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Energy Express

  • Editor: Bernard Kippelen
  • Vol. 18, Iss. S3 — Sep. 13, 2010
  • pp: A286–A292
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A strong antireflective solar cell prepared by tapering silicon nanowires

Jin-Young Jung, Zhongyi Guo, Sang-Won Jee, Han-Don Um, Kwang-Tae Park, and Jung-Ho Lee  »View Author Affiliations


Optics Express, Vol. 18, Issue S3, pp. A286-A292 (2010)
http://dx.doi.org/10.1364/OE.18.00A286


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Abstract

Vertically aligned silicon nanowires (SiNWs) were cost-effectively formed on a four-inch silicon wafer using a simple room temperature approach, i.e., metal-assisted electroless etching. Tapering the NWs by post-KOH dipping achieved separation of each NW from the bunched NW, resulting in a strong enhancement of broadband optical absorption. As electroless etching time increases, the optical crossover feature was observed in the tradeoff between enhanced light trapping (by graded-refractive index during initial tapering) and deteriorated reflectance (by decreasing the areal density of NWs during later tapering). Compared to the bunched SiNWs, tapered NW solar cells demonstrated superior photovoltaic characteristics, such as a short circuit current of 17.67 mA/cm2 and a cell conversion efficiency of ~6.56% under 1.5 AM illumination.

© 2010 OSA

1. Introduction

Silicon nanostructures have been intensely investigated for their potential use in cost-effective third-generation high efficiency solar cells due to their unique optical and electrical characteristics [1

1. B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007). [CrossRef] [PubMed]

4

4. Y. M. Song, J. S. Yu, and Y. T. Lee, “Antireflective submicrometer gratings on thin-film silicon solar cells for light-absorption enhancement,” Opt. Lett. 35(3), 276–278 (2010). [CrossRef] [PubMed]

]. In particular, silicon nanowire (SiNW) solar cells employing a radial p-n junction have been known to theoretically enhance the energy conversion efficiency while reducing the material consumption of high-purity silicon. Orthogonal separation in directions between sunlight irradiation and diffusion of minority carriers is the most distinctive feature of a radial p-n junction wired solar cell [5

5. 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(11), 114302 (2005). [CrossRef]

]. In nanowired solar cell applications without radial p-n junctions [6

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

,7

7. V. Sivakov, G. Andrä, A. Gawlik, A. Berger, J. Plentz, F. Falk, and S. H. Christiansen, “Silicon nanowire-based solar cells on glass: synthesis, optical properties, and cell parameters,” Nano Lett. 9(4), 1549–1554 (2009). [CrossRef] [PubMed]

], SiNW arrays vertically aligned to the substrate demonstrate broadband optical absorption due to strong light trapping by multiple scattering of the incident light [8

8. L. Tsakalakos, J. Balch, J. Fronheiser, M. Y. Shih, S. F. LeBoeuf, M. Pietrzykowski, P. J. Codella, B. A. Korevaar, O. Sulima, J. Rand, A. Davuluru, and U. Rapol, “Strong broadband optical absorption in silicon nanowire films,” J. Nanophotonics 1(1), 013552 (2007). [CrossRef]

] and the optical antenna effect [9

9. G. Chen, J. Wu, Q. Lu, H. R. Gutierrez, Q. Xiong, M. E. Pellen, J. S. Petko, D. H. Werner, and P. C. Eklund, “Optical antenna effect in semiconducting nanowires,” Nano Lett. 8(5), 1341–1346 (2008). [CrossRef] [PubMed]

]. In particular, tapering the nanowires further suppresses the Fresnel reflection over a broad wavelength range at various angles of incidence since a gradual transition in the effective refractive indexes is observed across the air-to-wire interface [10

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

,11

11. S. L. Diedenhofen, G. Vecchi, R. E. Algra, A. Hartsuiker, O. L. Muskens, G. Immink, E. P. A. M. Bakkers, W. L. Vos, and J. G. Rivas, “Broad-band and omnidirectional antireflection coating based on semiconductor nanorods,” Adv. Mater. 21(9), 973–978 (2009). [CrossRef]

]. Since the typical geometric factors of SiNWs, including wire diameter, length, and periodicity, are known to significantly affect the optical properties [12

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

,13

13. J. Li, H. Yu, S. M. Wong, G. Zhang, X. Sun, P. G. Lo, and D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95, 033102 (2009). [CrossRef]

], a cost-efficient, optimized technique is critically needed to precisely control the major dimensional variables for solar cell applications.

