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

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [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]
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    [CrossRef]
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    [CrossRef]

Other (34)

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

N. S. Lewis, “Toward cost-effective solar energy use,” Science315(5813), 798–801 (2007).
[CrossRef] [PubMed]

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

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]

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]

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]

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]

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]

T. Stelzner, M. Pietsch, G. Andrä, F. Falk, E. Ose, and S. Christiansen, “Silicon nanowire-based solar cells,” Nanotechnology19(29), 295203 (2008).
[CrossRef] [PubMed]

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

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]

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]

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]

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]

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

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]

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]

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]

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

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]

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]

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]

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]

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]

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

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]

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]

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]

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]

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

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]

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]

J. Thalken, Y. Chen, A. F. J. Levi, and S. Haas, “Adaptive quantum design of atomic clusters,” Phys. Rev. B69(19), 195410 (2004).
[CrossRef]

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]

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Figures (5)

Fig. 1
Fig. 1

Schematics of periodic (a) and aperiodic (b) silicon nanowire structures.

Fig. 2
Fig. 2

Top view of initial periodic (a) and optimal aperiodic (b) silicon nanowire arrays. Dashed lines indicate boundaries between super cells.

Fig. 3
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).

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.

Fig. 5
Fig. 5

Histogram of ultimate efficiencies in 1000 randomly-selected, aperiodic silicon nanowire structures. The ultimate efficiency of the initial periodic array (blue, dashed line) is plotted for reference.

Equations (1)

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η = 310 n m λ g I ( λ ) A ( λ ) λ λ g d λ 310 n m 4000 n m I ( λ ) d λ ,

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