academic Press, 555–568, 1985, I).

20.

Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol. 2(12), 770–774 (2007). [CrossRef] [PubMed]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(310.1210) Thin films : Antireflection coatings

ToC Category:
Diffraction and Gratings

History
Original Manuscript: May 8, 2013
Revised Manuscript: June 15, 2013
Manuscript Accepted: June 24, 2013
Published: June 27, 2013

Citation
Jean-Baptiste Brückner, Judikaël Le Rouzo, Ludovic Escoubas, Gérard Berginc, Cécile Gourgon, Olivier Desplats, and Jean-Jacques Simon, "Flat-top and patterned-topped cone gratings for visible and mid-infrared antireflective properties," Opt. Express 21, 16043-16055 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-13-16043


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References

  1. S. Chattopadhyay, Y. F. Huang, Y. J. Jen, A. Ganguly, K. H. Chen, and L. C. Chen, “Anti-reflecting and photonic nanostructures,” Mater. Sci. Engineering: R: Reports69(1-3), 1–35 (2010). [CrossRef]
  2. K. M. Baker, “Highly corrected close-packed microlens arrays and moth-eye structuring on curved surfaces,” Appl. Opt.38(2), 352–356 (1999). [CrossRef] [PubMed]
  3. D. M. Braun, “Design of single layer antireflection coatings for InP/In0.53Ga0.47As/InP photodetectors for the 1200-1600-nm wavelength range,” Appl. Opt.27(10), 2006–2011 (1988). [CrossRef] [PubMed]
  4. K. T. Park, Z. Guo, H. D. Um, J. Y. Jung, J. M. Yang, S. K. Lim, Y. S. Kim, and J. H. Lee, “Optical properties of Si microwires combined with nanoneedles for flexible thin film photovoltaics,” Opt. Express19(S1Suppl 1), A41–A50 (2011). [CrossRef] [PubMed]
  5. N. Yamada, T. Ijiro, E. Okamoto, K. Hayashi, and H. Masuda, “Characterization of antireflection moth-eye film on crystalline silicon photovoltaic module,” Opt. Express19(S2Suppl 2), A118–A125 (2011). [CrossRef] [PubMed]
  6. J. Oh, H. C. Yuan, and H. M. Branz, “An 18.2%-efficient black-silicon solar cell achieved through control of carrier recombination in nanostructures,” Nat. Nanotechnol.7(11), 743–748 (2012). [CrossRef] [PubMed]
  7. K. Forberich, G. Dennler, M. C. Scharber, K. Hingerl, T. Fromherz, and C. J. Brabec, “Performance improvement of organic solar cells with moth eye anti-reflection coating,” Thin Solid Films516(20), 7167–7170 (2008). [CrossRef]
  8. H. A. MacLeod, Thin-Film Optical Filters (Taylor & Francis Ed. IV, (2010) p. 668.
  9. P. B. Clapham and M. C. Hutley, “Reduction of lens reflection by the ‘moth eye’ principle,” Nature244(5414), 281–282 (1973). [CrossRef]
  10. M. Born and E. Wolf, in Principle of Optics (Pergamon, 1980) pp. 705–708.
  11. E. Grann, M. G. Varga, and D. Pommet, “Optimal design for antireflective tapered two dimensional subwavelength grating structures,” J. Opt. Soc. Am. A12(2), 333–339 (1995). [CrossRef]
  12. S. K. Srivastava, D. Kumar, K. Singh, M. Kar, V. Kumar, and M. Husain, “Excellent antireflection properties of vertical nanowire arrays,” Sol. Energy Mater. Sol. Cells94(9), 1506–1511 (2010). [CrossRef]
  13. J. Zhou, M. Hildebrandt, and M. Lu, “Self-organized antireflecting nano-cone arrays on Si (100) induced by ion bombardment,” J. Appl. Phys.109(5), 053513 (2011). [CrossRef]
  14. H. Yuan, V. E. Yost, M. R. Page, P. Stradins, D. L. Meier, and H. M. Branz, “Efficient black silicon solar cell with a density-graded nanoporous surface: Optical properties, performance limitations, and design rules,” Appl. Phys. Lett.95(12), 123501 (2009). [CrossRef]
  15. L. Escoubas, J. J. Simon, M. Loli, G. Berginc, F. Flory, and H. Giovannini, “An antireflective silicon grating working in the resonance domain for near infrared spectral region,” Opt. Commun.226(1-6), 81–88 (2003). [CrossRef]
  16. R. Bouffaron, L. Escoubas, J. J. Simon, P. Torchio, F. Flory, G. Berginc, and P. Masclet, “Enhanced antireflecting properties of microstructured flat-top pyramids,” J. Opt. Soc. Am. A16, 19304–19309 (2008).
  17. L. Escoubas, R. Bouffaron, V. Brissonneau, J. J. Simon, G. Berginc, F. Flory, and P. Torchio, “Sand-castle biperiodic pattern for spectral and angular broadening of antireflective properties,” Opt. Lett.35(9), 1455–1457 (2010). [CrossRef] [PubMed]
  18. 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. A12(5), 1068–1076 (1995). [CrossRef]
  19. E. D. Palik, in Handbook of Optical Constants, (Academic Press, 555–568, 1985, I).
  20. Y. F. Huang, S. Chattopadhyay, Y. J. Jen, C. Y. Peng, T. A. Liu, Y. K. Hsu, C. L. Pan, H. C. Lo, C. H. Hsu, Y. H. Chang, C. S. Lee, K. H. Chen, and L. C. Chen, “Improved broadband and quasi-omnidirectional anti-reflection properties with biomimetic silicon nanostructures,” Nat. Nanotechnol.2(12), 770–774 (2007). [CrossRef] [PubMed]

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