Abstract

Vertical arrays of direct band gap III-V semiconductor nanowires (NWs) hold the prospect of cheap and efficient next-generation photovoltaics, and guidelines for successful light-management are needed. Here, we use InP NWs as a model system and find, through electrodynamic modeling, general design principles for efficient absorption of sun light in nanowire arrays by systematically varying the nanowire diameter, the nanowire length, and the array period. Most importantly, we discover the existence of specific band-gap dependent diameters, 170 nm and 410 nm for InP, for which the absorption of sun light in the array is optimal, irrespective of the nanowire length. At these diameters, the individual InP NWs of the array absorb light strongly for photon energies just above the band gap energy due to a diameter-tunable nanophotonic resonance, which shows up also for other semiconductor materials of the NWs. Furthermore, we find that for maximized absorption of sun light, the optimal period of the array increases with nanowire length, since this decreases the insertion reflection losses.

© 2013 OSA

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2013 (2)

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

N. Anttu, “Geometrical optics, electrostatics, and nanophotonic resonances in absorbing nanowire arrays,” Opt. Lett. 38(5), 730–732 (2013).
[CrossRef] [PubMed]

2012 (6)

B. Wang, P. W. Leu, “Tunable and selective resonant absorption in vertical nanowires,” Opt. Lett. 37(18), 3756–3758 (2012).
[CrossRef] [PubMed]

P. M. Wu, N. Anttu, H. Q. Xu, L. Samuelson, M.-E. Pistol, “Colorful InAs nanowire arrays: From strong to weak absorption with geometrical tuning,” Nano Lett. 12(4), 1990–1995 (2012).
[CrossRef] [PubMed]

J. Li, H. Yu, Y. Li, “Solar energy harnessing in hexagonally arranged Si nanowire arrays and effects of array symmetry on optical characteristics,” Nanotechnology 23(19), 194010 (2012).
[CrossRef] [PubMed]

P. Kailuweit, M. Peters, J. Leene, K. Mergenthaler, F. Dimroth, A. W. Bett, “Numerical simulations of absorption properties of InP nanowires for solar cell applications,” Prog. Photovolt. Res. Appl. 20(8), 945–953 (2012).
[CrossRef]

N. Huang, C. Lin, M. L. Povinelli, “Broadband absorption of semiconductor nanowire arrays for photovoltaic applications,” J. Opt. 14(2), 024004 (2012).
[CrossRef]

N. Anttu, K. Namazi, P. Wu, P. Yang, H. Xu, H. Q. Xu, U. Håkanson, “Drastically increased absorption in vertical semiconductor nanowire arrays: A non-absorbing dielectric shell makes the difference,” Nano Res. 5(12), 863–874 (2012).
[CrossRef]

2011 (9)

Z. Gu, P. Prete, N. Lovergine, B. Nabet, “On optical properties of GaAs and GaAs/AlGaAs core-shell periodic nanowire arrays,” J. Appl. Phys. 109(6), 064314–064316 (2011).
[CrossRef]

J. Wallentin, M. T. Borgstrom, “Doping of semiconductor nanowires,” J. Mater. Res. 26(17), 2142–2156 (2011).
[CrossRef]

M. T. Borgström, J. Wallentin, M. Heurlin, S. Fält, P. Wickert, J. Leene, M. H. Magnusson, K. Deppert, L. Samuelson, “Nanowires with promise for photovoltaics,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1050–1061 (2011).
[CrossRef]

S. L. Diedenhofen, O. T. A. Janssen, G. Grzela, E. P. A. M. Bakkers, J. Gómez Rivas, “Strong geometrical dependence of the absorption of light in arrays of semiconductor nanowires,” ACS Nano 5(3), 2316–2323 (2011).
[CrossRef] [PubMed]

L. Wen, Z. Zhao, X. Li, Y. Shen, H. Guo, Y. Wang, “Theoretical analysis and modeling of light trapping in high efficicency GaAs nanowire array solar cells,” Appl. Phys. Lett. 99(14), 143116 (2011).
[CrossRef]

A. Luque, “Will we exceed 50% efficiency in photovoltaics?” J. Appl. Phys. 110(3), 031301–031319 (2011).
[CrossRef]

N. Anttu, H. Q. Xu, “Scattering matrix method for optical excitation of surface plasmons in metal films with periodic arrays of subwavelength holes,” Phys. Rev. B 83(16), 165431 (2011).
[CrossRef]

Q. G. Du, C. H. Kam, H. V. Demir, H. Y. Yu, X. W. Sun, “Broadband absorption enhancement in randomly positioned silicon nanowire arrays for solar cell applications,” Opt. Lett. 36(10), 1884–1886 (2011).
[CrossRef] [PubMed]

C. Lin, M. L. Povinelli, “Optimal design of aperiodic, vertical silicon nanowire structures for photovoltaics,” Opt. Express 19(S5Suppl 5), A1148–A1154 (2011).
[CrossRef] [PubMed]

2010 (5)

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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[PubMed]

Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
[CrossRef] [PubMed]

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

J. Kupec, R. L. Stoop, B. Witzigmann, “Light absorption and emission in nanowire array solar cells,” Opt. Express 18(26), 27589–27605 (2010).
[CrossRef] [PubMed]

N. Anttu, H. Q. Xu, “Coupling of light into nanowire arrays and subsequent absorption,” J. Nanosci. Nanotechnol. 10(11), 7183–7187 (2010).
[CrossRef] [PubMed]

2009 (6)

H. Goto, K. Nosaki, K. Tomioka, S. Hara, K. Hiruma, J. Motohisa, T. Fukui, “Growth of core–shell InP nanowires for photovoltaic application by selective-area metal organic vapor phase epitaxy,” Appl. Phys. Express 2, 035004 (2009).
[CrossRef]

J. A. Czaban, D. A. Thompson, R. R. LaPierre, “GaAs core--shell nanowires for photovoltaic applications,” Nano Lett. 9(1), 148–154 (2009).
[CrossRef] [PubMed]

J. Kupec, B. Witzigmann, “Dispersion, wave propagation and efficiency analysis of nanowire solar cells,” Opt. Express 17(12), 10399–10410 (2009).
[CrossRef] [PubMed]

C. Lin, 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]

J. Li, H. Yu, S. M. Wong, X. Li, G. Zhang, P. G.-Q. Lo, D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95(24), 243113 (2009).
[CrossRef]

L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[CrossRef] [PubMed]

2008 (1)