Although many other methods [1

1. B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007). [CrossRef] [PubMed]

,10

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

,14

14. Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999). [CrossRef]

] have been previously used for wire formation, in this paper, we present a simple, cost-effective process, the so-called metal-assisted electroless etching, which realizes a high process uniformity with controlled parameters across a four-inch wafer without using vacuum or high-temperature processes.

2. Experimental

Metal-assisted electroless etching [15

15. K. Q. Peng, Y. Wu, H. Fang, X. Zhong, Y. Xu, and J. Zhu, “Uniform, axial-orientation alignment of one-dimensional single-crystal silicon nanostructure arrays,” Angew. Chem. Int. Ed. Engl. 44(18), 2737–2742 (2005). [CrossRef] [PubMed]

] was performed on a p-type, 1−10 Ωcm, Si(100) wafer. First, silver nanoparticles were uniformly deposited onto a Si substrate using a mixed solution of de-ionized water, HF (4.8 M), and AgNO3 (0.01 M) at 20 °C for 1 min. Then, chemical etching in a mixed solution of deionized water, HF (4.8 M), and H2O2 (0.5 M) was used to form a vertically aligned SiNW array with a diameter range of 50−200 nm. Silver nanoparticles were easily removed using nitric acid after completion of the electroless etching. Immediately after the metal-assisted etching, nanowire bundles were observed due to agglomeration at their tops-ends [see Figs. 1 (a)
Fig. 1 (a) Schematic illustrations showing the fabrication procedures for bunched and tapered SiNWs. (b) Conceptual schematic for explaining how the SiNWs can be easily tapered at their top-ends using KOH post-etching. Bottom SEM images show the 30°-tilted-view corresponding to each KOH etching time step (0, 30, 60, 120 s from left to right, respectively). All scale bars are 1 μm.
and 2 (b)
Fig. 2 (a) Cross-sectional SEM images showing the SiNW array after metal-assisted electroless etching. Scale bar is 10 μm. 30°-tilted SEM images also show the morphological change of the SiNW tips according to the post-etching time of KOH: (b) 0 s, (c) 30 s, (d) 60 s, (e) 120 s, and (f) 240 s. Scale bars in (b)−(f) are 5 μm.
]. Nevertheless, the total reflectance was shown to less than 2.5% (average absorptance of ~97.5%) in the wavelength range of 300−1000 nm.

We easily separated the nanowires from the bundles by sharpening the top-ends of the nanowires (see Fig. 1). The anisotropic etching behavior of crystalline Si in a potassium hydroxide (KOH) solution has been utilized as a tapering process. Here, chemical etching using a 30 wt% aqueous KOH solution at 20 °C was used just after metal-assisted etching so as to decrease the areal density of NWs while tapering the nanowire morphology. During this step, SiNWs agglomerated due to Van der waals forces could be easily separated by tapering their tops. Since the wet etching rate depends heavily upon the bond strengths of the surface atoms [16

16. X. Li, H.-S. Seo, H.-D. Um, S.-W. Jee, Y. W. Cho, B. Yoo, and J.-H. Lee, “A periodic array of silicon pillars fabricated by photoelectrochemical etching,” Electrochim. Acta 54(27), 6978–6982 (2009). [CrossRef]

], top corner edges located in between flat (100) and (110) planes in a nanowire array lead to weak bond strength owing to a drastic transition of surface atom densities over the short distance of the corner edges. This results in a faster etching rate at the corner edges than at other flat regions [Fig. 1 (b)], thereby enabling the formation of sharp tips and a tapered shape on the top-ends of the NWs. The total reflectance of a tapered nanowire array was observed to be less than 1% (average absorptance of ~99%) due to strong light absorption, which also led to the considerably improved solar cell conversion efficiency compared to that of a bunched wire array.

