OSA's Digital Library

Energy Express

Energy Express

  • Editor: Bernard Kippelen
  • Vol. 19, Iss. S5 — Sep. 12, 2011
  • pp: A1148–A1154
« Show journal navigation

Optimal design of aperiodic, vertical silicon nanowire structures for photovoltaics

Chenxi Lin and Michelle L. Povinelli  »View Author Affiliations


Optics Express, Vol. 19, Issue S5, pp. A1148-A1154 (2011)
http://dx.doi.org/10.1364/OE.19.0A1148


View Full Text Article

Acrobat PDF (1253 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We design a partially aperiodic, vertically-aligned silicon nanowire array that maximizes photovoltaic absorption. The optimal structure is obtained using a random walk algorithm with transfer matrix method based electromagnetic forward solver. The optimal, aperiodic structure exhibits a 2.35 times enhancement in ultimate efficiency compared to its periodic counterpart. The spectral behavior mimics that of a periodic array with larger lattice constant. For our system, we find that randomly-selected, aperiodic structures invariably outperform the periodic array.

© 2011 OSA

The broadband absorption of a solar cell is characterized by the ultimate efficiency [29

29. W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961). [CrossRef]

]:
η=310nmλgI(λ)A(λ)λλgdλ310nm4000nmI(λ)dλ,
where λ is the wavelength, I(λ) is the spectral irradiance (power density) of the ASTM AM1.5 direct normal and circumsolar spectrum [30

30. ASTM, “Air Mass 1.5 Spectra,” http://rredc.nrel.gov/solar/spectra/am1.5.

], and A(λ) is the absorptance of the structure. For a silicon-based solar cell, the relevant wavelength range is from 310nm, where the solar irradiance becomes negligible, to λg = 1127nm, the wavelength corresponding to the band gap of crystalline silicon. The calculation assumes that each photon with energy greater than the band gap produces one electron-hole pair at the energy of the gap, and that all carriers are collected to produce current. In an actual solar cell, collection will be limited by factors including surface recombination [31

31. O. Gunawan and S. Guha, “Characteristics of vapor-liquid-solid grown silicon nanowire solar cells,” Sol. Energy Mater. Sol. Cells 93(8), 1388–1393 (2009). [CrossRef]

]. The ultimate efficiency thus provides an upper bound on the efficiency of the solar cell.

We used the ISU-TMM package [32

32. M. Li, X. Hu, Z. Ye, K.-M. Ho, J. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. 31(23), 3498–3500 (2006). [CrossRef] [PubMed]

], an implementation of the generalized transfer matrix method, to calculate optical properties of nanowire arrays. Absorptance was calculated as A(λ) = 1 - R(λ) - T(λ), where R(λ) and T(λ) are the reflection and transmission. We used the optical constants for intrinsic crystalline silicon listed in Ref. 31

31. O. Gunawan and S. Guha, “Characteristics of vapor-liquid-solid grown silicon nanowire solar cells,” Sol. Energy Mater. Sol. Cells 93(8), 1388–1393 (2009). [CrossRef]

, neglecting the effect of doping on the optical properties. The integrals were evaluated using the trapezoid rule with 915 sampling points.

Figure 1
Fig. 1 Schematics of periodic (a) and aperiodic (b) silicon nanowire structures.
shows schematics of the nanowire structures we study. We will consider the optical absorption within the nanowire. This model is appropriate to photovoltaic cells in which the nanowires serve as the photoactive material, for example, due to incorporation of radial p-n junction in nanowires [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]

,17

17. 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(3), 239–244 (2010). [CrossRef] [PubMed]

].

Figure 2(a)
Fig. 2 Top view of initial periodic (a) and optimal aperiodic (b) silicon nanowire arrays. Dashed lines indicate boundaries between super cells.
illustrates the top view of a periodic, vertically-aligned silicon nanowire array. Incident light propagates in the z-direction with the electric field polarized in the x-direction. The nanowire diameter d is 65nm. The nanowires are arranged in a square lattice with lattice constant a = 100nm and are surrounded by air. Each nanowire has a height of 2.33μm in the z-direction. Calculations were performed using a 500nm by 500nm super cell, containing 25 nanowires. The size of the super cell was limited by computational feasibility. The boundary conditions are periodic in x and y.