C. P. T. Svensson, T. Mårtensson, J. Trägårdh, C. Larsson, M. Rask, D. Hessman, L. Samuelson, J. Ohlsson, “Monolithic GaAs/InGaP nanowire light emitting diodes on silicon,” Nanotechnology 19(30), 305201 (2008).
[CrossRef] [PubMed]

2007 (2)

K. A. Dick, S. Kodambaka, M. C. Reuter, K. Deppert, L. Samuelson, W. Seifert, L. R. Wallenberg, F. M. Ross, “The morphology of axial and branched nanowire heterostructures,” Nano Lett. 7(6), 1817–1822 (2007).
[CrossRef] [PubMed]

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

2006 (1)

K. W. J. Barnham, M. Mazzer, B. Clive, “Resolving the energy crisis: nuclear or photovoltaics?” Nat. Mater. 5(3), 161–164 (2006).
[CrossRef]

2004 (1)

G. Kästner, U. Gösele, “Stress and dislocations at cross-sectional heterojunctions in a cylindrical nanowire,” Philos. Mag. 84, 3803–3824 (2004).
[CrossRef]

2001 (2)

M. A. Green, “Third generation photovoltaics: Ultra-high conversion efficiency at low cost,” Prog. Photovolt. Res. Appl. 9(2), 123–135 (2001).
[CrossRef]

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, “Band parameters for III-V compound semiconductors and their alloys,” J. Appl. Phys. 89(11), 5815–5875 (2001).
[CrossRef]

1998 (2)

A. A. Barybin, “Modal expansions and orthogonal complements in the theory of complex media waveguide excitation by external sources for isotropic, anisotropic, and bianisotropic media,” Prog. Electromagnetics Res. 19, 241–300 (1998).
[CrossRef]

R. Ferrini, M. Patrini, S. Franchi, “Optical functions from 0.02 to 6 eV of AlxGa1-xSb/GaSb epitaxial layers,” J. Appl. Phys. 84(8), 4517–4524 (1998).
[CrossRef]

1986 (1)

D. E. Aspnes, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlxGa1-xAs,” J. Appl. Phys. 60(2), 754–767 (1986).
[CrossRef]

1961 (1)

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

Åberg, I.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

Anttu, N.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

N. Anttu, “Geometrical optics, electrostatics, and nanophotonic resonances in absorbing nanowire arrays,” Opt. Lett. 38(5), 730–732 (2013).
[CrossRef] [PubMed]

N. Anttu, K. Namazi, P. Wu, P. Yang, H. Xu, H. Q. Xu, U. Håkanson, “Drastically increased absorption in vertical semiconductor nanowire arrays: A non-absorbing dielectric shell makes the difference,” Nano Res. 5(12), 863–874 (2012).
[CrossRef]

P. M. Wu, N. Anttu, H. Q. Xu, L. Samuelson, M.-E. Pistol, “Colorful InAs nanowire arrays: From strong to weak absorption with geometrical tuning,” Nano Lett. 12(4), 1990–1995 (2012).
[CrossRef] [PubMed]

N. Anttu, H. Q. Xu, “Scattering matrix method for optical excitation of surface plasmons in metal films with periodic arrays of subwavelength holes,” Phys. Rev. B 83(16), 165431 (2011).
[CrossRef]

N. Anttu, H. Q. Xu, “Coupling of light into nanowire arrays and subsequent absorption,” J. Nanosci. Nanotechnol. 10(11), 7183–7187 (2010).
[CrossRef] [PubMed]

Asoli, D.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

Aspnes, D. E.

D. E. Aspnes, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlxGa1-xAs,” J. Appl. Phys. 60(2), 754–767 (1986).
[CrossRef]

Atwater, H. A.

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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[PubMed]

Bakkers, E. P. A. M.

S. L. Diedenhofen, O. T. A. Janssen, G. Grzela, E. P. A. M. Bakkers, J. Gómez Rivas, “Strong geometrical dependence of the absorption of light in arrays of semiconductor nanowires,” ACS Nano 5(3), 2316–2323 (2011).
[CrossRef] [PubMed]

Bao, H.

Barnham, K. W. J.

K. W. J. Barnham, M. Mazzer, B. Clive, “Resolving the energy crisis: nuclear or photovoltaics?” Nat. Mater. 5(3), 161–164 (2006).
[CrossRef]

Barybin, A. A.

A. A. Barybin, “Modal expansions and orthogonal complements in the theory of complex media waveguide excitation by external sources for isotropic, anisotropic, and bianisotropic media,” Prog. Electromagnetics Res. 19, 241–300 (1998).
[CrossRef]

Bett, A. W.

P. Kailuweit, M. Peters, J. Leene, K. Mergenthaler, F. Dimroth, A. W. Bett, “Numerical simulations of absorption properties of InP nanowires for solar cell applications,” Prog. Photovolt. Res. Appl. 20(8), 945–953 (2012).
[CrossRef]

Bhat, R.

D. E. Aspnes, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlxGa1-xAs,” J. Appl. Phys. 60(2), 754–767 (1986).
[CrossRef]

Boettcher, S. W.

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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[PubMed]

Borgstrom, M. T.

J. Wallentin, M. T. Borgstrom, “Doping of semiconductor nanowires,” J. Mater. Res. 26(17), 2142–2156 (2011).
[CrossRef]

Borgström, M. T.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

M. T. Borgström, J. Wallentin, M. Heurlin, S. Fält, P. Wickert, J. Leene, M. H. Magnusson, K. Deppert, L. Samuelson, “Nanowires with promise for photovoltaics,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1050–1061 (2011).
[CrossRef]

Briggs, R. M.

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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
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L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
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Cao, L.

L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
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Chen, G.

L. Hu, G. Chen, “Analysis of optical absorption in silicon nanowire arrays for photovoltaic applications,” Nano Lett. 7(11), 3249–3252 (2007).
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Chueh, Y.-L.

Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
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Clemens, B. M.

L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
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Clive, B.

K. W. J. Barnham, M. Mazzer, B. Clive, “Resolving the energy crisis: nuclear or photovoltaics?” Nat. Mater. 5(3), 161–164 (2006).
[CrossRef]

Czaban, J. A.

J. A. Czaban, D. A. Thompson, R. R. LaPierre, “GaAs core--shell nanowires for photovoltaic applications,” Nano Lett. 9(1), 148–154 (2009).
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Demir, H. V.