Phosphorus doping was performed to form a bulk p-n junction using a p-type, 1−10 Ωcm, Si(100) wafer underneath the nanowire array. Specifically, phosphorus silicate precursors (P509, supplied by Filmtronics) were spin-coated on a dummy wafer. Then, a phosphorous coated dummy wafer prepared by this spin-on-doping (SOD) technique was maintained at a close distance to a target substrate (nanowired sample) inside a tube furnace while holding at 1050 °C for 30 min. Phosphorous ions vaporized from the SOD wafer were doped via gas-phase transport onto the surfaces of the NWs (called proximity diffusion) [17

17. H.-D. Um, J.-Y. Jung, H.-S. Seo, K.-T. Park, S.-W. Jee, S. A. Moiz, and J.-H. Lee, “Silicon nanowire array solar cell prepared by metal induced electroless etching with a novel processing technology,” Jpn. J. Appl. Phys. 49(4), 04DN02 (2010). [CrossRef]

] and the junction depths were detected to be ~1.1 μm by secondary ion mass spectroscopy.

3. Results and discussion

A cross-sectional SEM image in Fig. 2 (a) demonstrates the overall morphology of the electroless etched SiNWs, which also reflects superior control in diameter, length, and vertical alignment to the substrate. A tilted-SEM image [Fig. 2 (b)] was obtained for viewing the top-regions of a NW array, revealing a bunched morphology between the top-ends of the as-etched NWs. The 30°-tilted SEM images shown in Fig. 2 (b−f) illustrate the effect of KOH etching time on the nanowire morphologies. The agglomerated top-ends of the NW array could be easily separated from each other due to tapering resulting from even short time (30 s) treatments of KOH [Fig. 2 (c)]. Increasing the etching time to more than 60 s causes the areal density of tapered NWs to drastically decrease [Figs. 2 (d−f)]. Tapered NWs almost disappear at etching times of ~240 s, exposing the rugged surface morphology of a silicon substrate connected to the wire bottoms [Fig. 2 (f)].

The total reflectance spectra were measured using a Varian Cary 5000 UV/VIS/NIR spectrophotometer with an integrating sphere (Labsphere) in a wavelength range of 300–1000 nm, corresponding to the major spectral irradiance of sunlight. Compared to a polished Si wafer that shows a typical reflectance of ~40%, as shown in Fig. 3 (a)
Fig. 3 (a) Optical reflectance spectra of a Si wafer, bunched SiNWs, and various tapered samples, (b) reflectance spectra shown in a different scale than (a) for the tapered samples. Schematic illustrations showing the relevance between the wire morphology and the effective refractive index profile across the air-to-wire axis: (c) air-to-silicon wafer, (d) air-to-bunched NWs, (e) air-to-tapered NWs (60 s KOH dip), (f) air-to-tapered NWs (120 s dip). Black arrows denote the mismatch regions in the effective refractive indexes.
, the reflectance of the bunched NWs (without post-KOH etching) is greatly decreased, and the highest value of reflectance is no more than 2.5% with an average value of ~2.0% in a 300−1000 nm range [Fig. 3 (b)]. The ultrahigh surface area of the SiNWs causes the multiple scattering of sunlight between the nanowires to enhance light trapping. Thereby, superior antireflection characteristics, with an average reflectance of less than 1%, were observed in a tapered SiNWs sample after KOH etching for 60 s [Fig. 3 (b)]. Compared to the reflectance result for a random pyramid structure formed using a conventional texturing process [18

18. P. K. Singh, R. Kumar, M. Lal, S. N. Singh, and B. K. Das, “Effectiveness of silicon in aqueous alkaline solutions,” Sol. Energy Mater. Sol. Cells 70, 103 (2001). [CrossRef]

] in which the 10% average reflectance was observed, tapered SiNWs showed the excellent antireflection properties in the wavelength range of 300–1000 nm; especially, the reflectance in the UV region (λ< 400 nm) was greatly reduced due to subwavelength structured features. As shown in Fig. 3 (a), optical reflectance greatly increased with increasing etching time (120 and 240 s), corresponding to reflectances of more than 10 and 17%, respectively. This is because the areal densities of the NWs were accordingly decreased, as shown in Figs. 2 (e−f).