Starting from the periodic configuration, we adjusted the positions of the nanowires within the super cell one at a time to maximize the ultimate efficiency. An iterative random walk algorithm was used for the optimization. At each iteration, a nanowire in the super cell was randomly selected and moved to a new position. The new position was drawn from a uniform distribution around its original position over the whole super cell, under the constraint that the selected wire will not overlap with any other wire in the super cell after the move. The ultimate efficiency of the new structure was then calculated by TMM. If the ultimate efficiency was higher than that before the move, the new position of the selected wire was accepted and stored. Otherwise, the move was rejected and the selected wire was moved back to its original position. The procedure was iterated for 1000 times. The resulting structures, such as the one shown in Fig. 2(b), are partially aperiodic. Within the super cell, the rods are arranged aperiodically. From super cell to super cell, the aperiodic arrangement repeats.

We calculated the ultimate efficiency of the periodic structure of Fig. 2(a) to be 8.70%. The efficiency is lower than that of a solid, silicon thin film with the same thickness (13.83%). Aperiodicity provides dramatic absorption enhancement. The optimal, aperiodic structure in Fig. 2(b) has an ultimate efficiency of 20.44%, 2.35 times higher than the periodic array. Its efficiency is higher than a solid, thin film and also slightly higher than a solid, thin film with a Si3N4 antireflective coating (20.34% for optimized coating thickness of 63nm). The fact that the aperiodic structure is more absorptive than the thin film is notable, given that the volume of absorbing material is three times less.

We plot the absorptance spectrum for the periodic structure in Fig. 3(a)
Fig. 3 (a) Solar absorptance spectra for periodic (blue dotted) and optimal aperiodic (red solid) silicon nanowire structures. The absorptance spectrum for an equally-thick silicon thin film (gray dashed) is also plotted for reference. (b) Reflectance (black dotted), transmittance (red dashed), and absorptance (blue solid) of the optimal aperiodic array near 1.249eV (992.3nm).
. The absorptance spectrum for the thin film is plotted for reference. The absorptance of the periodic array is higher than the thin film in the high-energy range, which can be attributed to reduced reflection from the top surface. However, the absorptance is lower in the low energy range, which contains a large proportion of solar photon flux. As a result, the ultimate efficiency of the periodic array is lower than that of the thin film.

In Fig. 4
Fig. 4 Absorption profile of (a) periodic and (b) optimal aperiodic silicon nanowire structures at a horizontal cross section 0.233μm below the top surface of the nanowire array. White dashed lines indicate boundaries between super cells.
, we plot the power loss rate (or absorption profile) inside the periodic (Fig. 4(a)) and the optimal aperiodic (Fig. 4(b)) structures, normalized to the maximal power loss rate inside the periodic array. The incident wavelength is λ = 992.3nm, corresponding to a resonant absorption enhancement peak inside the aperiodic array as shown in Fig. 3(b). The power loss rate is calculated as 12 ωε|E| 2, where ω is the frequency of the incident light, ε″ is the imaginary part of the dielectric constant, and |E| 2 is the local electric field intensity. The power loss rate is only non-zero inside the silicon nanowires. The evaluation plane was located 0.233μm beneath the top surface of the nanowire array. Figure 4(b) shows several localized, strongly enhanced absorption regions in the optimal aperiodic array, consistent with the peak in the absorption spectrum.

For periodic structures, guided resonances result from the coupling of normally incident light to a superposition of modes propagating in the plane of the array. This mechanism decreases the fraction of light escaping the structure (either through reflection or transmission) and increases absorption. For the aperiodic structure, normally incident light excites localized resonances of the aperiodic array. Such resonances could be viewed as resulting from “multiple reflection” or “multiple scattering” between nanowires. This mechanism serves a similar function of resonant absorption enhancement.

In summary, we have demonstrated the optimal design of aperiodic, vertically-aligned silicon nanowire structures for photovoltaic applications. An optimization procedure based on the random walk algorithm enhanced the ultimate efficiency by 2.35 as compared to the periodic array. The solar absorptance spectrum of the optimal aperiodic array was found to resemble that of a periodic array with larger lattice constant and higher ultimate efficiency. In our study, the super cell size was restricted to make the optimization computationally feasible. We have verified that broadband absorption enhancement is also observed for super cells with sizes from 300nm-700nm.