Deppert, K.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

M. T. Borgström, J. Wallentin, M. Heurlin, S. Fält, P. Wickert, J. Leene, M. H. Magnusson, K. Deppert, L. Samuelson, “Nanowires with promise for photovoltaics,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1050–1061 (2011).
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K. A. Dick, S. Kodambaka, M. C. Reuter, K. Deppert, L. Samuelson, W. Seifert, L. R. Wallenberg, F. M. Ross, “The morphology of axial and branched nanowire heterostructures,” Nano Lett. 7(6), 1817–1822 (2007).
[CrossRef] [PubMed]

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K. A. Dick, S. Kodambaka, M. C. Reuter, K. Deppert, L. Samuelson, W. Seifert, L. R. Wallenberg, F. M. Ross, “The morphology of axial and branched nanowire heterostructures,” Nano Lett. 7(6), 1817–1822 (2007).
[CrossRef] [PubMed]

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S. L. Diedenhofen, O. T. A. Janssen, G. Grzela, E. P. A. M. Bakkers, J. Gómez Rivas, “Strong geometrical dependence of the absorption of light in arrays of semiconductor nanowires,” ACS Nano 5(3), 2316–2323 (2011).
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Dimroth, F.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

P. Kailuweit, M. Peters, J. Leene, K. Mergenthaler, F. Dimroth, A. W. Bett, “Numerical simulations of absorption properties of InP nanowires for solar cell applications,” Prog. Photovolt. Res. Appl. 20(8), 945–953 (2012).
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Du, Q. G.

Fält, S.

M. T. Borgström, J. Wallentin, M. Heurlin, S. Fält, P. Wickert, J. Leene, M. H. Magnusson, K. Deppert, L. Samuelson, “Nanowires with promise for photovoltaics,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1050–1061 (2011).
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Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
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R. Ferrini, M. Patrini, S. Franchi, “Optical functions from 0.02 to 6 eV of AlxGa1-xSb/GaSb epitaxial layers,” J. Appl. Phys. 84(8), 4517–4524 (1998).
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R. Ferrini, M. Patrini, S. Franchi, “Optical functions from 0.02 to 6 eV of AlxGa1-xSb/GaSb epitaxial layers,” J. Appl. Phys. 84(8), 4517–4524 (1998).
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H. Goto, K. Nosaki, K. Tomioka, S. Hara, K. Hiruma, J. Motohisa, T. Fukui, “Growth of core–shell InP nanowires for photovoltaic application by selective-area metal organic vapor phase epitaxy,” Appl. Phys. Express 2, 035004 (2009).
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J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
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S. L. Diedenhofen, O. T. A. Janssen, G. Grzela, E. P. A. M. Bakkers, J. Gómez Rivas, “Strong geometrical dependence of the absorption of light in arrays of semiconductor nanowires,” ACS Nano 5(3), 2316–2323 (2011).
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G. Kästner, U. Gösele, “Stress and dislocations at cross-sectional heterojunctions in a cylindrical nanowire,” Philos. Mag. 84, 3803–3824 (2004).
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H. Goto, K. Nosaki, K. Tomioka, S. Hara, K. Hiruma, J. Motohisa, T. Fukui, “Growth of core–shell InP nanowires for photovoltaic application by selective-area metal organic vapor phase epitaxy,” Appl. Phys. Express 2, 035004 (2009).
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S. L. Diedenhofen, O. T. A. Janssen, G. Grzela, E. P. A. M. Bakkers, J. Gómez Rivas, “Strong geometrical dependence of the absorption of light in arrays of semiconductor nanowires,” ACS Nano 5(3), 2316–2323 (2011).
[CrossRef] [PubMed]

Gu, Z.

Z. Gu, P. Prete, N. Lovergine, B. Nabet, “On optical properties of GaAs and GaAs/AlGaAs core-shell periodic nanowire arrays,” J. Appl. Phys. 109(6), 064314–064316 (2011).
[CrossRef]

Guo, H.

L. Wen, Z. Zhao, X. Li, Y. Shen, H. Guo, Y. Wang, “Theoretical analysis and modeling of light trapping in high efficicency GaAs nanowire array solar cells,” Appl. Phys. Lett. 99(14), 143116 (2011).
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N. Anttu, K. Namazi, P. Wu, P. Yang, H. Xu, H. Q. Xu, U. Håkanson, “Drastically increased absorption in vertical semiconductor nanowire arrays: A non-absorbing dielectric shell makes the difference,” Nano Res. 5(12), 863–874 (2012).
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H. Goto, K. Nosaki, K. Tomioka, S. Hara, K. Hiruma, J. Motohisa, T. Fukui, “Growth of core–shell InP nanowires for photovoltaic application by selective-area metal organic vapor phase epitaxy,” Appl. Phys. Express 2, 035004 (2009).
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C. P. T. Svensson, T. Mårtensson, J. Trägårdh, C. Larsson, M. Rask, D. Hessman, L. Samuelson, J. Ohlsson, “Monolithic GaAs/InGaP nanowire light emitting diodes on silicon,” Nanotechnology 19(30), 305201 (2008).
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M. T. Borgström, J. Wallentin, M. Heurlin, S. Fält, P. Wickert, J. Leene, M. H. Magnusson, K. Deppert, L. Samuelson, “Nanowires with promise for photovoltaics,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1050–1061 (2011).
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H. Goto, K. Nosaki, K. Tomioka, S. Hara, K. Hiruma, J. Motohisa, T. Fukui, “Growth of core–shell InP nanowires for photovoltaic application by selective-area metal organic vapor phase epitaxy,” Appl. Phys. Express 2, 035004 (2009).
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L. Hu, G. Chen, “Analysis of optical absorption in silicon nanowire arrays for photovoltaic applications,” Nano Lett. 7(11), 3249–3252 (2007).
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N. Huang, C. Lin, M. L. Povinelli, “Broadband absorption of semiconductor nanowire arrays for photovoltaic applications,” J. Opt. 14(2), 024004 (2012).
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J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
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Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
[CrossRef] [PubMed]

Janssen, O. T. A.

S. L. Diedenhofen, O. T. A. Janssen, G. Grzela, E. P. A. M. Bakkers, J. Gómez Rivas, “Strong geometrical dependence of the absorption of light in arrays of semiconductor nanowires,” ACS Nano 5(3), 2316–2323 (2011).
[CrossRef] [PubMed]

Javey, A.

Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
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Kailuweit, P.

P. Kailuweit, M. Peters, J. Leene, K. Mergenthaler, F. Dimroth, A. W. Bett, “Numerical simulations of absorption properties of InP nanowires for solar cell applications,” Prog. Photovolt. Res. Appl. 20(8), 945–953 (2012).
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Kapadia, R.

Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
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Kästner, G.

G. Kästner, U. Gösele, “Stress and dislocations at cross-sectional heterojunctions in a cylindrical nanowire,” Philos. Mag. 84, 3803–3824 (2004).
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D. E. Aspnes, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlxGa1-xAs,” J. Appl. Phys. 60(2), 754–767 (1986).
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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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[PubMed]

Kodambaka, S.

K. A. Dick, S. Kodambaka, M. C. Reuter, K. Deppert, L. Samuelson, W. Seifert, L. R. Wallenberg, F. M. Ross, “The morphology of axial and branched nanowire heterostructures,” Nano Lett. 7(6), 1817–1822 (2007).
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Kupec, J.

Kwong, D.-L.

J. Li, H. Yu, S. M. Wong, X. Li, G. Zhang, P. G.-Q. Lo, D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95(24), 243113 (2009).
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J. A. Czaban, D. A. Thompson, R. R. LaPierre, “GaAs core--shell nanowires for photovoltaic applications,” Nano Lett. 9(1), 148–154 (2009).
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Larsson, C.

C. P. T. Svensson, T. Mårtensson, J. Trägårdh, C. Larsson, M. Rask, D. Hessman, L. Samuelson, J. Ohlsson, “Monolithic GaAs/InGaP nanowire light emitting diodes on silicon,” Nanotechnology 19(30), 305201 (2008).
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Leene, J.

P. Kailuweit, M. Peters, J. Leene, K. Mergenthaler, F. Dimroth, A. W. Bett, “Numerical simulations of absorption properties of InP nanowires for solar cell applications,” Prog. Photovolt. Res. Appl. 20(8), 945–953 (2012).
[CrossRef]

M. T. Borgström, J. Wallentin, M. Heurlin, S. Fält, P. Wickert, J. Leene, M. H. Magnusson, K. Deppert, L. Samuelson, “Nanowires with promise for photovoltaics,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1050–1061 (2011).
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B. Wang, P. W. Leu, “Tunable and selective resonant absorption in vertical nanowires,” Opt. Lett. 37(18), 3756–3758 (2012).
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Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
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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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
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J. Li, H. Yu, Y. Li, “Solar energy harnessing in hexagonally arranged Si nanowire arrays and effects of array symmetry on optical characteristics,” Nanotechnology 23(19), 194010 (2012).
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J. Li, H. Yu, S. M. Wong, X. Li, G. Zhang, P. G.-Q. Lo, D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95(24), 243113 (2009).
[CrossRef]

Li, X.

L. Wen, Z. Zhao, X. Li, Y. Shen, H. Guo, Y. Wang, “Theoretical analysis and modeling of light trapping in high efficicency GaAs nanowire array solar cells,” Appl. Phys. Lett. 99(14), 143116 (2011).
[CrossRef]

J. Li, H. Yu, S. M. Wong, X. Li, G. Zhang, P. G.-Q. Lo, D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95(24), 243113 (2009).
[CrossRef]

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J. Li, H. Yu, Y. Li, “Solar energy harnessing in hexagonally arranged Si nanowire arrays and effects of array symmetry on optical characteristics,” Nanotechnology 23(19), 194010 (2012).
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Lin, C.

Lo, P. G.-Q.

J. Li, H. Yu, S. M. Wong, X. Li, G. Zhang, P. G.-Q. Lo, D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95(24), 243113 (2009).
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D. E. Aspnes, S. M. Kelso, R. A. Logan, R. Bhat, “Optical properties of AlxGa1-xAs,” J. Appl. Phys. 60(2), 754–767 (1986).
[CrossRef]

Lovergine, N.

Z. Gu, P. Prete, N. Lovergine, B. Nabet, “On optical properties of GaAs and GaAs/AlGaAs core-shell periodic nanowire arrays,” J. Appl. Phys. 109(6), 064314–064316 (2011).
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J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
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M. T. Borgström, J. Wallentin, M. Heurlin, S. Fält, P. Wickert, J. Leene, M. H. Magnusson, K. Deppert, L. Samuelson, “Nanowires with promise for photovoltaics,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1050–1061 (2011).
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Mårtensson, T.

C. P. T. Svensson, T. Mårtensson, J. Trägårdh, C. Larsson, M. Rask, D. Hessman, L. Samuelson, J. Ohlsson, “Monolithic GaAs/InGaP nanowire light emitting diodes on silicon,” Nanotechnology 19(30), 305201 (2008).
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Mazzer, M.

K. W. J. Barnham, M. Mazzer, B. Clive, “Resolving the energy crisis: nuclear or photovoltaics?” Nat. Mater. 5(3), 161–164 (2006).
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Mergenthaler, K.

P. Kailuweit, M. Peters, J. Leene, K. Mergenthaler, F. Dimroth, A. W. Bett, “Numerical simulations of absorption properties of InP nanowires for solar cell applications,” Prog. Photovolt. Res. Appl. 20(8), 945–953 (2012).
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I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, “Band parameters for III-V compound semiconductors and their alloys,” J. Appl. Phys. 89(11), 5815–5875 (2001).
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H. Goto, K. Nosaki, K. Tomioka, S. Hara, K. Hiruma, J. Motohisa, T. Fukui, “Growth of core–shell InP nanowires for photovoltaic application by selective-area metal organic vapor phase epitaxy,” Appl. Phys. Express 2, 035004 (2009).
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Z. Gu, P. Prete, N. Lovergine, B. Nabet, “On optical properties of GaAs and GaAs/AlGaAs core-shell periodic nanowire arrays,” J. Appl. Phys. 109(6), 064314–064316 (2011).
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N. Anttu, K. Namazi, P. Wu, P. Yang, H. Xu, H. Q. Xu, U. Håkanson, “Drastically increased absorption in vertical semiconductor nanowire arrays: A non-absorbing dielectric shell makes the difference,” Nano Res. 5(12), 863–874 (2012).
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H. Goto, K. Nosaki, K. Tomioka, S. Hara, K. Hiruma, J. Motohisa, T. Fukui, “Growth of core–shell InP nanowires for photovoltaic application by selective-area metal organic vapor phase epitaxy,” Appl. Phys. Express 2, 035004 (2009).
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C. P. T. Svensson, T. Mårtensson, J. Trägårdh, C. Larsson, M. Rask, D. Hessman, L. Samuelson, J. Ohlsson, “Monolithic GaAs/InGaP nanowire light emitting diodes on silicon,” Nanotechnology 19(30), 305201 (2008).
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Park, J.-S.