The multiple scattering and graded refractive index (GRI) effects might be able to explain why ultralow reflectivity was observed after tapering the NWs. First, untapered, agglomerated NWs act as a buffer layer to compensate for the large mismatch in effective refractive indexes (n) between air (n = 1) and a silicon substrate (n = 3.42), as shown in Figs. 3 (c−d). In addition, gradual change in the refractive indexes across the air-to-wire axis could be realized in a tapered nanowire array since the diameter of NWs gently increases from the wire-tops to the bottoms [see Fig. 3 (e)]. Note that a tiny mismatch in refractive index was also shown at the interface between the NWs and the substrate. Increasing the etching time to 120 s caused this mismatch value to increase according to the consistent decrease in the areal density of NWs [see the black arrows noted in Figs. 3 (e−f)].

As a result, tapered NWs etched for 60 s are expected to have a better antireflection behavior than the NWs etched for 120 s because of bigger mismatch in the interface between the Si NW arrays and the Si substrate due to a decrease in areal NW density. In the case of the sample etched for 240 s, tapered NWs almost disappeared, which caused the reflectance to further increase but still kept lower than that of a polished wafer. Compared to the untapered NW samples, our optical results clarify the effectiveness of a tapered NW solar cell from the viewpoint of light absorption in the wavelength range of 300–1000 nm.

From the view point of absorption enhancement, basically, the multiple scattering and the graded refractive index (GRI) effect could not be separately understood because they are acting equivalently to the absorption characteristics of nanowires. In fact, the reduction behavior in both specular and total reflections for nanowires could be explained by multiple scattering because of the surface areas increased remarkably compared to a wafer. The increased surface area causes the probability for interactions between light and wires to greatly increase, which results then in remarkable enhancement in total light paths inside the wire array.

From the viewpoint of the GRI effect, the nanowire array is explained to act as a buffer layer to intervene the difference in refractive indexes between air and a substrate. If the nanowire morphology is completely uniform without tapering, the nanowires act only as an intermediate index layer, having a certain index value, at the interface between air and the silicon substrate. Although much reduction in reflectance has been observed for this case, some amounts of mismatch in refractive indexes still remain at the interface between air-to-wires. To further enhance the antireflective behavior, a graded morphology by tapering in nanowires is effective for further reduction in reflectance (GRI effect).

To verify the effect of light absorption on the photovoltaic characteristics of NW solar cells, we attempted to compare the photovoltaic parameters of two typical NW samples, i.e., untapered and tapered NWs. Figure 4
Fig. 4 Typical photovoltaic I-V curves for bunched and tapered SiNWs (60 s KOH etching). Upper left inset: table comparing the representative photovoltaic parameters, Lower right inset: schematic illustration showing the top-contact structure.
shows the representative photovoltaic IV characteristics of untapered (bunched) and tapered SiNW samples measured at 1.5 AM illumination (100 mW/cm2 at 25 °C). The front contacts were made using Ga/In eutectic droplets with a gold probe tip on top of a wire array. As anticipated, the tapered sample yielded a higher performance with an open-circuit voltage (V oc) of 520 mV, a short-circuit current (J sc) of 17.67 mA/cm2, a fill-factor (FF) of 71.36, and a cell conversion efficiency (CE) of 6.56%, as shown in the inset of Fig. 4.

From our results, a major contribution to the CE increased by employing a tapered structure was estimated to be a series resistance lowered by efficient thermal doping (40% increases in FF compared to a bunched NW solar cell), but we also observed that a GRI effect contributed to enhance the CE through the ~1.5% increase in light absorption.

4. Conclusion

In summary, we have demonstrated that vertically aligned, tapered SiNWs prepared using a simple, low-cost, wet etching process including both electroless etching and post-KOH dipping were very attractive for nanowired solar cells because of their strong light trapping ability. Compared to the bunched NW array, tapered SiNWs could further suppress the optical reflectance over a broad range of wavelength due to a minimized Fresnel reflection originating from a gradual transition of the effective refractive indexes. Therefore, the conversion efficiency (~6.56%) of tapered SiNW solar cell was higher than that of bunched nanowires at 1.5 AM illumination.

Acknowledgments

This work was supported by the New & Renewable Energy R&D Program (No: 2009T100100614) of the MKE, Korea and by the Pioneer Research Center Program through the National Research Foundation of Korea funded by the MEST (No. 2009-0082820). J.-Y. Jung and Z. Guo contributed equally to this work.