While the random walk algorithm used in this work is relatively easy to implement, it is not guaranteed to reach the global optimum. Future work will employ adaptive optimization algorithms, such as simulated annealing or genetic algorithms, to help avoid getting stuck in local optima while insuring fast convergence [33

33. J. Thalken, Y. Chen, A. F. J. Levi, and S. Haas, “Adaptive quantum design of atomic clusters,” Phys. Rev. B 69(19), 195410 (2004). [CrossRef]

]. Further, the identification of “robust” optima [34

34. A. Ben-Tal, S. Boyd, and A. Nemirovski, “Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems,” Math. Program. 107(1-2), 63–89 (2006). [CrossRef]

], or configurations of nanowires that exhibit both high ultimate efficiency and low sensitivity to perturbations in the design parameters, is a challenging optimization problem for future research.

Acknowledgment

The authors thank Dr. A. F. J. Levi for helpful discussions. Computing resources were provided by the USC Center for High Performance Computing and Communications.

References and links

1.

T. Soga, ed., Nanostructured Materials for Solar Energy Conversion (Elsevier, 2006).

2.

N. S. Lewis, “Toward cost-effective solar energy use,” Science 315(5813), 798–801 (2007). [CrossRef] [PubMed]

3.

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

4.

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

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]

7.

L. Tsakalakos, J. Balch, J. Fronheiser, B. A. Korevaar, O. Sulima, and J. Rand, “Silicon nanowire solar cells,” Appl. Phys. Lett. 91(23), 233117 (2007). [CrossRef]

8.

O. L. Muskens, J. G. Rivas, R. E. Algra, E. P. Bakkers, and A. Lagendijk, “Design of light scattering in nanowire materials for photovoltaic applications,” Nano Lett. 8(9), 2638–2642 (2008). [CrossRef] [PubMed]

9.

T. Stelzner, M. Pietsch, G. Andrä, F. Falk, E. Ose, and S. Christiansen, “Silicon nanowire-based solar cells,” Nanotechnology 19(29), 295203 (2008). [CrossRef] [PubMed]

10.

E. Garnett and P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett. 10(3), 1082–1087 (2010). [CrossRef] [PubMed]

11.

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]

12.

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]

13.

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

14.

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]

15.

C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire and nanohole arrays for photovoltaic applications,” Proc. SPIE 7772, 17721G (2009).

16.

J. Li, H. Yu, S. M. Wong, G. Zhang, X. Sun, P. G.-Q. Lo, and D.-L. Kwong, “Si nanopillar array optimization on Si thin films for solar energy harvesting,” Appl. Phys. Lett. 95(3), 033102 (2009). [CrossRef]

17.

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(3), 239–244 (2010). [CrossRef] [PubMed]

18.

Y. Chen, R. Yu, W. Li, O. Nohadani, S. Haas, and A. F. J. Levi, “Adaptive design of nanoscale dielectric structures for photonics,” J. Appl. Phys. 94(9), 6065–6068 (2003). [CrossRef]

19.

I. L. Gheorma, S. Haas, and A. F. J. Levi, “Aperiodic nanophotonic design,” J. Appl. Phys. 95(3), 1420–1426 (2004). [CrossRef]

20.

Y. Jiao, S. Fan, and D. A. B. Miller, “Demonstration of systematic photonic crystal device design and optimization by low-rank adjustments: an extremely compact mode separator,” Opt. Lett. 30(2), 141–143 (2005). [CrossRef] [PubMed]

21.

P. Seliger, M. Mahvash, C. Wang, and A. F. J. Levi, “Optimization of aperiodic dielectric structures,” J. Appl. Phys. 100(3), 034310–034316 (2006). [CrossRef]

22.

A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett. 96(14), 143904 (2006). [CrossRef] [PubMed]

23.

J. Volk, A. Hakansson, H. T. Miyazaki, T. Nagata, J. Shimizu, and T. Chikyow, “Fully engineered homoepitaxial zinc oxide nanopillar array for near-surface light wave manipulation,” Appl. Phys. Lett. 92(18), 183114 (2008). [CrossRef]

24.

N. P. Sergeant, O. Pincon, M. Agrawal, and P. Peumans, “Design of wide-angle solar-selective absorbers using aperiodic metal-dielectric stacks,” Opt. Express 17(25), 22800–22812 (2009). [CrossRef] [PubMed]

25.