L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
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R. Ferrini, M. Patrini, S. Franchi, “Optical functions from 0.02 to 6 eV of AlxGa1-xSb/GaSb epitaxial layers,” J. Appl. Phys. 84(8), 4517–4524 (1998).
[CrossRef]

Peters, M.

P. Kailuweit, M. Peters, J. Leene, K. Mergenthaler, F. Dimroth, A. W. Bett, “Numerical simulations of absorption properties of InP nanowires for solar cell applications,” Prog. Photovolt. Res. Appl. 20(8), 945–953 (2012).
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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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
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Prete, P.

Z. Gu, P. Prete, N. Lovergine, B. Nabet, “On optical properties of GaAs and GaAs/AlGaAs core-shell periodic nanowire arrays,” J. Appl. Phys. 109(6), 064314–064316 (2011).
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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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
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C. P. T. Svensson, T. Mårtensson, J. Trägårdh, C. Larsson, M. Rask, D. Hessman, L. Samuelson, J. Ohlsson, “Monolithic GaAs/InGaP nanowire light emitting diodes on silicon,” Nanotechnology 19(30), 305201 (2008).
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Rathore, A. A.

Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
[CrossRef] [PubMed]

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K. A. Dick, S. Kodambaka, M. C. Reuter, K. Deppert, L. Samuelson, W. Seifert, L. R. Wallenberg, F. M. Ross, “The morphology of axial and branched nanowire heterostructures,” Nano Lett. 7(6), 1817–1822 (2007).
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K. A. Dick, S. Kodambaka, M. C. Reuter, K. Deppert, L. Samuelson, W. Seifert, L. R. Wallenberg, F. M. Ross, “The morphology of axial and branched nanowire heterostructures,” Nano Lett. 7(6), 1817–1822 (2007).
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Ruan, X.

Ruebusch, D. J.

Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
[CrossRef] [PubMed]

Samuelson, L.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

P. M. Wu, N. Anttu, H. Q. Xu, L. Samuelson, M.-E. Pistol, “Colorful InAs nanowire arrays: From strong to weak absorption with geometrical tuning,” Nano Lett. 12(4), 1990–1995 (2012).
[CrossRef] [PubMed]

M. T. Borgström, J. Wallentin, M. Heurlin, S. Fält, P. Wickert, J. Leene, M. H. Magnusson, K. Deppert, L. Samuelson, “Nanowires with promise for photovoltaics,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1050–1061 (2011).
[CrossRef]

C. P. T. Svensson, T. Mårtensson, J. Trägårdh, C. Larsson, M. Rask, D. Hessman, L. Samuelson, J. Ohlsson, “Monolithic GaAs/InGaP nanowire light emitting diodes on silicon,” Nanotechnology 19(30), 305201 (2008).
[CrossRef] [PubMed]

K. A. Dick, S. Kodambaka, M. C. Reuter, K. Deppert, L. Samuelson, W. Seifert, L. R. Wallenberg, F. M. Ross, “The morphology of axial and branched nanowire heterostructures,” Nano Lett. 7(6), 1817–1822 (2007).
[CrossRef] [PubMed]

Schuller, J. A.

L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[CrossRef] [PubMed]

Seifert, W.

K. A. Dick, S. Kodambaka, M. C. Reuter, K. Deppert, L. Samuelson, W. Seifert, L. R. Wallenberg, F. M. Ross, “The morphology of axial and branched nanowire heterostructures,” Nano Lett. 7(6), 1817–1822 (2007).
[CrossRef] [PubMed]

Shen, Y.

L. Wen, Z. Zhao, X. Li, Y. Shen, H. Guo, Y. Wang, “Theoretical analysis and modeling of light trapping in high efficicency GaAs nanowire array solar cells,” Appl. Phys. Lett. 99(14), 143116 (2011).
[CrossRef]

Shockley, W.

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

Siefer, G.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

Spurgeon, J. M.

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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[PubMed]

Stoop, R. L.

Sun, X. W.

Svensson, C. P. T.

C. P. T. Svensson, T. Mårtensson, J. Trägårdh, C. Larsson, M. Rask, D. Hessman, L. Samuelson, J. Ohlsson, “Monolithic GaAs/InGaP nanowire light emitting diodes on silicon,” Nanotechnology 19(30), 305201 (2008).
[CrossRef] [PubMed]

Takei, K.

Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
[CrossRef] [PubMed]

Thompson, D. A.

J. A. Czaban, D. A. Thompson, R. R. LaPierre, “GaAs core--shell nanowires for photovoltaic applications,” Nano Lett. 9(1), 148–154 (2009).
[CrossRef] [PubMed]

Tomioka, K.

H. Goto, K. Nosaki, K. Tomioka, S. Hara, K. Hiruma, J. Motohisa, T. Fukui, “Growth of core–shell InP nanowires for photovoltaic application by selective-area metal organic vapor phase epitaxy,” Appl. Phys. Express 2, 035004 (2009).
[CrossRef]

Trägårdh, J.

C. P. T. Svensson, T. Mårtensson, J. Trägårdh, C. Larsson, M. Rask, D. Hessman, L. Samuelson, J. Ohlsson, “Monolithic GaAs/InGaP nanowire light emitting diodes on silicon,” Nanotechnology 19(30), 305201 (2008).
[CrossRef] [PubMed]

Turner-Evans, D. B.

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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[PubMed]

Vurgaftman, I.

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, “Band parameters for III-V compound semiconductors and their alloys,” J. Appl. Phys. 89(11), 5815–5875 (2001).
[CrossRef]

Wallenberg, L. R.

K. A. Dick, S. Kodambaka, M. C. Reuter, K. Deppert, L. Samuelson, W. Seifert, L. R. Wallenberg, F. M. Ross, “The morphology of axial and branched nanowire heterostructures,” Nano Lett. 7(6), 1817–1822 (2007).
[CrossRef] [PubMed]

Wallentin, J.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

M. T. Borgström, J. Wallentin, M. Heurlin, S. Fält, P. Wickert, J. Leene, M. H. Magnusson, K. Deppert, L. Samuelson, “Nanowires with promise for photovoltaics,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1050–1061 (2011).
[CrossRef]

J. Wallentin, M. T. Borgstrom, “Doping of semiconductor nanowires,” J. Mater. Res. 26(17), 2142–2156 (2011).
[CrossRef]

Wang, B.

Wang, Y.

L. Wen, Z. Zhao, X. Li, Y. Shen, H. Guo, Y. Wang, “Theoretical analysis and modeling of light trapping in high efficicency GaAs nanowire array solar cells,” Appl. Phys. Lett. 99(14), 143116 (2011).
[CrossRef]

Warren, E. L.

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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
[PubMed]

Wen, L.

L. Wen, Z. Zhao, X. Li, Y. Shen, H. Guo, Y. Wang, “Theoretical analysis and modeling of light trapping in high efficicency GaAs nanowire array solar cells,” Appl. Phys. Lett. 99(14), 143116 (2011).
[CrossRef]

White, J. S.

L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[CrossRef] [PubMed]

Wickert, P.

M. T. Borgström, J. Wallentin, M. Heurlin, S. Fält, P. Wickert, J. Leene, M. H. Magnusson, K. Deppert, L. Samuelson, “Nanowires with promise for photovoltaics,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1050–1061 (2011).
[CrossRef]

Witzigmann, B.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

J. Kupec, R. L. Stoop, B. Witzigmann, “Light absorption and emission in nanowire array solar cells,” Opt. Express 18(26), 27589–27605 (2010).
[CrossRef] [PubMed]

J. Kupec, B. Witzigmann, “Dispersion, wave propagation and efficiency analysis of nanowire solar cells,” Opt. Express 17(12), 10399–10410 (2009).
[CrossRef] [PubMed]

Wong, S. M.

J. Li, H. Yu, S. M. Wong, X. Li, G. Zhang, P. G.-Q. Lo, D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95(24), 243113 (2009).
[CrossRef]

Wu, M.

Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
[CrossRef] [PubMed]

Wu, P.

N. Anttu, K. Namazi, P. Wu, P. Yang, H. Xu, H. Q. Xu, U. Håkanson, “Drastically increased absorption in vertical semiconductor nanowire arrays: A non-absorbing dielectric shell makes the difference,” Nano Res. 5(12), 863–874 (2012).
[CrossRef]

Wu, P. M.

P. M. Wu, N. Anttu, H. Q. Xu, L. Samuelson, M.-E. Pistol, “Colorful InAs nanowire arrays: From strong to weak absorption with geometrical tuning,” Nano Lett. 12(4), 1990–1995 (2012).
[CrossRef] [PubMed]

Xu, H.

N. Anttu, K. Namazi, P. Wu, P. Yang, H. Xu, H. Q. Xu, U. Håkanson, “Drastically increased absorption in vertical semiconductor nanowire arrays: A non-absorbing dielectric shell makes the difference,” Nano Res. 5(12), 863–874 (2012).
[CrossRef]

Xu, H. Q.

J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
[CrossRef] [PubMed]

P. M. Wu, N. Anttu, H. Q. Xu, L. Samuelson, M.-E. Pistol, “Colorful InAs nanowire arrays: From strong to weak absorption with geometrical tuning,” Nano Lett. 12(4), 1990–1995 (2012).
[CrossRef] [PubMed]

N. Anttu, K. Namazi, P. Wu, P. Yang, H. Xu, H. Q. Xu, U. Håkanson, “Drastically increased absorption in vertical semiconductor nanowire arrays: A non-absorbing dielectric shell makes the difference,” Nano Res. 5(12), 863–874 (2012).
[CrossRef]

N. Anttu, H. Q. Xu, “Scattering matrix method for optical excitation of surface plasmons in metal films with periodic arrays of subwavelength holes,” Phys. Rev. B 83(16), 165431 (2011).
[CrossRef]

N. Anttu, H. Q. Xu, “Coupling of light into nanowire arrays and subsequent absorption,” J. Nanosci. Nanotechnol. 10(11), 7183–7187 (2010).
[CrossRef] [PubMed]

Yang, P.

N. Anttu, K. Namazi, P. Wu, P. Yang, H. Xu, H. Q. Xu, U. Håkanson, “Drastically increased absorption in vertical semiconductor nanowire arrays: A non-absorbing dielectric shell makes the difference,” Nano Res. 5(12), 863–874 (2012).
[CrossRef]

Yu, H.

J. Li, H. Yu, Y. Li, “Solar energy harnessing in hexagonally arranged Si nanowire arrays and effects of array symmetry on optical characteristics,” Nanotechnology 23(19), 194010 (2012).
[CrossRef] [PubMed]

J. Li, H. Yu, S. M. Wong, X. Li, G. Zhang, P. G.-Q. Lo, D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95(24), 243113 (2009).
[CrossRef]

Yu, H. Y.

Yu, K.

Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
[CrossRef] [PubMed]

Zhang, G.

J. Li, H. Yu, S. M. Wong, X. Li, G. Zhang, P. G.-Q. Lo, D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95(24), 243113 (2009).
[CrossRef]

Zhang, X.

Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
[CrossRef] [PubMed]

Zhao, Z.

L. Wen, Z. Zhao, X. Li, Y. Shen, H. Guo, Y. Wang, “Theoretical analysis and modeling of light trapping in high efficicency GaAs nanowire array solar cells,” Appl. Phys. Lett. 99(14), 143116 (2011).
[CrossRef]

ACS Nano (1)

S. L. Diedenhofen, O. T. A. Janssen, G. Grzela, E. P. A. M. Bakkers, J. Gómez Rivas, “Strong geometrical dependence of the absorption of light in arrays of semiconductor nanowires,” ACS Nano 5(3), 2316–2323 (2011).
[CrossRef] [PubMed]

Appl. Phys. Express (1)

H. Goto, K. Nosaki, K. Tomioka, S. Hara, K. Hiruma, J. Motohisa, T. Fukui, “Growth of core–shell InP nanowires for photovoltaic application by selective-area metal organic vapor phase epitaxy,” Appl. Phys. Express 2, 035004 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

L. Wen, Z. Zhao, X. Li, Y. Shen, H. Guo, Y. Wang, “Theoretical analysis and modeling of light trapping in high efficicency GaAs nanowire array solar cells,” Appl. Phys. Lett. 99(14), 143116 (2011).
[CrossRef]

J. Li, H. Yu, S. M. Wong, X. Li, G. Zhang, P. G.-Q. Lo, D.-L. Kwong, “Design guidelines of periodic Si nanowire arrays for solar cell application,” Appl. Phys. Lett. 95(24), 243113 (2009).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