References and links

1.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007). [CrossRef] [PubMed]

2.

E. C. Garnett and P. D. Yang, “Silicon nanowire radial p-n junction solar cells,” J. Am. Chem. Soc. 130(29), 9224–9225 (2008). [CrossRef] [PubMed]

3.

C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express 17(22), 19371–19381 (2009). [CrossRef] [PubMed]

4.

Y. M. Song, J. S. Yu, and Y. T. Lee, “Antireflective submicrometer gratings on thin-film silicon solar cells for light-absorption enhancement,” Opt. Lett. 35(3), 276–278 (2010). [CrossRef] [PubMed]

5.

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(11), 114302 (2005). [CrossRef]

6.

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

7.

V. Sivakov, G. Andrä, A. Gawlik, A. Berger, J. Plentz, F. Falk, and S. H. Christiansen, “Silicon nanowire-based solar cells on glass: synthesis, optical properties, and cell parameters,” Nano Lett. 9(4), 1549–1554 (2009). [CrossRef] [PubMed]

8.

L. Tsakalakos, J. Balch, J. Fronheiser, M. Y. Shih, S. F. LeBoeuf, M. Pietrzykowski, P. J. Codella, B. A. Korevaar, O. Sulima, J. Rand, A. Davuluru, and U. Rapol, “Strong broadband optical absorption in silicon nanowire films,” J. Nanophotonics 1(1), 013552 (2007). [CrossRef]

9.

G. Chen, J. Wu, Q. Lu, H. R. Gutierrez, Q. Xiong, M. E. Pellen, J. S. Petko, D. H. Werner, and P. C. Eklund, “Optical antenna effect in semiconducting nanowires,” Nano Lett. 8(5), 1341–1346 (2008). [CrossRef] [PubMed]

10.

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

11.

S. L. Diedenhofen, G. Vecchi, R. E. Algra, A. Hartsuiker, O. L. Muskens, G. Immink, E. P. A. M. Bakkers, W. L. Vos, and J. G. Rivas, “Broad-band and omnidirectional antireflection coating based on semiconductor nanorods,” Adv. Mater. 21(9), 973–978 (2009). [CrossRef]

12.

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

13.

J. Li, H. Yu, S. M. Wong, G. Zhang, X. Sun, P. G. Lo, and D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95, 033102 (2009). [CrossRef]

14.

Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999). [CrossRef]

15.

K. Q. Peng, Y. Wu, H. Fang, X. Zhong, Y. Xu, and J. Zhu, “Uniform, axial-orientation alignment of one-dimensional single-crystal silicon nanostructure arrays,” Angew. Chem. Int. Ed. Engl. 44(18), 2737–2742 (2005). [CrossRef] [PubMed]

16.

X. Li, H.-S. Seo, H.-D. Um, S.-W. Jee, Y. W. Cho, B. Yoo, and J.-H. Lee, “A periodic array of silicon pillars fabricated by photoelectrochemical etching,” Electrochim. Acta 54(27), 6978–6982 (2009). [CrossRef]

17.

H.-D. Um, J.-Y. Jung, H.-S. Seo, K.-T. Park, S.-W. Jee, S. A. Moiz, and J.-H. Lee, “Silicon nanowire array solar cell prepared by metal induced electroless etching with a novel processing technology,” Jpn. J. Appl. Phys. 49(4), 04DN02 (2010). [CrossRef]

18.

P. K. Singh, R. Kumar, M. Lal, S. N. Singh, and B. K. Das, “Effectiveness of silicon in aqueous alkaline solutions,” Sol. Energy Mater. Sol. Cells 70, 103 (2001). [CrossRef]

OCIS Codes
(310.1210) Thin films : Antireflection coatings
(350.6050) Other areas of optics : Solar energy
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Photovoltaics

History
Original Manuscript: May 11, 2010
Revised Manuscript: June 23, 2010
Manuscript Accepted: June 23, 2010
Published: June 29, 2010

Citation
Jin-Young Jung, Zhongyi Guo, Sang-Won Jee, Han-Don Um, Kwang-Tae Park, and Jung-Ho Lee, "A strong antireflective solar cell prepared by tapering silicon nanowires," Opt. Express 18, A286-A292 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-S3-A286


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References

  1. B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007). [CrossRef] [PubMed]
  2. E. C. Garnett and P. D. Yang, “Silicon nanowire radial p-n junction solar cells,” J. Am. Chem. Soc. 130(29), 9224–9225 (2008). [CrossRef] [PubMed]
  3. C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express 17(22), 19371–19381 (2009). [CrossRef] [PubMed]
  4. Y. M. Song, J. S. Yu, and Y. T. Lee, “Antireflective submicrometer gratings on thin-film silicon solar cells for light-absorption enhancement,” Opt. Lett. 35(3), 276–278 (2010). [CrossRef] [PubMed]
  5. 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(11), 114302 (2005). [CrossRef]
  6. K. Peng, Y. Xu, Y. Wu, Y. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small 1(11), 1062–1067 (2005). [CrossRef]
  7. V. Sivakov, G. Andrä, A. Gawlik, A. Berger, J. Plentz, F. Falk, and S. H. Christiansen, “Silicon nanowire-based solar cells on glass: synthesis, optical properties, and cell parameters,” Nano Lett. 9(4), 1549–1554 (2009). [CrossRef] [PubMed]
  8. L. Tsakalakos, J. Balch, J. Fronheiser, M. Y. Shih, S. F. LeBoeuf, M. Pietrzykowski, P. J. Codella, B. A. Korevaar, O. Sulima, J. Rand, A. Davuluru, and U. Rapol, “Strong broadband optical absorption in silicon nanowire films,” J. Nanophotonics 1(1), 013552 (2007). [CrossRef]
  9. G. Chen, J. Wu, Q. Lu, H. R. Gutierrez, Q. Xiong, M. E. Pellen, J. S. Petko, D. H. Werner, and P. C. Eklund, “Optical antenna effect in semiconducting nanowires,” Nano Lett. 8(5), 1341–1346 (2008). [CrossRef] [PubMed]
  10. J. Zhu, Z. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Xu, Q. Wang, M. McGehee, S. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett. 9(1), 279–282 (2009). [CrossRef]
  11. S. L. Diedenhofen, G. Vecchi, R. E. Algra, A. Hartsuiker, O. L. Muskens, G. Immink, E. P. A. M. Bakkers, W. L. Vos, and J. G. Rivas, “Broad-band and omnidirectional antireflection coating based on semiconductor nanorods,” Adv. Mater. 21(9), 973–978 (2009). [CrossRef]
  12. L. Hu and G. Chen, “Analysis of optical absorption in silicon nanowire arrays for photovoltaic applications,” Nano Lett. 7(11), 3249–3252 (2007). [CrossRef] [PubMed]
  13. J. Li, H. Yu, S. M. Wong, G. Zhang, X. Sun, P. G. Lo, and D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95, 033102 (2009). [CrossRef]
  14. Y. Kanamori, M. Sasaki, and K. Hane, “Broadband antireflection gratings fabricated upon silicon substrates,” Opt. Lett. 24(20), 1422–1424 (1999). [CrossRef]
  15. K. Q. Peng, Y. Wu, H. Fang, X. Zhong, Y. Xu, and J. Zhu, “Uniform, axial-orientation alignment of one-dimensional single-crystal silicon nanostructure arrays,” Angew. Chem. Int. Ed. Engl. 44(18), 2737–2742 (2005). [CrossRef] [PubMed]
  16. X. Li, H.-S. Seo, H.-D. Um, S.-W. Jee, Y. W. Cho, B. Yoo, and J.-H. Lee, “A periodic array of silicon pillars fabricated by photoelectrochemical etching,” Electrochim. Acta 54(27), 6978–6982 (2009). [CrossRef]
  17. H.-D. Um, J.-Y. Jung, H.-S. Seo, K.-T. Park, S.-W. Jee, S. A. Moiz, and J.-H. Lee, “Silicon nanowire array solar cell prepared by metal induced electroless etching with a novel processing technology,” Jpn. J. Appl. Phys. 49(4), 04DN02 (2010). [CrossRef]
  18. P. K. Singh, R. Kumar, M. Lal, S. N. Singh, and B. K. Das, “Effectiveness of silicon in aqueous alkaline solutions,” Sol. Energy Mater. Sol. Cells 70, 103 (2001). [CrossRef]

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