P. Pavaskar and S. B. Cronin, “Iterative optimization of plasmon resonant nanostructures,” Appl. Phys. Lett. 94(25), 253102 (2009). [CrossRef]

26.

P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express 15(25), 16986–17000 (2007). [CrossRef] [PubMed]

27.

H. Bao and X. Ruan, “Optical absorption enhancement in disordered vertical silicon nanowire arrays for photovoltaic applications,” Opt. Lett. 35(20), 3378–3380 (2010). [CrossRef] [PubMed]

28.

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]

29.

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32(3), 510–519 (1961). [CrossRef]

30.

ASTM, “Air Mass 1.5 Spectra,” http://rredc.nrel.gov/solar/spectra/am1.5.

31.

O. Gunawan and S. Guha, “Characteristics of vapor-liquid-solid grown silicon nanowire solar cells,” Sol. Energy Mater. Sol. Cells 93(8), 1388–1393 (2009). [CrossRef]

32.

M. Li, X. Hu, Z. Ye, K.-M. Ho, J. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett. 31(23), 3498–3500 (2006). [CrossRef] [PubMed]

33.

J. Thalken, Y. Chen, A. F. J. Levi, and S. Haas, “Adaptive quantum design of atomic clusters,” Phys. Rev. B 69(19), 195410 (2004). [CrossRef]

34.

A. Ben-Tal, S. Boyd, and A. Nemirovski, “Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems,” Math. Program. 107(1-2), 63–89 (2006). [CrossRef]

OCIS Codes
(350.6050) Other areas of optics : Solar energy

ToC Category:
Photovoltaics

History
Original Manuscript: May 18, 2011
Revised Manuscript: July 19, 2011
Manuscript Accepted: August 12, 2011
Published: August 22, 2011

Citation
Chenxi Lin and Michelle L. Povinelli, "Optimal design of aperiodic, vertical silicon nanowire structures for photovoltaics," Opt. Express 19, A1148-A1154 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S5-A1148