M. T. Borgström, J. Wallentin, M. Heurlin, S. Fält, P. Wickert, J. Leene, M. H. Magnusson, K. Deppert, L. Samuelson, “Nanowires with promise for photovoltaics,” IEEE J. Sel. Top. Quantum Electron. 17(4), 1050–1061 (2011).
[CrossRef]

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A. Luque, “Will we exceed 50% efficiency in photovoltaics?” J. Appl. Phys. 110(3), 031301–031319 (2011).
[CrossRef]

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[CrossRef]

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

I. Vurgaftman, J. R. Meyer, L. R. Ram-Mohan, “Band parameters for III-V compound semiconductors and their alloys,” J. Appl. Phys. 89(11), 5815–5875 (2001).
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[CrossRef]

J. Mater. Res. (1)

J. Wallentin, M. T. Borgstrom, “Doping of semiconductor nanowires,” J. Mater. Res. 26(17), 2142–2156 (2011).
[CrossRef]

J. Nanosci. Nanotechnol. (1)

N. Anttu, H. Q. Xu, “Coupling of light into nanowire arrays and subsequent absorption,” J. Nanosci. Nanotechnol. 10(11), 7183–7187 (2010).
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N. Huang, C. Lin, M. L. Povinelli, “Broadband absorption of semiconductor nanowire arrays for photovoltaic applications,” J. Opt. 14(2), 024004 (2012).
[CrossRef]

Nano Lett. (5)

L. Hu, G. Chen, “Analysis of optical absorption in silicon nanowire arrays for photovoltaic applications,” Nano Lett. 7(11), 3249–3252 (2007).
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P. M. Wu, N. Anttu, H. Q. Xu, L. Samuelson, M.-E. Pistol, “Colorful InAs nanowire arrays: From strong to weak absorption with geometrical tuning,” Nano Lett. 12(4), 1990–1995 (2012).
[CrossRef] [PubMed]

K. A. Dick, S. Kodambaka, M. C. Reuter, K. Deppert, L. Samuelson, W. Seifert, L. R. Wallenberg, F. M. Ross, “The morphology of axial and branched nanowire heterostructures,” Nano Lett. 7(6), 1817–1822 (2007).
[CrossRef] [PubMed]

Z. Fan, R. Kapadia, P. W. Leu, X. Zhang, Y.-L. Chueh, K. Takei, K. Yu, A. Jamshidi, A. A. Rathore, D. J. Ruebusch, M. Wu, A. Javey, “Ordered Arrays of Dual-Diameter Nanopillars for Maximized Optical Absorption,” Nano Lett. 10(10), 3823–3827 (2010).
[CrossRef] [PubMed]

J. A. Czaban, D. A. Thompson, R. R. LaPierre, “GaAs core--shell nanowires for photovoltaic applications,” Nano Lett. 9(1), 148–154 (2009).
[CrossRef] [PubMed]

Nano Res. (1)

N. Anttu, K. Namazi, P. Wu, P. Yang, H. Xu, H. Q. Xu, U. Håkanson, “Drastically increased absorption in vertical semiconductor nanowire arrays: A non-absorbing dielectric shell makes the difference,” Nano Res. 5(12), 863–874 (2012).
[CrossRef]

Nanotechnology (2)

C. P. T. Svensson, T. Mårtensson, J. Trägårdh, C. Larsson, M. Rask, D. Hessman, L. Samuelson, J. Ohlsson, “Monolithic GaAs/InGaP nanowire light emitting diodes on silicon,” Nanotechnology 19(30), 305201 (2008).
[CrossRef] [PubMed]

J. Li, H. Yu, Y. Li, “Solar energy harnessing in hexagonally arranged Si nanowire arrays and effects of array symmetry on optical characteristics,” Nanotechnology 23(19), 194010 (2012).
[CrossRef] [PubMed]

Nat. Mater. (3)

L. Cao, J. S. White, J.-S. Park, J. A. Schuller, B. M. Clemens, M. L. Brongersma, “Engineering light absorption in semiconductor nanowire devices,” Nat. Mater. 8(8), 643–647 (2009).
[CrossRef] [PubMed]

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, H. A. Atwater, “Enhanced absorption and carrier collection in Si wire arrays for photovoltaic applications,” Nat. Mater. 9(3), 239–244 (2010).
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N. Anttu, H. Q. Xu, “Scattering matrix method for optical excitation of surface plasmons in metal films with periodic arrays of subwavelength holes,” Phys. Rev. B 83(16), 165431 (2011).
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J. Wallentin, N. Anttu, D. Asoli, M. Huffman, I. Åberg, M. H. Magnusson, G. Siefer, P. Fuss-Kailuweit, F. Dimroth, B. Witzigmann, H. Q. Xu, L. Samuelson, K. Deppert, M. T. Borgström, “InP Nanowire Array Solar Cells Achieving 13.8% Efficiency by Exceeding the Ray Optics Limit,” Science 339(6123), 1057–1060 (2013).
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Figures (10)

Fig. 1
Fig. 1

Schematic of the modeled InP NW array. The NWs stand on top of an (optically) infinitely thick InP substrate. There is air between and on top of the NWs. The NW diameter is D and the NW length is L. A unit cell in the x-y plane contains one NW and has the period p in both the x and the y direction. A plane wave of light is incident normally, with kx = ky = 0, toward the NW array from air on the top side.

Fig. 2
Fig. 2

(a) The 1000 W/m2 AM1.5 direct and circumsolar intensity spectrum (higher red values) [29]. Here, also the intensity usable from the AM1.5 spectrum for an InP solar cell is shown (lower green values), which is obtained by taking into account the band gap of InP (λbg = 925 nm) and thermalization losses. (b) Zoom-in of the intensity usable from the AM1.5 spectrum for an InP solar cell.

Fig. 3
Fig. 3

(a) Absorptance spectrum A(λ) of an InP NW array with period p = 680 nm and NWs of length L = 2000 nm on top of an InP substrate. We consider the cases of NWs of diameter D = 100 nm (i), 177 nm (ii), 221 nm (iii), and 441 nm (iv). The incident light is a plane wave incident at normal angle to the array from the top air side. (b) Ultimate efficiency η as a function of D for an InP NW array with p = 680 nm and L = 2000 nm. The circles (i) - (iv) mark the NW arrays whose absorptance spectra A(λ) are shown in (a). Here, also ηmax = 0.463, the maximum possible ultimate efficiency for InP, is shown (dashed line).

Fig. 4
Fig. 4

Ultimate efficiency η of the InP NW array as a function of the array period p and the NW diameter D for the fixed NW length L = 500 nm. There is one local maximum of η1 = 0.344 at D1 = 191 nm and p1 = 251 nm and a second local maximum of η2 = 0.341 at D2 = 438 nm and p2 = 530 nm. The inset shows a line-cut of η as a function of D for p = 530 nm (solid line). In this inset also ηmax = 0.463 (dashed line), the maximum possible ultimate efficiency of InP, is shown.

Fig. 5
Fig. 5

Ultimate efficiency η of the InP NW array as a function of the array period p and the NW diameter D for the fixed NW length L = 2000 nm. There is one local maximum of η1 = 0.431 at D1 = 184 nm and p1 = 340 nm, and a second local maximum of η2 = 0.410 at D2 = 441 nm and p2 = 680 nm. The inset shows a line-cut of η as a function of D for p = 340 nm (solid line). In this inset also ηmax = 0.463 (dashed line), the maximum possible ultimate efficiency of InP, is shown.

Fig. 6
Fig. 6

(a) NW diameter D1 (solid line) and array period p1 (dashed line), that give the local maximum η1 of the ultimate efficiency η of the InP NW array, for varying NW length L. (b) NW diameter D2 (solid line) and array period p2 (dashed line), that give the local maximum η2 of the ultimate efficiency η of the NW array, for varying NW length L. (c) Maximum ultimate efficiencies η1 (solid red line) and η2 (dashed blue line) plotted against the NW length L. Here, also the maximum possible value of η for InP, ηmax = 0.463, is shown (dashed-dotted black line).

Fig. 7
Fig. 7

Absorptance A as a function of wavelength λ and NW diameter D for an InP NW array with period p = 680 nm and NW length L = 2000 nm (see Fig. 1 in the main text for a schematic). A rapid drop to a zero value of the absorptance occurs for λ > λbg = 925 nm.

Fig. 8
Fig. 8

(a) Absorptance A (solid line) as a function of the NW diameter D for InP NWs of length L = 2000 nm placed in a square array of period p = 680 nm (see Fig. 1 in the main text for a schematic). Here also Rtop, the in-coupling reflection loss of the top air/NW interface, is shown (dashed-dotted line). The light is of 850 nm in wavelength and incident at normal angle to the NW array from the air top side. (b) The attenuation constant Imk of the two eigenmodes (1) and (2) of the NW array that show the lowest values of Imk (solid lines). Here, also the corresponding values of the HE11 [close to the values of eigenmode (1) of the NW array] and the HE12 [close to the values of eigenmode (2) of the NW array] waveguide modes of a single NW are shown (dashed lines). (c) Same as (b) but for Rek, the phase constant of the modes. We note that at D = 0, that is, when the NW array region consists of empty space, mode (1) is the diffracted zeroth order with k 1 =2π/λ7.4 10 7 m−1 and mode (2) is a (evanescent) diffracted order with k 2 = (2π/λ) 2 (2π/p) 2 i5.5 10 6 m−1.

Fig. 9
Fig. 9

Power P(z) [that is, the intensity integrated over the cross-section of one unit cell] of an InP NW array of period p = 680 nm. The NWs are of length L = 2000 nm and we consider varying NW diameters of D = 100 (a), 177 (c), 251 nm (e), and 437 nm (g). The air/NW top interface is located at z = 0 and the NW/substrate bottom interface is located at z = 2000 nm (see Fig. 1 for a Schematic). Here, light of a wavelength of 850 nm is incident at normal angle from the air top side. In (b), (d), (f), and (h) the forward [ P 1 + and P 2 + ] and backward [ P 1 and P 2 ] propagating self-powers of eigenmodes (1) and (2) of the NW array are shown [see Fig. 8 for the correspondence between mode (1) of the NW array and the HE11 waveguide mode of a single NW; and the correspondence between array mode (2) and the HE12 waveguide mode]. Here, also P 12 ct , the sum of all cross-powers between modes (1) and (2), is shown. All powers are expressed in the unit of Watt and the incident intensity is (1 [W])/p2. Thus, 0 ≤ P(z) ≤ 1.

Fig. 10
Fig. 10

The ηR-loss, the insertion reflection loss of ultimate efficiency η due to the reflection of incident light at the top NW/air interface, as a function of the diameter D and the period p of the InP NW array (see Fig. 1 for a schematic). These values are calculated by increasing L in the numerical modeling until further increase of L does not alter the results. In this limit case, the light intensity that is coupled into the NW array is absorbed in the NWs. Thus, ηR-loss is the in-coupling loss that limits η from reaching the value of ηmax = 0.463. The inset shows a line-cut of ηR-loss as a function of D for p = 680 nm (solid line). In this inset, we show also the value of 0.151 (dashed line), which is the value of the efficiency loss due to the reflection of light at a planar air/InP interface.

Equations (17)

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η= 0 λ λ λ bg I AM1.5 (λ)A(λ)dλ 0 I AM1.5 (λ)dλ
P(z)= 1 4 UC ( E * ×H +E× H * )· e ^ z dS
E xy (x)= a E a (x,y)( C a + e i k a z + C a e i k a z )
H xy (x)= a H a (x,y)( C a + e i k a z C a e i k a z ) .
P(z)= ab [ P ab ++ (z) + P ab + (z)+ P ab + (z)+ P ab (z)]
P ab ++ (z)= N ab ++ C a +* C b + e i( k b k a * )z ,
P ab + (z)= N ab + C a +* C b e i( k b k a * )z ,
P ab + (z)= N ab + C a * C b + e i( k b + k a * )z ,
P ab (z)= N ab C a * C b e i( k b + k a * )z ,
N ab ++ (z)= 1 4 UC ( E a * × H b + E b × H a * )· e ^ z dS,
N ab + (z)= 1 4 UC ( E a * × H b + E b × H a * )· e ^ z dS,
N ab + (z)= 1 4 UC ( E a * × H b E b × H a * )· e ^ z dS,
N ab (z)= 1 4 UC ( E a * × H b E b × H a * )· e ^ z dS.
P a + (z) P aa ++ (z)
P a (z) P aa (z)
P(z) a [ P a + (z) + P a (z)]
P 12 ct (z)= P 11 + (z)+ P 11 + (z)+ P 22 + (z)+ P 22 + (z)+ P 12 ++ (z)+ P 21 ++ (z)+ P 12 (z) + P 21 ++ (z)+ P 12 + (z)+ P 21 + (z)+ P 12 + (z)+ P 21 + (z),

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