Sort:  Journal  |  Reset  

References

  1. T. Soga, ed., Nanostructured Materials for Solar Energy Conversion (Elsevier, 2006).
  2. N. S. Lewis, “Toward cost-effective solar energy use,” Science315(5813), 798–801 (2007). [CrossRef] [PubMed]
  3. L. Tsakalakos, “Nanostructures for photovoltaics,” Mater. Sci. Eng. R., 62, 175–189 (2008). [CrossRef]
  4. K. Q. Peng, Y. Xu, Y. Wu, Y. J. Yan, S. T. Lee, and J. Zhu, “Aligned single-crystalline Si nanowire arrays for photovoltaic applications,” Small1(11), 1062–1067 (2005). [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. 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. Nanophotonics1(1), 013552 (2007). [CrossRef]
  7. L. Tsakalakos, J. Balch, J. Fronheiser, B. A. Korevaar, O. Sulima, and J. Rand, “Silicon nanowire solar cells,” Appl. Phys. Lett.91(23), 233117 (2007). [CrossRef]
  8. O. L. Muskens, J. G. Rivas, R. E. Algra, E. P. Bakkers, and A. Lagendijk, “Design of light scattering in nanowire materials for photovoltaic applications,” Nano Lett.8(9), 2638–2642 (2008). [CrossRef] [PubMed]
  9. T. Stelzner, M. Pietsch, G. Andrä, F. Falk, E. Ose, and S. Christiansen, “Silicon nanowire-based solar cells,” Nanotechnology19(29), 295203 (2008). [CrossRef] [PubMed]
  10. E. Garnett and P. Yang, “Light trapping in silicon nanowire solar cells,” Nano Lett.10(3), 1082–1087 (2010). [CrossRef] [PubMed]
  11. 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]
  12. 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]
  13. J. Zhu, Z. F. Yu, G. F. Burkhard, C. M. Hsu, S. T. Connor, Y. Q. Xu, Q. Wang, M. McGehee, S. H. Fan, and Y. Cui, “Optical absorption enhancement in amorphous silicon nanowire and nanocone arrays,” Nano Lett.9(1), 279–282 (2009). [CrossRef] [PubMed]
  14. C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire arrays with a large lattice constant for photovoltaic applications,” Opt. Express17(22), 19371–19381 (2009). [CrossRef] [PubMed]
  15. C. Lin and M. L. Povinelli, “Optical absorption enhancement in silicon nanowire and nanohole arrays for photovoltaic applications,” Proc. SPIE 7772, 17721G (2009).
  16. J. Li, H. Yu, S. M. Wong, G. Zhang, X. Sun, P. G.-Q. Lo, and D.-L. Kwong, “Si nanopillar array optimization on Si thin films for solar energy harvesting,” Appl. Phys. Lett.95(3), 033102 (2009). [CrossRef]
  17. 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(3), 239–244 (2010). [CrossRef] [PubMed]
  18. Y. Chen, R. Yu, W. Li, O. Nohadani, S. Haas, and A. F. J. Levi, “Adaptive design of nanoscale dielectric structures for photonics,” J. Appl. Phys.94(9), 6065–6068 (2003). [CrossRef]
  19. I. L. Gheorma, S. Haas, and A. F. J. Levi, “Aperiodic nanophotonic design,” J. Appl. Phys.95(3), 1420–1426 (2004). [CrossRef]
  20. Y. Jiao, S. Fan, and D. A. B. Miller, “Demonstration of systematic photonic crystal device design and optimization by low-rank adjustments: an extremely compact mode separator,” Opt. Lett.30(2), 141–143 (2005). [CrossRef] [PubMed]
  21. P. Seliger, M. Mahvash, C. Wang, and A. F. J. Levi, “Optimization of aperiodic dielectric structures,” J. Appl. Phys.100(3), 034310–034316 (2006). [CrossRef]
  22. A. Gondarenko, S. Preble, J. Robinson, L. Chen, H. Lipson, and M. Lipson, “Spontaneous emergence of periodic patterns in a biologically inspired simulation of photonic structures,” Phys. Rev. Lett.96(14), 143904 (2006). [CrossRef] [PubMed]
  23. J. Volk, A. Hakansson, H. T. Miyazaki, T. Nagata, J. Shimizu, and T. Chikyow, “Fully engineered homoepitaxial zinc oxide nanopillar array for near-surface light wave manipulation,” Appl. Phys. Lett.92(18), 183114 (2008). [CrossRef]
  24. N. P. Sergeant, O. Pincon, M. Agrawal, and P. Peumans, “Design of wide-angle solar-selective absorbers using aperiodic metal-dielectric stacks,” Opt. Express17(25), 22800–22812 (2009). [CrossRef] [PubMed]
  25. P. Pavaskar and S. B. Cronin, “Iterative optimization of plasmon resonant nanostructures,” Appl. Phys. Lett.94(25), 253102 (2009). [CrossRef]
  26. P. Bermel, C. Luo, L. Zeng, L. C. Kimerling, and J. D. Joannopoulos, “Improving thin-film crystalline silicon solar cell efficiencies with photonic crystals,” Opt. Express15(25), 16986–17000 (2007). [CrossRef] [PubMed]
  27. H. Bao and X. Ruan, “Optical absorption enhancement in disordered vertical silicon nanowire arrays for photovoltaic applications,” Opt. Lett.35(20), 3378–3380 (2010). [CrossRef] [PubMed]
  28. 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]
  29. W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys.32(3), 510–519 (1961). [CrossRef]
  30. ASTM, “Air Mass 1.5 Spectra,” http://rredc.nrel.gov/solar/spectra/am1.5 .
  31. O. Gunawan and S. Guha, “Characteristics of vapor-liquid-solid grown silicon nanowire solar cells,” Sol. Energy Mater. Sol. Cells93(8), 1388–1393 (2009). [CrossRef]
  32. M. Li, X. Hu, Z. Ye, K.-M. Ho, J. Cao, and M. Miyawaki, “Higher-order incidence transfer matrix method used in three-dimensional photonic crystal coupled-resonator array simulation,” Opt. Lett.31(23), 3498–3500 (2006). [CrossRef] [PubMed]
  33. J. Thalken, Y. Chen, A. F. J. Levi, and S. Haas, “Adaptive quantum design of atomic clusters,” Phys. Rev. B69(19), 195410 (2004). [CrossRef]
  34. A. Ben-Tal, S. Boyd, and A. Nemirovski, “Extending Scope of Robust Optimization: Comprehensive Robust Counterparts of Uncertain Problems,” Math. Program.107(1-2), 63–89 (2006). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited